Why the speed of light is constant?

[NickAtNight]

Or he may wish to start with the Pauli's lecture on electrodynamics.

Quote from page 3 a the end of Pauli's introduction of the subject:

"Electrodynamics can be presented in two ways:

1: Deductive:: starting with eh Maxwell equations and developing special cases

2: Inductive: beginning with the basic laws obtained from experiment and eventually building up to the Maxwell equations. This way corresponds more closely to the historical development.

In these lectures, we will employ the second approach"​

https://www.amazon.com/dp/0486414574/?tag=pfamazon01-20
by https://www.amazon.com/dp/0486414574/?tag=pfamazon01-20 (​

 

[Dale]

I want there to be an explanation that invokes some kind of intelligible mechanism

what is a mechanism?

 

[Sturk200]

It is known that Maxwell's electrodynamics -as it is interpreted today- leads to asymmetries when applied to moving bodies that seem not to be inherent to the [observed] phenomena.

I thought the point of this first sentence, and the "asymmetries" it meant to point out, was the fact that according to Maxwell's equations when you move a magnet near a conductor, it induces a current by means of an induced electric field; whereas if you move a conductor near a magnet, a current is induced by means of the magnetic force on charge carriers in the wire. In Einstein's (1905) words, "The observable phenomenon here depends only on the relative [italics added] motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases..." Einstein thought that there should be only one explanation for this one phenomenon, and thus came up with the idea that the magnetic field itself is merely a consequence of charges in relative motion. This is different, I think, than the claim that the Galilean transformations are not a symmetry group for the Maxwell equations.

Choose your poison and go have some fun.

Thanks for the encouragement! But wouldn't it be so much more fun if it were a question that other people also found frustrating? I think so.

The Maxwell paper is available, both in book form and online pdf. Perhaps Sturk200 would care to read it?

I ordered a pretty nice print copy of Maxwell's paper from Amazon a few months ago but haven't had the time to work through it yet. The old notation really slows things down. My electromagnetism professor helped me through some of it last semester and then basically told me that we end up covering most of it in modern form in our class, so I felt less like I had to read it. But I did read some of it. As I understand it, Maxwell's argument implies that the speed at which electromagnetic radiation propagates through a vacuum is a consequence of the value of the permittivity constants, so that the speed of light is somehow embedded into space itself, or embedded into the way in which electromagnetic fields interact with space. I agree wholeheartedly that this is an astonishing result, but as Nugatory points out it still doesn't answer that ever lingering "why" or mechanism question. As far as I can tell Einstein doesn't even try to answer that question -- of course he had his work cut out for him in trying to draw all the proper consequences of his axioms.

Other than not satisfying Sturk200, is this a problem? I don't think so. We have the same issue with Newton's first law - no one has ever been able to provide a mechanism that explains why Newton's first law has to be true as opposed to being a very well-supported assumption with no plausible alternative - and we've been able to make our peace with this foundational concern.

I am glad you mention Newton's first law, because it gives me the opportunity to share this thing from Hobbes that I find fun. Here is his argument for inertia (1655):

"Whatsoever is at rest, will always be at rest, unless there be some other body besides it, which, by endeavouring to get into its place by motion, suffers it no longer to remain at rest. For suppose that some finite body exist and be at rest, and that all space besides be empty; if now this body begin to be moved, it will certainly be moved some way; seeing therefore there was nothing in that body which did not dispose it to rest, the reason why it is moved this way is in something out of it; and in like manner, if it had been moved any other way, the reason of motion that way had also been in something out of it; but seeing it was supposed that nothing is out of it, the reason of its motion one way would be the same with the reason of its motion every other way, wherefore it would be moved alike all ways at once; which is ... not intelligible."

(1) Now you know where I get my requirement of "intelligible mechanism," perhaps out of nostalgia for a time when "not intelligible" was an adequate counterargument.
(2) It is possible to provide reason for believing Newton's first law. Hobbes' reasoning seems to be contradicted by our current understanding of quantum phenomena, in which isolated particles move "all ways at once" (and are not intelligible) as a rule, but then so too might Newton's first law be contradicted by quantum phenomena.
(3) I have not seen any argument for the constancy of c that is similar in intent to this one -- i.e. trying to render the claim intelligible by explaining why it must be so. In my opinion we have a choice: we can either say that these kinds of explanations are obsolete and old-fashioned, that we don't need them because we have empirical evidence; or we can say that we would like to have an explanation for the constancy of c, but we just haven't gotten there yet. As you can probably tell, I am leaning towards the latter. In my opinion relying on empirical evidence alone is like sinking to the level of political science or psychology or something. But I'm still somewhat doubtful as to what a mechanistic explanation would entail.

what is a mechanism?

