Ok. We’ve been over this before, and you always do it wrong. You have it in your mind that there is only one “system” involved and that the only clock that moves is the “A” clock.

But here is the correct way to set up the diagram:

AK/A’K’-----------------------BK/B’K’

Both clocks, A’ and B, are stationary with one another and are synchronized and synchronous. Before the motion begins, they both are stationary along the X axes (plural).

Use two pieces of paper, on one piece put:

A’K’----------------------------B’K’

This represents the K’ system, its A’ clock, and its two end points A’ and B’.

On another piece of paper, put:

AK------------------------------BK

This represents the K system, its B clock, and its two end points A and B.

Here’s what the two pieces of paper should show:

TWO DIAGRAMS ON TWO PIECES OF PAPER

Now overlap the two pieces of paper at AK and A’K’ and at BK and B’K’. Use a backlight so the markings on the bottom piece of paper will show up through the top piece of paper.

Now move the two pieces of paper relativity so that clocks A’ and B approach each other. Remember, during the motion, there are two different systems, K and K’, and each clock is in a different relatively moving system. Remember that the motion is only relative.

The motion is along the joint combined “X” axes (plural).

There are two axes in the thought experiment, the x axis of K and the x’ axis of K’.

In the 1905 thought experiment, the reader is tricked into thinking there is only one axis, x, but there are actually two axes, because the x’ axis is the axis of the K’ system, and it overlaps the x axis of the K system.

So, there are four points, not just two. They are points A and B of K, and points A’ and B’ of K’.

Relatively, K moves this way <

While, relatively, K’ moves this way >

And at the end we have:


Or, this might be an easier way for you to see what has happened:
Clock A’ in system K’, and clock B in system K, move relatively toward each other.

According to SR theory, observer B sees the A’ clock slow down and time dilate, while observer A’ sees the B clock slow down and time dilate. At the end of the thought experiment, observer B is supposed to see clock A’ “lag behind” clock B when they unite. However, this is not correct because, according to the symmetry terms of the theory, observer A’ will see clock B time dilate during the relative motion and “lag behind” at the end. Both observers will disagree at the end, and we have a paradox.

Why did Einstein not notice this paradox until several physicists pointed it out to him after the paper was published? Because he fixed his own mind as being “stationary” inside the K system, and at the end he reported only what the BK observer saw. He saw the A’ clock “moving” and slowing down its tick rate during the relative motion, and “lagging behind” at the end.

But any reader who fixes his mind as being “stationary” inside the K’ system will see the B clock “moving” and slow down during the relative motion, and “lagging behind” at the end. Thus the thought experiment ends in a paradox, because Einstein ignored what the A’K’ observer saw during the thought experiment and at the end.

Had he fixed his mind first with the K system and then with the K’ system, he would have noticed the paradox, and this thought experiment would have not been included in the paper, just as it was not included in his 1916 book.

Notice in your diagrams that you show only system K, from points A to B. You do not show system K’ from points A’ to B’.

Study this. Consider it. Learn from it.

With the diagram you clearly said:

You said the first horse, not the second horse, was “ahead” on Camera A.

You are becoming confused with your own thought experiments, just as Eintein became confused with his own thought experiments.

Sam5, I could demonstrate it to someone who cares to make an attempt to follow the math. The math isn't hard, it's no more difficult than geometry. I tried leading you through it in December, you wouldn't make any sort of attempt then to follow. I have no reason to believe that you would make any more of an attempt now.

The simple explanation is that this is an artifact of trying to impose one reference frame's ideas of simultaneity on another; SR says that that can't necessarily be done.
That's inaccurate and insulting, but that's pretty much what I expect from you.

If anyone other than Sam5 is curious, I can run through the numbers.

[edit to fix quotes]

You said earlier:

Horse A is the same as horse 1, right?

Camera A is the same as “an observer on the finish line, next to horse A”, right?

So, that’s the same as what you said with the diagram text, “Camera A sees Horse 1 cross 5 ns ahead of Horse 2.”

Now you are claiming that “the second horse is 5ns ahead on camera A”

So, you are just getting your thought experiments all mixed up.

Better double-check your weekly atomic clock calculations.

Observers do not disagree on what they both see, if they are together.
Which several physicists are you referring to?

