I Why the speed of light is constant?

[PeterDonis]

Here are the results of an experiment on the issue.

This is different from what we're discussing. The Hafele-Keating experiment realized a "twin paradox" type of scenario (plus it included gravitational time dilation, which is different from time dilation due to relative motion in SR). We're not talking about that; we're talking solely about the effects of changing reference frames in SR.

 

[NickAtNight]

We can't leave you scientists alone with anything for long without you breaking it... :)

headline "CERN scientists break the speed of light."

 

[NickAtNight]

Thank you for fixing it though...

CERN confirms its mistake, neutrinos obey the speed limit of light after all

http://www.theverge.com/2012/6/8/3072393/speed-of-light-neutrino-mistake-cern

 

[tadchem]

I always connect it to the Principle of Relativity: the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.
If the laws of physics were actually to vary from one frame of reference to another, then what is physically normal in one frame of reference would become physically impossible in another.
When applied to measurement of the speed of light in a vacuum, this means that two observers moving relative to each other in inertial frames of reference and making the measurement within their own frames of reference will obtain identical results.
Each, however, will see the other's measurement as deviating from his own due to the relative movement of the observer with respect to his counterpart's frame of reference.
The mathematical resolution to this apparent conundrum is found in the Lorentz Transformations - which relate the metrics (the relationship of time and distance) between two frames of reference in relative motion with respect to each other.
The Lorentz Transformations are mathematically indistinguishable from 4-dimensional rotations (in 'Minkowski Space') which 'mix' time and the direction of motion.
To keep the 'rotation' in scale so that coordinates are not stretched or compressed requires the quantity 'i' (the square root of -1) and the velocity (ratio of time to distance) 'c'.
Similarly, gravity is mathematically described using a quantity that is indistinguishable from a scalar field in 3-dimensional space with all the properties of 'curvature'.
When you boil it all down, these things (speed, rotation, curvature, etc.) are all mathematical *models* which just happen to mimic the inferred properties of the observable universe as precisely as we can measure them.
Even in QM, when we say that a photon 'is' a wave or a particle, what we mean is that in a given situation the mathematics we have defined for describing waves or particles also mimics what we observe of the photon.
The photon is really just a photon, whatever that is, but we can observe how the photon interacts with other things and say that interaction mimics the behavior of particles or of waves.
Never confuse physical reality with conceptual models.

 

[Hornbein]

That happens anyway, since different parts of those objects are at different distances from us. A typical galaxy might be 100,000 light years across; that means there could be a difference of up to 100,000 years in the light travel time to us between the closest and furthest part of that galaxy.
By this argument, they should be blurred anyway because of the difference in light travel times from different parts, as above. So your argument can't be right.

Thanks for pointing out that the finite speed of light causes distortion of the images of large structures.

What I had in mind was rotating objects.. If the speed of light depended on the relative velocity of the source, the light from the part of the object rotating toward the viewer would arrive sooner than the portion rotating away. So distant galaxies would appear stretched out or compressed, depending on their motion. The more distant the galaxy, the greater the effect. Distant galaxies might look like smeared streaks.

 

[PeterDonis]

gravity is mathematically described using a quantity that is indistinguishable from a scalar field in 3-dimensional space with all the properties of 'curvature'.

This is not correct. Gravity is certainly not described by a scalar field. The metric is a 2nd-rank tensor; the full description of spacetime curvature (the Riemann tensor) is a fourth-rank tensor.

 

[PeterDonis]

What I had in mind was rotating objects.. If the speed of light depended on the relative velocity of the source, the light from the part of the object rotating toward the viewer would arrive sooner than the portion rotating away, given that both light rays were emitted at the same time according to the source

I added a key qualifier in the quote above (and there are more complications lurking there as well, in that "at the same time", but I don't think we need to go into those here). But the source does not emit light all in an instant and then stop. It's continually emitting light. So all that would really happen, in the hypothetical case that the speed of the source affected the speed of light, would be that the light reaching our eyes (or telescopes) at a given instant would include light emitted at different times by different parts of the object--the same as for the distance effect I talked about before.

