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Non-geometric approach to gravity impossible?

by waterfall
Tags: gravity, impossible, nongeometric
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atyy
#19
Feb26-12, 10:53 AM
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Quote Quote by waterfall View Post
Bottom line is. If one models gravity as a physical field. There may be a way to shield gravity. In General Relativity, there is no way to shield it. So there is the limitation of GR. When we focus too much on GR, we would become limited by what is possible and beyond.
No, classical gravity as a field in flat spacetime is the same as classical gravity as curved spacetime geometry restricted to harmonic coordinates. If it is impossible in one framework, it is impossible in the other framework.
waterfall
#20
Feb26-12, 11:48 AM
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Quote Quote by atyy View Post
No, classical gravity as a field in flat spacetime is the same as classical gravity as curved spacetime geometry restricted to harmonic coordinates. If it is impossible in one framework, it is impossible in the other framework.
So in flat spacetime, how does light bend around the sun... via the Huygen's path Harrylin mentions? How else?

Harmonic coordinates mean near the singularities as you mentioned. Does this mean inside the event horizon (say 10 light years across) or most inner part of it near the center (near planck scale)? Whatever, in quantum gravity which goes beyond the planck scale, it can address the issues inside the event horizon or just near the singularities? This is because it is not possible to address black holes in flat spacetime. Then would quantum gravity of spin-2 field in flat spacetime be able to address black holes whose event horizon (say 10 light years across) is still much below the planck scale size? How? Note it is only near the singularity that planck scale physics address. Hope you get what I'm asking or I'd have to rewords this again. Thanks.
Chronos
#21
Feb26-12, 01:49 PM
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Gravity is described by a second rank tensor, hence the spin 2 designation. Electromagnetism is described by a first rank tensor.
yuiop
#22
Feb26-12, 04:55 PM
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Quote Quote by waterfall View Post
What I'm saying is that there is no mechanism in General Relativity to shield gravity while in gravity as field based, it is possible. So GR is limiting. In fact, so limiting that it makes physicists sure no shielding can occur.. but note GR is just a model that we mustn't mistake for the territory.
What makes physicists so sure that gravity cannot be shielded, is that if it was possible, perpetual motion of the kind that provides free energy would be possible. Long before GR was formulated it has long been recognised that energy cannot be created or destroyed and that law (conservation of energy) is unlikely to change in a hundred years or even a thousand years.

Quote Quote by waterfall View Post
But the sun has mass, won't it be enough to attract the photons classically? I think the argument is that it has no mass. But they say this can be modelled on flat spacetime. So what makes massless light bend around the sun in flat spacetime (what argument do proponents of this use?)?
Galileo discovered over 400 years ago that the rate that objects fall is independent of their mass, so it is reasonable to assume that even light which has no mass will fall at the same rate as everything else (although this requires we drop the concept of gravity being a force). This meant that bending of light by the Sun by an amount equal to that predicted by Newtonian acceleration was not convincing proof of GR, but the fact that light bends twice as much (due to the curvature of space as predicted by Einstein) was much more convincing.
Passionflower
#23
Feb26-12, 05:03 PM
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Quote Quote by yuiop View Post
Galileo discovered over 400 years ago that the rate that objects fall is independent of their mass
Yes but just as an aside that is not exactly true.

For an object to fall it takes two objects, both fall towards each other and the more mass is involved the faster it will be.
waterfall
#24
Feb26-12, 08:18 PM
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Quote Quote by pervect View Post
It might be helpful to read Einstein's description of rulers on a heated slab

http://www.bartleby.com/173/24.html

Einstein points out that being able to tile a surface with squares that don't overlap at all is possible only on a plane.


Einstein doesn't specifically mention the surface of a sphere as a counterexample, but you can imagine trying to do it, and realize that it won't work - for instance, the circumference of the earth at the equator (0 degrees lattitude) won't equal the circumference of the Earth a short distance above it (say 1 minute of an arc above the equator).

The point is that with the actual rulers we use, observable rulers, the geometry of space-time is measurably curved - at least according to General Relativity (and light bending experiments agree with this prediction).

We can't tile space with perfect cubes that fit perfectly together, nor can we tile space-time with perfect hypercubes. This happens because space-time isn't flat (and spatial slices of consant Schwarzschild time aren't flat either).

It turns out you can make such a "heated ruler" theory to describe gravity. You wind up with imaginary rulers and clocks that perfectly cover an unobservable flat background space-time with squares, like the marble slab, and real rulers that expand and contract and clocks that speed up and slow down due to "extra fields" that affect all matter uniformly (like the heated rulers), so that actual rulers can't tile the geometry (with hypercubes for the example of space-time).

