How fast is gravity?

[*Aqua*]

Feel free to give feedback if you can't follow, I am probably doing this too fast and should give more intermediate steps.

I had to wiki a bit but I think I could follow your explanations. Thank you!

I think what it illustrates really well is geodesics.

I thought it illustrate how a layman can easily imagine bended spacetime.

My first thought was "I never heard of something like compressed space, so the bended space must bend into somewhere or something". I wasn't sure if this assumption is correct, so I asked, if the two lines have the same length. If they have the same length the space is still there but not visible (= illustrations sucks). If they haven't my assumption is right. So... where did the space go to?

I ask that because I heard somewhere that space itself contains or is made out of energy. As no energy can ever be lost it has to go somewhere or convert into another kind of energy.

Or do I have the wrong kind of idea and it works in a completely different kind of way?

[K^2]

While reading this thread I came upon the question how bended spacetime would behave different compared to "unbended" spacetime.

Let's take this picture which is common to illustrate bended spacetime. But illustrations on that topic are often simplified and show some details wrong. My question is, do both marked lines have the same length? (If we use a folding yardstick or similiar.)

Image

No. In this picture the distance around any circle is defined as 2pi r, because this is how r is actually defined in Schwarzschild coordinates.

[cicatrix]

The above illustration is bad because it uses concentric circles instead of simple grid.

Here are better ones (they illustrate the trajectories of 'straight' lines within a gravity well). When you look at these pictures bear in mind that all lines are actually 'straight' and 'parallel':

Light is NOT attracted by gravity. Light travels along the 'straight' line but since gravity bends the spacetime it APPEARS that light travels along a curve. Even a spacecraft in what appears to be a circular orbit (or simply a thrown stone) are not actually 'pulled' by gravity - they travel 'straight' along the spacetime. It's the curvature of the spacetime itself that makes them APPEAR not to travel straight.

Edited February 6, 2015 by cicatrix

[Sirrobert]

So in a sense, gravity doesn't actually pull on mass/energy at all?

It bends space time, and THAT effects matter in such a way that it appears to be pulled towards something?

[cicatrix]

So in a sense, gravity doesn't actually pull on mass/energy at all?

It bends space time, and THAT effects matter in such a way that it appears to be pulled towards something?

Yes, gravity only bends the spacetime but does not affect matter in any other way. (According to Einstein, as far as I could comprehend the relativity theory)

The same picture from 'above' (as it would have been perceived by a planar 2d person) would look like this (as you can see - no curved grid - every line is straight):

Edited February 6, 2015 by cicatrix

[*Aqua*]

Ok, my picture shows the wrong thing. Cicatrix's ones are much better.

Here it's the same question. Does a bended line have the same length as the unbended line? From 'above' the appear unchanged, looking from a 45° angle the bended lines seem to have different lengths.

[cicatrix]

Ok, my picture shows the wrong thing. Cicatrix's ones are much better.

Here it's the same question. Does a bended line have the same length as the unbended line? From 'above' the appear unchanged, looking from a 45° angle the bended lines seem to have different lengths.

This depends on the reference point ... I mean it is a relative thing, you know...

Seriously though, can you define 'same length'? At any point of that picture you have no absolute ruler to measure distances. From the 'flat' point of view these distances are equal but if you go beyond 2d you would see they are not.

All these illustrations have a rather limited teaching potential. Although there are some similarities, a 4d spacetime curvature is different.

Consider this - it takes 100 seconds to get from A to B somewhere and it takes the same 100 seconds to get from C to D in some other place. Can we therefore conclude that AB = CD? No. The best example I could think of is air density. Wherever the air is denser you would cover less distance. The gravity does the same thing to time.

[Sirrobert]

Could you say there is the same amount of space-time between the 2 lines?

Not sure if you can even say such a thing about space-time.

But, in my limited attempt to wrap my head around it:

If space is compressed by high gravity (so deep inside the well), but space-time has to stay the same size, would that explain why time is stretched?

