General Relativity

[Perpetual Student]

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?

"Complete nonsense" right back at you! I said nothing about changing coordinates. I said, if I put top in motion, it is actually rotating (it has angular momentum) and the universe is actually not revolving around my top. We can tell because we can trace the chain of causality that resulted in the top's motion.

 

[sol invictus]

"Complete nonsense" right back at you! I said nothing about changing coordinates. I said, if I put top in motion, it is actually rotating (it has angular momentum) and the universe is actually not revolving around my top. We can tell because we can trace the chain of causality that resulted in the top's motion.

And that reasoning is complete nonsense. The chain of causality is identical in all coordinate systems.

 

[Roboramma]

"Complete nonsense" right back at you! I said nothing about changing coordinates. I said, if I put top in motion, it is actually rotating (it has angular momentum) and the universe is actually not revolving around my top. We can tell because we can trace the chain of causality that resulted in the top's motion.

How do you know that the top wasn't rotating the other way before you spun it, and your actions didn't simply stop it?

Or maybe it was already rotating in the direction in which you spun it, and now you've sped it up even more? Or something else?

No one is saying that you changed the rest of the universe by spinning the top, PS. They are saying that you can describe the universe in a frame in which the top was already rotating the other way (and is now at rest), and for everything that you can measure, it will be exactly the same as if you'd described it in a frame in which it was originally at rest and is now rotating.

So what's real? Perhaps none of the frames themselves are the reality, but rather the things that are true no matter what frame you choose: the relationships between things: the things that can actually be measured.

 

[Ziggurat]

It is your decision to ignore causality.

Unless you mean something completely different by the word "causality" from what everyone in physics means by the word, then this statement is completely wrong.

It's another source of information

Causality isn't a source of information. It's statements like this that make me think you must mean something completely different from what everyone else here means, but you haven't defined what you mean by causality. I suggest you do so in order to avoid further confusion.

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.

But you haven't decided questions of reality, you've only decided questions of preference, namely your own.

In Newtonian mechanics, the position you are advocating makes some sense. There are inertial reference frames, and non-inertial reference frames, and you can tell which is which by the existence of position-dependent forces which are always proportional to mass (such as centrifugal forces). We call these fictitious forces, and they disappear when we adopt an inertial reference frame. But even here, all you can do is select a class of reference frames which are special, you cannot pick a single reference frame which represents "reality".

But this position doesn't actually make sense in general relativity, because there literally is no difference between gravity and fictitious forces. So there is no way to remove all position-dependent forces which are proportional to mass. But there's also no need to. Everything works regardless of which frame you pick, as long as you handle it correctly.

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.

But all frames describe reality equally well. And the proof is that all frames provide the exact same description, because all frames will make 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.

You must have a strange definition of "better". Because from where I'm sitting, the ONLY criteria for how well any theory describes reality is the accuracy of its predictions. But if all reference frames provide the exact same answer, their accuracy is all identical. So there is no meaningful sense in which any description is better than any other description. What counts as "better" for you, then, is nothing objective. Because again, the only objective better or worse is accuracy. Anything beyond that is merely your personal preferences, which the universe doesn't care about.

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.

No. You missed my point completely. Your actions only changed the top. But that does not, and never did, preclude us from adopting a reference frame that rotates with respect to our table. Hell, we can choose such a reference frame even without a top. But it is the physics of the reference frame, NOT your hand, that makes the universe spin. If you thought otherwise, you completely failed to understand what reference frames are about.

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

No you aren't. You kept using the term "preferred". But the universe cannot prefer anything if it doesn't think.

 

[Michael C]

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

In order to describe a particular part of the universe there are certainly frames that are more convenient than others, but there is no single "best" frame to be used for every phenomenon in the universe.

What is the best frame for describing the motion of your grandchild's top? I'd choose a frame in which the floor on which it is spinning is at rest. If you were to use a frame based on the CMB, would that give a better description of what the top is "really" doing?

 

[ben m]

I suspect the thing you're missing, PS, is this. Let's talk about the table underneath your toy top.

1) I can write down a coordinate frame in which the table is rotating. In this coordinate system, distant objects (e.g., the stars) are moving under something you'd probably call a Coriolis force. This force obeys all of the laws of physics. By the way, you might happen to choose this coordinate system such that all coordinates on the top are stationary.

