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General Relativity

Hellbound said:
Nothing there contradicts me, that I can see.

The ball would follow an arc, but as the person holding the string is moving at the same rate as the ball, the string would be straight and moving sideways. I've attached a photo that should explain it (please don't criticize the lack of artistic talent ;) ).
[qimg]http://www.internationalskeptics.com/forums/imagehosting/thum_6874bc37fd6cb097.jpg[/qimg]

The blue represents the path the ball fills over the time, the straight black lines the string. The black circles are the positions of the ball at the various time intervals.

Just to make clear, it's the appearance of the string my earlier post was concerned with, not the ball path. Hope this clears up any confusion.
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Big thanks for taking the time to make the drawing. It's greatly appreciated. I did think you were referring to the path the ball followed rather than the string - a simple misunderstanding. Is there no reference frame where we could see the string as being curved? Part of my brain is nagging me that there is, but I haven't been able to envision it. When it comes to things like this, I am not confident enough in my knowledge to say that there isn't simply because I cannot figure it out.
 
Perpetual Student said:
From your previous post, you said, "But you can distinguish inertial frames in which it's accelerating (including rotating around, say, the origin) from those in which it's not (Newton's bucket is a famous example)."
So, that tells me that if the meter shows the forces associated with rotation, it is unambiguous that the rock/rope system is rotating and the universe is not revolving around the system. OK?
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I don't know, because you still haven't told us what it means to you to say that something is "really rotating".

If you mean "at rest in some inertial frame" then yes - but only in flat spacetime, because in curved spacetimes (such as the one we inhabit) there are no inertial frames.
 
What is Reality?

Perpetual Student said:
Can I conclude that the rocks are really rotating because the meter and string shows it or not?
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Tim Thompson said:
I don't think it is possible under any circumstances to know what is the reality of the universe. I think the best we can do is know the relationship of consistency between our model of the universe and our observations of the universe. When we find the two in high accord we tend to treat the model as if it is reality, but we must keep in mind that is it always only a model.
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I think I see two things at issue here. One of them is what "really" really means, and the other is the difference between coordinate systems and reference frames (the wikipedia pages tend to make the same mistake, in my view, of equating to two improperly).

I would say that "coordinate system" refers to your particular choice of orthogonal coordinates for identifying points and/or loci of points (e.g., Cartesian, spherical polar, ellipsoidal-hyperbolic, & etc.), whereas a "reference frame" refers to the fundamental properties of spacetime. So, an "inertial" reference frame is Euclidean (a geometric description) or non-accelerated (a kinematic description), and a non-inertial reference frame is either curved (a geometric description) or accelerated (a kinematic description). The geometric or kinematic descriptions are just different ways of treating the same physics.

On the surface of Earth we can assume we are in an inertial reference frame, subject to non-linear Coriolis forces, or we can assume we are in a non-inertial reference frame feeling the effect of rotation. A sufficiently local experiment will not distinguish between the two.

Then there is the philosophical vs the practical problem of defining real (if you want real headaches over reality, just look into quantum mechanics). You keep coming back to the concept of what is "really" happening, but I don't think there is any general agreement here over what "really" really means. I think that while you & Sol might use the same word, you are likely not saying the same thing with it.

I hold to a strictly limited concept of "real". As in the quote above, I don't think you are asking a meaningful question, because I don't think it is possible to ever know what is "really" happening, or even that anything at all is "really" happening, in the philosophical sense. Only practical reality means anything to me, and practical reality is what we observe when we do an experiment. Take Newton's rocks. If those two rocks and the rope between them are alone in the universe (in which case we cannot be there to observe them), then it is of no observational consequence whether they are rotating in an inertial (non-rotating) universe, or at rest in a non-inertial (rotating) universe. The system behaves exactly the same in every sense in either case. So we pick one for convenience sake. Pick "rocks are rotating" because it makes things easier to understand, but it is not correct to say that it is "really happening" and the alternative is "really not happening", because no experiment exists that can distinguish one from the other.

Therein lies the secret: You cannot pick the "real" alternative unless you can perform an experiment that will distinguish by its outcome between the two. You can pick one because it makes more sense to you, but if you call it "real", it is a subjective judgement, not a difference between objective realities.
 
Tim Thompson said:
the difference between coordinate systems and reference frames (the wikipedia pages tend to make the same mistake, in my view, of equating to two improperly).
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I equate them. I don't think there's any distinction.

