Einstein's clock

**chinglu** · 07-12-12, 07:21 PM

Originally Posted by RJBeery

Don't change the subject, Chinglu. Einstein's specific quotes supporting this effect are irrelevant because his SR postulate on the constancy of light only applies to inertial frames. This is well known. Haven't you ever heard of the time dilation effects of a centrifuge? All of these experiments are basically variants of the centrifuge concept. If you're just looking for attention then I'm done feeding the troll but it's already been explained to you why you haven't dismantled Relativity.

And you cannot just dismiss angular acceleration with a wave of your hand like that! hahaha

This is from another forum

Sure, we can include your ideas.

1) There is acceleration of the moving clock since it travels in a circle. You can calculate "a" using the usual equations and then you can use the SR constant acceleration equations and conclude it is extremely small as compared to time dilation.

2) You may also include the the gravity effect if you like.

However, where you are confused is that these effects are t' which I already accounted for. Since it is absolute, each from can adjust their times accordingly.

Yet, we still have this statement by Einstein which is where you are failing to understand the theory.

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 $\frac{1}{2}tv^2/c^2$ second slow.

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

If you refuse to include this conclusion in with your assessment of SR, then you are a crackpot in the eyes of the theory.

So, I include this conclusion and forced SR into a contradiction.

**chinglu** · 07-12-12, 07:23 PM

Originally Posted by RJBeery

Don't change the subject, Chinglu. Einstein's specific quotes supporting this effect are irrelevant because his SR postulate on the constancy of light only applies to inertial frames. This is well known. Haven't you ever heard of the time dilation effects of a centrifuge? All of these experiments are basically variants of the centrifuge concept. If you're just looking for attention then I'm done feeding the troll but it's already been explained to you why you haven't dismantled Relativity.

And you cannot just dismiss angular acceleration with a wave of your hand like that! hahaha

This is from another forum

Here is Einstein' statement.

Which part of it are you claiming is false?

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 $\frac{1}{2}tv^2/c^2$ second slow.

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

**arfa brane** · 07-12-12, 07:43 PM

chinglu still can't see that his "contradiction" is because he just doesn't understand SR. He can't find any contradiction unless he changes what Einstein is describing in his paper.
For instance, t/γ isn't tv²/2c². The moving clock follows a closed curve, it doesn't travel in a straight line. That means that (x,y,z) in the stationary frame is length-contracted in the moving frame.

**chinglu** · 07-12-12, 08:07 PM

Originally Posted by arfa brane

chinglu still can't see that his "contradiction" is because he just doesn't understand SR. He can't find any contradiction unless he changes what Einstein is describing in his paper.
For instance, t/γ isn't tv²/2c². The moving clock follows a closed curve, it doesn't travel in a straight line. That means that (x,y,z) in the stationary frame is length-contracted in the moving frame.

Hey bonehead, tv²/2c² is an approximation by Einstein.

You can see it here.

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by $\frac{1}{2}tv^2/c^2$ (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
http://www.fourmilab.ch/etexts/einstein/specrel/www/

**arfa brane** · 07-12-12, 09:33 PM

t / γ = t√(1- v²/c²) ≠ t (v²/2c²), which is what chinglu's been claiming.
And that last formula is the difference between two times, not an interval of time.

**chinglu** · 07-13-12, 06:34 PM

Originally Posted by arfa brane

t / γ = t√(1- v²/c²) ≠ t (v²/2c²), which is what chinglu's been claiming.
And that last formula is the difference between two times, not an interval of time.

I did not claim t / γ = t√(1- v²/c²) = t (v²/2c²)

I said t' = t/γ.

Einstein used the phrase slowed by. That is different.

Einstein claimed the moving clock was slowed by $\frac{1}{2}tv^2/c^2$ when ignoring magnitudes of 4th and higher order.

So, let's look at the math.

Einstein claimed t' = t/γ.

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

He then rewrote that as $t' = t\sqrt{1-v^2/c^2}$

That is also
$t' = t - (1 - \sqrt{1-v^2/c^2})t$

So, based on the above, Einstein claimed the moving clock is slowed by a factor of $1-\sqrt{1-v^2/c^2}$

So, we start with $1-v^2/c^2=1-v^2/c^2$

We are permitted to ignore magnitudes of 4th and higher order concerning the variables as indicated by Einstein, so we have the below.

$1-v^2/c^2+1/4(v^4/c^4)\approx1-v^2/c^2$

$(1-1/2(v^2/c^2))^2\approx1-v^2/c^2$

$(1-1/2(v^2/c^2))\approx\sqrt{1-v^2/c^2}$

$1-\sqrt{1-v^2/c^2}\approx1/2(v^2/c^2)$

Therefore, exactly, as I said, Einstein's assertion was an approximation of the amount of time that is removed from the stationary clock for the time of the moving clock.

