Dimensions of Time...?

[Jadzia]

Shaw, could you explain how we can use the one dimensional version of the metric you showed us to calculate the gravitational acceleration felt on the surface of an (unrealistically massive) planet, (mass m, radius r)

Say from the point of view of being on the surface, and then from the point of view of a distant observer.

I think this would help to consolidate ProtoAvatar's (and my own) understanding.

 

[Shaw]

Wow... that is a tall order.

I'm not sure I'd be able (or qualified at this point, having not done anything like that in more than 16 years) to present such a thing... specially in the form of a post.

But a few years ago I came across a lecture in which the professor did a direct comparison of Newtonian Gravitation and General Relativity that (as I recall) did pretty much what you are asking for (showing how the space-time curvature creates what we see as force).

I don't believe it was one of Susskind's lectures (though if someone wants to check them, he might have covered this), but I'm sure I made a note of the lecture somewhere (because I thought it was pretty good).

Let me see if I can find that lecture as it's presentation of this would most likely be infinitely better than anything I could do stumbling through it (which, after all, is all I've been doing so far).

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In principle, you can distinguish whether you're in a free space reference frame or a freely falling reference frame in a gravity field. A cloud of particles in the latter would exhibit tidal distortions due to the converging geodesics and the field gradient. You could also detect the gravitational field gradient across the frame by measuring the frequency shift in the Mössbauer effect. The two frames are only equivalent in the limit when they're vanishingly small.

Exactly... thanks for posting that.

 

[Shaw]

Okay... I think this is the lecture.

Einstein's Field Equations (YouTube version, course home page)​

I don't have time today to watch it (it is a little more than an hour long), but I should have some time tonight or tomorrow. If it is the wrong one, I'll keep looking for the right lecture.

 

[Shaw]

Okay, I got a chance to watch the video over again. I think the professor (Bertschinger) and I have some semantic differences, but on the whole the lecture covers all the things one needs to see on how General Relativity and Newton's Gravity can yield similar results. I'd still rather not classify gravity as a force though.

Hopefully that'll prove helpful. And as I said, it is a far better presentation than I could have done... specially in a post (and being as rusty at this stuff as I am).

 

[Kain]

Wow, this turned into a real HitchHiker's Guide to Astrophysics.
It will take some time for me to read all the information you have presented, and some more time to understand them. Afterwards, I'll see if my thought of Time Dimensions still makes some sense...

 

[ProtoAvatar]

Shaw:

"An experiment - you have a planet and an object in free-fall towards it. You are observing this from a POV outside the gravity field of the planet. The free-falling object's watch and yours were syncronized before the experiment.

If the clock on the free-falling object doesn't run slower than yours, this means that the mass of the planet doesn't really distort time, the mass only sucks space towards it.
It means that time (and space?) is distorted only by acceleration, not by gravity.
Do you know if any such expriment took place? If yes, do you know its result?"

Apparently, an experiment along those lines was performed - the Shapiro delay:
http://en.wikipedia.org/wiki/Shapiro_delay
A photon follows geodesics in a gravity field aka is in free fall.
And a photon sent near the sun was influenced by the time dilation generated by the sun's gravity aka the gravitational field is time dilation+space contraction+space moving toward the mass.

A question:
We have an elevator staying still in a gravitational field - it's an accelerated POVa.
And we have an elevator acceletating in space - it's POVb.

In POVa, time is running slower at the base of the elevator than at the top of the elevator.

In POVb, is time running slower at the base of this elevator than at its top?
If one puts two synchronised clocks, one at the base and one at the top of POVb elevator, will the clock from the base run slower than the clock from the top?

 

[Shaw]

Apparently, an experiment along those lines was performed - the Shapiro delay:

I'll have to read up on that. Thanks for pointing it out.

...If one puts two synchronised clocks, one at the base and one at the top of POVb elevator, will the clock from the base run slower than the clock from the top?

It should in POVb, but their is a way to reach that conclusion without the math... which I believe is how Einstein thought of it as early as 1912 as I recall. For all of the objects within the room, the forces that are experienced are transmitted by electromagnetism. That is to say, one atom pushing against another.

To take the extreme example of a light year long pole, if you start pushing it do both ends move at the same time? And if your push was such as to move the pole at a constant acceleration, even when both ends are moving at the constant acceleration, would both ends be passing the same velocities at the same time? And we're only talking about relative velocities, what really matters is the difference between the velocities being passed between the bottom of the pole and the top.

And if we go back to the room, if it was accelerating at a high enough rate, light would appear to bend. There is no constant velocity you can travel at in which you would see a beam of light bend, but there is an acceleration rate which will produce such an effect.

There is a lot to wrap one's head around in all this... and it took Einstein quite a few years to really work out all the details. And Einstein had published quite a bit about the ideas behind General Relativity before the final work was finished (starting as early as 1908 as I recall). That meant that Einstein wasn't the only person that could be working on this stuff... and it still took years to finally work out.

I know I'm not doing justice to these examples, and most treatises of the subject skip over all that stuff and look at it as if it was born whole and complete. I do think that the motivations are as important as the math that later described them (even if I'm not that good at verbalizing those motivations).

__________​

Wow, this turned into a real HitchHiker's Guide to Astrophysics.
It will take some time for me to read all the information you have presented, and some more time to understand them. Afterwards, I'll see if my thought of Time Dimensions still makes some sense...

Well, it sounded like you were interested in more than just physics (as you were referencing Flatland earlier). If you are interested in non-euclidean geometries, I started a thread on the subject a while back (here). In the end my interests lean more towards geometry/topology than towards physics.

 

[ProtoAvatar]

We have an accelerated room. Objects 'fall' towards the floor because the space which the objects occupy is travelling towards the floor.
A room staying still in a gravity field. Objects fall towars the floor because space is sucked towards the floor by the mass below.
This much is clear.

I think the only thing I would add to that is that you can treat (for the most part) constant velocity and zero velocity as equivalent in the empty space version.

Shaw, can you elaborate on why you said "for the most part"?
Under what conditions can't you treat constant velocity and zero velocity as equivalent in empty space?

 

[Haggis and tatties]

I feel my intelligence has increased slightly just by reading this thread....heavy stuff for me but very interesting nevertheless.

 

[Shaw]

Shaw, can you elaborate on why you said "for the most part"?
Under what conditions can't you treat constant velocity and zero velocity as equivalent in empty space?

With no other references in empty space, your only measurement would be against the speed of light. The speed of light... which appears the same to any observer in a reference frame of constant velocity, will always be the speed of light. So constant velocity and zero velocity are equivalent states in such (idealized) conditions.

In the end, velocity is a relative measure to some other object in space-time... not to space-time itself. Acceleration is measured relative to space-time though, so exists even in empty space.

The conditions would change if our test subjects are Hansel and Gretel. Each bread crumb they leave would provide a reference object by which they could figure out their relative velocity in empty space (including after some period of acceleration).

Good question.