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Astrodude · 15th December 2010, 11:14 AM

The Alcubierre Drive is a theoretical means of propulsion that is faster-than-light from an observer's frame of reference. If someone were to build a spaceship with Alcubierre Drive to leave Earth, if they could get to Neptune before the light from the Sun. Alcubierre's method is consistent with General Relativity because the propulsion essentially manipulates space-time.

Aside from numerous practical obstacles, the major problem with the theory of Alcubierre Drive is that it supposedly requires exotic matter, which is anything with a hypothetically negative mass. My question is how so?

I've carefully looked at the math. There is no reason mathematically that a traveler would need to obtain negative energy for this propulsion. The only mathematical need for negative energy is for the observer to witness the faster than light travel, or to be precise, the travel at the essentially superluminal speed. As far as I can tell, Alcubierre drive could be done without exotic matter with many bizarre consequences.

If a ship were to really travel at a speed of 1000c from the stationary observer's frame of reference with strict Alcubierre propulsion, the observer would simply see the ship to be one thousand times closer to him than it actually is. The ship reached its long destination traveling at 1000c and then returned to the observer using the Alcubierre drive, the observer would see the ship near him and far away at the same time. In fact, the observer could witness the spaceship's journey and the spaceship at the same time after the spaceship has been out of the bubble and near Earth for some time. Theoretically by altering speeds of the distortion in spacetime, the ship could appear to be in an infinite number of places at once for the observer.

The calculations used to claim that negative energy is required for the Alcubierre drive rely on the metric of the observer, but it's not the metric of the observer at the time of observation that's relevant because the ship is in the spacetime distortion. It's the metric of the of the observer at the time of flight, when he is ironically not observing, that matters concerning the flightpath.

Please point out any mistakes.

Bishadi · 15th December 2010, 11:29 AM

Space dont bend

ElMondoHummus · 15th December 2010, 11:37 AM

Huh... Alcubierre drive...

Originally Posted by Wikipedia article

"In 1994, the Mexican physicist Miguel Alcubierre proposed a method of stretching space in a wave which would in theory cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand.[1] The ship would ride this wave inside a region known as a warp bubble of flat space."

http://en.wikipedia.org/wiki/Alcubierre_drive

All I know is that it sounds like this:

Originally Posted by Futurama

Cubert J. Farnsworth: I understand how the engines work now. It came to me in a dream. The engines don't move the ship at all. The ship stays where it is, and the engines move the universe around it.

Astrodude · 15th December 2010, 12:12 PM

Originally Posted by ElMondoHummus

Huh... Alcubierre drive...
...

All I know is that it sounds like this:

Originally Posted by Futurama
Cubert J. Farnsworth: I understand how the engines work now. It came to me in a dream. The engines don't move the ship at all. The ship stays where it is, and the engines move the universe around it.

Alcubierre drive is a legitimate deduction from general relativity. From the traveler's perspective, it would look like Cubert Farnsworth is right.

RecoveringYuppy · 15th December 2010, 12:20 PM

But it's the best example of "Can't get there from here".

Metullus · 15th December 2010, 12:45 PM

Is it faster than a von Däniken Drive?

ElMondoHummus · 15th December 2010, 01:14 PM

Originally Posted by Astrodude

Alcubierre drive is a legitimate deduction from general relativity. From the traveler's perspective, it would look like Cubert Farnsworth is right.

Look, I don't know enough about physics to comment on this. My education was in chem and biology and it was nothing more than a bachelors. My physics knowledge is miniscule relative to folks like Sol Invictus, MattusMaximus, etc. So unfortunately, I'm not going to be able to get deep into the argument; I simply don't know enough.

But that said, from what little I do know, I can say this: Alcubierre's theory may indeed be a legitimate deduction from GR, but like anything with an FTL component, there's an inherent problem with causality that needs to be addressed. And until it is, that's reason enough to suspect its actual validity, legitimate deduction from proven theory nonwithstanding. If you can address such issues, please feel free. I wouldn't mind the education, and in fact would love to know how that aspect of the consequences get handled.

But as far as actual participation from me, I again simply don't have the knowledge. I'll turn back into an audience member and student and let you and others teach me what I need to know. So I'll bow out now and leave the details of that to be hashed out by the folks in here who're far smarter than I on the topic. But anyway, in the end, my point is that to elevate such a thing as the Alcubierre "drive" from interesting to possible, the consequences of FTL phenomenon must be addressed. Causality is the one I'm thinking of, and I'm sure others will chime in with more.

Thanks for your time.

RecoveringYuppy · 15th December 2010, 01:18 PM

Actually I don't the drive does raise causality issues because the same theory that the "drive" is deduced from also implies there can't be any causal relationship between objects in our space and objects in the space containing the drive.

Soapy Sam · 15th December 2010, 01:29 PM

The reason the universe looks like a rubber sheet is that sometimes, god wets the bed.

Astrodude · 15th December 2010, 01:53 PM

Originally Posted by RecoveringYuppy

Actually I don't the drive does raise causality issues because the same theory that the "drive" is deduced from also implies there can't be any causal relationship between objects in our space and objects in the space containing the drive.

Causality is not clearly defined in either general or special relativity. I contend that causality is an abstraction that depends on one's frame of reference.

Madalch · 15th December 2010, 02:16 PM

Originally Posted by Soapy Sam

The reason the universe looks like a rubber sheet is that sometimes, god wets the bed.

Yes, but he usually warns us before it happens.

At least one of us, anyway- that lucky person gets to build an ark.

Uncayimmy · 15th December 2010, 02:18 PM

In other words, this drive will make a cart go down space faster than the space???

KingMerv00 · 15th December 2010, 03:29 PM

Originally Posted by Bishadi

Space dont bend

*Can't resist*

Why do you think Einstein was wrong?

Astrodude · 15th December 2010, 04:24 PM

Originally Posted by UncaYimmy

In other words, this drive will make a cart go down space faster than the space???

Yes.

Vorpal · 15th December 2010, 05:43 PM

Originally Posted by Astrodude

The calculations used to claim that negative energy is required for the Alcubierre drive rely on the metric of the observer, but it's not the metric of the observer at the time of observation that's relevant because the ship is in the spacetime distortion. It's the metric of the of the observer at the time of flight, when he is ironically not observing, that matters concerning the flightpath.

That doesn't make any sense. There is no such thing as a "metric of the observer", because all observers have the same metric. The metric is a tensor--a geometrical object that's observer-independent. Its particular coordinate representation depends on the coordinate chart used, but that's not relevant to any observable quantity. Nor is any particular observer obliged to use a particular coordinate chart; all observers can use the same chart if they wish to, or different ones if it strikes their fancy.

