The WHY of speed of light vs. the FACT thereof

[JoeShiner]

I have puzzled over a couple of things relating to the speed of light as a constant to all observers. I fully recognize that it has been demonstrated to be so, and that those demonstrations have been confirmed by facts such as the existence and workability of GPS; however, these go much more to the FACT THAT the speed of light is a constant. I also recognize that, mathematically speaking (and I'm no math whiz), it MUST be a constant, since "somethin's got to give"; however, these do not satisfy my need to understand WHY the speed of light is a constant; or, put another way, HOW CAN IT BE that the speed is constant? I mean, everything else "gives" - the cars on the highway going toward one another or passing one another... and the trains, the planes, etc., but not light. HOW is it happening? Is light scrunching up or stretching out somehow as it needs to (but not as to speed [?!]), to the various and relevant observers?

As an aside - With reference to various experiments that have been conducted involving gravitational effects on time using atomic clocks aboard airplanes, if a quantum entanglement experiment was conducted involving photons that are "on" two different airplanes at two different gravitational states (and tied to atomic clocks, of course), what would be the result?

BTW, I am not a physicist and perhaps have no business at all sticking my nose in, but if some of you more well versed in these matters than I might take pity on me (and provide a bit of forgiveness of my ignorance, and benefit of the doubt, I'd be most appreciative). Thank you!

 

[martix]

It's not unlike asking why 2 parallel lines never intersect.

The best explanation I can come up with is that it's just part of our physical reality, like e, pi, h, G, the elementary charge, masses of elementary particles and a number of other constants that serve as parameters for the universe you and I reside in.

 

[Dale]

Hi JoeShiner, welcome to PF!

Are you asking why there is an invariant speed or are you asking why light travels at the invariant speed?

 

[Pengwuino]

You might like this



At some point, "Why?" has no answer. The speed of light is constant and it is what it is because that's just how it is. There is no deeper reason.

 

[Danger]

As the flippered one said, and has been expressed dozens of times over the past several years, science does not ask "why?", only "how?". "Why?" implies a purpose, and the universe has no such thing.

 

[bcrowell]

The speed of light is constant and it is what it is because that's just how it is. There is no deeper reason.

I disagree. Unfortunately there is a tendency for people to stay locked into the picture of physics that was available to Einstein in 1905. From the modern point of view constancy of c doesn't have to be a purely empirical fact -- see below.

As the flippered one said, and has been expressed dozens of times over the past several years, science does not ask "why?", only "how?". "Why?" implies a purpose, and the universe has no such thing.

I'm sure you don't mean that science *never* answers a "why" question? That would be an extreme point of view that I suspect very few physicists would subscribe to. For example, I assume you don't think there's no answer to the question of why an object moving with an acceleration of 1 m/s2, starting from rest, covers 0.5 m in 1 s.

FAQ: Why is the speed of light the same in all frames of reference?
The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you have to define what you think would be satisfying. If you ask Euclid why the Pythagorean theorem is true, he'll show you a proof based on his five postulates. But it's also possible to form a logically equivalent system by replacing his parallel postulate with one that asserts the Pythagorean theorem to be true; in this case, we would say that the reason the "parallel theorem" is true is that we can prove it based on the "Pythagorean postulate."
Einstein's original 1905 postulates for special relativity went like this:
P1 - "The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion."
P2 - "Any ray of light moves in the 'stationary' system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body."
From the modern point of view, it was a mistake for Einstein to single out light for special treatment, and we imagine that the mistake was made because in 1905 the electromagnetic field was the only known fundamental field. Really, relativity is about space and time, not light. We could therefore replace P2 with:
P2* - "There exists a velocity c such that when something has that velocity, all observers agree on it."
And finally, there are completely different systems of axioms that are logically equivalent to Einstein's, and that do not take the frame-independence of c as a postulate (Ignatowsky 1911, Rindler 1979, Pal 2003). These systems take the symmetry properties of spacetime as their basic assumptions.
For someone who likes axioms P1+P2, the frame-independence of the speed of light is a postulate, so it can't be proved. The reason we pick it as a postulate is that it appears to be true based on observations such as the Michelson-Morley experiment.
If we prefer P1+P2* instead, then we actually don't know whether the speed of light is frame-independent. What we do know is that the empirical upper bound on the mass of the photon is extremely small (Lakes 1998), and we can prove that massless particles must move at the universal velocity c.
In the symmetry-based systems, the existence of a universal velocity c is proved rather than assumed, and the behavior of photons is related empirically to c in the same way as for P1+P2*. We then have a satisfying answer to the "why" question, which is that existence of a universal speed c is a property of spacetime that must exist because spacetime has certain other properties.
W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972
Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51
Palash B. Pal, "Nothing but Relativity," http://arxiv.org/abs/physics/0302045v1
R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

 

[Phrak]

I couldn't agree with you more, bcrowell; science , or at least physics, is all about asking why--then answering how.

