General Relativity

[Astrodude]

Thanks for trying. As sol invictus and others have said, it would be easier to discuss GR if I had a handle on tensor calculus. Sadly, my MS in mathematics (some 45 years ago -- yikes!) included only a cursory introduction to tensors -- not much beyond defining them -- so as much as I have tried with this 72 year old brain, I have not made much headway. If anyone can recommend a book like "tensor calculus for dummies" I might give it a try again.

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

 

[sol invictus]

Thanks for trying. As sol invictus and others have said, it would be easier to discuss GR if I had a handle on tensor calculus. Sadly, my MS in mathematics (some 45 years ago -- yikes!) included only a cursory introduction to tensors -- not much beyond defining them -- so as much as I have tried with this 72 year old brain, I have not made much headway. If anyone can recommend a book like "tensor calculus for dummies" I might give it a try again.

Math is just a tool, and it sounds to me from your posts that you're interested in physics. If so, I recommend Hartle's book on general relativity - it's intended for physics undergrads, so it probably doesn't require a high level of math.

 

[Perpetual Student]

OK, thanks Astrodude and sol invictus. I'm going to give those a try. Starting with Introduction to Tensor Calculus for General Relativity (MIT) by Edmund Bertschinger. (I already downloaded it and printed it for easier reading.) Hartle's book on general relativity is a bit expensive, so I'll see how I do with the MIT paper first.
Beware: If these books give me the knowledge I need, I may overturn GR with a new theory. What should I call it? PerpetualStudentivity?
Vorpal, your argument makes perfect sense and seems to defy any good response -- other than -- the universe is not a bunch of lines and conics on a sheet of paper.
But -- seriously, don't you think the earth really rotates on its axis, rather than the rest of the universe revolving around the earth?
Isn't the latter an ugly picture of the universe?

 

[theprestige]

the universe as it actually is -- with the CMB stationary

The CMB is actually stationary relative to what, exactly?

We have been over this many times in this thread and some others, but I'll state the case on more time in an attempt to achieve some clarity.
Let's say the solar system is the whole universe to simplify the model a little. Now, GR will allow us to examine and describe this universe from the perspective of any frame we can imagine: Phobos, Titan, Princeton, or any molecule on or in any object we might choose. The universe does not care one iota; it is the same universe with the same physics every time. Some of these frames are very convenient for some particular purpose.
However, for me it is very compelling that the mathematics is dizzyingly complex for the whole universe when we choose any of these frames but simplifies strikingly when we have the sun in the "middle" with the planets orbiting with the moons orbiting around the planets, etc.

Actually, it's already been pointed out that you're flatly wrong about how the math simplifies in this scenario. Don't believe me? Try plotting your next trip to the bathroom in a heliocentric reference frame, and then tell us how strikingly simple the math is.

That tells me that GR is not telling the whole story. The heliocentric essence of the solar system is "missed" by GR. There simply must be more to it all than GR is capable of telling us!

Since GR tells us a) that the simplicity of a reference frame depends on your point of view, b) that there's more than one point of view, and c) that all points of view are equally valid, I'm not at all sure what you think is actually being missed by GR. Certainly GR easily accommodates the heliocentric "essence" of the solar system, just as it easily accommodates the geocentric "essence" of the Earth-Moon system, the Princeton-centric "essence" of Princeton, NJ, and the CMB-centric "essence" of the universe at large. Of course, GR accommodates all of these "essences" by not considering any of them actually "essential". Most physicists seem to consider this a feature. You for some, reason, insist on thinking of it as a bug.

 

[Perpetual Student]

So, I'm sitting here having a cup of coffee and decide to set my grandchild's spinning top in motion. Have I set the whole universe in motion revolving around the top? GR will allow me to describe the universe that way, but we all know the historical fact that it was the flick of my hand that did the job and I am not strong enough to move all the galaxies, CMB, and stuff of the whole universe.
A collapsing cloud of gas and dust gave rise to the sun and the planets. The angular momentum and other forces of the original cloud resulted in the motions of the planets and the rotating sun. This cloud of gas and dust did not set the whole universe in motion.
So, what's my point? We actually know the history and causality of things so we know how things happened -- how planets, stars and galaxies and the CMB came about. GR does not! The planets actually do go around the sun! We know how that happened. GR does not know history and seems to be oblivious to causality. GR is not the whole story!
OK, now back to my reading of Introduction to Tensor Calculus for General Relativity.