If you have an observer with four-velocity u (also a geometrical object independent of coordinate representation!) at some event in spacetime then T(u,u) is the energy density measured by that observer. The weak energy condition is equivalent to saying that all possible observers measure a non-negative energy density, and the Alcubierre spacetime violates this. There is nothing coordinate-dependent in this statement: if it's violated in one system of coordinates, then it's violated in all.

Vorpal · 15th December 2010, 05:55 PM

Originally Posted by Astrodude

Causality is not clearly defined in either general or special relativity. I contend that causality is an abstraction that depends on one's frame of reference.

That is simply not true. While "causality" in general may be considered a philosophically slippery concept, it does have a very clear, geometrical and observer-independent definition in relativity. In fact, several of them, of various 'strength'. One can discuss the merits of each and how well they match any pre-formed intuitive notion, but that doesn't seem to be a physical or mathematical issue.

Originally Posted by Astrodude

Yes.

No.

Astrodude · 15th December 2010, 06:42 PM

Originally Posted by Vorpal

That doesn't make any sense. There is no such thing as a "metric of the observer", because all observers have the same metric. The metric is a tensor--a geometrical object that's observer-independent. Its particular coordinate representation depends on the coordinate chart used, but that's not relevant to any observable quantity. Nor is any particular observer obliged to use a particular coordinate chart; all observers can use the same chart if they wish to, or different ones if it strikes their fancy.

I mean to say the space measured accurately. I could have used the wrong term, but I was taught that there is a difference between metric and metric tensor and that the metric changes according to relativity while the metric tensor does not. I was referring to measurement of the three dimensions of space in Minkowski space, independent of the time when I said 'metric'. Minkowski space considers time also so as a metric tensor it would not change. All stationary observers would have approximately the same metric but travelers would not. However, all travelers and stationary observers would have the same metric tensor because the yielded scalar doesn't change but the individual vectors do. If the coordinate system changes, as it does if only considering 3 of the four dimensions, the metric changes.

The different respective metrics for the traveler and the observer form the cornerstone of the Alcubierre drive.

Astrodude · 15th December 2010, 06:45 PM

Originally Posted by UncaYimmy

In other words, this drive will make a cart go down space faster than the space???

Did you mean the space making the cart move? I took that to mean gravity and said yes.

Did you mean actually racing the space bubble? If then, no.

sol invictus · 15th December 2010, 06:52 PM

Vorpal is correct. The stress-energy tensor of the Alcubierre metric either violates the weak energy condition or it doesn't (I haven't checked, but my understanding is that it does). There is no "observer dependence" - energy conditions in GR are formulated in coordinate invariant form.

Of course one can question whether the energy conditions must be obeyed, but one reason to think they must be is the fact that violating them allows faster-than-light travel, and all the very serious problems with causality that go along with it.

Astrodude · 15th December 2010, 07:35 PM

Originally Posted by Vorpal

That is simply not true. While "causality" in general may be considered a philosophically slippery concept, it does have a very clear, geometrical and observer-independent definition in relativity. In fact, several of them, of various 'strength'. One can discuss the merits of each and how well they match any pre-formed intuitive notion, but that doesn't seem to be a physical or mathematical issue.

This rebuttal is correct. There are definitions of causality in relativity but they aren't consistent with traditional definitions where a cause must have some type of instantaneous effect. Causality wouldn't be violated anyways because the observer couldn't signal the ship it watches travel.

The Kilted Yaksman · 15th December 2010, 07:49 PM

Originally Posted by Astrodude

This rebuttal is correct. There are definitions of causality in relativity but they aren't consistent with traditional definitions where a cause must have some type of instantaneous effect. Causality wouldn't be violated anyways because the observer couldn't signal the ship it watches travel.

Y'mean there'd be no transwarp beaming or subspace communications from Starfleet Command?

Astrodude · 15th December 2010, 07:51 PM

Originally Posted by Vorpal

If you have an observer with four-velocity u (also a geometrical object independent of coordinate representation!) at some event in spacetime then T(u,u) is the energy density measured by that observer. The weak energy condition is equivalent to saying that all possible observers measure a non-negative energy density, and the Alcubierre spacetime violates this. There is nothing coordinate-dependent in this statement: if it's violated in one system of coordinates, then it's violated in all.

All this shows is that the observer cannot measure the ship traveling at superluminal velocity!!!

Once the claim becomes that because it is impossible for something to be measured at one position, the claim then is coordinate dependent because a metric by definition is how you measure something.

Astrodude · 15th December 2010, 07:53 PM

Originally Posted by The Kilted Yaksman

Y'mean there'd be no transwarp beaming or subspace communications from Starfleet Command?

Oh there could be in a few thousand years.

Originally Posted by sol invictus

Of course one can question whether the energy conditions must be obeyed, but one reason to think they must be is the fact that violating them allows faster-than-light travel, and all the very serious problems with causality that go along with it.

Then I see no reason why they must be obeyed and the problems with causality are with causality.

sol invictus · 15th December 2010, 08:40 PM

Originally Posted by Astrodude

All this shows is that the observer cannot measure the ship traveling at superluminal velocity!!!

Once the claim becomes that because it is impossible for something to be measured at one position, the claim then is coordinate dependent because a metric by definition is how you measure something.

I can't make any sense of that.

Originally Posted by Astrodude

Then I see no reason why they must be obeyed and the problems with causality are with causality.

The problems with causality induced by FTL travel are extremely severe; most likely they render physics logically inconsistent. Since physics works extraordinarily well, that's a very strong argument against the possibility of FTL (and therefore for certain energy conditions).

Vorpal · 15th December 2010, 08:50 PM

Originally Posted by Astrodude

I could have used the wrong term, but I was taught that there is a difference between metric and metric tensor and that the metric changes according to relativity while the metric tensor does not.

The metric is by definition a certain rank-2 tensor. It exists over all of spacetime as part of the definition of being a Lorentzian manifold, and is the same thing for everyone up to a diffeomorphism. I'm not sure what you're referring to. What relativity does is tell how matter (and other stuff) determines the Ricci curvature of spacetime, and through div T = 0 how the Ricci curvature moves that matter.

Originally Posted by Astrodude

I was referring to measurement of the three dimensions of space in Minkowski space, independent of the time when I said 'metric'.

It still sounds like you're referring to different coordinates, since the Alcubierre metric is asymptotically flat. This is not a physically relevant difference. If not, then if you could do a simple example and point to the thing you mean, I could try to help clear up this issue. As a guess, it could be that you're confused about the global vs. local distinction. The weak energy condition is a local statement... is that where you're trying to go?

