Is the gravitational time dilatation a real effect?

[Kamil Szot]

That is completely arbitrary. You don't seem to understand that in GR the whole concept of simultaneity is up to the whim of whoever specifies the coordinate system. It is only a label attached to a set of events, with no significance other than to identify the events. You are free to re-label as desired.

In SR what is simultaneous depends on frame of reference.

You say that in GR what is simultaneous is not only dependent on frame of reference but also on which set from equivalent sets of coordinates you pick to describe events that you are interested in?

Does frame of reference and set of coordinates in GR precisely imply how you should define what it means to be 'simultaneous'?

If so then my question is still valid:

Do you know any frame of reference and any set of coordinates that imply simultaneity by which 12:00:00 PM 06.17.2010 Earth is after the event of some freefalling object passing some EH?


I think that you can't have full freedom in choosing how do you define simultaneity in GR. If that was the case I could use GR instead of Newton mechanics to describe my neighborhood and declare such simultaneity that event of me sitting at my computer now an event of my neighbors house being built (hundred years ago by Newtonian coordinates) are exactly simultaneous.


I find it very strange that GR might not have notion of simultaneity.

If you use simpler, less precise theory to describe reality some new qualities might crop up, like absolute time in Newton mechanics if you use it instead of SR. But this qualities are always (?) derived from similar qualities in more precise theory. Newtons absolute time is just SR time that is shared by all slowly moving inertial systems. Same way SR notion of simultaneity becomes Newtons absolute notion of simultaneity.

Can you explain how arbitrary simultaneity of GR can transform into very precisely defined notion of simultaneity in SR when you are using SR instead GR to describe world around you?




I want to apologize to you all for my poor quality English. Unfortunately I'm not a native English speaker and I'm always afraid that this might be the cause of me not being able to convey what I'm meaning. If you spot language barrier between us please ask me questions and I'll try to rephrase what I wrote somehow.

 

[Dale]

In SR what is simultaneous depends on frame of reference.

You say that in GR what is simultaneous is not only dependent on frame of reference but also on which set from equivalent sets of coordinates you pick to describe events that you are interested in?

Does frame of reference and set of coordinates in GR precisely imply how you should define what it means to be 'simultaneous'?

For practical purposes "reference frame" is synonymous with "coordinate system" (there are subtle differences that are not relevant here). So, simultaneity is simply the set of events whose time coordinate is the same. I don't know what distinction you are trying to make between "reference frame" and "coordinate system".

If so then my question is still valid:

Do you know any frame of reference and any set of coordinates that imply simultaneity by which 12:00:00 PM 06.17.2010 Earth is after the event of some freefalling object passing some EH?

Yes, I have already answered this question multiple times. You should read this paper: http://arxiv.org/abs/gr-qc/0311038 Note that you can specify B so as to make any given pair of events simultaneous.

I think that you can't have full freedom in choosing how do you define simultaneity in GR. If that was the case I could use GR instead of Newton mechanics to describe my neighborhood and declare such simultaneity that event of me sitting at my computer now an event of my neighbors house being built (hundred years ago by Newtonian coordinates) are exactly simultaneous.

Yes, you could do that in GR. All predictions of physics would remain unchanged under such a coordinate transformation.

I find it very strange that GR might not have notion of simultaneity.

If you use simpler, less precise theory to describe reality some new qualities might crop up, like absolute time in Newton mechanics if you use it instead of SR. But this qualities are always (?) derived from similar qualities in more precise theory. Newtons absolute time is just SR time that is shared by all slowly moving inertial systems. Same way SR notion of simultaneity becomes Newtons absolute notion of simultaneity.

Can you explain how arbitrary simultaneity of GR can transform into very precisely defined notion of simultaneity in SR when you are using SR instead GR to describe world around you?

Locally you can always construct an SR inertial frame which is valid only over a small region of spacetime without significant curvature. Just as the Newtonian concept becomes limited to objects that are moving slowly, so the SR concept becomes limited to objects that are nearby.

I want to apologize to you all for my poor quality English. Unfortunately I'm not a native English speaker and I'm always afraid that this might be the cause of me not being able to convey what I'm meaning. If you spot language barrier between us please ask me questions and I'll try to rephrase what I wrote somehow.

