Explaining C: How Space Changes with Speed

[Reflector]

So c is the same to all observers no matter what their speed. There must be a property of space that explains this? Maybe something like the angle of space changes as you increase speed. Like say your at the centre of a circle and you have no velocity. Currently lightspeed to you occurs parralel to the radius of the circle, but as you increase speed the angle of the light changes progressively making it seem to you that it stays at c speed. The greatest angle change (90 degrees) occurs when you reach lightspeed - but this would not be theoretically possible. This may sound like a stupid idea but I thought I'd post it anyway.

 

[selfAdjoint]

The real reason is electromagnetism. Maxwell's famous equations of EM, from 1868, predicts that light moving through a vacuum will move with a certain speed. And that prediction has no room in it for the relative speed of the observer, or of the emitter. Einstein's relativity is a theory in which this known fact finds a natural home.

 

[quantumdude]

Can we really say that electromagnetism is the reason for the invariance of the speed of light? It seems to me that it's exactly the other way around.

I know that SR was discovered through Maxwell's electrodynamics, but relativity is bigger that just EM. SR applies to all interactions, not just electromagnetic ones. I think that the invariance of c is a feature of spacetime, and the fact that electromagnetic (as well as all other) phenomena occur in that same spacetime is the reason that any correct theory of these interactions has to be Lorentz covariant.

 

[selfAdjoint]

All the interactions have EM inside them, at the Lagrangian level - for example it's the U(1) part of the gauge group in the standard model (gauge invariance of the EM four-potential). In quantum mechanics ontology recapitulates phylogeny, at least in the Maxwell-Einstein-Heisenberg-Dirac sequence.

 

[quantumdude]

I suppose I shouldn't have bothered mentioning the other interactions. They only obscure the point, which is that even in a universe in which the EM interaction were "turned off", SR should still hold. Otherwise, why would it apply to the kinematics of massive free particles, which are not described by Maxwell's equations? This is why I think that SR is the reason that EM takes the form it does, and not the other way around.

Now if you'll excuse me, I need to go look up the word "phylogeny".

 

[Janitor]

The dimensionless fine structure constant can be written in terms of the electron charge, the permittivity of free space, Planck's constant, and the speed of light. I wonder if physics will ever get to the point where there is good reason to choose some of these parameters as more fundamental than the others, so that we can say that Z is what it is because X and Y are what they are.

 

[zoobyshoe]

Can we really say that electromagnetism is the reason for the invariance of the speed of light? It seems to me that it's exactly the other way around.

I know that SR was discovered through Maxwell's electrodynamics, but relativity is bigger that just EM. SR applies to all interactions, not just electromagnetic ones. I think that the invariance of c is a feature of spacetime, and the fact that electromagnetic (as well as all other) phenomena occur in that same spacetime is the reason that any correct theory of these interactions has to be Lorentz covariant.

I came across this in a biography of Einstein:

"Lorentz had been among the first to postulate the electron, the negatively charged particle whose existence has finally been proved by J.J. Thomson at Cambridge. It now seemed to him that such a contraction could well be a result of electromagnetic forces produced when a body with its electrical charges as moved through the ether. These would disturb the equilibrium of the body, and its particles would assume new relative distances from one another. The result would be a chnge in the shape of the body, which would become flattened in the direction of its movement. The contraction could thus be explained, as Philipp Frank has put it, as `a logical consequence of several simultaneous hypotheses, namely the validity of the electromagnetic field equations and laws of force and the hypothesis that all bodies are built up of electric charges.'"

Ronald W. Clark

Einstein, The Life and Times

I haven't read the electrodynamic part of "On the Electrodynamics of Moving Bodies" yet, but I got the impression from the above quote that Einstein's point is going to turn out to be that all the relativistic effects are due to the atomic-level electrodynamics within the masses that show these effects. In other words, I have been under the impression that real SR is about relativistic effects on the level of charged particles. The macroscopic examples he starts with are to lead the reader into understanding what is happening on the microscopic scale. In other words, if you did actually turn all EM effects off there would be no SR, because the macroscopic effects in large masses are the result of the micro ones.