2) I can write down another coordinate frame, in which all coordinates on the table are stationary. In this frame, the coordinates of distant objects (e.g., the stars) are moving under something you'd probably call Newton's Laws. But the coordinates that describe a *point on the surface of the top* are now going in little circles.

3) Heck, I can write down a coordinate system that is of type (1) for all t < 0, then of type (2) for all t > 0. In this coordinate system, the actual laws of physics would have to be written with a "discontinuity" at t=0, which explains (in a way that passes all experimental tests) why a distant-star's coordinates would suddenly "brake", so that at t=-1 the star is orbiting the top and at t=+1 the star is at rest. That's a weird system, but those physical laws, expressed in those coordinates, are in fact correct. Why would you choose such a wacky coordinate system? Well, perhaps because they would label a point on the surface of the top as "stationary", even though a child reached over at t=0 and applied a force that stopped the top from spinning.

Does that make it clear how the "causality" works? "the stars grind to a halt at t=0" is the expected physical behavior of the stars according to an observer who has re-labeled their coordinate system at t=0.

 

[Perpetual Student]

... <rude comment snipped>... The chain of causality is identical in all coordinate systems.

Yes, but you continue to miss the point. See below.

 

[Perpetual Student]

I suspect the thing you're missing, PS, is this. Let's talk about the table underneath your toy top.

1) I can write down a coordinate frame in which the table is rotating. In this coordinate system, distant objects (e.g., the stars) are moving under something you'd probably call a Coriolis force. This force obeys all of the laws of physics. By the way, you might happen to choose this coordinate system such that all coordinates on the top are stationary.

2) I can write down another coordinate frame, in which all coordinates on the table are stationary. In this frame, the coordinates of distant objects (e.g., the stars) are moving under something you'd probably call Newton's Laws. But the coordinates that describe a *point on the surface of the top* are now going in little circles.

3) Heck, I can write down a coordinate system that is of type (1) for all t < 0, then of type (2) for all t > 0. In this coordinate system, the actual laws of physics would have to be written with a "discontinuity" at t=0, which explains (in a way that passes all experimental tests) why a distant-star's coordinates would suddenly "brake", so that at t=-1 the star is orbiting the top and at t=+1 the star is at rest. That's a weird system, but those physical laws, expressed in those coordinates, are in fact correct. Why would you choose such a wacky coordinate system? Well, perhaps because they would label a point on the surface of the top as "stationary", even though a child reached over at t=0 and applied a force that stopped the top from spinning.

Does that make it clear how the "causality" works? "the stars grind to a halt at t=0" is the expected physical behavior of the stars according to an observer who has re-labeled their coordinate system at t=0.

You use the phrase "I can...(choose such and such) a coordinate system." I have no basis to disagree with that. I am not a physicist; as a layman I accept what physicists say; specifically, GR makes all coordinate systems equally valid. That is one of the key features of GR, along with providing a theory of gravity that is consistent with experiments, consistent with SR and reduces to Newton's gravity at slow speeds and weak gravity. OK, it's a powerful mathematical description of the universe, of reality -- a mathematical model of reality.
But it is not the only tool we have when we ponder what reality is, what the universe is. Consider this:
You said, "I can write down a coordinate frame in which the table is rotating. In this coordinate system, distant objects (e.g., the stars) are moving under something you'd probably call a Coriolis force. This force obeys all of the laws of physics. By the way, you might happen to choose this coordinate system such that all coordinates on the top are stationary."
My contention is that even though the above comment is true (as far as I know -- I am a layman), it does not tell the whole story. We can still decide what is "really happening." Based on all I have heard and read, GR will not do this -- all coordinate systems tell us what is "really happening" according to GR. Do we stop thinking at this point? Do we just say, oh well, GR is king; there is no such thing as what is "really happening"? I don't accept that! We know the history and we know the causation of the spinning top. I did it! It is really spinning! GR is only a mathematical model; it is not real. It is limited.
Should that surprise anyone? -- that our best models of reality are limited?
There is every reason to believe that the universe is a real place with an ultimate reality that we will probably never fully comprehend. As a real object, the universe has a real time and a real place. The CMB tells us something about that real time and place. The theory of general relativity allows us to examine it from any frame of reference we choose for our own convenience; the physics will be the same regardless. But we have that CMB giving us information regarding which of these frames is the real thing.