I remain skeptical that there is a known rational that the proportionality constant between space and time is what it is, rather than something else.

Could you, if you have found it in the articles you mention, summarize why c is what it is? But, of course, the question was about the speed of light, rather than the constant, c.

 

[Pengwuino]

Could you, if you have found it in the articles you mention, summarize why c is what it is? But, of course, the question was about the speed of light, rather than the constant, c.

Do you mean why c has the value that is has?

 

[Dale]

Could you, if you have found it in the articles you mention, summarize why c is what it is? But, of course, the question was about the speed of light, rather than the constant, c.

As you mention, that is not what the OP is asking, but the answer is simple: c has the value it does because of the units chosen.

 

[ConradDJ]

In the symmetry-based systems, the existence of a universal velocity c is proved rather than assumed, and the behavior of photons is related empirically to c in the same way as for P1+P2*. We then have a satisfying answer to the "why" question, which is that existence of a universal speed c is a property of spacetime that must exist because spacetime has certain other properties.

I also think bcrowell is right on. But whichever way we want to think about this situation, there remains a question "why" -- why does spacetime have these symmetry properties? The fact that we don't have a good answer doesn't necessarily make it a bad question.

We usually think about space and time in terms of distances and time-intervals. Relativity seems to be telling us that this is a secondary, relative aspect of what space and time are about. In other words, what defines the spacetime structure of the universe is not distance and duration but something about velocity -- since there is an absolute constant c -- and accelerations, which are not relative (at least not the way space- and time-intervals are). Or maybe, something about the specific kinds of symmetry it has. So there may well be a better way of thinking about spacetime, that we might reach by taking such "why" questions seriously.

Of course there may be "why" questions that just have no answer... but when we say "Science doesn't tell us why," that usually just means we're satisfied with the way we imagine the world and don't feel the need to go further.

 

[grav-universe]

I remain skeptical that there is a known rational that the proportionality constant between space and time is what it is, rather than something else.

Could you, if you have found it in the articles you mention, summarize why c is what it is?

It really doesn't matter what the measured value for c is, as long as it is constant for all inertial frames and finite. For instance, we can synchronize all inertial frames to originally measure the constant c, then cut the tick rates of all clocks in the universe in half. In that case, all relative speeds will now be measured as twice as great and the constant c will double. Likewise, we can expand the standard length of a meter to triple the current length and all relative speeds will be cut to one-third along with the constant c. But none of this matters on a fundamental level, as it is all pure convention, depending only upon our standards for rulers and clocks and the parameters of the universe. As far as the parameters go, the universe must have some parameters in order to exist, but they could potentially be completely arbitrary so giving an arbitrary value for the constant c as well. So the only real question that remains is why the constant c is finite rather than infinite.

[ETA - Upon reading you statement again, it appears you may be asking for somewhat of a more technical view about how we measure the constant c given our current standards of measurement. If that is the case, then of course it would be answered differently than I have stated, by taking the parameters of the universe into account as they are measured through experiment.]

 

[Fredrik]

Q: Why is the invariant speed 299792458 m/s?

A: Because a meter is defined as the distance light travels in a vacuum in 1/299792458 seconds.



Q: Why is there an invariant speed?

A: There are only two kinds of answers to questions about reality: theories and garbage. Garbage isn't very interesting, so let's look at what the relevant theories say.

The oldest and simplest theory in which the invariant speed appears is special relativity (1905). The invariant speed is a part of the definition of that theory, so SR can't answer the question. The invariant speed is also a part of the definition of general relativity (1915), so GR can't answer it either. The quantum field theory called "the standard model" (the currently best theory of elementary particles) can't answer it either, because the spacetime of special relativity is a part of its definition. So to really answer the question, we would need something new, a new theory that makes better predictions about results of experiments than general relativity and the standard model. Such a theory might be able to tell us why the predictions of special relativity are so accurate, but you could of course ask why the assumptions that define this new theory are true, and the only thing that can answer that, is another theory. Science is a lot like that annoying woman on Lost*: "Every question I answer will simply lead to another question".