 

[Sturk200]

I have been looking up historical (pre-1905) alternative theories (I think that is permitted on PF?) and came across an idea due to Lorentz (and perhaps others) that wikipedia calls the "intermolecular theory." The idea, if I understand it properly, is that the intermolecular forces in matter are electromagnetic in nature, so that length contraction is a result of the relative motion between the molecules and the "lines of electric force" responsible for keeping them in a rigid structure -- this length contraction is in turn responsible for the apparent constancy of c (the theory, I think, was used primarily to explain the null result of the Michelson-Morley experiment). Here is the wiki: https://en.wikipedia.org/wiki/Lorentz_ether_theory#Length_contraction and
https://en.wikipedia.org/wiki/History_of_special_relativity#Search_for_the_aether (final paragraph of the section titled "Search for the Aether").
Here is what wiki says about why the theory was rejected:

"Although the possible connection between electrostatic and intermolecular forces was used by Lorentz as a plausibility argument, the contraction hypothesis was soon considered as purely ad hoc."
"For plausibility reasons, Lorentz referred to the analogy of the contraction of electrostatic fields. However, even Lorentz admitted that that was not a necessary reason and length-contraction consequently remained an ad hoc hypothesis."

What I am reading from these very brief excerpts is that the theory was considered ad hoc because it assumed that intermolecular forces were of electrostatic origin, a hypothesis for which there was no positive evidence at the time. First of all, am I getting that right? Is that the reason the theory was dismissed as ad hoc? And second, if I am getting that right, now that we know intermolecular forces are electrostatic in nature, why do we still reject the "intermolecular theory"?

Never confuse physical reality with conceptual models.

But isn't the ultimate aim to have the two coincide?

 

[PeterDonis]

Is that the reason the theory was dismissed as ad hoc?

At the time, I think it was, yes. But this was before Einstein's 1905 papers, which put all of this in a different perspective.

now that we know intermolecular forces are electrostatic in nature, why do we still reject the "intermolecular theory"?

We don't. We now would say that Lorentz's description, where "length contraction" is due to the way EM forces behave in objects in motion, and Einstein's description, where "length contraction" is due to the structure of spacetime (to put it simply), are not two alternative theories of what length contraction is; they are just two different ways of describing the same thing.

Also, it's important to draw a distinction between two different meanings that the term "length contraction" could have. One is: suppose we have an observer looking at an object that is moving relative to him. He measures the object to be length contracted. The other is: suppose we have an object at rest, and we put it in motion. Once it is in motion, the object will be length contracted. These two meanings of "length contraction" are related, but not quite the same; the first is more suggestive of Einstein's type of explanation (the structure of spacetime means the observer's perspective on the moving object is different than it would be if the object were at rest relative to him), while the second is more suggestive of Lorentz's type of explanation (when we put an object in motion, something has to happen to it to change its length, and that something should involve the forces between its parts that determine its shape and size). What links the two meanings is the realization that, once the object is established in its new state of motion, it should have the same internal forces between its parts, viewed in its own rest frame, as it did before.

 

[Sturk200]

We don't. We now would say that Lorentz's description, where "length contraction" is due to the way EM forces behave in objects in motion, and Einstein's description, where "length contraction" is due to the structure of spacetime (to put it simply), are not two alternative theories of what length contraction is; they are just two different ways of describing the same thing.

Lorentz's description seems to be something like the kind of "mechanistic" explanation I was looking for. Is it possible to explain time dilation from the point of view of the intermolecular theory?

 

[PeterDonis]

Is it possible to explain time dilation from the point of view of the intermolecular theory?

AFAIK, this can only be done indirectly, by noting that intermolecular theory predicts that the speed of light is the same in all reference frames (because EM forces are governed by Maxwell's Equations, and that's what Maxwell's Equations predict), and then deducing the necessity of time dilation from that plus length contraction.

 

[Dale]

@Sturk200 I still wonder why you don't think that Newtonian physics should be required to provide a mechanism for Euclidean geometry.

 

[Sturk200]

@Sturk200 I still wonder why you don't think that Newtonian physics should be required to provide a mechanism for Euclidean geometry.

It may be that at bottom the only thing supporting me here is a prejudice built on physical intuition, but let me try to give a non-prejudiced answer.

When we rotate an extended object in 3-space, the property that is preserved and that justifies us in saying that the object itself remains unchanged, is its length. You do not need to work any harder to convince me that the object remains unchanged, because I already believe (here is my intuition) that length is the property which constitutes this object.

If, on the other hand, we consider a rotation in space-time, you would have me believe that the property that is preserved and that justifies us in saying that the object (event) itself remains unchanged, is its space-time interval. The theory tells me that length and duration are altered, but the object itself is untouched, because, according to the theory, what truly constitutes an object is nothing other than its space-time interval. (If you say that the object does change insofar as its length and duration changes, while the space-time interval remains invariant, I will ask you to provide the force responsible for the change in the object -- there are no forces, therefore, if I understand you correctly, the object does not change). Now in order for me to accept this story, I have to believe that length and duration are not real properties of objects, but are rather, perhaps, illusory byproducts of the human being's insufficient sensory apparatus, which apparatus by an unlucky stroke was not endowed with the ability to perceive the underlying truth of space-time intervals. (Note the contrast with Euclidean geometry -- I never believed ordinate and abscissa to be essential properties of objects, and therefore the claim that the same object can be described by different coordinates strikes me as trivial, which, I think you would agree, it is.)

