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(Some Guy)   Under String Theory, a real life warp drive would only require 100kg of anti-matter. I hope you're right Ed Witten. Star Trek, here we come   ( divider line
    More: Wheaton, string theory, Star Trek, warp speed, time dilations, single electron, antimatters, faster than light, FTL  
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5363 clicks; posted to Geek » on 07 May 2012 at 3:27 AM (5 years ago)   |   Favorite    |   share:  Share on Twitter share via Email Share on Facebook   more»

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2012-05-07 07:59:44 AM  
2 votes:
Actually, in Special Relativity, if an object could exceed the speed of light (c), it wouldn't move backwards in time so much as "sideways".

tl;dr: In Special Relativity, the dimension of time behaves pretty much like an extra space dimension except that it's imaginary (in the mathematical, not literal sense). If you could somehow get a particle past the barrier of infinite energy at v=c, and take the equations of SR at face value, you find that time becomes a regular space dimension, and the space dimension in the direction of travel becomes the new time. Neat, no?

Long version:

[WARNING: the following is completely physically ungrounded speculation on my part. It makes no attempt to respect the real physics and is, at best, the seed of an interesting sci-fi story]

Special Relativity doesn't actually say that an object can't go faster than the speed of light. It actually says:

(1) If an object were to move faster than c, the equations for time dilation and length contraction give decidedly unphysical results;
(2) The equations for momentum give sensible answers for v >c, but there is a singularity in the equations at v=c where momentum and energy go to infinity. Loosely speaking, if an object is moving slower than c it would require infinite energy to reach c; and if it somehow starts out moving faster than c it can't ever move slower. It's an infinitely high barrier.

Now I'm going to handwave away (2): Usually in physics when an equation spits out infinities, physicists take it as a sign that they have pushed the theory beyond its limits of applicability. For example, I don't think any physicist takes seriously the prediction from GR that the center of a black hole is a singularity of zero size and infinite density. Instead, they assume that a theory of quantum gravity is required to explain what really happens. So for the moment I'm going to arbitrarily assume that the same is true of SR and pretend that there's some loophole that allows an object to "tunnel through" and emerge at v>c unscathed.

So what would actually happen if an object did arrive on the other side? Well, that's where the "sideways" comes in. A little digression: Physicists like to say that the universe of SR has a "signature", written [1, 1, 1, -1], meaning that we have three dimensions of space and one of time, and that the time behaves rather differently than the space ones, hence the -1. For example, if two events are separated in space along the three axes by distances x, y, and z, and separated in time by t, we can calculate their "distance" in spacetime as x^2 + y^2 + z^2 - (ct)^2; note the minus sign in front of the time term, that's what the -1 in the signature meant.

And this "distance" tells us something very fundamental about events in spacetime. If the number is positive, it means that the events are separated by more space than time; to put it prosaically, even a photon couldn't cross the space between them in the time between them. Conversely, if the number is negative, there is more time than space between the events, and an object could cross the space between them in the time available. The events are potentially causally connected, which is a fundamental concept in SR.

So finally we can get back to (1) above: the unphysical things that happen to time and length when v>c. It turns out (and the math for this is actually no harder than Pythagoras' Theorem, but is a PITA to show without a proper equation editor) that both time and length become imaginary, i.e. the square roots of negative numbers. This sounds very weird until you plug it into the above equations and discover that all that has really happened is that for an object traveling in (say) the z direction, it's as if the spacetime signature has changed from [1, 1, 1, -1] to [1, 1, -1, 1].

Or to put in another way, the time dimension for the object becomes like a space dimension, and the space dimension in the direction of travel becomes like time. And mathematically, everything else in SR continues to be perfectly well behaved, as far as I can see. So other than being mind-bendingly weird and impossible to picture conceptually, it seems perfectly reasonable.
2012-05-08 09:36:48 AM  
1 vote:
Dr. Weir has a better way:

ctzine.comView Full Size
2012-05-07 12:19:45 PM  
1 vote:

dragonchild: There isn't any defined Law of Conservation of Causality

It is taken as a law, even if it's not formally defined as such, like Conservation. Even the Law of Conservation is taken as true because we don't have any countervailing evidence and a lot of stuff would stop making sense if it weren't.

