How do you explain c?

[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.

[Tom Mattson]

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.

[Tom Mattson]

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". :redface:

[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/einstein/specrel/www/?CFID=4299126&CFTOKEN=28870118&jsessionid=06302662281082217897574

[Tom Mattson]

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 any body 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:

[Tom Mattson]

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?

[Tom Mattson]

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.



Seen the movie 'Contact'? 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? :rofl:

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

[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????

[Tom Mattson]

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?

[Tom Mattson]

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. 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 untill 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 refering 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.

[Tom Mattson]

"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).

[Tom Mattson]

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 refering to when he said the motion between conductor and magnet wasn't relative. I have to check on that.

[Tom Mattson]

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)(-D)]/[γ(v/c+1)(D/c)]

See how the factors in blue 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 realise 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 accomodated 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 accomodate 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.

[Tom Mattson]

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 experimentaly verified (some decades ago, in fact). The postulate doesn't need anyone to "make it good". The postulate is "good" all by itself.


I realise 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 experimentaly 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 accomodate 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.

[Tom Mattson]

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? :confused:

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 accomodate 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? :confused:
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 accomodate 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]

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: http://www.physicsforums.com/showpost.php?p=255677&postcount=112 :smile:

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

[Tom Mattson]

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.

[Tom Mattson]

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


Yes, and the key word is "was". 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 accomodate 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?

[Tom Mattson]

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.

[zoobyshoe]

He could have identical wires connected to the flares, and send an electrical signal from a common source to ignite the flares simultaneously.
Yes, but if he's interested in visually confirming that the flares are simultaneous in his rest frame, he has to be positioned equidistant from the flares when they go off. The light must have a path from the front flare to him that is equal in distance from the rear flare to him. Only by knowing that these distances are equal when he causes the emission (and we can stipulate he has the ability to hit the button at the right time to make it so) will he know that the flares were simultaneous because the light from both will reach him simultaneously, no?

[Tom Mattson]

Yes, but if he's interested in visually confirming that the flares are simultaneous in his rest frame, he has to be positioned equidistant from the flares when they go off. The light must have a path from the front flare to him that is equal in distance from the rear flare to him.


OK, fine let him be equidistant from the flares.


Only by knowing that these distances are equal when he causes the emission (and we can stipulate he has the ability to hit the button at the right time to make it so) will he know that the flares were simultaneous because the light from both will reach him simultaneously, no?

No. He doesn't have to actually see the light pulses at the same time. In fact, he needn't see them at all. He can know that the pulses ignited simultaneously with photodetectors that are connected to clocks. The photodetectors need not even be equidistant from the simultaneous flash. All that needs to be known is the position of each photodetector, the position of the flash, and the time at which the button was hit.

[zoobyshoe]

OK, fine let him be equidistant from the flares.



No. He doesn't have to actually see the light pulses at the same time. In fact, he needn't see them at all. He can know that the pulses ignited simultaneously with photodetectors that are connected to clocks. The photodetectors need not even be equidistant from the simultaneous flash. All that needs to be known is the position of each photodetector, the position of the flash, and the time at which the button was hit.
Ok, I'm confused about in which reference frame you want the flares to be simultaneous. It sounds like you want them to be simultaneous in the rods reference frame.

edit: You mean the detector/clocks are in the track reference frame with him?

[Tom Mattson]

Ok, I'm confused about in which reference frame you want the flares to be simultaneous. It sounds like you want them to be simultaneous in the rods reference frame.


No, the flares should ignite simultaneously in the frame of the track (the same frame as the guy who is watching the rod speed by). That's the only way his measurement could be called a "length" measurement.


edit: You mean the detector/clocks are in the track reference frame with him?

Yes.

[zoobyshoe]

No, the flares should ignite simultaneously in the frame of the track (the same frame as the guy who is watching the rod speed by). That's the only way his measurement could be called a "length" measurement.
Good.

The clock/detectors are more realistic, but for simplicity I'd rather stick with him being equidistant from the flares when they go off.

It is no problem to arrange it so the midpoint of the rod is directly in front of him when the flares ignite. This way the light has a path of equal length from each flare to him. If both beams of light reach him at the same instant, he knows the emission was simultaneous. Which it is.

The guy on the rod could be anywhere on the rod, but if we put him exactly at the midpoint of the rod something very interesting results: he too, recieves the beams of light simultaneously.

That seems ridiculous because he is in motion and should, intuitively reasoning, encounter the forward beam before the rear beam. However, that would mean you are adding and subtracting velocities, which you can't do with light. The speed of light is the same to all observers in all inertial frames. He can't encounter the forward beam at c plus his own velocity. He must regard himself as being at rest with the light approaching him at c, and the end of the rod approaching him at the velocity of the rod over the track.

The beam from the rear cannot approach him at less than c just because he is moving away from it. He must regard himself as at rest with the light approaching him at c and the back end of the rod moving away from him at the velocity of the rod over the track.

He is at the exact centerpoint of the rod, both beams of light have the same distance to travel to reach him, both will do it at the same velocity, c, both will reach him simultaneously.

Looking down, he will see a contracted rail and will expect the flare marks to measure greater than a meter apart when he goes back to measure them later in the rail rest frame.

[Tom Mattson]

The guy on the rod could be anywhere on the rod, but if we put him exactly at the midpoint of the rod something very interesting results: he too, recieves the beams of light simultaneously.


No, he doesn't, because the flares don't ignite simultaneously in his frame.

[zoobyshoe]

No, he doesn't, because the flares don't ignite simultaneously in his frame.
Let the time t when the midpoint of the rod is directly in front of the track observer be the point of synchrony between any clock that observer may have and any clock the rod observer may have such that t=o, the time of emission, is the point of synchrony of clocks for both observers.

[Tom Mattson]

Let the time t when the midpoint of the rod is directly in front of the track observer be the point of synchrony between any clock that observer may have and any clock the rod observer may have such that t=o, the time of emission, is the point of synchrony of clocks for both observers.

It doesn't matter when you zero both clocks. The flares ignite simultaneously in exactly one frame, and no other. If the flares were at the same location, then their ignition would be simultaneous in all frames. But that isn't what is happening here--these flares are spatially separated.

