Is the case for a Universal Speed Limit experimental or theoretical?

[geordief]

...Or even based on logic?

I understand that it is expected that there might be a Universal Speed Limit and that this seems with extremely high probability to coincide with the speed of em transmission in a vacuum.

This is borne out by experimentation and observation.

Are there any other approaches to reaching this conclusion?

Can it be argued that such a speed limit must exist and that the lack of such a speed limit would lead to fundamental contradictions?

Are there physical reasons why relative motion between any two bodies cannot exceed such a limit or is it simply the case that we observe this to be so and "cut our cloth" accordingly?

...and everything then falls into place.

Btw does the existence of this universal speed limit necessitate the invariance of the speed of light (and massless objects)?

 

[.Scott]

The "universal speed limit" is the speed of light - or the speed of EM propagation in a vacuum.
This is an essential part of the Special Theory of Relativity ... and it works!
https://en.wikipedia.org/wiki/Special_relativity

It has been around since 1905 and every prediction it has made has been spot on.

It was based on Einstein's insight an logic in trying to resolve measurement issues. One major issue was the result from the Michelson Morley experiments with their interferometer. Light seemed to be traveling at a set speed - but a set speed relative to what? Was it relative to the Sun? If so, we should be able to measure the difference that light travels relative to Earth as the light moves in the same direction of Earth's orbit in comparison with moving in the opposite direction. But no such difference was found. So was the Earth dragging some kind of ether that the light was moving through?
Einstein resolved the issue by coming up with a system where light would be traveling at the speed of light no matter the reference frame of the observer. Given that the speed of light is constant no matter the reference frame, you can logically deduce that that speed is a sort of "Universal Speed limit". BTW: That limit seems to be on the speed at which information can be transmitted from on location to another.

So, with regard to your question: "does the existence of this universal speed limit necessitate the invariance of the speed of light (and massless objects)?": It's the other way around. The invariance of the speed of light was the starting point. From there, it is deduced that that speed forms a limit.

 

[geordief]

True (it seems) that the invariance of the speed of light was first observed and not posited or expected.

I am trying to imagine a sort of "anti-thought" experiment whereby nobody had even thought to test the speed of light relative to different frames of reference...

Might it have been (at that innocent stage) possible to adopt as an assumption that there must be an upper speed limit and proceed from that assumption?

Is it possible to show without recourse to experimental observation (not ,of course rejecting those observations) that it would lead to contradictions if there was not an upper speed limit?

(I was previously under the impression that this would "cause all things to happen at the same time" but have been disabused of this belief.)

Are there any good reasons why there really must be an upper speed limit or is it simply the case that we have observed it to be so and that is the end of the matter?

Might it even be the case that in one of the hypothetical parallel or other universes that there might not be an upper speed limit and things would just proceed there along those lines?

 

[Nugatory]

Might it have been (at that innocent stage) possible to adopt as an assumption that there must be an upper speed limit and proceed from that assumption?

The assumption of an upper speed limit is equivalent to there being exactly one speed which will be the same for all observers; if you assume either one the other will follow. So as far as the logic is concerned, if you can proceed from one you can proceed just as well from the other. Of course in practice you'll start with assumptions that seem plausible to you, and that's what Einstein did; by 1905 nature had provided many hints that light speed would be invariant so that was the natural starting point.

The best one-word answer to the question in the title is "Both".

 

[PAllen]

See also:

https://www.physicsforums.com/insights/speed-light-frames-reference/

 

[russ_watters]

Are there any good reasons why there really must be an upper speed limit or is it simply the case that we have observed it to be so and that is the end of the matter?

I feel like this has been answered already; it's both. It is a key component of Special Relativity, and it has been confirmed experimentally.

Sorry, there are no loopholes here.

 

[geordief]

The assumption of an upper speed limit is equivalent to there being exactly one speed which will be the same for all observers; if you assume either one the other will follow.

Yes that had actually occurred to me too** ,but only as an intimation.(it felt to me as if ,as one approached the speed limit differences in measurements of relative motion to it might go to zero as a limit -but I was not confident about it)

Is there a way of showing that rigorously to be the case (on its own merits ,not because it is so and not because it is part of Relativity with all its successful predictions?

