General Relativity

[Farsight]

....When you move your fingers in opposing directions to spin the top, you're creating curvature in space time and this curvature results in the motion of the top...

Doo doo doo doo, doo doo doo doo. Welcome, to the Twilight Zone.

I've never heard such a load of old cobblers in my life.

 

[Roboramma]

It isn't your fault, you are having a conversation with a bunch of mystics, and it can be explained. Do not fall for "that's what GR tells you" when it just isn't true. Here's an example:

Farsight, don't you find it disingenuous to claim that you are presenting "the real GR" when you disagree with what is presented in university courses and their associated textbooks?

I don't have a problem with you saying that you're presenting GR as it should be understood, or as it is in reality or something like that. But anyone not familiar with your other threads would read your post and assume "Farsight is saying that other posters are not presenting GR as it's generally understood in the scientific community, whereas he is." when that is false.

 

[ynot]

You're assuming that it wasn't spinning to begin with. But you don't know that. If it was spinning along with the internal inertial reference frame (which is itself spinning with respect to the external inertial reference frame), then you would see any centrifugal force.

Did you mean to say "wouldn't"?

Don't know what stage you mean by "to begin with" but when the top was lying down on the table top it obviously wasn't spinning (we are talking about a top spinning on it's central axis aren't we?). Is "to begin with" when it was stood upright and before it was spun? If so then the table would also be spinning on the same axis and so would the whole planet. Unless the top was spinning at one of the poles the planet would be spinning on two axis at the same time.

You're asking the wrong question. They aren't spinning or not spinning because of the external shell. The external shell merely defines the internal inertial reference frame. Whether or not they tops are spinning relative to the internal inertial reference frame is a separate question, and it's determined by their unique histories. But the inertial reference frame inside the shell is itself rotating with respect to what's outside the shell, so anything inside which rotates with that inertial reference frame won't feel the rotation, and anything which doesn't rotate with it will feel the difference in rotation.

Have read that several times and can't arrive at sufficient understanding to be able to reply as yet.

 

[Farsight]

Farsight, don't you find it disingenuous to claim that you are presenting "the real GR" when you disagree with what is presented in university courses and their associated textbooks?

No. I take great pride in my honesty and sincerity. And I don't disagree with everything that's presented in university courses and textbooks, just those elements that contradict experimental evidence and what Einstein actually said.

I don't have a problem with you saying that you're presenting GR as it should be understood, or as it is in reality or something like that.

OK noted.

But anyone not familiar with your other threads would read your post and assume "Farsight is saying that other posters are not presenting GR as it's generally understood in the scientific community...

That's the size of it. On the black hole thread we had sol and Clinger saying space is falling inwards in a gravitational field. That's garbage. It isn't how GR is understood in the scientific community. And here we've got people advocating the sun rotating round the earth! That's garbage too. The whole point of the coordinate-independent approach is to see the big picture, like you do when you move your head from side to side to make out something unfamiliar. It isn't about all viewpoints are equal.

 

[edd]

You can tell the difference. You put a spoke in a wheel with a stick. And then you see that the spin of the rotating thing can change in an instant, whilst the rotation of a distant shell of mass cannot be altered faster than light can propagate. So you know that it's the thing rotating. At which point the mystics will huff and puff and say "you don't understand the math" or some other nonsense.

Changes in rotation are not in question, are they?

 

[ynot]

You're asking the wrong question. They aren't spinning or not spinning because of the external shell. The external shell merely defines the internal inertial reference frame. Whether or not they tops are spinning relative to the internal inertial reference frame is a separate question, and it's determined by their unique histories. But the inertial reference frame inside the shell is itself rotating with respect to what's outside the shell, so anything inside which rotates with that inertial reference frame won't feel the rotation, and anything which doesn't rotate with it will feel the difference in rotation.

[FONT=Verdana, sans-serif]Is this (these) otherwise unseen and undetected spinning external shell an actual thing with actual mass or is it (they) merely an abstract mathematical construct? You seem to be expressing them both ways when convenience suits.[/FONT]

 

[Farsight]

Changes in rotation are not in question, are they?

No. And because you can change rotation in a trice, rotations aren't either. Now go back and have a look at Perpetual Student's opening post. He's talking sense, and the people he's talking to are being absurd.

