Why the speed of light is constant?

[Hornbein]

Here is a question that might be somewhat more philosophical than this community cares for. If so, I apologize in advance.

Are there any reputable theories as to why the speed of light is constant? I know that it is an empirical fact and therefore that it does not need to be proven. But on the other hand, the aim of physics has historically been to come up with satisfying theoretical explanations for empirical facts. Anyway, I'm just wondering if there are any reputable ideas out there that modern physicists are considering.

Suppose the speed of light depended on the speed of the object that emitted it. Different parts of distant astronomical objects are moving at different speeds relative to us. Light from different parts of those objects would arrive at different times. Distant astronomical images would be all blurred. So looking at those Hubble images tells you that the speed of light is constant. Well... at least it tells you that it doesn't depend on the motion of the emitter.

 

[PeterDonis]

Light from different parts of those objects would arrive at different times.

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.

Distant astronomical images would be all blurred.

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.

 

[vanhees71]

and an iPad too ! AWESOME.


They seem a bit weak on the Gell-Mann's the 8fold way. Perhaps I just missed it.


Where are the great graphics locations for the Eightfold way. Here is one site, but only so so graphics. It really helps tie together the incredible particle zoo that appeared from the particle accelerators. (Note where the proton and neutron are: On the Baryon chart, top graphic, back of the bottom row. The neutron is on the left with two down quarks and one up quark. The proton is on the right with two up quarks and one down quark)

Unraveling the Confusion: the Eightfold Way
The first steps in resolving the particle proliferation problem were taken by Murray Gell-Mann and Yuval Ne'eman in 1962. They realized that many of the known particle could be fit into a series of families based on an abstract mathematical construct (called the su(3) group). Gell-Mann called this the Eightfold Way, after the Buddha's eightfold path to truth.

Some of these families are illustrated below.​

From that site. Meson family

and Baryon family

These diagrams are from the Review of Particle physics. There are great review articles:

http://pdg.lbl.gov/2014/reviews/contents_sports.html

For the Quark Model, see

http://pdg.lbl.gov/2014/reviews/rpp2014-rev-quark-model.pdf

 

[vanhees71]

However, all Einstein's argument here does is make it very plausible that the speed of light should be constant - indeed, once you've worked through the argument, you will be convinced that it would be really weird and logically inconsistent if it were not constant. But however well-motivated and convincing that assumption, it's still an assumption. Einstein's argument doesn't answer Sturk200's "What is the mechanism that makes it have to be that way?" question.

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.

The history is very clear, and Einsteins paper of 1905 resolves a several decades long big puzzle of 19th century physics. All the math was there before, but the physics understanding was due to Einstein in this paper, and the first sentence of this paper is very remarkable [translation from German mine; it's very hard to get Einstein's masterful prose]

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.

The point was that the Galilei transformations, which is the symmetry group of Galilei-Newton space time, is not a symmetry group for the Maxwell equations. Initially, Maxwell got his equations by making pretty abstract mechanical models by the assumption that electromagnetic fields are states of a substance dubbed the ether (or aether). From this point of view, it's not so surprising that Galilei symmetry may be broken, because there is simply a preferred reference frame, defined as the restframe of the ether. Maxwell's greatest achievement was the discovery that electromagnetic fields propagate as waves (thanks to his introduction of the "displacement current", i.e., the term $\partial_t \vec{E}/c$ on the right-hand side of Ampere's Law, extending it to one of the fundamental Maxwell equations, the Ampere-Maxwell Law), and that these transverse waves propagate with the speed of light and that also the known properties of light fit with the conclusion that light is nothing else than electromagnetic waves in a certain part of the spectrum (wavelength roughly from 400 to 800 nm). Now, if there is a preferred rest frame due to the presence of the ether, it should be possible to observe the motion of another reference frame against the ether. This however, was not the case. Einstein mentions the example of a wire loop moving against a magnet at rest and the other situation with the loop at rest and the magnet moving. There was also the famous Michelson-Morley experiment, trying to measure the motion of the Earth through the ether by measuring the difference in the velocity of light using the famous MM interferometer, which was ending with a negative result (to Michelson's great dismay, because he never liked relativity later).

Before, many brilliant physicists had found the symmetry of the Maxwell equation under transformations we now call Lorentz boosts (the earliest one I know of was by Woldemar Voigt in the 1880ies), and Poincare immediately figured out that these together with spatial rotations build a group. Of course also Lorentz wrote down these transformations in connection with his masterpiece, the theory of electrons, and there were many more physicists.

But Einstein was the one who found the much simpler but at his time most radical solution! It's not the Maxwell equations which are asymmetric under transformations from one inertial frame to another, moving relative to it with a constant velocity, but Newtonian mechanics was flawed, and this in its very foundations, namely the space-time model itself. So Einstein came to the conclusion that the space-time model must be adapted to get rid of the apparent "asymmetries" of Maxwell's equations, and the ingenious point of his paper is that he starts out from this right away by picking the one (for us today pretty simple) feature of the Maxwell equations which is related to the space-time structure, namely the appearance of the speed of light in the fundamental Maxwell equations (which at this time fortunately where written in terms of natural units, namely Gaussian units, where this is manifest, i.e., that there is only one fundamental constant in electromagnetism, which is the speed of light in vacuo). If now the entire set of Maxwell's equations should be invariant under boosts from one inertial frame to another this implies that the speed of light must be independent of the speed of its source, and thus he did not put the Maxwell equations as the postulates but just the Newtonian principle of inertia plus the invariance of the speed of light and then analyzed how one has to describe space and time to agree with these postulates, and the result is the Lorentz boost instead of the Galilei boost as the transformation equation from one inertial frame to another moving with constant velocity against the former. This derivation is easily understandable by high-school students, and this makes out the great value of this paper. The further parts are pretty difficult, but there Einstein shows that now indeed the Maxwell equations are invariant under Lorentz boosts and gives also the derivation of the relativistic mechanics of an electron. This was all correct but not in final form, which came with Minkowski's mathematical reanalysis of the space-time structure in terms of a four-dimensional affine manifold with an indefinite fundamental form of signature (1,-1,-1,-1).

 

[NickAtNight]

Very true.

Actually Maxwell did that in 1861, a half-century before Einstein. Einstein was using Maxwell's brilliant and widely appreciated discovery to motivate the "far-reaching assertion" about the invariance of the speed of light in a vacuum.

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

A Dynamical Theory of the Electromagnetic Field Paperback – November 6, 2013
by James Clerk Maxwell

2013 Reprint of 1865 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. One of the unquestioned triumphs of nineteenth century physics was Maxwell's discovery of the equations for the electromagnetic field. "A Dynamical Theory of the Electromagnetic Field" is the third of James Clerk Maxwell's papers regarding electromagnetism, published in 1865. It is the paper in which the original set of four Maxwell's equations first appeared. The concept of displacement current, which he had introduced in his 1861 paper "On Physical Lines of Force", was utilized for the first time, to derive the electromagnetic wave equation.​

 

[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?