# Speed of light - can it be exceeded?

1. Sep 26, 2007

### AzureNight

My knowledge of astrophysics is purely on a self-interest level (I just read about it on my own because it is extremely interesting); but I have read that the speed of light can be exceeded if there is a distortion in spacetime. What are the actual theories on this topic?

2. Sep 26, 2007

### genneth

3. Oct 10, 2007

### Ondon

FTL travel

The following article may be of interest.

http://www.newscientist.com/channel/fundamentals/mg18925331.200-take-a-leap-into-hyperspace.html

It proposes a testable theory that one a prize about ftlt. It is too bad no group has put forth the money to test it. What would be needed? A few.. hundred million?

With potentially earthlike planets like http://www.eso.org/public/outreach/press-rel/pr-2007/pr-22-07.html [Broken]

It would not seem a bad idea to test out such hypothesis.

Last edited by a moderator: May 3, 2017
4. Oct 10, 2007

### pervect

Staff Emeritus
The following quote grabbed my eye:

So the biggest problem with the Heim theory (which is what is being discussed here) is that its not clear what it actually predicts. How can you expect a group to put forth money to test a theory, when it seems that the proponents of the theory aren't willing to actually make a prediction?

5. Oct 13, 2007

### Lockheed

Well, not exactly. A distortion in spacetime may allow you to get around the light barrier (such as a wormhole or for a more exotic example "warp-drive"), but you are not really going faster than light, its that the space around you is moving. There are solutions in GR that allow this.

Otherwise, you cannot go faster than light because of the Lorentz Transformation, in which the denominator will end up being zero if you go at the speed of light.

Likewise, a photon can go at the speed of light because it has a zero rest mass.

Last edited: Oct 13, 2007
6. Oct 15, 2007

### rbj

without resorting to a concept such as or similar to the aether, what possible meaning can there be ascribed to the notion that "the space around you is moving"?

i don't think there is any operational meaning to the notion of the empty space around me moving. this is why the laws of nature, both qualitatively and quantitatively (which includes the values of $\epsilon_0$ and $\mu_0$ and therefore c), must be identical in every inertial frame.

Last edited: Oct 16, 2007
7. Oct 15, 2007

### OOO

The speed of light can't be exceeded because it is defined to be 299 792 458 m/s. This definition only assumes that the apparatus that defines the units of length and time is small compared to spacetime curvature. If you perform a measurement in one spacetime point what you actually do is locally diagonalize a matrix (the metric which describes the gravitational properties of spacetime). In diagonalized form it always looks like diag(c^-2,-1,-1,-1).

So by moving your measuring instruments to some piece of curved spacetime you will get the same speed of light as everywhere (as long as your instrument is not torn apart by tidal forces, which is again an indication of a too large instrument, see below) because it's the measuring device that is your contact to the real world. If you can't trust your apparatus you're lost.

However if you use a large measuring device (e.g. a laser interferometer millions of kilometers in extension) the speed of light may appear to be different because light gets parallel transported from one spacetime point to another and the metric is different in each one (parallel transport defines how to compare measuring devices between different points in curved spacetime).

In my opinion it is a matter of taste whether you say "speed of light varies over great distances" or "large measuring devices are unsuitable for determining the speed of light". If I remember correctly there is a similar statement in Weinberg.

Last edited: Oct 15, 2007
8. Oct 16, 2007

### Liger20

If it helps any, I have heard that our universe can expand faster than the speed of light. However, this is a very subtle situation. It's the universe ITSELF expanding faster than the speed of light as opposed to something contained within the universe.

9. Oct 16, 2007

### rbj

okay, so i'll define it to be 50 m/s and see that i cannot exceed that.

or, how 'bout before 1960 when the meter was not defined in terms of any radiation. then the speed of light was measured, not defined. does that mean it could have been exceeded before 1960?

dunno if your reasoning is solid.

10. Oct 16, 2007

### rbj

i realize that this is referring to the cosmological inflationary universe model. i admit that i don't understand this particular part of it. so my question is, what meaning is there to the universe itself expanding faster than c whereas the contents inside never move away from each other faster than c? so the universe is expanding more rapidly than the contents inside? what difference would it make if the universe was expanding at a speed less than c as long as it was not expanding at a speed slower than the contents inside?

r b-j

11. Oct 17, 2007

### OOO

In as far as "your meter" will be a very large unit compared to human dimensions, you will certainly not be able to exceed "your speed of light".

Since you wonder about history let's go straight to the meter prototype of 1799. If you build a space probe with the meter prototype on board and launch it to the surface of the sun (assume that inside the space probe temperature is kept constant) then you will not notice any difference in length (and likewise, time) measurements, thus no change in speed of light. This is because gravity affects every object (e.g. light, interatomic forces) inside the space probe in the same way. So I can't see your problem with this argument. This is standard GR with respect to the local Lorentz frame...

But, of course, I didn't want to indicate that it's trivial that we're able to simply define the speed of light. If gravity did affect some objects differently from others then this would not be possible.