 

[Perpetual Student]

Thanks for all the above comments. I don't have the time or stamina to respond to all, so I have chosen one to best make my point.

 

[Ziggurat]

You use the phrase "I can...(choose such and such) a coordinate system." I have no basis to disagree with that. I am not a physicist; as a layman I accept what physicists say; specifically, GR makes all coordinate systems equally valid. That is one of the key features of GR, along with providing a theory of gravity that is consistent with experiments, consistent with SR and reduces to Newton's gravity at slow speeds and weak gravity. OK, it's a powerful mathematical description of the universe, of reality -- a mathematical model of reality.
But it is not the only tool we have when we ponder what reality is, what the universe is.

Sure. If you want to ponder what reality is, we have philosophy too. But if you want to describe reality in a quantifiable manner, well, science is in fact the only thing we've got. And GR is our best large-scale theory for doing so.

My contention is that even though the above comment is true (as far as I know -- I am a layman), it does not tell the whole story. We can still decide what is "really happening."

How can we decide what's happening? Unless you're a solipsist, then nothing we decide has any effect on what reality actually is. It's not a choice we can make. We can choose how to represent reality, we can even choose what we believe reality to be, but we cannot actually choose what reality itself is.

Perhaps you mean we can determine what is "really happening". If so, well, you picked the wrong word. And the difference matters. Furthermore, how are we to determine what is "really happening" when all these different possibilities are identical? There is no one "really happening". There cannot be one "really happening". And that is true for the very simple reason that there is no difference between the different reference frames.

Based on what all I have heard and read, GR will not do this -- all coordinate systems tell us what is "really happening" according to GR. Do we stop thinking at this point?

No. We do one of three things.

1) We try to find out if GR is wrong, which we do by experimental tests. This is ongoing.
2) We look for alternative models which can describe observations equally well. Theorists have been doing this for decades, and so far we have nothing as good as GR.
3) We stop doing science and start doing philosophy.

You are, at best, engaged in option 3, but don't understand that you've stopped doing science.

There is every reason to believe that the universe is a real place with an ultimate reality that we will probably never fully comprehend. As a real object, the universe has a real time and a real place.

A real time and a real place? How do you know? Why must time and place be absolute in order to be real? Why is GR's picture any less real? Again, the only answers you will be able to provide would be philosophical, but at that point you've stopped doing science. We have another forum for philosophy.

 

[theprestige]

My contention is that even though the above comment is true (as far as I know -- I am a layman), it does not tell the whole story. We can still decide what is "really happening." Based on all I have heard and read, GR will not do this -- all coordinate systems tell us what is "really happening" according to GR. Do we stop thinking at this point? Do we just say, oh well, GR is king; there is no such thing as what is "really happening"? I don't accept that! We know the history and we know the causation of the spinning top. I did it! It is really spinning! GR is only a mathematical model; it is not real. It is limited.

Earlier you claimed that a heliocentric coordinate system is the best one for describing the solar system, because we know from causality that what is "really happening" in the solar system is that the planets are orbiting the sun.

But this is a false claim--or rather, it is only relatively true: What is "really happening" in the solar system depends on your point of view. From the point of view of the galactic center, for example, your bedtime story about heliocentric causality is totally wrong. From the point of view of the galactic center, the Earth isn't orbiting the sun at all. It's orbiting the galactic center, and its orbit is variously perturbed by its nearer neighbors.

From the point of view of the galactic center, your "causality" dictates that the solar system didn't form around the sun at all, but around the galactic center. There is probably no physically true property of your causally-heliocentric coordinate system, that is not equally true, equally valid, and equally preferable in a causally-galactocentric coordinate system.

You might prefer the heliocentric coordinates for philosophical reasons, or reasons of taste, or reasons of convenience. But there's no physical reason or scientific reason to prefer them (and 99% of the time you don't even prefer the heliocentric coordinates, since they're wildly inconvenient and counter-intuitive for daily life on the surface of the third rock from the sun).

