Is the gravitational time dilatation a real effect?

[nismaratwork]

I don't see the point in bringing up what someone said in another thread. He may have changed his mind since then. We are all going through a learning process. Try to stick to his arguments in this thread and try to avoid attacking people rather than their arguments.

Kev, that isn't another thread, that's a personal website with his name as the domain name. That implies a strong commitment to an idea, and when a thread is going in circles, sometimes it is a learning process, and sometimes it's a bastardized Socratic Method. There is nothing wrong with being alert to which is the case in a given situation, but in this case I am inclined to agree with you; this has no bearing on the discussion as it has played out here.

Kamil Szot: You have nothing to apologize for, especially given your willingness to take advice and do some Independent learning and asking specific questions. There is no drudgery here, as Kev says, it's learning.

@Starthaus: Stephen Hawking no longer believes in the Big Bang, so I'm not sure that can be considered a crazy idea. I haven't read the site (don't want to prejudice myself in this scenario), but unless it's something really nutty, it could be a valid, albeit uncommon view.

editing: I've read the site, it seems to be based on some pop-sci stuff about the highly controversial Dark Flow, and the notion of colliding bubble universes. While that is not commonly accepted, it's not claiming that aliens built the pyramids either. I think Kamil is genuinely interested in learning, but too likely to leap to conclusions; who here hasn't had that problem at some point?

 

[starthaus]

I am not disputing that the rotational effect can overwhelm the effect due to difference in gravitational potetial.

Then try treating the problem correctly, you have been given the tools.
As an aside, one of the best ,real life, proofs of the superposition of effects in calculating the correct gravitational time dilation is the way to calculate the GR corrections to the GPS. You can see that all the effects are important.

 

[starthaus]

but unless it's something really nutty,

It is.

 

[nismaratwork]

It is.

It is nutty, in the manner that Kamil presents it, but do you think it's nutty because he's a nut, or because he has misunderstood a host of popular theories and observations? I believe that he means well, wants to learn, but as I said, is too inclined to try and formulate conclusions prematurely. It is possible that you are correct in your implication, and he is a crackpot, but I didn't get that feel. He strikes me as a victim of learning physics as it is presented in media, and trying to make sense of it. In that context, we need to teach him, don't we? This is all about learning, and while his conclusions are nutty, it is one issue that is very popular. I'm willing to give him the chance to learn, and no longer be mislead by popsci. I've seen you in other threads, you are a very smart guy with a superior grasp of mathematics, maybe he could benefit from your expertise.

 

[yuiop]

Then try treating the problem correctly, you have been given the tools.

This is a vague statement leaving the readers of this thread unsure about what you think is not correct. Are you saying that the equations I gave are not generalised enough (they only apply to purely radial motion) or are you simply saying they are wrong?

Can we clear something up. The Schwarzschild metric is correct, but you seem to to define it as incorrect because it does not cover the fully generalised case of a rotating charged body. The Schwarzschild metric is a special case. A special case is not "incorrect" because it is not fully generalised. Your definition is that the Schwarzschild metric is "wrong" because it yields incorrect results if the body is rotating or charged. In future when you state something is wrong can you make it clear what you think is wrong or if you simply think the equation is not generalised enough and if you know the correct answer, please state it.

By your definition SR is wrong because it does not cover the generalised case of curved space. You do not seem to understand the meaning of a special case.

I was giving the special case of purely radial motion about a non-rotating uncharged body.

I tried to make that clear when I said in #59:

Keep it simple for now and assume r1>r2>2m and purely radial motion in Schwarzschild coordinates.

 

[nismaratwork]

Forgive me for this, but the mutual dislike that emerges whenever you guys (starthaus and kev) get on the same thread makes for really excellent reading. From the conflict, I find the content becomes more rigorous, but you two really should just kiss and make up.

In this case, I can't see how Kev is wrong, given the parameters he's offered (looks at starthaus).

 

[starthaus]

This is a vague statement leaving the readers of this thread unsure about what you think is not correct. Are you saying that the equations I gave are not generalised enough (they only apply to purely radial motion) or are you simply saying they are wrong?

What I have been telling you all along s that your two scenarios (A younger than B and A as old as B) are not the complete list of possible scenarios. You get the truncated list because you have been ignoring the effect of the angular speed. The angular speed can play tremendous influence on the outcome.
If you want to see how all the scenarios unfold, I can recommend a few excellent treatments of time dilation effects in GPS. http://relativity.livingreviews.org/Articles/lrr-2003-1/ is one of the best.

