B Relativity & Gravity: Resolving the Discrepancy

[Hornbein]

TL;DR Summary

Is Sabine wrong about GR?

I listened to and quite liked Sabine Hossenfelder's recent vid on relativity. Though one thing struck me as wrong. "Gravity is not a force," so it's effects does not cause true acceleration, so it has no effect on time. OK, but I'm pretty sure that satellites in different orbits have different timings. I once read that circular and elliptical orbits have different timing. How can this discrepancy be resolved or am I just wrong.

 

[FactChecker]

"Gravity is not a force," so it's effects does not cause true acceleration, so it has no effect on time.

Can you give a link to the video where she said that? I have difficulty believing that she would get a basic fact wrong. I just watched her video "Is Gravity a Force" and didn't see that statement about time. Did she say that somewhere else or is that your conclusion?

 

[Hornbein]

At 18:36 "It's not gravity that causes time to slow down because gravity is not a force. It's the acceleration that you need to not fall in the black hole that slows time down....The reason time slows down is acceleration."

It seems to me that this isn't exactly wrong but is highly misleading. She is talking about the context of being at rest relative to a gravitating body. OK, but neglects mentioning that proper time will be affected by said body even if you are in free fall. In such a case I would say that gravity is affecting proper time. The context has not been explicitly stated.

 

[FactChecker]

I will bow out and leave this to the experts.

 

[A.T.]

OK, but neglects mentioning that proper time will be affected by said body even if you are in free fall.

I think she talks about the local context, where space-time curvature is negligible and the gravitational field can be considered uniform. A free falling elevator here will accumulate the same proper-time for clocks at the floor and ceiling, while a hovering elevator won't.

But in general I find arguments about "causation" tricky. I prefer to say that the geometry of space-time "causes" both: the attraction we call gravity and the gravitational time dilation.

 

[Ibix]

Oh wow. That's a mess. Just after 18.00 she says that clocks run slower at sea level than on a mountain top because the acceleration is higher there. But that's wrong. If it were right, gravitational time dilation would fall to zero at the center of the Earth, and that's not what GR predicts. GR predicts that differences in clock rates in gravitational fields (at least in cases where it can be defined) are due to differences in gravitational potential, not acceleration. Acceleration will fall to zero at the center of the Earth; potential difference between there and infinity will continue to increase; therefore clocks will tick slower even as the acceleration needed to hover falls to zero.

And "acceleration causes time to slow down" manifestly isn't true in general. I have a nasty suspicion that she justifies that earlier in the video with reference to the twin paradox. If so (I haven't watched it), she's wrong about that too.

Ugh. This is why I don't watch popsci about anything I know anything about. I always end up wanting to write ten page essays correcting it.

 

[PeroK]

At 18:36 "It's not gravity that causes time to slow down because gravity is not a force. It's the acceleration that you need to not fall in the black hole that slows time down....The reason time slows down is acceleration."

It seems to me that this isn't exactly wrong but is highly misleading. She is talking about the context of being at rest relative to a gravitating body. OK, but neglects mentioning that proper time will be affected by said body even if you are in free fall. In such a case I would say that gravity is affecting proper time. The context has not been explicitly stated.

This is why such videos are not suitable material for discussion of GR on here. You are attempting to understand physics by getting the right words in the correct order. Physics is only unambiguous when it gives a precise mathematical model and quantitative answers to specific questions.

 

[Hornbein]

This is why such videos are not suitable material for discussion of GR on here. You are attempting to understand physics by getting the right words in the correct order. Physics is only unambiguous when it gives a precise mathematical model and quantitative answers to specific questions.

OK, then where am I supposed to discuss questions like this?

You are telling me that I am not welcome in this subgroup. What is the majority opinion on this? Is attempting to understand physics without math banned here?

 

[A.T.]

Oh wow. That's a mess. Just after 18.00 she says that clocks run slower at sea level than on a mountain top because the acceleration is higher there. But that's wrong.

Yes, that part is clearly wrong.

If you had two local elevators, each with ceiling and floor clocks, at the mountain top and bottom, then you could draw a connection between proper acceleration of an elevator and the proper time delta between its two clocks.

