Speed of Light is a Property of Massless Particles or Space?

[Islam Hassan]

The speed of light is a parameter that attaches itself to what exactly, an inertial frame of reference or a massless particle moving therein?IH

 

[wabbit]

Interesting question. I would say to both. We cannot speak of speed without a reference - at the very least something to which that speed is relative. And of course we can only speak of the speed of something

And the invariance of the speed of light requires of course at least two frames and a particle, since it is the property that any two observers will measure the same speed relative to them for a massless particle.

But this doesn't even really need space, which can be thought as an abstraction of such measurements.

 

[PeterDonis]

The speed of light is a parameter that attaches itself to what exactly

It doesn't "attach itself" to anything, except spacetime itself; it's a fundamental property of spacetime.

 

[m4r35n357]

The speed of light is a parameter that attaches itself to what exactly, an inertial frame of reference or a massless particle moving therein?
IH

Very interesting question, I'd like to have a go at answering this. Space-time itself specifies a top speed (possibly infinite), whereas Maxwell's equations tell us what the speed of EM waves is (so this determines the speed of light, c).
It just so happens that experimentally the top speed is the same as the value of c.

 

[wabbit]

Hmm is that right ? If the photon had mass wouldn't this modify Maxwell's equations ? And if it is massless it must travel at the invariant speed. I may be wrong here but I think Maxwell's equations as such are only compatible with the speed of light being both finite and equal to the invariant speed, no ?

Trying to recall SR derivation here, I think it goes Maxwell -> invariant speed of light -> SR with top speed =speed of light.

 

[bcrowell]

The question is much too vague to say anything about.

 

[m4r35n357]

Hmm is that right ? If the photon had mass wouldn't this modify Maxwell's equations ? And if it is massless it must travel at the invariant speed. I may be wrong here but I think Maxwell's equations as such are only compatible with the speed of light being both finite and equal to the invariant speed, no ?

Trying to recall SR derivation here, I think it goes Maxwell -> invariant speed of light -> SR with top speed =speed of light.

I'm not sure how to answer a question like "If the photon had mass . . .".
I'm just saying that as I understand things spacetime itself cannot define either the top speed or the value of the speed of light. Whether those two speeds can be identified is subject to experimental observation. Maxwell's equations on the other hand actually define the (invariant) speed of light but say nothing about whether it is the top speed.

 

[wabbit]

What I am saying is that there can be only one invariant speed and this is equal to the "top speed" since this top speed is invariant - once light speed is known to be invariant (which must be true if Maxwell equations hold), then it is also the top speed.

Now I agree this may be an overstatement: if we found experimentally two invariant speeds, then there would be the need for another non-SR theory of spacetime. I don't know if there are such theories where Maxwell's equations still hold, perhaps it is the case - that experiment would kill SR, but maybe not Maxwell, I don't know.

 

[m4r35n357]

I don't think we are disagreeing here. The light postulate says (I think) that the top speed = the invariant speed = the value of the speed of light. Finding two invariant speeds would mean that one of them isn't the top speed, and in any case Minkowski space only caters for one invariant speed, so I agree that would spell trouble for SR! BTW I think I've reached the limits of my understanding in this area, so I'll wait to find out if I've misunderstood something fundamental . . .

 

[Dale]

I think that we need some clarification from the OP before we can continue. @Islam Hassan if you could reach out to me by PM and clarify what you mean by the speed of light "attaching" itself to things, then I can reopen the thread.

 

[Islam Hassan]

Perhaps a clearer formulation of my question is as follows: is the speed of light a constant ascribed to the i) the movement of a particle proper due to inherent characteristics of this particle or some property of spacetime that puts a limit on the speed of this movement? Is it theoretically possible to have a different "species" of spacetime (alternative universes and the like...) where c has a different value? To my mind, if the answer is yes, then c is dependent on spacetime and is a property of spacetime and not the particle itself.