 

[Michael C]

The CMB tells us something about that real time and place. The theory of general relativity allows us to examine it from any frame of reference we choose for our own convenience; the physics will be the same regardless. But we have that CMB giving us information regarding which of these frames is the real thing.

So once more: if you describe the motion of your grandchild's top using a frame based on the CMB, does it tell us what is "really happening"? When we use this frame, does it give a better description of the reality of the top's motion than when we use a frame where the floor of the room is at rest?

 

[ynot]

How do you know that the top wasn't rotating the other way before you spun it, and your actions didn't simply stop it?

Or maybe it was already rotating in the direction in which you spun it, and now you've sped it up even more? Or something else?

No one is saying that you changed the rest of the universe by spinning the top, PS. They are saying that you can describe the universe in a frame in which the top was already rotating the other way (and is now at rest), and for everything that you can measure, it will be exactly the same as if you'd described it in a frame in which it was originally at rest and is now rotating.

So what's real? Perhaps none of the frames themselves are the reality, but rather the things that are true no matter what frame you choose: the relationships between things: the things that can actually be measured.

You obviously have no idea of the observable properties of whether a top is spinning or not (or perhaps you have temporarily forgotten).

 

[alexi_drago]

Probably another stupid question and not about a rotating frame, but I'm curious about this.
Say you have a spaceship travelling along and on one side of it there's a laser firing a beam across the width of the ship to a detector on the other side, does the point that the laser hits the detector vary as the ship speeds up or slows down?

 

[Perpetual Student]

Sure. If you want to ponder what reality is, we have philosophy too. But if you want to describe reality in a quantifiable manner, well, science is in fact the only thing we've got. And GR is our best large-scale theory for doing so.

The fact that GR is the best we have does not mean it is the only thing we have and, of course, some day we may have something better.

How can we decide what's happening? Unless you're a solipsist, then nothing we decide has any effect on what reality actually is. It's not a choice we can make. We can choose how to represent reality, we can even choose what we believe reality to be, but we cannot actually choose what reality itself is.

Rotating and revolving bodies have measurable forces associated with those motions. Conjuring up all the ficticious forces necessary to imagine such bodies are at rest is possible under GR, but should give us some clue about what is really happening.

Perhaps you mean we can determine what is "really happening". If so, well, you picked the wrong word. And the difference matters. Furthermore, how are we to determine what is "really happening" when all these different possibilities are identical? There is no one "really happening". There cannot be one "really happening". And that is true for the very simple reason that there is no difference between the different reference frames.

See my comment above.

No. We do one of three things.

1) We try to find out if GR is wrong, which we do by experimental tests. This is ongoing.
2) We look for alternative models which can describe observations equally well. Theorists have been doing this for decades, and so far we have nothing as good as GR.
3) We stop doing science and start doing philosophy.
You are, at best, engaged in option 3, but don't understand that you've stopped doing science.

4) We stay with science and we use our brains and any and all other available information to discover what model(s) best reflect reality.

A real time and a real place? How do you know? Why must time and place be absolute in order to be real? Why is GR's picture any less real? Again, the only answers you will be able to provide would be philosophical, but at that point you've stopped doing science. We have another forum for philosophy.

This post made by someone some time ago is interesting:

Sure, but that doesn't make everything equivalent. You can call a road race of Phobos equivalent to a road race on earth. But once you introduce cosmology, well, you really do have something unique and special. There may be an absurd number of possible road races in the universe, each with its simplest reference frame, but there's only one cosmos. And there's only one co-moving reference frame for that one cosmos. On a certain level, yes, it's not any more valid than any other reference frame. And Occam's razor is ultimately about convenience, not truth. But nonetheless, there still remains one reference frame which is unique for everyone, everywhere. I don't think you can construct any other reference frame which is similarly unique for everyone.

 

[Perpetual Student]

So once more: if you describe the motion of your grandchild's top using a frame based on the CMB, does it tell us what is "really happening"? When we use this frame, does it give a better description of the reality of the top's motion than when we use a frame where the floor of the room is at rest?

There are measurable forces associated with rotation. That's a big clue.

 

[Ziggurat]

4) We stay with science and we use our brains and any and all other available information to discover what model(s) best reflect reality.

What does that even mean?