[SolarLiner]

I have absolutely no idea. I'm obviously wrong (because black holes exist), but I can't configure how I'm wrong. If gravity weren't affected by space, then we'd see all sorts of weird anomalies (For instance, we'd still be feeling the gravity of Galaxies outside our observable Universe, because the expansion of space would have no effect on the propagation of the gravity waves of those Galaxies) On the flip side, if this weren't the case, Earth would orbit the Sun where it were 8 minutes ago (In fact, we orbit where the Sun is, not where it was 8 minutes ago when its light left).

Long post made shorter: I'm confused.

Earth is orbiting a 8 minute late Sun, because gravity transmits at the speed of light. However the effect is not that much noticeable because of the distances and speeds involved.

[Mr Shifty]

Earth is orbiting a 8 minute late Sun, because gravity transmits at the speed of light. However the effect is not that much noticeable because of the distances and speeds involved.

This is actually and perhaps surprisingly wrong. The Earth does, in fact, orbit the location of the sun's present location, not where it was 8 minutes ago. This has to do with velocity-dependent terms in the propagation interaction, which cancel out the propagation delay. See this paper for more detail. More exactly, the Earth orbits the location where the sun would be, given that you extrapolate its position and velocity from 8 minutes ago to the present.

[SolarLiner]

This is actually and perhaps surprisingly wrong. The Earth does, in fact, orbit the location of the sun's present location, not where it was 8 minutes ago. This has to do with velocity-dependent terms in the propagation interaction, which cancel out the propagation delay. See this paper for more detail. More exactly, the Earth orbits the location where the sun would be, given that you extrapolate its position and velocity from 8 minutes ago to the present.

Well this makes it even more awesome then. Thanks for the bedtime reading too

[K^2]

This is actually and perhaps surprisingly wrong. The Earth does, in fact, orbit the location of the sun's present location, not where it was 8 minutes ago. This has to do with velocity-dependent terms in the propagation interaction, which cancel out the propagation delay. See this paper for more detail. More exactly, the Earth orbits the location where the sun would be, given that you extrapolate its position and velocity from 8 minutes ago to the present.

Yes. This is a known result from electrodynamics as well. Electrostatic interactions work the same way. If Sun was to accelerate, however, that change would arrive 8 minutes late. As I have mentioned earlier, it is really changes that propagate at light speed. That is also what carries information.

On the topic of straight parallel lines. There is no such thing in GR. The lines of the grid only look straight in that coordinate system. I can chose another, and that grid will look all sorts of warped. Yet, all physics will remain exactly the same.

Likewise, lengths cannot be compared without taking time into consideration. Ordinary lengths are frame dependent. One must look at total distance in space and time.

[*Aqua*]

So we can't even measure a distance for sure because it's different in every frame of reference.

Gosh, how can it be that scientists didn't jump out of the windows yet? I guess they spend all day figuring out how to interprete measurements.

Edited February 7, 2015 by *Aqua*

[K^2]

So we can't even measure a distance for sure because it's different in every frame of reference.

Well, yeah. That's what length contraction in special relativity is all about. But it's not all that crazy. Think of it as measuring a height of a brick. It all depends on which end it stands on. Same deal with length being a frame-dependent quantity. Relative position of any two points in space-time involves time and space separation. So it's only natural that you need to first decide which direction is time and which is distance before you can measure length. And that's frame-dependence in a nut shell.

General Relativity is only further complicated by the fact that frames are only really defined locally. Just because you've decided on which direction is time in your immediate vicinity doesn't mean you don't have choices for everywhere else in the universe. This leads to all sorts of silliness, until you realize that overall coordinate choices don't matter. What matters is how these things transform as you gradually move along a particular trajectory. And that depends only on local curvature along your path. So all of the ambiguity of time and space is reduced to local differential geometry. It's still crazy math, one which takes a while to fully grasp, but it hasn't caused anyone to jump out of a window yet, that I'm aware of.

[cicatrix]

You can read this awesome book to get more understanding: Martin Gardner Relativity Simply Explained