The “math” is what led that professor astray during his accelerating clocks thought experiment. He said that since the B clock was seeing the light signals from the A clock faster than 1 second apart, that meant the A clock was ticking faster than the B clock. But his “math” gave him an incorrect result, as I showed with my “dropping marbles” thought experiment. Concentration on the “math” is also what gets Sean mixed up on the “peculiar consequence” thought experiment, because he is not considering the K’ “system”, thus, he sees the A’K’ clock “move” relative to the K system, but he doesn’t see the BK clock move relative to the K’ system.

Also, Milli was so intent on concentrating on the “math”, he said:

“After 4 years of waiting, Bob must experience a force related to acceleration, without moving”

“Bob doesn't sit in a gravity field attributable to matter, but for the length of time T, he feels an acceleration of (6/5)c/T.”

So, he’s got Bob “experiencing a force related to acceleration”, but WITHOUT either moving OR sitting in a gravity field attributable to matter.

You guys need to practice more on your conceptualizations.

This is why he did not tell what the K’ frame observer saw at the end. That’s why he only reported what the K frame observer saw. If he had reported what both observers saw, from their perspective and the symmetry rule (that caused both to see each other’s clock run slow during the relative motion), then he would have had to report that the K observer saw the K’ system clock “lag behind”, while the K’ system observer saw the K system clock “lag behind”, and the paradox would have been obvious.

#-o Yeah, I always do it wrong.

There is only one coordinate system to start with - both clocks are in it. That's a given - if two observers, two objects, two anything are at rest relative to each other, then they are in the same coordinate system. That is the definition of a coordinate system.

When the two clocks are moving relative to each other, they are in different coordinate systems. Again, that's the definition.

Thus if two clocks are motionless relative to each other at one point in time but in motion relative to each other at a later point in time, then at least one of those clocks must be in a different coordinate system at the later point in time than it was in at the former.

You seem to be under the mistaken impression that every observer has its own coordinate system, and never changes. That is not the way it works. A coordinate system cannot just start moving relative to another coordinate system.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2010 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

No, that is your first conceptual mistake. There are two coordinate systems, K’ and K and they OVERLAP at the beginning, before the relative motion begins. The so-called “clock at A” is the K’ system’s A’ clock, before the relative motion begins.

See the first paragraph in Section 3: “Let the axes of X of the two systems coincide, and their axes of Y and Z respectively be parallel.”

See? “Axes”, plural. Note that “X” is capitalized because it represents both the x and x’ axes.

You can say that before the relative motion begins, K’ = K or that K’ and K are in the same coordinate system. But when the relative motion begins, they split up into his two systems, K and K’. The A’ clock is in the K’ system, and the B clock is in the K system.

But if you read the paragraph at the start of Section 3, you can see where he says, “Let us in ‘stationary’ space take two systems of co-ordinates, i.e. two systems, each of three rigid material lines, perpendicular to one another, and issuing from a point. Let the axes of X of the two systems coincide, and their axes of Y and Z respectively be parallel.”

Those are TWO systems that overlap, K and K’, before any relative motion begins.

Einstein, 1905, Section 3:

“Let the axes of X of the two systems coincide....

Now to the origin of one of the two systems (K’) let a constant velocity v be imparted in the direction of the increasing x of the other stationary system (K), and let this velocity be communicated to the axes of the co-ordinates, the relevant measuring-rod, and the clocks.”

At the beginning of Section 3 he is defining the coordinate systems. They are identical except for the velocity v.

That's why in Section 4, when he starts talking about clocks, he says:

See? A single clock, which could be in either coordinate system - it doesn't automatically have its own.

Later:

See? Both clocks are in K to start with.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2010 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

To finish Einstein’s quote that you started:

“...to be located at the origin of the co-ordinates of K’, and so adjusted that it marks the time τ.”

Ok, in the “peculiar consequence” thought experiment, at the very start, before the relative motion begins, “the clock at A” is the A’K’ clock of the K’ frame

At the start, it is stationary with, synchronized with, and synchronous with the B clock of the K frame.

At the start, both the K’ and K systems overlap and they are both stationary relative to each other.

Thus, both clocks are adjusted to tick at the same rate before the “relative motion” begins, and when it begins, it is just “relative”.

K’ sees K “move” and K sees K’ “move”.

Fix yourself with the A’ clock in the K’ frame, and (maybe) you’ll see what I’m talking about.