Your English is fine, your physics is what is lacking. The problem is that you are asking the same questions over and over and rejecting the answers instead of trying to learn the new concepts. Perhaps you are assuming that your difficulty in understanding is due to your perceived language barrier, but to me it seems that what is foreign here is not so much the language as the physics.

I am really trying to be helpful, but frankly going in circles like this is extremely frustrating. Please stop asking the same questions and making the same assertions that I have already told you are wrong. If you don't understand an explanation then let's examine that in more detail by asking new questions that get at the root of your confusion, but if your only goal is to listen to yourself talk then you don't need me for that.

 

[nismaratwork]

If I understood it to the extent you do I wouldn't be asking questions about it here.

Purpose of my questions is broadening my understanding. And I already understand few things I have not understood before so from my point of view your responses are far from being pointless, and I'm very thankful to members of this forum that respond to this thread.

You're not listening, I'm not insulting your level of knowledge, I'm saying you need more basic study first, or to listen to the answers to your questions. In short I'm questioning your approach, not your mind, I want to make that clear. I don't mean to be insulting, I just think some time spent reading the papers DaleSpam referenced would do you a lot of good. Then, you can ask specific questions about that paper, and we can answer them, from which we can work back to this point.

 

[Kamil Szot]

For practical purposes "reference frame" is synonymous with "coordinate system" (there are subtle differences that are not relevant here). So, simultaneity is simply the set of events whose time coordinate is the same. I don't know what distinction you are trying to make between "reference frame" and "coordinate system".

Sorry. I didn't notice that coordinate system and frame of reference are used interchangeably so I thought that these are two different things. I thought coordinate system was just that (Cartesian, polar, hyperbolic, etc.) and frame of reference was some set of coordinates moving with some speed and acceleration.

Yes, I have already answered this question multiple times. You should read this paper: http://arxiv.org/abs/gr-qc/0311038 Note that you can specify B so as to make any given pair of events simultaneous.

Thank you. I promise not to ask anyone any question about simultaneity in GR before reading that.

Yes, you could do that in GR. All predictions of physics would remain unchanged under such a coordinate transformation.

That's very strange. If me sitting here now and event of my neighbors house being built 100 years ago can be simultaneous events that I could affect how this house was built.

I still can't get my head around the simultaneity being completely arbitrary. I guess I'll have to see some math to believe it. I hope I'll find it in paper you recommended.

Locally you can always construct an SR inertial frame which is valid only over a small region of spacetime without significant curvature. Just as the Newtonian concept becomes limited to objects that are moving slowly, so the SR concept becomes limited to objects that are nearby.

I though SR doesn't require locality. Just flat space and only inertial movement. As long as these things are true I can draw simultaneity line on the diagram and precisely decide if something on the other end of universe already happen or is yet to happen. It depends on my speed and direction of movement but that's all. Simultaneity in SR is precisely defined and quite limited, for example event lying inside my light cone can never be simultaneous with event of me being now, here.

Your English is fine, your physics is what is lacking.

Great to hear that.

The problem is that you are asking the same questions over and over and rejecting the answers instead of trying to learn the new concepts.

I'm trying. For example now I am trying to understand concept of simultaneity being completely arbitrary in GR and how it fits observable relations like gravitational time dilatation. It's not easy so I'm trying to rephrase my questions to get additional answers. I'm also asking new questions. I can't just learn concepts by heart. I need to understand them, how they are possible, how they work.

I am very grateful for each new piece of information that you give me by answering, what it for you seems to be, same question over and over again.

Perhaps you are assuming that your difficulty in understanding is due to your perceived language barrier, but to me it seems that what is foreign here is not so much the language as the physics.

Physics is definitely less foreign to me than English language. I was one of the laureates of national level of eliminations for IPhO at age 18. Unfortunately wasn't chosen for the international competition because there was enough laureates better than me that year. My country has population about 38 mln people. I'm also member of mensa, and firm believer in experiment, mathematical reasoning and science as a whole, so I think that I might have some capacity of understanding concepts that are new to me, especially in area of physics.

I am really trying to be helpful, but frankly going in circles like this is extremely frustrating.

I know how it's like, and I apologize for that. I once again want to thank you. All of you already helped me broaden my understanding of GR more than anyone I talked to before. I must admit I majored in CS not physics.

 

[Kamil Szot]

You're not listening, I'm not insulting your level of knowledge, I'm saying you need more basic study first, or to listen to the answers to your questions. In short I'm questioning your approach, not your mind, I want to make that clear.