Originally Posted by Astrodude

There are definitions of causality in relativity but they aren't consistent with traditional definitions where a cause must have some type of instantaneous effect.

??? By what tradition?

Originally Posted by Astrodude

All this shows is that the observer cannot measure the ship traveling at superluminal velocity!!!

Locally, what you just said is that T^α_βu^β is not spacelike. That is not equivalent to non-negativity of T_αβu^αu^β, and neither one implies the other.

Originally Posted by Astrodude

Once the claim becomes that because it is impossible for something to be measured at one position, the claim then is coordinate dependent because a metric by definition is how you measure something.

And the metric is coordinate-independent!

Astrodude · 15th December 2010, 09:43 PM

Originally Posted by Vorpal

The metric is by definition a certain rank-2 tensor. It exists over all of spacetime as part of the definition of being a Lorentzian manifold, and is the same thing for everyone up to a diffeomorphism. I'm not sure what you're referring to. What relativity does is tell how matter (and other stuff) determines the Ricci curvature of spacetime, and through div T = 0 how the Ricci curvature moves that matter.

I always thought that was the metric tensor.

Originally Posted by Vorpal

It still sounds like you're referring to different coordinates, since the Alcubierre metric is asymptotically flat. This is not a physically relevant difference. If not, then if you could do a simple example and point to the thing you mean, I could try to help clear up this issue. As a guess, it could be that you're confused about the global vs. local distinction. The weak energy condition is a local statement... is that where you're trying to go?

No, the global vs. local distinction I get. Let me try explaining what should happen according to the math in regular words:

1) When the ship travels under Alcubierre drive, space in front should contract while space in back should lengthen.
2) This contraction should effect the metric
3) The calculations show that a negative energy density is only necessary to observe the superluminal speed.
4) The real local energy density required just for the actual travel is positive.

Originally Posted by Vorpal

Locally, what you just said is that T^α_βu^β is not spacelike. That is not equivalent to non-negativity of T_αβu^αu^β, and neither one implies the other.

When did I say otherwise? I'm just suggesting that negative energy isn't needed to use an Alcubierre drive.

Drachasor · 15th December 2010, 10:06 PM

Here's a simple way of pointing out how it doesn't make sense.

What direction does this ship without negative mass go?

Think about it.

Vorpal · 15th December 2010, 10:59 PM

Originally Posted by Astrodude

When did I say otherwise? I'm just suggesting that negative energy isn't needed to use an Alcubierre drive.

You did just previously:

Originally Posted by Astrodude

Originally Posted by Vorpal

If you have an observer with four-velocity u (also a geometrical object independent of coordinate representation!) at some event in spacetime then T(u,u) is the energy density measured by that observer. The weak energy condition is equivalent to saying that all possible observers measure a non-negative energy density, and the Alcubierre spacetime violates this. ...

All this shows is that the observer cannot measure the ship traveling at superluminal velocity!!!

If you quote a discussion on the weak energy condition and its violation and make such a reply, any normal person would interpret the "this" as referring to the weak energy condition and its violation.

Originally Posted by Astrodude

I always thought that was the metric tensor.

Nope.

Originally Posted by Astrodude

Let me try explaining what should happen according to the math in regular words:

I would rather you give the math, actually.

Originally Posted by Astrodude

1) When the ship travels under Alcubierre drive, space in front should contract while space in back should lengthen.
2) This contraction should effect the metric
3) The calculations show that a negative energy density is only necessary to observe the superluminal speed.

If your claim is that the weak energy condition is not violated for subluminal Alcubierre drive, then you're in disagreement with Alcubierre's paper. If it's something else, then I've no idea what you mean. Either way, you should at least outline the math--what exactly are you calculating and how?

Originally Posted by Astrodude

4) The real local energy density required just for the actual travel is positive.

'Real'?

rwguinn · 16th December 2010, 07:51 AM

Originally Posted by Astrodude

The Alcubierre Drive is a theoretical means of propulsion that is faster-than-light from an observer's frame of reference. If someone were to build a spaceship with Alcubierre Drive to leave Earth, if they could get to Neptune before the light from the Sun. Alcubierre's method is consistent with General Relativity because the propulsion essentially manipulates space-time.

Aside from numerous practical obstacles, the major problem with the theory of Alcubierre Drive is that it supposedly requires exotic matter, which is anything with a hypothetically negative mass. My question is how so?

I've carefully looked at the math. There is no reason mathematically that a traveler would need to obtain negative energy for this propulsion. The only mathematical need for negative energy is for the observer to witness the faster than light travel, or to be precise, the travel at the essentially superluminal speed. As far as I can tell, Alcubierre drive could be done without exotic matter with many bizarre consequences.

If a ship were to really travel at a speed of 1000c from the stationary observer's frame of reference with strict Alcubierre propulsion, the observer would simply see the ship to be one thousand times closer to him than it actually is. The ship reached its long destination traveling at 1000c and then returned to the observer using the Alcubierre drive, the observer would see the ship near him and far away at the same time. In fact, the observer could witness the spaceship's journey and the spaceship at the same time after the spaceship has been out of the bubble and near Earth for some time. Theoretically by altering speeds of the distortion in spacetime, the ship could appear to be in an infinite number of places at once for the observer.

The calculations used to claim that negative energy is required for the Alcubierre drive rely on the metric of the observer, but it's not the metric of the observer at the time of observation that's relevant because the ship is in the spacetime distortion. It's the metric of the of the observer at the time of flight, when he is ironically not observing, that matters concerning the flightpath.

Please point out any mistakes.

Negative energy?
Would that not mean that energy is a vector?

Astrodude · 16th December 2010, 07:52 AM

My claim is that the weak energy condition would only be violated if the superluminal travel were to be observable. I see no reason why it would be violated if the travel merely took place. I'm looking at the steps where[edited for spelling] Alcubierre differentiated and he differentiated with respect to variables that aren't relevant to the actual flightpath.

Originally Posted by Vorpal

If your claim is that the weak energy condition is not violated for subluminal Alcubierre drive, then you're in disagreement with Alcubierre's paper. If it's something else, then I've no idea what you mean. Either way, you should at least outline the math--what exactly are you calculating and how?

'Real'?

By 'real', I mean the energy density actually required for the travel to occur.

Astrodude · 16th December 2010, 07:55 AM

Originally Posted by rwguinn

Negative energy?
Would that not mean that energy is a vector?

