[Centra (OP)]

With the dual beam laser rocket and the lightning train thought experiments, Einstein postulated that time would be dilated in one direction and simultaneously contracted in the other, or at least dilated to a different extent. Explain how that's possible. Don't just say "oh it's possible alright, because Einstein said", actually explain how. Pretty sure you can't have time dilated by different amounts on two ends of a moving object, presumably changing smoothly as you go from end to end, requiring a varying equation along the way. Where's the variable Lorentz transformation equation based on where you are from the middle of a moving frame? The Lorentz transformation provides a single time dilation factor for an entire moving object, so is it wrong or is the thought experiment proposed solution wrong? They can't both be right.

This shows that Einstein put forward two contradicting postulates, the relativity of simultaneity and the Lorentz transformation time dilation. If clocks at each end of a moving object show two different times, in accordance with the relativity of simultaneity, they can't also show the same times, in accordance with the Lorentz transformation which provides a single dilation factor for an entire moving object, not a range of them from end to end.

[Halc]

clocks on opposite ends of a moving rocket which fired two beams from the center to both ends were not synchronized, as if that makes the slightest sense.

Your personal incredulity is noted, but that does not count as the slightest evidence against it. People had similar incredulity that the world was round, but that also didn't change the fact of the matter.

With the dual beam laser rocket and the lightning train thought experiments, Einstein postulated that time would be dilated in one direction and simultaneously contracted in the other, or at least dilated to a different extent.

He postulated no such thing.

Pretty sure you can't have time dilated by different amounts on two ends of a moving object, presumably changing smoothly as you go from end to end, requiring a varying equation along the way.

For an inertial object, relative to any inertial frame in which the object is moving, the clocks anywhere on the object are dilated the exact same amount. But for an accelerating object, it's pretty much as you describe, even from the point of view of the guy on the rocket. This has been demonstrated.

This shows that Einstein put forward two contradicting postulates, the relativity of simultaneity and the Lorentz transformation time dilation.

Neither of those are postulates. The postulates are simply "physics is the same in any frame" and frame invariant speed of light. Those two postulates don't contradict each other, and technically it is a single postulate since if the 2nd wasn't true, the first wouldn't be either. The things you mention can be derived directly from the one postulate.

Explain how that's possible. ... actually explain how.

Your personal motivation, incredulity, and biases prevent that (especially the motivation one). As I said above, I can no more explain it to you than I can to my cat. The things you refuse to accept follow rather trivially from the actual postulate above. I can explain it to BC for instance, but I can't explain it to you.

[Bored chemist]

With the dual beam laser rocket and the lightning train thought experiments, Einstein postulated that

How did Einstein ( 14 March 1879 – 18 April 1955) come up with a thought experiment involving lasers which didn't exist before 1960?

Are you deliberately posting nonsense?

[Centra (OP)]

Okay Einstein didn't say time dilated by different amounts on the two ends of a moving object with two light beams going in opposite directions, that would mean the clocks were moving at different rates. What he did say is that they would move at the same rate but show different times. He didn't say "lasers", he probably said lanterns but I was just using a modern equivalent which works better because the light is all in one beam. He might not even have used the rocket scenario but it's in videos showing Einstein's theory.

However you present the thought experiment, how can you justify clocks at each end showing different times when there are two beams in opposite directions but if there was only one beam they would both show the same time? The only reason the two clocks were made to show different times was to try to get around the flaw in the Lorentz transformation that it can't correct the speeds of two beams in opposite directions at the same time.

[Centra (OP)]

I'll condense my point to a simple question, would the clocks on the rocket look the same if there was only one laser beam going forward as when there were two going in opposite directions? How would you explain the two clocks showing different times if you answer that question with a yes, does the Lorentz transformation state that clocks in a moving frame would be behind those in a stationary frame by different amounts depending on where they're positioned in the moving frame?

