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. Untill 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. Untill 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.

 

[zoobyshoe]

Once again, I deny Lorentz' point of view that the effect of Length contraction has anything to do with electrodynamic equilibrium.

Yes, I understand where you stand on this. I meant, you agree with Lorentz answer to the question "Is length contraction real or apparent?"

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.

Yes, that is what bothers me. The speed of light is all things to all kilometers and all seconds, however contracted or dilated.

The origin of this, according to selfAdjoint, is that the Maxwell equations "leave no room for" the speed of the emitter or the reciever. I wonder what he was thinking. Then there's this Faraday thing Einstein was trying to clear up, but I don't think he understood the circumstance Faraday was referring to when he said the motion between conductor and magnet wasn't relative. I have to check on that.

 

[quantumdude]

Yes, I understand where you stand on this. I meant, you agree with Lorentz answer to the question "Is length contraction real or apparent?"

My position is in fact much more in line with Eddigton's. The length of a rod is really shorter to a moving observer, and it makes no sense to speak of the length of the rod without specifying an inertial frame from which the length measurement is made.

Yes, that is what bothers me. The speed of light is all things to all kilometers and all seconds, however contracted or dilated.

The length contraction and time dilation does not occur in some arbitrary way though. It occurs precisely in such a way as to preserve the invariance of the speed of light.

Consider a light source that is stationary with respect to observer S. The source is a distance D away from S, and at time t=0 a light pulse is fired. Observer S detects this pulse in a time equal to T=D/c, and of course he measures a velocity of -c (negative because it is moving towards him).

Now let an observer S' be moving with speed v towards the source along the line joining the source and observer S. At time t=t'=0, the origin of S' is coincident with that of S. What speed will S' measure for the light pulse?

Event 1: Pulse Emitted
Spacetime coordinates in S: x₁=D, t₁=0
Spacetime coordinates in S': Use Lorentz transformation.
x₁'=γ(x₁-vt₁)=γ(D-0)=γD
t₁'=γ(t₁-vx₁/c²)(0-vD/c²)

Event 2: Pulse Detected
Spacetime coordinates in S: x₂=0, t₂=D/c
Spacetime coordinates in S': Use Lorentz transformation.
x₂'=γ(x₂-vt₂)=γ(0-vD/c)=-γvD/c
t₂'=γ(t₂-vx₂/c²)=γ(D/c+vD/c²)

Now let the speed of the light pulse in S be u and let the speed of the pulse in S' be u'.

u=Δx/Δt=(0-D)/(D/c-0)=-c

u'=Δx'/Δt'=[γ(-vD/c-D)]/[γ(D/c+vD/c²)]

Now factor the numerator and denominator as follows.

u'=Δx'/Δt'=[γ(v/c+1)[/color](-D)]/[γ(v/c+1)[/color](D/c)]

See how the factors in blue[/color] are exactly the same? They cancel out every time.

So...

u'=(-D)/(D/c)

u'=-c

So to answer your earlier question, yes the speed of light will always come out the same in every frame, and there really isn't any need to do a Lorentz transformation. But that doesn't mean it's not instructive to do the Lorentz transformation.


edit: fixed a subscript bracket

 

[zoobyshoe]

My position is in fact much more in line with Eddigton's. The length of a rod is really shorter to a moving observer, and it makes no sense to speak of the length of the rod without specifying an inertial frame from which the length measurement is made.

I think when you say the length of the rod is "really" shorter you miss the fine point Eddington puts on the matter when he said 1). nothing whatever happens to the length of the rod, because 2.) length is not a property of the rod.

It occurs precisely in such a way as to preserve the invariance of the speed of light.

Yes, this illuminates my point. The LT assumes c is always c and is designed to make it so in all cases.
(Incidently, what do the question marks in your equations represent?)

The time dilation and length contraction can only be figured from c and c, as you have just shown, can be figured from the time dilation and length contraction. The LT is "rigged" so to speak. I find this circular.