Yep, it would mean energy is a vector. Negative energy has been observed sometimes by Gravity Probe B and E.S. Miksch had a widely respected theory that posited negative energy of gravitational radiation, but I can't find what it is because he died. But, I don't see why negative energy is even needed for the Alcubierre drive.

edd · 16th December 2010, 08:12 AM

Originally Posted by rwguinn

Negative energy?
Would that not mean that energy is a vector?

Despite what astrodude just said, no it wouldn't. Scalars can have negative values.

edit to add: and don't forget what gravitational potential energy looks like, if you need further convincing.

sol invictus · 16th December 2010, 08:44 AM

Originally Posted by Astrodude

My claim is that the weak energy condition would only be violated if the superluminal travel were to be observable. I see no reason why it would be violated if the travel merely took place.

That makes no sense at all. How is "ship 1 departed point A and arrived at point B, 1 light year distant from A, 6 months later" not an observation of superluminal travel?

And regardless, as I said - either the metric violates the weak energy condition or it doesn't. Evidently this one does. That statement has nothing to do with any "observer"; it's a coordinate- and observer-independent fact.

Quote:

I'm looking at the steps were Alcubierre differentiated and he differentiated with respect to variables that aren't relevant to the actual flightpath.

So you're saying he made a mistake in his paper? If so, please show us what it is.

Astrodude · 16th December 2010, 09:45 AM

Originally Posted by edd

Despite what astrodude just said, no it wouldn't. Scalars can have negative values.

edit to add: and don't forget what gravitational potential energy looks like, if you need further convincing.

He's right, energy is usually considered a scalar and I goofed there, but it might be useful to represent it as a vector's magnitude. Particularly, I think it could be represented by the modulus of a complex number. It's a semantic issue and somewhat subjective because if energy is positional, you can consider it to have a direction. -5 does not equal 5, but they must have the same magnitude since magnitude cannot be negative. Only the directions can differ. This is where I think it gets a little subjective.

A scalar can have a negative value, but it only matters if it can be related to a vector. Energy can always be defined as a dot product classically so it is therefore dependent on a angle, a direction. To get a one-to-one function, limit the domain of theta from 0 to 90 degrees so only one possible angle can yield one possible work value for a given distance and force. A magnitude of a vector cannot be negative. Therefore, in order to distinguish between work in one direction from work in another direction, you would need to treat it like a vector. If you pushed a box at a 45 degree angle, and there a two possible angles defined as 45 degrees to get a one-to-one function, how else would you distinguish forward work from backwards work?

rwguinn · 16th December 2010, 09:52 AM

Originally Posted by Astrodude

He's right, energy is usually considered a scalar and I goofed there, but it might be useful to represent it as a vector's magnitude. Particularly, I think it could be represented by the modulus of a complex number. It's a semantic issue and somewhat subjective because if energy is positional, you can consider it to have a direction. -5 does not equal 5, but they must have the same magnitude since magnitude cannot be negative. Only the directions can differ. This is where I think it gets a little subjective.

A scalar can have a negative value, but it only matters if it can be related to a vector. Energy can always be defined as a dot product classically so it is therefore dependent on a angle, a direction. To get a one-to-one function, limit the domain of theta from 0 to 90 degrees so only one possible angle can yield one possible work value for a given distance and force. A magnitude of a vector cannot be negative. Therefore, in order to distinguish between work in one direction from work in another direction, you would need to treat it like a vector. If you pushed a box at a 45 degree angle, and there a two possible angles defined as 45 degrees to get a one-to-one function, how else would you distinguish forward work from backwards work?

By it's resultant on matter and the direction of motion induced [/engineering mode]
I get the point, but it is interesting to see how you folks in the "why is there air" fields define things.
In my case, as an engineer, I think of it as absorbing or releasing energy, so depending on your reference frame, I guess you could describe it as "Negative energy" and "positive energy"
Carry on--this is interesting stuff.

Fnord · 16th December 2010, 10:08 AM

Is anyone going to actually build one of these things and demonstrate whether or not it actually works? Or is everyone satisfied with arguing about the meanings of words?

This thread reminds me of a story about a controversy in the Vatican over the number of teeth in a horse’s mouth, involving great debates and learned philosophical discourses. Finally, someone suggested that they find a horse, open its mouth and count the teeth.

That person was immediately excommunicated.

Astrodude · 16th December 2010, 10:14 AM

Originally Posted by sol invictus

That makes no sense at all. How is "ship 1 departed point A and arrived at point B, 1 light year distant from A, 6 months later" not an observation of superluminal travel?

If ship 1 departed from point A, arrived at point B which is one light year away from A, and returned to point A in two months, the observer at point A would see the ship once it exited the bubble and was close to the point A. It would look like it came out of nowhere or literally skipped space if you could actually see it with all of the would-be radiation and from this alone the observer would not be able to calculate velocity because he would've observed a discontinuous flight.

However, a few months after the ship's arrival, the observer would be able to view the ship traveling from point B to point A but simply at a much slower apparent speed because the speed of light is the same in all frames of reference because the space has gotten longer than it was when the ship was actually traveling. If the ship could be piloted(another tough matter altogether) by a human pilot, the human pilot could theoretically watch himself fly the ship after he flew it with a telescope. However, it would look like he was traveling much more slowly. Also, with a hypothetically super powerful telescope, you could watch historical events on Earth by traveling superluminally to far away places.

I'll be glad to show the math when I can figure out how to write equations on the webforum; I need to remember LaTeX symbols.

Originally Posted by sol invictus

So you're saying he made a mistake in his paper? If so, please show us what it is.

As far as I can tell, on page 8 of his "The warp drive: hyper-fast travel within general relativity" at the bottom. Just because the velocity calculated by the observer would be sub-luminal, doesn't mean that the real velocity was sub-luminal.

Astrodude · 16th December 2010, 10:27 AM

Originally Posted by Fnord

Is anyone going to actually build one of these things and demonstrate whether or not it actually works? Or is everyone satisfied with arguing about the meanings of words?

This thread reminds me of a story about a controversy in the Vatican over the number of teeth in a horse’s mouth, involving great debates and learned philosophical discourses. Finally, someone suggested that they find a horse, open its mouth and count the teeth.

That person was immediately excommunicated.

Hell yeah! First, we need to build really tiny models and test the Alcubierre drive a subluminal velocities because we don't have enough energy to build a big one currently.

Plus, until it could be piloted, according to my apparently contentious observation, it is really difficult to determine whether it worked or not because we couldn't actually see it travel faster than light. If it traveled with the Alcubierre method at an overall speed slower than light to test it, I think we should see the ship traveling without length contraction and time would pass the same for the traveler and the observer. A good way to test it would be to measure if would be to see if time dilation was mitigated. Also, it's important to point out that we'd still observe the traveler moving at just a fraction of his actual velocity.