You also said that "d" would remain constant. It doesn't.
That's allowed in general relativity. Maybe you haven't got to that part yet.
So, I guess the answer to the question is that one should not study math, in learning relativity? That should be a relief.

The clock at A will eventually be in the K' frame - but to start with, it is in the K frame.

With the clock at B. Yes.

No. Both clocks are in the K system, neither clock is in K' yet. The K' system is already in relative motion to K, but neither of the clocks is in it.

Yes, but the clock at B stays in K and the clock at A changes to K'

There is no A' clock. There is one clock that starts at A in K and then switches to K' (which is in motion relative to K), and one clock that starts at B in K and remains there.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2010 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

I defined my “d” as the distance the marbles fall inside the box, and that is always 16 feet. He defined his “d” relative to the background grid of outside space, and that changes, but it does not change the rate of the A clock.

What Sam5 doesn't realize is that when you try to read a math-intensive paper without a solid grounding in math, you end up getting all the conceptualizations wrong.

See our latest posts regarding coordinate systems. Einstein's speaking "math," and Sam5 doesn't understand him.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2010 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

You can't have them experiencing the same acceleration, and staying the same distance apart, both. But that's another paradox, Bell's rope paradox.

No, sorry. That’s what you’ve been thinking for years and that causes conceptual problems for you.

See the first paragraph in Section 3. Both K and K’ overlap before they move relatively. In Section 4, the “clock at A” is the K’ frames clock, before the two frames move relatively. The two frames overlap at that time and point A of K coincides with point A’ of K’, so at that time, the K’ frame clock is at A. It’s also at A’ and it always remains at A’.

During blast-off, doesn’t the front of the Space Shuttle experience the same acceleration as the rear of the Space Shuttle, and doesn’t the front stay the same distance apart from the rear?

Only if the front of the Shuttle had a different engine that accelerated the front at a higher g than the rear, would the front and the rear separate.

Sam, no matter what you say, THE THEORY IS THE MATH. Everything is contained in the equations, both SR and GR. When you try to "translate" from the language of mathematics without fully understanding it, you run into conceptual problems. I won't pretend to be well versed in differential geometry (yet :wink: ) but I know enough to get my way through basic GR, and all of SR (since it takes place in locally inertial systems, the Christoffel symbols vanish, and the equations simplify). Go back and read my post that suggests what you need to do to debate any of this stuff forcefully. As I said before (to which you replied with a strawman), you aren't going to "disprove" SR without a lot of equations in your paper.

Sorry, that is what has misled you for years.

Here are the two clocks:

LINK

The two systems start out overlapped and not moving relatively, just as at the start of Section 3.

Then the relative motion begins. If you stay with K’, you see K move. If you stay with K you see K’ move.

If you stay with clock A’ you see clock B move and time dilate. If you stay with clock B you see clock A’ move and time dilate.

No, sorry. Apparently someone has misled you about math in relativity.

The theory is the concept. You can check the concept, and you can sometimes prove or disprove it with the math.

Einstein’s math in Section 4 says that during the relative motion, the K’ system observer will see the K system clock time dilate at the rate of:



It also says that the K system observer will see the K’ system clock time dilate at the rate of:



This should have told him that K’ and K would see exactly the same thing, and so neither clock would “lag behind” the other at the end of the thought experiment.

Where he lost it in the “peculiar consequence” thought experiment was when he fixed is mind only with the K frame and he did not switch over and fix his mind with the K’ frame. If he had done that, conceptually, he would have seen the paradox. The math would have revealed it to him.

Today's critics of SR are no longer die-hard, but well informed, reasoning and serious. SR, which required space & time to become distorted as a consequence of the observer's motion, preserved electromagnetic theory intact at the expense of classical mechanics & common sense.

You're turning into a comedian Sam5... It may be true that first principles (constant speed of light, validity of reference frames) were expressed conceptually, but they were only the starting point to the real math of relativity. Things like the 'peculiar consequence' are borne of, and solve by the math of relativity. How can you prove a mathematical concept by analysing a language?

Thing is though, that the math did reveal something to him. It revealed why there is only the appearance of a paradox. The math shows that it isn't really a paradox. The reason you have a problem is because you're operating without the math, and only seeing the words which talk about peculiarity...

It's getting tired.