There is only one way to make the postulate good, rob peter (time and space) to pay paul (light), and Einstein decided to do that rather than to wonder if the postulate had anything wrong with it. This is why I am wondering what Maxwell was thinking when he "left no room" for addition and subtraction of velocity for light. The postulate must have been primarily intended to conform to Maxwell's thinking because Einstein frequently said he concieved of the postulate prior to hearing about Michelson-Morley, so that MM didn't have much bearing on the matter, except to confirm the postulate was on the right track.
--------
I realize that raising the kinds of questions I do about relativity is regarded as a sign of being a crank or crackpot but the claims SR makes are just too extraordinary for me to accept without completely understanding every relationship of all parts to the whole and the whys of everything. It isn't enough, in my mind, to say that if we just shift our conception of time and space then this postulate about the properties of light can be accommodated with no further problems. Nor is the fact that Lorentz and Einstein found a convenient way to do this anything like a proof, in my mind, that this is what should be done. Before time and length are rendered flexible to accommodate the postulate it seems a much better case has to be made that the postulate needs accomodating. This is why I wonder what Maxwell was thinking when he "left no room" for addition and subtraction of velocities. In other words, I am more prone to look to the work of a human mathametician for something that needs adjustment, than to enormities like time and space.

 

[quantumdude]

I think when you say the length of the rod is "really" shorter you miss the fine point Eddington puts on the matter when he said 1). nothing whatever happens to the length of the rod, because 2.) length is not a property of the rod.

I am not missing any point of Eddington.

The simple fact of the matter is that one is free to measure the length of a rod in the rest frame of the rod. Furthermore, one is free to measure the length of the rod as the rod moves by at a speed v. And when one does measure the length of the rod as it speeds by, one measures its length to be something less than the "proper length".

By any measure, that implies that the rod is "really" shorter, and it does not contradict Eddington in any way, shape, or form.

Yes, this illuminates my point. The LT assumes c is always c and is designed to make it so in all cases.

How does this illuminate your point of "instability" of kilometers and seconds?

(Incidently, what do the question marks in your equations represent?)

There are no question marks in my equations. Perhaps your browser is not interpreting some symbols correctly.

The time dilation and length contraction can only be figured from c and c, as you have just shown, can be figured from the time dilation and length contraction. The LT is "rigged" so to speak. I find this circular.

It is not circular, it is simply a matter of being consistent.

There is only one way to make the postulate good, rob peter (time and space) to pay paul (light),

What are you talking about? The speed of light postulate has been experimentally verified (some decades ago, in fact). The postulate doesn't need anyone to "make it good". The postulate is "good" all by itself.

I realize that raising the kinds of questions I do about relativity is regarded as a sign of being a crank or crackpot

No, your questions do not mark you as a crackpot.

They mark you as someone who is curious about physics, and who needs to spend more time studying it.

A lot more.

 

[Janus]

This is why I am wondering what Maxwell was thinking when he "left no room" for addition and subtraction of velocity for light.

You make it sound as if you think it was a conscious decision on his part to do so; this is not the case. What he did was uncover rules of electromagnetic behavior that already existed.

 

[zoobyshoe]

You make it sound as if you think it was a conscious decision on his part to do so; this is not the case. What he did was uncover rules of electromagnetic behavior that already existed.

Thanks for addressing that. SelfAdjoint's wording suggested the slight possibility to me that "a conscious decision" was behind it, that Maxwell may, somehow, have had the option of including or excluding the addition and subtraction of velocities, and chose not to. You are clearly saying that he had no such option, which is what I was wondering about.

 

[selfAdjoint]

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

Scalar meaning having magnitude but no direction, no?

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?

If you have a three dimensional vector field, say U=(u,v,w), with the components, u, v, and w as functions of x, y, and z, then the divergence of U is
\nabla \cdot U = \frac {\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z}. the curly d's are partial derivatives from multivariable calculus. A divergence is a scalar, a number field.

The curl of U is a vector \nabla \times U = ((\frac{\partial u}{\partial y} - \frac{\partial v}{\partial x}), (\frac{\partial v}{\partial z} - \frac{\partial w}{\partial y}), (\frac{\partial w}{\partial x} - \frac{\partial u}{\partial z})). The three expressions in parentheses are the components of the vector.

So a vector equation has three components, which are scalar equations, but a scalar equation has only one component. Thus the Maxwell equations break down to 2(3) + 2 = 8 scalar equations.