 

[PeroK]

Is attempting to understand physics without math banned here?

"Whoever then has the effrontery to study physics while neglecting mathematics must know from the start that he will never make his entry through the portals of wisdom."

Roger Bacon (1214-84)

 

[Hornbein]

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?

 

[PeroK]

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?

It's impossible to understand GR without mathematics. There's nothing patronising about that. It's a plain fact.

 

[Ibix]

Is attempting to understand physics without math banned here?

It's doomed to failure, certainly. There's simply no way to express all the interactions and limitations in things you think you know without the maths. Ultimately, that's why physicists use maths to describe these phenomena - it's not really a matter of choice if you want to actually understand, rather than know some disconnected facts.

I mean, I'm pointing out errors in the video which wouldn't even be possible if she had used maths. I'm not using maths myself, so there are limitations in things I'm saying from other factors that come in to play if you change the scenarios (sometimes very little) from the one I'm thinking of. I can't even begin to tell you what they all are because I can't list every possible variation of a scenario - but it's all encoded in the maths.

 

[A.T.]

Is attempting to understand physics without math banned here?

People have different concepts of what "to understand" means. I think you can get a correct basic understanding of GR without much formulas. It's a geometrical theory after all. You might try this book:
https://archive.org/details/L.EpsteinRelativityVisualizedelemTxt1994Insight/mode/2up

 

[Ibix]

Fundamentally what "causes" time dilation is different path lengths for different clocks between a pair of specified spacelike planes, always, no exceptions. The only real difference between different circumstances is whether there are zero, one, or many ways to specify those hyperplanes in a reasonable non-arbitrary manner and the details of what those planes are and what paths clocks take, and how many unexamined assumptions there can be hidden in your analysis.

Gravitational time dilation is a useful special case where there's only one sensible way to specify planes, which allows you to separate out gravitational time dilation from kinematic time dilation. We often use this model for spacetime near Earth. But it's dangerous to generalise statements about "gravity" made near Earth to other scenarios without understanding (a) why we use this model near Earth, (b) why it's not correct to do that, (c) why you can get away with it anyway, and (d) a rough understanding of when and why it's all going to go wrong. And it's hard-to-impossible to express all those limits without maths.

Noting @A.T.'s post just above, I've seen visualisations of things from Epstein's book (I believe A.T. has animated a few himself). I certainly find such visualisations useful, but would have little confidence in my ability to actually manipulate anything more complex than a Minkowski diagram without understanding the maths.

 

[haushofer]

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 understand your frustration. And personally I think you can come far understanding these conceptual issues without diving too far into the mathematics. So if I take your quote,

""Gravity is not a force," so it's effects does not cause true acceleration, so it has no effect on time."

I would say the following:

- Indeed, gravity is not considered to be a force in GR. But that's mainly a matter of speaking terms. In GR, particles follow the shortest path (geodesics) between two events when there are no forces acting on it. In curved spacetime these geodesics curve along.
- I'm not sure what "true acceleration" means, but I think she says that in GR it's ambiguous to talk about "the acceleration due to gravity" because of the equivalence principle: locally, an acceleration can be interpreted as a gravitational field. So that makes the notion of "the acceleration due to gravity" a bit complicated and is the reason why gravity is not considered to be a force in GR: a force is something which results in an acceleration.
- The last conclusion, "hence gravity has no effect on time", I do not follow. I'd say that yes, curved spacetime certainly does result in time dilation, and I don't get how she draws this conclusion in the first place from the premisse.

Hope this helps.

 

[Vanadium 50]

A. Arguing with people by proxy is futile.
B. Some people believe that nobody really disagrees with them. Everybody secretly agrees with them - they're just too dishonest to admit it. Arguing with them is futile. Arguing with them by proxy is especially futile.
C. Bloggery anf Youtubery does not make one an expert.

 

[member 728827]

Sabine is not a snake-oil seller, and I would be very cautious about underestimating the Youtube video.

But also, she speaks to the general public, and perhaps she has to use some artist license to get to the general public, and would use other wording if she had to write a post in this forum.

 

[PeterDonis]

then where am I supposed to discuss questions like this?