[Centra (OP)]

From the article:ON THE ELECTRODYNAMICS OF MOVING BODIES
By A. EINSTEIN, June 30, 1905

Let there be given a stationary rigid rod; and let its length be l as measured by a measuring-rod which is also stationary. We now imagine the axis of the rod lying along the axis of x of the stationary system of co-ordinates, and that uniform motion of parallel translation with velocity v along the axis of x in the direction of increasing x is then imparted to the rod. We now inquire as to the length of the moving rod, and imagine its length to be ascertained by the following two operations:—

(a) The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest. (

b) By means of stationary clocks set up in the stationary system and synchronizing in accordance with § 1, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated “the length of the rod.”

In accordance with the principle of relativity the length to be discovered by the operation (a)—we will call it “the length of the rod in the moving system”— must be equal to the length l of the stationary rod. The length to be discovered by the operation (b) we will call “the length of the (moving) rod in the stationary system.” This we shall determine on the
basis of our two principles, and we shall find that it differs from l.

Current kinematics tacitly assumes that the lengths determined by these two operations are precisely equal, or in other words, that a moving rigid body at the epoch t may in geometrical respects be perfectly represented by the same body at rest in a definite position.We imagine further that at the two ends A and B of the rod, clocks are
placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the “time of the stationary system” at the places where they happen to be. These clocks are therefore
synchronous in the stationary system.”

We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in § 1 for the synchronization of two clocks. Let a ray of light depart from A at the time ta, let it be reflected at B at the time tB, and reach A again at the time tA′. Taking into consideration the principle of the constancy of the velocity of light we find that

 tB − tA = rAB/c − v 
 and
 t′A − tB = rAB/c + v

 where rAB denotes the length of the moving rod—measured in the stationary system. Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous.

Question: what is "c + v" in the preceding quote? How can c + v even exist when c is supposedly the maximum v in the universe? How, then, did Einstein add the v of the moving rod to c?

[Eternal Student]

Hi.

Question: what is "c + v" in the preceding quote?

  Sorry, no idea.
   The text states the following: 

t′A − tB = rAB/c + v

   Which might inlcude a mis-print or something undefned.  tA' was described but not t'A.
The text also refers to something established in S1  but we don't have  S1  printed, so I've no idea what that was.

Sorry.

[Kryptid]

Question: what is "c + v" in the preceding quote? How can c + v even exist when c is supposedly the maximum v in the universe? How, then, did Einstein add the v of the moving rod to c?

The equations aren't calculating a velocity. What's more (assuming the equations are written correctly in this transcript), order of operations says that you do division before you do addition, so you divide the length of the rod by the speed of light and then you add the velocity.

Looks like Halc came to the same conclusion.

[Centra (OP)]

Looks pretty straight forward to me, the equations are exactly as I showed, a fraction with rAB on top and c+v on the bottom, anyone can easily download the article pdf. According to his description, the people moving with the rod would be able to tell they're in inertial motion just by shooting a light beam back and forth and comparing the times, which Einstein says will be different, much like the Sagnac effect, but with straight line uniform motion, the time for the beam to go from A to B would be longer than from B to A, nothing ambiguous about it.

I haven't seen anyone explain how the Lorentz transformation can correct for two opposite direction light beams yet either. I assume nobody will say that clocks on each end of a rocket, in uniform motion, not accelerating, would show different times if beams were shot to the front and back simultaneously, because then they would have to say that the same clocks would also show the same different times when there were no beams involved, just a rocket moving by in uniform motion.

[Bored chemist]

Okay Einstein didn't say time dilated by different amounts on the two ends of a moving object with two light beams going in opposite directions, that would mean the clocks were moving at different rates. What he did say is that they would move at the same rate but show different times. He didn't say "lasers", he probably said lanterns but I was just using a modern equivalent which works better because the light is all in one beam. He might not even have used the rocket scenario but it's in videos showing Einstein's theory.

So, you are finally getting to grips with the fact that it's the ideas and the experimental data that matter not the man himself.
That's progress.
The reason it's important is that it pretty much destroys the silly idea of any "

Einstein Fan Club

.

