Speed of light - can it be exceeded?

[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?

 

[genneth]

Perhaps you can find something here: http://math.ucr.edu/home/baez/physics/

In particular: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html

Specifically, you're thinking of something similar to a wormhole, but just not as drastic.

 

[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

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

 

[pervect]

The following quote grabbed my eye:

For now, though, Lenard considers the theory too shaky to justify the use of the Z machine. "I would be very interested in getting Sandia interested if we could get a more perspicacious introduction to the mathematics behind the proposed experiment," he says. "Even if the results are negative, that, in my mind, is a successful experiment."

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?

 

[Lockheed]

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?

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.

 

[rbj]

but you are not really going faster than light, its that the space around you is moving.

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.

 

[OOO]

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?

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.

 

[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.

 

[rbj]

The speed of light can't be exceeded because it is defined to be 299792458 m/s.

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.

 

[rbj]

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.

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

 

[OOO]

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

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".

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?

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.

 

[rbj]

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

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".

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.

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.

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 1/299792458^th second. i guess i still don't get it.

 

[OOO]

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 1/299792458^th second. i guess i still don't get it.

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.

 

[Lockheed]

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.

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 ================================================================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

 

[OOO]

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

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.

 

[Lockheed]

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.

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).

 

[OOO]

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).

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

 

[Lockheed]

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

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.

 

[OOO]

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.

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) ?

 

[Huckleberry]

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

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.

 

[Lockheed]

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.

Yeah, but using equations is the easy part. It is quite possible to use them without understanding their meaning. It doesn't matter if you did them only 1 time or a million times.

Do you remember that the thread starter asked about distortions of spacetime (i.e. the domain of general relativity) ?

Yes, and that has already been addressed. What we are arguing now is over the reasons why the speed of light can't be exceeded, which is also relevant to this topic.

 

[Lockheed]

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.

I've also heard the expansion of the Universe being compared to expanding raisin bread in an oven. Personally, I think that is a better analogy then the balloon one, as one can avoid the "what is in the center" questions (which may not make any physical sense).

 

[rbj]

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.

okay, so we see that the same way...

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?

being that i am GR deficient (less so with SR), i wasn't thinking about any non-inertial frames of reference. there is a reason that c cannot be exceeded and it is more fundamental than GR. it's a fact to establish (with SR) before you start extending the model to accelerated frames of reference and their counterpart in gravitational fields (or "curved space-time" if you will).

The most natural way we have always done such comparisons is by means of our own body:

i agree with that. it is no accident that the meter is about as big as we are. to answer the question for why c is 299792458 m/s (besides the small adjustments that are historical accidents) we have to know why the size of atoms are 10²⁵ times bigger than the Planck Length, why biological cells are about 10⁵ atoms across and why sentient beings like us are 10⁵ bigger than the cells that make up us. and similarly, why the biological processes that determine how much time occurs for us to perceive things and to do mental calculations is about 10⁴⁴ times longer than the Planck Time. those are the fundamental dimensionless questions to answer and then, since (by definition) c is always 1 Planck Length per Planck Time, we can put that together to answer why light (or any other instantaneous interaction) propagates a distance that is about 10⁸ times our body size in the time it takes us to think a thought.

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 ?

they don't and that's because the speed of light (as well as the rest of quantitative physics) has to be the same in all inertial frames, including those that are free-falling.

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.

sounds to me that that is a consequence of the "laws of physics, both qualitatively and quantitatively, must be the same for all inertial frames of reference" being extended to "laws of physics, both qualitatively and quantitatively, must be the same for all frames of reference having the same acceleration" and then applying the equivalence principle that "unaccelerated" in a gravitational field g is the same (locally) as being accelerated (by g) in the middle of space.

but i think it's more than imprecise to say that "c can't change because it is defined that way". physics and nature don't give a rat's ass how we or anyone else defines anything. and i think it's also more than imprecise to say that "c can't be exceeded because it's value is defined".

c can't be exceeded or even equalled (as a velocity between two inertial reference frames) because of a consequence of the axiom that the laws of physics must be the same, both qualitatively and quantitatively (which means c is the same as well as h or G or any other parameter), for each of those inertial frames. in order for c to be the same, observational phenomena like time-dilation and length-contraction and Lorentzian velocity addition exists that can only make sense when the relative speed is less than c.

OOO, I'm not challenging your physics, it's more of a philosophical thing. you're saying A implies C because A implies B, but you haven't really convinced me that B implies C is axiomatic.

 

[pervect]

I've also heard the expansion of the Universe being compared to expanding raisin bread in an oven. Personally, I think that is a better analogy then the balloon one, as one can avoid the "what is in the center" questions (which may not make any physical sense).

There are some subtle points to using "the expanding space" idea correctly. One paper that talks about this is http://arxiv.org/abs/0707.0380

There are some other papers that recommend not using "expanding space" at all, this paper takes the position that the idea can be useful if applied correctly and points out some of the pitfalls.

Another more abstract approach points out that there are some fundamental ambiguities in the very concept of velocity when two particles are not at the same point in space-time.

See for instance http://www.math.ucr.edu/home/baez/einstein/node2.html

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.

The defintion of "velocity" used in Hubble's law depends strongly on the coordinate system used. This is brought out strongly in the example of the Milne universe (this is from http://arxiv.org/abs/0707.0380 previously mentioned)

However, as shown in Grøn & Elgarøy (2006) and Page (1993)
we can, by a co-ordinate transformation, describe simple
Minkowski space-time as the FRW metric of an
empty universe, known as the Milne model. In the
Minkowski special relativistic co-ordinates we of course
cannot have superluminal motion. However in the new
Milne model co-ordinates we do find that dD/dt > 1
beyond a certain distance from the origin. Thus we
have apparently described superluminal motion in a
spacetime that we know cannot permit such a phenomenon.