Did I make myself any clearer?

 

[Dale]

Is it theoretically possible to have a different "species" of spacetime (alternative universes and the like...) where c has a different value?

The value of c is entirely determined by your system of units. What matters is whether or not the invariant speed (aka c) is finite. If it is infinite then you get Galilean relativity, and if it is finite then you get Einstein's relativity.

 

[PeterDonis]

is the speed of light a constant ascribed to the i) the movement of a particle proper due to inherent characteristics of this particle or some property of spacetime that puts a limit on the speed of this movement?

As I said in post #3, it's a property of spacetime.

 

[nitsuj]

As I said in post #3, it's a property of spacetime.

Playing devil's advocate, we don't measure spacetime. How is it certain it's a property of spacetime itself.

Also for the OP's question...I'm seeing this as merely two interpretations, and not being of physical significance.

 

[PeterDonis]

we don't measure spacetime.

We measure the motion of freely falling objects, which marks out the geodesics of spacetime and tells us its geometry. That amounts to measuring spacetime, at least in the required sense for this discussion.

How is it certain it's a property of spacetime itself.

Because all massless particles travel at the same speed. If it were a property of particles, we would expect to see different values of $c$ for different particles and different interactions. But we don't.

 

[nitsuj]

We measure the motion of freely falling objects, which marks out the geodesics of spacetime and tells us its geometry. That amounts to measuring spacetime, at least in the required sense for this discussion.

The choice to use the phenomenon of a geodesic as describing the geometry of spacetime is just that...a choice. It is also that gravity is a field, and fair enough to infer that any changes in measure are due to a "field interaction" of sorts.

Of course I am splitting hairs, but yes my point is that it's (as the OP proposed) a matter of interpretation, and that's it. I think what you described is a field interaction, and yes a "gravity" unique one. (gravitons)

Because all massless particles travel at the same speed. If it were a property of particles, we would expect to see different values of $c$ for different particles and different interactions.

Why is that necessary? To be clear the difference here is "Spacetime limits propagation of fundamental forces." vs "Fundamental forces have a property; propagating at an invariant speed." Why would you not consider the "property" of the "particle" is traveling at an invariant speed? They've tried to directly measure spacetime (in this context), but failed.

This is good fun, I never thought of a speed as being a fundamental property of something but in the case of an invariant speed it is. Also enjoying thinking in the context of causation that Fundamental forces are the only "things" (force carriers) that can travel at an invariant speed. So across distances in spacetime causation isn't merely cause/effect, it's cause - force carrier at invariant speed - effect. Due to property of spacetime or implicit / fundamental property of physics in a continuum?

 

[PeterDonis]

The choice to use the phenomenon of a geodesic as describing the geometry of spacetime is just that...a choice.

Yes, but the field option doesn't really amount to an alternative as far as the topic of discussion here is concerned. See below.

It is also that gravity is a field

A field on what? On flat spacetime. So you still have spacetime structure underneath, and that spacetime structure still has a single invariant speed built into it.

(Also, even on the "gravity is a field" interpretation, the background flat spacetime on which the field is defined is not observable; only the curved spacetime produced by the field is. So even on the field interpretation, there's no way to separate out "measurements of the field" from "measurements of spacetime, separate from the field".)

To be clear the difference here is "Spacetime limits propagation of fundamental forces." vs "Fundamental forces have a property; propagating at an invariant speed."

But on the second interpretation, there is no reason to expect all fundamental interactions to propagate at the same invariant speed. There could be more than one. Only if the invariant speed is a property of spacetime, not the forces, would you expect it to be the same for all interactions.

(Of course, trying to model different invariant speeds for different interactions would require a very different model from the ones we're used to. But so what? Such a model is still logically possible.)

They've tried to directly measure spacetime (in this context), but failed.

Can you give a reference? I don't understand what you're referring to here.