Q: Why does light travel at the invariant speed?

A: Terms like "light" are defined by theories. So this is actually a different question in each theory.

Classical theories of particles in Minkowski spacetime (the spacetime of SR) are so bad at predicting the results of experiments involving light that we might as well ignore what they're saying, but I'm still going to mention that they simply define massless particles as particles moving at the invariant speed, and that we would have to take "light consists of massless particles" as an axiom motivated by results of experiments.

There is however a classical field theory that's quite good at predicting the results of many experiments involving light. This theory is called classical electrodynamics. It defines the electromagnetic field, and states as an axiom that this field satisfies Maxwell's equations. We can then prove as a theorem that the only solutions that describe waves have the waves moving at speed c in all inertial frames. This might seem like an answer, but it really isn't. The electromagnetic field is defined as a linear-operator-valued (or equivalently, matrix-valued) function on Minkowski spacetime, a mathematical object that's defined to describe space and time in a universe where there is an invariant speed. This property of the wave solutions is just a reflection of a property of the underlying spacetime, which was chosen to include an invariant speed.

The best theory of light that we have is called quantum electrodynamics. Unfortunately I don't have the relevant parts of the theory fresh in my memory, so I can't tell you exactly what it says about the speed of light, but I'm sure it says something similar to what I just said about solutions of Maxwell's equations, that ensures that given this theory's definition of "light", the speed of light must be c. But QED is just a quantum theory of fields on Minkowski spacetime, so this answer is just as circular as the corresponding answer in classical electrodynamics.



*) It's been more than 6 months, but I'm still pissed off about that stupid show.

 

[Darryl]

I would say the speed of light if fixed because it is a factor in the amount of energy that is required to make mass.

So if you can measure the amount of energy you create when you turn mass into energy you can use E=MC2 to derive the speed of light.

Or the maximum speed you could (not) accellerate mass too if you had almost infinate energy..
IANAP

What I would like to know is why it is the speed it is ?

Would it have to do with the total mass/energy in the universe?

When the universe was small and dense (first milliseconds) you would expect its gravity to be very high, therefore its own space/time would be slower ?

So would something that appears from the outside to be happening very quickly actually be occurring very slowly at its location.

Like a pulsar, do they really rotal at 600 revs per second or minute, and be that massive, or is space time at the pulsar much slower, but it appears to us, in our space time to be very fast ?

 

[JoeShiner]

I appreciate the responses, although some are beyond my ken - IANAP. However, their net net still seems to be (1) it is because it is, and (2) that's the way the math requires it. For some reason, I don't have the same problem with time being flexible (two seemingly incongruent sides of the same coin?). It's all amusing as heck.

 

[JoeShiner]

Oh, any thoughts on the quantum entanglement question? Or should I post that as a separate inquiry?

 

[Fredrik]

Oh, any thoughts on the quantum entanglement question? Or should I post that as a separate inquiry?

You asked what the result would be without really saying what experiment you had in mind.

 

[Phrak]

As you mention, that is not what the OP is asking, but the answer is simple: c has the value it does because of the units chosen.

I don't believe that's a definitive answer. A global rescaling would leave the results of experiment unchanged, but not local rescaling.

 

[Simplyh]

FAQ: Why is the speed of light the same in all frames of reference? ...other properties.

I think that we can put this in the following terms: in the process of thought we often use concepts that help us understand reality but which represent no reality at all. All mathematical concepts are of this kind. So there is no point on proving number 7 or discuss its properties as there is no sense on discussing the pythagorean postulates or their properties. Because, in both cases, it's assumed that these concepts can not influence reality.

Something different is to discuss Einstein's postulates because they are assumed to have certain physical properties and, through them, influence reality: in general terms, the constancy of light speed determines the distortion of space-time and, through it, influences the behaviour of reality.
It's exactly the same if we change your P2 by P2*: you postulate that space-time is a function of c which is very acceptable without any proof in the mathematical context where it starts. But then you say that space-time has some physical properties which have the power to change reality: that must be proved! The same can be said relatively to all other physical theories.