Last edited: Oct 17, 2007
12. Oct 17, 2007

### rbj

then what you are talking about is our (or "my") anthropocentric definition of the meter, again in terms of the speed of light (or, more fundamentally, the speed of propagation of all "instantaneous" interactions). that wasn't mentioned at the outset.

it's that in 1959 or 1799, the meter has a definition independent of c. so then c was not defined. c was measured in terms of the existing meter and second. then the speed of light was not defined yet still could not be exceeded.

the speed of light is what it is because the EM interaction, like gravity, like any fundamental interaction, has a common finite speed of propagation. it doesn't matter what that finite speed of propagation is other than that it is finite. the reason this speed (regarding one inertial reference frame to another) cannot be exceeded is because for every inertial observer, the laws of physics (both qualitatively and quantitatively) have to be the same each inertial observer. but it's not because we define the meter to be the distance that any of these interactions propagate in 1/299792458th second. i guess i still don't get it.

13. Oct 17, 2007

### OOO

Hmm, I hardly know what else to say about it. Especially your posting in the "How fast is gravity" thread seems to say basically the same as I do. As you said, c is dimensionful and thus its value is the direct consequence of the (arbitrary) system of units you chose.

Let me put it this way: given a certain dimensionful quantity, for example the meter prototype of Paris, what would you need to determine whether this quantity changes when you travel to a large gravitating object ? Of course, you would need a second quantity with the same dimension, which changes in relation to the first. If the ratio between both doesn't change then you could either assume that both have changed in the same proportion, or that nothing has changed at all.

The most natural way we have always done such comparisons is by means of our own body: if we see that an object has not grown relative to ourselves then we assume that its extension has remained constant. In a similar way we relate our measurement devices to each other.

General relativity tells us that in sufficiently small regions of spacetime all our (freely falling) measuring instruments behave in every possible way like they do in an inertial system. So how could they ever yield a different speed of light ?

As I have said, I have been a bit imprecise in saying that c can't change because it is defined that way. A better way would be to say, that the system of units can be defined by the value of c at all because gravity changes the relative spatio-temporal proportions of every object or instrument in the same way.

Last edited: Oct 17, 2007
14. Oct 18, 2007

### Lockheed

I know its a pretty bad term to use, but what I mean by "moving space (actually spacetime)" is, well, like making a fold in it or contract it or something like that to sort of "decrease" the distance the object or spacecraft has to travel. Basically, manipulating the geometry of spacetime itself.

Here is more info about it, and a clearer explanation: http://www.nasa.gov/centers/glenn/research/warp/ipspaper.html [Broken]

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And if you guys are wondering why the speed of light cannot be exceeded, it is because of the Lorentz Factor, in which at the speed of light you are basically dividing by zero. Wikipedia has a pretty good article on it: http://en.wikipedia.org/wiki/Lorentz_factor

Last edited by a moderator: May 3, 2017
15. Oct 19, 2007

### OOO

If you do an experiment, you don't divide anything by zero. It's as if you say, your car doesn't drive faster than 123 mph because you can't push the gas pedal any further. So I'm reluctant to accept this as an explanation, although it expresses some aspect of finite speed of light.

16. Oct 19, 2007

### Lockheed

You are approaching it the wrong way. All of our equations and theories are based on experiment in that they describe what is happening, and the Lorentz Factor is no different. Just look at the equation and do the math yourself. Plug in the speed of light for "v".

If you can't accept that explanation, well then I don't know what else I can tell you, because that really is the best one there is. Otherwise you will go into the realm of metaphysics (which is about the nature of things, and at this point really isn't provable).

17. Oct 19, 2007

### OOO

I always appreciate being taught the right way of thinking by an expert.

18. Oct 19, 2007

### Lockheed

And thus you seem to prefer the appeal to authority fallacy, which is the wrong way of thinking...

Whether or not any explanation or information comes from an expert is irrelevant. Unless a better explanation can be found, the one I gave you is the best one there is, and the one that most "experts" usually give.

I don't know why you are reluctant to accept it, it is a perfectly fine explanation and provable via mathematics. You can try them yourself, just take any of the Lorentz Transformations and see what happens when you plug in the speed of light as your velocity.

Last edited: Oct 19, 2007
19. Oct 19, 2007

### OOO

You're so cute. The first time I have done what you say has been twenty years ago and since then I have done it a thousand times. Do you remember that the thread starter asked about distortions of spacetime (i.e. the domain of general relativity) ?

Last edited: Oct 19, 2007
20. Oct 19, 2007

### Huckleberry

The explanations I have heard describe space-time as an expanding balloon. If two marks are drawn on a balloon and then it is inflated the marks will appear to move away from each other. As the universe expands the anti-gravity force becomes stronger and pushes the galaxies apart faster. As the expansion exceeds the speed of light galaxies go past the event horizon of space-time. The energy from these galaxies never reaches us. The expansion eventually results in the feezing death of the universe.

The objects in the universe never need move at all. The space-time between them may expand faster than light.