Several months ago on a thread about relativity, there was a discussion concerning the concept that all frames of reference are equally valid under general relativity. The physicists who participated asserted that (as an extreme example) it would be equally valid to view the whole universe as revolving around Phobos (one of the moons of Mars) compared to any other perspective (the CMBR, for example). The mathematics, of course would be vastly more complicated, but that would not invalidate that particular consequence of GR.

At that time, I argued that we all really know that the whole universe is not really revolving around Phobos, even though GR allows that perspective for anyone who might be inclined to use it. The professionals told me I was dead wrong! -- All frames of reference are equally valid! To my dissatisfaction, that’s where the discussion ended.

What bugs me is that he ends up thinking that GR is at fault, when it isn't:

After several months of further reflection, it still seems to me that if that is the case, if we cannot use Occam’s razor (or some similar concept), to conclude that the universe is not really revolving around Phobos, it is a fundamental flaw of GR. It simply contradicts common sense, intuition and rationality to view things otherwise. And, as far as I can tell, there is no utility in viewing the universe in such an absurd manner. Any comments?

 

[edd]

No. And because you can change rotation in a trice, rotations aren't either. Now go back and have a look at Perpetual Student's opening post. He's talking sense, and the people he's talking to are being absurd.

What you're saying there could have an analogy drawn to linear rather than angular velocities, and yet you wouldn't argue that velocity wasn't relative would you?

 

[edd]

I found http://einstein.stanford.edu/SPACETIME/spacetime4.html to be a particularly readable page on all this, by the way.

 

[sol invictus]

You can tell the difference. You put a spoke in a wheel with a stick. And then you see that the spin of the rotating thing can change in an instant, whilst the rotation of a distant shell of mass cannot be altered faster than light can propagate. So you know that it's the thing rotating.

What does that have to do with anything? The question I was addressing is whether you can tell if some small object in any apparent state of rotation is "really" rotating or not. You can't, at least not unless you can be sure there isn't some huge shell of mass out near infinity that's rotating. Your experiment can't distinguish between the two.

In other words, rotation in GR is relative - it's relative to infinity, or to distant matter if there is any.

 

[sol invictus]

[FONT=Verdana, sans-serif]Is this (these) otherwise unseen and undetected spinning external shell an actual thing with actual mass or is it (they) merely an abstract mathematical construct? You seem to be expressing them both ways when convenience suits.[/FONT]

It's either, in the sense that either one can alter the locally inertial frame. But in the real universe we live it, there's real mass out there, at least as far out as we can see.

 

[sol invictus]

I found http://einstein.stanford.edu/SPACETIME/spacetime4.html to be a particularly readable page on all this, by the way.

Here's a quote from there:

Here is a simple experiment that almost anyone can perform on a clear night: pirouette freely around while looking up at the stars. You will notice two things: one, that the stars seem to spin around in the sky, and two, that your arms are pulled upwards by centrifugal force. Are these phenomena connected in some physical way? Not according to Newton.
......
We know that the concept of absolute space(time) is retained in general relativity, so we might have expected that the same coincidental alignment of our local inertial frame with that of the global matter distribution would carry over to Einstein's theory as well. Astonishingly, however, it does not. If general relativity is correct, then there are strong indications that our local "compass of inertia" has no choice but to be aligned with the rest of the universe — the two are linked by the frame-dragging effect. These indications do not come from experiment, but from theoretical calculations similar to that performed by Lense and Thirring.
.....
Would the earth still bulge, if it were
standing still and the universe were
rotating around it?

To put the cosmological significance of frame-dragging in concrete terms, imagine that the earth were standing still and that the rest of the universe were rotating around it: would its equator still bulge? Newton would have said "No". According to standard textbook physics the equatorial bulge is due to the rotation of the earth with respect to absolute space. On the basis of Lense and Thirring's results, however, Einstein would have had to answer "Yes"! In this respect general relativity is indeed more relativistic than its predecessors: it does not matter whether we choose to regard the earth as rotating and the heavens fixed, or the other way around: the two situations are now dynamically, as well as kinematically equivalent.

 

[Hellbound]

It's either, in the sense that either one can alter the locally inertial frame. But in the real universe we live it, there's real mass out there, at least as far out as we can see.

