WHY stationary things START falling: an informal 'quantum' gravity suggestion

[danR]

"danR
This nicely puts what has been a problem for me: we've imbedded motion in a static 4-space geometry. Why should particles 'simply start following' the geodesics...? What does 'following' mean? Is it simply a description of the necessary direction of entropy? But isn't entropy in this case is driven by the influence of a gravitational 'force'? What is 'forcing' the system? I seem to come back to some kind of 'force'."
​

Newtonwannabe:

Well geodesic are curves of extremal length. One can derive the geodesic equation by applying the principle of stationary action so particles following geodesics are particles following extremal curves. All particles in classical mechanics seem to obey this principle (analogous to the statement that objects in free fall in flat space follow straight lines) as long as they are in free fall and I don't think we actually know WHY its just the way things are.​

____________

The above, from another discussion, is a preamble to the following conjecture:

A particle 'P' in a field, here gravity, has a wave-function describing the probability that its position will be here or there in time. Suppose the probability is skewed by the gradient of the field so that P's probability of being 'there' is more likely, or being there more often than not; then the centre of the probability distribution (which we will hold equivalent to P's centre of mass) will shift to regain symmetrical distribution of probability. This is a struggle it cannot win: the probability/mass centre constantly moves there-ward, or tries to.

Naturally it has to answer many questions: why would P's behaviour be identical in an accelerated frame? How does an ensemble of particles behave? Does it explain the motion of a photon in a gravity field? Do all elementary particles behave identically?

Perhaps this is already out there, or is similar to something, or too naive. Any merit? Is it fixable? Too dumb?

 

[Polyrhythmic]

I think I get your idea. But why would the probability distribution "try" to become symmetric again?

 

[danR]

I think I get your idea. But why would the probability distribution "try" to become symmetric again?

That's where I paper over a crack, and hope it's not fatal. Anyway, the solution to Fermat's last theorem initially had a flaw, but it was repaired.

Suggestion: all things being equal, nature seeks a spherical symmetry of everything, including probability distributions.

Is there any similarity of this to something better?

 

[muppet]

A particle 'P' in a field, here gravity, has a wave-function describing the probability that its position will be here or there in time. Suppose the probability is skewed by the gradient of the field so that P's probability of being 'there' is more likely, or being there more often than not; then the centre of the probability distribution (which we will hold equivalent to P's centre of mass) will shift to regain symmetrical distribution of probability. This is a struggle it cannot win: the probability/mass centre constantly moves there-ward, or tries to.

If you're talking about wavefunctions, then you're already thinking about quantum mechanics, rather than some object with a definite position moving along definite trajectories. So I don't think this is really about why things "start falling".

What it sounds more like is a rough, and incorrect, description of how fields influence the wavefunction. You're right to the extent that a given field changes the wavefunction of a particle. Essentially, this is what the Schroedinger equation describes; you specify the field experienced by your system, and solve the equation to find the wavefunction.

The key phrase, however, is "skewed by the gradient of the field". The wavefunction doesn't "want" or "try" to be symmetric if it's influenced by something asymmetric, being pushed one way or the other.

As an aside, if you're looking for an answer as to why General Relativity works, it turns out to be more or less a consequence of special relativity plus the equivalence principle- that the gravitational mass (a measure of how strongly gravity pulls on some object, analagous to electric charge) and the inertial mass (a measure of how hard it is to get something moving) are the same, even though they're logically distinct ideas.

The equivalence principle, in turn, amazingly turns out to follow from certain assumptions about the quantum theory of gravity (specifically, if you assume that gravity is mediated by a massless symmetric spin-2 field). However, as you've probably heard the quantum theory of gravity poses plenty of conceptual and calculational problems, so nobody can really be certain that this is the ultimate answer yet.

 

[danR]

If you're talking about wavefunctions, then you're already thinking about quantum mechanics, rather than some object with a definite position moving along definite trajectories. So I don't think this is really about why things "start falling".

What it sounds more like is a rough, and incorrect, description of how fields influence the wavefunction. You're right to the extent that a given field changes the wavefunction of a particle. Essentially, this is what the Schroedinger equation describes; you specify the field experienced by your system, and solve the equation to find the wavefunction.

The key phrase, however, is "skewed by the gradient of the field". The wavefunction doesn't "want" or "try" to be symmetric if it's influenced by something asymmetric, being pushed one way or the other.

As an aside, if you're looking for an answer as to why General Relativity works, it turns out to be more or less a consequence of special relativity plus the equivalence principle- that the gravitational mass (a measure of how strongly gravity pulls on some object, analagous to electric charge) and the inertial mass (a measure of how hard it is to get something moving) are the same, even though they're logically distinct ideas.