 

[nitsuj]

But on the second interpretation, there is no reason to expect all fundamental interactions to propagate at the same invariant speed. There could be more than one. Only if the invariant speed is a property of spacetime, not the forces, would you expect it to be the same for all interactions.

(Of course, trying to model different invariant speeds for different interactions would require a very different model from the ones we're used to. But so what? Such a model is still logically possible.)

Fundamental interactions are the "in between" of the changes we are performing physics* on. Force carriers move at an invariant speed, and unless I can formulate a well rounded argument for an invariant speed due to causation it'll have to be postulated that c is invariant...as it is now. c isn't the important part, the invariance is.

For my "daily experience" why would I see a difference if the fundamental forces had different speeds? so long as they were invariant. That said my gut feel is causation falls apart if we could measure different invariant values of things that in effect are the passage of happenings that are being measured and in turn comparing those measurements...according to what coordinates?? Suppose coordinates wouldn't have any comparative significance if motion was involved.

Can you give a reference? I don't understand what you're referring to here.

Was referring to theories & experiments regarding the invariance of light, looking for properties specific to spacetime, like aether.*measurements / observations

 

[PeterDonis]

For my "daily experience" why would I see a difference if the fundamental forces had different speeds?

You probably wouldn't in your daily experience, but it would be straightforward (though possibly technically quite challenging) to do experiments to show the different speeds if they existed.

Was referring to theories & experiments regarding the invariance of light, looking for properties specific to spacetime, like aether.

These experiments were looking for a preferred frame, which could be interpreted as a "property of spacetime", but is certainly not the only possible one.

 

[nitsuj]

You probably wouldn't in your daily experience, but it would be straightforward (though possibly technically quite challenging) to do experiments to show the different speeds if they existed.

I'm not saying we couldn't measure different values of whatever invariant speed, fundamental interactions cannot happen more slowly then matter, most matter we perform physics on is held together by these fundamental interactions, what of a "force carrier" that can go faster then another type of "force carrier" in order to accelerate a bit of matter faster than the interaction that caused that effect of more velocity? The four forces must have all the same invariant speed, as we can accelerate matter with the strong force too, I'm thinking this is all a matter of interaction :p

These experiments were looking for a preferred frame, which could be interpreted as a "property of spacetime", but is certainly not the only possible one.

Thought preferred frames where a some while after Maxwell. To get a fine tip on my point.. theories/experiments looking for something between "here and there" interacting with the light traveling from here to there causing the invariance of light.

 

[PeterDonis]

what of a "force carrier" that can go faster then another type of "force carrier" in order to accelerate a bit of matter faster than the interaction that caused that effect of more velocity?

Obviously interactions, and the matter that is interacting, would behave differently in a universe which had different speeds for different interactions. My point is not that we have any evidence for such a thing; of course we don't. The interactions in our actual universe all have the same invariant speed, and behave accordingly, as does the matter that is interacting. I'm only pointing out that different behaviors are logically possible. But we are getting pretty far off topic at this point.

 

[nitsuj]

we are getting pretty far off topic at this point.

We did, I enjoyed it. Fun musing, though I'm going to have a hard time saying "it's the geometry of spacetime". Maybe I'll trade that in for "it's the geometry of "xyz" field interactions. meh, tomayto-tomahto**edited ...potato-potato didn't read as well

 

[strangerep]

Trying to recall SR derivation here, I think it goes Maxwell -> invariant speed of light -> SR with top speed =speed of light.

I think you might like the (less well-known) derivations of SR that don't assume the light principle, (which I'm guessing you're not already familiar with?). Cf. Rindler's SR textbook (and various others -- I could dig out more specific references if needed).

It turns out that if we ask for the most general group of transformations compatible with the relativity principle (i.e., that all inertial observers perceive the same laws of physics), then a universal constant with dimensions of speed emerges as one possibility (among very few).

The properties of unitary irreducible representations (field representations) of the group then enables an identification between massless spin-1 reps and light. That enables the value of "c" to be identified with light speed empirically.