**AlphaNumeric** · 07-13-12, 06:41 PM

Originally Posted by chinglu

You are not telling the truth.

Coming from you that's pretty rich! You've repeatedly lied about what you think I said about Cantor, even after I've corrected you. Complaining about the injustice you feel when you think people lie about you is a touch hypocritical.

Originally Posted by chinglu

I provided the complete mathematics to solve the problem.

No, you didn't. Other people have already pointed out your mistaken logic. You're always doing this, you think what you provide is 'the complete mathematics' when in fact it's almost completely devoid of mathematics. In several places you just assert what you think SR says, you don't show it. It's those places where your argument stands or falls and since you haven't justify your claims properly you haven't demonstrated them correct. Now they've been shown to be wrong, as highlighted by others.

Do you think your posts are mathematically detailed?

Originally Posted by chinglu

Here it is for the 3rd time.

If I said after the first time "You have no provided enough detail to justify your claim" why do you think I'd accept it after the 2nd or 3rd time of you repeating it? I read it the first time, that's why I said it wasn't detailed enough.

For someone who claims you understand logic and analysis you have no idea what 'justified' means.

Also, I gave you a 6 step procedure to my conclusion. You have still been completely unable to refute any of the steps that lead to the fatal conclusion that SR is logically false. What is the problem?

Originally Posted by chinglu

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

I can only hazard a guess that you've never opened a book on special relativity because there's a lot more mathematics involved in the scenario you describe than the maths you provide. You haven't actually done any calculations. Is there some reason you refuse to flesh out your argument? Are we at the limits of your mathematical capabilities?

Originally Posted by chinglu

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.

Rather than asserting the formulae you state why don't you actually do the calculations, line by line, equation by equation? You haven't worked out what SR says, you've just stated what you think it says. You're relying on your intuitive grasp of relativity and as has been seen in various threads on light spheres, you cannot even do simple 2+1 dimensional Lorentz calculations for objects moving along a common line, never mind polygon circumferences.

Originally Posted by chinglu

There is the specific math and logic.

How naive you are to think what you just provided was 'specific math and logic'. Have you ever actually done a course in maths or logic?

**AlphaNumeric** · 07-13-12, 06:46 PM

Originally Posted by chinglu

I did not claim t / γ = t√(1- v²/c²) = t (v²/2c²)

I said t' = t/γ.

Einstein used the phrase slowed by. That is different.

Einstein claimed the moving clock was slowed by $\frac{1}{2}tv^2/c^2$ when ignoring magnitudes of 4th and higher order.

So, let's look at the math.

Einstein claimed t' = t/γ.

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

He then rewrote that as $t' = t\sqrt{1-v^2/c^2}$

That is also
$t' = t - (1 - \sqrt{1-v^2/c^2})t$

So, based on the above, Einstein claimed the moving clock is slowed by a factor of $1-\sqrt{1-v^2/c^2}$

So, we start with $1-v^2/c^2=1-v^2/c^2$

We are permitted to ignore magnitudes of 4th and higher order concerning the variables as indicated by Einstein, so we have the below.

$1-v^2/c^2+1/4(v^4/c^4)\approx1-v^2/c^2$

$(1-1/2(v^2/c^2))^2\approx1-v^2/c^2$

$(1-1/2(v^2/c^2))\approx\sqrt{1-v^2/c^2}$

$1-\sqrt{1-v^2/c^2}\approx1/2(v^2/c^2)$

Therefore, exactly, as I said, Einstein's assertion was an approximation of the amount of time that is removed from the stationary clock for the time of the moving clock.

Are we seeing the ham fisted way you go about calculating things? Your way is extremely ad-hoc and doesn't generalise. The simplest, most direct and more general approach is a Taylor series,

$t' = t\left( 1 - \frac{v^{2}}{c^{2}}\right)^{-\frac{1}{2}} = t\left( 1 - \frac{1}{2} \frac{v^{2}}{c^{2}} + O( \frac{v^{4}}{c^{4}} )\right)$

1 line of work! It's just the truncation of $(1+x)^{\alpha} = 1 + \alpha x + \frac{1}{2!}\alpha(\alpha-1)x^{2} + \ldots = \sum_{n}\binom{\alpha}{n} x^{n}$ , something children learn in high school.