Here is fine. The issue is not where you posted this thread.

You are telling me that I am not welcome in this subgroup.

No, he is telling you, correctly, that the video you referenced, even though it is by a physicist, is still a pop science source and is not a good source from which to learn the actual physics.

Is attempting to understand physics without math banned here?

No. But I think you will find it a lot more difficult and the understanding you will be able to achieve will be a lot more limited than if you did it with math.

To make just one obvious point: even if you give a qualitative, non-mathematical explanation for something, how do you know it's right? How did the physicists who built the theory you are using know it was right? The only way to do that is to make detailed, quantitative predictions and test them using detailed, quantitative experiments. That requires math.

 

[member 728827]

To make just one obvious point: even if you give a qualitative, non-mathematical explanation for something, how do you know it's right?

Prestige, and she also sings

 

[Ibix]

Sabine is not a snake-oil seller, and I would be very cautious about underestimating the Youtube video.

This is actually the problem. She's well known and widely respected - yet completely wrong in at least one thing she says in the one minute of her video that I watched.

 

[member 728827]

But that's wrong. If it were right, gravitational time dilation would fall to zero at the center of the Earth, and that's not what GR predicts. GR predicts that differences in clock rates in gravitational fields (at least in cases where it can be defined) are due to differences in gravitational potential, not acceleration. Acceleration will fall to zero at the center of the Earth; potential difference between there and infinity will continue to increase; therefore clocks will tick slower even as the acceleration needed to hover falls to zero.

If the Earth is considered a perfect sphere, the Gravitational potential at the center of the Earth will be the same as the Gravitational potential at the surface. The time dilation from a clock at the center of the Earth to infinite will be the same as the clock at the surface to infinite.

Sabine is right.

 

[vanhees71]

You think the earth is a shell with vacuum inside?

 

[Ibix]

If the Earth is considered a perfect sphere, the Gravitational potential at the center of the Earth will be the same as the Gravitational potential at the surface.

If that were the case you'd be in free fall inside the Earth, since $\vec g=\vec\nabla\phi$ would be zero everywhere.

The time dilation from a clock at the center of the Earth to infinite will be the same as the clock at the surface to infinite.

Feel free to look at the Schwarzschild interior metric (here's my Insight on the topic). It's trivial to see from the $g_{tt}$ term that you are wrong.

 

[PeterDonis]

Sorry for posting ChatGPT stuff here, just found it an interesting case study:

ChatGPT is not an acceptable source for PF. Do not post further ChatGPT content as it will just continue to get you warned, and eventually banned.

 

[PeterDonis]

If the Earth is considered a perfect sphere, the Gravitational potential at the center of the Earth will be the same as the Gravitational potential at the surface. The time dilation from a clock at the center of the Earth to infinite will be the same as the clock at the surface to infinite.

No, it won't. For the case of a constant density Earth the exact solution is known and does not have this property--the clock at the center runs slower than the clock at the surface. But even for the case of non-constant density, the Einstein Field Equations for any static, spherically symmetric object is sufficient to prove that gravitational potential continues to decrease as you go deeper inside the object.

Sabine is right.

I don't think Sabine is making the same wrong claims you are making.

 

[malawi_glenn]

Is attempting to understand physics without math banned here?

It is not banned, it is doomed. Physics is explaining and understanding nature using mathematics. The languange of physics is math.

 

[PAllen]

I like that she begins by saying popular science descriptions of relativity left her confused as a teenager. Then, she went on to get doctorate in theoretical physics. Now it is her turn to try a popular exposition, she says. I guess we see that she could no more avoid all the pitfalls than anyone else.

 

[martinbn]

There is a link to transcript, references and discussion on her blog. I thought it would be easier and faster to read it than to watch the video. But the link takes me to the subscription page and expects me to pay. And it is not the only thing that is for money. I get the impression that she tries to sell everything. For instance she has "talk to a scientist" option for $50 per 20min. I understand that she wants to be paid for the her efforts, but it is very off putting.

 

[malawi_glenn]

I understand that she wants to be paid for the her efforts, but it is very off putting.

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

 

[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.