B Relativity & Gravity: Resolving the Discrepancy

[martinbn]

perhaps it is language and cultural, after all, she is german

Well, there are other germans that have blogs, vlogs, websites where the put there writings/videos (popular or not) etc. but don't ask for a credit card for every other click.

 

[pinball1970]

You did not answer my question. I find your communications patronizing to a degree that I find insulting. Do you understand what I am saying?

I was in your position. I bought all the wrong books and watched all the wrong videos.
I learned ABOUT some physics and about the history of physics but that's it.
I still yearn for non mathematical explanations sometimes but I try and keep them at bay.
That will not get me anywhere.

 

[MikeeMiracle]

I find relativity to be a tricky one to understand even for other non relativity physics tutors. I have seen various youtube physics channel's which are generally reputable reporting on the twins paradox and claiming the "time difference" all occurs during the deceleration / acceleration phase when they turn around at the other end instead of being caused by the change of reference frame. Had it not been for reading this forum I would have believed that was the case also. Sadly hearing Sabine make the same reference is not at all surprising.

I have learnt basic concepts from watching youtube video's from "reputable" channels but had it not been for the use of this forum to get some "meat on the bones" of the claim and the finer details I would never have gained the understanding I now have.

 

[Sagittarius A-Star]

I always end up wanting to write ten page essays correcting it.

You can do this for only 2 € / Month (+ VAT). But I don't think, that she published this error intentionally to get money from you.

Unfortunately, I see the same error also in other publications, even in otherwise good textbooks.

Example 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/

 

[Ibix]

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.

 

[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."

 

[member 728827]

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.