__________________
bunk: Empty talk; nonsense.
de·bunk: To expose or ridicule the falseness, sham, or exaggerated claims of.
http://home.iprimus.com.au/eddo/images/fredheadtsp.gif

So, just to recap, doing it your way leads to an unworkable paradox while doing it my way actually works.

Therefore, your way must be the correct way.

Right. :roll:

No, K' does not overlap with K "before they move relatively." He is simply defining the second coordinate frame, Sam5, and he defines it as being a duplicate of K with the exception of the relative motion.

The clock at A is not at A' in K' until the time when it switches into the K' frame. That exact moment in spacetime is the only time points A (in K) and A' (in K') coincide. From then on (or at least until it reaches B), it remains at A'.

But the clocks were never synchronized in K'.

Actually, no it doesn't. That equation is just a simplification of

τ = t * sqr( 1 - v^2/c^2)

τ is the time shown on the clock in K' while t is the time shown on the clock in K. To do it the other way, you have to solve for t, which gives:

t = τ / sqr( 1 - v^2/c^2)

Not the same thing.

And in both cases, it's a coordinate transformation, not a simple time dilation.

That's why you need to know math to understand this, Sam5.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2010 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

Pais ("Albert Einstein lived here", 1994) says that Einstein was "reticent" about the Michelson-Morley experiment, and that "the ether drift experiments were still on Einstein's mind" when he wrote to Grossman in 1901, 4 years before SR.

This suggests that MM was the real problem that his theories were intended to overcome. It might have been too direct to have praised Einstein for overcoming the implications of MM, for this would've drawn the attention of the public to the subject. He was therefore adulated for his "brilliant mind" that "had changed the face of science". That his theory had overcome the problem of the MM experiment could then be treated as an incidental item, or better still, turn the whole experiment into a "confirmation" of his theory. This deflected attention from the fact that it was "a troublesome" result that had generated an ad hoc need for something like SR to "explain it away".

You are ignoring what the K' observer sees. That's the same mistake he made.



Yes they were. He said:

“If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous;

Well, BOTH systems were stationary at that point, and obviously, if clock at A is synchronized and synchronous with the clock at B, then clock at B is synchronized and synchronous with the clock at A. There are only 2 clocks in this thought experiment, not several in each system.

The one he calls “the clock at A” is the K’ frame clock before the motion begins. Like the two overlapping systems at the start of Section 3, the two frames overlap when they are both stationary before the motion begins.

Remember that earlier he synchronized several “stationary” clocks while they were declared to be “stationary”, and he synchronized several “moving” clocks while they were declared to be “moving”.

But in Section 4, he has only 2 clocks, the K and K’ clock, and he synchronizes them and makes them synchronous together before the motion begins. This helped cause the paradox, because both are synchronized and running at the same rate before the relative motion begins. Since the motion is relative and both systems are equal, and both system observers see the same thing in each other’s clocks, if K sees the K’ clock run slow then K’ must see the K clock run slow.


You’ve got to take the SR theory from the beginning and follow it on through to the end. He introduces the two relatively moving systems and their thought experiments in Section 3.

Go to Section 3, first paragraph:

”Let us in ‘stationary’ space take two systems of co-ordinates, i.e. two systems, each of three rigid material lines, perpendicular to one another, and issuing from a point. Let the axes of X of the two systems coincide, and their axes of Y and Z respectively be parallel.”

Both systems, K and K’ overlap before the motion begins.

If ”at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; ”, then τ = t because both systems are “stationary” before the relative motion begins, and both clocks are synchronized and synchronous. Then when the relative motion begins, both systems see themselves as “stationary” and the other as “moving”.

If “It is clear that the same results hold good of bodies at rest in the ‘stationary’ system, viewed from a system in uniform motion,” then K’ sees K “move” and the K clock “time dilate” the same amount as K sees K’ “move” and the K’ clock “time dilate”.

No one can say which one is “really moving”, since we don’t have any acceleration effects considered, and that is why he placed the word “stationary” in quotes. Because K’ observers see the K’ frame as “stationary” and K observers see the K frame as “stationary”. They both see each other as “moving”.

See? When you are a body at rest in the K’ system, then it is the K system that appears to “move”.

Sam5, go learn what a coordinate system is, and come back when you understand what you're talking about.

Until then, I think I'm done.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2010 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

Hmmmmm, where have I heard this before? :wink:

__________________
Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth