B Relativity & Gravity: Resolving the Discrepancy

[Ibix]

If I'm not wrong (again), when you do the integral of the metric to find the "length" of the path of the worldline, which is the proper time, there're clearly two terms: one lets say that is somehow "geometric", and the other is relative to speed.

I don't know what "two terms" you're thinking of here.

So, seems to me that the time dilation, at least for calculating its value, comes from some geometric properties of the spacetime, and the velocity in which you travel relative to something in that spacetime.

It's primarily about your choice of how to "slice" spacetime and the relationship of the worldlines of your clocks to that slicing. The geometry of spacetime comes into it by affecting what kind of slicings are possible and/or sensible, and in determining the path lengths between nearby slices. The calculation you need (as I've said already) is simply the path length of the two clocks between two nearby slices. You can characterise that in terms of an orthogonal distance between planes and a "transverse" displacement if you want, but it's unnecessarily clunky. It's like insisting on specifying any distance in terms of a displacement north and a displacement east. It's not wrong, but why bother if you don't need to?

 

[PeterDonis]

If I'm not wrong (again), when you do the integral of the metric to find the "length" of the path of the worldline, which is the proper time, there're clearly two terms: one lets say that is somehow "geometric", and the other is relative to speed.

This is true if you make a particular choice of coordinates. But there is nothing that requires you to do that. You could choose coordinates in which the object following the path is at rest, in which case there would be only one term in the integral. Or you could choose coordinates (for example, Kruskal coordinates) in which none of the individual terms in the integral have any straightforward physical interpretation.

 

[Jarvis323]

Fundamentally what "causes" time dilation is different path lengths for different clocks between a pair of specified spacelike planes, always, no exceptions.

To me this sounds something like saying the cause for changes in clock rates is different amounts of time between clock ticks.

If this is exactly the best you can possibly do in assigning a cause for time dilation, then I would say GR doesn't tell you much about the causality of time dilation.

 

[PeterDonis]

To me this sounds something like saying the cause for changes in clock rates is different amounts of time between clock ticks.

No, it's saying that viewing time dilation as "changes in clock rates" is not correct. Every clock ticks at one second per second along its worldline. The only difference is in the path lengths along the worldlines.

You can choose coordinates that make it seem like the difference is due to "changes in clock rates", but that is always an artifact of your choice of coordinates. The only invariants involved are the path lengths.

 

[Jarvis323]

No, it's saying that viewing time dilation as "changes in clock rates" is not correct. Every clock ticks at one second per second along its worldline. The only difference is in the path lengths along the worldlines.

You can choose coordinates that make it seem like the difference is due to "changes in clock rates", but that is always an artifact of your choice of coordinates. The only invariants involved are the path lengths.

The point is that the cause of something changing is being defined as the thing becoming different.

 

[PeterDonis]

The point is that the cause of something changing is being defined as the thing becoming different.

No, the point is that to look for a separate "cause" in this case is simply mistaken. There isn't one. It's just path lengths along worldlines. There isn't anything else to be "caused".

 

[PAllen]

The point is that the cause of something changing is being defined as the thing becoming different.

Why are different curves on a plane between two points different lengths? Can you give any "deeper" cause for that?

 

[Jarvis323]

Why are different curves on a plane between two points different lengths? Can you give any "deeper" cause for that?

Firstly, you need to define cause. It is not generally the same as "reason" or "explanation". In which sense are you considering these differences to be a cause?

You can have two observers be in non-intersecting light cones, and have different properties, and use those different properties to explain some other differences they have. But to call this cause and effect is iffy. You need to first propose a framework where this is a valid claim. If we are bringing light cones into it, what help is that when the cause we are defining isn't even based on physical interaction or propagation of information?

When I said I think Sabine is making a philosophical argument, and that to talk about the causality of time dilation you may need to go further than just the math, I mean you either need to establish a clear definition of causality and interpretation of the math or you need to have a more fundamental theory like a theory of quantum gravity.

 

[PeterDonis]

Firstly, you need to define cause

No, firstly, you need to explain why you think that the difference in elapsed times along different worldlines needs a "cause" over and above simple spacetime geometry. You're the one that brought up "cause" in the first place.

you either need to establish a clear definition of causality and interpretation of the math

This has already been explained for GR in earlier posts in this thread. The fact that you don't appear to like those explanations does not mean they are wrong.