Note that in a space-time geometry, clocks play the role of rulers, in that they measure "distances in time".

More formally, one actually uses the Lorentz interval of special relativity than the usual concept of distance, but it probably won't be too confusing to gloss over this point.

There are some limits to this approach, that Weinberg didn't mention. For instance, you can't make a flat background spacetime have wormholes, because the topology isn't the same. You also tend to run into problems trying to model black holes (a black hole, fully extended with the Kruskal extentions, is equivalent to a wormhole, so the topology is basically different).
When you say flat spacetime can't have black holes. Is it because flat spacetime can't model the planck scale or is it because right at the start of the event horizon, flat spacetime can't model say the 10 light years event horizon down to near the planck scale? If so, then why do people like atyy say spin-2 field in flat spacetime is equal to general relativity in spacetime covered by harmonic coordintes (near planck scale). It is not equivalent when you can't even model the 10 light year event horizon down to near the planck scale.
PAllen
#25
Feb26-12, 11:11 PM
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Quote Quote by Passionflower View Post
Yes but just as an aside that is not exactly true.

For an object to fall it takes two objects, both fall towards each other and the more mass is involved the faster it will be.
Yes, I once made the joke that if Galileo dropped Jupiter it would 'fall' (move towards earth's surface) a lot faster than a canonball.
harrylin
#26
Feb27-12, 01:16 PM
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Quote Quote by waterfall View Post
What models? pls mention them. [..]
A recent one that I found back is by Ilja Schmelzer (just Google for it). He also published a related paper in Foundations of Physics, but his Arxiv papers and website are more to the point. I also found this:
http://www.physicsforums.com/showthread.php?t=14258
yuiop
#27
Feb27-12, 07:09 PM
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Quote Quote by Passionflower View Post
Yes but just as an aside that is not exactly true.

For an object to fall it takes two objects, both fall towards each other and the more mass is involved the faster it will be.

Quote Quote by PAllen View Post
Yes, I once made the joke that if Galileo dropped Jupiter it would 'fall' (move towards earth's surface) a lot faster than a canonball.

if you were at a midpoint between Jupiter and the Earth (and not falling) then the rate that Jupiter falls towards the Earth would be the same as the rate that a canonball falls towards the Earth. What is different is the rate that the Earth accelerates towards Jupiter or the cannonball. So even a massless object could fall towards the Earth at the same rate as any other object, but the Earth would not accelerate towards the massless object.
PAllen
#28
Feb27-12, 07:48 PM
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Quote Quote by yuiop View Post
if you were at a midpoint between Jupiter and the Earth (and not falling) then the rate that Jupiter falls towards the Earth would be the same as the rate that a canonball falls towards the Earth. What is different is the rate that the Earth accelerates towards Jupiter or the cannonball. So even a massless object could fall towards the Earth at the same rate as any other object, but the Earth would not accelerate towards the massless object.
That's true, but doesn't get at the issue of sloppy wording. Someone standing on the ground would see a Jupiter mass black hole dropped from a tower fall faster than cananball dropped earlier. That is a fact, period. The principle intended is that rate of fall is independent of composition, and is essentially independent of mass over many orders of magnitude (atom to mountain), but not exactly independent of mass.

Midpoint is also incorrect - you mean center of mass.

Also, in GR, the mass dependence of 'free fall' has another component - gravitational radiation, which is a nonlinear phenomenon.
TrickyDicky
#29
Feb28-12, 03:49 AM
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Quote Quote by yuiop View Post
What makes physicists so sure that gravity cannot be shielded, is that if it was possible, perpetual motion of the kind that provides free energy would be possible. Long before GR was formulated it has long been recognised that energy cannot be created or destroyed and that law (conservation of energy) is unlikely to change in a hundred years or even a thousand years.
There is contradictory views about this (even from experts).
Precisely GR is formulated in a way that doen't assure energy conservation, or as Hilbert put it: General relativity has improper energy theorems instead of proper energy theorems.
We have a FAQ in the cosmology subforum that deals with this and asserts that energy is not conserved in the cosmological models based on GR.
That would lead me to think that according to GR it is not so sure that gravity cannot be shielded, in a way it could (see "relative energy of a black hole" thread, especially peterdonis posts). It would seem the gravitational energy is shielded, in the sense that it is not a source of curvature (meaning it is not part of the stress-energy tensor as explained by peter donis in the abovementioned thread).
waterfall
#30
Feb28-12, 04:39 AM
P: 381
I need to know something about this spin-2 field in flat spacetime = curved spacetime.

