Einstein's clock

[chinglu]

How many times does someone have to tell you, observers in relative motion are never "at the same place".

This is not what this thread is about.

I have said it over and over, here it is again by Einstein.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be $$\frac{1}{2}tv^2/c^2$$ second slow.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[chinglu]

So you can not show (mathematically) that relativity fails for a clock traversing a simple polygonal path? Oh well.

Who cares? I proposed a circular path.

 

[Neddy Bate]

So you can not show (mathematically) that relativity fails for a clock traversing a simple polygonal path? Oh well.

Who cares? I proposed a circular path.

Yes, but if you analyze the polygonal path using SR, you can see how the speed of light is c for the traveling clock as it traverses each side of the polygon. The answer to your "paradox" lies in the change of frames that occurs whenever the traveling clock encounters a vertex of the polygon. Whenever there is a change of frames, there is also a change in simultaneity. For the circular path, such change of frames happens constantly, because the polygonal path approaches the circular path in the limit as the number of vertices approaches infinity, and the length of each side approaches zero.

 

[AlphaNumeric]

No, show the cantor thread where you proved the emergence of the continuum from the natural numbers using only one sequence.

Next, Konig's theorem is trivial, You proceed by transfinite induction for each ordinal n. At each level, you associate an element at the level with both sides. Then, you choose the R least element in the difference set at that level since the levels do not contain the same number of elements.

At limit ordinals, it is trivial since you union all successors in which the condition holds. The union of all true is true.

This is why you aren't allowed to talk about it in the main forum. You are so completely ignorant that you can't understand multiple explanations from people. You've already been corrected on your misrepresentation yet you continue to post it. You simply don't understand Cantor's work or how it was explained to you by us. This illustrates how you're not worth talking to, you're just too damn stupid and dishonest.

It must be horrible to have such a small mind.

 

[RJBeery]

Let's keep this simple.

The sun is at the center of the grid.

So do you actually think all observers place this in a different region of space? that would be a contradiction.

Therefore, do you agree or disagree when the earth returns to (x,y,z), all observers in the solar system agree on this? if not, that is also a contradiction.

Finally, if they disagree on the position of the light sphere when the earth returns to (x,y,z), that would also be a contradiction.


Looks, like we have absolute time.

Why not replace the sun with a digital clock and declare its reading to be your absolute time? I mean, that's a lot simpler than worrying about (x, y, z) coordinates of planets, right?

If the solar system observers are not in relative motion then the digital clock CAN be used to keep their own clocks synched. If they are in relative motion then they will discover that their clock and the clocks of the others (as well as the sun-clock) are progressing at different rates.

In other words, absolute time is only available if all observers are in a co-moving frame OR are willing to lengthen or shorten their local definition of a second (like the GPS sats do) to match your "universal time synchronizer"...this doesn't mean that Relativity is wrong or that you have uncovered any contradictions.

 

[Neddy Bate]

Why not replace the sun with a digital clock and declare its reading to be your absolute time? I mean, that's a lot simpler than worrying about (x, y, z) coordinates of planets, right?

If the solar system observers are not in relative motion then the digital clock CAN be used to keep their own clocks synched. If they are in relative motion then they will discover that their clock and the clocks of the others (as well as the sun-clock) are progressing at different rates.

In other words, absolute time is only available if all observers are in a co-moving frame OR are willing to lengthen or shorten their local definition of a second (like the GPS sats do) to match your "universal time synchronizer"...this doesn't mean that Relativity is wrong or that you have uncovered any contradictions.

Not so fast, RJB, perhaps chinglu has uncovered the greatest contradiction of all time! That although relativity predicts the solar system observers find their clocks progressing at different rates, (as you say), very few realize that relativity might also surreptitiously predict that their clocks all progress at the same rate! Holee poo! :m:

Oh wait, no it doesn't. Nevermind.

 

[chinglu]

This is why you aren't allowed to talk about it in the main forum. You are so completely ignorant that you can't understand multiple explanations from people. You've already been corrected on your misrepresentation yet you continue to post it. You simply don't understand Cantor's work or how it was explained to you by us. This illustrates how you're not worth talking to, you're just too damn stupid and dishonest.

It must be horrible to have such a small mind.

It is quite clear, here is the math refute it or submit.

Further, in this thread, I am very specific, a light pulse is emitted when the clocks are common.