Let Event 1 be the rear flare igniting and Event 2 be the front flare igniting.

For observer S (the guy watching the rod zip by):
Δx=x2-x1=L (the length of the rod according to him)
Δt=t2-t1=0 (the flares ignite simultaneously according to him)

For observer S' (the guy standing on the rod):
Δt'=t2'-t1'=γ(Δt-vΔx/c2)
Δt'=γ(0-vL/c2)
Δt'=-γvL/c2

See? Δt' is negative (not zero). This means that, according to the guy on the rod, event 1 (the rear flare igniting) occurs later than event 2 (the front flare igniting). If the two flares ignite at different times, and the observer is at their midpoint, then there is no way that he is going to receive both pulses simultaneously.

[zoobyshoe]

Tom,

I'm having question mark troubles again. I'm going to type in an example of what your equations look like, including question marks:

?t'=t2 ' -11'=?(?t-v?x/c2)

Does this show up on your screen with 4 question marks in the equation? If so, that's what it looks like to me. If not my browser lacks some ability to properly translate whatever it is you are typing in. Latex seems to work fine on my browser.

[Tom Mattson]

?t'=t2 ' -11'=?(?t-v?x/c2

Does this show up on your screen with 4 question marks in the equation?

Yes, I see 4 question marks. I haven't learned how to use LaTeX yet ( :redface: ), but the equation should look like this:

Delta(t')=t2'-t1'=(gamma)(Delta(t)-vDelta(x)/c2)

It's the Lorentz transformation for a time interval. It's the "interval" version of equation 1d on this page:

http://www.physics.nyu.edu/courses/V85.0020/node45.html

[zoobyshoe]

It's the Lorentz transformation for a time interval. It's the "interval" version of equation 1d on this page:

http://www.physics.nyu.edu/courses/V85.0020/node45.html
Tom,

That site is very interesting. I have never seen so many different manifestations of the Lorentz Transformation.

Now the one you used, you say, is the one for a time interval. The time interval you are applying it to is the interval between event one and event two, the times of emission of the rear and forward beams of light.

My first thought is to wonder if this is the right interval to be applying it to. It seems to me that the simultaneity shouldn't be obviously relative to anyone till the time of detection. I think the interval we're supposed to be applying the transformation to, is the interval between detection of the light from the two separate sources by the rail observer: the interval between his detection of the light from the rear flare and his detection of the light from the forward flare. What do you think?

[Tom Mattson]

My first thought is to wonder if this is the right interval to be applying it to. It seems to me that the simultaneity shouldn't be obviously relative to anyone till the time of detection.


No, we should be using the emissions as events, because it is the simultaneous emissions that mark the length of the rod. Whether or not the detctions are simultaneous is irrelevant to the thought experiment. Indeed, as has been noted, the pulses need not be seen by anyone at all.


I think the interval we're supposed to be applying the transformation to, is the interval between detection of the light from the two separate sources by the rail observer: the interval between his detection of the light from the rear flare and his detection of the light from the forward flare. What do you think?

As I said, the time interval between the flares being detected is not relevant. However, it just so happens that in this case (because you've got both observers equidistant from the flares) that the chronological order of emission will be the same as the chronological order of detection.

So the guy in the frame of the track sees the pulses at the same time, and the guy on the rod doesn't.

[zoobyshoe]

No, we should be using the emissions as events, because it is the simultaneous emissions that mark the length of the rod. Whether or not the detctions are simultaneous is irrelevant to the thought experiment. Indeed, as has been noted, the pulses need not be seen by anyone at all.
Yes, the simultaneous emissions mark the length of the rod, but the whole point of the experiment is to compare what the rail observer sees with the marks, and ask the question: will the marks be separated by a length equal to the length the rod looked to be when it was in motion?

The observer can't see the emissions at the time of emission. He is ignorant about any apparent length interval between them untill their light reaches him.
As I said, the time interval between the flares being detected is not relevant.
I can't agree with this. The detection is all important. The detection tells the observer when the emission occured. Detecting the light simultaneously when he is equidistant from the sources, assures him that the emissions were simultaneous in his frame.
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).

When you say nobody even has to be there to see them, that is only because you offer a mechanical substitute for the observer which is the same thing: an observer. There has to be an observer, human or mechanical, to detect the light simultaneously. Otherwise the conditions of the experiment are not fullfilled. The whole thing is about the difference, if any, between what happens and what an observer sees.
However, it just so happens that in this case (because you've got both observers equidistant from the flares) that the chronological order of emission will be the same as the chronological order of detection.
I can't claim to understand the formula you're using very well but it seems, from what you say, to be one you can use to transform the value of a measured time interval in one frame to what that interval will measure in another frame. If that's the case, then yes it should apply equally well to the detection interval.

However, I believe that transforming the emission interval is barking up the wrong tree. The time of emission is a time of ignorance for both observers: the rail guy and the guy on the rod. I believe the thought experiment, as presented, allow us only one objective piece of information which can be transformed from the rail frame to the rod guy: the interval of detection for the rail guy.

[Tom Mattson]

Yes, the simultaneous emissions mark the length of the rod, but the whole point of the experiment is to compare what the rail observer sees with the marks, and ask the question: will the marks be separated by a length equal to the length the rod looked to be when it was in motion?

The observer can't see the emissions at the time of emission. He is ignorant about any apparent length interval between them untill their light reaches him.


Whether or not he can see the flashes is irrelevant. All he needs to know is that they are simultaneous (and he does not need to see them to know that) and how far apart they are. If he knows that they were simultaneous, then he can go up to the marks at his leisure and measure the distance between them.


Tom: As I said, the time interval between the flares being detected is not relevant.

zoobyshoe: I can't agree with this. The detection is all important. The detection tells the observer when the emission occured. Detecting the light simultaneously when he is equidistant from the sources, assures him that the emissions were simultaneous in his frame.


I mean that the time interval between the two lights being detected is not relevant to the calculation with the Lorentz transformation. Yes, we need to know the time and location of the detection so that we can go back and determine when and where the emission occured. But you were inquiring about what we should be applying the Lorentz transformation to, and the time interval for detection of the pulses is not it. We need to apply it to the time interval for emission to get the length of the rod in each frame.


