General Relativity & The Sun: Does it Revolve Around Earth?

[JohnNemo]

Still wrong. You have not grasped that the amount of "slowing down" you get due to the time dilation factor is less than the "slowing down" you actually see through your telescope, which is what "Doppler shift" means.

So, as I understand it, the whole phenomenon, as observed through the telescope, is called the Doppler shift. The reason for the Doppler shift is two contributing effects

1. varying light transit time

2. time dilation

You also continue to ignore the case where the spaceship moves towards you, and the Doppler effect you see through your telescope is a blueshift--speeding up, not slowing down.

True, but only a temporary ignoring while I try to get my head round the redshift.

 

[PeterDonis]

as I understand it, the whole phenomenon, as observed through the telescope, is called the Doppler shift.

Yes.

The reason for the Doppler shift is two contributing effects

1. varying light transit time

2. time dilation

That's one way of looking at it, yes. The other way of looking at it is that Doppler shift is the fundamental thing (since that's what is actually observed), and "time dilation" is due to two contributing effects: Doppler shift and varying light travel time.

The first viewpoint (the one you described in the above quote) is going to seem more natural if you're used to thinking about SR in terms of inertial frames. The second (the one I described in the previous paragraph) is likely to seem more natural if you're used to thinking about SR in terms of spacetime geometry. I favor the second approach, but both are mathematically equivalent, so it's really a matter of personal preference.

 

[JohnNemo]

Yes.
That's one way of looking at it, yes. The other way of looking at it is that Doppler shift is the fundamental thing (since that's what is actually observed), and "time dilation" is due to two contributing effects: Doppler shift and varying light travel time.

The first viewpoint (the one you described in the above quote) is going to seem more natural if you're used to thinking about SR in terms of inertial frames. The second (the one I described in the previous paragraph) is likely to seem more natural if you're used to thinking about SR in terms of spacetime geometry. I favor the second approach, but both are mathematically equivalent, so it's really a matter of personal preference.

The reason why I wanted to mention the Doppler effect in my write-up when talking about Special Relativity is that when someone is learning SR it is tempting to think that the phenomena are just illusions and that behind it all there is something non-relative which is 'actually' happening. So I wanted to make clear that time dilation is a real thing and should not be confused with varying light transit time which is only responsible for an appearance of slowness - an optical illusion. I was inclined to call this varying light transit time effect the Doppler effect. Is it wrong to do that or is the word capable of being used in that restricted sense? If it is wrong, is there some other word which describes the varying light transit effect (isolated from the time dilation effect).

 

[PeterDonis]

when someone is learning SR it is tempting to think that the phenomena are just illusions and that behind it all there is something non-relative which is 'actually' happening

And that is correct. The thing that is non-relative that is actually happening is spacetime and events in spacetime, such as you receiving light from some source with a particular redshift/blueshift at some event along your worldline. "Time dilation" is what might be termed an "illusion", since it's an artifact of your choice of coordinates (see below).

Relativity does not say "everything is relative". In fact Einstein at one point said the theory was misnamed, and should have been called the "theory of invariants"--the things that do not change when you change your choice of coordinates.

I wanted to make clear that time dilation is a real thing and should not be confused with varying light transit time which is only responsible for an appearance of slowness - an optical illusion

But here's the thing: time dilation is only a "real thing" if you say that things that depend on your choice of coordinates are "real things"; and doing that is problematic in relativity, since relativity says your choice of coordinates doesn't affect any physics. Whereas the actual observed redshift/blueshift in light coming from some other observer is a "real thing" in the simplest sense: it's what you directly observe.

 

[JohnNemo]

But here's the thing: time dilation is only a "real thing" if you say that things that depend on your choice of coordinates are "real things"; and doing that is problematic in relativity, since relativity says your choice of coordinates doesn't affect any physics. Whereas the actual observed redshift/blueshift in light coming from some other observer is a "real thing" in the simplest sense: it's what you directly observe.

If we only do one experiment then I can see an argument could be made that the single observation of redshift/blueshift is all there is. But if we do many experiments we can show that redshift/blueshift is related to the speed at which the object is approaching/receding, in our direction (single dimension), and that there is a separate element - time dilation - which is related to the object's speed in 3D. So having done all the experiments with objects traveling at different angles and produced our mathematical theory which we believe models reality, is it not the case that we can then distinguish the time dilation element from the varying light transit time element?

 

[PeterDonis]

if we do many experiments we can show that redshift/blueshift is related to the speed at which the object is approaching/receding

How do you measure the speed? You are aware that the standard way of doing this for distant objects is...using the Doppler shift?

In other words, this "speed" you talk about is not an independent variable in the usual case; it's just another way of describing the observed redshift/blueshift. To make it an independent variable, you would need to make other independent measurements of it, and that would require having a fleet of observers distant from you whose clocks were synchronized with yours and who were verified to be at rest relative to you, who could make local measurements of the object that is emitting the light you are receiving. In other words, to set up an actual concrete "inertial frame" centered on you.