Drachasor · 16th December 2010, 12:22 PM

It won't work without negative mass.

Again, without negative mass, what direction does the ship travel in?

Astrodude · 16th December 2010, 12:36 PM

Originally Posted by Drachasor

It won't work without negative mass.

Again, without negative mass, what direction does the ship travel in?

I think it would travel with the bubble without negative rest mass.

I'm logging off for now, but I'll be back Saturday.

15th December 2010, 11:14 AM	#1
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Alcubierre Drive The Alcubierre Drive is a theoretical means of propulsion that is faster-than-light from an observer's frame of reference. If someone were to build a spaceship with Alcubierre Drive to leave Earth, if they could get to Neptune before the light from the Sun. Alcubierre's method is consistent with General Relativity because the propulsion essentially manipulates space-time. Aside from numerous practical obstacles, the major problem with the theory of Alcubierre Drive is that it supposedly requires exotic matter, which is anything with a hypothetically negative mass. My question is how so? I've carefully looked at the math. There is no reason mathematically that a traveler would need to obtain negative energy for this propulsion. The only mathematical need for negative energy is for the observer to witness the faster than light travel, or to be precise, the travel at the essentially superluminal speed. As far as I can tell, Alcubierre drive could be done without exotic matter with many bizarre consequences. If a ship were to really travel at a speed of 1000c from the stationary observer's frame of reference with strict Alcubierre propulsion, the observer would simply see the ship to be one thousand times closer to him than it actually is. The ship reached its long destination traveling at 1000c and then returned to the observer using the Alcubierre drive, the observer would see the ship near him and far away at the same time. In fact, the observer could witness the spaceship's journey and the spaceship at the same time after the spaceship has been out of the bubble and near Earth for some time. Theoretically by altering speeds of the distortion in spacetime, the ship could appear to be in an infinite number of places at once for the observer. The calculations used to claim that negative energy is required for the Alcubierre drive rely on the metric of the observer, but it's not the metric of the observer at the time of observation that's relevant because the ship is in the spacetime distortion. It's the metric of the of the observer at the time of flight, when he is ironically not observing, that matters concerning the flightpath. Please point out any mistakes.

15th December 2010, 11:37 AM	#3
ElMondoHummus 0.25 short of being half-witted Join Date: Oct 2006 Location: Somewhere north of the South Pole Posts: 11,967	Huh... Alcubierre drive... Originally Posted by Wikipedia article "In 1994, the Mexican physicist Miguel Alcubierre proposed a method of stretching space in a wave which would in theory cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand.[1] The ship would ride this wave inside a region known as a warp bubble of flat space." http://en.wikipedia.org/wiki/Alcubierre_drive All I know is that it sounds like this: Originally Posted by Futurama Cubert J. Farnsworth: I understand how the engines work now. It came to me in a dream. The engines don't move the ship at all. The ship stays where it is, and the engines move the universe around it.
	__________________ must take this very carefully....booze is wise men's drink..... -pillory "... I'm quite willing to have everyone use my rejection of the 9/11 conspiracy theory as a basis for assessing my intelligence, judgment, and trustworthiness" -Prof. Ann Althouse

15th December 2010, 12:12 PM	#4
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by ElMondoHummus Huh... Alcubierre drive... ... All I know is that it sounds like this: Originally Posted by Futurama Cubert J. Farnsworth: I understand how the engines work now. It came to me in a dream. The engines don't move the ship at all. The ship stays where it is, and the engines move the universe around it. Alcubierre drive is a legitimate deduction from general relativity. From the traveler's perspective, it would look like Cubert Farnsworth is right.

15th December 2010, 12:20 PM	#5
RecoveringYuppy Illuminator Join Date: Nov 2006 Location: Tucson, AZ Posts: 3,877	But it's the best example of "Can't get there from here".
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15th December 2010, 12:45 PM	#6
Metullus Forum ¾-Wit Pro Tem Join Date: Jan 2005 Location: Waldo's Pond Posts: 4,015	Is it faster than a von Däniken Drive?
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15th December 2010, 11:29 AM	#2
Bishadi Banned Join Date: Sep 2010 Location: Here Posts: 2,279	Space dont bend

15th December 2010, 01:14 PM	#7
ElMondoHummus 0.25 short of being half-witted Join Date: Oct 2006 Location: Somewhere north of the South Pole Posts: 11,967	Originally Posted by Astrodude Alcubierre drive is a legitimate deduction from general relativity. From the traveler's perspective, it would look like Cubert Farnsworth is right. Look, I don't know enough about physics to comment on this. My education was in chem and biology and it was nothing more than a bachelors. My physics knowledge is miniscule relative to folks like Sol Invictus, MattusMaximus, etc. So unfortunately, I'm not going to be able to get deep into the argument; I simply don't know enough. But that said, from what little I do know, I can say this: Alcubierre's theory may indeed be a legitimate deduction from GR, but like anything with an FTL component, there's an inherent problem with causality that needs to be addressed. And until it is, that's reason enough to suspect its actual validity, legitimate deduction from proven theory nonwithstanding. If you can address such issues, please feel free. I wouldn't mind the education, and in fact would love to know how that aspect of the consequences get handled. But as far as actual participation from me, I again simply don't have the knowledge. I'll turn back into an audience member and student and let you and others teach me what I need to know. So I'll bow out now and leave the details of that to be hashed out by the folks in here who're far smarter than I on the topic. But anyway, in the end, my point is that to elevate such a thing as the Alcubierre "drive" from interesting to possible, the consequences of FTL phenomenon must be addressed. Causality is the one I'm thinking of, and I'm sure others will chime in with more. Thanks for your time.
	__________________ must take this very carefully....booze is wise men's drink..... -pillory "... I'm quite willing to have everyone use my rejection of the 9/11 conspiracy theory as a basis for assessing my intelligence, judgment, and trustworthiness" -Prof. Ann Althouse

15th December 2010, 01:18 PM	#8
RecoveringYuppy Illuminator Join Date: Nov 2006 Location: Tucson, AZ Posts: 3,877	Actually I don't the drive does raise causality issues because the same theory that the "drive" is deduced from also implies there can't be any causal relationship between objects in our space and objects in the space containing the drive.
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15th December 2010, 01:29 PM	#9
Soapy Sam NLH Join Date: Oct 2002 Posts: 25,907	The reason the universe looks like a rubber sheet is that sometimes, god wets the bed.
Soapy Sam NLH Join Date: Oct 2002 Posts: 25,907

15th December 2010, 01:53 PM	#10
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by RecoveringYuppy Actually I don't the drive does raise causality issues because the same theory that the "drive" is deduced from also implies there can't be any causal relationship between objects in our space and objects in the space containing the drive. Causality is not clearly defined in either general or special relativity. I contend that causality is an abstraction that depends on one's frame of reference.