When you say nobody even has to be there to see them, that is only because you offer a mechanical substitute for the observer which is the same thing: an observer. There has to be an observer, human or mechanical, to detect the light simultaneously. Otherwise the conditions of the experiment are not fullfilled. The whole thing is about the difference, if any, between what happens and what an observer sees.


No, the light does not have to be detected at all. The reason is that the light is not the only indicator of the ignition. For instance, you can have each flare trip a switch that stops a stopwatch at the moment of ignition.

Yes, we have to take experimental data of some sort on the time and place of ignition in each frame.

No, the light from the flares need not be observed by anyone or anything. The flares and the light from them are purely incidental. The exact same thought experiment could be done with lightless markers, and it wouldn't change a thing.


I can't claim to understand the formula you're using very well but it seems, from what you say, to be one you can use to transform the value of a measured time interval in one frame to what that interval will measure in another frame. If that's the case, then yes it should apply equally well to the detection interval.


The Lorentz transformation does apply to any interval, including the detection interval. But I am not bothering with Lorentz transforming the detection interval, because that interval is not related to the length of the rod in any frame. The observer could be anywhere in his frame, and the time interval between detections could be anything according to him. It makes no never mind whatsoever to the simultaneity (or lack thereof) of the events, except of course that whatever time interval he does measure between detected light pulses will be consistent with the simultaneity/nonsimultaneity of the events in his frame.


However, I believe that transforming the emission interval is barking up the wrong tree. The time of emission is a time of ignorance for both observers: the rail guy and the guy on the rod. I believe the thought experiment, as presented, allow us only one objective piece of information which can be transformed from the rail frame to the rod guy: the interval of detection for the rail guy.

No. You can use the information about the detection to calculate back to the information about the emission, and indeed you must. That's the only way we can say anything about the length of the rod according to any observer. It's not the detections that are used to measure the length of the rod, it's the emissions.

[zoobyshoe]

Tom,
I think I found the equations you are using in one of my books.

Are these them? :

\Delta t=\gamma(\Delta t'+v\Delta x'/c^2)

\Delta t'=\gamma(\Delta t-v\Delta x/c^2)

[Tom Mattson]

Tom,
I think I found the equations you are using in one of my books.

Are these them? :

\Delta t=\gamma(\Delta t'+v\Delta x'/c^2)

\Delta t'=\gamma(\Delta t-v\Delta x/c^2)

Those are them. I'll learn to TeX this weekend.

[zoobyshoe]

Here's gamma:

\gamma = \frac{1}{\sqrt{1- \beta^2}}

\beta = \frac {v}{c}

[zoobyshoe]

Or:

\gamma = \frac{1}{\sqrt{1 -(\frac{v}{c})^2}}



Tex tips:

gamma = \gamma

fraction = \frac followed by {stuff in numerator}{denominator} (that is: you indicate the difference with these: {}{} numerator first, then denominator

Square root = \sqrt followed by: {everything you want under the square root sign}

beta =\beta

Delta (different than \delta) = \Delta

squared = number to be squared followed by ^2

[/ tex] to end the whole line, and [tex] to begin it.

Add more to your store of abilities as you go by clicking on the quote button of any post with some Tex you want to be able to use, and observe how they did it, or look through the Tex thread till you find what you need.

Always good to preview your post before submitting because it's easy to miss a \ or an ending } when you're typing along. The "preview post" feature in any thread can be used to practise to your heart's content, I also realised. (Just abandon it when you're done, don't hit "submit reply".)

[zoobyshoe]

In Halliday and Resnick the thought experiment goes like this:
Interestingly enough, I found these:

\Delta t=\gamma(\Delta t'+v\Delta x'/c^2)

\Delta t'=\gamma(\Delta t-v\Delta x/c^2)

in Halliday and Resnik. I didn't even realise I had this book. I pick up physics texts all the time at the swap meet for peanuts just in case one will have a explanation of something that's easier to grasp than some other source.

Any way, what edition do you have? I can't find the flare gedanken in mine, at least not in the relativity part. They spread some relativity into other parts, though.

[Tom Mattson]

Any way, what edition do you have?


I have the 2nd, 4th, and 5th editions.

Mind you, the thought experiment in H+R may not have actually involved flares. I really don't remember, because it's been awhile. As I said, the flares are totally incidental. But the basic idea is taught there: Only simultaneous measurements of the position of the ends of the rod constitute a "length measurement".

[zoobyshoe]

I have the 2nd, 4th, and 5th editions.
We're clearly fated to be out of phase, Tom. I have the third edition, 1988.
Mind you, the thought experiment in H+R may not have actually involved flares. I really don't remember, because it's been awhile. As I said, the flares are totally incidental. But the basic idea is taught there: Only simultaneous measurements of the position of the ends of the rod constitute a "length measurement".
Yeah, hehehehehe. I think the flare experiment is more of a Tom Mattson original than you think. In my copy all they do is warn you to mark the positions of the head and tail of your goldfish simultaneously (in your reference frame) rather than arbitrarily. They don't propose any mechanism to do this.

What they actually say about the "reality" of length contraction is essentially what Eddington says:

"The questions, `Does the rod really shrink?' and `Do the atoms in the rod really get pushed closer together?' are not proper questions within the framework of relativity. The length of the rod is what you measure it to be and motion affects measurements."

p.962 3rd edition 1988.

They don't have any gedakens where the moving thing actually leaves physical marks on the stationary one. It is clear that you fully believe your flare and rod thing is an obvious extrapolation of what they're saying, but they, like Eddington, are carefully avoiding saying exactly what you think they're saying.

If you proposed your flare thing to Halliday and Resnik, I believe they would say what they said: "It's not a proper question in the framework of relativity."

[Tom Mattson]

Yeah, hehehehehe. I think the flare experiment is more of a Tom Mattson original than you think. In my copy all they do is warn you to mark the positions of the head and tail of your goldfish simultaneously (in your reference frame) rather than arbitrarily. They don't propose any mechanism to do this.


Well, the flares certainly provide a means to do it.