Good that you clarify because I didn't get that from what you wrote. What I understood was more like 'Is it morally wrong to ignore him until he goes away, because he obviously doesn't know or get anything?' :-)

I don't mean to be insulting, I just think some time spent reading the papers DaleSpam referenced would do you a lot of good. Then, you can ask specific questions about that paper, and we can answer them, from which we can work back to this point.

I think you are right and I am going to do just that. If you can think of some other materials that might help me with understanding of GR, time dilatation, deformation of space, simultaneity and how EH works as long as objects in remote stationary frame of reference are concerned, please direct me to them.

Also if you could address any questions that I asked in this thread by answering them or pointing out why there is no answer to them I'll also be grateful.

I'm very sorry if for you this thread was more of a drudgery than a thing of interest.

 

[yuiop]

I though SR doesn't require locality. Just flat space and only inertial movement. As long as these things are true I can draw simultaneity line on the diagram and precisely decide if something on the other end of universe already happen or is yet to happen. It depends on my speed and direction of movement but that's all. can never be simultaneous with event of me being now, here.

SR does not require locality, but SR applied in GR does. In GR the spacetime very near a particle is like SR but further you move away from it, the greater the distortion due to curvature and SR can not be applied non-locally in GR. You have to be careful talking about the other end of the universe in SR because as long as there is significant mass etc in the universe, you can not safely just assume flatness. SR does not require locality in an idealised hypothetical empty universe. This "locality" for a particle in GR need not be a single point, but can be worldline of a free falling particle.

 

[yuiop]

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]

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 netwrok 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.

You need to do the calculations, you can't simply list two possibilities only (ther are more) since the result depends on the radial distance between A and B and on the angular speed. You really need to calculate the proper time as a function of the radial distance and of the angular speed. I'll give you a hint, you know the integrand:

\sqrt{1-r_s/r}\sqrt{1-(\omega r/c)^2/(1-r_s/r)}

 

[yuiop]

You need to do the calculations, you can't simply list only the two possibilities since the result depends on the radial distance between A and B. You really need to calculate the proper time as a function of the radial distance. I'll give you a hint, you know the integrand.

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

The proper time is easy to calculate. For a stationary clock ds = dt\sqrt{(1-2m/r)}. The twin that spends the most time at r2 experiences the least proper time when they meet. Therefore answer (1) is the correct solution and gravitational time dilation is a real effect. The journey downwards is identical for both twins so we can ignore that.

 

[starthaus]

Keep it simple for now and assume r1>r2>2m.

The proper time is easy to calculate. For a stationary clock ds = dt\sqrt{(1-2m/r)}.

Umm, no. I gave you the correct expression. Look above.

 

[yuiop]

Umm, no. I gave you the correct expression. Look above.

You missed my edit. I am considering radial motion only so w=0 and are expressions are the same in that case.

 

[starthaus]

You missed my edit. I am considering radial motion only so w=0 and are expressions are the same in that case.

Always looking for the hack, eh? Position the clocks as follows:

-one on the top of a tower
-one at the bottom of a tower (like in the Pound-Rebka experiment).

What if the tower is very tall? What if the tower is very short?

 

[Dale]

That's very strange. If me sitting here now and event of my neighbors house being built 100 years ago can be simultaneous events that I could affect how this house was built.

I still can't get my head around the simultaneity being completely arbitrary. I guess I'll have to see some math to believe it. I hope I'll find it in paper you recommended.

I think this point deserves some clarification. Let's first speak only about SR.

In SR, if two events are simultaneous then they are outside of each others light-cone and therefore neither event may be the cause of the other. On the other hand, if one event causes another event then the second event is inside the light-cone of the first and is therefore in the future of the first event in all reference frames. Events which are inside the light cone are called timelike, events which are on the light cone are called lightlike or null, and events which are outside the lightcone are called spacelike. This designation is frame-invariant, so the universe seems to care about causality, as defined by the light cone, and not about simultaneity and simultaneity is thus seen to be simply a matter of convention (the Einstein synchronization convention for a given set of clocks mutually at rest). The fact that two events share the same time coordinate is thus just a convention and is not physically meaningful in SR.

