Relativity & Gravity: Resolving the Discrepancy

[Sagittarius A-Star]

She definitely isn't alone in making the mistake. But in your textbook example you could at least argue that "weaker gravitational field" is talking about depth in the potential well, unless that's stated to mean the acceleration due to gravity elsewhere (or it's unambiguous in German). Depth in the potential well would be correct, if not clearly stated as "strength" of a gravitational field. The original video explicitly equates acceleration with time dilation, which is wrong.

To my understanding, a "weak gravitational field" is the opposite of a "strong gravitational field". I did not interpret "it is in a weaker gravitational field" as "it is located higher in the potential well".

 

[Ibix]

To my understanding, a "weak gravitational field" is the opposite of a "strong gravitational field". I did not interpret "it is in a weaker gravitational field" as "it is located higher in the potential well".

I tend to agree, and would use "gravitational field strength" to mean $\left|\vec g\right|$ myself. But there's a tiny bit of wiggle room there.

 

[vanhees71]

This whole debate only underlines once more: It's impossible to talk about physics in an adequate way without mathematics, and with mathematics it becomes utmost clear and unambigues. The entire twin paradox is just about comparing clock (i.e., proper-time) readings at a common place at the begin and at the end of the journey, and all gravitational and kinematic effects concerning the duration of the journey measured by either of the twins clock are simply given by the proper times of the twins,
$$\tau=\int_{\lambda_1}^{\lambda_2} \mathrm{d} \lambda \sqrt{\dot{x}^{\mu} \dot{x}^{\nu} g_{\mu \nu}(x)},$$
where you put in $x^{\mu}=x^{\mu}(\lambda)$ for each twin, and this also tells you that the question who aged more is entirely independent on the chosen reference frame, within which this calculation of the proper times is done as well as on the chosen parametrization for the world lines.

 

[PAllen]

In contrast to the simplicity of the math of @vanhees71 post #38, every common attempt to explain differential aging without math ends up needing caveats, making it unnecessarily complex:

1) Sabine chooses to emphasize acceleration as an easily understood physical mechanism. This leads to a clear cut mistake in her GR case, and also would fail to explain the well known pure SR scenario where twins start and end at rest, with each having 3 periods of accelerations - away from starting point in opposite directions, turnaround to approach starting point, and and (negative) acceleration to come to rest at initial location. The 3 acceleration profiles are identical, but the timing of the second and third differs. The result is differential aging despite 3 identical acceleration periods. People have gone to great lengths to propose rules about timing of acceleration, or distance (itself non-invariant) at time of acceleration to accommodate this case, but the simple answer remains that acceleration per se is simply not a cause of differential aging.

2) Changing frames. The problem here is that a frame is not a physical attribute of anything, and everything is in every frame. If one means changing rest frames, this becomes a euphemism for change of velocity, i.e. acceleration, and you are back to (1).

3) The triplet paradox has always seemed a bit of sophistry to me. The plane geometry analog is saying that "it is false that the need to bend a straight wire to follow a path proves it is non-geodesic (acceleration); instead you can use two straight rulers, thus there is no bending (acceleration)". The reality remains that change in direction of tangent means a path is non-geodesic, and in spacetime, this is called acceleration. However, the bends themselves only mean a path is non-geodesic. To compare two non-geodesic paths, there is nothing simpler than just measuring them.

All of this to avoid the simple statement that different paths between two points generally have different lengths. Or, in spacetime, post #38.

 

[A.T.]

Sabine chooses to emphasize acceleration as an easily understood physical mechanism. This leads to a clear cut mistake in her GR case,

Using acceleration is not the problem as such. The confusion starts when accelerating reference frames (which can have clocks going at different rates at different locations) are conflated with the proper acceleration of the clocks (which doesn't affect the clock rate).

 

[PeterDonis]

Using acceleration is not the problem as such.

It is if acceleration is claimed to be the cause of time dilation, which appears to be what the video is claiming.

 

[Sagittarius A-Star]

The confusion starts when accelerating reference frames (which can have clocks going at different rates at different locations) are conflated with the proper acceleration of the clocks (which doesn't affect the clock rate).

I even doubt she is aware, that gravitational time dilation also happens in the pseudo-gravity of an accelerated reference frame in flat spacetime.

In the above video she says, related to experiments of gravitational time dilation between a mountain top and sea level, at 18m28s:

And yea, it also proves, that the earth isn't flat.

In an older video about the (wrong) flat earth hypothesis, she said at 01m00s:

They mostly agree though that gravity does not exist, and that the observations we normally attribute to gravity come instead from the upward acceleration of the flat earth.

 

[Jarvis323]

I thought her video wasn't about the math so much as about causality, and her claim seemed to be that gravity is not a force and so it cannot be the cause of time dilation.

Veritisium made a similar video, where he says things like, "Gravity is not a force ... there are no gravitational fields... gravity is more like an illusion..."



I am not sure how to evaluate such statements, not just because I am not an expert in relativity, but because I don't think they are claims about the math of relativity, but more like philosophical argument and interpretation.

Personally, I don't think the cause of time dilation is something which is explicit in relativity or known in general, and explanations like,

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

seem iffy, if we are trying to get to the bottom of the causality. At least you need to go beyond the math of general relativity to talk about causality don't you?

 

[PeterDonis]

her claim seemed to be that gravity is not a force and so it cannot be the cause of time dilation.

Which is wrong. There is nothing that says the cause of time dilation must be a force.

I don't think the cause of time dilation is something which is explicit in relativity or known in general

You are wrong. The cause of time dilation is perfectly well understood. Ultimately, it comes down to spacetime geometry and path lengths along timelike curves. There is nothing at all mysterious or ill-understood about it.

 

[Jarvis323]

You are wrong. The cause of time dilation is perfectly well understood. Ultimately, it comes down to spacetime geometry and path lengths along timelike curves. There is nothing at all mysterious or ill-understood about it.

I am not wrong, you are not understanding what I said.

 

[PeterDonis]

I am not wrong, you are not understanding what I said.

What you said that I quoted was perfectly clear, and wrong.

If you actually meant something else, you need to rephrase what you said.

 

[PeterDonis]

you need to go beyond the math of general relativity to talk about causality don't you?

No. Causality is perfectly well-defined in GR: the causal structure of spacetime is the light cone structure.

 

[Ibix]

Personally, I don't think the cause of time dilation is something which is explicit in relativity

Depends what you mean by "explicit in relativity".

or known in general,

No, the reason for time dilation is very much known.

explanations like,

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

seem iffy,

It's not iffy. The path length of a worldline is the elapsed time along it. If I "slice" spacetime into a stack of sheets, each sheet is "space at a given instant" for some definition of "instant". But different worldlines can make different angles with the slices, or can be in places where the separation between slices varies, so the path length along worldlines between the same sheets can be different. The time dilation between two clocks is just the ratio of the lengths of their worldlines between those two sheets. That's the same explanation whether we're talking about special relativistic time dilation (the thing that varies here is the "angle" of the worldlines to the sheet normals), or gravitational time dilation (the "distance" between adjacent sheets varies as a function of $r$) or something more outré.

At least you need to go beyond the math of general relativity to talk about causality don't you?

Causality in GR is entirely about light cones. Time dilation has little - if anything - to do with it.

 

[Vanadium 50]

It's impossible to talk about physics in an adequate way without mathematics

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."

 

[Lluis Olle]

You are wrong. The cause of time dilation is perfectly well understood. Ultimately, it comes down to spacetime geometry and path lengths along timelike curves. There is nothing at all mysterious or ill-understood about it.

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.

 

[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).