PDA

View Full Version : Does the second law of thermo-dynamics prevent faster than light travel?

Andonyx
28th January 2003, 12:09 PM
This is really a fluff topic. It arose from reading some short stories around the subjects of lightspeed travel and a couple books on the subject by physicists.

Now, I'm an armchair physicist at best with merely an undergrad minor in the subject, so bare with me, and please correct me on assumptions, and vocabulary, etc.

Here's how I got to the question.....

I have a pretty good understanding of the math that establishes the relationship between mass and acceleration. I also understand that to approach the speed of light for any non-zero mass requires an increasing amount of energy to achieve any further acceleration.

As I recall from calc class, this relation can be defined with the velocity of light being a limit, such that it can always be approached but never achieved. The physical reasoning is given such that for any matter with non-zero mass, it would require an inifinite amount of force, or energy to accelerate to the speed of light. Fine, that all makes sense to me, I can deal with that.

So in various literature regarding the prospect of covering huge distances in space, different physicists have proposed alternative mthods for long-distance travel. They all seem to revolve around warping space, or folding it, or bending it in such a way that two points previously far apart in a linear conception of space, have been brought togther by "folding space."

Okay, I understand that there may be a non-euclidian curvature to space in general. And that in specific cases the effect of gravity from large masses, or incredibly dense bodies "warps" space around it.

So far so good. It all makes sense to me.

But when pressed for the practicality of any of these warping ideas, the answer always seems to be that it would require more energy to accomplish than we could possibly generate or imagine at this point in human history. Sometimes the estimates are more energy than we believe to currently exist in the universe. Which can also, I assume, mean more matter since they essentially can equal the same thing.

Some of these bending methods suggest things as simple as large enough black holes to have a huge event horizon with a very fuzzy edge that can be escaped by a high enough velocity...to something as seemingly bizarre and fictitious as getting two dimensional strings to stay close to each other in paralell which I guess creates massive gravitational effects around them...

No it's not from Star Trek, it's from a real physics book, whose pertinent info I will add as soon as I get home. I can't really describe the theory better, because I simply don't understand it well enough.

But the common thread is, even if these ideas were possible, it would create travel conditions for only infinitesimally small amounts of matter. Something the size of a man would still require more energy than is apparent in the universe.

So is it possible that these two ideas are linked?

That is, we know it would take an impossible amount of energy to accelerate a Hyundai to light speed.

And it looks like it would take an impossible amount of energy to fold enough space near a Hyundai to make it traverse the same distance in the same amount of time as if it HAD traveled that fast.

Could it be that regardless of how it travels, it takes a certain amount of energy or force to move a certain mass a certain distance in a certain amount of time, and there is NO way around it.

Folding space enough to get from here to the moon in 30 seconds would take the same amount of energy as accelerating yourself to a speed that would accomplish the same thing?

In other words, it's all work right?

Work means using force to move something from somewhere to somewhere. So regardless of what method you choose wether it is crossing space, or moving space around you, the same amount of work has to be done.

Is this already taken for granted, and I just realized it myself, or is this nonsense?

Yeah, I know it's not really the second law of thermo-dynamics, but it seems like a type of inescapable conservation to me.

CurtC
28th January 2003, 03:24 PM
The physical reasoning is given such that for any matter with non-zero mass, it would require an inifinite amount of force, or energy to accelerate to the speed of light.Slight nitpick, but to my mind this isn't the fundamental reason. If you start with the idea that the speed of light, and the laws of physics are the same for all observers, then it follows that "faster than light" is a meaningless phrase. Our relative snail's pace has made us think of velocity in a way that we can easily imagine going faster than light, and imagine that there's some hard-to-understand physics of increasing mass keeping us from achieving it, while the reality is that our brains don't perceive that there is really no there there.

Physicists, do I have this basically right?

As to the question in your post, I have no idea. But I don't expect that mankind will ever warp space enough to allow us to get somewhere before a photon does.

28th January 2003, 03:30 PM
Originally posted by CurtC

Physicists, do I have this basically right?

I'm not following you here. He never mentioned going FASTER than light, did he?

If I remember correctly, mass asymptotically approaches infinity as your speed approaches c, thus requiring the thrust required for any acceleration to also go to infinity.