 

[Vorpal]

Vorpal, your argument makes perfect sense and seems to defy any good response -- other than -- the universe is not a bunch of lines and conics on a sheet of paper.

Not so different in any sense relevant here. Coordinates are book-keeping device for whatever you're measuring. Be that the trajectory of electrons or lines or conic sections or other geometric figures is not important.

Actually, it's even more appropriate for the subsequent discussion: in relativity events are causally connected if and only one is within the other's light cone. So you're pretty much literally picking different coordinates to describe those cones. And just as the geometric figures don't care about which coordinates you pick, neither do those light cones--causal relationships.

But -- seriously, don't you think the earth really rotates on its axis, rather than the rest of the universe revolving around the earth?

No. I think those kinds of questions of "really" are just metaphysical fluff at best. Physical reality is whatever can be measured.

Isn't the latter an ugly picture of the universe?

No. I think it's much more beautiful. Or to be more precise, the generality of laws that don't care about which book-keeping devices humans use is to me a much more beautiful picture of the universe.

So, I'm sitting here having a cup of coffee and decide to set my grandchild's spinning top in motion. Have I set the whole universe in motion revolving around the top? GR will allow me to describe the universe that way, but we all know the historical fact that it was the flick of my hand that did the job and I am not strong enough to move all the galaxies, CMB, and stuff of the whole universe.

Of course you aren't. The events that cause what you see on the distant galaxies around you are causally disconnected from you. Absolutely nothing you do can affect them. (Though in principle you have some ability to affect sufficiently later events in those galaxies.) Causal relations are real things. If event A caused event B, then this relationship holds regardless what coordinates you pick to keep track of things.

It seems to me that you're begging the question. Your argument starts with the supposition that picking a rotating frame actually does something physical, and then you correctly conclude that this leads to completely nonsensical conclusions. But then we diverge on what to draw from this:
1) You keep the supposition and find GTR at fault for not respecting it.
2) Others simply throw the supposition out.
Or at least, that's my impression--you seem to be treating picking a rotating frame as the same thing as physically spinning around. But it isn't at all! I can predict what I would see if I spin around without picking a rotating frame. Or I can pick a rotating frame and predict what I would see while staying inertial.

All those coordinate choices affect is the system I use to write down the observations I make. It's no different than deciding to graph data on a log-log graph or a Cartesian graph, or write my notes in English or German. It does not change reality in anyway; it's just a representation.


P.S. There are very good reasons to believe that GTR is not the whole story, but they 't have little to do with the issues raised here.

 

[sol invictus]

So, I'm sitting here having a cup of coffee and decide to set my grandchild's spinning top in motion. Have I set the whole universe in motion revolving around the top? GR will allow me to describe the universe that way

Complete nonsense. Changing coordinates does not in any way change anything physical, imply causality, imply any motive force of any kind, and it doesn't happen at a particular time (because nothing "happens" at all, and anyway the coordinates include time).

If you click your mouse to zoom in on a digital map, you've suddenly forced everything to expand to ten times its previous size! How could your mouse possibly be so powerful?

 

[Farsight]

Again, I'd like to reiterate that the problem here is with what people say general relativity says, rather than with what general relativity actually says. Here's an example:

....Since GR tells us a) that the simplicity of a reference frame depends on your point of view, b) that there's more than one point of view, and c) that all points of view are equally valid...

However all points of view aren't equally valid. To understand this, take out a CD and put it on a table. Look down at it, and note that from this point of view it looks circular. Now take a couple of steps back and look at it again. It now looks ovoid rather than circular. But it isn't. When you see an unfamiliar object, think about what you do. You look at it, then you move your head and look at it again from another angle. To make out what it is, you combine different points of view to understand what it is you're looking at. You don't just say "all points of view are equally valid". You try to see the big picture, which is what GR tries to do.