The equivalence principle, in turn, amazingly turns out to follow from certain assumptions about the quantum theory of gravity (specifically, if you assume that gravity is mediated by a massless symmetric spin-2 field). However, as you've probably heard the quantum theory of gravity poses plenty of conceptual and calculational problems, so nobody can really be certain that this is the ultimate answer yet.

Keep in mind the point of this post is the word 'start'. It doesn't seem to get discussed, whereas the path is more or less a major topic of GR itself.

But since 'starting' is equivalent to 'a moving object accelerating'=incrementing an instantaneous given rate, perhaps a simple GR explanation would be possible without any gratuitous quantum rigamarole.

 

[Goldstone1]

Just look at the most famous tensor equation of GR... it states that space tells matter where to go, and how matter moves in it. Geodesics is just the fancy mathematical name for the principle of least action; especially when energy is implied in the relations of SR.

 

[danR]

Just look at the most famous tensor equation of GR... it states that space tells matter where to go, and how matter moves in it. Geodesics is just the fancy mathematical name for the principle of least action; especially when energy is implied in the relations of SR.

As long as the vector 'where to go' is equivalent to 'giving it a kickstart'. I can't do the math. You have to tell me that's what GR does for it: "Hey you, you don't want to move? I give you a push, right now, step lively mate..."

And off the reluctant particle goes.

 

[Goldstone1]

As long as the vector 'where to go' is equivalent to 'giving it a kickstart'. I can't do the math. You have to tell me that's what GR does for it: "Hey you, you don't want to move? I give you a push, right now, step lively mate..."

And off the reluctant particle goes.

I can tell you what GR says:

$$R_{ab} - \frac{1}{2}Rg_{ab}= k T_{ab}$$

is what tells a piece of matter how to react to spacetime, as does spacetime inversely correspond to the density of the matter or energy in question.

 

[Goldstone1]

When we talk about Geodesics, I said that it required an understanding of the principle least of action, you can also talk of the Einstein-Hilbert action - which gives any equation if unified properly, gives the principle of least action in a generalistic sense.

 

[Polyrhythmic]

I can tell you what GR says:

$$R_{ab} - \frac{1}{2}Rg_{ab}= k T_{ab}$$

is what tells a piece of matter how to react to spacetime, as does spacetime inversely correspond to the density of the matter or energy in question.

The Einstein Field Equations tell you how the spacetime is shaped in the presence of matter, it doesn't tell you anything about geodesics.

 

[Polyrhythmic]

[...], you can also talk of the Einstein-Hilbert action - which gives any equation if unified properly, gives the principle of least action in a generalistic sense.

What do you mean by this? What unification are you talking about? The Einstein-Hilbert action already relies on the principle of least action.

 

[danR]

[Edit: in answer to Goldstone1]

Would Feynman have said to me,

"That's a dumb way of putting it, but since you're a non-physics major, the answer is approximately yes." ?

 

[bcrowell]

Goldstone1's description of the Einstein field equation is not particularly relevant (since the OP is talking about quantum gravity, not classical gravity), and also, as Polyrhythmic pointed out in #10, not accurate.

danR, I think the basic answer to your question is that for quantum mechanics with Newtonian gravity, you just need to use the Schrodinger equation, and there is no big mystery. People have, for example, observed neutron interference patterns for neutrons that have moved up and down in a gravitational potential. It works as expected from the Schrodinger equation. The Schrodinger equation doesn't care about the origin of the potential that you plug into it.

However, if you want to use quantum mechanics with GR's description of gravity, then you run into all kinds of problems. As an example of the kinds of problems you get, there is the black hole information paradox: http://en.wikipedia.org/wiki/Black_hole_information_paradox

 

[danR]

Goldstone1's description of the Einstein field equation is not particularly relevant (since the OP is talking about quantum gravity, not classical gravity), and also, as Polyrhythmic pointed out in #10, not accurate.

danR, I think the basic answer to your question is that for quantum mechanics with Newtonian gravity, you just need to use the Schrodinger equation, and there is no big mystery. People have, for example, observed neutron interference patterns for neutrons that have moved up and down in a gravitational potential. It works as expected from the Schrodinger equation. The Schrodinger equation doesn't care about the origin of the potential that you plug into it.

However, if you want to use quantum mechanics with GR's description of gravity, then you run into all kinds of problems. As an example of the kinds of problems you get, there is the black hole information paradox: http://en.wikipedia.org/wiki/Black_hole_information_paradox

OK. Well it sounds from everyone that no theory has a problem getting things moving.

Now, if someone will look at my gedankenexperiment on synthetic 'magnetic monopoles, please , in the Classical Physics section. That's one I've been carrying around for years and never got around to asking until now, and the response in that thread has been either summary dismissal or a joke. Naturally it's not a particle, but is it an anything?

It really puzzles me what I would wind up with.

 

[danR]

General Physics, I mean. 'A mechanical monopole'(?)