**yesterday I was laid up with a headache and had a bit of time to think on my own when it eased.

 

[PAllen]

Yes that had actually occurred to me too** ,but only as an intimation.(it felt to me as if ,as one approached the speed limit differences in measurements of relative motion to it might go to zero as a limit -but I was not confident about it)

Is there a way of showing that rigorously to be the case (on its own merits ,not because it is so and not because it is part of Relativity with all its successful predictions?

**yesterday I was laid up with a headache and had a bit of time to think on my own when it eased.

Please Check out the link I provided. It has links to papers showing from pure symmetry considerations, there are only two possibilities: an infinite invariant speed (Newtonian physics) or a finite invariant speed (SR). Experiment has shown the latter.

 

[geordief]

Please Check out the link I provided. It has links to papers showing from pure symmetry considerations, there are only two possibilities: an infinite invariant speed (Newtonian physics) or a finite invariant speed (SR). Experiment has shown the latter.

Thanks very much . I will have a look.

 

[russ_watters]

Is there a way of showing that rigorously to be the case (on its own merits ,not because it is so and not because it is part of Relativity with all its successful predictions?

That's how Relativity was derived, but every line of logic has to start with some assumptions. Nothing is ever fully from scratch.

 

[bob012345]

I feel like this has been answered already; it's both. It is a key component of Special Relativity, and it has been confirmed experimentally.

Sorry, there are no loopholes here.

As an aside, what constitutes a loophole? A material object cannot move through space faster than light but a patch of space itself can and it can in theory carry an object along (the Alcubierre 'Warp Drive' concept). Also, the 'wormhole' concept would allow an object to circumvent the universal speed limit. The universe as a whole apparently violated it during its inflationary period. Entanglement seems to violate it. Aren't these loopholes in a way?

 

[PAllen]

As an aside, what constitutes a loophole? A material object cannot move through space faster than light but a patch of space itself can and it can in theory carry an object along (the Alcubierre 'Warp Drive' concept). Also, the 'wormhole' concept would allow an object to circumvent the universal speed limit. The universe as a whole apparently violated it during its inflationary period. Entanglement seems to violate it. Aren't these loopholes in a way?

First, the topic was special relativity, not general, so that excludes all your examples except entanglement. Further, most physicists do not view entanglement as a loophole because neither mass/energy nor information travel faster than c.

As to GR, cosmological recession rates are fundamentally distinct from relative velocity. In GR, relative velocity for separated objects is ambiguous, but still less than c even during inflation.

Finally, while GR does allow alcubierre drives and wormholes, there are good reasons to believe they cannot exist in our universe (the degree of violation of energy conditions required, and that either actually existing means closed timelike curves are also possible and accessible).

 

[russ_watters]

As an aside, what constitutes a loophole? A material object cannot move through space faster than light but a patch of space itself can and it can in theory carry an object along (the Alcubierre 'Warp Drive' concept). Also, the 'wormhole' concept would allow an object to circumvent the universal speed limit. The universe as a whole apparently violated it during its inflationary period. Entanglement seems to violate it. Aren't these loopholes in a way?

I don't want to take this too far off topic, but I agree with you and might have chosen a different word if I'd thought about it more. I tend to see a "loophole" as a way around a limit without breaking a theory. The OP seems to be looking to see if the theory itself might be wrong. A missing piece in its development.

 

[bob012345]

Are there physical reasons why relative motion between any two bodies cannot exceed such a limit or is it simply the case that we observe this to be so and "cut our cloth" accordingly?

Physically, the mass of an object goes to infinity as it's speed approaches c (as calculated by an observer in the reference frame the speed is in reference to).

Interestingly, the relative motion between two bodies can exceed light speed as observed by another observer. Suppose two ships are traveling virtually at c for convenience away from Earth in opposite directions. While I can't say, and both ships can't say either moves faster than c in any frame of reference, I can say they are moving apart as I see them at a rate of almost 2c. I didn't call it speed but the distance between them is growing faster than light could cover it...according to me.

 

[Mister T]

Is it possible to show without recourse to experimental observation (not ,of course rejecting those observations) that it would lead to contradictions if there was not an upper speed limit?

I don't think so. It is only through experiment and observation that we justify Einstein's assumption that the speed of light is independent of the speed of the source. From that, as has already been pointed out in this thread, a universal speed limit follows.