So, do you now accept that's nonsense?

[Origin]

Looks pretty straight forward to me, the equations are exactly as I showed, a fraction with rAB on top and c+v on the bottom, anyone can easily download the article pdf.

Seem straight forward to you because you apparently do not understand arithmetic.  Your quoted paper does not say c + v.  That is like saying that 1/2 + 1 means 1 over 2 + 1.

[Eternal Student]

Hi.

Looks pretty straight forward to me, the equations are exactly as I showed, a fraction with rAB on top and c+v on the bottom

    Maybe, I haven't seen the original and my German isn't good enough to translate anyhting like this.   Einstein didn't have modern computers and he certainly didn't create that pdf document.   Someone typed it up or scanned in it and presumably translated it from German.  There do seem to be some minor errors.     See the   t'A as opposed to tA' discussed earlier.
    Halc and Kryptid are right, as written the   c+v   does not have to be the denominator.

More generally,  Einstein revised and developed his theory of special and especially general realtivity in little stages - sometimes just presenting arguments for why something couldn't be the way it was described with existing physics like a simple Gallilean transformation between two frames of reference.   I'm guessing that this section uses some ideas from a Gallilean transformation to show that not everything would work out.   To say that another way:  It's unlikely that the finished version of Special relativity is being discussed here, just some indication that the Gallilean transformation might fail.

....the time for the beam to go from A to B would be longer than from B to A, nothing ambiguous about it....

   You seem to suggest that measuring the one-way speed of light is a simple task.  There have been other threads about this.  It's not easy.    The generally accepted view is that it can't be done, you always have to measure the two-way speed of light by setting up something like a mirror to reflect the light back to the source where it was emitted etc.

Best Wishes.

[Halc]

Looks pretty straight forward to me, the equations are exactly as I showed, a fraction with rAB on top and c+v on the bottom, anyone can easily download the article pdf.

Seem straight forward to you because you apparently do not understand arithmetic.  Your quoted paper does not say c + v.  That is like saying that 1\2 + 1 means 1 over 2 + 1.

Actually working it out from the paper changes my mind. It is a poor translation error. rAB is a length, and dividing that by c gives something in units of seconds. You can't add velocity to time since the units don't match, and the math works out when interpreted as rAB / (c ± v).
As krypid correctly points out, we're computing the time it takes (in some other frame) for light to travel the length of the moving rod.

That said, relativity very much allows valid expressions of speeds higher than c.  Given a fast enough ship, I can get to Betelgeuse before I die, which is over 600 light years in maybe 20 years, which is a proper velocity of over 30c, despite my not moving at that velocity relative to any inertial frame. The theory doesn't forbid the expression of such values.

[Centra (OP)]

Actually working it out from the paper changes my mind. It is a poor translation error. rAB is a length, and dividing that by c gives something in units of seconds. You can't add velocity to time since the units don't match, and the math works out when interpreted as rAB / (c ± v).
As krypid correctly points out, we're computing the time it takes (in some other frame) for light to travel the length of the moving rod.

That said, relativity very much allows valid expressions of speeds higher than c.  Given a fast enough ship, I can get to Betelgeuse before I die, which is over 600 light years in maybe 20 years, which is a proper velocity of over 30c, despite my not moving at that velocity relative to any inertial frame. The theory doesn't forbid the expression of such values.

What Einstein was saying with that equation is that if the motion of the moving frame with the rod and clocks was, say, 100,000 km/s that the time for the beam to travel from A to B would be the length of the rod, say 1 km, divided by (300,000 km/s minus 100,000 km/s = 200,000 km/s) = 0.000005 second, and the time from B back to A would be 1 km divided by (300,000 km/s + 100,000 km/s=400,000 km/s) = 0.0000025 second, thus, they would conclude that the two clocks were not synchronized, because if they had been then both ways would have taken the same time, 0.0000033... second. They would think that clock A was running at half the speed of clock B.

