Can causality exist without time?

[arthwollipot]

A question for those who know a lot more about physics, cosmology and philosophy than I do.

I'm engaged in a discussion on another forum (http://www.religious-science.com/message-board-forum/viewtopic.php?t=768), and the topic has drifted to the idea of causality. My erstwhile opponent (who is a religious moderate with fundamental leanings, if that makes any sense - he is also not stupid and a very good debating partner, so please don't underestimate him) is suggesting that causality can exist without time. Otherwise, how could the universe have begun? Since time began at the instant of the universe's creation, then the creation's cause must have existed outside of time. Of course, this "cause" is God.

My contention is that causality cannot exist without time, because any sequence of events requires the existence of time. Otherwise, how can any one event even be said to occur "after" another, let alone be caused by it. My contention is also that there can be uncaused events (qv. the Kalam Cosmological Argument).

Is he right? Can one event cause another in the absence of time?

[Jeff Corey]

I'm not a philosopher, but a behavioral scientist who tries to discover what variables influence behavior. A determinist. It seems to me that cause and effect relationships need to have a time frame, whereby the causal agent has to come before the effect. Or in more complex cases, a response is made and a positive reinforcer follows, resulting in an increase in the probability of the response.
All these involve attending to what comes first. And a timer would be handy.

[dasmiller]

. . . is suggesting that causality can exist without time. Otherwise, how could the universe have begun? Since time began at the instant of the universe's creation, then the creation's cause must have existed outside of time. Of course, this "cause" is God.

My contention is that causality cannot exist without time, because any sequence of events requires the existence of time. Otherwise, how can any one event even be said to occur "after" another, let alone be caused by it. My contention is also that there can be uncaused events (qv. the Kalam Cosmological Argument).

Is he right? Can one event cause another in the absence of time?

Well, let's take it into a domain that I understand better than reality. I sometimes program, so let's imagine that I write and run a program that creates a little virtual world, with little virtual creatures speculating about philosophy. In their universe, time started when I ran the program, so I'm outside of their time and I caused them to come into existence. They measure time in "blarnons" and sometimes the program runs fast, sometimes I pause it, etc - their time really isn't our time, and it's pretty meaningless for them to ask what was happening 10 blarnons before the program started.

So I'd consider this to be an existence proof that your friend's view isn't ruled out.

I have no reason to believe that he's right, just that we can't rule it out.

My personal theory is that God didn't create the universe, but He was around at the beginning and decided to name all the protons individually. Unfortunately, He ran out of names after a while, so fully 83% of all protons are named "Sally."

AFAIK, my theory is exactly as testable as your friend's.

[athon]

I think there are a couple of issues here.

First of all (now, keep in mind I'm not a physicist and am happy to be corrected), the whole Big Bang thing is often easily misrepresented. Essentially, from how I understand it, the laws we use to describe our universe currently cannot explain events at the moment of the Big Bang. In other words, we simply lack the means to say anything about causality on that level. We can't say 'time didn't exist', we can only say 'time as we describe it on our macro level can't be used to explain how things operate within a singularity'. The rules change on that level, and we're only slowly working out what this really means. I hear quite often how people think this means there is no 'cause' to the expansion of space and time, which I find makes no sense on any level, especially on a religious one.

The way I see it, time might simply be our observation of other relationships. It doesn't exist as a thing itself, but rather it is the observation of some deeper phenomenon that describes how events are related. We observe entropy as being linked with time as we're part of that same system, making it look as if it has a direction. Greg Egan's sci-fi novel 'Permutation City' does a good job of exploring the notion of the subjectivity of time.

Athon

[sol invictus]

I'm not sure this answers the question, but in physics the term "casuality" has a specific meaning1 - one which makes no sense without time.

ETA: Athon's point is worth emphasizing. We have no good reason to think that time began at the big bang - we simply don't know what happened then.


1If you're curious: to determine the state at a point in spacetime it is necessary and sufficient to specify the state at every point in the past lightcone of that point, which in turn implies that one need only specify the state along a spacelike volume slicing the past lightcone.

[MrQhuest]

Can the cause be at time = -x ?
In the concept of a "big bounce" where the previous universe collapsed to a singularity only to spawn a new universe.

But then you get the same first cause argument. What/when/how was the previous universe caused.

It's late...
I need to study more cosmology, and less mixology.

MrQ

[Tricky]

The concept of "without time" is meaningless in our universe. "Cause" is a time-based concept. To "happen" requires a before and after. Even "exist" suggests that there is a "now".

And just try conjugating verbs without a reference to time.:D

[dasmiller]

It's late...
I need to study more cosmology, and less mixology.

MrQ

All in all, I think my time spent dabbling in mixology has been more productive than my time spent dabbling in cosmology.

The jury is still out on which has led to more embarrassment.

[ElMondoHummus]

I'm not sure this answers the question, but in physics the term "casuality" has a specific meaning1 - one which makes no sense without time.


1If you're curious: to determine the state at a point in spacetime it is necessary and sufficient to specify the state at every point in the past lightcone of that point, which in turn implies that one need only specify the state along a spacelike volume slicing the past lightcone.

Well, even outside of any strict physics treatment, I think the whole concept of causality implies time, since its definition is that one event follows another. I don't see how that can hold true outside of time.

I guess if you wanted to speak strictly philisophically, if you accept an agent involved in the creation of the universe, then the starting point may have been outside of time up until the point the universe came to be, but the moment the universe was created, it automatically brings that "point" into a timeframe. This is sort of a "it takes two points to define a line" argument, with the "line" being time, the first dot being outside of "time", and the second creating a situation where the first gets dragged in. But I'm bending over backwards to make this argument, and personally I don't like it. It feels more like a silly rationalization than a serious treatment of the concept of causality.

Anyway, I think the bottom line is that it's plain illogical to discuss causality and explicity exclude time, since time is implicit in the definition of causality.

ETA: Blaaah! I see that others have beat me to it, and put things more economically than I. Drat...

[KingMerv00]

In the concept of a "big bounce" where the previous universe collapsed to a singularity only to spawn a new universe.


Considering the evidence for an accelerating rate of universal expansion, isn't the Big Bounce unlikely?.

[Perpetual Student]

It has been pointed out several times on other threads that our current models cannot account for t = 0 and t < 0. As s. i. points out, in the real physical world (as explored by physicists) causality has no meaning without time. Consequently, I don't know how we get around the contradiction that if there was no t < 0, it would violate causality. Conclusion: The deficiency of our models notwithstanding, time always existed and so did causality.
By the way, regarding the OP, if one includes a creator in one's world view, then causality is obviously violated by the existence of a creator, since no one or thing created the creator. However, one might argue if the universe always existed in one form or another (bubble universes or whatever), that fact also violates causality – at least, in that one respect

[JFrankA]

I'm not a physicist either. (I don't think I even spelled it correctly :) ), but isn't there a theory about the 11th dimension (called M-Theory) where our universe was created by a collision between branes? http://en.wikipedia.org/wiki/String_theory

If this theory is true, and..if I understand it corretly, then there time and a causality even at the beginning of our universe.

Uhm...someone who actually is a physicist please correct me if I got it wrong....?

[Vorpal]

It has been pointed out several times on other threads that our current models cannot account for t = 0 and t < 0. As s. i. points out, in the real physical world (as explored by physicists) causality has no meaning without time. Consequently, I don't know how we get around the contradiction that if there was no t < 0, it would violate causality.
You seem to be making a lot of unstated assumptions about causality. If your notion of causality requires that every event has a prior cause, then it is certainly logically possible for a finite time interval to contain an infinite chain of causes. If your notion of causality doesn't require that, then there's plainly no contradiction either. As such, I'm at a loss of what you mean--what notion of causality are you using and how does the nonexistence of t<=0 present problems for it?

[GreedyAlgorithm]

Depends on what you mean by "causality". As stated above, the physics usage assumes time. But at least one representation of causality, explored among other places in Judea Pearl's Causality, does not require causes and effects to obey relativity. This may be because it's a purely mathematical generalization of a physical concept, or because our physics only happens to implement a certain subset of possible causal relationships.

[The Man]

As one of the most proficient physicist of our time John Archibald Wheeler (http://en.wikipedia.org/wiki/John_Archibald_Wheeler
)
said.


Time is what prevents everything from happening at once.


So, yes, as far as the physics of casualty go, without time there is no causality.


I think there are a couple of issues here.

First of all (now, keep in mind I'm not a physicist and am happy to be corrected), the whole Big Bang thing is often easily misrepresented. Essentially, from how I understand it, the laws we use to describe our universe currently cannot explain events at the moment of the Big Bang. In other words, we simply lack the means to say anything about causality on that level. We can't say 'time didn't exist', we can only say 'time as we describe it on our macro level can't be used to explain how things operate within a singularity'. The rules change on that level, and we're only slowly working out what this really means. I hear quite often how people think this means there is no 'cause' to the expansion of space and time, which I find makes no sense on any level, especially on a religious one.

The way I see it, time might simply be our observation of other relationships. It doesn't exist as a thing itself, but rather it is the observation of some deeper phenomenon that describes how events are related. We observe entropy as being linked with time as we're part of that same system, making it look as if it has a direction. Greg Egan's sci-fi novel 'Permutation City' does a good job of exploring the notion of the subjectivity of time.

Athon

Technically under the current mathematical considerations (that I am aware) of the big bang singularity it is consider as being a causal singularity. In that no time like or light like (and as far as I know space like) separations extend past that singularity. Some work on Loop quantum gravity has some variance on this, not so much in a causal relationship but that in a possible big bounce, that can be asserted form those calculations, some aspects of a pervious universe may be similar to aspects in our current universe. If my thinking is correct those calculations might entail a space like separation between those two universes, but I’m probably wrong. As I am only an armature theoretical physicist, I will of course defer to any one with more experience or the referenced information one could gather on their own. So please take what I say in that consideration.

[martu]

The time we experience is a property of our universe bound to the shape, size and energy it has.

At t=0 picture the universe as a lump of solid matter all in one place. How can all matter be in one place? Well without any movement and no ‘gaps’ in the matter there isn’t any distance so to speak of and if nothing is moving there isn’t any time. All matter is therefore in the same ‘place’ (x, y, z) = (0, 0, 0).

This universe has no causality because nothing can happen. This universe has no time because nothing is happening.

Then Bang! it explodes and we have matter flying off in all directions and as a consequence time is ‘created’ or, to put it another way, time is the expansion of the universe and without this expansion time doesn’t exist.

The cause of this event defines t=0 and time keeps ticking as long as the universe keeps expanding. But there is no reason to assume anything about what caused this explosion. Maybe it is an endless series of contractions and expansions. Maybe there are lots of these lumps of matter floating around somewhere and two hit each other causing them to explode. Maybe there is powerful being who kicked it all off by hitting this clump of matter with a large hammer. Who knows? I doubt we ever will. What we do know is that causality in this universe starts at t=0 and anything before that is meaningless to us as we can’t ‘get out’ of our universe to take a look (there is a speed limit stopping us doing that).

If Theists want to retreat to unobservable events as proof of their God then let them though maybe one could question their faith. They have no evidence for this however, no evidence at all, and while we can postulate other causes as plausible as a Super Being no reason to resort to a God.

[sol invictus]

It has been pointed out several times on other threads that our current models cannot account for t = 0 and t < 0. As s. i. points out, in the real physical world (as explored by physicists) causality has no meaning without time. Consequently, I don't know how we get around the contradiction that if there was no t < 0, it would violate causality. Conclusion: The deficiency of our models notwithstanding, time always existed and so did causality.

I agree with Vorpal - this doesn't follow. There is no causality without time, granted, but how does that imply that a finite time interval violates causality?

An example: it doesn't make sense to speak of an ordering on numbers (as in 5>3.2) if you don't have any numbers to order. Does that mean one can't define an ordering on the set of strictly positive real numbers? Does the non-existence of negatives in that set cause a contradiction and "violate ordering"?

[Perpetual Student]

You seem to be making a lot of unstated assumptions about causality. If your notion of causality requires that every event has a prior cause, then it is certainly logically possible for a finite time interval to contain an infinite chain of causes. If your notion of causality doesn't require that, then there's plainly no contradiction either. As such, I'm at a loss of what you mean--what notion of causality are you using and how does the nonexistence of t<=0 present problems for it?

Yes, the universe consists within the context of an endless chain of causes. If there was no t < 0, then something happened without any prior event, i.e., without cause, which is not possible. Hence there was a t < 0.

[Vorpal]

Yes, the universe consists within the context of an endless chain of causes. If there was no t < 0, then something happened without any prior event, i.e., without cause, which is not possible. Hence there was a t < 0.
However, if there is no t = 0 either, then nothing happened without any prior event. The nonexistence of t = 0, as you said in this thread, is predicted by our current best models. (Whether they're correct is, of course, a different matter.)

Although in general, I'm not sure that if a cosmological model was otherwise successfully predictive and had cosmological time behaving more like a half-closed interval [0,inf) rather than (0,inf), the apparent contradiction with certain theories of causality should be counted against the cosmological model or the theory of causality. I can't think of any a priori reason why every event should have a cause before it in time; the only relevant reason seems to me something along the lines of "thinking in that way gives good models about the world", which makes particular notions of causality scientific (or meta-scientific?) theories in themselves, and hence potentially open to falsification and revision.

[Perpetual Student]

I agree with Vorpal - this doesn't follow. There is no causality without time, granted, but how does that imply that a finite time interval violates causality?


If there were no t < 0, then there can be no cause for events at t = 0 and later.

An example: it doesn't make sense to speak of an ordering on numbers (as in 5>3.2) if you don't have any numbers to order. Does that mean one can't define an ordering on the set of strictly positive real numbers? Does the non-existence of negatives in that set cause a contradiction and "violate ordering"?

The difference is that the negatives do not "cause" the positives. Events in the real world are always linked through causality.

Vorpal -- However, if there is no t = 0 either, then nothing happened without any prior event. The nonexistence of t = 0, as you said in this thread, is predicted by our current best models.

My understanding is that current models say nothing about t = 0; they do not claim there was no t = 0.

[sol invictus]

Make the following analogy: event a causally influenced event b is like a<b. That's rather close to real causality, actually - more than close enough for our purposes, and if your argument were valid (which it isn't) it would apply to this. OK?

Then, take the "universe" to be the open set of real numbers t such that t>0.

If there were no t < 0, then there can be no cause for events at t = 0 and later.

Every number t>0 has a number less than it (t/2, for example). t=0 is not in the set and so is irrelevant.

My understanding is that current models say nothing about t = 0; they do not claim there was no t = 0.

True, but nevertheless this is an explicit counterexample to your argument. There is no logical problem with a universe that contains all times t>0 - for example, every time has an infinite chain of causes before it.

[arthwollipot]

Interesting discussion. Thanks everyone.

I think so far the conclusion is that causality does require time. But strange things happen as T->0.

[theneedtoknow]

Well I could never understand "time" myself...isn't "time" just relative changes in positions between two previously selected entities? Just a little thought experiment - if we centre the point of the birth of the universe at the origin of a coordinate system, and at the time the universe comes into existence, a photon starts travelling along the x-axis of this coordinate system, wouldn't we be able to decribe everything else in the universe by relating it to this one photon? If we measure the x-coordinte of the position of this photon a number of times, and the only property of photons we knew is that they travel in straight lines, wouldn't we be able to replace "before" with "lower value of x-coordinate" and after with "higher value of x-coordinate" when we compare two events, and then describe events in the universe with the coordinates (x, y, z, x-position of the primordial photon)?

[The Man]

Given the invariant nature of the speed of light, time and distance are related by that proportion. So when we speak of a length of time T we are also speaking of a distance T*c. Likewise we can also refer to spatial distance as a measure of time D*c-1 or light travel time. So even if one were to consider no change in relative position over a period of time there is still a change in position with regard to time as T*c. It might be easier to just think of time as that constantly changing position relative to T=0. Basically it is what you are essentially saying.

[martu]

Given the invariant nature of the speed of light, time and distance are related by that proportion. So when we speak of a length of time T we are also speaking of a distance T*c. Likewise we can also refer to spatial distance as a measure of time D*c-1 or light travel time. So even if one were to consider no change in relative position over a period of time there is still a change in position with regard to time as T*c. It might be easier to just think of time as that constantly changing position relative to T=0. Basically it is what you are essentially saying.

This change in position with regard to time is what we consider as things getting older am I right? What are the consequences for light that moves at c, does it mean it doesn't get older?

[The Man]

This change in position with regard to time is what we consider as things getting older am I right? What are the consequences for light that moves at c, does it mean it doesn't get older?

In the proper parlance it is said that a photon experiences no passage of Proper Time (http://en.wikipedia.org/wiki/Proper_time). However as a photon is never stationary it is always changing spatial position which can also be represented in units of time or Coordinate Time (http://en.wikipedia.org/wiki/Coordinate_time). Since time is not absolute, ones reference to how “old” something is would depend on the relative time applied in that consideration. Although proper time is defined as basically a clock that a reference frame caries with itself, so in that respect a photon does not get “older”.

[martu]

In the proper parlance it is said that a photon experiences no passage of Proper Time (http://en.wikipedia.org/wiki/Proper_time). However as a photon is never stationary it is always changing spatial position which can also be represented in units of time or Coordinate Time (http://en.wikipedia.org/wiki/Coordinate_time). Since time is not absolute, ones reference to how “old” something is would depend on the relative time applied in that consideration. Although proper time is defined as basically a clock that a reference frame caries with itself, so in that respect a photon does not get “older”.

Thanks, very interesting.

So if I have this right if you go faster than light you go backwards in time and time itself must be expressed as some sort of spatial dimension in our universe.

My post about time being defined by the expansion of the universe seems quite sensible now.

[Perpetual Student]

Make the following analogy: event a causally influenced event b is like a<b. That's rather close to real causality, actually - more than close enough for our purposes, and if your argument were valid (which it isn't) it would apply to this. OK?

*************

Then, take the "universe" to be the open set of real numbers t such that t>0.

**************

Every number t>0 has a number less than it (t/2, for example). t=0 is not in the set and so is irrelevant.

**************
True, but nevertheless this is an explicit counterexample to your argument. There is no logical problem with a universe that contains all times t>0 - for example, every time has an infinite chain of causes before it.

I see no validity to these mathematical analogies. They simply do not apply. Numbers do not cause each other.
If there were no t < 0, then there must have been a causeless event, namely, the universe, which would have to incorporate the creation of space and time. I find that illogical. If there was once "no time," and no causality, then there would still be "no time." and no causality.

[Belz...]

A question for those who know a lot more about physics, cosmology and philosophy than I do.

I'm engaged in a discussion on another forum (http://www.religious-science.com/message-board-forum/viewtopic.php?t=768), and the topic has drifted to the idea of causality. My erstwhile opponent (who is a religious moderate with fundamental leanings, if that makes any sense - he is also not stupid and a very good debating partner, so please don't underestimate him) is suggesting that causality can exist without time. Otherwise, how could the universe have begun? Since time began at the instant of the universe's creation, then the creation's cause must have existed outside of time. Of course, this "cause" is God.

My contention is that causality cannot exist without time, because any sequence of events requires the existence of time. Otherwise, how can any one event even be said to occur "after" another, let alone be caused by it. My contention is also that there can be uncaused events (qv. the Kalam Cosmological Argument).

Is he right? Can one event cause another in the absence of time?

Assuming causality could exist without time, there'd be no way to tell since all events happen simultaneously.

[martu]

I see no validity to these mathematical analogies. They simply do not apply. Numbers do not cause each other.
If there were no t < 0, then there must have been a causeless event, namely, the universe, which would have to incorporate the creation of space and time. I find that illogical. If there was once "no time," and no causality, then there would still be "no time." and no causality.

Not if time is created by the universe and is a property of that universe only, time is relative after all. Time can't exist without matter and movement and it easy to imagine a universe without movement isn't it?

[Perpetual Student]

Assuming causality could exist without time, there'd be no way to tell since all events happen simultaneously.

Or:

There would be no "events."

[martu]

Or:

There would be no "events."

Or there could some events that happened all at once and some that didn't.

I just had a thought - if light speed was unbounded wouldn't that result in a universe without causality?

[sol invictus]

I see no validity to these mathematical analogies. They simply do not apply. Numbers do not cause each other.
If there were no t < 0, then there must have been a causeless event, namely, the universe, which would have to incorporate the creation of space and time. I find that illogical. If there was once "no time," and no causality, then there would still be "no time." and no causality.

What you said above makes no sense - "the universe" is not an event. If you mean to say "the creation of the universe at t=0", that fails as well, since as I keep trying to explain to you, one can simply remove the point t=0. Then every time has an infinite sequence of times preceding it.

Your claim was that a universe which has existed since t=0 is impossible because there would be an event with no cause. That claim is false.

The whole point of logic is that it's formal - that is, it doesn't matter what the specific objects in question are, only the formal rules they obey. If there's some formal rule you think applies to cause that does not apply to >, or vice versa, what is it?

[Richard Masters]

The concept of "without time" is meaningless in our universe. "Cause" is a time-based concept. To "happen" requires a before and after. Even "exist" suggests that there is a "now".

And just try conjugating verbs without a reference to time.:D

You can do this in some languages.

[Perpetual Student]

What you said above makes no sense - "the universe" is not an event. If you mean to say "the creation of the universe at t=0", that fails as well, since as I keep trying to explain to you, one can simply remove the point t=0. Then every time has an infinite sequence of times preceding it.

Your claim was that a universe which has existed since t=0 is impossible because there would be an event with no cause. That claim is false.

The whole point of logic is that it's formal - that is, it doesn't matter what the specific objects in question are, only the formal rules they obey. If there's some formal rule you think applies to cause that does not apply to >, or vice versa, what is it?

Formal rules will apply to two systems in the same way if there is an underlying identity of the two systems. You cannot demonstrate the identity of the real numbers and rules of causality and time. The real numbers form a field with all the defined rules of that structure. As I'm sure you know, there are other fields: The rationals, the complex numbers, etc. To be sure, a definition within the real numbers like "all real numbers" > 0 has a counterpart in time -- all t > 0. However there is a well defined 0 within the real numbers; there is no t = 0 in your models. The analogy fails!
Again: If there once was no time and no causality, then there would still be no time and no causality.

[sol invictus]

You didn't answer the question. What feature of causality does > not have which is necessary for your argument? If there isn't one, the argument is invalid.

However there is a well defined 0 within the real numbers; there is no t = 0 in your models. The analogy fails!

Apparently you didn't read what I wrote. Please re-read my posts (or Vorpal's) more carefully.

[The Man]

Thanks, very interesting.

So if I have this right if you go faster than light you go backwards in time and time itself must be expressed as some sort of spatial dimension in our universe.

My post about time being defined by the expansion of the universe seems quite sensible now.

Well that was just one, the relativistic, consideration and we know that relativity alone can not completely describe a photon. There are quantum mechanical considerations as well. Where relativity is continuous and specifically maintains causality (at least as we currently understand it) quantum mechanics is discrete and our current understanding of causality becomes tenuous at best. Currently we have no quantum theory of relativity so this is the conundrum of modern physics. In a quantum mechanical sense it is basically meaningless to consider time scales below the Plank Time (http://en.wikipedia.org/wiki/Planck_time) about 5.39 x 10-44 Seconds. So in that sense we can place that as a quantum limit on the proper time a photon might experience. Experimental limits on the proper time for a photon are currently orders of magnitude above that quantum limit. When considering the Planck limits, space time has been proposed to be a sheathing froth of virtual particles, cause and effect become interchangeable and our current understanding of casualty breaks down at those scales. To further exemplify this point, under the considerations of the Path Integral (http://en.wikipedia.org/wiki/Path_integral_formulation) a traveling electron can interact with a virtual positron, resulting in annihilation and a virtual photon of gamma radiation. That photon can then become a virtual positron electron pair with the electron of that pair being the real electron that we might eventually detect. The virtual positron (basically being an electron traveling backwards in time) can be the positron that resulted in the initial annihilation event. Although these events have a strict temporal sequence with annihilation event preceding pair production event, a strict interpretation of causality is more of a problem. As the cause of the annihilation event is the virtual positron and the cause of the virtual positron is the virtual gamma photon resulting from the annihilation event caused by the virtual positron. These are more then just theoretical musing as we must consider such events if we want to accurately calculate the probability of detecting that electron at some point in the future. In fact it is only the consideration of such virtual events that permit us to calculate the anomalous magnetic moment (http://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment) of the electron, a calculation that agrees with experimental results to perhaps the highest degree of accuracy of any physical consideration. So although we can fundamentally assert that without time there is no causality we can not assert that without causality there is no time, at least not within our current understanding.

[Perpetual Student]

You didn't answer the question. What feature of causality does > not have which is necessary for your argument? If there isn't one, the argument is invalid.



Apparently you didn't read what I wrote. Please re-read my posts (or Vorpal's) more carefully.



OK, I re-read your and Vorpal’s posts and I understood the continue to understand the points made, specifically one can have an infinite chain of moments of time as one approaches t = 0. The analogy with the positive real numbers is quite clear. However, if t and x can approach 0 as close as we want, it does not follow "causes" can do the same. "Causes" cause things; numbers and moments in time do not. All the numbers x and moments t are independent mathematical entities (independently existing members of a set); "causes" are not independent, they cause one another.

OK, here’s another issue. As the above poster reminds us, the plank time is 5.39x10^-44 seconds, so that we cannot have an infinite chain of moments in time. That destroys the analogy between time and the real numbers. There is no equivalence of the real numbers and time, as defined in the “quantum world.”

Finally, you have not addressed my point that: If there were no t < 0 and no causality, then there would still be no t and no causality.

[Vorpal]

However, if t and x can approach 0 as close as we want, it does not follow "causes" can do the same.
Why not?

"Causes" cause things; numbers and moments in time do not.
The point is simply this: what is to prevent an infinite chain of causes located at some chain of events with time coordinates all monotonically decreasing to zero, but staying positive? Hence my first post--you seem to have some particular notion of causality in mind, but I've no idea what it is. What I can say is that in GTR there is a mathematically rigorous definition for what it means for a spacetime to have a causal structure, and that the family of solutions commonly used to model the Big Bang do not violate it.

OK, here’s another issue. As the above poster reminds us, the plank time is 5.39x10^-44 seconds, so that we cannot have an infinite chain of moments in time.
I'm not sure how that follows. If you want to talk about quantum mechanics, since quantum states evolve deterministically in time, it makes sense to say that a past state "causes" a future state. In the more esoteric areas like string theory, time is still continuous, and even loop quantum gravity does not quantize time per se (as far as I'm aware of--they may have fuzzyness at the hypervolume level).

Again, if you've some other notion of what a "cause" is, this discussion won't progress if you keep it private.

That destroys the analogy between time and the real numbers. There is no equivalence of the real numbers and time, as defined in the “quantum world.”
Cf. Schrödinger's equation.

[sol invictus]

"Causes" cause things; numbers and moments in time do not. All the numbers x and moments t are independent mathematical entities (independently existing members of a set); "causes" are not independent, they cause one another.

I gave a precise mathematical definition of causality earlier in the thread. For these purposes, it's not much different than >. Do you have a different definition in mind?

OK, here’s another issue. As the above poster reminds us, the plank time is 5.39x10^-44 seconds, so that we cannot have an infinite chain of moments in time.

Why not? All the Planck time tells us is that if physics extrapolates unchanged to the Planck energy, quantum effects on gravity become large. So?


Finally, you have not addressed my point that: If there were no t < 0 and no causality, then there would still be no t and no causality.

Take an eternal universe that lasts from t=-infinity to t=+infinity. Now change coordinates to T=e^t. The description in the new coordinates is just as valid as the original. Nothing happens to causality - this is just a change in how you choose to label events. But T>0.

[arthwollipot]

The discussion lost me some time ago... :)

I linked to this thread in the other forum - I don't know whether my erstwhile opponent has seen it yet.

[Perpetual Student]

I gave a precise mathematical definition of causality earlier in the thread. For these purposes, it's not much different than >. Do you have a different definition in mind? (s. i.)

Are you referring to this? ” 1If you're curious: to determine the state at a point in spacetime it is necessary and sufficient to specify the state at every point in the past lightcone of that point, which in turn implies that one need only specify the state along a spacelike volume slicing the past lightcone.”


OK, lets try this: a causes b is a very different statement than a < b. For example, a,b,…,n < z can all be true and a,b,…n can all not cause z. Or only c may cause z. These are not equivalent concepts. Does your definition somehow refute that?

The point is simply this: what is to prevent an infinite chain of causes located at some chain of events with time coordinates all monotonically decreasing to zero, but staying positive? Hence my first post--you seem to have some particular notion of causality in mind, but I've no idea what it is. What I can say is that in GTR there is a mathematically rigorous definition for what it means for a spacetime to have a causal structure, and that the family of solutions commonly used to model the Big Bang do not violate it. (V.)

If an infinite chain of events monotonically approached any point in time, would we not run into problems with the uncertainty principle? I am not knowledgeable enough about quantum theory to be certain, but what little I do know tells me we could not have such an infinite progression.

Why not? All the Planck time tells us is that if physics extrapolates unchanged to the Planck energy, quantum effects on gravity become large. So? (s. i.)
Well, I am out of my league here. Does the Planck time not limit how many events can occur in a given time interval? Does it not quantize time?

Take an eternal universe that lasts from t=-infinity to t=+infinity. Now change coordinates to T=e^t. The description in the new coordinates is just as valid as the original. Nothing happens to causality - this is just a change in how you choose to label events. But T>0. (s. i.)
Your new coordinates do more than you think. If you say that t < 0 does not exist, that implies that a finite amount of time has passed from t = 0 until now. In your changed coordinates, you have allowed an infinite amount of time going back in time. In your T = e^t system, as t approaches 0, T approaches 1, so if there is no t < 0, there is no time T < 1, which leads to the same question. Namely, if there is no t < 0 and no causality, there can never be any t or causality.
************************************************** ******************************
I would like to thank you both for indulging me in this discussion. What can be more fascinalting than the nature of the universe, including questions about its age?

[Vorpal]

If an infinite chain of events monotonically approached any point in time, would we not run into problems with the uncertainty principle?
As I said, that depends on what you mean by "cause". If "causes" can be quantum states, then no, since those are [wave-]functions of (continuous) time.

I am not knowledgeable enough about quantum theory to be certain, but what little I do know tells me we could not have such an infinite progression.
If by "causes", you mean the sort of things we get from measurements of quantum systems, then it seems that QM alone breaks that sort of causality without the need for cosmological matters. Since QM only determines probability distributions of such measurements (also cf. Bell's theorem), then although prior measurements influence future ones, it's hard to see how they "cause" them.

In fact, because their "influence" is due to their effect on the wavefunction, trying make sense of measurements causing other measurements seems to lead back to "causes" being the quantum states themselves, just as previously. If you can think some other way, I'd be very interested in discussing it, but right now I just can't see it.

Your new coordinates do more than you think. If you say that t < 0 does not exist, that implies that a finite amount of time has passed from t = 0 until now.
That's a fair point. To remove such ambiguities, in GTR we can talk about lengths of geodesics rather than time coordinates.

[politas]

Yes, the universe consists within the context of an endless chain of causes. If there was no t < 0, then something happened without any prior event, i.e., without cause, which is not possible. Hence there was a t < 0.
Actually, no. A chain of causes exists within the context of the universe. There is no reason that the universe itself should be tied to the same laws as events within it. At t=0, the laws of physics that we are familiar with cease to apply, and that includes causality.

[sol invictus]

OK, lets try this: a causes b is a very different statement than a < b. For example, a,b,…,n < z can all be true and a,b,…n can all not cause z. Or only c may cause z. These are not equivalent concepts. Does your definition somehow refute that?

Yes. Any spacetime point in the past lightcone of a is causally connected to it. The state at all those points goes into determining the state at a - you cannot leave any of them out, or the state at a will be indeterminate (ok, to be more precise you could specify just a Cauchy surface, but you can always choose it to pass through any of those points).

If an infinite chain of events monotonically approached any point in time, would we not run into problems with the uncertainty principle?

In standard QM time is continuous, so there are always such infinite chains of events. Very roughly, the uncertainty principle tells you that as the times get closer, the energy of the relevant physics gets higher - that's all.


Well, I am out of my league here. Does the Planck time not limit how many events can occur in a given time interval? Does it not quantize time?

No, not as far as we know.


Your new coordinates do more than you think. If you say that t < 0 does not exist, that implies that a finite amount of time has passed from t = 0 until now. In your changed coordinates, you have allowed an infinite amount of time going back in time. In your T = e^t system, as t approaches 0, T approaches 1, so if there is no t < 0, there is no time T < 1, which leads to the same question. Namely, if there is no t < 0 and no causality, there can never be any t or causality.

You really don't read very carefully, do you? I specified that t goes from -infinity to +infinity. Then T goes from 0 to infinity - that was the whole point of the example.

Does that mean a finite amount of time has passed? You can't answer that, not without knowing the metric in at least one of the two coordinate systems. In particular if the t coordinates are flat an infinite time has passed, which provides yet another counterexample to your claim (since there is obviously nothing wrong with causality even though T<0 doesn't exist).

[dasmiller]

Take an eternal universe that lasts from t=-infinity to t=+infinity. Now change coordinates to T=e^t. The description in the new coordinates is just as valid as the original. Nothing happens to causality - this is just a change in how you choose to label events. But T>0.

Oh! I was trying to work up a good absolute zero analogy, but your coordinate mapping is better.

At first blush, I'd pictured the +/-infinite t timeline to have progressively less activity per increment of t as t headed for -infinity because the t increments were getting infinitely short as measured in T. But I'm a little slow until I've had my coffee (and sometimes even after that), and upon further reflection-

As t heads for -infinity, the universe is smaller and hotter, so the particles are closer together and travelling faster and thus interacting more often as measured in T. This suggests (but doesn't require) that with a proper mapping (my math isn't up to it, and maybe it really is as simple as T=e^-t) that there's a constant amount of interaction and "causing" per increment of t.

So - in a meaningful sense, the universe really is infinitely old, because there's been "time" for an infinite amount of interaction among particles? Or does the integral not work that way? Hmmm . . . "infinite amount of interaction between particles" doesn't sound consistent with the rationale for inflation.

A little help?

[Perpetual Student]

You really don't read very carefully, do you? I specified that t goes from -infinity to +infinity. Then T goes from 0 to infinity - that was the whole point of the example.

I read it quite carefully, thank you. There is no point to your example. If t < 0 does not exist in one coordinate system, then T < 1 does not exist in the other. By admitting to -t values in one system you merely create 0 < T < 1 in the other. If you think by devising a system that limits T to values > 0 and permits an infinite past time , you have somehow demonstrated that in a system where t < 0 does not exist, causes or time can be infinite, you are mistaken. If for some reason it were useful to express time in T, we would be asking the question, "is there T < 1?" You have not eliminated the question; you have changed its form.
Now try to read my post carefully.

[Vorpal]

As t heads for -infinity, the universe is smaller and hotter, so the particles are closer together and travelling faster and thus interacting more often as measured in T. This suggests (but doesn't require) that with a proper mapping (my math isn't up to it, and maybe it really is as simple as T=e^-t) that there's a constant amount of interaction and "causing" per increment of t.
The Minkowski spacetime in Cartesian coordinates, as simple as it gets:
ds² = dt² - (dx²+dy²+dz²). t,x,y,z in (-inf,+inf)
Vanishing curvature, and hence no matter or radiation or anything interesting at all.
Minkowski spacetime in Invictus time, T = exp(t):
ds² = (dT/T)² - (dx²+dy²+dz²). T in (0,inf).
There is still vanishing curvature everywhere. There's nothing to get 'hot'; it doesn't get 'smaller' in any physical sense--in fact, nothing at all is changed, because it's the same spacetime.

[Perpetual Student]

Originally Posted by Perpetual Student
If an infinite chain of events monotonically approached any point in time, would we not run into problems with the uncertainty principle?
(Vorpal) As I said, that depends on what you mean by "cause". If "causes" can be quantum states, then no, since those are [wave-]functions of (continuous) time.

I'm not familiar enough with the "quantum world" to understand what that means. Why would waves not be limited by the uncertainty principle? Isn't it true that if we try to pinpoint the location of a photon (which is a wave packet) we lose information about its energy (wavelength)? It would appear that the exact location of a photon is the same as an exact time for the photon, since the speed of the photon is exactly known. So as we approach t = 0 the wavelength of the photon could approach infinity? If so, that would (for me) represent another nail in the coffin of the idea that there is no t < 0. Since otherwise we reach absurd results like infinite energy and wavelength.

[sol invictus]

I read it quite carefully, thank you. There is no point to your example. If t < 0 does not exist in one coordinate system, then T < 1 does not exist in the other. By admitting to -t values in one system you merely create 0 < T < 1 in the other. If you think by devising a system that limits T to values > 0 and permits an infinite past time , you have somehow demonstrated that in a system where t < 0 does not exist, causes or time can be infinite, you are mistaken. If for some reason it were useful to express time in T, we would be asking the question, "is there T < 1?" You have not eliminated the question; you have changed its form.
Now try to read my post carefully.

For god's sake.

Your argument was that if the time coordinate didn't exist for negative values there was a problem with causality. That is obviously false, because T is a perfectly good time coordinate, it runs from 0 to infinity, and it manifestly does not have any problems with causality (because the physics it describes are identical in every way to those of t from -infinity to infinity).

One can of course go the other way as well. If we start with t in the range 0,+infinity, define T = log(t). Then T (a perfectly good time coordinate) runs from -infinity to infinity.

The point is, statements about whether the time coordinate has a finite range are utterly meaningless, because they are not invariant under trivial coordinate transformations. You cannot reason that way, as I have been trying to explain to you for the last five posts - it's wrong, period.

[Vorpal]

I'm not familiar enough with the "quantum world" to understand what that means. Why would waves not be limited by the uncertainty principle?
They are. Fourier analysis even a corresponding "Heisenberg uncertainty principle" (more than one, even, and in fact a large collection of inequalities sometimes also called "uncertainty principles"). However, it doesn't mean what you appear to think it means. In particular, it doesn't mean that the wave itself is in any sense "fuzzy" or takes ill-defined values, but simply that "position" and "wavelength" are not sharply defined for waves.

And why should they be? If the wave is far from periodic, wavelength ceases to make sense; if the wave is extended in space, asking its exact position is bit silly--it's more or less everywhere. For the former case, think of the distribution φ(x) = δ(x-x0), the Dirac delta. Position is well-defined, but wavelength is not. For the latter extreme, think of ψ(x) = sin(kx). Wavelength is very well-defined, but position is not.

Isn't it true that if we try to pinpoint the location of a photon (which is a wave packet) we lose information about its energy (wavelength)?
I'm not sure if that's physically meaning, since one cannot detect a photon without absorbing it, and therefore wouldn't have meaningful position eigenstates. But in any case, see above.

So as we approach t = 0 the wavelength of the photon would approach infinity? If so, that would (for me) represent another nail in the coffin of the idea that there is no t < 0. Since otherwise we reach absurd results like infinite energy and wavelength.
ΔEΔt ≥ hbar/2. As t→0, Δt→0, and therefore ΔE diverges. OK. Why is that a problem? Even plain vanilla GTR (or even Newtonian gravity) predicts diverging energy density as t→0 anyway.

[sol invictus]

As t heads for -infinity, the universe is smaller and hotter, so the particles are closer together and travelling faster and thus interacting more often as measured in T. This suggests (but doesn't require) that with a proper mapping (my math isn't up to it, and maybe it really is as simple as T=e^-t) that there's a constant amount of interaction and "causing" per increment of t.