That's a good question. As you know, I am not an expert, but from what I have seen of physics Einstein's claim that the geometry of spacetime must transform as a consequence of relative motion is unique in that it suggests an effect without indicating a cause. More specifically, it suggests that something happens without indicating what force is responsible for that something. The force, in other physical explanations, is the reason that things change from how they are. With Einstein, I am tempted to see it as rule by fiat rather than rule by reason. So a mechanism, I guess, would be something that tells us what forces light to move at constant speed, or what forces the geometry of spacetime to change due to relative motion.

 

[PeterDonis]

Einstein's claim that the geometry of spacetime must transform as a consequence of relative motion

That wasn't Einstein's claim, and it's not what GR says. In fact, GR says exactly the opposite: the geometry of spacetime does not change as a consequence of relative motion. The geometry of spacetime is the invariant underlying structure of spacetime, that's the same for all observers, regardless of their state of motion.

it suggests that something happens without indicating what force is responsible for that something

No, it says exactly the opposite, that nothing "happens" without an actual, measurable force being involved. GR is actually more consistent on this point than Newtonian mechanics. Newtonian mechanics says that gravity is a force, but an object moving solely under the influence of gravity feels no force; it is in free fall. GR, by contrast, says that gravity is due to the geometry of spacetime, and is not a force, so it doesn't have to do any special pleading to explain why objects that have a "force of gravity" acting on them don't feel any force, as Newtonian mechanics does.

a mechanism, I guess, would be something that tells us what forces light to move at constant speed, or what forces the geometry of spacetime to change due to relative motion.

I've already disposed of the second point above. Regarding the first point, if light is moving at a constant speed, why would a force be needed to keep it doing so?

Perhaps it will help if I rephrase what GR says in a way that may make "the geometry of spacetime" seem more intuitive. When we say that a particular state of motion is due to "the geometry of spacetime", what we're really saying is that that state of motion is the "natural" one, the one that objects subject to no force will have. And physically, the way we can tell which objects are in that "natural" state of motion is by measuring the force they feel; if they feel no force, they are in the "natural" state of motion, free fall, and their motion can be explained solely by looking at the geometry of spacetime. If, on the other hand, the object feels a force, then its motion will not be due solely to the geometry of spacetime; you also have to look at the force it feels and what effect it has on the object.

Given the above, we can now rephrase my previous statements about light as follows: moving at the speed of light, and having the same state of motion regardless of the motion of its source, is the "natural" state of motion for light; it's the state of motion light has when it isn't being subjected to any force. You still need to add the fact that light has zero rest mass to this, but at least this accounts for the "geometry of spacetime" part.

 

[Sturk200]

That wasn't Einstein's claim, and it's not what GR says. In fact, GR says exactly the opposite: the geometry of spacetime does not change as a consequence of relative motion. The geometry of spacetime is the invariant underlying structure of spacetime, that's the same for all observers, regardless of their state of motion.

Correct me if I'm wrong but isn't the whole point of special relativity that space contracts and time dilates as a consequence of relative motion -- i.e. that the geometry of spacetime is warped due to relative motion. Why does spacetime warp due to relative motion? Is there a force responsible for this? No, not that I am aware of. Spacetime warps because that's how it works (more specifically, it warps because it must as a consequence of our axioms -- so the "causation" is "top-down," if you will). This was what I meant when I said that the theory suggests a consequence without positing a force -- which, I think, is different from the kind of physical explanation that existed before relativity.

 

[PeterDonis]

isn't the whole point of special relativity that space contracts and time dilates as a consequence of relative motion -- i.e. that the geometry of spacetime is warped due to relative motion.

No. That's not what length contraction and time dilation are. They are just changes in your point of view, similar to what happens with rotation in ordinary 3-space.