 

[bob012345]

First, the topic was special relativity, not general, so that excludes all your examples except entanglement. Further, most physicists do not view entanglement as a loophole because neither mass/energy nor information travel faster than c.

As to GR, cosmological recession rates are fundamentally distinct from relative velocity. In GR, relative velocity for separated objects is ambiguous, but still less than c even during inflation.

Finally, while GR does allow alcubierre drives and wormholes, there are good reasons to believe they cannot exist in our universe (the degree of violation of energy conditions required, and that either actually existing means closed timelike curves are also possible and accessible).

Thanks, but I thought that the original question was fairly general, it didn't limit the discussion only to SR which was brought up only in the responses.

 

[Nugatory]

Physically, the mass of an object goes to infinity as it's speed approaches c.

Even after setting aside the standard objections to the notion of relativistic mass increase, we cannot suggest this as an explanation for the speed limit. The problem is that the relativistic mass increase is a mathematical consequence of the speed limit, so using it to explain the speed limit is circular logic.

Interestingly, the relative motion between two bodies can exceed light speed as observed by another observer. Suppose two ships are traveling virtually at c for convenience away from Earth in opposite directions. While I can't say, and both ships can't say either moves faster than c in any frame of reference, I can say they are moving apart as I see them at a rate of almost 2c. I didn't call it speed but the distance between them is growing faster than light could cover it...according to me.

True, but as you say that change in distance with time isn’t the speed of anything.

 

[PAllen]

I don't think so. It is only through experiment and observation that we justify Einstein's assumption that the speed of light is independent of the speed of the source. From that, as has already been pointed out in this thread, a universal speed limit follows.

As the FAQ link I provided earlier shows, there are ways that get close to what the OP wants. You can assume only isotropy, homogeneity, and that physical laws are the same in any inertial frame (without assuming anything about them, e.g. Maxwell or light), and conclude there there must be an invariant speed, with Galilean relativity resulting in the limit of infinite invariant speed. Then, indeed, experiment must choose among these two possibilities.

 

[PAllen]

Interestingly, the relative motion between two bodies can exceed light speed as observed by another observer. Suppose two ships are traveling virtually at c for convenience away from Earth in opposite directions. While I can't say, and both ships can't say either moves faster than c in any frame of reference, I can say they are moving apart as I see them at a rate of almost 2c. I didn't call it speed but the distance between them is growing faster than light could cover it...according to me.

It is important to distinguish a separation speed in some coordinates from a relative velocity. Even in SR, there is no upper bound on separation speed (e.g. if you set up cosmological type coordinates in special relativity you get a separation speed = recession rate in these coordinates that can be any multiple of c at all). The same is true of separation speeds = recession rate in GR.

Meanwhile, relative velocity is the comparison of one object speed to the the other, as if either was at rest. As I'm sure you know, this is always less than c in SR, e.g. the relative velocity corresponding to two objects moving .9c apart in some frame is about .994c. This operation is unambiguous in SR because parallel transport of vectors is path independent, so you can unambiguously bring vectors together and compare them (the vectors being 4-velocities). In GR, parallel transport of vectors is path dependent, but no matter what path you use, you still have a relative velocity of less than c - you just can't pick which one.

The more interesting notion of FTL is beating a light signal. Cosmology provides no example of a body outracing a light ray from some start event to some destination world line.

Wormoles and albubierre drive do provide and example of winning such a race by virtue of 'shortcuts' through spacetime. Even in alcubierre drive, the body inside a warp bubble is not locally outracing light, and its relative velocity to some outside observer remains less than c (essentially because every possible parallel transport path crosses the bubble), but compared to light following an a altogether different path to some common ending world line, the drive gets there first. Ultimately this is all because in GR there can be multiple lightlike geodesics from a starting event to a given world line (destination). In normal cases (e.g. gravitational lensing), this provides no apparent shortcuts, but in exotic cases, it does.

 

[bob012345]

It is important to distinguish a separation speed in some coordinates from a relative velocity. Even in SR, there is no upper bound on separation speed (e.g. if you set up cosmological type coordinates in special relativity you get a separation speed = recession rate in these coordinates that can be any multiple of c at all). The same is true of separation speeds = recession rate in GR.