 

[zoobyshoe]

So a vector equation has three components, which are scalar equations, but a scalar equation has only one component. Thus the Maxwell equations break down to 2(3) + 2 = 8 scalar equations.

OK, I see: all the terminology I didn't follow is from calculus.

 

[zoobyshoe]

By any measure, that implies that the rod is "really" shorter, and it does not contradict Eddington in any way, shape, or form.

Eddington does not consider the question "Is the rod really shorter?" a proper question under the circumstances. If he did he could just have said "Yes, it is really shorter." Instead, he phrases the whole situation such that the questioner is diverted from asking about it in those terms, which, he feels, are not enlightening.

How does this illuminate your point of "instability" of kilometers and seconds?

It doesn't. It illuminates my complaint that light doesn't seem to have a property to which the concept of speed can accurately be attached.

There are no question marks in my equations. Perhaps your browser is not interpreting some symbols correctly.

Yes, it is probably my browser. The same thing happened to some equations someone else gave me in another thread.

It is not circular, it is simply a matter of being consistent.

I will mull this over.

What are you talking about? The speed of light postulate has been experimentally verified (some decades ago, in fact). The postulate doesn't need anyone to "make it good". The postulate is "good" all by itself.

What I'm talking about, obviously, is not proving the speed of light postulate, but explaining it in terms of everything else. If the speed of light is the same to all observers in all inertial frames it is doing something it shouldn't be able to do. The speed of light postulate bothered Einstein for something like ten years:

"In short, let us assume that the simple law of the constancy of the velocity of light c (in vacuum) is justifiably believed by the child at school. Who would imagine that this simple law has plunged the conscientiously thoughtful physicist into the greatest intellectual difficulties? Let us consider how these difficulties arise."

Then he goes on to explain how light doesn't comply with the addition and subtraction of velocities. That being the case, he says, we find ourselves faced with an impossibility.

"In view of this dilemma there appears to be nothing else for it than to abandon either the principle of relativity or the simple law of the propagation of light in vacuo."

That's from a chapter entitled "The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity", which is chapter VII of his book Relativity, The Special and the General Theory.

Instead of abandoning either, Einstein has arrived at a brilliant solution that makes both good, an extremely creative and counter-intuitive theory:

"This theory has been called the special theory of relativity to distinguish it from the extended theory, of which we shall deal later. In the following pages we shall present the fundamental ideas of the special theory of relativity."

(Quotes from pages 17, 19, and 20, respectively, of the 1961 edition of that book.)

The speed of light postulate is not "good" by itself. At least, Einstein didn't think so. He felt it needed some intense explaining. So much so, that in order to accommodate it, he felt justified in theorizing that time and space were not the absolute things we think them to be.

Chapter 7. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity. Einstein, Albert. 1920. Relativity: The Special and General Theory
Address:http://www.bartleby.com/173/7.html

 

[selfAdjoint]

Eddington does not consider the question "Is the rod really shorter?" a proper question under the circumstances. If he did he could just have said "Yes, it is really shorter."

No that is not a proper question. What observer corresponds to "really"? The correct statement is that the observation of someone in another inertial frame, who measures the rod as shorter, is just as valid physics as the observation of someone in the rest frame of the rod, who sees it unshortened. There is no "reality" higher or deeper than this.

 

[quantumdude]

Eddington does not consider the question "Is the rod really shorter?" a proper question under the circumstances. If he did he could just have said "Yes, it is really shorter." Instead, he phrases the whole situation such that the questioner is diverted from asking about it in those terms, which, he feels, are not enlightening.

What I mean is that the length of the rod when it is measured in two different states of motion is really different. This another way of saying that the length of the rod is "indeterminate" (to use Eddington's term) until the state of motion of the rod is specified. Note that, due to the reciprocity of relative velocities, specifying the state of motion of the rod is the same as specifiying the observer.

It doesn't. It illuminates my complaint that light doesn't seem to have a property to which the concept of speed can accurately be attached.

But it does. If light covers a distance of 3x10⁸ m in 1 second, then that's the speed of light, and it's perfectly well-defined.

What I'm talking about, obviously, is not proving the speed of light postulate, but explaining it in terms of everything else. If the speed of light is the same to all observers in all inertial frames it is doing something it shouldn't be able to do.

Says who?