OK, you REAL physicists, tear us up.

Andonyx
28th January 2003, 03:43 PM
Originally posted by sundog

I'm not following you here. He never mentioned going FASTER than light, did he?

If I remember correctly, mass asymptotically approaches infinity as your speed approaches c, thus requiring the thrust required for any acceleration to also go to infinity.

OK, you REAL physicists, tear us up.

Right...

But to be even more nitpicky, and hopefully demonstrate that I've done some reasearch on the topic...

I believe that technically it's not the mass that increases, but the inertia. That is the body's tendency to stay moving at that velocity becomes so great with speed that to change it's velocity eventually requires infinite force.

By the way, the book that discusses all these freaky methods of long distance travel is:

Time Travel in Einstein's Universe
J Richard Gott
Houghton Mifflin Company
Boston, New York 2001
ISBN 0-395-95563-7

The great thing about this book is not it's time travel / space travel ideas necessarily, but the last chapter in which he uses an obscure postulate of Copernicus to estimate to within 95% accuracy the time span of existence for any thing, institution or species.

Very very cool idea.

Also, in Curtis' defense, the title of the thread is, "Does blah blah blah prevent FASTER than light travel?" So to be clear I'm thinking about as fast, or faster.

Walter Wayne
28th January 2003, 06:42 PM
Originally posted by Andonyx
Folding space enough to get from here to the moon in 30 seconds would take the same amount of energy as accelerating yourself to a speed that would accomplish the same thing?I don't think so in this case.

To get a non-zero mass to travel at c requires an infinite amount of energy.

IIRC, to warp space so that a man-sized object could travel at c with respect to space outside the warped area requires (theoretically) more energy than there is in the universe, but which is otherwise finite.

Anybody want to correct me? This isn't my area.

Walt

Andonyx
28th January 2003, 07:28 PM
Originally posted by Walter Wayne
I don't think so in this case.

To get a non-zero mass to travel at c requires an infinite amount of energy.

IIRC, to warp space so that a man-sized object could travel at c with respect to space outside the warped area requires (theoretically) more energy than there is in the universe, but which is otherwise finite.

Anybody want to correct me? This isn't my area.

Walt

That's an excellent point.

It's still theoretical, since we've never done it. I wonder if we might find that it is indeed infinite....

But how we would find that out I have no idea.

28th January 2003, 07:36 PM
Originally posted by Andonyx

I believe that technically it's not the mass that increases, but the inertia.

Huh? I thought the two were inextricably intertwined, or am I being hopelessly Newtonian?

Andonyx
28th January 2003, 07:48 PM
Originally posted by sundog

Huh? I thought the two were inextricably intertwined, or am I being hopelessly Newtonian?

Well, simply put, I heard it explained this way:

For all intents and purposes, mass is energy, and vice versa.

They can be mathematically converted from one to the other and perfectly conserved.

But energy has no inertia. And no mathematical way to express it.

In that sense, they cannot be mathematically the same quantity, since inertia would disappear suddenly when converted to energy.

Hmm, Isn't Stimpson a physicist?

28th January 2003, 07:51 PM
Originally posted by Andonyx

Hmm, Isn't Stimpson a physicist?

I think he's probably about THREE physicists.

I can't find a flaw in that explanation. Hmmmm... You've really got me thinking. I like it. :D

Andonyx
28th January 2003, 08:00 PM
Originally posted by sundog

I think he's probably about THREE physicists.

Can one of them come help us?

Heh heh heh...

rwald
28th January 2003, 08:30 PM
Going back to the initial post, you've got a good point about work, Andonyx. That is, unless the warping of space is a non-conservative force, in which case it would require more energy than just using conservative forces...

Of course, I know less physics than all of you here put together (yea...that makes sense...trust me), so I'll defer to the majority's opinion. Or Stimpy's, if he ever comes around.

Tez
28th January 2003, 09:14 PM
I dont know what the exact proposal in that book is Andonyx, but I suspect its based around a PRL of Kip Thorne and some others from a few years ago - which is essentially to hold a wormhole (a valid solution to the equations of General Rel.) open.

Unfortunately to do so requires a negative energy density.