**chinglu** · 07-13-12, 06:54 PM

Originally Posted by AlphaNumeric

Are we seeing the ham fisted way you go about calculating things? Your way is extremely ad-hoc and doesn't generalise. The simplest, most direct and more general approach is a Taylor series,

$t' = t\left( 1 - \frac{v^{2}}{c^{2}}}\right)^{\frac{1}{2}} = t( 1 - \frac{1}{2} \frac{v^{2}}{c^{2}}} + O( \frac{v^{4}}{c^{4}}} )$

1 line of work! It's just the truncation of $(1+x)^{\alpha} = 1 + \alpha x + \frac{1}{2!}\alpha(\alpha-1)x^{2} + \ldots = \sum_{n}\pmatrix{ \alpha \\ n }x^{n}$ , something children learn in high school.

Since I am trying to follow Einstein's thoughts to these simpletons, why would I introduce more logic that would generate even more questions?

My reasoning did not require a generalization and only needed to comply with Einstein's statements.

So, I did that.

But, that in and of itself puts you in an impossible situation.

You are required to comply with Einstein's conclusions about the clock moving in a circle and you are also required to comply with the lack of length contraction in the y direction.

Finally, you are required to apply SR to these conclusions and assert ignoring GR effects, the frames must agree the speed of light is c.

So, we have different times on the clocks when they are again common.

We have the same exact same position of the light sphere along the y axis and we also have that the frames measure the speed of light as c for all these facts.

Exactly how are you going to make all of Einstein's assertions true for this experiment?

You are a mod and self proclaimed expert.

So, make it happen.

Otherwise, SR is a false theory.

**AlphaNumeric** · 07-13-12, 07:27 PM

Originally Posted by chinglu

Since I am trying to follow Einstein's thoughts to these simpletons, why would I introduce more logic that would generate even more questions?

It illustrates the sort of poor, inefficient thinking you have when it comes to maths and physics.

Originally Posted by chinglu

Finally, you are required to apply SR to these conclusions and assert ignoring GR effects, the frames must agree the speed of light is c.

So, we have different times on the clocks when they are again common.

We have the same exact same position of the light sphere along the y axis and we also have that the frames measure the speed of light as c for all these facts.

Exactly how are you going to make all of Einstein's assertions true for this experiment?

I don't have to do anything. You continue to fail to do the necessary calculations to justify your claim. You're just repeating assertion after assertion. Do every line of calculation. Don't just say "Oh SR says this....", prove it. The onus is on you. If you cannot present and justify your case I have nothing to respond to. You've shown in the past you cannot do light sphere Lorentz transforms in just 1d, never mind moving around a polygon. You're relying on your grasp of relativity to make heuristic statements and that is insufficient.

Originally Posted by chinglu

Otherwise, SR is a false theory.

Prove to me you're not a serial killer. Otherwise you are.

If I wanted to be slightly less dramatic I could use your logic to say that since you haven't provided the necessary calculations to demonstrate your claims your claims are false. Besides, in the past when I have done line by line explicit calculations which demonstrate your claims about light spheres incorrect you just ignored them. Or do you now accept that Andrew Banks was wrong about light spheres under Lorentz transforms? Note that if you refuse to answer this direct question then I refuse to answer yours. I'm saying this because if you're unwilling to acknowledge previous explicit calculations have demonstrated you wrong then there's no point in providing more explicit calculations for you just to ignore again.

**chinglu** · 07-13-12, 08:02 PM

Originally Posted by AlphaNumeric

It illustrates the sort of poor, inefficient thinking you have when it comes to maths and physics.

I don't have to do anything. You continue to fail to do the necessary calculations to justify your claim. You're just repeating assertion after assertion. Do every line of calculation. Don't just say "Oh SR says this....", prove it. The onus is on you. If you cannot present and justify your case I have nothing to respond to. You've shown in the past you cannot do light sphere Lorentz transforms in just 1d, never mind moving around a polygon. You're relying on your grasp of relativity to make heuristic statements and that is insufficient.

Prove to me you're not a serial killer. Otherwise you are.

If I wanted to be slightly less dramatic I could use your logic to say that since you haven't provided the necessary calculations to demonstrate your claims your claims are false. Besides, in the past when I have done line by line explicit calculations which demonstrate your claims about light spheres incorrect you just ignored them. Or do you now accept that Andrew Banks was wrong about light spheres under Lorentz transforms? Note that if you refuse to answer this direct question then I refuse to answer yours. I'm saying this because if you're unwilling to acknowledge previous explicit calculations have demonstrated you wrong then there's no point in providing more explicit calculations for you just to ignore again.

AN, you have been given an opportunity to refute the precise calculations I have made.

If I am wrong on any point, specifically indicate why using math.

Otherwise, comply with my conclusions.

If you provide any math that counters my own for this problem, I will blow you out of the water.

**Aqueous Id** · 07-13-12, 08:29 PM

Originally Posted by chinglu

Otherwise, SR is a false theory.

That's ludicrous.

It's corrected for in GPS, and you already acknowledged that. Besides conquering the math, you still have the real world to contend with.

**chinglu** · 07-13-12, 08:36 PM

Originally Posted by Aqueous Id

That's ludicrous.

It's corrected for in GPS, and you already acknowledged that. Besides conquering the math, you still have the real world to contend with.

I never said all SR was verified with GPS.

Now, can you refute the math I presented which shows SR arrives at a contradiction?

Simply show which part of my math is wrong.

Otherwise, you have to comply with my math.

**AlexG** · 07-13-12, 08:41 PM

This is just getting crankier as it goes along.

**brucep** · 07-13-12, 10:27 PM

If this isn't trolling then I don't know what trolling is.

**chinglu** · 07-14-12, 07:57 PM

It must be noted that there has been no one that has refuted the findings of this thread that SR results in a contradiction given the Einstein thought experiment of a clock moving in a circle when combined with an emission of a light pulse when the two clocks were initially common.

**arfa brane** · 07-14-12, 09:40 PM

It must be noted that there has been no one that has refuted the findings of this thread that SR results in a contradiction given the Einstein thought experiment of a clock moving in a circle when combined with an emission of a light pulse when the two clocks were initially common.

It should also be noted that chinglu has not found a contradiction; the contradiction is between what chinglu "understands" Einstein's paper to be saying and what it's actually saying.
This can happen if you aren't too good at math, or logic.
It also illustrates how someone can keep insisting that nobody can refute their "math" or "logic", despite having their ass handed to them on an internet forum, more than once. chinglu is certain that his "math" is correct, despite several people pointing out that it isn't, it doesn't even correspond to Einstein's thought experiment, it isn't what happens in the real world. It's just wrong, but some people actually enjoy living in a state of delusion. Especially if they see "evidence" that people are "blindly following" some idea which they know must be wrong, because, well, because nobody can "refute" their logic. And around we go again.

This thread is more interesting for being a display of wilful and persistent ignorance than any science it might (just) have in it. A textbook example, I'd say.

Now, where's that bottle of valium. . .

**chinglu** · 07-15-12, 06:30 PM

Originally Posted by arfa brane

It should also be noted that chinglu has not found a contradiction; the contradiction is between what chinglu "understands" Einstein's paper to be saying and what it's actually saying.
This can happen if you aren't too good at math, or logic.
It also illustrates how someone can keep insisting that nobody can refute their "math" or "logic", despite having their ass handed to them on an internet forum, more than once. chinglu is certain that his "math" is correct, despite several people pointing out that it isn't, it doesn't even correspond to Einstein's thought experiment, it isn't what happens in the real world. It's just wrong, but some people actually enjoy living in a state of delusion. Especially if they see "evidence" that people are "blindly following" some idea which they know must be wrong, because, well, because nobody can "refute" their logic. And around we go again.

This thread is more interesting for being a display of wilful and persistent ignorance than any science it might (just) have in it. A textbook example, I'd say.

Now, where's that bottle of valium. . .

Here is the math. Indicate why there is an error or confess you are a troll.

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.

**Aqueous Id** · 07-15-12, 06:48 PM

Originally Posted by chinglu

Here is the math. Indicate why there is an error
:
By SR, c = d/t.

Here is your first error. You are omitting the definition of what this means. Without clarifying this initial principle, you set up the false conclusion.

**arfa brane** · 07-15-12, 08:20 PM

Originally Posted by chinglu

Since I am trying to follow Einstein's thoughts to these simpletons, why would I introduce more logic that would generate even more questions?

My reasoning did not require a generalization and only needed to comply with Einstein's statements.

But Einstein implies a Taylor expansion (although he doesn't explicitly state it), he uses the phrase "ignoring higher order terms" which, to anyone who has done calculus means "use a Taylor expansion and leave out everything with degree > 2".
Taylor series are ubiquitous in math and physics, but by no means the only type of expansion. In short, you're pointing out to everyone that you don't really understand Einstein's paper let alone the math in it.

So you're looking a bit simpleton-ish.

You are required to comply with Einstein's conclusions about the clock moving in a circle and you are also required to comply with the lack of length contraction in the y direction.

And you are required to define what "lack of length contraction" means, in terms of the stationary and moving (frames of reference for the) clocks. However, it seems all you are able to do is repeat yourself and repeat the same basic errors each time. Are you expecting something different, or are you convinced you aren't capable of making mistakes?

Since, here we are, n pages later and you haven't admitted any. Intelligent people make mistakes, but usually man up and admit they did.