 

[yuiop]

What I have been telling you all along s that your two scenarios (A younger than B and A as old as B) are not the complete list of possible scenarios. You get the truncated list because you have been ignoring the effect of the angular speed. The angular speed can play tremendous influence on the outcome.
If you want to see how all the scenarios unfold, I can recommend a few excellent treatments of time dilation effects in GPS. http://relativity.livingreviews.org/Articles/lrr-2003-1/ is one of the best.

We have examined the effect of angular speed in great detail in several other threads. This thread is about time dilation due to gravitational potetial. We should focus on that and come to a yes/no answer as to whether it is real or not.

I am not disputing that gravitational time dilation is real, I am disputing your method of illustrating it.

I take it from the above quote that your vote (along with mine) is yes, gravitational time dilation is real and clocks (and biological processes etc) really do slow down low down in a gravitational field.

Although this seems a clear cut issue, there is an implication that time stops exactly at the event horizon. There are however some get out clauses. The time dilation equations assume a stationary observer and the conventional view is that it is not possible to remain stationary at the EH. The equations for time dilation can also be formulated in such a way that the time dilation is indeterminate when r = 2M.

 

[starthaus]

We have examined the effect of angular speed in great detail in several other threads. This thread is about time dilation due to gravitational potetial. We should focus on that and come to a yes/no answer as to whether it is real or not.

It is real, that was never in debate. Your scenarios A and B are not.

 

[yuiop]

It is real, that was never in debate. Your scenarios A and B are not.

What is wrong with the scenarios here in the special case of a non-rotating massive body and purely radial motion?

I have not read all this thread, but I think I can shed some light on the question posed in the title of this thread, "Is the gravitational time dilation a real effect?".

Gravitational twins paradox thought experiment:

Twins A and B are r1. Twin A slowly descends to r2 and waits there. A network of stationary observers monitor the descent rate of A. After about 50 years by B's clock, B descends slowly to r2 and stops alongside twin A. The network of observers confirm that B descended at the same rate as A.

Two solutions.

1) If it is agreed that twin A is now younger than twin B (assuming they were the same age at the start) then gravitational time dilation is a real effect.

2) If it is agreed that twin A and twin B are biologically the same age after the experiment then gravitational time dilation is just an illusion or artifact of using coordinate measurements.

My intuition is with answer (1) but others may have a different physical interpretation.

 

[starthaus]

For the top of the tower use:

$$ds_1 = dt\sqrt{1-2M/r_1}$$

For the bottom of the tower use:

$$ds_2 = dt\sqrt{1-2M/r_2}$$

Vary r1 and r2 according to your taste in tower heights. For any tower with r1 greater than r2, the proper time ds2 will always be less than ds2 when the twins meet (for purely radial motion and a non-rotating uncharged massive body and non-rotating uncharged twins).

No,


$$d\tau_A/d\tau_B=\frac{\sqrt{1-r_s/r_1}}{\sqrt{1-r_s/r_2}}\frac{\sqrt{1-(\omega r_1/c)^2/(1-r_s/r_1)}}{\sqrt{1-(\omega r_2/c)^2/(1-r_s/r_2)}}$$

If $$r_1>r_2$$

$$\frac{\sqrt{1-r_s/r_1}}{\sqrt{1-r_s/r_2}}>1$$

and

$$\frac{\sqrt{1-(\omega r_1/c)^2/(1-r_s/r_1)}}{\sqrt{1-(\omega r_2/c)^2/(1-r_s/r_2)}}<1$$

so the effects counter each other. The net effect may be either greater or smaller than unity. This is what I have been telling you all along.

 

[DrGreg]

For the top of the tower use:

$$ds_1 = dt\sqrt{1-2M/r_1}$$

For the bottom of the tower use:

$$ds_2 = dt\sqrt{1-2M/r_2}$$

Vary r1 and r2 according to your taste in tower heights. For any tower with r1 greater than r2, the proper time ds2 will always be less than ds2 when the twins meet (for purely radial motion and a non-rotating uncharged massive body and non-rotating uncharged twins).