15th December 2010, 02:16 PM	#11
Madalch The Jester Join Date: Nov 2006 Location: The wet coast. Posts: 8,745	Originally Posted by Soapy Sam The reason the universe looks like a rubber sheet is that sometimes, god wets the bed. Yes, but he usually warns us before it happens. At least one of us, anyway- that lucky person gets to build an ark.
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15th December 2010, 02:18 PM	#12
Uncayimmy Banned Join Date: Oct 2008 Posts: 7,485	In other words, this drive will make a cart go down space faster than the space???
Uncayimmy Banned Join Date: Oct 2008 Posts: 7,485

15th December 2010, 03:29 PM	#13
KingMerv00 Penultimate Amazing Join Date: Nov 2004 Location: Philadelphia, PA...USA Posts: 14,482	Originally Posted by Bishadi Space dont bend Can't resist Why do you think Einstein was wrong?
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15th December 2010, 04:24 PM	#14
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by UncaYimmy In other words, this drive will make a cart go down space faster than the space??? Yes.

15th December 2010, 05:43 PM	#15
Vorpal Extrapolate! Join Date: Jan 2005 Posts: 1,013	Originally Posted by Astrodude The calculations used to claim that negative energy is required for the Alcubierre drive rely on the metric of the observer, but it's not the metric of the observer at the time of observation that's relevant because the ship is in the spacetime distortion. It's the metric of the of the observer at the time of flight, when he is ironically not observing, that matters concerning the flightpath. That doesn't make any sense. There is no such thing as a "metric of the observer", because all observers have the same metric. The metric is a tensor--a geometrical object that's observer-independent. Its particular coordinate representation depends on the coordinate chart used, but that's not relevant to any observable quantity. Nor is any particular observer obliged to use a particular coordinate chart; all observers can use the same chart if they wish to, or different ones if it strikes their fancy. If you have an observer with four-velocity u (also a geometrical object independent of coordinate representation!) at some event in spacetime then T(u,u) is the energy density measured by that observer. The weak energy condition is equivalent to saying that all possible observers measure a non-negative energy density, and the Alcubierre spacetime violates this. There is nothing coordinate-dependent in this statement: if it's violated in one system of coordinates, then it's violated in all.
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15th December 2010, 05:55 PM	#16
Vorpal Extrapolate! Join Date: Jan 2005 Posts: 1,013	Originally Posted by Astrodude Causality is not clearly defined in either general or special relativity. I contend that causality is an abstraction that depends on one's frame of reference. That is simply not true. While "causality" in general may be considered a philosophically slippery concept, it does have a very clear, geometrical and observer-independent definition in relativity. In fact, several of them, of various 'strength'. One can discuss the merits of each and how well they match any pre-formed intuitive notion, but that doesn't seem to be a physical or mathematical issue. Originally Posted by Astrodude Yes. No.
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15th December 2010, 06:42 PM	#17
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by Vorpal That doesn't make any sense. There is no such thing as a "metric of the observer", because all observers have the same metric. The metric is a tensor--a geometrical object that's observer-independent. Its particular coordinate representation depends on the coordinate chart used, but that's not relevant to any observable quantity. Nor is any particular observer obliged to use a particular coordinate chart; all observers can use the same chart if they wish to, or different ones if it strikes their fancy. I mean to say the space measured accurately. I could have used the wrong term, but I was taught that there is a difference between metric and metric tensor and that the metric changes according to relativity while the metric tensor does not. I was referring to measurement of the three dimensions of space in Minkowski space, independent of the time when I said 'metric'. Minkowski space considers time also so as a metric tensor it would not change. All stationary observers would have approximately the same metric but travelers would not. However, all travelers and stationary observers would have the same metric tensor because the yielded scalar doesn't change but the individual vectors do. If the coordinate system changes, as it does if only considering 3 of the four dimensions, the metric changes. The different respective metrics for the traveler and the observer form the cornerstone of the Alcubierre drive.

15th December 2010, 06:45 PM	#18
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by UncaYimmy In other words, this drive will make a cart go down space faster than the space??? Did you mean the space making the cart move? I took that to mean gravity and said yes. Did you mean actually racing the space bubble? If then, no.

15th December 2010, 06:52 PM	#19
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 8,434	Vorpal is correct. The stress-energy tensor of the Alcubierre metric either violates the weak energy condition or it doesn't (I haven't checked, but my understanding is that it does). There is no "observer dependence" - energy conditions in GR are formulated in coordinate invariant form. Of course one can question whether the energy conditions must be obeyed, but one reason to think they must be is the fact that violating them allows faster-than-light travel, and all the very serious problems with causality that go along with it.

15th December 2010, 07:35 PM	#20
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by Vorpal That is simply not true. While "causality" in general may be considered a philosophically slippery concept, it does have a very clear, geometrical and observer-independent definition in relativity. In fact, several of them, of various 'strength'. One can discuss the merits of each and how well they match any pre-formed intuitive notion, but that doesn't seem to be a physical or mathematical issue. This rebuttal is correct. There are definitions of causality in relativity but they aren't consistent with traditional definitions where a cause must have some type of instantaneous effect. Causality wouldn't be violated anyways because the observer couldn't signal the ship it watches travel.

15th December 2010, 07:49 PM	#21
The Kilted Yaksman Sense Offender Join Date: Mar 2005 Posts: 549	Originally Posted by Astrodude This rebuttal is correct. There are definitions of causality in relativity but they aren't consistent with traditional definitions where a cause must have some type of instantaneous effect. Causality wouldn't be violated anyways because the observer couldn't signal the ship it watches travel. Y'mean there'd be no transwarp beaming or subspace communications from Starfleet Command?
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15th December 2010, 07:51 PM	#22
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by Vorpal If you have an observer with four-velocity u (also a geometrical object independent of coordinate representation!) at some event in spacetime then T(u,u) is the energy density measured by that observer. The weak energy condition is equivalent to saying that all possible observers measure a non-negative energy density, and the Alcubierre spacetime violates this. There is nothing coordinate-dependent in this statement: if it's violated in one system of coordinates, then it's violated in all. All this shows is that the observer cannot measure the ship traveling at superluminal velocity!!! Once the claim becomes that because it is impossible for something to be measured at one position, the claim then is coordinate dependent because a metric by definition is how you measure something.