When you change the direction from which you look at an object in ordinary 3-space, the object's apparent size in various dimensions can change. That's not a change in the object or in the geometry of space, it's just a change in your point of view.

Similarly, changing your frame of reference changes the "angle in spacetime" from which you perceive an object, and the object's apparent size in different dimensions changes (i.e., it appears length contracted and time dilated) because you have changed your point of view, not because the object or spacetime has changed.

 

[Sturk200]

No. That's not what length contraction and time dilation are. They are just changes in your point of view

I think maybe you are trying to point out that the spacetime interval remains invariant? (I think it is hard to discuss this using these kinds of analogies to 3-space). Right, so the interval is invariant but the independent dimensions of space and time are changed. From what I have read on this topic, your suggestion that this is merely a change in "perspective" or a change in our "perception" is a decidedly minority position. Einstein defined time to be how you measure it (the 1905 definition of simultaneity, e.g., is entirely dependent upon how time is measured). Therefore if you in your spaceship measure time to be different from how I measure it here on earth, then time itself is different (not just our perceptions of it).

Anyway, I am talking about length contraction and time dilation. If you don't want to call this a change in "geometry" because the intervals remain invariant, so be it. But certainly the theory entails a change in the dimensions of space and time consequent to relative motion.

 

[Dale]

That's a good question. As you know, I am not an expert, but from what I have seen of physics Einstein's claim that the geometry of spacetime must transform as a consequence of relative motion is unique in that it suggests an effect without indicating a cause. More specifically, it suggests that something happens without indicating what force is responsible for that something. The force, in other physical explanations, is the reason that things change from how they are. With Einstein, I am tempted to see it as rule by fiat rather than rule by reason. So a mechanism, I guess, would be something that tells us what forces light to move at constant speed, or what forces the geometry of spacetime to change due to relative motion.

Ok, if I understand what you are asking then the answer to your question seems to me to be that the "reason that things change" is the Einstein field equations. In other words, the EFE describes the mechanism for determining the geometry of spacetime based on the distribution of matter and energy.

That said, your description of what the theory says in this regard is fundamentally flawed, as others have pointed out. So it is a little hard to tell for sure, but it seems like the EFE is the mechanism (per your definition) for setting the spacetime geometry.

 

[PeterDonis]

I think maybe you are trying to point out that the spacetime interval remains invariant?

That is one manifestation of what I'm talking about, yes. The invariance of the interval corresponds to the invariance of lengths under rotation in ordinary 3-space.

the interval is invariant but the independent dimensions of space and time are changed

No; the interval is invariant but the coordinate lengths in the "space" and "time" directions are changed, just as the coordinate lengths of an object in the $x$ and $y$ directions change if it is rotated. Nothing about the object itself, or the underlying space (or spacetime), changes.

what I have read on this topic, your suggestion that this is merely a change in "perspective" or a change in our "perception" is a decidedly minority position.

I don't know what you have read, but your impression is incorrect. What I am describing is not a "position", it is how relativity works. Not all texts describe it in the words I've used, but they're all describing the same thing, and they all agree on the key points, that nothing about the object itself or the geometry of spacetime changes when you change frames.

I am talking about length contraction and time dilation.

I know you are, but you have an incorrect understanding of what they mean.

If you don't want to call this a change in "geometry" because the intervals remain invariant, so be it.

It's not a question of what I, or you, or anyone "want" to call it. The term "geometry", and more particularly "geometry of spacetime", has a definite meaning in relativity. That meaning is what I'm using the term to refer to. And with that meaning, your statements are incorrect. Changing the words we use to avoid the term "geometry" won't change that fact, because the underlying claim you are making is that what happens when you change reference frames is "the same kind of thing" as what happens due to the presence of matter and energy. That is incorrect, and if you keep trying to reason from this incorrect understanding, you are going to get yourself very confused.

If you don't want to call this a change in "geometry" because the intervals remain invariant, so be it. But certainly the theory entails a change in the dimensions of space and time consequent to relative motion.

You are incorrect. I strongly suggest that you take time to consider, in detail, the analogy with rotations in ordinary 3-space that I have given you. By your logic, the geometry of space would change if I rotate my spatial coordinates and thereby change the $x$ and $y$ dimensions of an object. Do you think it does?