 

[Perpetual Student]

Vorpal and sol invictus:
Your responses are weak. I think I have made a convincing argument that history and causality can give us information so we have preferred frames of reference at various levels.
Looking at the solar system, the heliocentric one is preferred since we know how the solar system formed and how its parts went into motion. Yes, the earth and the planets are really going around the sun.
Looking at the galaxy, we know that certain forces gave the galaxy its shape and its motions, so its preferred frame gives us a information as to what the galaxy really is.
We may not have precise knowledge about how galaxy clusters were formed, but we are familiar with the forces involved, dark matter, etc. so we can hypothesize historical accounts for clusters and super clusters. The more we understand the genesis of these structures -- the great voids and walls, the clearer the preferred frame becomes.
The motion of the spinning top on my table has a known genesis so we know it's spinning and the universe has not been set in motion revolving around the top.
Finally, we know about the big bang and the CMB, so we have knowledge of its genesis and the ultimate preferred frame of the known universe is unambiguously revealed to us.
So, it is our knowledge of history and causality that supplies the information lacking in GR to discover preferred frames -- including the ultimate one, so thankfully GR is not the only tool in our bag.

 

[Vorpal]

PS, your argument is nothing more than bare assertion.

We do know the history and causality of many of those things... and coordinates and in no way enter in those relationships. If solar flare erupts and takes out a satellite, then this a completely frame-independent relationship and no frame whatsoever will make it false. Not Earth-centric, not Princeton-centric, not anything. And so forth for every causal relationship whatsoever.

You simply state that questions like "what goes around what" is a frame-independent relationship of that sort. It's just begging the question.

 

[corbin]

I agree that GR gives no preferred reference frame, but I don't think causality is what does.

To me, it seems like the only place where you are going to get an answer as to why one particular arrangement of physical reality really is the case (or why none are preferred) is the place where nobody in this thread wants to go - metaphysics.

Note: A "metaphysical" answer to the question of "why isn't there a preferred reference frame?" would be something along the lines of "because raw sense data is itself subjective" or "because all referents are in the same category." Any answer uses elements outside the realm of science in its explanation, like the idea of a referent or the idea of raw sense data as qualia, and is therefore in a branch of philosophy called metaphysics, rather than part of science.

 

[Ziggurat]

Vorpal and sol invictus:
Your responses are weak. I think I have made a convincing argument that history and causality can give us information so we have preferred frames of reference at various levels.

Causality has nothing to do with this. All reference frames preserve causality.

Looking at the solar system, the heliocentric one is preferred since we know how the solar system formed and how its parts went into motion.

No, you are wrong. The development of the solar system can be tracked in any reference frame. If it couldn't, then different reference frames wouldn't be equivalent. But the entire point of GR is making them all equivalent, and it accomplishes that.

Perhaps you really mean is that solar dynamics are easier to track in a heliocentric coordinate system. And that's true. But my walk to the bathroom becomes harder than a geocentric reference frame. And the motion of other stars within our galaxy is also harder in a heliocentric coordinate system than in a coordinate system based on the galaxy's center of mass. And so on, and so on. There are, for practical reasons, very good reasons to prefer one reference frame over another for a particular problem. But which frame works best will change from problem to problem, and if you don't have any problem in mind, then there truly is no reason to prefer one reference frame over another.

Yes, the earth and the planets are really going around the sun.
Looking at the galaxy, we know that certain forces gave the galaxy its shape and its motions, so its preferred frame gives us a information as to what the galaxy really is.

No, it doesn't. Every reference frame will provide the exact same predictions.

We may not have precise knowledge about how galaxy clusters were formed, but we are familiar with the forces involved, dark matter, etc. so we can hypothesize historical accounts for clusters and super clusters. The more we understand the genesis of these structures -- the great voids and walls, the clearer the preferred frame becomes.

Necessarily false, since (again) all reference frames will produce identical predictions.

The motion of the spinning top on my table has a known genesis so we know it's spinning and the universe has not been set in motion revolving around the top.

That is in fact no more valid than a reference frame which was always spinning with respect to the earth. You simply momentarily placed a top at rest in that frame, but your actions did nothing more than change the motion of that top.