One clock moves in a circle and returns to the other clock.

Here is Einstein's statement.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be second slow.

Next, since the y-axis is perpendicular to the line of travel, it is not length contracted. So, assume both frames the distance the pulse traveled is d.

Also, assume the time on the clock with the stationary observer is t.

By SR, c = d/t.

However, since the moving clock moves in a circle, then there exists some very very small time differential from the stationary clock, say t'.

Then, we must apply Einstein reasoning, the moving clock shows a time of t/γ.

So, the actual time on the moving clock is t' + t/γ.

According to Einstein, c is a constant between the frames and time dilation is a result of this assumption.

Now, since t' is absolute, we can remove t' from the calculations and all we have left is what Einstein claimed as the time on the moving clocks as t/γ.

But, that means, c' = d/(t/γ) for the moving clock.

We also have c = d/t for the stationary clock. But, under SR all observers must measure c as the speed of light.

Hence, c = d/t = c' = d/(t/γ). This means γ=1.

But, if γ=1, then v = 0, which is a contradiction.


There is the specific math and logic.

Your turn with your math.

 

[chinglu]

Why not replace the sun with a digital clock and declare its reading to be your absolute time? I mean, that's a lot simpler than worrying about (x, y, z) coordinates of planets, right?

If the solar system observers are not in relative motion then the digital clock CAN be used to keep their own clocks synched. If they are in relative motion then they will discover that their clock and the clocks of the others (as well as the sun-clock) are progressing at different rates.

In other words, absolute time is only available if all observers are in a co-moving frame OR are willing to lengthen or shorten their local definition of a second (like the GPS sats do) to match your "universal time synchronizer"...this doesn't mean that Relativity is wrong or that you have uncovered any contradictions.

My experiment is fine.

 

[chinglu]

Not so fast, RJB, perhaps chinglu has uncovered the greatest contradiction of all time! That although relativity predicts the solar system observers find their clocks progressing at different rates, (as you say), very few realize that relativity might also surreptitiously predict that their clocks all progress at the same rate! Holee poo! :m:

Oh wait, no it doesn't. Nevermind.

I posted the exact math.

Refute it or retreat.

 

[arfa brane]

Now, since t' is absolute, we can remove t' from the calculations and all we have left is what Einstein claimed as the time on the moving clocks as t/γ.

Can you explain (without simply repeating it) what "t' is absolute" means?

Since we have what Einstein claimed, and we have what you claim. If you can't do this you should admit you don't know what you're talking about. Or you could just retreat.

But, if γ=1, then v = 0, which is a contradiction.

You see a contradiction because you're assuming something which is wrong.

How many times are you going to post your crap interpretation of what Einstein "claimed"?
There are two synchronised clocks at the origin; one then moves in a closed curve and returns to the other. Why does v have to be greater than 0 at this point?
Why does the clock that moved have to keep moving? Where does Einstein mention that condition in his paper?

 

[Prof.Layman]

shinglu, c=c' in SR. The speed of light should not be considered to have a prime value, should always drop the prime on it because it assumes that the speed of light is the same in every frame of reference. So toward the end of your math you set up the speed of light that was supposed to be the same value to two different values, you shouldn't have done that. So then c' would just equal d/t just like c would, and not d/(t/y) pardon my french it is not so good, lol.

 

[brucep]

My experiment is fine.

Your experiment isn't fine. It's stupid ignorant. But who really cares about a dufus experiment you claim is just fine.

 

[AlphaNumeric]

It is quite clear, here is the math refute it or submit.

Further, in this thread, I am very specific

You're ignoring the various criticisms/problems people have put forth about your claims. And as I've said, if you think what you've provided is mathematically formal and detailed then you're just plain ignorant.

It would appear you're incapable of having a rational informed discussion.

 

[chinglu]

Can you explain (without simply repeating it) what "t' is absolute" means?

Yes, t' is the effect on the accelerating clock. Under SR constant acceleration, the effect on an accelerating clock is absolute moaning both frames agree on the exact deviation to the time.

For example, one solution to the so called twins paradox uses the fact that the twin that leaves the earth must accelerate and hence its time on its clock is less than the stay at home twin. Both frames will agree on this time value.

Since we have what Einstein claimed, and we have what you claim. If you can't do this you should admit you don't know what you're talking about. Or you could just retreat.