The only answer science will provide in regards to how well a model reflects reality is how accurate its predictions are. ANYTHING beyond that is no longer science. This is what you refuse to come to terms with. You aren't doing science anymore.

 

[Ziggurat]

There are measurable forces associated with rotation. That's a big clue.

Correction: there are measurable forces associated with your choice of coordinates. But that is true for any and all coordinate choices. Rotation is not special in this regard.

ETA: we can even take it a step further with a concrete example. Let's say we take a big patch of empty, flat space-time. In the middle of it, we stick a really massive spherical shell. Around the shell, spacetime becomes curved, and "fictitious forces" appear. Inside the shell, though, spacetime remains flat. Very far away from the shell, spacetime also remains close to flat.

Now let's spin our spherical shell. What happens inside? Well, inside, if we use coordinates which are not rotating with respect to distant objects, then we actually get forces. And those forces look like the forces one introduces in Newtonian mechanics when one adopts a rotating reference frame. Except we're not rotating. But to remove these forces from our equations of motion, we would actually need to adopt a reference frame which rotated. But if we do that, then we re-introduce those fictitious forces for distant objects. So it turns out that it isn't even possible to remove all these fictitious forces from any reference frame.

 

[Perpetual Student]

Earlier you claimed that a heliocentric coordinate system is the best one for describing the solar system, because we know from causality that what is "really happening" in the solar system is that the planets are orbiting the sun.

But this is a false claim--or rather, it is only relatively true: What is "really happening" in the solar system depends on your point of view. From the point of view of the galactic center, for example, your bedtime story about heliocentric causality is totally wrong. From the point of view of the galactic center, the Earth isn't orbiting the sun at all. It's orbiting the galactic center, and its orbit is variously perturbed by its nearer neighbors.

From the point of view of the galactic center, your "causality" dictates that the solar system didn't form around the sun at all, but around the galactic center. There is probably no physically true property of your causally-heliocentric coordinate system, that is not equally true, equally valid, and equally preferable in a causally-galactocentric coordinate system.

You might prefer the heliocentric coordinates for philosophical reasons, or reasons of taste, or reasons of convenience. But there's no physical reason or scientific reason to prefer them (and 99% of the time you don't even prefer the heliocentric coordinates, since they're wildly inconvenient and counter-intuitive for daily life on the surface of the third rock from the sun).

I can look at the universe quite well at various levels. The biggest is the universal CMB with the great walls, super clusters and voids of galaxies all moving about in random elliptical motions about local centers of gravity. Within that, then I can visualize our local cluster with galaxies doing a similar dance on a smaller scale. Within that I can visualize our galaxy, a great pinwheel with our sun out on one of the arms rotating about the central black hole every 200 million years or so, while the planets revolve around the sun in their various orbits, with moons revolving around them. It is one magnificent dance of countless huge structures, clusters, galaxies, stars, planets, moons, comets and asteroids. I can imagine quite well a single frame that takes it all in -- the one with the CMB stationary -- as a naturally occurring preferred frame of reference.

Having said all that, the earth has a bulge at the equator telling us it is rotating.

 

[Perpetual Student]

Correction: there are measurable forces associated with your choice of coordinates. But that is true for any and all coordinate choices. Rotation is not special in this regard.

ETA: we can even take it a step further with a concrete example. Let's say we take a big patch of empty, flat space-time. In the middle of it, we stick a really massive spherical shell. Around the shell, spacetime becomes curved, and "fictitious forces" appear. Inside the shell, though, spacetime remains flat. Very far away from the shell, spacetime also remains close to flat.

Now let's spin our spherical shell. What happens inside? Well, inside, if we use coordinates which are not rotating with respect to distant objects, then we actually get forces. And those forces look like the forces one introduces in Newtonian mechanics when one adopts a rotating reference frame. Except we're not rotating. But to remove these forces from our equations of motion, we would actually need to adopt a reference frame which rotated. But if we do that, then we re-introduce those fictitious forces for distant objects. So it turns out that it isn't even possible to remove all these fictitious forces from any reference frame.

As I mentioned above, the earth has a central bulge revealing its rotation. Saturn, which rotates much faster has an even more marked central bulge, which I believe is a ratio of about 11 to 10 when compared to the distance from pole to pole.