On the Electrodynamics of Moving Bodies
Address:http://www.fourmilab.ch/etexts/eins...N=28870118&jsessionid=06302662281082217897574

 

[quantumdude]

I haven't read the electrodynamic part of "On the Electrodynamics of Moving Bodies" yet, but I got the impression from the above quote that Einstein's point is going to turn out to be that all the relativistic effects are due to the atomic-level electrodynamics within the masses that show these effects. In other words, I have been under the impression that real SR is about relativistic effects on the level of charged particles.

In the 1905 paper, no reference is made to atomic level electrodynamics though. The progression goes like this:

1. Find a coordinate transformation that leaves the EM wave equation invariant.
2. Come up with the Lorentz transformation.
3. Apply the Lorentz transformation to all bodies, whether or not they even have electromagnetic interactions.

That is, you could take a particle that doesn't interact electromagnetically in any way, shape, or form and it should still obey SR, as long as the spacetime in which it lives can be considered flat. Indeed, the Lorentz transformation does not carry any electromagnetic information whatsoever (that is charges and magnetic moments do not show up in it at all).

The macroscopic examples he starts with are to lead the reader into understanding what is happening on the microscopic scale. In other words, if you did actually turn all EM effects off there would be no SR, because the macroscopic effects in large masses are the result of the micro ones.

That's not what SR predicts at all though. As I said, if you turn off EM (that is, all charges and magnetic moments go to zero) the Lorentz transformation survives. If the universe were full of nothing but neutrinos, for example, then we have no reason to think that their kinematics would not still be governed by SR (in a locally flat metric).

 

[Reflector]

If you want to see something similar to what I imagined, go see the movie 'Predator' and watch the way the Predator creature tracks the trajectory of a rock or something that's thrown to find where it came from. This is an awesome simple principal though, explaining such a huge phenomenon. Angle changing as you increase your speed towards lightspeed. Feeling enlightened? It's kind of like the angle changes until it finally locks on to 90 degrees when you reach lightspeed. That is just way too cool... Think of the possibilities...

 

[zoobyshoe]

In the 1905 paper, no reference is made to atomic level electrodynamics though.

OK. Einstein discusses the relativity of "a unit electric point charge" "in motion in an electromagnetic field." I took this, erroneously I guess, to be indirectly supportive of Lorentz' notion expressed in the quote that, at speed, matter literally rearranges itself at the level of fundamental charges to be shorter in the direction of motion. (Lorentz is on the wrong track with that, no?)

As I said, if you turn off EM (that is, all charges and magnetic moments go to zero) the Lorentz transformation survives. If the universe were full of nothing but neutrinos, for example, then we have no reason to think that their kinematics would not still be governed by SR (in a locally flat metric).

I tried to read through "II Electrodynamical Part" as best I could today, and I find the following which supports what you say:

"The analogy holds with `magnetomotive forces'.We see that electromotive force plays in the developed theory (i.e. SR) merely the part of an auxilliary concept, which owes its introduction to the circumstances that electric and magnetic forces do not exist independently of the state of motion of the system of co-ordinates."

He is saying that electric and magnetic forces are just as relative as kinematic forces. He is not saying, as I erroneously thought, that the macroscopic relativistic effects are the result of effects on the level of charged particles.

Thanks for clearing that up.

-Zooby

 

[zoobyshoe]

The real reason is electromagnetism. Maxwell's famous equations of EM, from 1868, predicts that light moving through a vacuum will move with a certain speed. And that prediction has no room in it for the relative speed of the observer, or of the emitter. Einstein's relativity is a theory in which this known fact finds a natural home.

I have terrible, terrible trouble with this concept. If the speed of light is independent of the motion of the observer or emitter, then how can we ascribe any rate to that speed? Rather than becoming a "constant" the speed of light strikes me as the most non-constant thing imaginable. Whenever I ask myself "300,000 km/s relative to what?" there is no answer: space is not absolute, time is not absolute, motion is not absolute, there doesn't seem to be anything anywhere against which to fix a rate of 300,000 km/s for electromagnetic propagation.

In defying the addition and subtraction of velocities light defies being measured to have an authentic rate. The fact it adjusts itself to the dilated or non-dilated time frame of anybody in motion strongly suggests to me that the whole notion of speed is impossible to apply to light.