Physics is not an a priori discipline, because the universe is not known a priori. What light should and should not be able to do is determined by experimental results and nothing else.

Then he goes on to explain how light doesn't comply with the addition and subtraction of velocities. That being the case, he says, we find ourselves faced with an impossibility.

It's not an impossibility unless one insists on holding to the notion that velocities should be combined by simple addition and subtraction.

The speed of light postulate is not "good" by itself.

When I say "good", I don't mean "a comprehensive theory of motion", I mean "true".

In that sense, the speed of light postulate is "good" all by itself. It is a feature of the universe we inhabit, and no sleight of hand is required to justify it.

At least, Einstein didn't think so. He felt it needed some intense explaining. So much so, that in order to accommodate it, he felt justified in theorizing that time and space were not the absolute things we think them to be.

You keep posting all this history of the development of SR, but it is really not necessary. We all know that SR in its finished form is necessary to understand the whole picture, and we all know that neither postulate of relativity is consistent with the Galilean transforms.

 

[quartodeciman]

Lewis Epstein in the book "Relativity Visualized" does a trick I have not seen exploited anywhere else.

Instead of explaining the Minkowski 4-space idea with its new ct dimension, he postulates that all motion is in 4 spatial dimensions (x, y, z, s). 's' is, of course, the same as the space-time metric of an event from the zero event in a given frame of reference. But Epstein exploits our more current tolerance of extra spatial dimensions to postulate s as a 4th added to the classical 3. Then he postulates that natural motions of bodies in a framework always have total speed of c through all 4 dimensions. A lightlike object travels only through the first 3; the rate of motion along s is 0. Nothing can travel through the classical 3 dimensions at a faster rate without violating the total speed c assumption. A sub-lightlike object travels through s, meaning the speed through x, y and z must be less than c. In the case that the rate is 0 for x, y and z, the object is stationary in the reference frame and the full speed of c is carried in the s dimension.

Of course, this just transfers the open question from why light travels only at speed c to why things travel at exactly speed c in the 4 dimensions. Also, I don't know just how this helps with handling spacelike intervals of Minkowski theory or General Relativity, and I don't recall that Epstein exploits it there. I decided for myself that Epstein's 4th dimension s is a quadratic slack quantity. Standard linear slack (time expended) is something like one task team of a project having like 3 hours of inactivity before they can continue their contribution to the whole project because some concurrent activity is critical for completion of the current milestone and requires more time.

In this application, the total motion is

x² + y² + z² + s² = (ct)²

. s is just as quadratic slack quantity of incompleted classical spatial motion.

Again, rearrange and get

(ct)² - x² - y² - z² = s²

 

[zoobyshoe]

What I mean is that the length of the rod when it is measured in two different states of motion is really different. This another way of saying that the length of the rod is "indeterminate" (to use Eddington's term) until the state of motion of the rod is specified. Note that, due to the reciprocity of relative velocities, specifying the state of motion of the rod is the same as specifiying the observer.

The way you have just put it here is a good paraphrase of Eddington.

But it does. If light covers a distance of 3x10⁸ m in 1 second, then that's the speed of light, and it's perfectly well-defined.

I haven't managed to express what is confusing me well enought to convey it to you.

Says who?

I think you understand what I'm talking about: the fact the speed of light doesn't behave according to the addition and subtraction of velocities was a great surprise to everyone.

Physics is not an a priori discipline, because the universe is not known a priori. What light should and should not be able to do is determined by experimental results and nothing else.

People have expectations and are surprised if a measurement doesn't support what they expected.

It's not an impossibility unless one insists on holding to the notion that velocities should be combined by simple addition and subtraction.

That is right, but you are trivializing what an enormous step it was for Einstein to decide if that is what was called for or if the postulate or the principle of relativity should be abandoned.

When I say "good", I don't mean "a comprehensive theory of motion", I mean "true".

Yes I know, but I used it first, so I have dibs on the meaning.

In that sense, the speed of light postulate is "good" all by itself. It is a feature of the universe we inhabit, and no sleight of hand is required to justify it.

Again, you are trivializing the fact that to accommodate it Einstein had to theorize that time and space were not absolute. That's interesting. That's exiting. That's controversial. It's not peanuts.

You keep posting all this history of the development of SR, but it is really not necessary.