No,


$$d\tau_A/d\tau_B=\frac{\sqrt{1-r_s/r_1}}{\sqrt{1-r_s/r_2}}\frac{\sqrt{1-(\omega r_1/c)^2/(1-r_s/r_1)}}{\sqrt{1-(\omega r_2/c)^2/(1-r_s/r_2)}}$$

If $$r_1>r_2$$

$$\frac{\sqrt{1-r_s/r_1}}{\sqrt{1-r_s/r_2}}>1$$

and

$$\frac{\sqrt{1-(\omega r_1/c)^2/(1-r_s/r_1)}}{\sqrt{1-(\omega r_2/c)^2/(1-r_s/r_2)}}<1$$

so the effects counter each other. The net effect may be either greater or smaller than unity. This is what I have been telling you all along.

The bit in bold implies $\omega = 0$. Please address the problem kev is talking about instead of inventing your own problem.

 

[starthaus]

The bit in bold implies $\omega = 0$. Please address the problem kev is talking about instead of inventing your own problem.

Please start reading at post 58 which is an answer to kev's post 57. There is no $$\omega=0$$ specified in 57 , hence my correction(s).

 

[DrGreg]

Please start reading at post 58 which is an answer to kev's post 57. There is no $$\omega=0$$ specified in 57 , hence my correction(s).

So what? Kev forgot to explicitly specify $\omega=0$ when he first formulated his own thought experiment and then clarified it later. It's his example, he's entitled to impose any restrictions he likes, as long as they're not impossible.

 

[Dale]

starthaus, I don't know why you have it out for kev, but it is pretty ridiculous. Usually, after several pages of acrimonious diatribe, it turns out that all of kev's original claims were factually correct and your only criticism is that he didn't derive the most general case to your satisfaction.

It is not necessary to do so on an internet forum for every single post (particularly since you almost never do so either). Here you have hijacked the thread for no benefit to anyone. I hope the OP got what he needed before you joined.

 

[starthaus]

So what? Kev forgot to explicitly specify $\omega=0$ when he first formulated his own thought experiment and then clarified it later. It's his example, he's entitled to impose any restrictions he likes, as long as they're not impossible.

He clarified a few posts later, after he realized that his statements are incorrect.

 

[starthaus]

starthaus, I don't know why you have it out for kev, but it is pretty ridiculous. Usually, after several pages of acrimonious diatribe, it turns out that all of kev's original claims were factually correct and your only criticism is that he didn't derive the most general case to your satisfaction.

I don't have anything against kev, I don't like his hacky methods that involve putting in results by hand followed by shaky proofs.

It is not necessary to do so on an internet forum for every single post (particularly since you almost never do so either). Here you have hijacked the thread for no benefit to anyone. I hope the OP got what he needed before you joined.

Hopefully the OP got that the rotational effects need to be considered since they can overwhelm the difference in gravitational potential. The OP (and kev) also got a reference to a real life proof of the time dilation effects, the GPS. I wouldn't call that nothing.

 

[Dale]

I don't have anything against kev

Then I would hate to read what you would write to someone that you do have something against.

 

[starthaus]

Then I would hate to read what you would write to someone that you do have something against.

Try keeping it professional, ok? No point in getting personal.

 

[Dale]

Try keeping it professional, ok? No point in getting personal.

 

[nismaratwork]

Try keeping it professional, ok? No point in getting personal.

I remember that other thread you and kev fought for a few hundred posts. I think there is clearly something here. Maybe you two could PM a bit and come to an understanding? From the outside looking in, I'm just here, and I assume you two have a longstanding grudge.

 

[Al68]

Try keeping it professional, ok? No point in getting personal.

I don't have anything against kev, I don't like his hacky methods that involve putting in results by hand followed by shaky proofs.

Then why not just say that you disapprove of his method and why, show your own if you like, and move on instead of hijacking threads for hundreds of posts?

That would preserve the usefulness of the thread to others.

 

[starthaus]

Then why not just say that you disapprove of his method and why, show your own if you like,

This is precisely what I did.

 

[Al68]

Then why not just say that you disapprove of his method and why, show your own if you like,

This is precisely what I did.

LOL. The key word in my post is just.

 

[starthaus]

LOL. The key word in my post is just.

If you trolled less and you read more , you'd be so much better off.

 

[nismaratwork]

It would be trolling if it were not completely accurate, and a sentiment echoed by others.

 

[Passionflower]

What I wanted to say is that universe might end before you receive last signal no matter how long finite time of existence universe has ahead of itself. Maybe not if universe final fate is big crunch.

In principle one can only have a fully developed event horizon if spacetime is not closed.