A more general analysis yields fractional linear transformations instead of the usual linear Lorentz transformations, and a universal length constant suspiciously connected to the cosmological constant also emerges.

So I'd answer the OP's question this way: the principle that all inertial observers perceive the same laws of physics (the relativity principle, "RP") admits a universal speed constant. The homogeneous space for the resulting group (Poincare group) is what we call Minkowski spacetime. IOW, Minkowski spacetime is just a convenient (but artificial) stage for representing the (1-particle) action of the Poincare group. Unitary irreducible representations of the Poincare group include the massless spin-1 case, which is seen to correspond to light when the details are analyzed, thus determing the value of "c" empirically.

I.e., RP -> group of transformations with a "c" constant -> Minkowski space as homogeneous space of the group
-> massive and massless field representations ("elementary particles").

In this sense, the "geometry of spacetime" is subordinate to the RP.

(I've skipped over some details, of course, but could add them if needed.)

 

[wabbit]

A more general analysis yields fractional linear transformations instead of the usual linear Lorentz transformations, and a universal length constant

would you have a reference/link ? I have a vague recollection of seeing that but can't remember where, nor the details.

 

[nitsuj]

It turns out that if we ask for the most general group of transformations compatible with the relativity principle (i.e., that all inertial observers perceive the same laws of physics), then a universal constant with dimensions of speed emerges as one possibility (among very few).

The properties of unitary irreducible representations (field representations) of the group then enables an identification between massless spin-1 reps and light. That enables the value of "c" to be identified with light speed empirically.

So what makes it "turn out" that given one SR postulate we can deduce a "universal constant with dimensions of speed" and is that the same as saying an invariant speed? It doesn't seem like it, just seems to say there would be a max speed and that's it. My musing of it lead me to think it's implicit, that "force carriers" would move fastest and be an invariant speed, in turn coordinate transforms can be done and observation is continuity in causation.

 

[Ibix]

So what makes it "turn out" that given one SR postulate we can deduce a "universal constant with dimensions of speed" and is that the same as saying an invariant speed?

Pal's paper Nothing but relativity derives a general transform from the principle of relativity. The transform contains an unknown constant, K. There are only two "types" of value for K - zero and positive. The former gives you Newton; the latter gives you Einstein with K=1/c^2.

The paper uses nothing more complex than matrix multiplication.

 

[nitsuj]

Pal's paper Nothing but relativity derives a general transform from the principle of relativity. The transform contains an unknown constant, K. There are only two "types" of value for K - zero and positive. The former gives you Newton; the latter gives you Einstein with K=1/c^2.

The paper uses nothing more complex than matrix multiplication.

Cool I'm going to check it out! Hope I can understand it lolGave it a reading, in that paper he mentions "Isotropy" & "homogeneity" of spacetime as being "given". Is that from the principal of relativity postulate? Either I'm not sure that spacetime really needed to be addressed, just the general postulate that speaks to performing physics.

 

[strangerep]

would you have a reference/link ? I have a vague recollection of seeing that but can't remember where, nor the details.

I discussed it in more detail in various posts in this thread:
https://www.physicsforums.com/threads/could-sr-not-be-built-from-only-one-postulate.754310/
which also contains some references.

Unfortunately, I don't know a good, comprehensive reference. I'm trying to write a comprehensive paper about it, but it's already 100+ pages, so of course no one wants to proof-read it...

 

[strangerep]

So what makes it "turn out" that given one SR postulate we can deduce a "universal constant with dimensions of speed" and is that the same as saying an invariant speed?

It drops out of an analysis which asks for the maximal group of transformations which map inertial motion into inertial motion. Basically, it's from the assumption that velocity boosts in a fixed direction form a 1-parameter Lie group.

It doesn't seem like it, just seems to say there would be a max speed and that's it.