They don't have any gedakens where the moving thing actually leaves physical marks on the stationary one. It is clear that you fully believe your flare and rod thing is an obvious extrapolation of what they're saying, but they, like Eddington, are carefully avoiding saying exactly what you think they're saying.


It is an obvious extrapolation of what they say. It makes no comment whatsoever on what "really" happens to the rod. It simply provides a means of simultaneously recording the positions of the two ends of it.


If you proposed your flare thing to Halliday and Resnik, I believe they would say what they said: "It's not a proper question in the framework of relativity."

They would not say that at all, because it's a perfectly proper question in the framework of relativity.

"Proper questions" in the framework of relativity are questions that relate to intervals in spacetime. That much should be clear from even a glance at the Lorentz transformation. The measurement scheme I have used does only one thing: It records the places and times of events.

If that thought experiment is not a proper question in the framework of relativity, then there are no proper questions in the framework of relativity.

What makes you think otherwise?

[pmb_phy]

I'm new to this thread so please bear with me. I took a look at the first posts in this thread but there are too many for me to read (due to my back and the pain of sitting and reading). But I agree with the original post to some extent, and to the extent that I understood what he was trying to say.

He was suggesting that the reason that the speed of light is constant has something to do with space changing. That is true. The reason why c is invariant is due to a combination of Lorentz contraction and time dilation. A close and thoughful look at the transformation rules for velocity shows that.

Also there is nothing electromagnetic about Lorentz contraction. Its distances that contract and that's why the lengths of rods contract. All one need to do in order to see that is true is to consider the distance between two point particles which are seperated in space. The distance between them is contracted and there is no physical connection between them.

Pete

[zoobyshoe]

If that thought experiment is not a proper question in the framework of relativity, then there are no proper questions in the framework of relativity.

What makes you think otherwise?
Ah! Don't ask me! Ask them. I am merely quoting their respose:"The questions`Does the rod really shrink?' and `Do the atoms in the rod really get pushed closer together?' are not proper questions in the framework of relativity"

Is your thought experiment proper in my estimation? Is it "proper" to try and pin down the most literal possible proof of length contraction? Absolutely.

My point is that "In Halliday and Resnik the thought experiment goes like this" ought to have been something more like: "Extrapolating from what Halliday and Resnik say we can use flares and a rod", and so on, and so forth. The way you phrased it gives the unequivocal impression that very set up is to be found in their book. (They do have a thing with a train and clocks, and they have a goldfish, but they don't have a rod and flares, or anything where the moving body leaves physical marks on the stationary one.)

[zoobyshoe]

He was suggesting that the reason that the speed of light is constant has something to do with space changing. That is true.
Hi Pete,

Yes, but he also had some point about the angle at which you encounter the light changing untill at c you would theoretically be encountering it at 90º. Could you make any sense out of that?

-Zooby

[pmb_phy]

Hi Pete,

Yes, but he also had some point about the angle at which you encounter the light changing untill at c you would theoretically be encountering it at 90º. Could you make any sense out of that?

-Zooby
No. I was totally lost on what he was talking about. Too bad we can't have a black board here huh? :biggrin:

Pete

[zoobyshoe]

No. I was totally lost on what he was talking about. Too bad we can't have a black board here huh? :biggrin:
I'm not sure it wouldn't just give people an even greater capacity to confuse me. :-)

[Tom Mattson]

Ah! Don't ask me! Ask them. I am merely quoting their respose:"The questions`Does the rod really shrink?' and `Do the atoms in the rod really get pushed closer together?' are not proper questions in the framework of relativity"


But I don't need to ask them. "Proper questions" in SR pertain to spacetime intervals, and that's precisely what this thought experiment is about. I could go down the hall and ask Resnick (he's at my school) to verify that, but he'd probably think I'm a simpleton.


Is your thought experiment proper in my estimation? Is it "proper" to try and pin down the most literal possible proof of length contraction? Absolutely.


It would help both this discussion and your personal understanding of relativity a great deal if you would have a good look at the Lorentz transformation. Then, you could see for yourself that questions of spacetime intervals are proper questions in SR, in the strictest sense.


My point is that "In Halliday and Resnik the thought experiment goes like this" ought to have been something more like: "Extrapolating from what Halliday and Resnik say we can use flares and a rod", and so on, and so forth. The way you phrased it gives the unequivocal impression that very set up is to be found in their book.


I double checked, and the scenario in fact does not appear exactly as I described it (more on this below). But so what? This isn't about flares or identical wires, it's about the Lorentz transformation, simultaneity, and length measurements. In other words, it's about everything that isn't being discussed, because we are so lost in these irrelevant tangents about the actual mechanisms of the thought experiments and who saw which light pulse in what order. I'm sorry I ever mentioned "flares", because it has become a focal point of the discussion.


(They do have a thing with a train and clocks, and they have a goldfish, but they don't have a rod and flares, or anything where the moving body leaves physical marks on the stationary one.)

They do in the 4th and 5th editions.

Upon double checking, I found that the length contraction thought experiments are done with stopwatches and trains, as you say. But flipping back a page to the section on the relativity of simultaneity, we find in my copies of the text the "flare" thought experiment that I tried unsuccessfully to recall in all its details. The scenario has 2 rocket ships passing each other. They are close enough so that 2 flares ignite simultaneously in one frame, but not in another, and they leave permanent marks on the ships. The thought experiment stops with the discussion of simultaneity, but since length contraction can be derived from it, I see no reason not to say what I said before: This is an obvious extrapolation of what Halliday and Resnick does say.

[pmb_phy]

Hi Pete,

Yes, but he also had some point about the angle at which you encounter the light changing untill at c you would theoretically be encountering it at 90º. Could you make any sense out of that?

-Zooby

Perhaps the angles he was speaking of were from his vizualization of the moving body. We think in terms of math and coordinate systems. Perhaps he's thinking of what he sees as a body passes him by, like a train passing a person staning on one side of the track. Our heads are atr first looking to one direction, the direction the train is comming. Then that line of sight changes angularly. Perhaps that's the angle he was speaking of. And it is true that angles do change upon Lorentz transformation.

Pete

[zoobyshoe]

This is an obvious extrapolation of what Halliday and Resnick does say.
Only in the sense that it's an obvious extrapolation of any good text on relativity.