Meanwhile, relative velocity is the comparison of one object speed to the the other, as if either was at rest. As I'm sure you know, this is always less than c in SR, e.g. the relative velocity corresponding to two objects moving .9c apart in some frame is about .994c. This operation is unambiguous in SR because parallel transport of vectors is path independent, so you can unambiguously bring vectors together and compare them (the vectors being 4-velocities). In GR, parallel transport of vectors is path dependent, but no matter what path you use, you still have a relative velocity of less than c - you just can't pick which one.

The more interesting notion of FTL is beating a light signal. Cosmology provides no example of a body outracing a light ray from some start event to some destination world line.

Wormoles and albubierre drive do provide and example of winning such a race by virtue of 'shortcuts' through spacetime. Even in alcubierre drive, the body inside a warp bubble is not locally outracing light, and its relative velocity to some outside observer remains less than c (essentially because every possible parallel transport path crosses the bubble), but compared to light following an a altogether different path to some common ending world line, the drive gets there first. Ultimately this is all because in GR there can be multiple lightlike geodesics from a starting event to a given world line (destination). In normal cases (e.g. gravitational lensing), this provides no apparent shortcuts, but in exotic cases, it does.

Thanks for expanding your earlier answers. I wasn't aware of the GR perspective of separation speeds. BTW, I've always wondered, if an Alcubierre warp bubble carrying a ship crosses paths with a material object, I assume it's going to be a real bad day for those inside the ship? In other words, the bubble doesn't push objects out of the way does it?

 

[PAllen]

Thanks for expanding your earlier answers. I wasn't aware of the GR perspective of separation speeds. BTW, I've always wondered, if an Alcubierre warp bubble carrying a ship crosses paths with a material object, I assume it's going to be a real bad day for those inside the ship? In other words, the bubble doesn't push objects out of the way does it?

Actually, a real bad day for both. Stopping a warp bubble near a planet would vaporize the planet.

https://arxiv.org/abs/1202.5708
From the conclusion:

"any people at the destination would be gamma ray and high energy particle blasted into oblivion"

 

[geordief]

The OP seems to be looking to see if the theory itself might be wrong. A missing piece in its development.

Didn't think I was questioning the theory (I don't have the basic mastery to do that)

Apologise if I gave that impression

 

[OCR]

Didn't think I was questioning the theory (I don't have the basic mastery to do that)

There is however, sometimes, a small distinction that needs to be made, that

involves the actual meaning of the term. . . speed of light. . One-way speed of light - Wikipedia
.

 

[PAllen]

There is, sometimes, a small distinction that needs to be made, that involves the actual

meaning of the term. . . speed of light. . One-way speed of light - Wikipedia
.

True, but there are so many reasons to expect isotropy of physical laws, it is in practice, absurd to consider anisotropy of the speed of light. Allowing it while matching all experiment is indeed possible, but almost every equation in physics then becomes more complex. In modern symmetry focused physics, isotropy is taken as an assumption. This would be questioned only if it led to complexity rather than simplification.

 

[A.T.]

...Or even based on logic?

You need some premises to derive conclusions using logic.

 

[geordief]

You need some premises to derive conclusions using logic.

Yes I appreciate your point.There is a temptation to expect logic to work,as it were in a vacuum.

It reminds me of Relativity which needs two FORs to apply **and where the origin of radiation may be inconsequential ( in measuring its speed for example).

Logical reasoning ,on the other hand is relentlessly attached to its original premise even though we have the illusion that it exists in its own right.

I am just making an analogy -not drawing any consequences.

Your point has undercut one of the bases of my question and I would need to clarify what premise I had in mind.

Interesting that Einstein claimed not to rely on the MM result (very interesting really)

** perhaps a mischarecterization but it is just an analogy.Relativity requires to know one's relationship with what is being observed,I would say.

 

[x-vision]

Is it possible to show without recourse to experimental observation (not ,of course rejecting those observations) that it would lead to contradictions if there was not an upper speed limit?

The upper speed limit follows from the Lorentz transformation. The Lorentz factor becomes an imaginary number for speeds higher than the speed of light.

 

[Nugatory]

The upper speed limit follows from the Lorentz transformation. The Lorentz factor becomes an imaginary number for speeds higher than the speed of light.

It is true that the Lorentz transformations don't make sense for $v$ greater than $c$, but that doesn't mean that the upper speed limit follows from them.