I'm not sure what you're disagreeing with here. The universal constant happens to be an upper limit on relative speed. It is found simply by looking for fixed points in the velocity boost composition formula that drops out of the analysis.

My musing of it lead me to think it's implicit, that "force carriers" would move fastest and be an invariant speed, in turn coordinate transforms can be done and observation is continuity in causation.

"Force carriers" implies an interacting theory, but what I described is applicable to the simpler free case, i.e., transformations between inertial (unaccelerated) frames.

 

[strangerep]

[Pal's] paper uses nothing more complex than matrix multiplication.

IIRC, Pal uses some sleight of hand to dismiss the K<0 case. Actually, most treatments are a bit weak on that point.

 

[strangerep]

Gave [Pal's paper] a reading, in that paper he mentions "Isotropy" & "homogeneity" of spacetime as being "given". Is that from the principal of relativity postulate?

No. Spatial isotropy is an extra assumption. Spacetime homogeneity is also an addition assumption to reduce the fractional linear equations to linear equations. But in fact, that common form of the spacetime homogeneity postulate is unnecessary: the more general fractional linear case (not treated by Pal) yields a de Sitter space which has constant curvature. This is a more general version of the idea that space "looks the same" everywhere. I.e., spatial homogeneity (in the sense of constant curvature) need not be assumed.

 

[nitsuj]

No. Spatial isotropy is an extra assumption. Spacetime homogeneity is also an addition assumption to reduce the fractional linear equations to linear equations. But in fact, that common form of the spacetime homogeneity postulate is unnecessary: the more general fractional linear case (not treated by Pal) yields a de Sitter space which has constant curvature. This is a more general version of the idea that space "looks the same" everywhere. I.e., spatial homogeneity (in the sense of constant curvature) need not be assumed.

So there is more than just one postulate in his paper in order to reach the conclusions he did. I'd be able to assume if all physics is the same (inertial) that would imply isotropy and homogeneity of where / when the "physics" plays out. That said I understood it as the invariance of c speaks to isotropy and homogeneity of space.

If as you say isotropy and homogeneity are not from SR relativity principal, did he not include significant assumptions of the invariance of c postulate?

 

[nitsuj]

"Force carriers" implies an interacting theory, but what I described is applicable to the simpler free case, i.e., transformations between inertial (unaccelerated) frames.

Well what do you suppose is traveling between the inertial observers that leads to observing "something happening"? In the simple free case I'd think the observer is relying on Force Carriers (photons) to shed some light (ahaha funny pun).

I'm not sure what you're disagreeing with here. The universal constant happens to be an upper limit on relative speed. It is found simply by looking for fixed points in the velocity boost composition formula that drops out of the analysis.

Whether max speed & it's invariance were determined separately. or is one assumed because of the other?

"The universal constant happens to be an upper limit on relative speed." seems to brush over the difference between invariance and maximum. For me, the "universal constant" is really universal constancy in the order of "co-located" events, or said differently the isotropy / homogeneity of spacetime.

Is his paper not circumnavigating the out right stipulation of the invariance of c postulate, while relying on its key features?

 

[Ibix]

IIRC, Pal uses some sleight of hand to dismiss the K<0 case. Actually, most treatments are a bit weak on that point.

It didn't seem tricksy to me (maybe I've fallen for it). He seems to be saying that if K<0 then it is possible to find frames where the transform does not reduce to the identity operation in the case of zero velocity. He notes that there are similar problems in the Einsteinian K>0 case for velocities greater than c, but observes that those frames are rendered inaccessible by the relativistic velocity addition law. In contrast, the velocity addition law for K<0 doesn't protect you from having to consider the problematic frames.

 

[wabbit]

The case K<0 is weird, you get supraluminal velocities by adding three subluminal velocities, or even infinite ones, e.g. $3×(c/\sqrt{3})=\infty$ and the invariant speed is imaginary. Not very appealing but perhaps it has in interpretation.