It's not because we use a lot of maths that we can just postulate. In maths, we just need to prove that, from our axioms to our theorems and formulas, everything works all right in our brains: but by using maths we can only describe reality, not understand it; in physics, we need to prove that the whys and hows (the understanding) of our theory matches the real thing outside our brains.

 

[Dale]

A global rescaling would leave the results of experiment unchanged, but not local rescaling.

I believe that a local rescaling of c would also leave the results of experiments unchanged provided the dimensionless constants were unchanged, but I have to admit that I have not worked the math on that. Have you done so?

 

[GregAshmore]

FAQ: Why is the speed of light the same in all frames of reference? ...other properties.

I think that we can put this in the following terms: in the process of thought we often use concepts that help us understand reality but which represent no reality at all. All mathematical concepts are of this kind. So there is no point on proving number 7 or discuss its properties as there is no sense on discussing the pythagorean postulates or their properties. Because, in both cases, it's assumed that these concepts can not influence reality.

Something different is to discuss Einstein's postulates because they are assumed to have certain physical properties and, through them, influence reality: in general terms, the constancy of light speed determines the distortion of space-time and, through it, influences the behaviour of reality.
It's exactly the same if we change your P2 by P2*: you postulate that space-time is a function of c which is very acceptable without any proof in the mathematical context where it starts. But then you say that space-time has some physical properties which have the power to change reality: that must be proved! The same can be said relatively to all other physical theories.

It's not because we use a lot of maths that we can just postulate.In maths, we just need to prove that, from our axioms to our theorems and formulas, everything works all right in our brains: but by using maths we can only describe reality, not understand it; in physics, we need to prove that the whys and hows (the understanding) of our theory matches the real thing outside our brains.

To put your final point in my own words, we must always be aware of the distinction between the theories by which we represent reality and reality itself. Ultimately, this is a recognition that our knowledge of the universe is incomplete.

Failure to maintain that distinction leads to assertions about reality which cannot be demonstrated by measurement.

It seems to me that an example of such as assertion is, "Nothing moves faster than light."

Exercise 3-15 of Taylor-Wheeler's "Spacetime Physics" begins this way:

We look westward across the United States and see the rocket [which is emitting a flash of light at some given frequency] approaching us at four times the speed of light.

Question [from student]: How can this be, since nothing moves faster than light?

Answer: We did not say that the rocket moves faster than light; we said only that we see it moving faster than light.

Here is what happens...

In the discussion which follows, the position of the rocket at the time of each flash is plotted. Then, the time at which each flash reaches the observer's eye is calculated, based on SR. The conclusion is that the apparent speed of the rocket is not its real speed.

But can it be demonstrated by direct measurement (that is, measurements made without recourse to SR in the set up of the instruments or the interpretation of their readings) that the measured speed of the rocket is not its real speed?

Perhaps another way to ask the same question is, Why should one set of measurements (those upon which SR is based) take precedence over another set of measurements (those in this exercise) when determining what is real?

 

[ghwellsjr]

Can you post the entire Exercise and explanation please.

Thank you.

 

[bcrowell]

I believe that a local rescaling of c would also leave the results of experiments unchanged provided the dimensionless constants were unchanged, but I have to admit that I have not worked the math on that.

We had a thread on claims that dimensionless constants do change: https://www.physicsforums.com/showthread.php?t=425163 (The thread eventually got locked because it drifted into discussions of research that hadn't been published.) That thread prompted me to write the FAQ entry below. I think the Duff paper constitutes the math that is required in order to back up the conjecture that you stated. I think Duff is clearly right, but others are apparently not convinced; he wrote the paper in response to published claims that changes c *could* be distinguished from changes in the other ingredients in the fine structure constant.

FAQ: Has the fine structure constant changed over cosmological timescales?
It has been claimed based on astronomical observations that the unitless fine-structure constant alpha=e^2/hbar*c actually varies over time, rather than being fixed.[Webb 2001] This claim is probably wrong, since later attempts to reproduce the observations failed.[Chand 2004] Webb et al. responded with even more extraordinary claims that the fine structure constant varied over the celestial sphere.[Webb 2010] Extraordinary claims require extraordinary proof, and Webb et al. have not supplied that; their results are at the margins of statistical significance compared to their random and systematic errors.