If you do this, then yes, you can separate out "light travel time" from "time dilation", but now "time dilation" doesn't mean the same thing as it meant before. It now means, not a coordinate-dependent quantity that you calculate, but actual measurements that your fleet of observers is making, comparing their clock readings with those of the object emitting the light. Similarly, "light travel time" is now not something you calculate, but something your fleet of observers directly measures (by recording their clock readings as the light rays from the object pass them).

 

[JohnNemo]

@JohnNemo the corrections you made look fine, but I did spot one other item:

"if a mass is accelerating that adds to the distortion"

What are you referring to here?

I was basing this on https://en.wikipedia.org/wiki/Frame-dragging but I am not sure about this. Is it just acceleration or any movement which adds to the distortion?

 

[PeterDonis]

I was basing this on https://en.wikipedia.org/wiki/Frame-dragging but I am not sure about this. Is it just acceleration or any movement which adds to the distortion?

Neither. Frame dragging, which can be thought of as an extra "distortion" to spacetime, yes, is due to the source of gravity having nonzero angular momentum, where "angular momentum" here is has a technical definition that is probably closest to "rotating with respect to the distant stars" of the concepts we've discussed--and where "rotating" here is to be taken in the intuitively obvious sense that someone "at rest" on the rotating object will see a given distant star as moving in a big circle around his sky instead of staying at a single fixed point in his sky.

This concept is different from any of the indicators of rotation we have discussed in this thread. For example, a black hole can be rotating in this sense, and a black hole is a vacuum solution, so there is no matter anywhere and therefore nothing that can have any proper acceleration or "motion" of any kind. It's all just spacetime geometry.

 

[JohnNemo]

Neither. Frame dragging, which can be thought of as an extra "distortion" to spacetime, yes, is due to the source of gravity having nonzero angular momentum, where "angular momentum" here is has a technical definition that is probably closest to "rotating with respect to the distant stars" of the concepts we've discussed--and where "rotating" here is to be taken in the intuitively obvious sense that someone "at rest" on the rotating object will see a given distant star as moving in a big circle around his sky instead of staying at a single fixed point in his sky.

This concept is different from any of the indicators of rotation we have discussed in this thread. For example, a black hole can be rotating in this sense, and a black hole is a vacuum solution, so there is no matter anywhere and therefore nothing that can have any proper acceleration or "motion" of any kind. It's all just spacetime geometry.

https://en.wikipedia.org/wiki/Frame-dragging#Effects also mentions linear frame dragging. Is this also recognised n GR?

 

[PeterDonis]

linear frame dragging

I haven't seen anything about this in the GR textbooks and papers I've read. Unfortunately the Wikipedia article does not give a link to the Einstein lecture where he apparently mentioned it.

Offhand I would not expect an "similar" effect for linear momentum as opposed to angular momentum, for the same (heuristic) reasons as linear motion relative to the distant stars is not locally detectable the way that angular motion (rotation) relative to the distant stars is (putting aside all the subtleties we've been discussing about that). But it is true that for an object moving at high speed past a gravitating mass, GR makes different predictions than Newtonian gravity; it could be that this is what "linear frame dragging" is supposed to refer to.

 

[JohnNemo]

Neither. Frame dragging, which can be thought of as an extra "distortion" to spacetime, yes, is due to the source of gravity having nonzero angular momentum, where "angular momentum" here is has a technical definition that is probably closest to "rotating with respect to the distant stars" of the concepts we've discussed--and where "rotating" here is to be taken in the intuitively obvious sense that someone "at rest" on the rotating object will see a given distant star as moving in a big circle around his sky instead of staying at a single fixed point in his sky.

This is where I am having difficulty understanding because you often say (e.g. In #152) that a region of space a long way from the nearest star is flat (because the matter and energy in the universe is spherically symmetrical) but here we appear to have a distortion of spacetime caused by the distant stars moving in a big circle.

 

[Nugatory]

This is where I am having difficulty understanding because you often say (e.g. In #152) that a region of space a long way from the nearest star is flat (because the matter and energy in the universe is spherically symmetrical) but here we appear to have a distortion of spacetime caused by the distant stars moving in a big circle.

Frame dragging only appears in the egregiously non-flat regions of spacetime near a massive rotating body; the distant stars are completely irrelevant to the spacetime curvature in such a region.

The only reason we mention the distant stars is that we said "near a massive rotating body" so we have be clear about what we mean by "rotating", and in this context an intuitive definition of "rotating" involves the distant stars.

 

[JohnNemo]

Frame dragging only appears in the egregiously non-flat regions of spacetime near a massive rotating body; the distant stars are completely irrelevant to the spacetime curvature in such a region.

The only reason we mention the distant stars is that we said "near a massive rotating body" so we have be clear about what we mean by "rotating", and in this context an intuitive definition of "rotating" involves the distant stars.

Is the bulge around the Earth’s equator caused by this type of frame dragging effect?

 

[Nugatory]

Is the bulge around the Earth’s equator caused by this type of frame dragging effect?

No. That's a classical phenomenon, well understood since Newton.
Googling for "equatorial bulge cause" will find some good explanations.