 

[Reflector]

Do you guys not get my point? It can not be refutiated with jargon. Imagination is more important than knowledge... It just 'seems' to make sense to me. Seen the movie 'Contact'? The guy who put the puzzle together somehow with geometry. This idea is just like that... except it's REAL. And if it's wrong, well that doesn't make much of a difference... Maybe you want to steal the idea, when I've been convinced it's wrong and forgotten about it... :surprise:

 

[quantumdude]

OK. Einstein discusses the relativity of "a unit electric point charge" "in motion in an electromagnetic field." I took this, erroneously I guess, to be indirectly supportive of Lorentz' notion expressed in the quote that, at speed, matter literally rearranges itself at the level of fundamental charges to be shorter in the direction of motion.

When you say, "atomic level electrodynamics" I think "quantum mechanics of charged particles" or "quantum electrodynamics". Einstein may have mentioned electrons, but the electrodynamical theory under consideration (Maxwell's equations) is not quantum mechanical at all. That's why I say that the 1905 paper isn't specific to atomic level electrodynamics.

(Lorentz is on the wrong track with that, no?)

Lorentz agrees that the moving body would appear contracted, which is correct. But he seems to think that the contraction is somehow caused by electrodynamic equilibrium. That is the same notion that prompted my first post in this thread: If SR is due to the EM interaction, then why are particles that do not interact electromagnetically constrained by SR? It seems to me that it's the other way around: The equations that describe the EM interaction assume the form that they do because of SR.

 

[Reflector]

You guys seem to know what you're talking about... Can I contribute?

 

[quantumdude]

If you want to see something similar to what I imagined, go see the movie 'Predator'[/color] and watch the way the Predator creature tracks the trajectory of a rock or something that's thrown to find where it came from.

Seen the movie 'Contact'[/color]? The guy who put the puzzle together somehow with geometry.

Do you guys not get my point?

Is your point that you watch too many movies?

You'll learn a lot more physics by studying physics books, then by sci-fi.

 

[Reflector]

Okay, so what is your idea about this. The only thing concievable is that the angle of the speed of light has to change for it to remain constant to you. I don't know how you can go straight and then the light just goes more straight ahead of you. Is it because the furthermost photon takes it's own speed to reach your eye, so that by the time it has done that, it has already gone lightspeed more ahead?

 

[quantumdude]

The only thing concievable is that the angle of the speed of light has to change for it to remain constant to you.

Nope. Let a light pulse come at you at speed c. Then move towards it at 0.5c. Intuition might tell you that you now observe the same pulse coming at you at 1.5c, but this is not the case. It still comes at you with speed c, and the angle does not change: It is still headed straight for you.

What does change is the frequency and wavelength of the light. Furthermore, after you start moving, objects are shorter and clocks tick slower than prior to the acceleration. This gives a clue as to the way universe makes room for an absolute speed of light: by not having an absolute spacetime.

 

[zoobyshoe]

Einstein may have mentioned electrons, but the electrodynamical theory under consideration (Maxwell's equations) is not quantum mechanical at all.

Yep, I see what you're saying.

Lorentz agrees that the moving body would appear contracted, which is correct.

Lorentz, apparently, thought it would more than just appear contracted. He was certain it physically shortened:

"The difference between the earlier view and that of Einstein was exemplified by what Max Born, one of the first expositors of relativity, called `the notorious controversy as to whether the contraction is real or only apparent'. Lorentz had one view. `Asked if I consider this contraction a real one, I should answer yes,' he said. `It is as real as anything we can observe.'"

-ibid

P.120

Einstein's language tends to indicate he also thought the contraction was physically real:

"The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter is the rod."

-Relativity, The Special and the General Theory
Albert Einstein p. 35

But this is not in direct answer to someone asking him "Is the contraction real?", so we don't know if he would have qualified it in any way if someone tried to pin him down. Lorentz was pinned down and clearly thought it was more than a matter of appearances.

 

[zoobyshoe]

If SR is due to the EM interaction, then why are particles that do not interact electromagnetically constrained by SR? It seems to me that it's the other way around: The equations that describe the EM interaction assume the form that they do because of SR.

Yes, I see your point here.

 

[zoobyshoe]

This gives a clue as to the way universe makes room for an absolute speed of light: by not having an absolute spacetime.

With no absolute spacetime how can we fix a rate of 300,000 km/s for light? One man's kilometer is another man's fraction of a kilometer, and one man's second is another man's one second plus a fraction of a second depending on their speeds relative to each other. Where is the kilometer and the second stable enough for us to use to ascribe a km/s speed to light?