Even if this claim it is correct, it is not evidence that c is changing, as is sometimes stated in the popular press. If an experiment is to test whether a fundamental constant is really constant, the constant must be unitless.[Duff 2002] If the fine-structure constant does vary, there is no empirical way to assign blame to c as opposed to hbar or e.

J.K. Webb et al., arxiv.org/abs/astro-ph/0012539v3

J.K. Webb et al., http://arxiv.org/abs/1008.3907

H. Chand et al., Astron. Astrophys. 417: 853

Duff, http://arxiv.org/abs/hep-th/0208093

 

[bcrowell]

But whichever way we want to think about this situation, there remains a question "why" -- why does spacetime have these symmetry properties? The fact that we don't have a good answer doesn't necessarily make it a bad question.

Right, I agree. We do not have a more fundamental answer to the question of why spacetime has these symmetry properties. For instance, if loop quantum gravity becomes a complete and workable theory, and is somehow verified by experiments, then we might be able to answer this why question by showing that a spacetime with this symmetry naturally emerges as a generic solution to the equations of LQG. Until something like that happens, we can only take it as an observed fact.

On the other hand, I think there are clear reasons to prefer the modern, symmetry-based axiomatizations over Einstein's 1905 axiomatization. In 1905, light was the only known fundamental field, so it made sense to give it special logical status. Nowadays we know that it's only one of many fundamental fields, so it doesn't make sense to single it out for special treatment. Also, the modern point of view about metrics and light cones is that they're fundamentally a description of possible causal relationships, so, e.g., c should be thought of as the maximum speed of propagation of cause and effect, not as the speed of light.

 

[GregAshmore]

Right, I agree. We do not have a more fundamental answer to the question of why spacetime has these symmetry properties. For instance, if loop quantum gravity becomes a complete and workable theory, and is somehow verified by experiments, then we might be able to answer this why question by showing that a spacetime with this symmetry naturally emerges as a generic solution to the equations of LQG. Until something like that happens, we can only take it as an observed fact.

On the other hand, I think there are clear reasons to prefer the modern, symmetry-based axiomatizations over Einstein's 1905 axiomatization. In 1905, light was the only known fundamental field, so it made sense to give it special logical status. Nowadays we know that it's only one of many fundamental fields, so it doesn't make sense to single it out for special treatment. Also, the modern point of view about metrics and light cones is that they're fundamentally a description of possible causal relationships, so, e.g., c should be thought of as the maximum speed of propagation of cause and effect, not as the speed of light.

It seems to me that here, too, we run up against the distinction between reality and our measurement of reality. We postulate that c is the maximum speed of propagation of cause and effect. When we evaluate quantum events on that basis (as in Bell's theory), we conclude that such events can have no cause. That conclusion is logically correct given the assumption. However, the acceptance of that conclusion comes at a heavy price, as it forces us to abandon the postulate that events have causes.

To turn this around, if one begins with the postulate that every event is the observed effect of some cause, then our observations of quantum events become evidence that the postulate "c is the maximum speed of propagation of cause and effect" is invalid.

By this logic, it is not true that no experiment has ever been done which is at odds with the predictions of relativity. For relativity predicts that no cause can propagate at a speed faster than c, yet we observe an effect which is evidently propagated from the site of its cause at a speed faster than c.

What experimental means is there of determining which postulate is true to reality?

What I find surprising in this discussion is that no mention is made (in the context of this discussion, in the books which I have read) that GR allows for speeds of real objects which are faster than c. It seems to me that this feature of GR is suggestive of a reality in which the effect of a cause can propagate at a speed faster than c, yet we are unable to directly measure the velocity of propagation due to the limits of the equipment currently available to us.

To put my argument in even simpler terms, consider the instantaneous collapse of the photon wavefront upon striking a suitable receptor of its energy. If one views the strike of a suitable receptor as a cause, and the collapse of the wave as an effect, then the cause is propagated to the full extent of the photon wavefront at a speed that is faster than c.

[edit]
Perhaps, then, this is a better summary of our current knowledge:

Metrics and light cones are fundamentally a mathematical description of the current limit of our ability to measure the propagation of cause and effect.

 

[bcrowell]

We postulate that c is the maximum speed of propagation of cause and effect.

In the symmetry-based axiomatizations, this is not a postulate but a theorem.