Now, in GR this is taken further, and the concept of simultaneity is essentially dropped. You may have a coordinate system with a coordinate called "time" and completely arbitrary surfaces may share the same value of this coordinate. But the conventionality of that surface is recognized and no physical results depend on it. All of the physical results are expressed in terms of coordinate independent things such as the timelike or spacelike separation of events. The event of you sitting at your desk is inside the light cone of the event of your neighbor's house being built. So they are timelike separated and the physical results depend on that, not on some completely arbitrary label applied to the time coordinate.

I though SR doesn't require locality. Just flat space and only inertial movement. As long as these things are true I can draw simultaneity line on the diagram and precisely decide if something on the other end of universe already happen or is yet to happen. It depends on my speed and direction of movement but that's all. Simultaneity in SR is precisely defined and quite limited, for example event lying inside my light cone can never be simultaneous with event of me being now, here.

That is correct, SR does not require locality, GR does. Similarly, Newtonian physics does not require v<<c, SR does. Newtonian physics gives wrong predictions when velocities are high, and SR gives wrong predictions when curvatures are high. Also, SR is fine with non-inertial movement, it is only the coordinate systems that are required to be inertial.

I'm trying. For example now I am trying to understand concept of simultaneity being completely arbitrary in GR and how it fits observable relations like gravitational time dilatation. It's not easy so I'm trying to rephrase my questions to get additional answers. I'm also asking new questions. I can't just learn concepts by heart. I need to understand them, how they are possible, how they work.

I am very grateful for each new piece of information that you give me by answering, what it for you seems to be, same question over and over again.

OK, if you can make an effort to ask questions with new content rather than simply new wording then I will make an effort to be more patient.

 

[yuiop]

Always looking for the hack, eh?

If we are looking for the time dilation effect of gravity it is best to try and eliminate the effects due to motion so analysing the effects due to orbital motion is not helpful in this case. The expression I gave is the time dilation purely due to being stationary in a gravitational field and so there can be no disputing that gravitational time dilation is real.

 

[starthaus]

If we are looking for the time dilation effect of gravity it is best to try and eliminate the effects due to motion so analysing the effects due to orbital motion is not helpful in this case.

You can't do that since for certain combinations the rotational effect can overwhelm the effect due to difference in gravitational potential. You need to consider both effects because they occur together (last I checked, the Earth rotates).

There is no "orbital motion" in my example.The clocks are placed in a tower and there is an elevator that can bring either clock to the location of the other clock. Are you suggesting that we can ignore the Earth rotation?

The expression I gave is the time dilation purely due to being stationary in a gravitational field and can be no sidputing that gravitational time dilation is real.

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

 

[starthaus]

If I understood it to the extent you do I wouldn't be asking questions about it here.

Purpose of my questions is broadening my understanding. And I already understand few things I have not understood before so from my point of view your responses are far from being pointless, and I'm very thankful to members of this forum that respond to this thread.

Aren't you the fellow that disputes the big bang http://www.kamil.szot.eu/ ?

 

[yuiop]

Position the clocks as follows:

-one on the top of a tower
-one at the bottom of a tower (like in the Pound-Rebka experiment).

What if the tower is very tall? What if the tower is very short?

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).

 

[yuiop]

There is no "orbital motion" in my example.The clocks are placed in a tower and there is an elevator that can bring either clock to the location of the other clock. Are you suggesting that we can ignore the Earth rotation?

I am suggesting that in principle we can find a planet somewhere in the universe that is not rotating and use that. I don't think I specified the Earth in particular. I did mention I was using Schwarzschild coordinates which implies a non-rotating planet. For the Earth you should technically be using the Kerr metric.

 

[yuiop]

Aren't you the fellow that disputes the big bang http://www.kamil.szot.eu/ ?

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.

 

[yuiop]

You can't do that since for certain combinations the rotational effect can overwhelm the effect due to difference in gravitational potential. You need to consider both effects because they occur together (last I checked, the Earth rotates).

I am not disputing that the rotational effect can overwhelm the effect due to difference in gravitational potential. I am just suggesting that in a thread titled "Is the gravitational time dilation a real effect?" it is helpful to isolate the effect purely due to gravitational potential.

 

[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&gt;r_2

\frac{\sqrt{1-r_s/r_1}}{\sqrt{1-r_s/r_2}}&gt;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)}}&lt;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&gt;r_2

\frac{\sqrt{1-r_s/r_1}}{\sqrt{1-r_s/r_2}}&gt;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)}}&lt;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.