In fact, it's the other way around: the Lorentz transformations are derived from the assumption of the invariance of light speed, and this assumption is equivalent to assuming the upper speed limit. Thus, the imaginary numbers that appear in the Lorentz transformations when plug in values of $v$ greater than speed of light aren't proving anything. They're just reminding us that we started with the assumption that faster than light travel is impossible.

To derive the speed limit logically, it's most natural to follow the same path that Einstein did in 1905, starting with the assumption of lightspeed invariance.

 

[bob012345]

Actually, a real bad day for both. Stopping a warp bubble near a planet would vaporize the planet.

https://arxiv.org/abs/1202.5708
From the conclusion:

"any people at the destination would be gamma ray and high energy particle blasted into oblivion"

Well, we don't typically stand on the tracks when a train comes. I'm sure a sufficiently advanced civilization could deal with it. Thanks.

 

[bob012345]

It is true that the Lorentz transformations don't make sense for $v$ greater than $c$, but that doesn't mean that the upper speed limit follows from them.

In fact, it's the other way around: the Lorentz transformations are derived from the assumption of the invariance of light speed, and this assumption is equivalent to assuming the upper speed limit. Thus, the imaginary numbers that appear in the Lorentz transformations when plug in values of $v$ greater than speed of light aren't proving anything. They're just reminding us that we started with the assumption that faster than light travel is impossible.

To derive the speed limit logically, it's most natural to follow the same path that Einstein did in 1905, starting with the assumption of lightspeed invariance.

Did Einstein actually derive what value that the speed of light had to have independent of measured data? Didn't it come out of the Maxwell equations first as a consequence of the properties of space?

 

[Nugatory]

Did Einstein actually derive what value that the speed of light had to have independent of measured data?

No, but he did assume that whatever it was, it was invariant; and that assumption was motivated by Maxwell's equations of electricity and magnetism. At a somewhat handwavy level, we can say that two observers moving relative to one another in a vacuum shouldn't see different laws of E&M, and if they're using the same laws of E&M then the electromagnetic waves predicted by these laws should behave the same for both of them.

As an aside... it turns out (although this was not recognized until many decades later) that if there is an invariant speed it doesn't make sense to try measuring or calculating it. Instead we can take advantage of its invariance to define our units, and that's we now do. The meter is defined to be 1/299792458 of the distance that light travels in one second so $c$ necessarily is exactly 299792458 meters per second. If I tried measuring and got any other result that would just tell me that one or both of my clock and meter stick need to be recalibrated.

 

[bob012345]

No, but he did assume that whatever it was, it was invariant; and that assumption was motivated by Maxwell's equations of electricity and magnetism. At a somewhat handwavy level, we can say that two observers moving relative to one another in a vacuum shouldn't see different laws of E&M, and if they're using the same laws of E&M then the electromagnetic waves predicted by these laws should behave the same for both of them.

As an aside... it turns out (although this was not recognized until many decades later) that if there is an invariant speed it doesn't make sense to try measuring or calculating it. Instead we can take advantage of its invariance to define our units, and that's we now do. The meter is defined to be 1/299792458 of the distance that light travels in one second so $c$ necessarily is exactly 299792458 meters per second. If I tried measuring and got any other result that would just tell me that one or both of my clock and meter stick need to be recalibrated.

Thanks. Since you need both a clock and a stick to measure it, don't you need some other independent metric? Like the radius of a hydrogen atom for instance?

 

[jbriggs444]

Thanks. Since you need both a clock and a stick to measure it, don't you need some other independent metric? Like the radius of a hydrogen atom for instance?

You can define the meter using the distance between two scratches on an artifact and then measure the speed of light in meters per second.

Or you can define the meter in terms of the speed of light, measure the distance between the two scratches in light-seconds and convert to meters. The point is that the latter is our current and preferred practice.

 

[bob012345]

You can define the meter using the distance between two scratches on an artifact and then measure the speed of light in meters per second.

Or you can define the meter in terms of the speed of light, measure the distance between the two scratches in light-seconds and convert to meters. The point is that the latter is our current and preferred practice.

In either case you have one invariant quantity, a speed, so to convert it to a distance you need an independent definition for a second. You can't define both a meter and a second from c.

 

[jbriggs444]

In either case you have one invariant quantity, a speed, so to convert it to a distance you need an independent definition for a second. You can't define both a meter and a second from c.

Right. And we have an independent definition for the second.