I posted it to answer your question "What are you talking about?"

The history of SR is actually quite enlightening. Actually, I find all physics history quite enlightening. Einstein appreciated physics history. He co-authored a book called The Evolution of Physics with Leopold Infield. Despite the frustrations relativity causes me, I find Einstein's attitude toward physics to be a very beautiful one.

 

[zoobyshoe]

Then he postulates that natural motions of bodies in a framework always have total speed of c through all 4 dimensions.

Wow! This is interesting.

A lightlike object travels only through the first 3; the rate of motion along s is 0.

s, you said, is the space-time metric. What does it mean about the lightlike object that it has no travel in the dimension of the spacetime metric?

 

[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.

This won't work, then, because if we have a guy sitting on the rod while it is in motion he will look down at the track and see it is shorter than when at rest. He will expect the flares to leave marks more than a meter apart when he checks afterward in the track rest frame.

 

[Doc Al]

when the relativity bug bites...

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.

This won't work, then, because if we have a guy sitting on the rod while it is in motion he will look down at the track and see it is shorter than when at rest. He will expect the flares to leave marks more than a meter apart when he checks afterward in the track rest frame.

You have forgotten that from the point of view of the observer on the rod, those marks are not made at the same time.

Well, zoobyshoe, it seems like the relativity bug has bitten you again, even though you threw in the towel in this post: https://www.physicsforums.com/showpost.php?p=255677&postcount=112

Have you gotten any of the books I recommended? (https://www.physicsforums.com/showpost.php?p=255747&postcount=114)

 

[quantumdude]

This won't work, then, because if we have a guy sitting on the rod while it is in motion he will look down at the track and see it is shorter than when at rest. He will expect the flares to leave marks more than a meter apart when he checks afterward in the track rest frame.

You have forgotten that from the point of view of the observer on the rod, those marks are not made at the same time.

Right. To the guy on the rod, the measurement is not a length measurement, because the two flares do not ignite simultaneously.

 

[quantumdude]

I think you understand what I'm talking about: the fact the speed of light doesn't behave according to the addition and subtraction of velocities was[/color] a great surprise to everyone. People have expectations and are surprised if a measurement doesn't support what they expected.

Yes, and the key word is "was[/color]". After a hundred years, peoples' expectations have changed. Now it seems strange to physicists for the speed of light not to be Lorentz invariant.

Tom: It's not an impossibility unless one insists on holding to the notion that velocities should be combined by simple addition and subtraction.

zoobyshoe: That is right, but you are trivializing what an enormous step it was for Einstein to decide if that is what was called for or if the postulate or the principle of relativity should be abandoned.

I'm not trivializing it, but I also do not allow it to stunt my growth. You could make the above remark about any of the theories of modern physics. But at some point, acceptance has to take hold, and we have to get on with the business of doing physics.

Yes I know, but I used it first, so I have dibs on the meaning.

OK, fine: The SOL postulate by itself is not enough to explain what we observe. But as I keep remarking, we all know that.

Again, you are trivializing the fact that to accommodate it Einstein had to theorize that time and space were not absolute. That's interesting. That's exiting. That's controversial. It's not peanuts.

I agree that it's interesting, but it's also old news.

And in fact, the more you get used to SR, the more strange Galilean relativity seems. One can be totally baffled by SR thinking, "How can the photon have the same speed in every frame? That shouldn't be! How can the Lorentz transform be right?"

Once you get past it, the other point of view seems nonsensical, and one will be wondering, "How can inertial frames be distinguished without making reference to an external point. That shouldn't be! How can the Galilean transform be right?"

Tom: You keep posting all this history of the development of SR, but it is really not necessary.

zoobyshoe: I posted it to answer your question "What are you talking about?"

I just needed to know what you meant by making the SOL postulate "good".

 

[zoobyshoe]

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).

Tom,

How does the rail observer have everything arranged so that the flares are seen by him to ignite simultaneously in his frame?

 

[quantumdude]

Tom,

How does the rail observer have everything arranged so that the flares are seen by him to ignite simultaneously in his frame?

It makes no difference to the thought experiment what the actual mechanism is, but...

He could have identical wires connected to the flares, and send an electrical signal from a common source to ignite the flares simultaneously.