Finally, we know about the big bang and the CMB, so we have knowledge of its genesis and the ultimate preferred frame of the known universe is unambiguously revealed to us.

Define "preferred". Because as far as I can tell, the universe has no preferences at all.

 

[dasmiller]

Looking at the solar system, the heliocentric one is preferred since we know how the solar system formed and how its parts went into motion. Yes, the earth and the planets are really going around the sun.

No, they really are not.

The simplest possible system would consist of 2 rigid point-masses revolving around their common center of mass, so even a hugely-simplified solar system wouldn't have particularly simple math in a true heliocentric coordinate system. Since there are more than 2 bodies in the solar system, and since none of 'em are perfectly rigid or perfectly spherical, things are quite a bit more complicated than that, none of which makes a simple heliocentric system any more elegant for accurate orbit predictions.

 

[Perpetual Student]

Causality has nothing to do with this. All reference frames preserve causality.

It is your decision to ignore causality. It's another source of information to assist in deciding questions about what body is revolving and/or rotating with respect to another. Choosing to ignore information is an option but It can only impoverish our understanding.

No, you are wrong. The development of the solar system can be tracked in any reference frame. If it couldn't, then different reference frames wouldn't be equivalent. But the entire point of GR is making them all equivalent, and it accomplishes that.

Yes that's true and I did not say anything to contradict that. Using causality to decide questions of reality is a logical and scientifically valid procedure.

Perhaps you really mean is that solar dynamics are easier to track in a heliocentric coordinate system. And that's true. But my walk to the bathroom becomes harder than a geocentric reference frame. And the motion of other stars within our galaxy is also harder in a heliocentric coordinate system than in a coordinate system based on the galaxy's center of mass. And so on, and so on. There are, for practical reasons, very good reasons to prefer one reference frame over another for a particular problem. But which frame works best will change from problem to problem, and if you don't have any problem in mind, then there truly is no reason to prefer one reference frame over another.

I am not discussing which frame might be best for some particular purpose. I am using all available tools to decide which frame best describes reality.

No, it doesn't. Every reference frame will provide the exact same predictions.

Yes they do. All frames provide the same predictions but some describe reality better than others and I am proposing that there is a best one.

Necessarily false, since (again) all reference frames will produce identical predictions.

Wrong! See my response above.

That is in fact no more valid than a reference frame which was always spinning with respect to the earth. You simply momentarily placed a top at rest in that frame, but your actions did nothing more than change the motion of that top.

That's the point. My actions changed the top, not he universe; therefore we know the universe has not been changed by my actions and the top is really moving.

Define "preferred". Because as far as I can tell, the universe has no preferences at all.

The universe does not have thoughts. I am describing the reality of the universe.

dasmiller
No, they really are not.

The simplest possible system would consist of 2 rigid point-masses revolving around their common center of mass, so even a hugely-simplified solar system wouldn't have particularly simple math in a true heliocentric coordinate system. Since there are more than 2 bodies in the solar system, and since none of 'em are perfectly rigid or perfectly spherical, things are quite a bit more complicated than that, none of which makes a simple heliocentric system any more elegant for accurate orbit predictions.

That has nothing to do with my point.

 

[W.D.Clinger]

Causality has nothing to do with this. All reference frames preserve causality.

It is your decision to ignore causality. It's another source of information to assist in deciding questions about what body is revolving and/or rotating with respect to another. Choosing to ignore information is an option but It can only impoverish our understanding.

Ziggurat isn't ignoring causality. Please pay attention to what he wrote, especially the part I highlighted.

No, it doesn't. Every reference frame will provide the exact same predictions.

Yes they do. All frames provide the same predictions but some describe reality better than others and I am proposing that there is a best one.

Please define what you mean by "better".

Necessarily false, since (again) all reference frames will produce identical predictions.

Wrong! See my response above.

Your disagreement with Ziggurat's correct statement suggests that your argument is based upon some misunderstanding of general relativity.

Define "preferred". Because as far as I can tell, the universe has no preferences at all.

The universe does not have thoughts. I am describing the reality of the universe.