 

[strangerep]

So there is more than just one postulate in his paper in order to reach the conclusions he did.

Yes. Apart from the RP, spatial isotropy (and then spatiotemporal homogeneity) there are also assumptions about continuity, including the assumption that the transformations form a Lie group.

I'd be able to assume if all physics is the same (inertial) that would imply isotropy and homogeneity of where / when the "physics" plays out.

Sorry -- I don't know what you mean. The RP does not imply isotropy or homogeneity by itself.

That said I understood it as the invariance of c speaks to isotropy and homogeneity of space.

One requires only the RP, spatial isotropy, and the mathematical features above involving continuity, to deduce the invariant constant c.

 

[strangerep]

Whether max speed & it's invariance were determined separately. or is one assumed because of the other?

The assumed Lie group property of the velocity transformations gives rise to an invariant speed c. Imposition of the group multiplication property gives rise to a velocity addition formula, from which the role of c as a limiting relative speed becomes obvious.

"The universal constant happens to be an upper limit on relative speed." seems to brush over the difference between invariance and maximum. For me, the "universal constant" is really universal constancy in the order of "co-located" events, or said differently the isotropy / homogeneity of spacetime.

The velocity transformation formulas are derived between observers for which the origins of their frames of reference are collocated (and suitably rotated so that the spatial axis direction coincide).

Is his paper not circumnavigating the out right stipulation of the invariance of c postulate, while relying on its key features?

No.

Perhaps you should try another treatment, such as that in Rindler's textbook on special relativity. I get the feeling you have not yet worked through the math, pen-in-hand? There's not much more I can say until you at least attempt this.

 

[strangerep]

It didn't seem tricksy to me (maybe I've fallen for it). [Pal] seems to be saying that if K<0 then it is possible to find frames where the transform does not reduce to the identity operation in the case of zero velocity. He notes that there are similar problems in the Einsteinian K>0 case for velocities greater than c, but observes that those frames are rendered inaccessible by the relativistic velocity addition law. In contrast, the velocity addition law for K<0 doesn't protect you from having to consider the problematic frames.

OK, yes, that's the basic idea. I just felt the way he expressed the argument could be strengthened.

 

[strangerep]

The case K<0 is weird, you get supraluminal velocities by adding three subluminal velocities, or even infinite ones, e.g. $3x(c/\sqrt{3})=\infty$ and the invariant speed is imaginary. Not very appealing but perhaps it has in interpretation.

I think it has no good interpretation, but rather hints at a guiding principle. I'm not sure if it already has a name, but I call it the "Principle of Physical Regularity". The idea is as follows: the relative parameters that we think of a kinematical (or dynamical) variables, such as velocity, spatial orientation, spatial displacement, temporal delay, etc, characterize how one inertial observer differs from another, and hence the particular transformation which must be performed to convert one observer into the other. If (say) observer B has (finite) relative velocity $v_{AB}$ relative to A, and observer C has (finite) relative velocity $v_{BC}$ relative to B, it must be the case that $v_{AC}$ is finite also, else we do not have a good physical theory. Moreover, this must hold for all (relative) velocities in a nontrivial open neighbourhood of $v=0$.

Appealing to this principle is essentially equivalent to what you described: for K<0 it is possible to choose velocities whose composition yields $\infty$. Such embarrassment is only avoided if we restrict the allowed relative velocities to $v=0$, which makes the "theory" trivial.

 

[nitsuj]

I get the feeling you have not yet worked through the math, pen-in-hand? There's not much more I can say until you at least attempt this.

You're absolutely right I have not worked through the math. I can't read math, so is why I was asking about the relations, assumptions ect most of which is likely explicitly shown (or easily deduced from) in the math.

Thanks for explaining it to me, but yea I really should put effort into the math. Concepts & their relations just get to a point where...it's "more than words" are capable of communicating a clear 'n concise way. lol