There is nothing in principle to stop the claim about length and duration from being true, but this suggestion that these two properties, which I have until now taken to be quite real, are in fact illusions, is not something to be met without some skepticism. This skepticism is further compounded by the fact that the theory is incapable of explaining on physical grounds why the speed of light is measured to be constant in all inertial frames, but rather would have me swallow the constancy of c axiomatically and undiluted. Empirical measurements are indeed adequate to convince me of the veracity of the axiom, but I cannot be induced to jump from here to the claim that length and duration are illusory without first understanding more of why the axiom is correct. Moreover, I can't see why anyone should be led to doubt the "realness" of length and duration -- i.e. to resort to this extreme interpretation that the coordinate lengths of space-time themselves are altered by relative motion -- when there is this other, in my opinion more physically intuitive, intermolecular explanation available.

That said, I am perfectly comfortable with accepting the rotation in Minkowski space as an accurate mathematical description of the phenomenon, but, at present at least, am a bit skeptical as to whether it doesn't leave out some physical substance, namely of how length and duration are altered. In other words, I don't yet accept that my senses deceive me. Out of curiosity, what percentage of physicists do you think interpret special relativity as a mathematically useful model, as compared to those who interpret it as a physical truth?

By the way, does anyone have any references to modern sources that treat of this intermolecular theory of length contraction? All I've been able to dig up so far are Lorentz's papers, which are unfortunately riddled with the assumption that all motion must be considered relative to the luminiferous aether.

 

[PeterDonis]

in order for me to accept this story, I have to believe that length and duration are not real properties of objects

Yep. That's the price you pay for using a correct theory; you have to throw away some of your intuitions. Welcome to modern physics.

This skepticism is further compounded by the fact that the theory is incapable of explaining on physical grounds why the speed of light is measured to be constant in all inertial frames

By "physical grounds" here you actually mean "grounds that my intuition will accept". In other words, you are assuming that any "explanation" must be in accord with your intuitions. You're not alone; everybody starts out thinking that way. Modern physics, as Feynman once said (he was talking about QM, but it applies just as well to relativity), "was not wished upon us by theorists". We don't use relativity and QM because some intellectual just happened to have a neat idea. We use them because the intuitively more plausible theories they replaced have been falsified by experiment. It took time and effort for this changeover to happen; many physicists had to be dragged kicking and screaming out of Newtonian physics and into relativity (and QM). So your skepticism is not at all unusual. But you should be aware that that does not make your skepticism justified.

I am perfectly comfortable with accepting the rotation in Minkowski space as an accurate mathematical description of the phenomenon, but, at present at least, am a bit skeptical as to whether it doesn't leave out some physical substance, namely of how length and duration are altered

As above, your skepticism is perfectly understandable and not at all unusual. But, again, that does not make it justified. There is no "physical substance" in the place you are looking for it. "Length" and "duration" are simply not "real properties" of objects in the sense you are using that term. That's what our experimentally verified modern theories tell us.

does anyone have any references to modern sources that treat of this intermolecular theory of length contraction?

I don't know of any, and I wouldn't expect to, because the modern understanding is as I've already described it: this "intermolecular theory of length contraction" is just another way of describing what happens when you change reference frames in relativity; it's not a separate, alternative "theory" of what's going on.

 

[Sturk200]

By "physical grounds" here you actually mean "grounds that my intuition will accept"

Not so! I mean any grounds at all apart from direct axiomatization. And the grounds can't be based in the theory itself, since that's circular.

 

[Sturk200]

I just pulled these from another post on PF and thought it might be good to put them under this discussion too. They are modern discussions of the comparative virtues of what have here been called the intermolecular ("constructive") and geometrical (deductive or "principle") theories.

http://www.euregiogymnasium.ch/alumni/images/pdf/aeneas_wiener-lorentz_contraction.pdf
http://www.lophisc.org/wp-content/uploads/Frisch.pdf

https://www.physicsforums.com/threads/the-mechanism-of-length-contraction.749883/

 

[PeterDonis]

I mean any grounds at all apart from direct axiomatization.

How about the fact that Maxwell's Equations predict that the speed of light is the same for all observers? Does that count as separate grounds? If not, why not?