 

[selfAdjoint]

Maxwell's equations comprise two scalar equations (divergences on the left side) and two vector equations (curls on the left side). Altogether in three dimensional space eight scalar equations. In relativity they are expressed as two four-vector equations.

Although it was Maxwell's equations that inspired the discovery of relativity, relativity is a theory that applies to all physics except gravity. Observation of fast particles of all kinds has shown that relativity does apply to them.

 

[zoobyshoe]

Maxwell's equations comprise two scalar equations (divergences on the left side) and two vector equations (curls on the left side).

"Divergences" and "curls" are what, terms from calculus?

Altogether in three dimensional space eight scalar equations.

Scalar meaning having magnitude but no direction, no?

In relativity they are expressed as two four-vector equations.

Two four vector equations? I am familiar with the four equations that comprise the Lorentz transformation as presented by Einstein in the above quoted book on relativity. I thought there was just one for each vector: x,y,z,t. What am I misconstruing here?

 

[quantumdude]

Lorentz, apparently, thought it would more than just appear contracted. He was certain it physically shortened:

Poor choice of words on my part. It is physically shortened.

With no absolute spacetime how can we fix a rate of 300,000 km/s for light? One man's kilometer is another man's fraction of a kilometer, and one man's second is another man's one second plus a fraction of a second depending on their speeds relative to each other. Where is the kilometer and the second stable enough for us to use to ascribe a km/s speed to light?

Because when it comes to velocity transformations for the speed of light, it turns out that in every possible case one man's kilometers and his seconds are distorted from mine by precisely the same multiplicative factor[/color]. That means that, no matter whose kilometers and seconds are used, the correction factor cancels out when we divide the distance by the time.

"Divergences" and "curls" are what, terms from calculus?

Yes, from vector calculus. They are used throughout the 1905 paper, as they figure centrally into Maxwell's equations.

Scalar meaning having magnitude but no direction, no?

More specifically, it means that the equations do not change form under rotations.

Two four vector equations? I am familiar with the four equations that comprise the Lorentz transformation as presented by Einstein in the above quoted book on relativity. I thought there was just one for each vector: x,y,z,t. What am I misconstruing here?

He's not talking about the Lorentz transformation, but about Maxwell's equations. In Euclidean 3-space, they are presented as 4 distinct equations (2 vector, 2 scalar, as he said). In Minkowski 4-space, when the equations are written in manifestly covariant form, they assume the form of 2 equations that are both 4-vectors (4 component vectors in Minkowski space).

 

[zoobyshoe]

Poor choice of words on my part. It is physically shortened.

I am not sure it was a poor choice of words. Ronald W. Clark's point, not quite stated in so many words but implied, seems to be that he thinks Lorentz was taking the contraction too literally. I say that because he goes on from the Lorentz quote I cited above to this one from Sir Arthur Eddington:

"Sir Arthur Eddington, the later great exponent of Einstein, held a rather different view. `When a rod is started from rest into uniform motion, nothing whatever happens to the rod,' he has written.`We say it contracts; but length is not a property of the rod; it is a relation between the rod and the observer. until the observer is specified the length of the rod is quite indeterminate.'"

-Einstein, The Life and Times
Ronald W. Clark
p. 120

By giving Eddington the last word on "the notorious controversy" Clark seems to be promoting Eddington's interpretation as the more insightful. Given that Lorentz' original belief that the particles in a body would assume new relative distances from each other, literally, as a result of being perturbed by motion through the ether, it seems safe to conclude his literal interpretation of authentic physical shortening, is just the unfortunate result of barking up the wrong (ether) tree. For some reason Lorentz held onto this literal notion of length contraction even after Einstein abandoned the ether and adapted the Lorentz length contraction to the etherless environment of special relativity.

Eddington's argument that the rod has no property called length until you specify an observer strikes me as more faithfully relative, and is free of any need to postulate a mechanism whereby its constituent particles assume authentically closer spacing to each other in the dimension of the direction of motion. For him, the "shortening" has nothing to do with the rod in and of itself, but is the exclusive result of the relationship between rod and observer.