So - in a meaningful sense, the universe really is infinitely old, because there's been "time" for an infinite amount of interaction among particles? Or does the integral not work that way? Hmmm . . . "infinite amount of interaction between particles" doesn't sound consistent with the rationale for inflation.

A little help?

Vorpal gave one example - start with flat space and transform to T. Then you have an empty flat space in funny coordinates. A slightly more interesting example is to take a real cosmology with a big bang singularity, and then do the inverse map T = log(t) on it. If t runs from 0 to infinity, T runs from -infinity to infinity - but of course nothing has actually changed, just our choice of labels for spacetime events.

To answer your question about the amount of real time, there's something called "proper time" in general relativity. That's the time that an observer would actually record on a clock, and it's invariant under coordinate changes like this (since it's a physical quantity). Mathematically, it's defined by the integral over time of the coordinate function multiplying dt in the metric - in Vorpal's T metric, one would integrate dT/T = log(T)=log(e^t)=t. In other words, t is the proper time in that case.

[Perpetual Student]

Your argument was that if the time coordinate didn't exist for negative values there was a problem with causality. That is obviously false, because T is a perfectly good time coordinate, it runs from 0 to infinity, and it manifestly does not have any problems with causality (because the physics it describes are identical in every way to those of t from -infinity to infinity).

What is it about this that you don't get? If T runs from 0 to infinity, as you have defined T, there would be an infinite past; consequently there is no problem with causality. If there were no T < 1, you create the same problem as there would be if there were no t < 0. You can't make the problem go away by changing coordinates.

[dasmiller]

Vorpal gave one example - start with flat space and transform to T. Then you have an empty flat space in funny coordinates. A slightly more interesting example is to take a real cosmology with a big bang singularity, and then do the inverse map T = log(t) on it.

Yes, I was thinking of the big bang - that was why I had the universe getting denser & hotter as the-time-ordinate-now-known-as-big-T headed for -infinity.

If t runs from 0 to infinity, T runs from -infinity to infinity - but of course nothing has actually changed, just our choice of labels for spacetime events.

Oh, hey, if I had a way to actually change the universe by coming up with a new mapping, the universe probably wouldn't have survived my freshman physics class.

To answer your question about the amount of real time, there's something called "proper time" in general relativity. That's the time that an observer would actually record on a clock, and it's invariant under coordinate changes like this (since it's a physical quantity). Mathematically, it's defined by the integral over time of the coordinate function multiplying dt in the metric - in Vorpal's T metric, one would integrate dT/T = log(T)=log(e^t)=t. In other words, t is the proper time in that case.

At that point, I was considering "time" to have a more casual meaning related to the amount of stuff that happens, and taking "stuff that happens" to mean interactions among particles and photons and whatever else might be interacting.
So - let's say I define my own "special" time interval - the T100, which is the time it takes for there to be a total of 10^100 interactions among the particles & photons in the universe. (yes, I can come up a bunch of reasons that this isn't a very usable defintion, starting with the argument about whether we're in an infinite universe, then the fact that the definition assumes a meaningful concept of simultaneity across the universe, then- oh, nevermind). Nowadays, a T100 interval takes a few femtoseconds or millenia of 'normal' time.
As we go back closer to the big bang, particles were closer together and moving faster so they interacted more often, and the T100 interval was shorter.
Does the T100 interval go to zero proper time as we approach the big bang? And does it go there quickly enough that there have been infinite number of T100 intervals since the Big Bang? (which stops looking like a bang in this perspective) Or is T100 too flawed to make any such assertions?

[sol invictus]

What is it about this that you don't get? If T runs from 0 to infinity, as you have defined T, there would be an infinite past; consequently there is no problem with causality. If there were no T < 1, you create the same problem as there would be if there were no t < 0. You can't make the problem go away by changing coordinates.

Perpetual, I don't think I can explain this any more clearly than I already have. Forget how I defined T. Call it t instead if you prefer. Now we have a universe described by a time coordinate t that runs from 0 to infinity, yet manifestly has no causality problem. That proves that there is no general problem with bounded time intervals - and that's obvious anyway, because the existence of such a boundary is completely coordinate dependent. End of story.

I'm sorry you're having so much difficulty understanding that (or admitting that you were wrong, whichever it is), but I'm not going to repeat it again, so if you still don't understand it you'll have to look elsewhere for help.

[Vorpal]

Yes, I was thinking of the big bang - that was why I had the universe getting denser & hotter as the-time-ordinate-now-known-as-big-T headed for -infinity.
Ah, I see. I took your reply to sol's "eternal universe" to mean that you were adopting his scenario, whereas in fact you were making your own, leading to this misunderstanding (I've also interpreted 'eternal' in the sense of 'infinite extensible' for at least some geodesics, rather than 'exists at all times', which would be tautologically true for any spacetime). Mea culpa.

[The Man]

Perpetual, I don't think I can explain this any more clearly than I already have. Forget how I defined T. Call it t instead if you prefer. Now we have a universe described by a time coordinate t that runs from 0 to infinity, yet manifestly has no causality problem. That proves that there is no general problem with bounded time intervals - and that's obvious anyway, because the existence of such a boundary is completely coordinate dependent. End of story.

I'm sorry you're having so much difficulty understanding that (or admitting that you were wrong, whichever it is), but I'm not going to repeat it again, so if you still don't understand it you'll have to look elsewhere for help.

Indeed, I think that is the crux of the issue with Perpetual S. here. In a clopen (http://en.wikipedia.org/wiki/Clopen_set) time interval where 0 ≤ T0 > ∞ (where one boundary is included in that interval but not the other) we only need to know the current state at that boundary condition T0 = 0 or even just at sometime T0 > 0 in an open interval where 0 < T0 > ∞ (unbounded at both ends, or no boundaries are included within that interval) in order to apply a deterministic (or generally causal) view. How it got to that condition at T0 = 0 or T0 > 0 is irrelevant in those considerations. It seems Perpetual S. is arguing that we must know the conditions that resulted in the state at T0 = 0 or T0 > 0 and not just that state itself at T0 in order to apply that general causal view for T1 > T0. Is that your primary argument Perpetual S.?

[Vorpal]

Indeed, I think that is the crux of the issue with Perpetual S. here. In a clopen (http://en.wikipedia.org/wiki/Clopen_set) time interval where 0 ≤ T0 > ∞ (where one boundary is included in that interval but not the other) ...
You've a very strange notation for intervals (are you sure you didn't mean '<' instead of '>'?), and 'clopen' doesn't mean what you think it means. A half-closed real interval is never clopen under the standard Euclidean topology, since the endpoint at which the interval is closed is not an interior point. In fact, there are no clopen sets in the reals other than the trivial ones--the empty set and the entire real line itself.

... we only need to know the current state at that boundary condition T0 = 0 or even just at sometime T0 > 0 in an open interval where 0 < T0 > ∞ (unbounded at both ends, or no boundaries are included within that interval) in order to apply a deterministic (or generally causal) view.
There's a theorem in GTR that says basically that if for every point, the intersection of the interiors of the past and future light cones is compact and there are no closed timelike curves, then the spacetime admits a Cauchy foliation. That's exactly what you want--a family of surfaces "slicing up" spacetime having the property that the entire spacetime is determined by local conditions on any of the surfaces. That's about as strict a causality as possible, since one can think of those surfaces as "nows", with each "now" completely determining both past and future.

How it got to that condition at T0 = 0 or T0 > 0 is irrelevant in those considerations. It seems Perpetual S. is arguing that we must know the conditions that resulted in the state at T0 = 0 or T0 > 0 and not just that state itself at T0 in order to apply that general causal view for T1 > T0. Is that your primary argument Perpetual S.?
It looks to me to be a lot simpler than that--just a correspondence of underlying logic. The objection of moving the question to talk about extensible geodesics instead has been already addressed.

[MattusMaximus]

Interesting discussion. Thanks everyone.

I think so far the conclusion is that causality does require time. But strange things happen as T->0.

Allow me to throw another nugget into the discussion. As we currently understand physics, time intervals cannot actually approach zero - we make a fundamental flaw in assuming that time (and also space) is a continuum. Time and space are actually discrete and quantized, just at such a small level that in our macroscopic view of the universe it appears they are a continuum - see Planck length (http://en.wikipedia.org/wiki/Planck_length) and Planck time (http://en.wikipedia.org/wiki/Planck_time) for more info on this.

ETA: I see now that Sol has already brought up the issue of Planck time. My bad.

[The Man]

You've a very strange notation for intervals (are you sure you didn't mean '<' instead of '>'?), and 'clopen' doesn't mean what you think it means. A half-closed real interval is never clopen under the standard Euclidean topology, since the endpoint at which the interval is closed is not an interior point. In fact, there are no clopen sets in the reals other than the trivial ones--the empty set and the entire real line itself.

Well I was not using the standard notation for those intervals (my fault and my intent), but just giving the limits for those internals in an attempt to make it more understandable. You are correct thought, that where I used ‘>’ in defining the limits of T in those intervals should have been ‘<’. Thanks, and I don’t know how I missed that as I had not started drinking yet (ok, maybe I did not start soon enough). From my understanding an open interval is one where that interval does not include the endpoints as interior points, but I’m always willing to be wrong. Certainly an interval is dependent on the set which it is a subset of and the interval [0,∞] (in the proper notation) in this consideration is a subset of the set of real numbers defining the set of positive real numbers. However, since the set of positive real numbers is the whole space being considered for T (negative T being before the big bang singularity) would it not be clopen in that regard? Again I remain willing as always.


There's a theorem in GTR that says basically that if for every point, the intersection of the interiors of the past and future light cones is compact and there are no closed timelike curves, then the spacetime admits a Cauchy foliation. That's exactly what you want--a family of surfaces "slicing up" spacetime having the property that the entire spacetime is determined by local conditions on any of the surfaces. That's about as strict a causality as possible, since one can think of those surfaces as "nows", with each "now" completely determining both past and future.

Oh, I do not doubt that, but you have to put that in terms and notations so that the people who what to be educated can be educated or at least get down to the problem they are having in the terms or concepts they do not understand. Not everyone is going to take “Cauchy foliation” to mean anything other then what happens to the Captain Crunch when your pour milk on it (which would just be a family of surfaces “slicing up” that milk) and having the causal result of just getting soggy by the local conditions on any of those surfaces. The problem is that the consideration (or our understanding) of “each "now" completely determining both past and future” breaks down at T = 0 (big bang singularity) or even as T approaches 0. You seem to be making the same augment as Perpetual S. In that T = 0 (big bang singularity) must have some determinate or determining T[sub]-1[sub] otherwise subsequent causality fails, which I do not think arguing for. In other words my Captain Crunch does not get soggy until I pour milk on it and if we take the cereal in the bowl with milk to be T = 0, it does not matter how they came together for the causal result of it to get soggy sometime after T = 0.


It looks to me to be a lot simpler than that--just a correspondence of underlying logic. The objection of moving the question to talk about extensible geodesics instead has been already addressed.


Funny, I did not see Prpetual S. “moving the question to talk about extensible geodesics instead”. It just seems to me that on a discussion forum for an educational foundation those of us with some knowledge might make a better effort (an effort I often find myself lacking) to put things in terms that might be, well, more educational for those with questions and perhaps not the same education.

[Perpetual Student]

It is claimed by some physicists that, before the big bang, time did not exist. It seems to me that if that were the case, then there would have been no causality before the big bang and (in plain English) nothing could happen. Consequently, there would have been no big bang, there would still be no time and nothing would ever have happened, and nothing would be happening today or ever.
Playing with coordinate changes for time is merely an irrelevant exercise, since, as I attempted to point out above, there would be a time for the big bang and a time (or not) before the big bang in whatever coordinate system were chosen. For example, in the T discussed above, the big bang would presumably occur at T = 1? However, I'm not sure that's what s. i. intended but it really doesn't matter at this point and I don't believe it’s worth pursuing further.
So, if there were no time before the big bang, there would have been no big bang, or anything else, now or ever. It appears to me that is an inescapable conclusion. Therefore, since there was a big bang, there was "time" before the big bang!
Physicists say their models say nothing about t = 0 or t < 0, so it is left for philosophers, and all other people (including physicists) who love to think and speculate about the universe and its origins to think about it, speculate about it, discuss it, and, as best they can, come to whatever conclusions may be reached about it.

BTW, when I am shown to be wrong, I readily and quickly come to terms with it and move on. I have found out that learning often involves a sequence of false starts and corrections. There is no shame and there should be no remorse for being wrong along the way to gaining more knowledge and understanding.

[dasmiller]

Playing with coordinate changes for time is merely an irrelevant exercise, since, as I attempted to point out above, there would be a time for the big bang and a time (or not) before the big bang in whatever coordinate system were chosen. For example, in the T discussed above, the big bang would presumably occur at T = 1? However, I'm not sure that's what s. i. intended but it really doesn't matter at this point and I don't believe it’s worth pursuing further.


I wouldn't dismiss the significance of the coordinate transforms so quickly. Yes, if you measure time by the vibrations of cesium atoms (the second is defined in terms of cesium state transitions), and project that scheme backwards to a period before there were any cesium atoms, eventually your time scale would go past the big bang. But in other ways of mapping time, the big bang is infinitely far back.