Anyway, what is the signifigance of a negative value for the time interval in the t' frame? What's negative time?

[Chronos]

Anyway, what is the signifigance of a negative value for the time interval in the t' frame? What's negative time?

Short answer is, the past. Negative t is a problem when you try to do the math. The solutions end up being the square root of a negative number. Those results do not have predictive value [using the term 'predictive' in the future tense].

[Tom Mattson]

Only in the sense that it's an obvious extrapolation of any good text on relativity.

Well, I'm sorry that swapping two rocket ships for a rod and rail has confused you so much, but the fact of the matter is that the thought experiment described in Halliday and Resnick can be used to teach length contraction with just a line or two of math. But if you don't understand the Lorentz transformation, then it would seem as though they were worlds apart.


Anyway, what is the signifigance of a negative value for the time interval in the t' frame? What's negative time?

If you set your stopwatch to t=0 when a flare ignites, then t<0 corresponds to those moments before the flare ignited. I'm sure that at some point you've heard the countdown to a rocket launch: "T-minus-10....T-minus-9...etc."

It's the same thing.

However, I wasn't talking about negative time. I was talking about a negative time interval. If t2-t1 is less than zero, it means that t1 is greater than t2. That means that t event 1 occurs later than event 2.

[zoobyshoe]

Short answer is, the past. Negative t is a problem when you try to do the math. The solutions end up being the square root of a negative number. Those results do not have predictive value [using the term 'predictive' in the future tense].
Thanks Chronos,

The specific situation is this, from Tom's breakdown of the flare/rod gedanken:
For observer S' (the guy standing on the rod):
?t'=t2'-t1'=?(?t-v?x/c2)
?t'=?(0-vL/c2)
?t'=-?vL/c2

See? ?t' is negative (not zero). This means that, according to the guy on the rod, event 1 (the rear flare igniting) occurs later than event 2 (the front flare igniting). If the two flares ignite at different times, and the observer is at their midpoint, then there is no way that he is going to receive both pulses simultaneously.
The interval in the t frame, an interval of 0, becomes a negative interval in the t' frame, which is not 0. (It has some very small value which, given a meter rod, varies according to what specific speed it has.)

How do we "locate" this negative, "past" interval of time with respect to t? Does one end of the negative interval fall on t=0, and the other at t= -.0000000001 (for instance)?

[Tom Mattson]

How do we "locate" this negative, "past" interval of time with respect to t?

The same way the folks at NASA locate "T-minus-10": with a clock.


Does one end of the negative interval fall on t=0, and the other at t= -.0000000001 (for instance)?

Yes.

[zoobyshoe]

The same way the folks at NASA locate "T-minus-10": with a clock.
I think you were composing your post to me at the same time I was composing mine to chronos. Your answer wasn't up yet when I submitted. I wasn't ignoring it.

So, you are saying if we get a value of, for example, t' = -.00000001 one end of the interval would be located at that position and the other at 0'?

[Tom Mattson]

So, you are saying if we get a value of, for example, t' = -.00000001 one end of the interval would be located at that position and the other at 0'?

If the event to which you ascribe t' = -.00000001 occurs .00000001 time units earlier than the event to which you ascribe 0', then the time coordintate of the first event is as you say.

[zoobyshoe]

OK. You want me to be more familiar with the LT. Let's practise:

\Delta t' = \gamma(\Delta t - v\Delta x/c^2)

Let's plug a value of .5 c in for rod velocity.

For gamma that gives \gamma = 1.1547005

x= length of rod = 1 meter = 1

\Delta t = 0, c^2 = 9^1^0

Therefore: \Delta t' = 1.1547005(-150,000/9^1^0)

so: \Delta t' = 1.1547005(1.6667^-^0^6) = 1.9245^-^0^6

I am reasonably sure this is right, but it would be best if you checked it thoroughly to see if I have misconstrued anything.

[Tom Mattson]

Almost. c2=9*1016 m2/s2, so your final answer should be 1.9245*10-9 s. But I didn't intend for you to get bogged down in numerical calculations. What I think you need to do is learn what the Lorentz transformation means.

First, look at what it accepts as inputs: spacetime coordinates. So, experiments designed to test SR (aka the "proper questions in the framework of SR") are those experiments that record spacetime coordinates. This can be done with clocks, meter sticks, flares ( :biggrin: ), electrical switches, what have you. If it accurately captures the spacetime coordinates of events, then it is a pertinent issue in SR.

Second, think about what your numerical result means. As has been discussed, a time interval in frame S' given by \Delta t\'\; = \gamma(\Delta t - v\Delta x/c^2) (look ma, I'm TeX-ing!) is taken to be the difference between times t_2-t_1. So, if \Delta t\'\; = \gamma(\Delta t - v\Delta x/c^2) comes out negative, then it means that t_1 is greater than t_2. This means that Event 1 happens later than Event 2 in the frame S'.

With me so far?

[zoobyshoe]

Almost. c2=9*1016 m2/s2, so your final answer should be 1.9245*10-9 s.
This is because I failed to keep my units consistent, right? If I choose meters for the rod I can't use kilometers for the velocities. (DOH!) I could have stuck with the kilometers had I used .001 for x, I guess.
But I didn't intend for you to get bogged down in numerical calculations. What I think you need to do is learn what the Lorentz transformation means.
For some reason, I can't grasp any equation till I can plug values into it and work them out. Till I can do that, it's a meaningless abstraction to me.
First, look at what it accepts as inputs: spacetime coordinates.
Yep, I get this aspect.
Second, think about what your numerical result means. As has been discussed, a time interval in frame S' given by \Delta t\'\; = \gamma(\Delta t - v\Delta x/c^2) (look ma, I'm TeX-ing!) is taken to be the difference between times t_2-t_1. So, if \Delta t\'\; = \gamma(\Delta t - v\Delta x/c^2) comes out negative, then it means that t_1 is greater than t_2. This means that Event 1 happens later than Event 2 in the frame S'.
Glad you explained that. I was wondering how you'd determined which was first.

So the events in frame t' take place 1.9245 -09 seconds apart? That is: .0000000019245 of a second apart?

[zoobyshoe]

Ground control to Major Tom. We have lost your signal. Do you read us?