15th December 2010, 07:53 PM	#23
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by The Kilted Yaksman Y'mean there'd be no transwarp beaming or subspace communications from Starfleet Command? Oh there could be in a few thousand years. Originally Posted by sol invictus Of course one can question whether the energy conditions must be obeyed, but one reason to think they must be is the fact that violating them allows faster-than-light travel, and all the very serious problems with causality that go along with it. Then I see no reason why they must be obeyed and the problems with causality are with causality.
	Last edited by Astrodude; 15th December 2010 at 08:00 PM.

15th December 2010, 08:40 PM	#24
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 8,434	Originally Posted by Astrodude All this shows is that the observer cannot measure the ship traveling at superluminal velocity!!! Once the claim becomes that because it is impossible for something to be measured at one position, the claim then is coordinate dependent because a metric by definition is how you measure something. I can't make any sense of that. Originally Posted by Astrodude Then I see no reason why they must be obeyed and the problems with causality are with causality. The problems with causality induced by FTL travel are extremely severe; most likely they render physics logically inconsistent. Since physics works extraordinarily well, that's a very strong argument against the possibility of FTL (and therefore for certain energy conditions).
	Last edited by sol invictus; 15th December 2010 at 08:41 PM.

15th December 2010, 08:50 PM	#25
Vorpal Extrapolate! Join Date: Jan 2005 Posts: 1,013	Originally Posted by Astrodude I could have used the wrong term, but I was taught that there is a difference between metric and metric tensor and that the metric changes according to relativity while the metric tensor does not. The metric is by definition a certain rank-2 tensor. It exists over all of spacetime as part of the definition of being a Lorentzian manifold, and is the same thing for everyone up to a diffeomorphism. I'm not sure what you're referring to. What relativity does is tell how matter (and other stuff) determines the Ricci curvature of spacetime, and through div T = 0 how the Ricci curvature moves that matter. Originally Posted by Astrodude I was referring to measurement of the three dimensions of space in Minkowski space, independent of the time when I said 'metric'. It still sounds like you're referring to different coordinates, since the Alcubierre metric is asymptotically flat. This is not a physically relevant difference. If not, then if you could do a simple example and point to the thing you mean, I could try to help clear up this issue. As a guess, it could be that you're confused about the global vs. local distinction. The weak energy condition is a local statement... is that where you're trying to go? Originally Posted by Astrodude There are definitions of causality in relativity but they aren't consistent with traditional definitions where a cause must have some type of instantaneous effect. ??? By what tradition? Originally Posted by Astrodude All this shows is that the observer cannot measure the ship traveling at superluminal velocity!!! Locally, what you just said is that T^α_βu^β is not spacelike. That is not equivalent to non-negativity of T_αβu^αu^β, and neither one implies the other. Originally Posted by Astrodude Once the claim becomes that because it is impossible for something to be measured at one position, the claim then is coordinate dependent because a metric by definition is how you measure something. And the metric is coordinate-independent!
Vorpal Extrapolate! Join Date: Jan 2005 Posts: 1,013	__________________ For every philosopher, there exists an equal and opposite philosopher. They're both wrong.

15th December 2010, 09:43 PM	#26
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by Vorpal The metric is by definition a certain rank-2 tensor. It exists over all of spacetime as part of the definition of being a Lorentzian manifold, and is the same thing for everyone up to a diffeomorphism. I'm not sure what you're referring to. What relativity does is tell how matter (and other stuff) determines the Ricci curvature of spacetime, and through div T = 0 how the Ricci curvature moves that matter. I always thought that was the metric tensor. Originally Posted by Vorpal It still sounds like you're referring to different coordinates, since the Alcubierre metric is asymptotically flat. This is not a physically relevant difference. If not, then if you could do a simple example and point to the thing you mean, I could try to help clear up this issue. As a guess, it could be that you're confused about the global vs. local distinction. The weak energy condition is a local statement... is that where you're trying to go? No, the global vs. local distinction I get. Let me try explaining what should happen according to the math in regular words: 1) When the ship travels under Alcubierre drive, space in front should contract while space in back should lengthen. 2) This contraction should effect the metric 3) The calculations show that a negative energy density is only necessary to observe the superluminal speed. 4) The real local energy density required just for the actual travel is positive. Originally Posted by Vorpal Locally, what you just said is that T^α_βu^β is not spacelike. That is not equivalent to non-negativity of T_αβu^αu^β, and neither one implies the other. When did I say otherwise? I'm just suggesting that negative energy isn't needed to use an Alcubierre drive.

15th December 2010, 10:06 PM	#27
Drachasor Graduate Poster Join Date: Nov 2010 Posts: 1,718	Here's a simple way of pointing out how it doesn't make sense. What direction does this ship without negative mass go? Think about it.

