Relativity & Gravity: Resolving the Discrepancy

[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

 

[Lluis Olle]

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