The obvious problem there is that it should in fact have taken the same amount of time both ways, because it should have been exactly the same as if they had been stationary. So Einstein violated his own postulate that "1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion."  He assumed that the light would behave as if it was in the stationary frame and the moving frame was traveling as if it were catching up with the beam when the beam went forward to clock B and like it was closing in on it on its way back to clock A.

Logically, it should actually have been the other way around, the moving observers should have seen the two clocks as synchronized and the stationary observers should have seen them as running at different speeds, if anybody should have.

[Halc]

What Einstein was saying with that equation is that if the motion of the moving frame with the rod and clocks was

The rod is moving relative to the chosen frame. The clocks (four of them?) are not moving in this frame, and are in sync relative to this frame. You didn't explicitly say otherwise (yet), but I want to be clear. It isn't a 'moving frame' except relative to the proper frame of the rod.

say, 100,000 km/s that the time for the beam to travel from A to B would be the length of the rod, say 1 km, divided by (300,000 km/s minus 100,000 km/s = 200,000 km/s) = 0.000005 second, and the time from B back to A would be 1 km divided by (300,000 km/s + 100,000 km/s=400,000 km/s) = 0.0000025 second

Right.

thus, they would conclude that the two clocks were not synchronized

The clocks are presumed synchronized in the frame in question. It really does take light twice as long to go 4/3 km as it does to go 2/3 km.

because if they had been then both ways would have taken the same time, 0.0000033... second.

No, not for a moving rod. That would be true only for a stationary 1 km object, and there's no stationary 1 km object in any frame in your example.  The rod has a proper length of about 1.06 km in your example to get the numbers you quote.

They would think that clock A was running at half the speed of clock B.

Nonsense. If one clock was defective, a repeat of the experiment would yield different times to go from one end to the other, not 5 and 2.5 μsec again. And the measurement can only be done once, after which the rod has passed by the clock. Maybe they can time multiple identical rods going by.

The obvious problem there is that it should in fact have taken the same amount of time both ways, because it should have been exactly the same as if they had been stationary.

Once again, nonsense. The emission and detection events one way are twice as far apart as the emission and detection events the other way. Light cannot take the same time to go two distances, one twice the other.

[Centra (OP)]

What Einstein was saying with that equation is that if the motion of the moving frame with the rod and clocks was

The rod is moving relative to the chosen frame. The clocks (four of them?) are not moving in this frame, and are in sync relative to this frame. You didn't explicitly say otherwise (yet), but I want to be clear. It isn't a 'moving frame' except relative to the proper frame of the rod.

say, 100,000 km/s that the time for the beam to travel from A to B would be the length of the rod, say 1 km, divided by (300,000 km/s minus 100,000 km/s = 200,000 km/s) = 0.000005 second, and the time from B back to A would be 1 km divided by (300,000 km/s + 100,000 km/s=400,000 km/s) = 0.0000025 second

Right.

thus, they would conclude that the two clocks were not synchronized

The clocks are presumed synchronized in the frame in question. It really does take light twice as long to go 4/3 km as it does to go 2/3 km.

because if they had been then both ways would have taken the same time, 0.0000033... second.

No, not for a moving rod. That would be true only for a stationary 1 km object, and there's no stationary 1 km object in any frame in your example.  The rod has a proper length of about 1.06 km in your example to get the numbers you quote.

They would think that clock A was running at half the speed of clock B.

Nonsense. If that were true, a repeat of the experiment would yield different times to go from one end to the other, not .000005 and .0000025 seconds again. And the measurement can only be done once, after which the rod has passed by the clock. Maybe they can time multiple identical rods going by.

The obvious problem there is that it should in fact have taken the same amount of time both ways, because it should have been exactly the same as if they had been stationary.

Once again, nonsense. The emission and detection events one way are twice as far apart as the emission and detection events the other way. Light cannot take the same time to go two distances, one twice the other.