The solution I favor is pointing out that the definition of velocity used in cosmology depends on the coordinates used, and that this is not avoidable. (The notion of distance used in cosmology also has hidden coordinate dependencies as well).

 

[OOO]

physics and nature don't give a rat's ass how we or anyone else defines anything.

That's right. But sometimes the way we define certain things has consequences that don't depend on nature. Would you say the number Pi is a natural constant ? I would say no, because the value of Pi is a consequence of our operational definitions of the terms "circle", "radius", "area". Would you say, that the average number of kings during a chess game is two with a standard deviation of zero because this is a natural constant ? I'd say no again.

Do you understand now what I was thinking of when I tried to say that the value and constancy of c has no meaning by itself, which we can read off from the fact that it can be defined ? Let's measure length and let's measure time and ohhh wow, this turns out to be nearly the same, didn't expect this, there must be a deeper reason for that...

I admit this is a bit intuitive and I have no ambitions to clarify this idea any further. Maybe I'm even wrong. Maybe I'm not even wrong

c can't be exceeded or even equalled (as a velocity between two inertial reference frames) because of a consequence of the axiom that the laws of physics must be the same, both qualitatively and quantitatively (which means c is the same as well as h or G or any other parameter), for each of those inertial frames. in order for c to be the same, observational phenomena like time-dilation and length-contraction and Lorentzian velocity addition exists that can only make sense when the relative speed is less than c.

I was assuming SR as a known fact, so we won't have to debate about c in SR any longer. The thread starter has asked about distortions of spacetime. So I tried to say (in my short-circuit manner) that the constancy of c in curved spacetime is a consequence (similar to the above light bulb moment) of us using the same definition of inertial system in connection with the same measuring instruments and the same operational definition of measurements, again in curved spacetime. Later I complemented my imprecise (I continue to use this term) claim by referring to the fact that this is only possible since GR affects all objects in the same way.

 

[rbj]

Would you say the number Pi is a natural constant ?

depends on what you mean. it's not a "natural constant" in the sense of \alpha is a constant presented to us by physical reality. but it is natural in the sense it is not human made (or some specific alien).

I would say no, because the value of Pi is a consequence of our operational definitions of the terms "circle", "radius", "area".

the geometry of circles and such (which include their fundamental constants) have meaning in mathematics that transcend any accident of history in the human or any other alien race. \pi (or maybe it would be 2 \pi or 4 \pi) has as much natural meaning as e or 0 or 1 or 2 or -1 or \pm \sqrt{-1}.

this mathematical meaning has natural consequence in the physical world. planets and stars are pretty cicular and if there was no spinning, i think they would be perfectly circular. the concept of flux which is basic to Gauss's Law has a direct relation to the surface area of a sphere, so 4 \pi appears naturally there. i guess i remain unpersuaded.

Would you say, that the average number of kings during a chess game is two with a standard deviation of zero because this is a natural constant ? I'd say no again.

that's totally different. that is, at first blush, a strawman.

Do you understand now what I was thinking of when I tried to say that the value and constancy of c has no meaning by itself,

i think we agree on that but not for the same reasons (at least not expressed reasons). the fact that c is finite is a meaningful physical fact. the fact that it has any particular finite value is not meaningful from a fundamental physical POV. may as well set it to 1.

which we can read off from the fact that it can be defined ?

no, i don't get that. the fact that it can be defined is not sufficient to support the notion that it is constant nor sufficient that it cannot be exceeded. we can define the meter to be the distance that sound in some mixure of air at STP is travel in the time elaped by (340.29)^-1 second. you cannot build the same argument on that.

Let's measure length and let's measure time and ohhh wow, this turns out to be nearly the same, didn't expect this, there must be a deeper reason for that...

I admit this is a bit intuitive and I have no ambitions to clarify this idea any further. Maybe I'm even wrong. Maybe I'm not even wrong

shades of Woit.

I was assuming SR as a known fact, so we won't have to debate about c in SR any longer.

well, a consequence of SR is that c cannot be exceeded. but i thought the question was asking why looking for an explanation other than just "SR says so".

The thread starter has asked about distortions of spacetime. So I tried to say (in my short-circuit manner) that the constancy of c in curved spacetime is a consequence (similar to the above light bulb moment) of us using the same definition of inertial system in connection with the same measuring instruments and the same operational definition of measurements, again in curved spacetime. Later I complemented my imprecise (I continue to use this term) claim by referring to the fact that this is only possible since GR affects all objects in the same way.

well, just that one statement that "c cannot be exceeded because c is (or can be) defined", didn't cut it as a philosophical persuasion. that's why i piped in. we just don't see sufficiency of the argument the same.

 

[OOO]

well, a consequence of SR is that c cannot be exceeded. but i thought the question was asking why looking for an explanation other than just "SR says so".

well, just that one statement that "c cannot be exceeded because c is (or can be) defined", didn't cut it as a philosophical persuasion. that's why i piped in. we just don't see sufficiency of the argument the same.

Okay, I'll retract the statement that c is constant in GR because it can be defined, and replace it by a politically correct version:

We get c as the speed of light in every local inertial system in GR, because by definition in a local inertial system the metric is \eta=diag(1,-1,-1,-1).