[off-topic aside]
I wonder if one could develop a theory that has the observable universe rotating wrt some exterior mass, and the resulting centrifugal force causes the expansion? I suspect it wouldn't fit...but it does give me some ideas for a light-hearted sf story (imagine the first FTL spaceship travelling as far as it can and running into...the side of a universe-encompasing fishbowl!)
[/off-topic aside]

 

[sol invictus]

[off-topic aside]
I wonder if one could develop a theory that has the observable universe rotating wrt some exterior mass, and the resulting centrifugal force causes the expansion? I suspect it wouldn't fit...but it does give me some ideas for a light-hearted sf story (imagine the first FTL spaceship travelling as far as it can and running into...the side of a universe-encompasing fishbowl!)
[/off-topic aside]

It's a nice idea. But I think it immediately runs into difficulty explaining the observed isotropy of the universe - things are expanding equally in all three dimensions, not just out along a plane perpendicular to an axis.

 

[Perpetual Student]

Here's a quote from there:

... If general relativity is correct, then there are strong indications that our local "compass of inertia" has no choice but to be aligned with the rest of the universe — the two are linked by the frame-dragging effect. These indications do not come from experiment, but from theoretical calculations similar to that performed by Lense and Thirring.
.....
Would the earth still bulge, if it were
standing still and the universe were
rotating around it?

To put the cosmological significance of frame-dragging in concrete terms, imagine that the earth were standing still and that the rest of the universe were rotating around it: would its equator still bulge? Newton would have said "No". According to standard textbook physics the equatorial bulge is due to the rotation of the earth with respect to absolute space. On the basis of Lense and Thirring's results, however, Einstein would have had to answer "Yes"!
...

I am perplexed as to how the revolving universe can result in this frame dragging effect to account for the earth's bulge. If the universe is homogeneous and isotropic, would not the net gravitational influence on earth be zero? Of course the sun, galaxy, etc are nearby, but that's not mentioned above as a factor in this reasoning? What am I missing?

 

[sol invictus]

I am perplexed as to how the revolving universe can result in this frame dragging effect to account for the earth's bulge. If the universe is homogeneous and isotropic, would not the net gravitational influence on earth be zero? Of course the sun is nearby, but that's not mentioned above as a factor in this reasoning? What am I missing?

In a frame where the earth is not rotating, the universe isn't homogeneous and isotropic - at least not the part we can see. Rotation automatically breaks both isotropy and (probably, it's a little less obvious if you allow expansion too) homogeneity.

The same goes for a frame in which the earth (or the sun, or the Milky Way) are at rest. In any of those frames, the CMB has a largish dipole moment, meaning the universe is neither homogeneous nor isotropic.

When people say that the universe is homogeneous and isotropic, what they really mean is that there exists one frame in which that holds. And there's always the caveat, often unspoken but crucial to this discussion, that we only know that such a frame exists locally, because we can only see a small part of the universe. The rest might be very different indeed.

 

[edd]

The standard gravitational field would cancel but there's a gravitomagnetic contribution which doesn't. I'm not sure of a terribly intuitive way to think of it but I am looking.

These are properly interesting and insightful questions you're asking by the way PS. Sorry it's hard to explain the answers sometimes.

 

[Perpetual Student]

There are some great, quick sites to learn basic tensor calculus. MIT open course ware, Khan academy, lots of Youtube videos, and others can do the trick. Try Edmund Bertschinger's textbook "Introduction to Tensor Calculus for General Relativity"
http://web.mit.edu/edbert/GR/gr1.pdf

Thanks again, Astrodude. I have been "on the verge" of studying this stuff for two years now. I may be too old at this point, but your information has finally got me off my butt. It's interesting that basic linear algebra is a stumbling block for me. I taught freshman calculus and linear algebra (45 years ago) while getting my MS. The calculus has stayed with me, while linear algebra (seemingly the easier part) is loaded with brain cobwebs. My old linear algebra text (Paul C. Shields -- 1964) is getting a new work out. I know I'll never be able to master this stuff -- all I want is to be able to generally follow the mathematical arguments.

 

[Hellbound]

It's a nice idea. But I think it immediately runs into difficulty explaining the observed isotropy of the universe - things are expanding equally in all three dimensions, not just out along a plane perpendicular to an axis.

But if it's a hypersphere that's spinning in three dimensions along a two-dimenional axis? Is there sucha thing as 3d centrifugal force?

Sorry, I'm done with my aside now. Back to the main topic

 

[sol invictus]

But if it's a hypersphere that's spinning in three dimensions along a two-dimenional axis? Is there sucha thing as 3d centrifugal force?

You're correct that in four space dimensions you can spin independently along two axes simultaneously - the one perpendicular to the xy plane, and the one perpendicular to the zw plane. But that kind of rotation still breaks 3D rotation invariance (i.e. isotropy).