The clocks are on the ends of the rod, which is moving, there are two in the stationary frame and two in the moving frame, on the ends of the rod, you seem to have difficulty comprehending that. The light was emitted inside the moving rod frame  Did you even read Einstein's article? Apparently not. I won't bother pointing out the rest of your mistakes, it would take too long. Let's just say, when you start out that wrong, the rest is not going to get any righter.

[Halc]

The clocks are on the ends of the rod, which is moving

The clocks placed at the ends of the moving rod are synced with the stationary clocks in their presence, and then tested for being in sync by the moving observers, and found not to be in sync, as per the equations shown.

Let's just say, when you start out that wrong, the rest is not going to get any righter.

Well illustrated, thank you.

[Centra (OP)]

So why would the observers moving with the moving rod find the two clocks not to be synchronous? Does light travel at different speeds in a moving frame, slower in the direction of motion and faster opposite the direction of motion? That's exactly what Einstein said. I know others can't speak for Einstein but everyone who has been posting here seems to support his theories so maybe you would like to help him out by explaining how that makes sense?

We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in § 1 for the synchronization of two clocks. Let a ray of light depart from A at the time tA, let it be reflected at B at the time tB, and reach A again at the time tA′. Taking into consideration the principle of the constancy of the velocity of light we find that

 tB − tA = rAB/c − v
 and
 t′A − tB = rAB/c + v

 where rAB denotes the length of the moving rod—measured in the stationary system. Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous.

[Halc]

So why would the observers moving with the moving rod find the two clocks not to be synchronous?

Because they were explicitly synced to the first frame, not the frame of the rod:
"We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system"

Does light travel at different speeds in a moving frame, slower in the direction of motion and faster opposite the direction of motion?

No. That would violate both postulates of the theory, and lacking an empirical test for it, no such anisotropy can be demonstrated.

That's exactly what Einstein said.

The part you just quoted just says that the two observers in different frames would find the pair of moving clocks to be synchronized and not synchronized relative to their respective frames. It is an empirical illustration and quantification of relativity of simultaneity and little else.

Usually tests are done with one clock so sync issues are avoided.  Shine a light the length of a rod and reflect it back, timing the round trip.  If there was a 300 km rod with such a clock and mirror at opposite ends, light should take 2 msec to make the round trip if light moved at constant speed in both directions. But if it moved at say 150000 km/sec in one direction and 450000 km/sec in the other, it would take 2msec to move one way and 2/3 sec the other way, for a total of 2 2/3 msec, which would be empirically different than the 2 msec that Galilean relativity demands. At slower speeds the difference would be less, but measurable nevertheless with accurate enough devices, and as has been pointed out above, it has been measured to be frame invariant to at least 17 digits.
This falsifies the Newtonian view of absolute time and space that you seem to naively have been pushing. The view was falsified well before Einstein came along and first providing a complete theory to replace the one they knew was wrong. Parts of the theory came from earlier works by Poincare, Lorentz, Minkowski, and others.
Personally, I think the Lorentz transformation would better be named the Poincare transformation who originated the current symmetric form.

[Centra (OP)]

Shine a light the length of a rod and reflect it back, timing the round trip.  If there was a 300 km rod with such a clock and mirror at opposite ends, light should take 2 msec to make the round trip if light moved at constant speed in both directions. But if it moved at say 150000 km/sec in one direction and 450000 km/sec in the other, it would take 2msec to move one way and 2/3 sec the other way, for a total of 2 2/3 msec, which would be empirically different than the 2 msec that Galilean relativity demands. At slower speeds the difference would be less, but measurable nevertheless with accurate enough devices, and as has been pointed out above, it has been measured to be frame invariant to at least 17 digits.
This falsifies the Newtonian view of absolute time and space that you seem to naively have been pushing.

What's your point? The observers moving with the rod apparently got two different times for the light to travel from A to B and from B to A, because why else would they conclude that the clocks were not synchronous?