[zoobyshoe]

Anyway, whoever's reading this:

my next question is how far apart, exactly, will the marks left by the flares be according to Tom's method.

First I asked myself, how long would it take something to travel one meter at 150,000 km/s?

150,000 km/s = 1.5 08 m/s

1/1.508 = 6.6667-09

The speed of the rod at .5c is 1 meter every 6.6667-09 seconds.

We've determined the time interval between the flashes in the t' frame will be 1.9245-09 seconds.

How far wll any point on the rod travel in 1.9245-09 seconds at 1 meter each 6.6667-09 seconds?

1.9245-09 times 6.6667-09 = 1.283006415-17 meters.


If event 1 (the rear flare) is first, as Tom says, then it goes off, the rod moves 1.283006415-09 meters, then the front flare goes off.

This will leave marks 1.00000000000000001283006415 meters apart. Or perhaps even more if we consider that the track is contracted to the guy on the rod.

If, perhaps, we've been wrong about event 1 (the rear flare) being first, then the flares will leave marks that are .99999999999999998716993584 of a meter apart, or perhaps more if we consider the track is contracted to the rod guy.

In all cases these marks are too far apart to stand in support of Tom's argument. By the Lorentz Transformation for length contraction, a meter-rod traveling at .5c should leave marks that are .8660254 of a meter apart (if you want to claim that length contraction is real).

[Tom Mattson]

Whoops, I hadn't noticed that you'd responded.

This is because I failed to keep my units consistent, right? If I choose meters for the rod I can't use kilometers for the velocities. (DOH!) I could have stuck with the kilometers had I used .001 for x, I guess.


Right. Notice that you were off by a power of 10. When you're working in SI units, that's a strong indicator that you mixed up "kilo-units", "milli-units", etc..., with the "regular" units.


For some reason, I can't grasp any equation till I can plug values into it and work them out. Till I can do that, it's a meaningless abstraction to me.


Nothing wrong with that.


So the events in frame t' take place 1.9245 -09 seconds apart? That is: .0000000019245 of a second apart?

Yes.

I'll respond to your other post later.

edit: fixed a bracket

[Doc Al]

my next question is how far apart, exactly, will the marks left by the flares be according to Tom's method.
By "Tom's method" I presume you mean having the flares go off simultaneously according to the track frame (the unprimed frame) and then measuring where the marks appear on the track. This would give you a meaningful measurement of the length of the rod according to the track observers.

First I asked myself, how long would it take something to travel one meter at 150,000 km/s?
Uh oh. Let's put this aside for the moment.

We've determined the time interval between the flashes in the t' frame will be 1.9245-09 seconds.
OK, I'll take your word for that. But the time interval in the track (unprimed) frame is zero.

How far wll any point on the rod travel in 1.9245-09 seconds at 1 meter each 6.6667-09 seconds?
Careful. In the rod (primed) frame, the rod doesn't move at all! (And in the track (unprimed frame) the flares are simultaneous so the rod doesn't have time to move.)

If event 1 (the rear flare) is first, as Tom says, then it goes off, the rod moves 1.283006415-09 meters, then the front flare goes off.
You are mixing up frames. The rear flare goes off first according to the rod frame, not according to the track frame.

This will leave marks 1.00000000000000001283006415 meters apart. Or perhaps even more if we consider that the track is contracted to the guy on the rod.
Nope.

If, perhaps, we've been wrong about event 1 (the rear flare) being first, then the flares will leave marks that are .99999999999999998716993584 of a meter apart, or perhaps more if we consider the track is contracted to the rod guy.
The right way to find the \Delta x measured by the track frame is to use the LT for distance: \Delta x' = \gamma (\Delta x - v\Delta t). Since \Delta t = 0, \Delta x = \Delta x'/\gamma--thus the usual length contraction is seen, as expected.

In all cases these marks are too far apart to stand in support of Tom's argument. By the Lorentz Transformation for length contraction, a meter-rod traveling at .5c should leave marks that are .8660254 of a meter apart (if you want to claim that length contraction is real).
Oh, it's real... and it's spectacular! :smile:

[zoobyshoe]

By "Tom's method" I presume you mean having the flares go off simultaneously according to the track frame (the unprimed frame) and then measuring where the marks appear on the track. This would give you a meaningful measurement of the length of the rod according to the track observers.
Correct.
But the time interval in the track (unprimed) frame is zero.
I'm perfectly aware of that.
In the rod (primed) frame, the rod doesn't move at all! (And in the track (unprimed frame) the flares are simultaneous so the rod doesn't have time to move.)
Sophistry.
You are mixing up frames. The rear flare goes off first according to the rod frame, not according to the track frame.
Yes, I know. I haven't mixed the frames.
Nope.
Yup.
The right way to find the \Delta x measured by the track frame is to use the LT for distance:
We are exploring Tom's gedanken and methods here. So far they don't seem to work.
Oh, it's real... and it's spectacular! :smile:
A bald assertion.

[Tom Mattson]

I agree to a certain extent that zoobyshoe has not mixed frames, but only unwittingly and by the wrong reasoning. He takes a time interval from S' and multiplies it by (what he thinks is) the speed of the rod. Of course, we all know that the speed of the rod is zero in S', but by reciprocity S' does see the track moving backwards at the same speed that S sees the rod moving forwards. So, multiplying that time by that speed is physically meaningful. It is the length of track that S' sees go by.

The real problems in zoobyshoe's analysis are these.

First:


How far wll any point on the rod travel in 1.9245-09 seconds at 1 meter each 6.6667-09 seconds?

1.9245-09 times 6.6667-09 = 1.283006415-17 meters.


In a word: No.

You are being careless with units again, and this time it is more severe than the last, because you aren't just off by a numerical factor. This time, your answer doesn't even have the same dimensions as the left hand side. The number 1.9245*10-9 is a number of seconds. And the number 6.6667*10-9 is also a number of seconds. You do not get a distance by multiplying two times together.

Second:


If event 1 (the rear flare) is first, as Tom says, then it goes off, the rod moves 1.283006415-09 meters, then the front flare goes off.


You're mistaken. I said that Event 1 occurs later in S'. Of course, if it occurs first, then this analysis will fail.

edit: fixed superscript bracket

[Tom Mattson]

Doc AI: By "Tom's method" I presume you mean having the flares go off simultaneously according to the track frame (the unprimed frame) and then measuring where the marks appear on the track. This would give you a meaningful measurement of the length of the rod according to the track observers.

zoobyshoe: Correct.


In that case, you are mistaken: the method is not mine, but Einstein's.

All I have done is stipulate the setup. The method of analysis is SR. If you say the method doesn't work, then you are saying that SR doesn't work. Needless to say, that statement would require a great deal of explanation and evidence before being moved to Theory Development.


zoobyshoe: This will leave marks 1.00000000000000001283006415 meters apart. Or perhaps even more if we consider that the track is contracted to the guy on the rod.

Doc AI: Nope.

zoobyshoe: Yup.


Nope.

And furthermore, there is no "perhaps" about the issue. The Lorentz transformation is not vague or fuzzy.


We are exploring Tom's gedanken and methods here. So far they don't seem to work.


They do if you don't screw up the math.


A bald assertion.

Again: Nope.

Do you think you could possibly tone down the know-it-all attitude until you've demonstrated some ability to properly conduct this analysis? At this stage of your education, when you get a result that contradicts SR the first thing that should enter your mind is the question, "Where did I go wrong?"

If you want to ask questions, go right ahead. I'm here. But if you want to tell this Forum "how it is", then you can teach yourself relativity as far as I'm concerned. I, for one, certainly don't need to hear how SR works from someone who would flunk a relativity course in real life.

PS: The points that you label "sophistry" and "bald assertion" were exactly right, on the part of Doc AI.

edit: fixed bracketing errors

[zoobyshoe]

I agree to a certain extent that zoobyshoe has not mixed frames, but only unwittingly and by the wrong reasoning. He takes a time interval from S' and multiplies it by (what he thinks is) the speed of the rod. Of course, we all know that the speed of the rod is zero in S', but by reciprocity S' does see the track moving backwards at the same speed that S sees the rod moving forwards. So, multiplying that time by that speed is physically meaningful. It is the length of track that S' sees go by.
My lack of rigour in refering to the speed of the rod as opposed to the speed of the track is noted. But, as you point out, this is not what is causing the problem at all:
The real problems in zoobyshoe's analysis are these....You are being careless with units again, and this time it is more severe than the last, because you aren't just off by a numerical factor. This time, your answer doesn't even have the same dimensions as the left hand side. The number 1.9245*10-9 is a number of seconds. And the number 6.6667*10-9 is also a number of seconds. You do not get a distance by multiplying two times together.
I meter per 6.6667-09 seconds is a rate of speed. As far as I can tell, it is a valid expression of rate of speed. Somehow, I am misunderstanding how to relate it too 1.9245 -09 to get the distance traveled by the rod in that time.
You're mistaken. I said that Event 1 occurs later in S'. Of course, if it occurs first, then this analysis will fail.
You are absolutely correct, that is what you said. I have no conception of how I reversed it in my mind. My bad, though.

[zoobyshoe]

Do you think you could possibly tone down the know-it-all attitude until you've demonstrated some ability to properly conduct this analysis?
What comes off as a know-it-all attitude is actually something else: a profound desperation not to be further confused.
At this stage of your education, when you get a result that contradicts SR the first thing that should enter your mind is the question, "Where did I go wrong?"
This is, in fact, the first thing I suspected and always do suspect. However, I'm generally not in a position to figure out where I went wrong. I can only present the contradiction to you as it looks to me, and let you spot my mistake. When you're right, when you've hit the nail on the head about what I'm doing wrong or what I'm misconstruing, your corrections are suddenly quite clear and meaningful. When someone's confidently wrong about what I'm doing wrong, it's just painful and confusing. I develope an attitude because I have been run ragged in other threads by people pushing me to follow red herrings about what is confusing me.

At the same time I am aware you have been gratuitously stressed in other threads, arguing with people who arrive announcing the death of relativity and such like. I'm sure if it weren't for those people I wouldn't look like such a pain in the neck.

[zoobyshoe]

OK. I have discovered that the correct way to relate them is division: 1.9245-09/6.6667-09 = .288673557 meters.

This means that the front flare will go off, the rail beneath the rod will move .288673557 meters, then the rear flare will go off. 1 meter-.288673557 meters = .711326443 meters.

The marks will be .711326443 meters apart, but I figure what seems to be .711326443 meters to the rod guy is actually a contracted version of the proper length in the rail frame.

It seems the .288673557 and .711326443 have to be uncontracted somehow to arrive at the distance the marks will be from each other when measured in the rail frame.

If I take .866025 which is the length were supposed to end up measuring in the rail frame, and contract it for a speed of .5c, I get .749999301, which is kinda, sorta promising, being kinda, sorta close to .711326443.

So, If I can contract a length by multiplying by .866025 is seems I should be able to uncontract a length by dividing by .866025

.711326443/.866025 = .82136941. Hmmmm. Kinda, sorta close to .866025, but off enough to suggest there's something else to be done.

[Doc Al]

Pardon me for jumping in again, but I think I see what zoobyshoe is trying to do. (I find this thread hard to follow due to all the numbers flying around.)

First off, I believe you are using the wrong value for \Delta t', the time interval between the flares according to the rod frame. From the LT, \Delta t' = -\Delta x' v/c^2, thus \Delta t' = 0.1667E-8 seconds.

So let's look at the events from the view of the rod frame:
The first flare goes off and makes its mark. Then the rails move a distance D = VT = (0.5c)(0.1667E-8s) = 0.25m. Then the second flare makes its mark. So, according to the rod frame, the distance between the marks is only 0.75m.

Of course, the rail frame thinks that distances measured by the rod frame will be too short by a factor of \gamma = 1.1547. So the rail frame will measure the distance between the marks to be (1.1547)x(0.75m) = 0.866m.

Of course, for the rail observers, the distance between the marks is the length of the meterstick seen contracted by \gamma, or (1m)/(1.1547) = 0.866m.

So, as far as I can see, everything makes sense. Is this what you were looking for zoobyshoe?