I would say that "coordinate system" refers to your particular choice of orthogonal coordinates for identifying points and/or loci of points (e.g., Cartesian, spherical polar, ellipsoidal-hyperbolic, & etc.), whereas a "reference frame" refers to the fundamental properties of spacetime.
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That's non-standard. For example it's very common to refer to "different" inertial reference frames in special relativity (e.g. two that are in motion with respect to each other) - but the spacetime in SR is always the same (Minkowski space).

Therein lies the secret: You cannot pick the "real" alternative unless you can perform an experiment that will distinguish by its outcome between the two. You can pick one because it makes more sense to you, but if you call it "real", it is a subjective judgement, not a difference between objective realities.
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That's my view, which is why I argue that one cannot decide whether the universe is "really" rotating - because I can always find frames in which it is and frames in which it isn't, without changing my predictions for any experiment.
 
That's my view, which is why I argue that one cannot decide whether the universe is "really" rotating - because I can always find frames in which it is and frames in which it isn't, without changing my predictions for any experiment.
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Is it possible that you 'cannot decide whether the universe is "really" rotating' because of a deficiency of your state of knowledge and models, not a characteristic of the universe, which must be either unambiguously rotating or not? I am aware that physicists do believe that the universe is actually ambiguous (relative) in this way, but it seems to me this may be more hubris than science. There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong!
 
UncaYimmy said:
Big thanks for taking the time to make the drawing. It's greatly appreciated. I did think you were referring to the path the ball followed rather than the string - a simple misunderstanding. Is there no reference frame where we could see the string as being curved? Part of my brain is nagging me that there is, but I haven't been able to envision it. When it comes to things like this, I am not confident enough in my knowledge to say that there isn't simply because I cannot figure it out.
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No, I don't think there is, but I reserve the right to be corrected by those more knowledgeable :)

I could see a situation where, say, a black hole (or some equally dense gravitational anomoly) bent light to make it appear curved, or refraction effects, but that's a bit beyond reference frame ;)
 
Perpetual Student said:
Is it possible that you 'cannot decide whether the universe is "really" rotating' because of a deficiency of your state of knowledge and models, not a characteristic of the universe, which must be either unambiguously rotating or not?
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Of course - anything is possible (particularly since you still haven't said what "really rotating" is, so the statement is so vague as to be entirely meaningless).

But as I told you, if one cannot choose coordinates in which an initially non-rotating universe rotates, then GR is not just incomplete - it's entirely and completely wrong, and in a way that I frankly cannot even imagine.

I am aware that physicists do believe that the universe is actually ambiguous (relative) in this way, but it seems to me this may be more hubris than science.
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You don't think assertions like "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" illustrate a certain degree of hubris?

It may well be the case that there exists a good definition of angular momentum for cosmological spacetimes (as there is for asymptotically flat spacetimes), and one could then choose to call spacetimes with zero angular momentum "non-rotating", and those with it non-zero "rotating". But as I've been trying to explain, one can always choose coordinates on a non-rotating object so it rotates.... and the physics in the new coordinates will be (and must be) identical.

There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong!
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If you want to draw some lessons from the history of physics, I suggest the following:

1) "common sense" doesn't apply at all in regimes outside the human scale and the human environment, and not even always there

2) Established theories very rarely - if ever - prove to be entirely wrong. Instead they turn out to be approximations that are valid and useful in certain regimes, but must be replaced by something more general and complete in others.
 
UncaYimmy said:
Is there no reference frame where we could see the string as being curved?
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No. The curvature of something is an invariant that doesn't depend on reference frame.

Perpetual Student said:
There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong!
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It's attributed to William Thomson (Lord Kelvin), but that's actually disputed.
 
sol invictus said:
Of course - anything is possible (particularly since you still haven't said what "really rotating" is, so the statement is so vague as to be entirely meaningless).
But as I told you, if one cannot choose coordinates in which an initially non-rotating universe rotates, then GR is not just incomplete - it's entirely and completely wrong, and in a way that I frankly cannot even imagine.
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It appears that it is my ignorance of GR that is the problem. Because GR replaces Newton's theory of gravity, I have not regarded Newton's theory as wrong, but simply limited. I have seen GR as extending not replacing Newton's gravity. There are many physical laws that break down at extreme sizes, pressure, etc. But, I have never regarded that as making those laws wrong, but only limited.