 

[Jarvis323]

No, firstly, you need to explain why you think that the difference in elapsed times along different worldlines needs a "cause" over and above simple spacetime geometry.

First, I never agreed that lengths of paths is a proper cause, I also didn't disagree. As presented, "It's not even wrong."

Second, I never argued we need to assign it a cause.

You're the one that brought up "cause" in the first place.

This is false. Cause was brought up in the OP and has been the main issue being discussed. Causality is what this thread is about.

This has already been explained for GR in earlier posts in this thread. The fact that you don't appear to like those explanations does not mean they are wrong.

I never said they are wrong. They are not even wrong in my opinion.

 

[PeterDonis]

I never agreed that lengths of paths is a proper cause, I also didn't disagree. As presented, "It's not even wrong."

Sorry, but if you're going to make a claim like this, you need to justify it. With references. Expecting others to defend what is standard in the field and has been for decades is not a reasonable position. Either back up your claims or drop them--or receive a warning.

 

[PeterDonis]

Cause was brought up in the OP and has been the main issue being discussed.

Yes, this is a fair point.

 

[PeroK]

If I'm not wrong (again), when you do the integral of the metric to find the "length" of the path of the worldline, which is the proper time, there're clearly two terms: one lets say that is somehow "geometric", and the other is relative to speed.

So, seems to me that the time dilation, at least for calculating its value, comes from some geometric properties of the spacetime, and the velocity in which you travel relative to something in that spacetime.

The mistake you are making is to forget that time is also part of the geometry. A lot of confusion about SR/GR comes from imagining the spacetime geometry and then adding or thinking about another time dimension on top of this. If you have a spacetime path, then any velocity is already defined by that path.

This is different from classical physics, where we may have some sort of spatial geometry. And a particle with a path through that geometry is not fully defined until we add a time parameter to the path, which essentially adds the velocity with which the particle moved along that path.

But, if we have a path in spacetime, then all the information about the particle's motion is contained in the geometry.

 

[Ibix]

Firstly, you need to define cause. It is not generally the same as "reason" or "explanation". In which sense are you considering these differences to be a cause?

You're the one who thinks our explanations are inadequate. Trying to put the burden on us to define what you mean by an adequate explanation is not going to get anywhere - only you can answer what you think is adequate.

Even if you have a definition of adequacy, in answer to @PAllen's question, Sabine's time dilation explanation ("acceleration causes it") would translate to "because one of the lines is curved", which is what an accelerating worldline is. That's not a philosophical argument.

Let's also not lose sight of the fact that her argument is completely wrong, as has been stated several times on this thread. Acceleration is not related to time dilation, although it can look like it if you are only familiar with a couple of special cases that happen to be famous.

Finally, the problem here IMO is that time dilation genuinely is nothing more than a cool name for the fact that the distance between two planes depends on the path you take between them. But that's (a) trivial, and (b) justified by a chain of maths and experiment that most people don't know. That triviality means that some of the people who don't know the maths (see a theme here?) find it really hard to accept and start insisting that there must be something more than that. There really isn't, not about time dilation.

You can ask "why is GR the way it is", which is a valid question but not one anyone has an answer to. And I find it difficult to read "what causes time dilation" as actually wanting to know the current state of quantum gravity research.

 

[vanhees71]

You believe this, and I believe this, and I expect that most of PF believes this, But does Dr. Hossenfelder? Remember, she has a business where crtackpots aspiring theoristspay her and in return she says "There, there. The bad old establishment physicists are being mean to you."

I don't comment on my colleague next door. Just search the arXiv for her newest scientific writings on the foundations of quantum mechanics. You can imagine what I think about this...

 

[Jarvis323]

You're the one who thinks our explanations are inadequate. Trying to put the burden on us to define what you mean by an adequate explanation is not going to get anywhere - only you can answer what you think is adequate.

We aren't on the same page if you think causality and explanation mean the same thing.

Even if you have a definition of adequacy, in answer to @PAllen's question, Sabine's time dilation explanation ("acceleration causes it") would translate to "because one of the lines is curved", which is what an accelerating worldline is. That's not a philosophical argument.

I am not trying to defend her position, I honestly am not sure that I fully understand what she is saying. But it seems she started out with a viewpoint that GR isn't needed to model time dilation from acceleration, you can still use special relativity and ...