[zoobyshoe]

Pardon me for jumping in again, but I think I see what zoobyshoe is trying to do. (I find this thread hard to follow due to all the numbers flying around.)

First off, I believe you are using the wrong value for \Delta t', the time interval between the flares according to the rod frame. From the LT, \Delta t' = -\Delta x' v/c^2, thus \Delta t' = 0.1667E-8 seconds.
Here's the full equation again:

\Delta t'=\gamma(\Delta t-v\Delta x/c^2)

It seems to me that in boiling it down you have forgotten the gamma:

\Delta t' = -\Delta x' v/c^2,

I'm not sure we can do without that. What do you think?

Is this what you were looking for zoobyshoe?
I think you may understand what I'm going for. It seems to me there should be a neat and tidy way to get from the time interval in the t' frame to the exact length that will be marked in the t frame by the flares, which should be exactly the length of a contracted meter rod at .5c, the speed I've selected as a sample.

I am kind of baffled that I have managed to get kinda, sorta close, but not exactly there. Everything is done by LT, it should be neat and consistent, on paper anyway.

But I think you are possibly right that there could be an error in some previous math somewhere which is throwing things off. I'm not sure it is the time interval, though.

Thanks for keeping an open mind!

[zoobyshoe]

Doc Al,

Posts #87 and #88 are where we hashed out the time interval and other stuff, if you want to look them over.

[Doc Al]

Here's the full equation again:

\Delta t'=\gamma(\Delta t-v\Delta x/c^2)

It seems to me that in boiling it down you have forgotten the gamma:

\Delta t' = -\Delta x' v/c^2,

I'm not sure we can do without that. What do you think?
I think you are using the wrong equations. The equation you need is this:

\Delta t=\gamma(\Delta t' + v\Delta x'/c^2)

We are given that the events (the flares) occur simultaneously in the rail frame, so \Delta t = 0. Which allows us to conclude that:

\Delta t' = - v\Delta x'/c^2

As you can see, there is no gamma.

I think you may understand what I'm going for. It seems to me there should be a neat and tidy way to get from the time interval in the t' frame to the exact length that will be marked in the t frame by the flares, which should be exactly the length of a contracted meter rod at .5c, the speed I've selected as a sample.
The way to relate things is as I described in my last post. Remember that to the rod observers the marks do not represent a measurement of the length of the meterstick. To the rod observers, those flares fired at different times. But you can certainly figure out what the rod observer would measure as the distance between those marks, and then relate that to what the rail observers would measure.
Thanks for keeping an open mind!
As long as you can restrain yourself from accusing me of sophistry, I'm happy to work with you. :smile:

PS: Regarding my earlier comment "it's real... and it's spectacular": I take it you are not a Seinfeld fan?

[zoobyshoe]

I think you are using the wrong equations. The equation you need is this:

\Delta t=\gamma(\Delta t' + v\Delta x'/c^2)
Hmm. Dunno what to say. Halliday and Resnik say this equation is for transforming from the primed into the unprimed frame. We are definitely going the other way.Remember that to the rod observers the marks do not represent a measurement of the length of the meterstick. To the rod observers, those flares fired at different times. But you can certainly figure out what the rod observer would measure as the distance between those marks, and then relate that to what the rail observers would measure.
The main objective is to find the length that someone will measure the marks left by the rod in the rail frame to be. There should be two burn marks left by the flares which are .866025 apart, which prove the rod has "really" contracted while at speed .5c.
As long as you can restrain yourself from accusing me of sophistry, I'm happy to work with you. :smile:
I can promise you that, yes, but it won't help you: I have an extensive vocabulary of alternatives. :-)
PS: Regarding my earlier comment "it's real... and it's spectacular": I take it you are not a Seinfeld fan?
I love Seinfeld, but that line doesn't ring a bell at all. I just figured you were witnessing your Faith in The Church Of Relativity. Praise Einstein!

[Doc Al]

Posts #87 and #88 are where we hashed out the time interval and other stuff, if you want to look them over.
I looked over post #87 and I see the error made.
\Delta t' = \gamma(\Delta t - v\Delta x/c^2)

Let's plug a value of .5 c in for rod velocity.

For gamma that gives \gamma = 1.1547005

x= length of rod = 1 meter = 1
Remember that the rod frame is the primed frame and the rail frame is the unprimed frame. There is absolutely nothing wrong with the formula, but I believe you mixed up \Delta x' and \Delta x. \Delta x' = 1 meter; \Delta x does not.

[Doc Al]

Halliday and Resnik say this equation is for transforming from the primed into the unprimed frame. We are definitely going the other way.
Here are the complete set of Lorentz Transformations:

\Delta t' = \gamma(\Delta t - v\Delta x/c^2)

\Delta x' = \gamma(\Delta x - v\Delta t)

\Delta t = \gamma(\Delta t' + v\Delta x'/c^2)

\Delta x = \gamma(\Delta x' + v\Delta t')

Sure, the first two allow you to go from unprimed measurements to primed measurements. And vice versa, for the last two, which are called the inverse LTs. But remember, these are just equations like any other--you can use them any way you want, as long as you plug in the right values.

The main objective is to find the length that someone will measure the marks left by the rod in the rail frame to be. There should be two burn marks left by the flares which are .866025 apart, which prove the rod has "really" contracted while at speed .5c.
Right. So we need to find \Delta x. What are we given? We know that its a meterstick, so \Delta x' = 1m. We also know that the flares go off simultaneously in the unprimed frame, so \Delta t = 0. Now which LT relates those three values? Try the second one:

\Delta x' = \gamma(\Delta x - v\Delta t)

Plugging in what we know, it becomes:

\Delta x' = \gamma\Delta x

or:

\Delta x = \Delta x'/\gamma

Which tells you that the measured length is the expected 0.866m.

I can promise you that, yes, but it won't help you: I have an extensive vocabulary of alternatives. :-)
Lucky for you I'm a mentor here. In "real life" I'd rip you to shreds without mercy! (Just kidding. :tongue:)

I love Seinfeld, but that line doesn't ring a bell at all. I just figured you were witnessing your Faith in The Church Of Relativity. Praise Einstein!
The original line is: "They're real... and they're spectacular!".