1. What is the reason for the Equivalence Principle in this Spin-2 field in Flat Spacetime Field Theory of Gravitation?

2. A larger ball with more mass should suppose to fall faster because the gravitational field between the earth and the object is more (in this spin-2 flat spacetime version). Yet Galileo showed they fell at the same rate. Is there a version of asympototic freedom in flat spacetime where larger mass would have fewer emitted gravitons to match the smaller sized object hence they falling at the same rate?
Passionflower
#31
Feb28-12, 10:44 AM
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Quote Quote by yuiop View Post
if you were at a midpoint between Jupiter and the Earth (and not falling) then the rate that Jupiter falls towards the Earth would be the same as the rate that a canonball falls towards the Earth.
In order to keep that midpoint one would have to accelerate and the acceleration would not be constant.

So in that case what do you think your measurements would actually prove?
atyy
#32
Feb28-12, 11:04 AM
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Quote Quote by waterfall View Post
1. What is the reason for the Equivalence Principle in this Spin-2 field in Flat Spacetime Field Theory of Gravitation?
http://arxiv.org/abs/1105.3735
"Asking for consistent self interactions leads essentially uniquely to GR and full general coordinate invariance [4, 5, 6, 7, 8, 9, 10] (see also chapter 13 of [2], which shows how helicity 2 implies the equivalence principle)."

http://arxiv.org/abs/1007.0435
"As argued by Weinberg [38], the equivalence principle can be recovered as the spin-two case of his low energy theorem. ... In other words, massless particles of spin-two must couple in the same way to all particles at low energies."
waterfall
#33
Feb28-12, 01:58 PM
P: 381
Thanks. I need to understand 2 basic things:

1. Say in the future gravitons were finally detected. Does it mean spin-2 fields actually existed and they occur in the backdrop of flat spacetime. Or do gravitons imply spacetime curvature is a priori? But in what sense is there spacetime curvature and at the same time gravitons existing when the two are more of a dual much like photons and electromagnetic wave (these are dual descriptions)? Unless you mean detection of gravitons don't tell us whether spacetime is really curved or dynamics just occuring in flat spacetime by spin-2 fields?

2. Can Loop Quantum Gravity be formulated as spin-2 field in flat spacetime? Or does LQG stay valid only if spacetime is actually curved?
atyy
#34
Feb28-12, 02:21 PM
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Quote Quote by waterfall View Post
But in what sense is there spacetime curvature and at the same time gravitons existing when the two are more of a dual much like photons and electromagnetic wave (these are dual descriptions)?
The classical electromagnetic wave is a coherent state of photons on flat spacetime. Similarly, classical curved spacetime (that can be covered by harmonic coordinates) is a coherent state of gravitons on flat spacetime.

Within string theory, gravitons are only approximate degrees of freedom, and strings are more primary. So in the string theory picture, curved spacetime is a coherent state of strings on flat spacetime. In the AdS/CFT picture, strings and space are both emergent, and neither are primary.
yuiop
#35
Feb28-12, 05:04 PM
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Quote Quote by PAllen View Post
Midpoint is also incorrect - you mean center of mass.
Yes, that is what I meant, more precisely I should of said for an observer at rest in the centre of mass frame.

Quote Quote by PAllen View Post
That's true, but doesn't get at the issue of sloppy wording. Someone standing on the ground would see a Jupiter mass black hole dropped from a tower fall faster than cananball dropped earlier. That is a fact, period. The principle intended is that rate of fall is independent of composition, and is essentially independent of mass over many orders of magnitude (atom to mountain), but not exactly independent of mass.
I agree that it is true that in the rest frame of the the Earth that more massive objects fall faster than less massive objects (as long as they are not dropped at the same time) but the point that I was making (and I am sure you understood what I was getting at) in the rest frame of centre of mass of the Earth and falling object, the acceleration of the falling object is independent of its mass in Newtonian physics. Agree?

Put it another way. In the rest frame of the Earth the acceleration of a falling object is proportional to G(M+m) where M is the mass of the Earth and m is the mass of the falling object. It is easy to see that if m goes to zero, that the acceleration does not go to zero.
PAllen
#36
Feb28-12, 05:08 PM
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Quote Quote by yuiop View Post
Yes, that is what I meant, more precisely I should of said for an observer at rest in the centre of mass frame.



I agree that it is true that in the rest frame of the the Earth that more massive objects fall faster than less massive objects (as long as they are not dropped at the same time) but the point that I was making (and I am sure you understood what I was getting at) in the rest frame of centre of mass of the Earth and falling object, the acceleration of the falling object is independent of its mass in Newtonian physics. Agree?

Put it another way. In the rest frame of the Earth the acceleration of a falling object is proportional to G(M+m) where M is the mass of the Earth and m is the mass of the falling object. It is easy to see that if m goes to zero, that the acceleration does not go to zero.
Yes, this is fine now for Newtonian gravity.


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