 

[Nugatory]

Correct me if I'm wrong but isn't the whole point of special relativity that space contracts and time dilates as a consequence of relative motion -- i.e. that the geometry of spacetime is warped due to relative motion.

No. In special relativity relativity spacetime is always flat and unwarped. In general relativity, spacetime is either flat or not flat according to whether there are zero or non-zero gravitational effects are present (the "special" in special relativity means that the theory applies to the special case of flat spacetime, whereas the "general" in general relativity means that the theory will work for the general case in which the curvature takes on any value, zero or non-zero). In neither theory does relative motion warp spacetime in any way; the time dilation and length contraction effects between observers in relative motion to one another happen because they assign different time and position coordinates to events in that spacetime.

 

[Sturk200]

It's not a question of what I, or you, or anyone "want" to call it. The term "geometry", and more particularly "geometry of spacetime", has a definite meaning in relativity. That meaning is what I'm using the term to refer to. And with that meaning, your statements are incorrect. Changing the words we use to avoid the term "geometry" won't change that fact, because the underlying claim you are making is that what happens when you change reference frames is "the same kind of thing" as what happens due to the presence of matter and energy. That is incorrect, and if you keep trying to reason from this incorrect understanding, you are going to get yourself very confused.

No. In special relativity relativity spacetime is always flat and unwarped.

These are very helpful criticisms - thank you. I guess it would be wise for me to hold off on using the language of GR until I study it in greater depth. :)

No; the interval is invariant but the coordinate lengths in the "space" and "time" directions are changed, just as the coordinate lengths of an object in the xx and yy directions change if it is rotated. Nothing about the object itself, or the underlying space (or spacetime), changes.

Ok, so the right way to say what I mean is that the coordinate lengths change. And I now appreciate your analogy with a rotation in 3-space. The coordinates change while the underlying property remains the same. The difference is that in 3-space the underlying property is length, whereas in spacetime the underlying property is -- would it be right to say the spacetime interval, or can I say the four-vector?

In saying that the object itself doesn't change in a relativistic transformation, are you then suggesting that length is somehow not a real property of objects, but that the only real property is the four-vector of an event? Surely the length changes, as does the duration, but maybe you wish to say that these things constitute an object or event only when taken conjointly as components of a four-vector, which latter does not change. Is that something like it?

I don't know what you have read, but your impression is incorrect. What I am describing is not a "position", it is how relativity works. Not all texts describe it in the words I've used, but they're all describing the same thing, and they all agree on the key points, that nothing about the object itself or the geometry of spacetime changes when you change frames.

So according to what you are saying, when Jackson says, "A clock moving relative to an observer is found to move more slowly than one at rest relative to him," what he means is that time itself is not moving slower, but only the clock is? I don't get that. What is time but what a clock measures?

And even if it is just that relative motion causes clocks to move slower (and measuring rods to "measure shorter"?) -- then what force is responsible for these effects? Am I right to say that it is a new thing with Einstein, this idea that there is some physical effect but no force responsible for it? Or is it just that moving is like tilting your head through spacetime?

 

[NickAtNight]

Well, this appears to be a good place for you to start.

A clock moving relative to an observer is found to move more slowly than one at rest relative to him," what he means is that time itself is not moving slower, but only the clock is? I don't get that. What is time but what a clock measure

Here are the results of an experiment on the issue.

In 1971, American physicists Joseph Hafele and Richard Keating verified time dilation at low relative velocities by flying extremely accurate atomic clocks around the Earth on commercial aircraft. They measured elapsed time to an accuracy of a few nanoseconds and compared it with the time measured by clocks left behind. Hafele and Keating’s results were within experimental uncertainties of the predictions of relativity. Both special and general relativity had to be taken into account, since gravity and accelerations were involved as well as relative motion. Source: http://www.wright.edu/~guy.vandegrift/openstaxphysics/chaps/28 Special Relativity.pdf​

 

[vanhees71]

I thought the point of this first sentence, and the "asymmetries" it meant to point out, was the fact that according to Maxwell's equations when you move a magnet near a conductor, it induces a current by means of an induced electric field; whereas if you move a conductor near a magnet, a current is induced by means of the magnetic force on charge carriers in the wire. In Einstein's (1905) words, "The observable phenomenon here depends only on the relative [italics added] motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases..." Einstein thought that there should be only one explanation for this one phenomenon, and thus came up with the idea that the magnetic field itself is merely a consequence of charges in relative motion. This is different, I think, than the claim that the Galilean transformations are not a symmetry group for the Maxwell equations.