15th December 2010, 10:59 PM	#28
Vorpal Extrapolate! Join Date: Jan 2005 Posts: 1,013	Originally Posted by Astrodude When did I say otherwise? I'm just suggesting that negative energy isn't needed to use an Alcubierre drive. You did just previously: Originally Posted by Astrodude Originally Posted by Vorpal If you have an observer with four-velocity u (also a geometrical object independent of coordinate representation!) at some event in spacetime then T(u,u) is the energy density measured by that observer. The weak energy condition is equivalent to saying that all possible observers measure a non-negative energy density, and the Alcubierre spacetime violates this. ... All this shows is that the observer cannot measure the ship traveling at superluminal velocity!!! If you quote a discussion on the weak energy condition and its violation and make such a reply, any normal person would interpret the "this" as referring to the weak energy condition and its violation. Originally Posted by Astrodude I always thought that was the metric tensor. Nope. Originally Posted by Astrodude Let me try explaining what should happen according to the math in regular words: I would rather you give the math, actually. Originally Posted by Astrodude 1) When the ship travels under Alcubierre drive, space in front should contract while space in back should lengthen. 2) This contraction should effect the metric 3) The calculations show that a negative energy density is only necessary to observe the superluminal speed. If your claim is that the weak energy condition is not violated for subluminal Alcubierre drive, then you're in disagreement with Alcubierre's paper. If it's something else, then I've no idea what you mean. Either way, you should at least outline the math--what exactly are you calculating and how? Originally Posted by Astrodude 4) The real local energy density required just for the actual travel is positive. 'Real'?
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16th December 2010, 07:51 AM	#29
rwguinn Philosopher Join Date: Apr 2003 Location: 16 miles from 7 lakes Posts: 8,505	Originally Posted by Astrodude The Alcubierre Drive is a theoretical means of propulsion that is faster-than-light from an observer's frame of reference. If someone were to build a spaceship with Alcubierre Drive to leave Earth, if they could get to Neptune before the light from the Sun. Alcubierre's method is consistent with General Relativity because the propulsion essentially manipulates space-time. Aside from numerous practical obstacles, the major problem with the theory of Alcubierre Drive is that it supposedly requires exotic matter, which is anything with a hypothetically negative mass. My question is how so? I've carefully looked at the math. There is no reason mathematically that a traveler would need to obtain negative energy for this propulsion. The only mathematical need for negative energy is for the observer to witness the faster than light travel, or to be precise, the travel at the essentially superluminal speed. As far as I can tell, Alcubierre drive could be done without exotic matter with many bizarre consequences. If a ship were to really travel at a speed of 1000c from the stationary observer's frame of reference with strict Alcubierre propulsion, the observer would simply see the ship to be one thousand times closer to him than it actually is. The ship reached its long destination traveling at 1000c and then returned to the observer using the Alcubierre drive, the observer would see the ship near him and far away at the same time. In fact, the observer could witness the spaceship's journey and the spaceship at the same time after the spaceship has been out of the bubble and near Earth for some time. Theoretically by altering speeds of the distortion in spacetime, the ship could appear to be in an infinite number of places at once for the observer. The calculations used to claim that negative energy is required for the Alcubierre drive rely on the metric of the observer, but it's not the metric of the observer at the time of observation that's relevant because the ship is in the spacetime distortion. It's the metric of the of the observer at the time of flight, when he is ironically not observing, that matters concerning the flightpath. Please point out any mistakes. Negative energy? Would that not mean that energy is a vector?
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16th December 2010, 07:52 AM	#30
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	My claim is that the weak energy condition would only be violated if the superluminal travel were to be observable. I see no reason why it would be violated if the travel merely took place. I'm looking at the steps where[edited for spelling] Alcubierre differentiated and he differentiated with respect to variables that aren't relevant to the actual flightpath. Originally Posted by Vorpal If your claim is that the weak energy condition is not violated for subluminal Alcubierre drive, then you're in disagreement with Alcubierre's paper. If it's something else, then I've no idea what you mean. Either way, you should at least outline the math--what exactly are you calculating and how? 'Real'? By 'real', I mean the energy density actually required for the travel to occur.
	Last edited by Astrodude; 16th December 2010 at 09:02 AM.

16th December 2010, 07:55 AM	#31
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by rwguinn Negative energy? Would that not mean that energy is a vector? Yep, it would mean energy is a vector. Negative energy has been observed sometimes by Gravity Probe B and E.S. Miksch had a widely respected theory that posited negative energy of gravitational radiation, but I can't find what it is because he died. But, I don't see why negative energy is even needed for the Alcubierre drive.

16th December 2010, 08:12 AM	#32
edd Graduate Poster Join Date: Nov 2007 Posts: 1,615	Originally Posted by rwguinn Negative energy? Would that not mean that energy is a vector? Despite what astrodude just said, no it wouldn't. Scalars can have negative values. edit to add: and don't forget what gravitational potential energy looks like, if you need further convincing.
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16th December 2010, 08:44 AM	#33
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 8,434	Originally Posted by Astrodude My claim is that the weak energy condition would only be violated if the superluminal travel were to be observable. I see no reason why it would be violated if the travel merely took place. That makes no sense at all. How is "ship 1 departed point A and arrived at point B, 1 light year distant from A, 6 months later" not an observation of superluminal travel? And regardless, as I said - either the metric violates the weak energy condition or it doesn't. Evidently this one does. That statement has nothing to do with any "observer"; it's a coordinate- and observer-independent fact. Quote: I'm looking at the steps were Alcubierre differentiated and he differentiated with respect to variables that aren't relevant to the actual flightpath. So you're saying he made a mistake in his paper? If so, please show us what it is.

16th December 2010, 09:45 AM	#34
Astrodude Critical Thinker Join Date: Nov 2010 Location: University of Rhode Island Posts: 360	Originally Posted by edd Despite what astrodude just said, no it wouldn't. Scalars can have negative values. edit to add: and don't forget what gravitational potential energy looks like, if you need further convincing. He's right, energy is usually considered a scalar and I goofed there, but it might be useful to represent it as a vector's magnitude. Particularly, I think it could be represented by the modulus of a complex number. It's a semantic issue and somewhat subjective because if energy is positional, you can consider it to have a direction. -5 does not equal 5, but they must have the same magnitude since magnitude cannot be negative. Only the directions can differ. This is where I think it gets a little subjective. A scalar can have a negative value, but it only matters if it can be related to a vector. Energy can always be defined as a dot product classically so it is therefore dependent on a angle, a direction. To get a one-to-one function, limit the domain of theta from 0 to 90 degrees so only one possible angle can yield one possible work value for a given distance and force. A magnitude of a vector cannot be negative. Therefore, in order to distinguish between work in one direction from work in another direction, you would need to treat it like a vector. If you pushed a box at a 45 degree angle, and there a two possible angles defined as 45 degrees to get a one-to-one function, how else would you distinguish forward work from backwards work?

16th December 2010, 09:52 AM	#35
rwguinn Philosopher Join Date: Apr 2003 Location: 16 miles from 7 lakes Posts: 8,505	Originally Posted by Astrodude He's right, energy is usually considered a scalar and I goofed there, but it might be useful to represent it as a vector's magnitude. Particularly, I think it could be represented by the modulus of a complex number. It's a semantic issue and somewhat subjective because if energy is positional, you can consider it to have a direction. -5 does not equal 5, but they must have the same magnitude since magnitude cannot be negative. Only the directions can differ. This is where I think it gets a little subjective. A scalar can have a negative value, but it only matters if it can be related to a vector. Energy can always be defined as a dot product classically so it is therefore dependent on a angle, a direction. To get a one-to-one function, limit the domain of theta from 0 to 90 degrees so only one possible angle can yield one possible work value for a given distance and force. A magnitude of a vector cannot be negative. Therefore, in order to distinguish between work in one direction from work in another direction, you would need to treat it like a vector. If you pushed a box at a 45 degree angle, and there a two possible angles defined as 45 degrees to get a one-to-one function, how else would you distinguish forward work from backwards work? By it's resultant on matter and the direction of motion induced [/engineering mode] I get the point, but it is interesting to see how you folks in the "why is there air" fields define things. In my case, as an engineer, I think of it as absorbing or releasing energy, so depending on your reference frame, I guess you could describe it as "Negative energy" and "positive energy" Carry on--this is interesting stuff.
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