The vibrations-of-cesium-atoms metric has a lot of practical applications, but (and I say this as someone who worked for years on a system that assumed that cesium clocks were the preferred reality) why is the #@$*&%# vibrations-of-cesium-atoms way of measuring time so much more important than, say, a measurement that relates time interval to the apparent size of the universe? Or Sol's exponential time? Or any of an infinite number of other ways to measure time? Taking a subset of those ways (those that have 0 <= T < infinity) and saying that they're the "real" ones and thus causality has a problem is . . . well, it's not immediately obvious to me that it's the only correct approach.

This doesn't necessarily mean that it's wrong. In some domains, that trick works just fine. Engineers routinely pick special coordinate transforms to simplify problems and it's a perfectly valid approach because in those domains, if a thing is true in one coordinate system, then it's true in all. For other kinds of problems (relativity springs to mind), that sort of logic can get you into deep trouble.

So, what kind of domain is this question in? I honestly don't know. But I don't think it's fair to simply assume that the time-measurement system that you're accustomed to has some special status that can be used for assessing the origin of the universe.

[sol invictus]

So - let's say I define my own "special" time interval - the T100, which is the time it takes for there to be a total of 10^100 interactions among the particles & photons in the universe. (yes, I can come up a bunch of reasons that this isn't a very usable defintion, starting with the argument about whether we're in an infinite universe, then the fact that the definition assumes a meaningful concept of simultaneity across the universe, then- oh, nevermind). Nowadays, a T100 interval takes a few femtoseconds or millenia of 'normal' time.
As we go back closer to the big bang, particles were closer together and moving faster so they interacted more often, and the T100 interval was shorter.
Does the T100 interval go to zero proper time as we approach the big bang? And does it go there quickly enough that there have been infinite number of T100 intervals since the Big Bang? (which stops looking like a bang in this perspective) Or is T100 too flawed to make any such assertions?

Well, interaction rates tend to go at least as the square of the density. The density times the volume is some total number of particles which we'll take to be fixed (it actually could increase, so that's conservative). So then the number of interactions would increase like the density, which for a standard big bang is something like t^{-3/2}. That diverges when you integrate, so yes - by that rough reasoning there are an infinite number of T100s.

It is claimed by some physicists that, before the big bang, time did not exist. It seems to me that if that were the case, then there would have been no causality before the big bang and (in plain English) nothing could happen. Consequently, there would have been no big bang, there would still be no time and nothing would ever have happened, and nothing would be happening today or ever.

That reasoning is flat-out wrong - my -infinity<t<infinity ---> 0<T<infinity is an explicit counterexample.

The truth is, there are a number of proposals for how to "resolve" the big bang. Some imply that there is no time before t=0 - and they are perfectly self-consistent - and some that there was.

In theories of quantum gravity the situation can be really murky. In many such theories, our spacetime is an approximation (it's a local maximum in the wavefunction). There are other such approximations, and they may be present in the wavefunction as well. Each would have its own time and space. When these begin to mix, the whole notion of causality becomes very problematic.

[Perpetual Student]

...
The truth is, there are a number of proposals for how to "resolve" the big bang. Some imply that there is no time before t=0 - and they are perfectly self-consistent - and some that there was.

In theories of quantum gravity the situation can be really murky. In many such theories, our spacetime is an approximation (it's a local maximum in the wavefunction). There are other such approximations, and they may be present in the wavefunction as well. Each would have its own time and space. When these begin to mix, the whole notion of causality becomes very problematic.

And there are proposals that the universe is eternally existing, and thus does not require a unique beginning and a beginning of time. The chaotic inflation theory or eternal inflation model of Andrei Linde is a prominent example. There are other such proposals of a universe with an infinite past time. I guess the point here is that these are proposals made by serious theorists as are the proposals you mention above. In the absence of solid evidence, we poor laymen are stuck with our limited wits to come to our own conclusions.

[quarky]

A single photon not bound by C is all that is required.

[sol invictus]

And there are proposals that the universe is eternally existing, and thus does not require a unique beginning and a beginning of time. The chaotic inflation theory or eternal inflation model of Andrei Linde is a prominent example.

http://prola.aps.org/abstract/PRL/v90/i15/e151301

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating—or just expanding sufficiently fast—must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.


There are other such proposals of a universe with an infinite past time.

That is true.

I guess the point here is that these are proposals made by serious theorists as are the proposals you mention above. In the absence of solid evidence, we poor laymen are stuck with our limited wits to make up our own minds.

It's one thing to acknowledge the existence of various possibilities. It's another to claim that an entire class of them are impossible due to some trivial (and invalid) logical syllogism.

[Perpetual Student]

...
It's one thing to acknowledge the existence of various possibilities. It's another to claim that an entire class of them are impossible due to some trivial (and invalid) logical syllogism.

OK, let's say we have a situation (one cannot use terms like era or epoch) of no time and no causality. Tell me how the big bang or anything happens.

[sol invictus]

OK, let's say we have a situation (one cannot use terms like era or epoch) of no time and no causality. Tell me how the big bang or anything happens.

It's simply not a sensible question (in that situation). It's - rather precisely - like asking what happened before t=-infinity.

[Perpetual Student]

It's simply not a sensible question (in that situation). It's - rather precisely - like asking what happened before t=-infinity.

The question is quite sensible in the context of the situation described, namely the claim that there was no time before the big bang. It's the situation that is not sensible and leads to contradictions and absurdities, which has been my point all along.

[69dodge]

If there were no t < 0, then there must have been a causeless event, namely, the universe, which would have to incorporate the creation of space and time. I find that illogical.

And if there were times t < 0, extending back infinitely far? What caused the universe in that case?

The universe as a whole has no cause, either way.

Why is one more logical than the other?

If there was once "no time," and no causality, then there would still be "no time." and no causality.

Doesn't saying "there was once x" implicitly assert the existence of a time at which there was x?

It seems to me that it does. So, "there was once no time" is a contradiction in terms.

Don't think, "there was once no time." Think, "there never was any time t <= 0."

[The Man]

The question is quite sensible in the context of the situation described, namely the claim that there was no time before the big bang. It's the situation that is not sensible and leads to contradictions and absurdities, which has been my point all along.

You keep coming back to the assertion of “no time before the big bang” whereas as all one can really assert is that time like geodesics have no extension past that singularity (since the question was being moved that way anyway). All that means is that currently we can assert no definitive casual relationship between T < 0 and T > 0 even if we consider a T < 0. Certainly that lack of causality, as I tried to point out before, does not mean that time can not or does not exist before T = 0, but from just a relativistic standpoint we have no way of demonstrating that causality (or even time) extends past that singularity. We know that relativity is not a complete description and from a quantum standpoint we lose our normal consideration of causality at the Planck time even before getting back to T = 0 and the singularity (perhaps even avoiding the problems inherent with a singularity). When we have a more complete theory that encompasses both we will most likely have a better understanding of time going back to and perhaps even before T = 0. It just does not seem constructive to focus on an assertion of a lack of time before the big bang when it is really just our lack of understanding about the big bang around T = 0 where time and casualty are just some of our basic concepts that we simply can not currently effectively apply to that singularity or to get around it.

[Perpetual Student]

You keep coming back to the assertion of “no time before the big bang” whereas as all one can really assert is that time like geodesics have no extension past that singularity (since the question was being moved that way anyway). All that means is that currently we can assert no definitive casual relationship between T < 0 and T > 0 even if we consider a T < 0. Certainly that lack of causality, as I tried to point out before, does not mean that time can not or does not exist before T = 0, but from just a relativistic standpoint we have no way of demonstrating that causality (or even time) extends past that singularity. We know that relativity is not a complete description and from a quantum standpoint we lose our normal consideration of causality at the Planck time even before getting back to T = 0 and the singularity (perhaps even avoiding the problems inherent with a singularity). When we have a more complete theory that encompasses both we will most likely have a better understanding of time going back to and perhaps even before T = 0. It just does not seem constructive to focus on an assertion of a lack of time before the big bang when it is really just our lack of understanding about the big bang around T = 0 where time and casualty are just some of our basic concepts that we simply can not currently effectively apply to that singularity or to get around it.
I am quite comfortable with the reality that current models cannot deal with questions about t <(=) 0. The target of my objections has been confined to dogmatic assertions that there was no time before t = 0. Such assertions seem to be based on the fact that the current models are inadequate. The logic seems to be something like: "Our current models do not account for t <(=) 0, hence there was no t <(=) 0." I find those assertions logically inconsistent for the reasons I have stated (too) many times already.

[Perpetual Student]

And if there were times t < 0, extending back infinitely far? What caused the universe in that case?

The universe as a whole has no cause, either way.

Why is one more logical than the other?



Doesn't saying "there was once x" implicitly assert the existence of a time at which there was x?

It seems to me that it does. So, "there was once no time" is a contradiction in terms.

Don't think, "there was once no time." Think, "there never was any time t <= 0."



I don't get the point about "there was once no time” or "there never was any time." "There never was any time" is just as tautological since the word "never" implies time. Nevertheless, if you think you have a better way of saying it, that's OK.

I am not looking for a "cause of the universe." I find a universe that goes back in time infinitely as logically acceptable. A universe that goes back to a finite point in time and simply stops or ceases to exist is not logical.

[Moochie]

A question for those who know a lot more about physics, cosmology and philosophy than I do.

I'm engaged in a discussion on another forum (http://www.religious-science.com/message-board-forum/viewtopic.php?t=768), and the topic has drifted to the idea of causality. My erstwhile opponent (who is a religious moderate with fundamental leanings, if that makes any sense - he is also not stupid and a very good debating partner, so please don't underestimate him) is suggesting that causality can exist without time. Otherwise, how could the universe have begun? Since time began at the instant of the universe's creation, then the creation's cause must have existed outside of time. Of course, this "cause" is God.

My contention is that causality cannot exist without time, because any sequence of events requires the existence of time. Otherwise, how can any one event even be said to occur "after" another, let alone be caused by it. My contention is also that there can be uncaused events (qv. the Kalam Cosmological Argument).

Is he right? Can one event cause another in the absence of time?


I think "time" is about as meaningful as "meridians" in acupuncture.


M.

[sol invictus]

A universe that goes back to a finite point in time and simply stops or ceases to exist is not logical.

For the fifth time, going back to "a finite point in time" and then stopping is an utterly meaningless statement. In order to give it meaning, you must specify the metric on time.

To try to make that easy for you to see I've shown you how to map infinite intervals to finite, and finite to infinite, with coordinate transformations. You can map any interval (finite or infinite) to any other (modulo boundary points) and so if you don't keep track of the metric factors, you can't draw any conclusions at all from the nature of the interval.

So your claims about this are patently absurd - they're like saying "it's logically impossible to measure time using seconds, but hours are fine". If you want to say something less completely stupid, give us a metric you think is logically inconsistent.

[69dodge]

For the fifth time, going back to "a finite point in time" and then stopping is an utterly meaningless statement. In order to give it meaning, you must specify the metric on time.

To try to make that easy for you to see I've shown you how to map infinite intervals to finite, and finite to infinite, with coordinate transformations. You can map any interval (finite or infinite) to any other (modulo boundary points) and so if you don't keep track of the metric factors, you can't draw any conclusions at all from the nature of the interval.

So your claims about this are patently absurd - they're like saying "it's logically impossible to measure time using seconds, but hours are fine". If you want to say something less completely stupid, give us a metric you think is logically inconsistent.

I think you're way over his head. (No offense intended, Perpetual Student.) Don't you agree? Over my head too, though perhaps by less.

If he didn't understand the point of your t -> et transformation, just repeating it, more or less verbatim, isn't going to help.

Anyway, saying that the universe is x billion years old is really different from saying that it's infinitely old. No? The difference is not just a mere relabeling of events, as by t -> et.

Can you describe the difference in simple terms? Can you explain why, even though there is some difference, that difference doesn't invalidate the analogy between a universe in which time goes back to infinity and one in which time goes back only to 0?

Leaving aside questions of strict logical consistency or inconsistency, it certainly feels stranger for the universe to have existed for a finite amount of time without anything having existed "before" it, than for it to have existed forever without anything having existed "before" it. If it existed forever, of course nothing existed before it---there was no opportunity for anything to exist before it, because it always existed---whereas if it existed for x billion years, one could at least imagine that something might have existed x + 1 billion years ago, even though in fact nothing did.

Presumably, that's wrong. But why?

In summary, dumb it down for us, please. :D

[Perpetual Student]

OK, I'll try this one more time. Our current estimate is that the universe we know is approximately 13.5 billion years old. We can ask and get answers to the question, "what was the universe like 12 billion years ago?" Similarly, we can ask about 13.4 billion years ago. Because of the uncertainty of the 13.5 figure when going back in time further, we rephrase our questions to "what was the universe like, say, 100,000 years after the big bang," or 10^-15 seconds after
the big bang.

So, I am now asking the question, "what was the universe like 16 billion years ago?" (years are defined as we all know, ultimately using the cesium atom.)

Now, the answer to that question may be among the following:

1. Our current models do not tell us; we do not know.

2. Our current bubble had not yet started in an endless, number of bubble universes. (The Linde proposal)

3. The universe consisted of Swiss cheese, made by God, which he later changed to the singularity leading to the big bang.