They muttered some vague things about Casimir energy at the time. Since Casimir effects always have a "non-vacuum fluctuation" (i.e. no need for -'ve energy) explanation I just filed the paper off in the "strange mathematics" section of my brain.

However in the last year its become clear that the the vacuum has a negative energy of about a milli ev per cubic metre - a cosmological constant that gives rise to -'ve pressure (and thankfully probably ensures the universe is flat, so we dont die in a fiery heat death)

So who knows - it might be valid after all.

rwald
28th January 2003, 09:19 PM
A fiery heat death? Wasn't a heat death what happened if the universe is open, and eventually all energy gets "frozen" as mass, with matter forever flying away from everything else? Or am I confusing the above scenerio with a "Big Crunch"?

Tez
28th January 2003, 09:37 PM
Originally posted by rwald
A fiery heat death? Wasn't a heat death what happened if the universe is open, and eventually all energy gets "frozen" as mass, with matter forever flying away from everything else? Or am I confusing the above scenerio with a "Big Crunch"?

yep - youre right.

Its a fiery big crunch. Blame it on jetlag. (Speaking of which, does anyone know a magic cure?)

I used to favour a closed universe for aesthetic reasons - but then I read a great article by Freeman Dyson in Reviews of Modern Physics (intelligible to the layman) about survival of intelligent life in flat/open universes. Ever since then I've found the thought of a closed universe positively claustrophobic....

The Don
31st January 2003, 03:06 AM
Physics very rusty, prepared to be shot down in flames...

The travelling at c - infinite energy thing is down to this equation

mass = mass at rest/square root of (1 - (velocity^2 /c^2))

as the velocity increases, the square root approaches 0 and thus the mass approaches infinity. An infinite mass requires an infinite force, hence infinite energy to accellerate it.

A few points to note:

Special relativity is, like Newtonian physics, a set of equations which produce results which match experimental observation. I suspect that there are newer and better equations these days.

Newtonian physics provide an accurate estimate for things travelling slowly (i.e. up to millions of miles an hour). Special relativity describes things travelling quickly very well. THings probably get very funky as velocity approaches c.

Best way to time travel forward is to wait

rwald
31st January 2003, 07:48 AM
All correct to my knowledge, except for the last line. There's a far better way to travel forward in time. Hop in a spaceship and travel near to the speed of light. Time will move much more slowly for you in your ship, so what seems like five minutes for you could in fact be a year in everyone else's time. This is actually due to the effects of special and general relativity. So, it is in fact possible to time-travel to the future.

The problem is, once you're there, you can't get back.

31st January 2003, 07:50 AM
Originally posted by The Don

as the velocity increases, the square root approaches 0 and thus the mass approaches infinity. An infinite mass requires an infinite force, hence infinite energy to accellerate it.

That's what I thought. What about Andonyx's assertion that mass and inertia can be separated?

FFed
31st January 2003, 08:02 AM
How do we know how much energy it takes to warp space?

Andonyx
31st January 2003, 08:55 AM
Originally posted by FFed
How do we know how much energy it takes to warp space?

We don't. That's what we're trying to figure out.

Agammamon
31st January 2003, 09:37 AM
In physics, as its currently formulated, it is impossible to go faster than the speed of light in a vacuum. This speed is the same for all observers regardless of their frame of reference. this means that if you are traveling at .75c and another ship approaches you at .75c you will not see the other ship moving at 1.5c.
This limit does not apply to the motion of spacetime itself. It is theoretically possible to move a portion of spacetime at an arbitrary velocity while an object is contained within. the object never need exceed c (in fact the object never need accelerate at all).
The energy requirements to accelerate an object with a greater than zero mass to light speed do increase asymptotically. The reason is that as you input energy to increase velocity you increase the objects kinetic energy. Since mass and energy are equivalent you are effectively incresing the objects mass which requires an even greater amount of energy to accelelrate further.