The point is that in any case the current is due to the interaction of the conduction electrons with the electromagnetic field, i.e., it can be understood by Maxwell's equations and the Lorentz force, which are relativistic equations of motion.

In the case that the magnet is at rest and the loop is moving, it's indeed the magnetic force $q \vec{v} \times \vec{B}/c$ which sets the electrons in motion. In case of the moving magnet, an electric field is induced due to Faraday's Law (one of Maxwell's equations),
$$\vec{\nabla} \times \vec{E} =-\frac{1}{c} \partial_t \vec{B},$$
and the electrons are set in motion (mostly for small velocities of the electrons) due to the electric force $q \vec{E}$ of this induced field. With the Lorentz transformation you can map one situation into the other, but not with the Galilei transformation, and this was among the puzzles solved by Einstein's reinterpretation of the transformation laws found by Voigt, Poincare, Lorentz, and others before.

 

[Dale]

So according to what you are saying, when Jackson says, "A clock moving relative to an observer is found to move more slowly than one at rest relative to him," what he means is that time itself is not moving slower, but only the clock is? I don't get that. What is time but what a clock measures?

And even if it is just that relative motion causes clocks to move slower (and measuring rods to "measure shorter"?) -- then what force is responsible for these effects? Am I right to say that it is a new thing with Einstein, this idea that there is some physical effect but no force responsible for it? Or is it just that moving is like tilting your head through spacetime?

This is all just geometry. You are acting as though you think that geometry requires a force and that Einstein uniquely neglected the force for geometry. That is simply wrong. Geometry has been part of physics from the beginning and no force was introduced to explain it prior to Einstein.

If I switch to polar coordinates what is the force that bends a straight line? If I switch from magnetic north to true North what is the force that changes the distance north and the distance east from my home to my friend down the street and what force keeps the distance the same? If I switch between different Newtonian reference frames, what is the force that changes the energy and momentum?

None of this is new. The only thing that is new with SR is including time in the geometry. Furthermore, GR does bring in a mechanism for the spacetime geometry itself, something which was absent from Newtonian physics.

So, if anything your criticism is exactly backwards as far as which theory is actually subject to it.

 

[PeterDonis]

The difference is that in 3-space the underlying property is length, whereas in spacetime the underlying property is -- would it be right to say the spacetime interval

Yes.

In saying that the object itself doesn't change in a relativistic transformation, are you then suggesting that length is somehow not a real property of objects, but that the only real property is the four-vector of an event?

The real property of an object is the 4-dimensional spacetime "world tube" occupied by the object. The "length" of the object is a cross section of that world tube "cut" by a particular spacelike plane. Different reference frames "cut" the world tube with planes oriented at different angles, which is why the "length" of the object in different frames is different. ("Lengths" in the time dimension work similarly, but this time the "cut" is in the time direction at different angles.)

when Jackson says, "A clock moving relative to an observer is found to move more slowly than one at rest relative to him," what he means is that time itself is not moving slower, but only the clock is?

No. Jackson is trying to describe something in ordinary language, that ordinary language is not well suited to describe. If you actually unpack what Jackson says according to the underlying math and physics, you will find that what I said above is at least as good an ordinary language description. But if you really want to understand what's going on, you have to discard all the ordinary language descriptions and actually learn the underlying math and physics.

even if it is just that relative motion causes clocks to move slower (and measuring rods to "measure shorter"?) -- then what force is responsible for these effects?

There isn't one. Consider the analogy with rotation in 3-space again. Suppose you rotate your point of view so an object appears thinner to you than it did before. Is there a force that compressed it to make it thinner? Of course not; all that changed was your perspective. Changing reference frames in relativity works the same way; as I have said several times now, nothing about the object itself or the underlying spacetime geometry changes. Only your perspective changes. So no force is required.

is it just that moving is like tilting your head through spacetime?

Yes.

 

[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.