There are perhaps some clues to what she is saying here:

http://backreaction.blogspot.com/2013/09/what-is-special-relativity.html?m=1

Let's also not lose sight of the fact that her argument is completely wrong, as has been stated several times on this thread. Acceleration is not related to time dilation, although it can look like it if you are only familiar with a couple of special cases that happen to be famous.

I'm not her lawyer. You should at least make an effort to get on the same page with her.

Finally, the problem here IMO is that time dilation genuinely is nothing more than a cool name for the fact that the distance between two planes depends on the path you take between them. But that's (a) trivial, and (b) justified by a chain of maths and experiment that most people don't know. That triviality means that some of the people who don't know the maths (see a theme here?) find it really hard to accept and start insisting that there must be something more than that. There really isn't, not about time dilation.

Causality is a non trivial concept that is seemingly being treated here in a trivial, unspecific, and colloquial way.

You can ask "why is GR the way it is", which is a valid question but not one anyone has an answer to.

If you want to imply there is no cause, or no known cause, that wouldn't be incompatible with anything I have said as far as I can tell.

 

[Sagittarius A-Star]

I don't comment on my colleague next door.

The main author of the SR book, I cited in posting #34, worked before his retirement also there.

 

[Ibix]

I am not the one making claims about cause and effect.

However, you are the only one saying we aren't addressing the question. And you are utterly failing to communicate what it is you think we should be doing differently to address whatever you think the claims are.

For example, how do you think PAllen's question about line lengths should be addressed? It's an exact analogy for time dilation, just using Euclidean geometry instead of Minkowski. Your only answer so far has been to try to shift the burden of defining "cause" in a way you recognise onto us, and then waffle about light cones that isn't relevant to time dilation and definitely isn't relevant to the Euclidean analogy.

You should at least make an effort to get on the same page with her though I think.

...but she's making statements that are already known to be false. It's not a matter of interpretation or different emphasis. It is just plain wrong to say that gravitational time dilation is linked to gravitational acceleration. You can have gravitational time dilation without acceleration, and you can have the same acceleration with different aging effects.

But it seems she started out with a viewpoint that GR isn't needed to model time dilation from acceleration, you can account for it with SR by properly incorporating acceleration.

No, she doesn't say that. She says (correctly) that you do not need GR to describe situations in flat spacetime. That does not mean you can do away with GR and I don't think she says that. Where she goes wrong there is just abandoning the correct maths she does earlier in favour of incorrect hand-waving about acceleration.

 

[Jarvis323]

No, she doesn't say that. She says (correctly) that you do not need GR to describe situations in flat spacetime. That does not mean you can do away with GR and I don't think she says that. Where she goes wrong there is just abandoning the correct maths she does earlier in favour of incorrect hand-waving about acceleration.

Maybe I have stated her point incorrectly.

Here is a direct quote from her, albeit from her previous blog post on special relativity.• (note her new blog post/youtube video which is the topic of this thread is titled "Special Relativity ..." as well.

Chris,

I would really suggest you read some modern textbook on the topic, you're just reinforcing your misconceptions. You say "an induced gravitational field during the accelerated turnaround". An acceleration in flat space does not 'induce a gravitational field.' Space is either flat or it isn't. That's an observer-independent statement. I repeat: you do not need gravity to solve the twin paradox. All you need is to know how to deal with accelerated observers in special relativity (flat space). And, yes, this acceleration is *locally* indistinguishable from a gravitational field, but that doesn't mean there are suddenly sources for an actual gravitational field (curvature of space-time).

B.

https://backreaction.blogspot.com/2...omment=1378475158879&m=1#c3866947122385147587

 

[vanhees71]

The main author of the SR book, I cited in posting #34, worked before his retirement also there.

In this book, however, is not the claim that time dilation is due to acceleration. Also one has to distinguish between time dilation and the twin paradox. The former relates to the difference of times between events when measured with clocks in different inertial frames and the latter to the different aging of twins when comparing their clocks (i.e., the difference of the duration of the trip when measured in terms of the proper times of these twins).

 

[Sagittarius A-Star]

In this book, however, is not the claim that time dilation is due to acceleration.