Agammamon
31st January 2003, 09:42 AM
As for time travel into the past, it is also not countered by current theory. Check out info on a Tipler machine.
Basically this is a superdense cylinder set rotating at near c. The high mass and fast rotation can wrap spacetime around itself and allowing (again in theory) someone to follow a worldline that intersects itself. of course you can not travel to a point that exists before the creation of the Tipler machine.

rwald
31st January 2003, 09:56 AM
Tippler machines, rotating superdense columns, blah blah blah. I've heard that mentioned before, and I'm pretty sure that it would probably require more energy than exists in the universe to create one. Of course, I have no numbers to support that one, but it seems like one of those things where the energy requirements increase asymptotically. Besides, you could only travel into the machine's own past, so re-visiting famous historical events is out, anyway.

Oh, you forgot to mention the wormhole theory of time travel. Here, I'll include for you a section from an article I once wrote on time travel. The original article is here (http://www.bbc.co.uk/dna/h2g2/alabaster/A274105); my nick at that site is PhysicsMan.

One classic method of achieving time travel is the wormhole theory. The concept of wormholes may need some explaining. Here's an analogy to help. Imagine an ant living on a piece of paper. As far as the ant is concerned, there are only two dimensions - length and width. Joe comes along, and sees that the ant wants to go from point A to point B without passing the space in between. To help the ant, Joe does the following: he first bends the paper almost in half. Then, he takes a pencil, and drills two holes in points A and B. Then, he takes part of a straw, and sticks it in the two holes. Now the ant can just walk the length of the straw to get from A to B, rather than walking on the paper. He (or she) is able to do this by traveling through the third spacial dimension. The straw is like a wormhole. (It is also similar to the concept of a "tesserect", from the book series "A Wrinkle in Time".) Now, extrapolate this into our universe, which has three spatial dimensions. The wormhole exists in the forth spatial dimension. While this could happen, there are reasons to doubt it. This assumes that there are more than three spacial dimensions. This may or may not be true. Also, time may distort things. According to relativity, time is the fourth dimension; experiments have proven that actions which occur in the first three (spacial) dimensions can affect time (see Time Dilation). However, common logic says that, if anything, time is the zeroth dimension (after all, you could have a two-spacial-dimension world with time, see the book Flatland for an example of this). Perhaps time is not directly related to the other dimensions at all, but is unique. Anyway, another possible explanation for wormholes' impossibility is that only four-spacial-dimensional beings could create them. The ant could not have made the 'wormhole' in the demonstration above. It may turn out that wormholes are fully possible - as long as you work one dimension below your own.

Anyway, for the sake of argument, imagine that wormholes do exist, and that we can make them. According to the wormhole theory, time travel is achieved by doing the following: first, create a stable wormhole. This already causes problems. Natural wormholes (if they existed) would be very unstable. They would want to collapse the instant they were created. So, in order to prop them up, antigravity would be needed. That is, one would need some sort of 'exotic matter' which, instead of pulling other matter towards it via gravity, actually pushes matter away. Current research into 'dark matter', 'dark energy', 'quintessence', and other unusual entities is looking into this. But for the moment, 'exotic matter' with negative gravity is not known to exist. However, again for the sake of argument, make believe that such matter exists. So, now there are two points in space, X and Y, which are connected by a stable wormhole. Next, move the end of the wormhole that is at point Y around very fast. How? Some on the message boards have suggested dumping a large supply of magnetic material into the wormhole at point Y, and using electromagnets to move it. This is not guaranteed to work; quite possibly, the magnetic material would simply go through the wormhole and pop out the other side. But this is not important. Imagine that point Y has been moved around very rapidly. Now, according to Einstein's theory of relativity, the moving end should go forward in time faster than the stationary end. As a result, Y is farther in the future than X. So, if one travels from Y to X, one travels back in time. Sadly, so many parts of this theory are merely speculation that it would probably never work.Personally, I like Hawking's "Chronology Protection Conjecture." It states that the universe will protect itself from time paradox by not allowing time machines to be made. I know it's kind of contrived, but I like it nonetheless.

FFed
31st January 2003, 11:48 AM
Originally posted by Agammamon
In physics, as its currently formulated, it is impossible to go faster than the speed of light in a vacuum.
It is only impossible if you have mass. The laws of physics do not stop you from going faster then the speed of light if you have no mass. So if you can figure out how to cancel out your mass, ie antigravity, then it should be possible to go any speed you want.
As is my understanding.