4. There was no universe and no time.

OK, now #1. seems like a reasonable answer. #2. although highly speculative, is interesting. #3. and #4. are absurd. #4. is absurd because there is no basis for such a statement and it leads to all the contradictions I have already amply described. If the universe were nothing with no time 16 billion years ago, then there would still be nothing.

[Vorpal]

From my understanding an open interval is one where that interval does not include the endpoints as interior points, but I’m always willing to be wrong. Certainly an interval is dependent on the set which it is a subset of and the interval [0,∞] (in the proper notation) in this consideration is a subset of the set of real numbers defining the set of positive real numbers. However, since the set of positive real numbers is the whole space being considered for T (negative T being before the big bang singularity) would it not be clopen in that regard?
If you're using it that way, then it's true but without content--every space is clopen in itself, no matter what topology or other structure is defined on it. It's also extremely confusing, since in the same breath we're discussing differences of [0,inf) and (0,inf), so if they're both clopen in themselves (and neither is in the reals), what's the point of introducing topological distinctions? The word you're looking for as it applies to intervals is "half-open" (or "half-closed").

You seem to be making the same augment as Perpetual S.
I've been consistently making the exact opposite of his argument in various forms throughout this thread, including in the part you've just quoted.

Funny, I did not see Prpetual S. “moving the question to talk about extensible geodesics instead”.
Well, that explains why he's slowly driving Sol insane (j/k). I made no claims about what PS has or hasn't done in that post, but since doing so would be a direct way to meet Sol's objection to him, so it was relevant.

[sol invictus]

I think you're way over his head. (No offense intended, Perpetual Student.) Don't you agree? Over my head too, though perhaps by less.

Probably - be he claims to know some math, so that's why I took that approach.

Anyway, saying that the universe is x billion years old is really different from saying that it's infinitely old. No? The difference is not just a mere relabeling of events, as by t -> et.

That's correct. As I said somewhere above, a good definition is what's called "proper time", which is invariant under these coordinate transformations. The amount of proper time back to the big bang in our universe is approximately 13.7 billion years.

Can you describe the difference in simple terms? Can you explain why, even though there is some difference, that difference doesn't invalidate the analogy between a universe in which time goes back to infinity and one in which time goes back only to 0?

I never said that, exactly - I simply objected to PS's naive and wrong arguments about causality. One relevant point is that even in a universe that has existed for a finite proper time, there are still an infinite number of events in any arbitrary interval near 0. That was Vorpal's point, and my coordinate transform simply makes it more apparent (or at least I thought so). So even there, all events have a cause - in fact, an infinite chain of causes (at least if we exclude the single point at t=0).

Leaving aside questions of strict logical consistency or inconsistency, it certainly feels stranger for the universe to have existed for a finite amount of time without anything having existed "before" it, than for it to have existed forever without anything having existed "before" it.

It may feel that way, but I'm not sure that intuition has much validity. In physics one deals with this kind of question by asking what initial or boundary conditions are necessary. In other words, you have some equations that describe the system, but they generally have many solutions - so you ask what is necessary to specify a particular one. Usually that's a boundary condition.

Now, in an eternal universe you'll still have to specify a "boundary" condition everywhere at some specific time. Once that is done you can evolve forward or back as long as you want. In a future-eternal universe (i.e. one with a big bang) you'll have to do precisely the same, but when you evolve back something different happens: the equations become singular. Except that it sometimes happens that for a very special class of solutions they don't become singular, and one might prefer such solutions - in which case a finite universe of that type requires less outside input, and is in some sense more unique and perhaps more natural.

If it existed forever, of course nothing existed before it---there was no opportunity for anything to exist before it, because it always existed---whereas if it existed for x billion years, one could at least imagine that something might have existed x + 1 billion years ago, even though in fact nothing did.

Presumably, that's wrong. But why?

Well.... what's one mile north of the north pole? (The class of solutions I mentioned above are quite a bit like that - they "round off" smoothly at t=0 just like a sphere.)

Actually dasmiller provided another interesting possibility above. Even if the proper time is finite, it might be that whatever kind of clock you care most about ticks faster and faster as you approach the big bang, in such a way that it ticks an infinite number of times "before" you arrive there. In that case, the universe is effectively eternal.

[Vorpal]

I am quite comfortable with the reality that current models cannot deal with questions about t <(=) 0. The target of my objections has been confined to dogmatic assertions that there was no time before t = 0.
Slow down a bit. What "dogmatic assertions" to that effect? No one here has claimed such in any absolute terms, and even you make no mention of this motivation until now. It's quite plain in (your) post #11 of this thread that this sub-discussion started with the claim that no times t≤0 logically contradicts causality. It doesn't. In fact, the core of the matter isn't even empirical in the ordinary sense--it's just a question of whether X is logically consistent with Y.

Imagine A and B talking about their favorite models of the universe. They're mathematicians, so they leave most of the empirical work to the physicists and concentrate on internal properties instead.
A: I've this model in which there's a cosmological time t takes only positive values.
B: Doesn't that contradict causality? I mean, every event should be preceded by a cause.
A: Well, the state of the universe at every t has a prior state that determines it, which is as strong a sense of "cause" as it gets.
B: But what about t≤0? What happens then?
A: That makes no sense in this model; the entire universe has t>0. That's all there is.
B: I still think there's a contradiction. I like the idea of t in (-inf,inf) better, since it avoids it. Your model has nothing before t = 0; this one does!
A: What are you talking about? The model satisfies causality as you defined it. If you've some version of causality in mind, what is it?

The question is quite sensible in the context of the situation described, namely the claim that there was no time before the big bang. It's the situation that is not sensible and leads to contradictions and absurdities, which has been my point all along.
At no point have you exhibited the contradiction, merely claimed there is one. You gave a criterion of causality that's essentially "prior to any stuff, there's other stuff [that fully determines it?]", and this is fully consistent with a universe that only has t>0.

I don't understand why you think there's a contradiction; I can only speculate. If it has something to do with the treatment of times as real numbers and that one can talk about negatives ones too (as your post #77 is coached in those lines), well, one can always find contraptions to do that (e.g., the long line to include "before" t=-inf) directly, or indirectly just by applying a suitable transformation.

[69dodge]

A: I've this model in which there's a cosmological time t takes only positive values.
B: Doesn't that contradict causality? I mean, every event should be preceded by a cause.
A: Well, the state of the universe at every t has a prior state that determines it, which is as strong a sense of "cause" as it gets.
B: But what about t≤0? What happens then?
A: That makes no sense in this model; the entire universe has t>0. That's all there is.
B: I still think there's a contradiction. I like the idea of t in (-inf,inf) better, since it avoids it. Your model has nothing before t = 0; this one does!
A: What are you talking about? The model satisfies causality as you defined it. If you've some version of causality in mind, what is it?

I suppose it could be formalized thus: Not only every individual event has a cause that precedes it, but also every set of events, provided they all lie within a finite time interval.

[Perpetual Student]

OK, we have an unmistakable dissonance here. Thanks everyone for your responses. I will very carefully reread and study all the comments about the subject of t <(=) 0 to see what I'm missing. Clearly, either I have not understood some of the comments made and/or I have not articulated my thoughts well.

[69dodge]

So, I am now asking the question, "what was the universe like 16 billion years ago?" (years are defined as we all know, ultimately using the cesium atom.)

Now, the answer to that question may be among the following:
[...]
4. There was no universe and no time.
[...]
#4. is absurd because there is no basis for such a statement and it leads to all the contradictions I have already amply described. If the universe were nothing with no time 16 billion years ago, then there would still be nothing.

Language is funny.

Is the king of France bald?

Neither "yes" nor "no" is a correct answer. France doesn't have a king, who could have, or fail to have, hair. The question appears to ask about a particular person, but it really doesn't. There is no such person to ask about. The only reasonable response is that the question is meaningless.

"There was no universe and no time" is not an answer to the question "what was the universe like 16 billion years ago?" It's an explanation of why the question is meaningless. There never was a time called "16 billion years ago", so one can't meaningfully ask what the universe was like then. There is no such 'then' to ask about.

[The Man]

If you're using it that way, then it's true but without content--every space is clopen in itself, no matter what topology or other structure is defined on it. It's also extremely confusing, since in the same breath we're discussing differences of [0,inf) and (0,inf), so if they're both clopen in themselves (and neither is in the reals), what's the point of introducing topological distinctions? The word you're looking for as it applies to intervals is "half-open" (or "half-closed").


Actually what I was looking for was to make a comparison between a discrete space at the Planck scales with one at ‘universals’ scales, where even though the space of our current universe might be continuous it would still be discrete from some possible universe before and perhaps another after. I guess the Clopen reference was just a hold over from that consideration where [0,∞) would be the entire space for any one of those discrete universes but (0,∞) would just be a proper subset. You are correct though, since I choose not to go that route, by including that “content”, and just decided to keep it simple instead, the clopen reference was completely out of place in what I did end up writing and that was entirely my fault. Sorry, everyone.



I've been consistently making the exact opposite of his argument in various forms throughout this thread, including in the part you've just quoted.


Correct again, which is why I tried to address how it might seem supportive of his assertions, how it was not actually and specifically that I did not think you were arguing for his assertions. Of course all of that was in the text and context that was originally around that one single statement you’ve just quoted.


Well, that explains why he's slowly driving Sol insane (j/k). I made no claims about what PS has or hasn't done in that post, but since doing so would be a direct way to meet Sol's objection to him, so it was relevant.


Also correct, you’re batting 1000. Although you were making no claims about what PS has or hasn't done in that post, I was specifically addressing PS and his claims in the post to which you were responding. The question I was asking was specifically directed at PS and his claims which had nothing to do with any objections that might have already been addressed about or where others where moving the question (apparently without PS as his claims basically have not moved). So relevant, certainly, just not that relevant to what I was specifically asking PS.


Again, I am sorry for any confusion I might have caused as that was not my intent.

[Vorpal]

I guess the Clopen reference was just a hold over from that consideration where [0,∞) would be the entire space for any one of those discrete universes but (0,∞) would just be a proper subset.
But (0,∞) is not clopen in [0,∞) either, so how would that work? If you mean 'discrete' in the sense of that there is always a well-defined 'next moment in time', then you would have the opposite problem of every subset of [0,∞) being clopen under the induced topology (which would be, appropriately enough, the discrete topology).

Of course all of that was in the text and context that was originally around that one single statement you’ve just quoted.
Well, I confess I didn't parse your next sentence back then because of insomnia, but looking back, the missing word and your intended meaning should have been dead obvious, and the next part even more so. My mistake; apologies.

[The Man]

But (0,∞) is not clopen in [0,∞) either, so how would that work? If you mean 'discrete' in the sense of that there is always a well-defined 'next moment in time', then you would have the opposite problem of every subset of [0,∞) being clopen under the induced topology (which would be, appropriately enough, the discrete topology).


If your remember (0,∞) was the open interval (as a proper subset of the ‘Clopen’ [0,∞)). The idea really was a discrete series of [0,∞) intervals each representing the whole space (or in this case proper time) for some given universe like ours. The problem was representing them as equivalent disjoint connected components. As intervals of the set of real numbers with say the next universe (after our current one) being Universe1 as interval [2,3], the previous universe perhaps Universe-1 as [-3,-2] and our current universe then being as Universe0 being [-1,1]. Which would give the topological space U for those three universes as the union of [-3,-2], [-1,1] and [2,3]. Those sets would be Clopen in space U and would make that space discrete, if I was thinking right. Set theory and topology have never been my forte. I was going to do a similar thing for a discrete space in our current universe where instead of universes being considered it would be Planck units. So Universe1 as interval [2,3] becomes Planck1 as interval [2,3]. The real problem was at our current universe (or Planck value) at [-1,1] spanning two units and thus giving it a distinguishing feature. If I could have gotten it to make sense to me I might have actually put it in the post, but as it was just confusing me I figured it would most likely cause me to make it incomprehensible to others. So I opted for the “hey let’s try to make things actually understandable for most readers” approach, but still must have had the clopen aspect stuck in my head.



Well, I confess I didn't parse your next sentence back then because of insomnia, but looking back, the missing word and your intended meaning should have been dead obvious, and the next part even more so. My mistake; apologies.


No problems and thanks again for pointing out my oversights.

[Vorpal]

Well, you could just define the topology to have the basis of consisting of all the open real intervals (which by itself forms the standard Euclidean topology) together with the singleton sets {n} for nonzero integers n. Then the connectied components include {..., (-3,-2),(-2,-1),(-1,1),(1,2),...}, all of which would now be clopen. This is almost what you describe, just lacking the endpoints and not skipping intervals. It might represent something like the cyclic version of a closed universe with its "parts" completely separated from each other, since the [nonzero] integer singletons are now topologically isolated. But why have a special two-unit interval?

Which would give the topological space U for those three universes as the union of [-3,-2], [-1,1] and [2,3]. Those sets would be Clopen in space U and would make that space discrete, if I was thinking right.
They would be clopen in their union, yes, but not 'discrete' as the word is used in topology (having nontrivial clopen subsets just means the space is disconnected, not discrete). However, somehow I get the feeling you are doing something other than what you literally described here. If you define an equivalence relate identifying the points in each individual subintervals (but not across the subintervals), that would be a discrete space, but then it seems like an overly complicated way of just taking the induced topology of the nonzero integers from the reals. The end results are identical. If that's not what you're doing, then I don't understand your intended connection to Planck units.