You don't think assertions like "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" illustrate a certain degree of hubris?
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:busted OK, fair enough. I was trying to be provocative. I have a deep respect for physicists and their area of expertise. Unfortunately, there is much of modern physics that is not readily intuitive for a layman. If I thought my assertions here were actually correct, I would not bother people on this forum; instead, I would write a book like Terence Witt or establish a website and launch an ant-GR campaign like a certain Mr. Mozina does with his EU stuff.

It may well be the case that there exists a good definition of angular momentum for cosmological spacetimes (as there is for asymptotically flat spacetimes), and one could then choose to call spacetimes with zero angular momentum "non-rotating", and those with it non-zero "rotating". But as I've been trying to explain, one can always choose coordinates on a non-rotating object so it rotates.... and the physics in the new coordinates will be (and must be) identical.
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Actually, I do think I am beginning to understand this. The point appears to be that the nature of GR under discussion here is so fundamental, that if there were some "outside" way of establishing some single thing as absolutely rotating, it would invalidate the whole theory.



If you want to draw some lessons from the history of physics, I suggest the following:

1) "common sense" doesn't apply at all in regimes outside the human scale and the human environment, and not even always there

2) Established theories very rarely - if ever - prove to be entirely wrong. Instead they turn out to be approximations that are valid and useful in certain regimes, but must be replaced by something more general and complete in others.
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Two excellent and relevant points. I really hope this exchange has not been too tedious for you. If it has, perhaps you can gain some small satisfaction in knowing that it has been very helpful for me.

BUT: I still do hate it that I can't view the earth as really rotating.
 
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Perpetual Student said:
BUT: I still do hate it that I can't view the earth as really rotating.
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Why do you think water spins down the plughole one way in the northern hemisphere and the opposite way in the southern?

I have as much if not more trouble accepting Relativity as you do by the way.
 
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ynot said:
Why do you think water spins down the plughole one way in the northern hemisphere and the opposite way in the southern?
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It doesn't (and yes, I've actually checked myself). Coriolis force is too weak to matter much on the scale of a bathtub or sink. A better question is why large storms curl opposite ways in the two hemispheres.

If you want to explain Corliois force without rotation, it's simple - you must simply introduce a force field that acts on all mass uniformly with a force exactly proportional to the mass.

Kind of like gravity, huh?
 
Maybe tangential, or even OT, but perhaps not tooo much ...

How does the core of the discussion in this (excellent, many thanks PS! :) ) thread relate to equivalence principle(s)?

IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase?

Lastly, if it's any help PS, the relationship between a well-established theory in contemporary physics and 'reality' is a topic not for the faint of heart. Among other things, IM(NSH)O, those who tackle this from a philosophical background all too often make serious mistakes (albeit rather subtle ones; these folk tend to be, after all, really really smart), and those from a strong physics background all too often show they have not bothered to absorb some painfully learned core lessons in philosophy. In any case, here's something you might like to start with: how can you, PS, determine what's real (part of reality), and what's not? In principle, of course :p
 
DeiRenDopa said:
Maybe tangential, or even OT, but perhaps not tooo much ...

How does the core of the discussion in this (excellent, many thanks PS! :) ) thread relate to equivalence principle(s)?
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Do you mean, for example, the equivalence of gravitational and inertial mass?
I guess the relationship is fundamental, since, as I understand things, under GR, going from one reference frame to another inevitably involves the interchangeability of these two aspects of mass.

IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase?
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As a layman, I have come to the (provisional) conclusion that the term "laws of physics" is a bit of a stretch. All we really have are models, that tell us (approximately) how nature behaves. If there are any real fundamental descriptions of reality, that we could label as absolute laws, these remain to be discovered.

Lastly, if it's any help PS, the relationship between a well-established theory in contemporary physics and 'reality' is a topic not for the faint of heart. Among other things, IM(NSH)O, those who tackle this from a philosophical background all too often make serious mistakes (albeit rather subtle ones; these folk tend to be, after all, really really smart), and those from a strong physics background all too often show they have not bothered to absorb some painfully learned core lessons in philosophy. In any case, here's something you might like to start with: how can you, PS, determine what's real (part of reality), and what's not? In principle, of course :p
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Based on my latter comment, I would guess there is no way to make such a determination.
 