You have a problem. I assumed what Einstein was true. Frames must agree the speed of light is c, ignoring gravity and acceleration, and I also assumed that his statement that a clock traveling in a circle will be time dilated relative to the one that did not.

But, by introducing a light pulse when the origins were common, then the origins are again common, both of Einstein's statements cannot be made to be true.

If so, make both of them true.

How many times are you going to post your crap interpretation of what Einstein "claimed"?
There are two synchronised clocks at the origin; one then moves in a closed curve and returns to the other. Why does v have to be greater than 0 at this point?

The effect on the moving clock is caused by the constant relative v for the trip and not the instantaneous v when the clocks are again common..

 

[chinglu]

shinglu, c=c' in SR. The speed of light should not be considered to have a prime value, should always drop the prime on it because it assumes that the speed of light is the same in every frame of reference. So toward the end of your math you set up the speed of light that was supposed to be the same value to two different values, you shouldn't have done that. So then c' would just equal d/t just like c would, and not d/(t/y) pardon my french it is not so good, lol.

You can assume anything you want, but the case must show c'=c for any way you calculate c'.

Now, if you agree "c would, and not d/(t/y)", then you confess the 2nd observer did not measure c as the speed of the light pulse that was emitted when the 2 clocks were at first common.

So, you simply agreed with my position.

 

[chinglu]

Your experiment isn't fine. It's stupid ignorant. But who really cares about a dufus experiment you claim is just fine.

If this statement is true, then you can prove my conclusions are false.

But, since you have been completely unable to do that, good luck!!

 

[chinglu]

You're ignoring the various criticisms/problems people have put forth about your claims. And as I've said, if you think what you've provided is mathematically formal and detailed then you're just plain ignorant.

It would appear you're incapable of having a rational informed discussion.

Well, since my math is very specific and since none of the statements made by you or anyone else refutes the math, then your statements are vacuous.

Here it is again.

1) 2 clocks are common and synched.
2) A light pulse is emitted.
3) One clock moves as claimed by Einstein in a circular path at some constant speed v immediately after light emission.
4) Einstein claimed when the clocks are common again, the moving clock will show t/γ where t is the time that elapsed on the stationary clock since they were first common.
5) Any distance measurement in the y direction relative to the direction of travel of the moving clock has common units of measurement between the two frames.
6) Therefore, since the frames agree the light pulse is a common distance y1 from their common location and their clocks read 2 different times since the light pulse was emitted, then they disagree on the speed of light, which is a contradiction.


Specifically, which of the six steps above is false?

 

[arfa brane]

Here's my analysis of what Einstein's paper says:

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be $$\frac{1}{2}tv^2/c^2$$ second slow.

I assume "t seconds" is measured by the stationary clock at A. Seems reasonable, although not stated. . .

Adding the pulse of light emitted at t = t' = 0 for both clocks, you should also add a way to measure the distance travelled by the pulse of light in respect of t and t'. But that's easy, just arrange a fixed mirror at a distance ct/2 for the non-moving clock such that the mirror is perpendicular to the direction of travel for the moving clock (relative to the stationary one).

So the non-moving clock sees the light pulse arrive back at t seconds (since c is constant). The moving clock when it returns sees the light pulse arrive back at $$\frac{1}{2}tv^2/c^2$$ seconds. Why?
Because during the movement of the travelling clock, the distance to the mirror is length-contracted (for that clock).
According to the moving clock, the light pulse takes less time to get to the mirror and return to A, hence the clock that moved (and is again stationary wrt A) shows a smaller interval of elapsed time, so t' < t.

 

[chinglu]

Here's my analysis of what Einstein's paper says:

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be $$\frac{1}{2}tv^2/c^2$$ second slow.

I assume "t seconds" is measured by the stationary clock at A. Seems reasonable, although not stated. . .

Adding the pulse of light emitted at t = t' = 0 for both clocks, you should also add a way to measure the distance travelled by the pulse of light in respect of t and t'. But that's easy, just arrange a fixed mirror at a distance ct/2 for the non-moving clock such that the mirror is perpendicular to the direction of travel for the moving clock (relative to the stationary one).