That's correct. The clock in the satellite has no proper acceleration. But he should have described the influence of the gravitational time dilation with "because it is located higher in the potential well" than "because it is in a weaker gravitational field".

From page 32, chapter 3.5.2 Time dilation (my translation from German to English):

A clock that moves with the satellite runs slower than a clock that is stationary on the earth. On the other hand, it runs faster than this one because it is in a weaker gravitational field.

Source - book "Spezielle Relativitätstheorie" (Schröder):
https://www.amazon.de/dp/3808556536/

 

[Vanadium 50]

A simple thought experiment:

A tree is 10 meters to my left. I turn 45 degrees and now its only 7 meters to my left (and 7 meters in front). What is the mechanism behind that? I don't wanto to hear any garbage from you priests in white coats about sines and cosines and rotation matrices ant Euclidean metrcs and the like. I want the physical mechanism - the underlying cause - for left-contraction.

Can't explain it, can you? You smarty-pants geometers! You can't hide your ignorance with math!

 

[student34]

You can have gravitational time dilation without acceleration, and you can have the same acceleration with different aging effects.

How would this be possible? Can you provide an example?

 

[student34]

Acceleration is not related to time dilation, although it can look like it if you are only familiar with a couple of special cases that happen to be famous.

I have a problem with this too. Surely acceleration can be a cause/reason for time dilation, no?

 

[weirdoguy]

no?

No, as the text you quoted explicitly states.

 

[student34]

No, as the text you quoted explicitly states.

I thought that if the twin only accelerates to get back to the other twin that there would be time dilation. Wouldn't it be correct to say that the acceleration of the twin is a reason (not the only reason) why there is time dilation in the paradox?

 

[Ibix]

How would this be possible? Can you provide an example?

Being at the center of the Earth for the first, and two twins who travel at the same speed with the same accelerations at start, turnover, and end, but one turns back earlier than the other.

 

[student34]

Being at the center of the Earth for the first,

I was asking about this. I should have been specific.

With what observer is the observer at the center of Earth comparing time?

 

[DrGreg]

I was asking about this. I should have been specific.

With what observer is the observer at the center of Earth comparing time with?

An observer "at infinity" i.e. a very distant observer.

These sketch graphs are for an idealised planet rather than Earth. It's the shape of the curves that matters rather than the numbers. In particular, the dilation for Earth is way, way less than* the graph shown here.

(*i.e. factor much, much closer to 1)

 

[Dale]

It does not make sense to talk about a cause for time dilation. Causes, by definition, occur before effects, and “before” is an ordering in time. But time dilation is an aspect of time itself, so any cause would need to happen before time. But before time doesn’t make sense because before is an ordering in time.

So I simply don’t see how the concept of a cause of time dilation makes sense in general. Perhaps one could talk in principle about the cause of the time dilation of a specific clock in a specific scenario. But even that is fraught since none of the equations of time dilation are in a causal form

In any case, not only is time dilation not caused by acceleration, it is also not a function of acceleration. Kinematic time dilation is a function of velocity and gravitational time dilation (in spacetimes where it can even be defined) is a function of gravitational potential. Acceleration is only relevant insofar as it impacts either velocity or gravitational potential.

The experimental confirmation of the clock hypothesis by Bailey proves the non-existence of a separate acceleration effect on the kinematic time dilation for accelerations of about $10^{18}\mathrm{\ g}$

 

[student34]

An observer "at infinity" i.e. a very distant observer.

View attachment 320418
These sketch graphs are for an idealised planet rather than Earth. It's the shape of the curves that matters rather than the numbers.

Interesting. But infinity (if it even exists) always breaks rules and causes paradoxes. I was hoping for a more realistic example.

One other thing, doesn't the travelling observer have to synchronize clocks at the center of "Earth" and then accelerate to infinity?

 

[Dale]

Interesting. But infinity (if it even exists) always breaks rules and causes paradoxes. I was hoping for a more realistic example.

One other thing, doesn't the travelling observer have to synchronize clocks at the center of "Earth" and then accelerate to infinity?

An observer “at infinity” is standard in relativity and is perfectly acceptable in an explanation. Please do not try to ignore a perfectly valid and correct answer to your question simply because it was surprising to you.

Also, please do not hijack this thread. Keep your questions focused on the topic of the thread itself

 

[member 728827]

I don't know what "two terms" you're thinking of here.