DeiRenDopa said:
How does the core of the discussion in this (excellent, many thanks PS! :) ) thread relate to equivalence principle(s)?
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The equivalence principle states that a being held at a constant position in a uniform gravitational field is indistinguishable from being at a constant position in a uniformly accelerated (relative to an inertial frame) reference frame. A change-of-coordinates to an inertial frame would get rid of the gravitational field, i.e. a frame of reference where an object in freefall is at rest is indistinguishable from an inertial frame of reference.

If we're really naive, we can assume this suggests that gravitational forces are fictitious. But real gravitational fields aren't uniform, so they can't be completely gotten rid of by a change-of-coordinates. The equivalence principle still suggests an equivalence between 'fictitious' and gravitational forces, however, so the other conclusion---that what we call 'fictitious' forces in Newton's formulation of mechanics should be described as gravitational forces in the coordinate systems in which they appear---is taken. After all, there's no fundamental reason that any particular perceived gravitational force should be taken as either real or fictitious, as all of them are indistinguishable from a fictitious force, and it's impossible to get rid of all of them at once: and there's no way to determine the coordinate system that correctly determines which are real and which aren't.

Of course, that's fairly sloppy reasoning, but it's the best way I can think to relate the equivalence principle to the discussion. (I'm open to corrections to my sloppy reasoning. I'm here to learn as much as anything.) The better reason for taking the coordinate system dependent forces as being legitimate gravitational forces in the coordinate system in which they appear, as opposed to some mathematical artifact as in Newton's mechanics, is that we can formulate the laws of physics so that they're the same in all coordinate systems, suggesting that none of the coordinate systems is in any way special and we cannot determine a special coordinate system which tells us which forces are real and which are fictitious.

DeiRenDopa said:
IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase?
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The laws of physics are fairly generalized formulas from which the motion and behavior of matter can be derived. The Einstein Field Equations, for instance, are a law of physics: they, together with a few initial conditions (they are differential equations), can be used to figure out the behavior of the gravitational field. The geodesic equation, when given a spacetime geometry and some initial conditions, can be used to calculate the path that it will take. Both of these are formulated in a way that's the same in all coordinate systems.

Maxwell's equations, in their common form, only apply to inertial frames of reference. They have been reformulated so that they are true in all coordinate systems (and all spacetime geometries, including curved ones).

http://en.wikipedia.org/wiki/Maxwell's_equations_in_curved_spacetime
(If I'm not mistaken, even in a flat Minkowski spacetime, a change to curvilinear coordinates will still require that covariant differentiation be done, so the Maxwell laws need their form changed a bit even though the curvature tensors will be zero.)
 
Some comments made recently on another thread have stimulated some further thoughts about this subject. We have many situations in solving mathematical equations for some real physical system where we get negative or imaginary numbers that we toss aside because they are clearly not viable solutions for our specific analysis. For example: If we had some quadratic equation involving money, (√-1)$100.00 would make no sense and we would reject it and consider only real solutions to the quadratic as our real answer.
(Note that this has nothing to do with situations and systems where imaginary numbers are meaningful and even essential.)
So, my question is, could it not be that even though GR renders all coordinate systems valid, the one where everything revolves around Princeton NJ, for example, would be rejected as a real description of the entire universe even though it might have some specific utility? It would be rejected as not real just as we would reject i$100 as a mathematical solution for a financial problem.
I seems that there should be a place for common sense and judgement here, just as there would be judgement used in rejecting a negative or imaginary number where it would make no sense.
I am anticipating the response that there can be no preferred frame under GR -- end of discussion.
OK, similarly, from the perspective of pure mathematics, there can be no preferred solution to a quadratic -- all solutions are equally valid. Consider that all solutions may not be meaningful for some real situation that is being modeled but by choosing a preferred solution to a quadratic we are not rejecting quadratic equations. Can we not treat GR in the same way?
 
We discard (√-1)$100 and keep, say, $44 because they have different implications for our financial situation and one of them does not match how money works. Other times, we discard solutions if they don't satisfy constraints/boundary conditions on our problem.

If different coordinate systems had different implications for our physical situation, that's indeed a lot of incentive to keep one and discard another. But they don't. And given that they don't, making a criteria to sort them in the first place is more than a little ad hoc and of no practical value.

And that, by the way, doesn't inherently have to do with GTR per se. It is just one example of physical theory that doesn't care about coordinates. A universe that comes with its own coordinates seems to me to be quite bizarre, but YMMV.
 
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