Stimpson J. Cat
31st January 2003, 12:04 PM
FFed,

In physics, as its currently formulated, it is impossible to go faster than the speed of light in a vacuum.
--------------------------------------------------------------------------------

It is only impossible if you have mass. The laws of physics do not stop you from going faster then the speed of light if you have no mass. So if you can figure out how to cancel out your mass, ie antigravity, then it should be possible to go any speed you want.
As is my understanding.

Two points.

1) Something with zero rest-mass cannot go faster than c. In fact, any particle with zero rest-mass goes at exactly c.

2) Antigravity != anti-mass.

That said, the formula for determining the inertial mass of a particle moving at velocity v, with rest-mass m0, is:

m = m0 / sqrt(1 - (v/c)^2)

This means that for velocities greater than c, such an object would have imaginary mass/energy, which of course cannot correspond to anything physical. What this amounts to is that for a particle to have real energy, but be moving faster than c, its rest mass would have to be imaginary. This leads to all sorts of interesting effects. For example, it would take an infinite amount of energy to slow the thing down to c. On the other hand, obtaining an infinite velocity would require only a finite amount of energy.

This could serve to explain why such critters are never observed. The uncertainty principle allows for arbitrarily large fluctuations in energy, as long as the time-scale is small enough. A fluctuation in energy that brings the particle's energy near zero would give it enough velocity to disappear from the observable Universe before the fluctuation ended. In effect, any such particles would "quantum tunnel" out of the Universe instantaneously!

Dr. Stupid

Andonyx
31st January 2003, 02:04 PM
Hey Stimpson!

Would you know off-hand if I am correct in interpreting mass and inertia as two different properties for the purposes of measurement?

Stimpson J. Cat
31st January 2003, 02:35 PM
Andonyx,

Would you know off-hand if I am correct in interpreting mass and inertia as two different properties for the purposes of measurement?

It really depends. The term "mass" is somewhat ambiguous. To be specific, scientists usually either say "rest mass", which specifically refers to the mass of the object as measured from its own inertial frame, or "inertial mass", which is the mass of the object measured from a specific inertial frame in which the object is moving. Inertial mass is a direct measure of the object's inertia. It is also a measure of the object's energy. A basic premise of General Relativity is that inertial mass and gravitational mass are exactly the same thing. Observations seem to support this hypothesis.

Dr. Stupid

FFed
31st January 2003, 06:16 PM
Originally posted by Stimpson J. Cat
FFed,

Two points.

1) Something with zero rest-mass cannot go faster than c. In fact, any particle with zero rest-mass goes at exactly c.

2) Antigravity != anti-mass.

That said, the formula for determining the inertial mass of a particle moving at velocity v, with rest-mass m0, is:

m = m0 / sqrt(1 - (v/c)^2)

This means that for velocities greater than c, such an object would have imaginary mass/energy, which of course cannot correspond to anything physical. What this amounts to is that for a particle to have real energy, but be moving faster than c, its rest mass would have to be imaginary. This leads to all sorts of interesting effects. For example, it would take an infinite amount of energy to slow the thing down to c. On the other hand, obtaining an infinite velocity would require only a finite amount of energy.

This could serve to explain why such critters are never observed. The uncertainty principle allows for arbitrarily large fluctuations in energy, as long as the time-scale is small enough. A fluctuation in energy that brings the particle's energy near zero would give it enough velocity to disappear from the observable Universe before the fluctuation ended. In effect, any such particles would "quantum tunnel" out of the Universe instantaneously!

Dr. Stupid
Thanks for the response.
As much as I like this stuff, I am pretty dumb when it comes to it so bear with me.
Aren't tachyons a mathematical possiblility? If so, then they exists beyond the speed of light, and we exist before it. But the speed of light cannot be reached from either direction.

Stimpson J. Cat
1st February 2003, 12:40 AM
FFed,

Thanks for the response.
As much as I like this stuff, I am pretty dumb when it comes to it so bear with me.
Aren't tachyons a mathematical possiblility? If so, then they exists beyond the speed of light, and we exist before it. But the speed of light cannot be reached from either direction.

Exactly.