The bulk of your #24 seems to be based on a misunderstanding of quantum-mechanical entanglement. Entanglement does not propagate signals at >c.

What I find surprising in this discussion is that no mention is made (in the context of this discussion, in the books which I have read) that GR allows for speeds of real objects which are faster than c.

We've been discussing SR. GR is locally equivalent to SR. GR does not allow for objects to have speeds greater than c on a local basis, i.e., relative to other nearby objects. When you get to the case of distant objects, GR does not even provide an unambiguous definition of the notion of relative velocity. E.g., you can say that distant galaxies are receding from us at >c, but someone who picks a different coordinate system can get a different answer.

 

[GregAshmore]

In the symmetry-based axiomatizations, this is not a postulate but a theorem.

The bulk of your #24 seems to be based on a misunderstanding of quantum-mechanical entanglement. Entanglement does not propagate signals at >c.

My understanding is that Bell's theorem, which is considered to eliminate all deterministic causes for quantum events, assumes that no signal can travel faster than c. I further understand that at least one theory has been proposed which explains quantum events as effects caused by signals which propagate faster than c. I can look up the references upon which this understanding is based, if you feel that I have misunderstood what I have read.

My point is that if one starts with the notion that an event is the effect of a cause, then our observations of quantum events can be taken as evidence that the effect of at least one cause can propagate faster than c.

On the other hand, if one starts with the notion that no effect can propagate faster than c, then other observations can be taken as evidence that at least some events have no cause.

Is there any definitive empirical evidence which eliminates one of these alternatives?

We've been discussing SR. GR is locally equivalent to SR. GR does not allow for objects to have speeds greater than c on a local basis, i.e., relative to other nearby objects. When you get to the case of distant objects, GR does not even provide an unambiguous definition of the notion of relative velocity. E.g., you can say that distant galaxies are receding from us at >c, but someone who picks a different coordinate system can get a different answer.

Wald, in his discussion of the Hubble constant, notes that the relative velocity of two galaxies can exceed c if the distance between them is large enough. "This does not contradict the fundamental tenet of SR and GR that "nothing can travel faster than the speed of light", since this tenet refers to the locally measured relative velocity of two objects at the same spacetime event, not a globally defined velocity between distant objects." Wald is not suggesting that quantum events can be explained by a signal which travels faster than the speed of light. But he is saying that on the global scale--invisible to our measurements--objects can indeed have a relative velocity greater than c. I am suggesting that if there are global conditions which we cannot measure, there may also be local conditions which we cannot measure--effects which propagate faster than c.

In short, GR allows for a reality which we cannot measure. That being the case, we ought not to be dogmatic about the existence (or non-existence) of causes for quantum events--knowing as we do that we are unable to measure these events dynamically. (That is, no one has measured the actual collapse of a photon, for example.)

 

[Dale]

I think the Duff paper constitutes the math that is required in order to back up the conjecture that you stated.

Thanks, I'll check it out.

 

[Dale]

It seems to me that here, too, we run up against the distinction between reality and our measurement of reality.

Have you a good definition of "reality" yet? If not, then this statement is literally nonsense.

What I find surprising in this discussion is that no mention is made (in the context of this discussion, in the books which I have read) that GR allows for speeds of real objects which are faster than c.

Not in a coordinate-independent sense. You can certainly make coordinate systems, even in SR, where the coordinate speed of some object is greater than c. But a timelike worldline will be timelike in all coordinate systems and therefore will always be slower than c in a coordinate-independent sense.

 

[yuiop]

My understanding is that Bell's theorem, which is considered to eliminate all deterministic causes for quantum events, assumes that no signal can travel faster than c. I further understand that at least one theory has been proposed which explains quantum events as effects caused by signals which propagate faster than c. I can look up the references upon which this understanding is based, if you feel that I have misunderstood what I have read.

Yes, one explanation for the observed violation of Bell's inequalities is that entangled photons can communicate with each other at FTL speeds, the so called "non local" condition. There are other competing theories such as the Many Worlds Interpretation which does not require non local FTL communication. What is certain is that if Bob and Alice have a source of entangled photons between them, then however they manipulate their detectors, they are not able to transmit information to each other at superluminal velocities. With this in mind it might be better to restate "c is the maximum speed of propagation of cause and effect" as "c is the maximum speed that matter or information can be transmitted between inertial observers". So while it does seem, in one interpretation of quantum entanglement experiments, that quantum particles can communicate/interact with each other at superluminal velocities, this does not translate into superluminal communications between macroscopic sentient observers. There are many other scenarios where there are apparent superluminal relations (e.g. a wave hitting a shore obliquely or sweeping a laser pointer across a distant surface) but none of these can be used to transmit information or matter at superluminal speeds.

 

[bcrowell]

My understanding is that Bell's theorem, which is considered to eliminate all deterministic causes for quantum events, assumes that no signal can travel faster than c.

As in #24, I think you're confusing an assumption of a theorem with the result of a theorem. This may also be relevant: http://en.wikipedia.org/wiki/No-communication_theorem

I further understand that at least one theory has been proposed which explains quantum events as effects caused by signals which propagate faster than c.

This would seem to violate the no-communication theorem.

I can look up the references upon which this understanding is based, if you feel that I have misunderstood what I have read.

Sure, please do.

My point is that if one starts with the notion that an event is the effect of a cause, then our observations of quantum events can be taken as evidence that the effect of at least one cause can propagate faster than c.

No, this is incorrect.

On the other hand, if one starts with the notion that no effect can propagate faster than c, then other observations can be taken as evidence that at least some events have no cause.

The notion of causality that we're discussing here really doesn't require any notion that A causes B. The laws of physics, e.g., Newton's laws or the Einstein field equations, are just differential equations. Differential equations don't make statements like "A causes B." The notion of causality that is relevant here only really requires that if A comes earlier in time than B according to one observer, then this is also true for all other observers.

Is there any definitive empirical evidence which eliminates one of these alternatives?

There is a sticky at the top of this forum, titled "FAQ: Experimental Basis of Special Relativity." Every experiment in that sticky constitutes empirical evidence that causality is satisfied, as predicted by SR.

Wald, in his discussion of the Hubble constant, notes that the relative velocity of two galaxies can exceed c if the distance between them is large enough. "This does not contradict the fundamental tenet of SR and GR that "nothing can travel faster than the speed of light", since this tenet refers to the locally measured relative velocity of two objects at the same spacetime event, not a globally defined velocity between distant objects." Wald is not suggesting that quantum events can be explained by a signal which travels faster than the speed of light.

Wald is not discussing quantum mechanics at all.

But he is saying that on the global scale--invisible to our measurements--objects can indeed have a relative velocity greater than c.

Your interpretation of Wald assumes that such a relative velocity is uniquely defined, which it isn't.

I am suggesting that if there are global conditions which we cannot measure, there may also be local conditions which we cannot measure--effects which propagate faster than c.

But there is no logical connection between the given information you start with and the conclusion you claim, and there is a century's worth of experimental evidence against your conclusion.

In short, GR allows for a reality which we cannot measure.

As DaleSpam has pointed out, you haven't provided a definition of "reality."

 

[Phrak]

I believe that a local rescaling of c would also leave the results of experiments unchanged provided the dimensionless constants were unchanged, but I have to admit that I have not worked the math on that. Have you done so?

I'm not sure about any of this anymore. You might also like to look at reference [2] of the Duff paper.

 

[elect59]

Is it possible that the invariant speed of light could be a result of the limit at which a spatial expansion can occur? In other words, could it be possible that as an object moves through space it creates a wave front due to the displacement and expansion of space created by the object? So could it be that if the fastest space can expand (or be displaced by mass) as an object moves through it is C then the limit at which the object can move through it would also be C? Am I making any sense here?

 

[bcrowell]

Is it possible that the invariant speed of light could be a result of the limit at which a spatial expansion can occur?

No, because the invariant speed of light occurs in SR, where there is no such thing as spatial expansion.

 

[GregAshmore]

As in #24, I think you're confusing an assumption of a theorem with the result of a theorem. This may also be relevant: http://en.wikipedia.org/wiki/No-communication_theorem

I read the linked article and several other related articles.

The notion of causality that we're discussing here really doesn't require any notion that A causes B. The laws of physics, e.g., Newton's laws or the Einstein field equations, are just differential equations. Differential equations don't make statements like "A causes B." The notion of causality that is relevant here only really requires that if A comes earlier in time than B according to one observer, then this is also true for all other observers.

The causality I have in mind is the notion that the act of measuring one particle determines the state of that particle and the state of a distant particle. The measurement is thus the cause; the effect is the combination of states [spin up and spin down, e.g.] taken on by the two particles.

There is a sticky at the top of this forum, titled "FAQ: Experimental Basis of Special Relativity." Every experiment in that sticky constitutes empirical evidence that causality is satisfied, as predicted by SR.

I read through the full page. I don't think there were any experiments in the list which dealt with entangled particles. If one accepts the premise that the measurement of a particle is a cause and the state of a distant (non-local) particle is an effect of that cause, then it seems true on the face of it that the effect of the cause has propagated at a speed faster than c.

[edit]
That said, I read this statement in an article about the De Broglie-Bohm theory:

The de Broglie–Bohm theory describes the physics in the Bell test experiments as follows: to understand the evolution of the particles, we need to set up a wave equation for both particles; the orientation of the apparatus affects the wavefunction. The particles in the experiment follow the guidance of the wavefunction. It is the wavefunction that carries the faster-than-light effect of changing the orientation of the apparatus. An analysis of exactly what kind of nonlocality is present and how it is compatible with relativity can be found in Maudlin.[18] Note that in Bell's work, and in more detail in Maudlin's work, it is shown that the nonlocality does not allow for signaling at speeds faster than light.

I don't doubt the truth of the two fragments in bold--but neither can I make sense of them with my current knowledge of quantum mechanics [which is even more limited than my knowledge of relativity--draw your own conclusions :)]

Your interpretation of Wald assumes that such a relative velocity is uniquely defined, which it isn't.

I'm not sure what you are getting at here. If you mean that I cannot identify two Lorentz inertial frames which have a relative velocity greater than c, I agree. But as I understand Wald, that failure is a consequence of the fact that GR is a manifold onto a Lorentz space. (I'm sure I'm not speaking the technical language with precise correctness, but I believe I have sufficient gist of the math for the purposes of this discussion.) That is, inertial frames are inherently local ['nearby'] in GR, while the two objects which have a relative velocity greater than c are necessarily not local ['nearby']. Born asserts that "if gravitational fields are present the velocity either of material bodies or of light can assume any numerical value". ("Einstein's Theory of Relativity", VII-11)

But there is no logical connection between the given information you start with and the conclusion you claim

I believe the logical connection is clarified in the above.

and there is a century's worth of experimental evidence against your conclusion.

As noted, the listed experiments do not deal with entangled particles.

As DaleSpam has pointed out, you haven't provided a definition of "reality."

I don't believe that a comprehensive definition of reality is a precondition for this discussion. Einstein, Born, Taylor-Wheeler, Schumm ("Deep Down Things"), Ford ("The Quantum World") all address the issue of reality as distinct from measurement; none of them presents a comprehensive definition of reality (in the books I have read).

I would argue that the assertion of fundamental probability in quantum theory is itself a statement about the nature of reality, as distinct from the measurements we make in the lab. Yet so far as I know neither the standard model nor the Copenhagen model presents a formal definition of reality.

Here's Treiman on the subject of quantum mechanics and classical reality (in "The Odd Quantum"): "Within quantum mechanics itself, there seems to be an unbridgeable divide between the future and the present instant. The future is intrinsically statistical, with probabilities governed by the equations of quantum mechanics. The trouble is that this way of looking at the situation seems something of a cop-out. In effect, it abandons the idea of explaining how facts come about, taking as the main function of science merely to correlate them. When a fact in fact happens, the quantum mechanical wave function is simply declared to have collapsed; after all, it's only a correlational tool! And that's that."

Treiman is no doubter of quantum mechanics--for that matter neither am I insofar as the measurements are concerned--yet he expresses dissatisfaction with its approach to reality. He makes these comments without attempting a formal definition of reality.

Which brings us back to the question in the original post: The WHY vs. the FACT of c.

I agree with Treiman that science is intimately concerned with the WHY, because scientists, as human beings, are motivated to understand what they observe in nature, not merely to organize the facts.

 

[Dale]

I don't believe that a comprehensive definition of reality is a precondition for this discussion.

Having a definition of a word certainly is a precondition if you want to make meaningful statements using the word. If I were to try to discuss my opinion about "the distinction between farglmoger and our measurement of farglmoger" wouldn't you consider it necessary for me to define "farglmoger"?

If you can't define "real" then stop using the word. Otherwise you are literally writing nonsense.