So the non-moving clock sees the light pulse arrive back at t seconds (since c is constant). The moving clock when it returns sees the light pulse arrive back at $$\frac{1}{2}tv^2/c^2$$ seconds. Why?
Because during the movement of the travelling clock, the distance to the mirror is length-contracted (for that clock).
According to the moving clock, the light pulse takes less time to get to the mirror and return to A, hence the clock that moved (and is again stationary wrt A) shows a smaller interval of elapsed time, so t' < t.

Nope, you have changed the experiment.

You can look at the 6 steps I provided to AN.

 

[Aqueous Id]

It is a standard configuration in the sense that at the instant they measure, the axis of measurement, it is perpendicular to the instantaneous line of motion.

I agree that GPS proves time dilation exists for the satellite. So, we are in agreement with that point.

I also agree the one rotating has a GR time effect that makes its time less than the one that is not rotating all other thing being equal.

So, as in GPS, we have two operations of time differentials, GR (acceleration) and time dilation.

Now, let's cancel the GR effects since that effect allows the frames to disagree on the speed of light.

OK, so we factor that.

But, now we have the time dilation effect that is not explained. However, unlike GR effects which allows frames to disagree on the speed of light, time dilation does not since its derivation assumes both frames measure c.

But, as proven by GPS, time dilation exists and so one clock must read a different clock reading than the other.

However, since the 2 observers are at the same place again, and they measure the light sphere along a y-axis, and they read different times on their clocks, then they disagree on the speed of light for the time dilation component. But, the time dilation component was built on the condition that the speed of light measured c for both frames.

So, we have a contradiction.

To me, the only contradiction I see is the one that formulates this kind of test. You are projecting to a hypothetical, based on what two observers would calculate, not what they observe. There is no actual phenomenon here. No one "sees" the back side of the sphere with "light-backward-detecting one-way radar" of some kind. The unreality of this is what props up the weird notion that you can overturn something already demonstrated, by oversimplification and blur.

As for trying to decouple GR willy-nilly, that's unsupportable. At least the satellite is at altitude. But in your putative experiment the two observers are in the same cafe on the Champs-Élysées debating SR/GR, with their cosmic screwdrivers deployed, and only for some infinitessimal time period before sun-guy gets whisked off the planet to regain his place in the cafe in space back at t[sub]0[/sub] = t[sub]0[/sub] + 1 Y. In other words, for an instant they were in the same gravitational field.

With time dilation comes the pancaking of the sphere. So now you have an actual sphere in the inertial frame intersected with the spheroid. Model that and find out what kind of geometry describes the intersection, i.e., where the agreement might occur. It's not going to be on any y-axis. There will be a set of az-el angles at which the imaginary spheres intersect, depending on relative velocity, but not at 90° elevation as you imagine.

It's unclear what you think is happening in the transverse direction. If the earth was "coming into" a sphere of its own diameter, it would be as severe a transverse effect as you might imagine. Pushing it out 1 LY to appear flat solves nothing. It's just a trick, to pretend something doesn't exist by scaling it so disproportionately as to wipe it away. However, if it weren't for that nagging little Lorentz factor, there wouldn't be any correction needed for GPS would there? You could just wipe out that 7.2 μs per day and then just deny relativity until the cows come home. The problem is, that little 8.3E-11 variation per day, if not corrected, will place you in Shanghai when you were actually posting from Bugtussle.

If you could formulate an actual realizable experiment, that would be another thing. Of course that's not going to happen. Having admitted (after denying) that GPS proves that relativity is demonstrated, what do you expect to gain by continuing to push styrofoam as science?

I don't see anything that resembles the kind of curiosity that would accompany true inquiry. In general, most people would be less willing to assert their opinions in place of demonstrated results (like GPS) for fear of contaminating their own objectivity, which is a very hard thing to keep in its virgin state, so to speak.

As long as you seem to continue to maintain that the basis for overturning what you know is already demonstrated, based on the imagined "unobservable observation of the distance to the backside of a light sphere", you are sacrificing that objectivity on the altar of . . . what--naive narcissism? Something's not right, anyway, and it's not relativity.

It's just that you don't understand the cause of your presumed contradiction because the circuitous "experiment" is flawed in its premise and assumptions. By the same kind of logic, you can prove that water runs uphill, or that you can read minds, or just about anything that suits you.

Why bother? Any of us could spend our whole lives in actual discovery mode, confronting nature and forcing it to cough up a few more tokens of data. At best we'd know some mote of wisdom at the hour of our death more than we did on the day we were born.