Or what if we axiomatized relativity differently, so that the speed of light being the same in all inertial frames became a derived prediction from something else? For example, it has been shown that the constancy of the speed of light can be derived from the isotropy of space plus the principle of relativity. Would that count?

 

[Dale]

If you say that the object does change insofar as its length and duration changes, while the space-time interval remains invariant, I will ask you to provide the force responsible for the change in the object

This is the part that is illogical. Regardless of your belief of the claim you clearly recognize that the nature of the claim is geometric. You also clearly recognize that there is no force required to explain geometry. So it is inconsistent to ask for a force for the claim.

That said, I have already pointed out the mechanism is provided by GR in the form of the Einstein field equations.

 

[Sturk200]

How about the fact that Maxwell's Equations predict that the speed of light is the same for all observers? Does that count as separate grounds? If not, why not?

Or what if we axiomatized relativity differently, so that the speed of light being the same in all inertial frames became a derived prediction from something else? For example, it has been shown that the constancy of the speed of light can be derived from the isotropy of space plus the principle of relativity. Would that count?

I'm not sure I know enough about your second suggestion to respond adequately. Could you explain the argument in a bit more detail or point me towards a source? As for the first suggestion, I'll give it a try, noting that I'm sort of making it up as I go along.

I think you mean the application of the relativity principle to Maxwell's derivation of c. Strictly speaking, Maxwell's equations predict that the speed of propagation of an electromagnetic wave in free space is dependent upon the permittivity constants. Applying the principle of relativity, we find that the speed of light must therefore be the same in all inertial reference frames. There is, however, an ambiguity. Does the principle of relativity require that the speed of light be measured to be the same for all inertial observers, or does it require that the speed actually be the same in all inertial frames. I would think the latter, since the underlying idea is that the permittivity constants of free space must be the same for all inertial frames, and clearly no moving frame will carry free space along with it. Now note that a frame traveling in the same direction in which light is propagated will augment the necessary distance traveled by the light beam between coordinates of that frame, as compared to a frame traveling in a direction opposite to the propagation (i.e. into the beam). Now if the actual speed must be the same, then the measured speeds are different. Therefore the principle of relativity as I have here understood it (concerning actual rather than measured quantities) does not, when taken with Maxwell's equations, give rise to the principle of the constancy of c. Maybe this is why Einstein considered it necessary to base his theory on two postulates, rather than one.

This is the part that is illogical. Regardless of your belief of the claim you clearly recognize that the nature of the claim is geometric. You also clearly recognize that there is no force required to explain geometry. So it is inconsistent to ask for a force for the claim.

Ok, let me rephrase. The point here is precisely what you are saying, that the nature of the claim is geometric. What I say is this: If you do not give me a force, then you are not allowed to tell me that the object has changed. Instead, you must accept that the coordinates have been transformed while the object itself is preserved. But in relativity the transformation of coordinates means the transformation of the length and duration of an event. Now since the nature of the claim is geometric, and since the theory does not involve a force, you must say that the length and duration of the event has changed, while the event has not changed (the space-time interval has not changed). This implies that length and duration are not real properties of objects, but are merely illusory. The point I have made is that this implication is a lot to swallow when it is founded on an axiom (the constancy of c) that the theory does not bother to justify on any more primary grounds.

That said, I have already pointed out the mechanism is provided by GR in the form of the Einstein field equations.

This is confusing to me. If the nature of the claim is geometric, then there should be no need for a mechanism (understood to mean some play of forces responsible for the transformation). It's also confusing because others have said -- I think -- that the Lorentz transformation is not a consequence of the warping of space-time seen in general relativity. But you are saying that it is?

 

[Dale]

@Sturk200 Sorry, I was not very pleased with my previous post and tried to delete it to make my objection to your reasoning clear, but you were too fast and had already responded I do apologize for a sub-standard response on my part.

This is confusing to me. If the nature of the claim is geometric, then there should be no need for a mechanism (understood to mean some play of forces responsible for the transformation).

Let me be clear about my objection to your reasoning. I believe that there is a mechanism (per your definition) which explains the geometry of spacetime in relativity. That is the EFE. So the problem with your reasoning is not that you are asking a question for which there is no answer or a question which is unfair to ask.

The objection is that you are applying a double-standard by NOT asking for the mechanism behind Euclidean geometry. Do you not see the clear inconsistency in your position? In your own words you accept Euclidean geometry with no mechanistic explanation simply "because I already believe", but you require such an explanation of Lorentzian geometry. Once you apply the same standard to both geometries you see that there is simply no logical basis for holding to Euclidean geometry. It enjoys no logical privilege, only your intuitive prejudice.

Suppose that I were to ask you the same question that you are asking us: What is the force that causes Euclidean geometry, or the mechanism behind it? Applying your own standard, your own preferred geometry completely fails. There is to my knowledge no mechanistic explanation in Newtonian physics for the Euclidean geometry of space. It is taken as a given.

It's also confusing because others have said -- I think -- that the Lorentz transformation is not a consequence of the warping of space-time seen in general relativity. But you are saying that it is?

Flat spacetime is the solution of the EFE in the special case where there is no significant mass present. Others merely said that relative speed does not warp spacetime, if it is flat then it remains flat.

 

[Sturk200]

Sorry, I was not very pleased with my previous post and tried to delete it to make my objection to your reasoning clear, but you were too fast and had already responded

The pratfalls of instantaneous communication!

The objection is that you are applying a double-standard by NOT asking for the mechanism behind Euclidean geometry. Do you not see the clear inconsistency in your position? In your own words you accept Euclidean geometry with no mechanistic explanation simply "because I already believe", but you require such an explanation of Lorentzian geometry.

Let me see if I can try to clear this up. I do not ask for a mechanism for any geometrical procedure -- geometry is geometry and does not require forces. What I "already believe" is not that Euclidean geometry requires no mechanism, but rather that objects in the real world are constituted by their lengths and durations, both of which features happen to be preserved by a Euclidean rotation, neither of which are preserved by a Minkowski rotation.

My gripe, then, is not mathematical or geometrical. Rather, it is ontological. The battle between Euclid and Minkowski is really over the question of what constitutes an object -- is it length and duration or is it the space-time interval? By explaining, for instance, length contraction using a Minkowski rotation, and insisting that this geometrical explanation is the full physical explanation, we are awarding ontological priority to the space-time interval. This, again, is because the rotation does not invoke a mechanism (therefore does not change the underlying object), and yet alters the length and duration of an event.

What grounds have we for awarding ontological priority to the space-time interval? Simply that the speed of light is constant (on which the entire theory is based). Might we find a non-geometrical explanation of length contraction by further inquiring as to why the speed of light is constant? My contention, considering how little was known about the composition of matter in Einstein's day as compared with our own, is that we might. And apparently I am not alone in this hope (http://www.euregiogymnasium.ch/alumni/images/pdf/aeneas_wiener-lorentz_contraction.pdf). The idea is that the physical reason for the constancy of the speed of light may also explain length contraction without invoking space-time geometry.

I believe that there is a mechanism (per your definition) which explains the geometry of spacetime in relativity.

Is this not going to get you in trouble when I ask you, in the interest of consistency, to provide a mechanism for Euclidean geometry?

Flat spacetime is the solution of the EFE in the special case where there is no significant mass present.

My understanding is that special relativity was "written in" to the EFE, but I probably don't know enough about GR yet to hold my own.

 

[Dale]

My gripe, then, is not mathematical or geometrical. Rather, it is ontological.

Then there is nothing to discuss here. This forum is for science, not philosophy. You are welcome to any ontology that you like, provided that it is consistent with experiment.

Thread closed.

 

[PeterDonis]

Does the principle of relativity require that the speed of light be measured to be the same for all inertial observers, or does it require that the speed actually be the same in all inertial frames.

The principle of relativity does not draw the implicit distinction you are making. The measured speed is the "actual" speed.

My understanding is that special relativity was "written in" to the EFE

I don't understand what you mean by this. The statement that flat Minkowski spacetime is a solution of the Einstein Field Equation for a zero stress-energy tensor is easily proved; textbooks on GR often assign this as a homework problem. There's nothing "written in"; it's a simple consequence of the equation.

clearly no moving frame will carry free space along with it.

This amounts to assuming what you are trying to prove, that Maxwell's Equations don't require $c$ to be the same in all inertial frames. You can't just help yourself to this assumption; you have to justify it. Can you? To me it's obviously false, since "free space" does not have a state of motion at all, so it doesn't have to be "carried along".

Now note that a frame traveling in the same direction in which light is propagated will augment the necessary distance traveled by the light beam between coordinates of that frame, as compared to a frame traveling in a direction opposite to the propagation (i.e. into the beam). Now if the actual speed must be the same, then the measured speeds are different.

I don't understand this reasoning. How are you defining the "actual" speed?

Also, are you taking into account length contraction? Remember that the Michelson-Morley experiment was done in the 1880's, well before Einstein published his SR papers, and Einstein was not the first one to propose length contraction as an explanation of that result; Lorentz and Fitzgerald both did so in, IIRC, the early 1890's. Also, Mach made a similar claim to the one I made above: that there is no such thing as the "actual length" of an object apart from its measured length.