Dr. Stupid

BillyJoe
1st February 2003, 09:10 PM
Originally posted by rwald
Hop in a spaceship and travel near to the speed of light. Time will move much more slowly for you in your ship. Three points...

(1) You don't need to travel "near to the speed of light". Any speed will do. Of course, the greater the speed the greater the effect.

(2) You should always say what your speed is relative to.

(3) Time for you does not run more slowly. It is unchanged. For you (from your point of view), your clock runs the same when your spaceship is travelling at close to the speed of light away from Earth as when your spaceship was stationary on Earth.
As for relative time, however......
If someone on Earth were able to view the clock in your spaceship, he would see it running slower than his own clock on Earth. And if you were able to view his clock on Earth, it would be running slower than the clock in your spaceship.

You probably know all this but it can be confusing for someone trying to come to grips with relativity

regards,
BillyJoe

rwald
1st February 2003, 09:13 PM
Yea...I often forget that there are people out there who don't fully understand the concept of time dialation... ;)

BillyJoe
1st February 2003, 09:54 PM
Originally posted by rwald
Yea...I often forget that there are people out there who don't fully understand the concept of time dialation... ;) Yes and that word "dilation" doesn't help either (even when it's spelt correctly ;) ).

It obviously refers to the fact that the time between ticks on the clock stretches out. But, confusingly, this means time is slowed which seems to be the opposite of what is implied by "dilation".

But, perhaps it's just me.

rwald
1st February 2003, 09:56 PM
My spell-checker didn't complain about dialation...

Maybe it's time I get a new spell-checker.

BillyJoe
1st February 2003, 10:12 PM
Well, ****, I thought it was a typo.

rwald
1st February 2003, 11:06 PM
Seriously, a second spell-checker confirmed your opinion. Anyway, I think we've talked about spelling enough now...

BillyJoe
1st February 2003, 11:30 PM
Originally posted by rwald
Anyway, I think we've talked about spelling enough now... What about avatars then.......

Do you think my little mouse might have drawn your double-slit experiment?

harrije
3rd February 2003, 08:18 AM
I am not a professional physicist, but I would like to point out that the original post and the thread topic are completely unrelated save the word "Newton."

F = ma is Newton's second law of motion, not his second law of thermodynamics (which deals with entropy).

Einstein's E = mc^2 is derived from Newton's F = ma, and it is Einstein's theory of relativity which precludes the passing of the speed-of-light barrier, so there is likely at least a glimmer of merit in the OP's query. But Einstein never claimed that travelling faster than light was impossible; merely that approaching the speed-of-light barrier (from either side) would require an infinite amount of energy. The equations allow for there to exist particles travelling faster than light, but they would be unable to slow down to the light barrier. We would also not have any direct evidence of their existence. (These are the 'tachyons' which are apparantly all too real and observable in the Star Trek universe.)

This is all very much in the "just about anything goes" regions of science, which makes the whole subject a potential triple-decker baloney sandwich.

Andonyx
3rd February 2003, 08:53 AM
Originally posted by harrije
I am not a professional physicist, but I would like to point out that the original post and the thread topic are completely unrelated save the word "Newton."

F = ma is Newton's second law of motion, not his second law of thermodynamics (which deals with entropy).

Actually, I already stated that this is NOT about the 2nd law of thermo dynamics, and that the thread title is mis-leading. I simply was referring to some forced conservation of energy that may prohibit accelerating a non-zero rest mass to faster than or equal to light speeds.

Of course, many other observations and theories already prohibit this as you mentioned. I was just curious if any of these implied a theoretical limit to the amount of energy necessary, not just the amount of force.

But your post is a nice breakdown of some of the differences in how each theory applies.

Plutarck
3rd February 2003, 06:09 PM
OK, I don't understand much of anything here, but I just thought some of us light-in-the-physics-brain-compartment might enjoy a nice bit of modern sci-fi on the topic, sufficiently complicated so that I barely even know what it's talking about.

Faster Than Light Communication (http://www.eve-online.com/background/communication/)
Interstellar Travel (http://www.eve-online.com/background/jump/)

And now we return you to your previously scheduled discussion vastly beyond my areas of understanding...

xouper
11th February 2004, 09:36 AM
bump