As do all admissible frames.

So far as I can tell, your argument is based upon ascribing your own preferences to the universe, or to your own arbitrary use of the word "reality" to describe some frames while decrying others' use of that same word to describe other frames that use different numbers to describe exactly the same physical reality.

 

[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

Edmund Bertschinger's textbook "Introduction to Tensor Calculus for General Relativity" is fantastic. Thanks! I also found a YouTube video of a 70 minute lecture by the same author about general relativity. He is an excellent lecturer.
I am making some progress.

 

[Perpetual Student]

W.D.Clinger

Originally Posted by Ziggurat
Causality has nothing to do with this. All reference frames preserve causality.

It is your decision to ignore causality. It's another source of information to assist in deciding questions about what body is revolving and/or rotating with respect to another. Choosing to ignore information is an option but It can only impoverish our understanding.

Ziggurat isn't ignoring causality. Please pay attention to what he wrote, especially the part I highlighted.

I am not contesting that all reference frames preserve causality. I am suggesting that causality can guide us to a better understanding of reality -- as in, "I caused the top on my table to spin so it is spinning and the universe is not rotating around my top."

Please define what you mean by "better".

bet·ter adj. Comparative of good.
. Greater in excellence or higher in quality.
. More useful, suitable, or desirable: found a better way to go; a suit with a better fit than that one.
. More advantageous or favorable; improved: a better chance of success.

Your disagreement with Ziggurat's correct statement suggests that your argument is based upon some misunderstanding of general relativity.

My understanding of GR is not at issue and you have no basis for that statement since I am basing my arguments on information outside of GR.

So far as I can tell, your argument is based upon ascribing your own preferences to the universe, or to your own arbitrary use of the word "reality" to describe some frames while decrying others' use of that same word to describe other frames that use different numbers to describe exactly the same physical reality.

Then clearly you have not understood my argument.

 

[W.D.Clinger]

Your disagreement with Ziggurat's correct statement suggests that your argument is based upon some misunderstanding of general relativity.

My understanding of GR is not at issue and you have no basis for that statement since I am basing my arguments on information outside of GR.

Why, then, did you say Ziggurat's correct statement was "wrong"?

Then clearly you have not understood my argument.

Although I have read your argument, I do not understand it.

As in your response to Ziggurat, your argument has included several statements that are flat-out incorrect. If those incorrect statements are irrelevant to your argument, then omitting them from your argument might make your argument easier to understand.

 

[Perpetual Student]

Why, then, did you say Ziggurat's correct statement was "wrong"?

If you trace the progress of the dialog, you will see that I intended to say that he was "wrong" in his insistence that causality cannot be used to decide which frame(s) describe reality, not that he is wrong that all reference frames preserve causality. Sorry for my lack of clarity.

Although I have read your argument, I do not understand it.

As in your response to Ziggurat, your argument has included several statements that are flat-out incorrect. If those incorrect statements are irrelevant to your argument, then omitting them from your argument might make your argument easier to understand.

Obviously, I don't believe anything I said is incorrect. I cannot and do not intend to contest GR; it would be absurd for me to do so. In any case, sweeping generalities like the above statement are useless in a discussion like this.

 

[W.D.Clinger]

If you trace the progress of the dialog, you will see that I intended to say that he was "wrong" in his insistence that causality cannot be used to decide which frame(s) describe reality, not that he is wrong that all reference frames preserve causality. Sorry for my lack of clarity.

I understood that the first time.

Please explain how it is possible to interpret your "wrong" response as anything other than flat-out incorrect. As Ziggurat had noted:

Causality has nothing to do with this. All reference frames preserve causality.

....Every reference frame will provide the exact same predictions.

....(again) all reference frames will produce identical predictions.

According to general relativity, all admissible reference frames are in complete, 100% mathematically precise agreement about all matters of causality.

Why, then, are you arguing that causality can be used to decide which frames describe reality better than others?

How can that aspect of your argument be regarded as anything other than flat-out incorrect?

(Unless, of course, you are rejecting the relevant parts of general relativity, but I don't think rejection of general relativity is part of your argument.)