[Perpetual Student]

Question:

Using current big bang models, is the universe's past considered to be a finite period of time or an infinite one?

[martu]

Question:

Using current big bang models, is the universe's past considered to be a finite period of time or an infinite one?

Finite.

[The Man]

Well, you could just define the topology to have the basis of consisting of all the open real intervals (which by itself forms the standard Euclidean topology) together with the singleton sets {n} for nonzero integers n. Then the connectied components include {..., (-3,-2),(-2,-1),(-1,1),(1,2),...}, all of which would now be clopen. This is almost what you describe, just lacking the endpoints and not skipping intervals. It might represent something like the cyclic version of a closed universe with its "parts" completely separated from each other, since the [nonzero] integer singletons are now topologically isolated. But why have a special two-unit interval?

The two unit interval was a problem not intent. Yeah, I did consider excluding the endpoints, I also considered just having the central intervals half open like {…, [-3,-2], [-1,0), (0,1], [2,3], …}but wasn’t quite sure if that would work also it made those intervals special (or inconsistent with the others) and both of those considerations had the problem of loosing 0 as a member meaning not having any definitive ordinate for “now”, although they do get rid of the two-unit interval.



They would be clopen in their union, yes, but not 'discrete' as the word is used in topology (having nontrivial clopen subsets just means the space is disconnected, not discrete). However, somehow I get the feeling you are doing something other than what you literally described here. If you define an equivalence relate identifying the points in each individual subintervals (but not across the subintervals), that would be a discrete space, but then it seems like an overly complicated way of just taking the induced topology of the nonzero integers from the reals. The end results are identical. If that's not what you're doing, then I don't understand your intended connection to Planck units.

Form my understanding a topological space “is discrete if and only if all of its subsets are clopen”. Again if I had felt it significant or could have gotten it to make sense to myself, I most likely would have actually posted it before. Without that understanding myself it is highly unlikely that I can effectively explain it to anyone else. Really it was just something that clicked in my head when thinking about an actual no time after T = 0 limit for this universe. Then [0,∞) becomes the whole space that any discrete or continuous topology could be applied (at least for time). The one fact that did stick with me that I did include in that post is that as the whole space (at least for time in this universe) it would be clopen. Although, as I said, including that was really pointless in what I did end up writing (especialy without explaing it). As usual with me I have got to mull things over until they make sense to me otherwise I just do not make sense myself when talking with others. Most times I’ve just got to leave it alone for a wile until something else clicks that brings it up again, sometimes it just gets tossed away when some better understanding comes along or it just remains as another dead end of my understanding. I certainly do appreciate your tying to help but I’ve just got to get it right in my head first before I can try to put it in someone else's head.

[arthwollipot]

Okay. Well, the discussion has definitely passed waaaaay over my head now and I no longer have any clue what you guys are talking about. :D

My opponent has indicated on the other board that he has registered here, and intends to come and post in this thread. Try to be nice to him, okay? He's really a good bloke.

[orange31]

Ultimately (no pun intended), Time is a dimension that is no more or less 'real' than the other 3, so perhaps this dimension simply didn't exist prior to the bang. That doesn't rule out 'something' existing prior to the bang.
We have difficulty conceptualizing a universe without time, but we also have difficulty conceptualizing things proven to exist like nonlocality in QM.

[ynot]

In my non-academic opinion - Time is a verb not a noun. Time is no more a thing than bounce is. Time describes the actions of things but time is not a thing. One event causing another event is what we generically describe as time. Time doesn’t become a thing just because a theory requires it to be so.

[arthwollipot]

In my non-academic opinion - Time is a verb not a noun. Time is no more a thing than bounce is. Time describes the actions of things but time is not a thing. One event causing another event is what we generically describe as time. Time doesn’t become a thing just because a theory requires it to be so.Time can be a transitive verb - you can "time" how long someone takes to finish a race. But in general, time is not a verb. It is a noun - technically an abstract noun, since it refers to something that cannot in principle be placed in a box. Time in the sense of this thread is definitly not a verb.

Just because time is not reified doesn't mean that the word is not a noun. You can't put thought in a box either.

I agree that by some definitions, "time" is simply the word we use to label the fact that things don't all occur at once.

[RevDisturba]

Hi Mr Arthwollipot and hello to everyone. I will post a proper intro in the intro section. I am known as Rev Binary in the other forum where I and Arthwollipot have some spirited and productive debates. We don’t agree on a lot of topics I being a Open Christian Theist (think liberal Christian theist) and he a spirited and somewhat evangelical atheist. (I am not sure of his position about being a hard or soft atheist etc).

Thanks to everyone for attempting to define and encapsulate our question. Has anyone definitely answered the question yet? ie can causality operate independent of time (I think it can although its very counter intuitive). I apologize for not reading all the replies in their entirety.

We may need a professor of mathematics to give us a ‘slam dunk answer‘. I approached the professor of mathematics (a PhD) at the state university where I do some volunteer work at and asked him the question. He told me that quite frankly, physics wasn’t his specialty but he would research it and give me a definite answer as soon as time allowed.

I have a Masters in comparative theology which is not heavy on physics! I now wish I had took some electives in advanced math, and still may as I am taking some night classes.

Anyway my understanding is that time is a dimension in ‘space’. We can present time and space as definite equal, or equivalent members of space time. There is no preferred direction like up down back or forward (but there is, of course an ‘arrow of time’ .

I think what confuses us is that we think of cause and effect as related to time, when its really not! We are really trying to explain causality by the arrow of time rather than time itself. Time does not ‘care’ if events run forwards or backwards etc. Yes, time as one physicists said exists only to keep everything from happening at once.

However these individual things still exist but without time. Time is not a requirement for the 'existence' of events. Time is only a coordinate. Nevertheless, our intuition lies to us telling us that they need the effect of time to unfold! So I do not think that time is necessary for events to remain separate.

I need to get an answer from that professor fast!

Thanks for everyones replies.

: {>

[Modified]

However these individual things still exist but without time. Time is not a requirement for the 'existence' of events. Time is only a coordinate. Nevertheless, our intuition lies to us telling us that they need the effect of time to unfold! So I do not think that time is necessary for events to remain separate.

Even if you define things that way, separate events does not get you causation.

[RevDisturba]

Why? The events exist eh?

; {>

[sol invictus]

Anyway my understanding is that time is a dimension in ‘space’. We can present time and space as definite equal, or equivalent members of space time. There is no preferred direction like up down back or forward (but there is, of course an ‘arrow of time’ .

That's incorrect. Time is mathematically distinct and different from the spatial dimensions.

I think what confuses us is that we think of cause and effect as related to time, when its really not!

Again, incorrect. I don't know of any definition of causality that does not involve time - certainly the physics definitions do.

Time does not ‘care’ if events run forwards or backwards etc.

It's true that the laws of physics look essentially identical if you reverse the direction of time. But that has little to do with the technical definition of causality (which I gave early on).

In causal theories you can start from any point in time and go forward or backward. The fact that we perceive time as going forward is irrelevant.

[martu]

Hi Mr Arthwollipot and hello to everyone. I will post a proper intro in the intro section. I am known as Rev Binary in the other forum where I and Arthwollipot have some spirited and productive debates. We don’t agree on a lot of topics I being a Open Christian Theist (think liberal Christian theist) and he a spirited and somewhat evangelical atheist. (I am not sure of his position about being a hard or soft atheist etc).

Thanks to everyone for attempting to define and encapsulate our question. Has anyone definitely answered the question yet? ie can causality operate independent of time (I think it can although its very counter intuitive). I apologize for not reading all the replies in their entirety.

We may need a professor of mathematics to give us a ‘slam dunk answer‘. I approached the professor of mathematics (a PhD) at the state university where I do some volunteer work at and asked him the question. He told me that quite frankly, physics wasn’t his specialty but he would research it and give me a definite answer as soon as time allowed.

I have a Masters in comparative theology which is not heavy on physics! I now wish I had took some electives in advanced math, and still may as I am taking some night classes.

Anyway my understanding is that time is a dimension in ‘space’. We can present time and space as definite equal, or equivalent members of space time. There is no preferred direction like up down back or forward (but there is, of course an ‘arrow of time’ .

I think what confuses us is that we think of cause and effect as related to time, when its really not! We are really trying to explain causality by the arrow of time rather than time itself. Time does not ‘care’ if events run forwards or backwards etc. Yes, time as one physicists said exists only to keep everything from happening at once.

However these individual things still exist but without time. Time is not a requirement for the 'existence' of events. Time is only a coordinate. Nevertheless, our intuition lies to us telling us that they need the effect of time to unfold! So I do not think that time is necessary for events to remain separate.

I need to get an answer from that professor fast!

Thanks for everyones replies.

: {>

No. Time is required for events to happen, without time there are no events.

[Perpetual Student]

I have extracted and pasted together the following from Wikipedia:

"Extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. This singularity signals the breakdown of general relativity. How closely we can extrapolate towards the singularity is debated—certainly not earlier than the Planck epoch.[The Planck epoch ... is the earliest period of time in the history of the universe, from zero to approximately 10−43 seconds (one Planck time), during which quantum effects of gravity were significant.] The early hot, dense phase is itself referred to as "the Big Bang", and is considered the "birth" of our universe. Based on measurements of the expansion using Type Ia supernovae, measurements of temperature fluctuations in the cosmic microwave background, and measurements of the correlation function of galaxies, the universe has a calculated age of 13.73 ± 0.12 billion years. The agreement of these three independent measurements strongly supports the ΛCDM model that describes in detail the contents of the universe."



"Stephen Hawking in particular has addressed a connection between time and the Big Bang. ... Hawking says that even if time did not begin with the Big Bang and there were another time frame before the Big Bang, no information from events then would be accessible to us, and nothing that happened then would have any effect upon the present time-frame. Upon occasion, Hawking has stated that time actually began with the Big Bang, and that questions about what happened before the Big Bang are meaningless. This less-nuanced, but commonly repeated formulation has received criticisms from philosophers such as Aristotelian philosopher Mortimer J. Adler."

"Scientists have come to some agreement on descriptions of events that happened 10−35 seconds after the Big Bang, but generally agree that descriptions about what happened before one Planck time (5 × 10−44 seconds) after the Big Bang will likely remain pure speculation."

After having re-read and re-thought my comments about time and causality if t > 0, I see several flaws in my comments. Nevertheless, a "beginning of time (as viewed by Hawking)" is not a satisfactory concept for me. "Time having a beginning" is profoundly counterintuitive. Proposals like the following (hopefully in time there will be more work done) are promising:

"__brane cosmology models in which inflation is due to the movement of branes in string theory; the pre-big bang model; the ekpyrotic model, in which the Big Bang is the result of a collision between branes; and the cyclic model, a variant of the ekpyrotic model in which collisions occur periodically.
__chaotic inflation, in which inflation events start here and there in a random quantum-gravity foam, each leading to a bubble universe expanding from its own big bang."*

*The above is also taken from a Wikipedia article.

[Belz...]

Or:

There would be no "events."

Even better :)

[Modified]

Why? The events exist eh?

But can't be causally related, because they all have space-like separation. Of course, as others have pointed out, without time there are no events anyway.

[69dodge]

Has anyone definitely answered the question yet? ie can causality operate independent of time (I think it can although its very counter intuitive).

I guess I don't know what you mean by "causality". Given a pair of events, how do you decide whether one is the cause of the other? It's hard to give a precise definition, but can you give some examples?

I figure that most people, even if they couldn't say exactly what they mean by "cause", would not hesitate to say that a later event couldn't possibly cause an earlier one. So, time certainly seems to be involved in causality.

[orange31]

Has anyone definitely answered the question yet? ie can causality operate independent of time..

Well, a beam of light from your perspective has had it's time stopped.
Yet the beam of light can still cause a photoelectric effect, or a sunburn, etc on another planet- 'causality' - so I'd say the answer is 'yes'.

[The Man]

Has anyone definitely answered the question yet? ie can causality operate independent of time (I think it can although its very counter intuitive). I apologize for not reading all the replies in their entirety.


Yes, the question has been answered, causality has no meaning without time. If you want to assert causality without time you’re going to run into problems. However, the reverse is different, time can exist without causality. Time can be measured by changes, that those changes may not be causally related to past times makes no difference in the ability to observe such changes. Fortunately, we currently live in a universe where the future is (to some probabilistic degree) related to the past. As by some of our current understanding that causal relationship ends sometime in the past. Does this mean that time ends? Not as far as we can tell, all we can say is that from our current understanding we may not be able to find any definitive causal extent past that time or the big bang singularity.

[RevDisturba]

Well, a beam of light from your perspective has had it's time stopped.
Yet the beam of light can still cause a photoelectric effect, or a sunburn, etc on another planet- 'causality' - so I'd say the answer is 'yes'.

Yes I have to agree with you. You used the PE effect, we could use gravity from a black hole where in theory time stops. The man (above) is confusing the concept (the arrow of time with time). The events exist with or without time. They could theoretically be accessed from an observer outside time. So I think that causality can and does exist independent of time. Remember what Kurt Gödel proved in conjunction with his walking buddy at Princeton (Albert Einstein), which was that time did not exist. If time doesn’t exist, we see that causality does everyday. I will include the book where I got the Gem about time from one of my heroes Kurt Gödel. it’s a fantastic small book, I would highly recommend it to anyone interested in such things.