I think that your original wording, that it "appears" contracted, is the best choice of words when referring to the effect in passing. It would be nice to have a specific answer by Einstein to "the notorious controversy," (i.e.: an answer to the specific question "Is the contraction real or only apparent?) but Clark doesn't quote one and I haven't run into one elsewhere.

 

[zoobyshoe]

Speaking of math, in an extremely compact explanation of relativity (the special and general theory in only five pages!) that Einstein wrote in 1949 he says"

"Lorentz tranformations are formally characterized by the demand that the expression

dx² + dy² + dz² - c²dt²,

which is formed from the coordinate differences dx, dy, dz, dt of two infinitely close events, be invariant (i.e. that through the transformation it goes over into the same expression formed from the coordinate differences in the new system)."

-Out of My Later Years
Albert Einstein
Citadel press, 1956, p.44

I don't know what "d"s means. Are these the "d"s of calculus, meaning "an element of", "a little bit of"?

 

[Doc Al]

I don't know what "d"s means. Are these the "d"s of calculus, meaning "an element of", "a little bit of"?

Yes, those are the ordinary differentials of calculus.

 

[quantumdude]

"Sir Arthur Eddington, the later great exponent of Einstein, held a rather different view. `When a rod is started from rest into uniform motion, nothing whatever happens to the rod,' he has written.`We say it contracts; but length is not a property of the rod; it is a relation between the rod and the observer. until the observer is specified the length of the rod is quite indeterminate.'"

I agree with that. When I say that the rod is physically shortened, I mean that the rod is really, physically shorter to a moving observer than it is in the rest frame of the rod.

In Halliday and Resnick the thought experiment goes like this:

Put flares on the ends of a rod of proper length L₀, and connect them to a switch so that an observer can ignite them. Let the rod move by at a velocity v on a track, so that the ingited flares can leave marks on the track. Now let the observer ignite the flares simultaneously, in his frame (The reason for simultaneous ignition is that it is the only way you could correctly say that the distance between the marks is equal to the length of the rod).

SR predicts that when the observer goes to the track and measures the distance between the marks, he will measure a distance that is equal to L=L₀/γ. According to SR then, the length of the rod moving at speed v is really less than the length of the rod at speed 0.

 

[zoobyshoe]

SR predicts that when the observer goes to the track and measures the distance between the marks, he will measure a distance that is equal to L=L₀/γ. According to SR then, the length of the rod moving at speed v is really less than the length of the rod at speed 0.

OK, you say you agree with Eddington, but from the example you gave you are really much more in agreement with Lorentz.

 

[zoobyshoe]

Because when it comes to velocity transformations for the speed of light,

I am not sure what you mean here: "velocity transformation for the speed of light". When do we need to do such a thing? I thought the whole point was that it's always going to be 300,000 km/s (no transformation necessary).

 

[quantumdude]

OK, you say you agree with Eddington, but from the example you gave you are really much more in agreement with Lorentz.

The only example I cited was the thought experiment with the rod and the flares, so I'll assume you are referring to that. I that case, my agreement with the example only implies one thing: That I agree with special relativity. It is impossible to determine which interpretation of SR is correct by merely doing a thought experiment. Once again, I deny Lorentz' point of view that the effect of Length contraction has anything to do with electrodynamic equilibrium. By any measure, SR seems to be "bigger" than EM theory, for the reason I mentioned. Specifically, the Lorentz transformation does not depend on any electrodynamic variables. If you set all EM sources equal to zero (effectively "turning off" electromagnetism), the Lorentz transformation survives.

I am not sure what you mean here: "velocity transformation for the speed of light". When do we need to do such a thing?

We need such a thing when predicting the speed of light from a moving source. Yes, SR postulates that this speed will be c. Since the Lorentz transformation is consistent with that postulate (indeed, it is derived from it) that means that we can show from the LT that the speed of light is going to be 'c'.

I thought the whole point was that it's always going to be 300,000 km/s (no transformation necessary).

I was answering your question regarding the "stability" of kilometers and seconds. If you look at the LT and perform such a velocity transformation for light from a moving source, you will see that the variances in "kilometers" and "seconds" completely vanish when transforming the speed of light from one frame to another. This is because your kilometers and mine, and your seconds and mine, are different by precisely the same multiplicative factor. So when we divide our respective kilometers and seconds to determine the speed of light, those differences cancel out exactly.