Causality pretty much falls into the same bucket: effects might precede causes, but if that were true, the universe would look very different than it does now.

It is worth noting that entanglement can happen in atemporal fashions. It's not so much that causes proceed the effects, as much as the details of the cause can be dependent upon the effect.

darthmarth28: Time Dilation just wreaks merry hell with it.

I'd disagree, slightly. Time dilation wreaks merry hell with our understanding of time. From a physical perspective, the effects of time dilation are pretty simple and easy to understand. It's just exceedingly counter-intuitive because our brains didn't evolve to act at significant proportions of the speed of light.

Relativity simply tells us that temporal relationships, like spatial relationships, are a function of the reference frame doing the measuring, and might not reconcile consistently across reference frames.
2012-05-07 11:37:53 AM  
1 vote:

Epicedion: The equations that describe these things work extremely well. You might say they're what really happens. The problem is that they use the gamma coefficient, which is defined as 1/( sqrt(1 - (v/c)^2) ).

So when your velocity equals the speed of light, the equations are undefined, because you have to divide by zero. If velocity is greater than the speed of light, the answer is complex (square root of a negative number -- imaginary, if you want).

It could very well be Special Relativity is yet another approximation, just like Newton's laws were before them. The reason why the question is open is because there is no proof that FTL travel is physically impossible, and that's because SR is defined (if "imaginary") for v > c. While the equation works well for we've observed, the math we've established at this point does not disprove FTL.

This is where laymen get all excited for no good reason. Reality is complete; the math isn't. It's far more likely the equations needs revision than FTL travel is possible, but there are two factors to consider:
1) Since v > c corresponds to no known particles with mass and is technologically impossible for the foreseeable future, there's no hurry to update the equation to explain phenomena that haven't been observed, and
2) There isn't any defined Law of Conservation of Causality, so scientifically the anti-FTL crowd has only lack of evidence to go on. Which isn't the sort of thing that prevents science from trying.

So we have an arguably incomplete equation that allows for FTL travel on some wonky level and scientists rigorously testing that incompleteness. The media thinks this means we're trying to develop FTL when it's far more likely everyone thinks FTL is impossible and they're just trying to improve the math. Improving one of Einstein's famous equations is a real feather in any physicist's cap, and the best way to improve an equation is to try to break it.
2012-05-07 10:19:49 AM  
1 vote:

Baron Harkonnen: Bacon Bits: That's idiotic. You're also simultaneously interacting with light that won't reach you for one day, so by this same logic you're simultaneously travelling [sic] one day into the future.

You'll have to explain what's idiotic to me, because your logic escapes me. You're correct in that I would be traveling one day into the future as observed from the opposite direction of my travel. Observers would see me blink out and then re-appear 24 hours later in a location one light-day more distant. But time-traveling to the future does not create paradoxes, and is allowed by physics. In the direction I'm heading, I'd be observed to have arrived a day earlier than I departed, because the light of my spacecraft departing would take a day to arrive from my departure point, and in the meantime, I would have been at my destination for that entire day. To the observers at my destination point, I would be existing at two different places at the same time, and not only that, I could potentially interact with my own self at an earlier point in time, creating any number of unresolvable paradoxes.

Light != Time
Appearing to be in two places does not mean you are in two places. It just means that light that bounced off of you from two different locations in arriving at one destination at the same time. That doesn't mean that you can communicate with that you that you're seeing.
2012-05-07 04:22:40 AM  
1 vote:
Considering that just a several years ago producing any amount of antimatter was not possible, and now we can make and hold several hundreds anti protons for up to 17 minutes, it is entirely possible that 100kg could be made in just a few billion years.
2012-05-07 03:09:51 AM  
1 vote:
There was one article I read about warp drives (no, I can't find it again, so no citation) that the problem isn't so much the travel itself, but what happens outside the bubble. When you slow down and arrive at your location, there's a shiat load of energy that needs to be dissipated. This results in your destination being blown to bits. Kinda defeats the purpose of traveling there....

\well, unless your goal was to vaporize that start system
2012-05-06 10:23:48 PM  
1 vote:
They worked out that under string theory, a warp drive would no longer require exotic matter, and the required energy would be roughly 100kg of antimatter (1019J) to warp the space around a ship the size of the space shuttle.

Well, I'm sure we'll never need a larger ship than that.
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