Yes I have to agree with you. The man (above) is confusing the concept (the arrow of time with time). The events exist with or without time. They could theoretically be accessed from an observer outside time. So I think that causality can and does exist independent of time. Remember what Kurt Gödel proved in conjunction with his walking buddy at Princeton (Albert Einstein), which was that time did not exist. If time doesn’t exist, we see that causality does everyday. I will include the book where I got the Gem about time from one of my heroes Kurt Gödel. it’s a fantastic small book, I would highly recommend it to anyone interested in such things.

A World Without Time : The Forgotten Legacy Of Godel And Einstein ...
He added a philosophical argument that demonstrates, by Goedel's lights, that as a consequence, time does not exist in our world either. If Goedel is right, ...
- 40k

; {>

[RevDisturba]

But can't be causally related, because they all have space-like separation. Of course, as others have pointed out, without time there are no events anyway.

If there are no events independent of time how can a (the 'interior') black hole exist and effect the outside universe ie in quantum entanglement and other processes such as Bekenstein-Hawking radiation?

If one of a pair of virtual particle falls into the event horizon and the other escapes as per Hawking radiation the particle in the hole should be connected via quantum entanglement outside of the hole, correct?

; {>

[RevDisturba]

As by some of our current understanding that causal relationship ends sometime in the past. Does this mean that time ends?

I don't understand you. We know that time begin to exist a fraction of a nano second after the big bang. So before time zero there was no time. However this is where things get interesting in a first cause cosmological argument and is the reason for the question.

If everything that begins to exist has a cause for its existence that means that the universe had a 'cause' to allow it to begin to exist.

Ahhh' yes! The rub! The 'cause' (for the universe to begin to exist) according to deductive logic existed 'before' time was created in the big bang! So hence the question!)

; {?

[martu]

I don't understand you. We know that time begin to exist a fraction of a nano second after the big bang. So before time zero there was no time. However this is where things get interesting in a first cause cosmological argument and is the reason for the question.

If everything that begins to exist has a cause for its existence that means that the universe had a 'cause' to allow it to begin to exist.

Ahhh' yes! The rub! The 'cause' (for the universe to begin to exist) according to deductive logic existed 'before' time was created in the big bang! So hence the question!)

; {?

No time began at t=0 the Big Bang and not a fraction after.

Your second paragraph assumes it's conclusion.

[Mashuna]

I don't understand you. We know that time begin to exist a fraction of a nano second after the big bang. So before time zero there was no time.

I don't know that this is an accurate inference you're drawing here. We know that our current model shows time beginning after the big bang. The current model breaks down at t=0 and has no information about what was going on before the big bang.

At least, that's my layman's understanding of it.

[martu]

If there are no events independent of time how can a (the 'interior') black hole exist and effect the outside universe ie in quantum entanglement and other processes such as Bekenstein-Hawking radiation?

If one of a pair of virtual particle falls into the event horizon and the other escapes as per Hawking radiation the particle in the hole should be connected via quantum entanglement outside of the hole, correct?

; {>

Do the maths, specifically Einstein’s General Relativity equations.

As to your second paragraph I do not know and I do not know how we could know as we can’t interact with the particle ‘lost’ to the black hole.

[sol invictus]

If there are no events independent of time how can a (the 'interior') black hole exist and effect the outside universe ie in quantum entanglement and other processes such as Bekenstein-Hawking radiation?

The interior has a perfectly good time variable. That stuff about time stopping is wrong. Moreover, the interior of a black hole cannot and does not affect the outside.

If one of a pair of virtual particle falls into the event horizon and the other escapes as per Hawking radiation the particle in the hole should be connected via quantum entanglement outside of the hole, correct?

That's the wrong way to think about it - but the reason is not relevant to this discussion. Nothing goes wrong with time at the horizon or in the interior, and there's a perfectly sensible causal structure inside (it's just that time ends at the singularity - or rather, the equations break down there, just as they do near the big bang).

I don't understand you. We know that time begin to exist a fraction of a nano second after the big bang.

No we don't.

So before time zero there was no time. However this is where things get interesting in a first cause cosmological argument and is the reason for the question.

If everything that begins to exist has a cause for its existence that means that the universe had a 'cause' to allow it to begin to exist.

Ahhh' yes! The rub! The 'cause' (for the universe to begin to exist) according to deductive logic existed 'before' time was created in the big bang! So hence the question!)


If you would bother to read the thread, that point was extensively discussed. Even if time did begin at t=0 that does not imply that there was a first cause. All you have to do is pick the set t>0, rather than t>=0, and there is no first moment. One can pick a time variable - one which might be better suited to describing physics near the singularity - in which t=0 gets mapped to t=-infinity.

[The Man]

I don't understand you. We know that time begin to exist a fraction of a nano second after the big bang. So before time zero there was no time. However this is where things get interesting in a first cause cosmological argument and is the reason for the question.


As Mashuna said and I alluded to before, our understanding of specifically causality breaks down at T = 0 or at some T > 0, depending on which consideration you focus on, relativistic or quantum. The mere ascription of T = 0 infers that time exists at T= 0. We just have no verifiable models that allow us to assert time or casualty before T = 0. This lack of understanding certainly does not demonstrate a lack of time or casualty before T = 0. We model the universe based on our understanding not by our lack of understanding.



If everything that begins to exist has a cause for its existence that means that the universe had a 'cause' to allow it to begin to exist.

Ahhh' yes! The rub! The 'cause' (for the universe to begin to exist) according to deductive logic existed 'before' time was created in the big bang! So hence the question!)

; {?

Time does not require or infer causality. In a completely random universe there would be no casualty, so any measurement of time in that universe would be, well, random. Not inconceivable but just not a very useful universe and fortunately one that we do not find ourselves in at this time.

[The Man]

The interior has a perfectly good time variable. That stuff about time stopping is wrong. Moreover, the interior of a black hole cannot and does not affect the outside.


That brings up a good point Sol, so the interior of the black hole is casually related to the exterior (stuff falling through the event horizon) but the exterior is not causally related to the interior (nothing escapes the event horizon). Would that be a fair statement based on our current understanding?

[sol invictus]

That brings up a good point Sol, so the interior of the black hole is casually related to the exterior (stuff falling through the event horizon) but the exterior is not causally related to the interior (nothing escapes the event horizon). Would that be a fair statement based on our current understanding?

That's the case in classical gravity.

The situation in quantum gravity is extremely subtle, but the best current understanding is that the region outside the horizon is actually causally complete - no information is ever lost into the hole, because before it crosses the horizon it is vaporized by Hawking radiation and eventually radiated away (just like the smoke and light from something burning).

[The Man]

Yes I have to agree with you. The man (above) is confusing the concept (the arrow of time with time). The events exist with or without time. They could theoretically be accessed from an observer outside time. So I think that causality can and does exist independent of time. Remember what Kurt Gödel proved in conjunction with his walking buddy at Princeton (Albert Einstein), which was that time did not exist. If time doesn’t exist, we see that causality does everyday. I will include the book where I got the Gem about time from one of my heroes Kurt Gödel. it’s a fantastic small book, I would highly recommend it to anyone interested in such things.


I must have missed something. What concept am I confusing, particularly considering you’re making a similar point that time can exist without causality? However, if you want to assert casualty without time you must have a very unique definition of casualty.

[The Man]

That's the case in classical gravity.

The situation in quantum gravity is extremely subtle, but the best current understanding is that the region outside the horizon is actually causally complete - no information is ever lost into the hole, because before it crosses the horizon it is vaporized by Hawking radiation and eventually radiated away (just like the smoke and light from something burning).

Right, I forgot about the loss of information approaching event horizon, thanks.

[Perpetual Student]

If you would bother to read the thread, that point was extensively discussed. Even if time did begin at t=0 that does not imply that there was a first cause. All you have to do is pick the set t>0, rather than t>=0, and there is no first moment. One can pick a time variable - one which might be better suited to describing physics near the singularity - in which t=0 gets mapped to t=-infinity.

Looks like the "time" version of Zeno's paradox!

[The Man]

I think some of the confusion of this thread may be the result of what the “0” in T = 0 represents. As a measurement a zero value denotes a lack of whatever you are trying to measure. However, as an ordinate position zero is just a location on a line or within a set. The latter is the case in this consideration. We could just as easily ascribe “now” as our zero ordinate position for time. From our perspective it is always “now” so we would not move along that timeline, events in the past just get further away from us as events in the future move closer. So as an ordinate position zero does not represent a lack of time as a zero measurement would.

[The Man]

RevDisturba, is it the general interpretation of causality (past resulting in future) being related to the arrow of time that has you thinking I am confusing the concept? There are considerations that define causality as being time symmetrical, involving both retarded (forward time) and advanced (reverse time) waves. They are Wheeler Feynman Absorber Theory ( http://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory) and The Transactional Interpretation of Quantum Mechanics (http://www.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html). However, they do have their own problems involving free emission and self interaction.

[arthwollipot]

Welcome, Rev! Heh heh heh. I did warn you that it would be like this. :D

[The Man]

I was just reading the October 2008 issue of Scientific American, specifically the article “Following the Bouncing Universe” by Martin Bojowald, describing the Big Bounce application of Loop Quantum Gravity that I had mentioned before. It seems form those calculations, as one might figure, the only possible remnants of a pervious universe might be the least interacting particles, neutrinos and gravitational waves (or gravitons as theoretical particles). I recommend reading the article as it is interesting and relevant to this discussion.


Here is the link for that article

http://www.sciam.com/article.cfm?id=big-bang-or-big-bounce

ETA: I keep most of my unread magazines in the can, so I might be behind in my reading (if you’ll pardon the pun).

[Perpetual Student]

Here is an interesting article What Happened Before the Big Bang?
by Paul Davies, a theoretical physicist. http://www.fortunecity.com/emachines/e11/86/big-bang.html
He discusses the origin of the universe and questions of time and causality. Much of what he says relates to discussions on this thread. It is worth reading.

He says, "Gravitational theory predicts that under the extreme conditions that prevailed in the early universe, space and time may have been so distorted that there existed a boundary, or "singularity," at which the distortion of space-time was infinite, and therefore through which space and time cannot have continued. ... It did not stretch back for all eternity."

and,

"The lesson of quantum physics is this: Something that "just happens" need not actually violate the laws of physics. The abrupt and uncaused appearance of something can occur within the scope of scientific law, once quantum laws have been taken into account. Nature apparently has the capacity for genuine spontaneity.
It is, of course, a big step from the spontaneous and uncaused appearance of a subatomic particle-something that is routinely observed in particle accelerators-to the spontaneous and uncaused appearance of the universe. But the loophole is there. If, as astronomers believe, the primeval universe was compressed to a very small size, then quantum effects must have once been important on a cosmic scale. Even if we don't have a precise idea of exactly what took place at the beginning, we can at least see that the origin of the universe from nothing need not be unlawful or unnatural or unscientific. ..."

and,


"In spite of the space-time linkage, however, space is space and time is time under almost all circumstances. Whatever space-time distortions gravitation may produce, they never turn space into time or time into space. An exception arises, though, when quantum effects are taken into account. That all-important intrinsic uncertainty that afflicts quantum systems can be applied to space-time, too. In this case, the uncertainty can, under special circumstances, affect the identities of space and time. For a very, very brief duration, it is possible for time and space to merge in identity, for time to become, so to speak, spacelike-just another dimension of space. ...


The spatialization of time is not something abrupt; it is a continuous process. Viewed in reverse as the temporalization of (one dimension of) space, it implies that time can emerge out of space in a continuous process. (By continuous, I mean that the timelike quality of a dimension, as opposed to its spacelike quality, is not an all-or-nothing affair; there are shades in between. This vague statement can be made quite precise mathematically.)...


The essence of the Hartle-Hawking idea is that the big bang was not the abrupt switching on of time at some singular first moment, but the emergence of time from space in an ultrarapid but nevertheless continuous manner. On a human time scale, the big bang was very much a sudden, explosive origin of space, time, and matter. But look very, very closely at that first tiny fraction of a second and you find that there was no precise and sudden beginning at all. So here we have a theory of the origin of the universe that seems to say two contradictory things: First, time did not always exist; and second, there was no first moment of time. Such are the oddities of quantum physics."

[sol invictus]

The essence of the Hartle-Hawking idea is that the big bang was not the abrupt switching on of time at some singular first moment, but the emergence of time from space in an ultrarapid but nevertheless continuous manner. On a human time scale, the big bang was very much a sudden, explosive origin of space, time, and matter. But look very, very closely at that first tiny fraction of a second and you find that there was no precise and sudden beginning at all. So here we have a theory of the origin of the universe that seems to say two contradictory things: First, time did not always exist; and second, there was no first moment of time. Such are the oddities of quantum physics."

That doesn't require quantum physics at all - just the set of positive reals is good enough, as we've discussed ad nauseum.

The way time emerges in the Hartle-Hawking instanton is closer to the way north and south emerge when you move away from the north or south pole, which is why I used that as an example earlier. In fact the instanton actually is a sphere, albeit a 4D one.

[Perpetual Student]

That doesn't require quantum physics at all - just the set of positive reals is good enough, as we've discussed ad nauseum.

The way time emerges in the Hartle-Hawking instanton is closer to the way north and south emerge when you move away from the north or south pole, which is why I used that as an example earlier. In fact the instanton actually is a sphere, albeit a 4D one.

Yes. The analogy is now clear, thanks.