I'm not very knowledgeable in this matter, but for what I see, when you integrate the metric to obtain the proper time for a worldline, the x, y and z coordinates are differentiated with respect the time coordinate, and that naively seems to me somehow related to the coordinate velocity of the object in the geometry of the spacetime considered (this is what I called second term). And the first term is the g₀₀.

 

[DrGreg]

Interesting. But infinity (if it even exists) always breaks rules and causes paradoxes. I was hoping for a more realistic example.

A very distant observer will have negligible (too small to measure) gravitational acceleration but maximum gravitational dilation relative to the planetary centre (see the graphs and imagine them extrapolated further to the the right).

One other thing, doesn't the travelling observer have to synchronize clocks at the center of "Earth" and then accelerate to infinity?

In this case ("gravitational" time dilation between two observers at rest relative to each other) it turns out that it's enough for one observer to send a radio signal to the other and measure the doppler ratio. A signal sent in the opposite direction will have the reciprocal ratio (which is a practical way of confirming they are mutually at rest).

 

[Ibix]

I'm not very knowledgeable in this matter, but for what I see, when you integrate the metric to obtain the proper time for a worldline, the x, y and z coordinates are differentiated with respect the time coordinate

Not in general. Generally you pick a parameter that increases monotonically along the worldline (e.g. proper time) and differentiate with respect to that. In some cases it's convenient to pick coordinate time as the parameter, and if the metric is diagonal then you certainly get something like $\sqrt{g_{00}-\mathrm{velocity}^2}dt$ as the integrand. But that's a special case of the general $\sqrt{g_{ab}\frac{dx^a}{d\lambda}\frac{dx^b}{d\lambda}}d\lambda$ when (a) you have a $t$ coordinate, and (b) a diagonal metric, and (c) it makes sense to use $t$ as the parameter $\lambda$ for the line you are integrating along. And even in that special case there are metric components in the "velocity squared" term, so this is no more or less geometric than the $g_{00}$ term.

 

[PeterDonis]

Surely acceleration can be a cause/reason for time dilation, no?

We recently added a sticky thread about this in this forum:

https://www.physicsforums.com/threads/when-discussing-the-twin-paradox-read-this-first.1048697/

 

[Ibix]

Interesting. But infinity (if it even exists) always breaks rules and causes paradoxes. I was hoping for a more realistic example.

Consider a dumbell, two large masses held apart by a rod. There is no exact GR solution known for this, but the situation is manifestly static so gravitational time dilation applies, and we can consider weak fields and use the Newtonian potential to get a qualitative description that won't differ from the exact solution in any way that matters here. There are three places one can hover permanently without accelerating - one near the center of each mass and one at the point part way along the rod where the two masses' gravitational attractions cancel out. If the masses are unequal then all three clocks see both others run either fast or slow - the one on the rod fastest and the one at the center of the larger mass slowest.

Some asteroids that are the result of gentle collisions between two roughly spherical asteroids approximate this system, although you'd have to stop them spinning to do the experiment.

 

[Sagittarius A-Star]

Here is a direct quote from her, albeit from her previous blog post on special relativity.• (note her new blog post/youtube video which is the topic of this thread is titled "Special Relativity ..." as well.

Chris,
I would really suggest you read some modern textbook on the topic, you're just reinforcing your misconceptions. You say "an induced gravitational field during the accelerated turnaround". An acceleration in flat space does not 'induce a gravitational field.' Space is either flat or it isn't. That's an observer-independent statement. I repeat: you do not need gravity to solve the twin paradox. All you need is to know how to deal with accelerated observers in special relativity (flat space). And, yes, this acceleration is *locally* indistinguishable from a gravitational field, but that doesn't mean there are suddenly sources for an actual gravitational field (curvature of space-time).
B.

https://backreaction.blogspot.com/2...omment=1378475158879&m=1#c3866947122385147587

This discussion was about Einstein's 1918 paper (see in the middle of the text), according to the backreaction-link.

I think she should have made clear in her answer, that what Einstein called in an accelerated reference frame in flat spacetime a "gravitational field", is called today mostly a "pseudo-gravitational field" and that it comes along with a (frame-dependent) gravitational time-dilation.

 

[jedishrfu]

It seems this thread has run its course and now it’s time to close.

Thank you all for contributing here.

Jedi