EM Force and GR

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Quick Question(s):

Who was it that tried to account for the EM force in terms of spatial curvature; i.e., who tried to expand GR in order to explain EM attraction and repulsion?

Also, on what grounds was his account refuted?
 

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  • #2
JesseM
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You're probably thinking of the Kaluza-Klein theory, which requires spacetime to have 5 dimensions rather than 4 as in relativity (I believe Kaluza came up with the main theory and Klein just added the idea of having the extra spatial dimension be 'rolled up' so that it would be two small to notice). I don't think the idea was really refuted per se, my understanding is that some version of it has been incorporated into superstring theory, see this thread for instance.
 
  • #3
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Kaluza-Klein theory is still an active area of research, with many papers in the last 10 years.

The most recent paper is well worth a look because it claims that K-K in more than 3 dimensions does not fit the data. This is a surprise because I thought it made no bad predictions.

http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.5690v1.pdf
 
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  • #4
bcrowell
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There have been many, many unified theories proposed.

The Weyl theory is one that tried to unify gravity and electromagnetism: http://books.google.com/books?id=uU1WAAAAMAAJ&pg=PA167

You're probably thinking of the Kaluza-Klein theory [...] I don't think the idea was really refuted per se, my understanding is that some version of it has been incorporated into superstring theory, see this thread for instance.
One thing to keep in mind is the distinction between a classical unified theory and a quantum-mechanical one. Both the Weyl theory and the Kaluza-Klein theory originated before quantum mechanics.

Here is a review article on classical unified theories: http://www.livingreviews.org/lrr-2004-2

I don't think the Weyl theory has been definitively disproved, but the motivation for it is no longer compelling. The idea was to unify gravity and electromagnetism, which were the only two fundamental fields known at the time. They also wanted to unify the electron and proton, which were the only known fundamental particles. The theory has a length scale that they assumed was equal to the classical electron radius. We no longer think that the classical electron radius has special, fundamental status, as they did at the time (when the electron was one of only two known fundamental particles).
 
  • #5
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Thank you all for your responses. I'm sure that the links you've supplied me will themselves supply me with a wealth of information.

Forgive me, but, is there a simple answer to the following question: Why must there be a one-to-one correspondence between forces and dimensions?

That is to say, if four dimensional spacetime wasn't postulated in order to explain gravity, but rather, in order to explain the propagation of light (an EM phenomenon, I might add), then why must an additional dimension be postulated just in order to account for an additional force (the EM force, I might add)? Along this line of reasoning, it (seems like it) would be necessary to posit a sixth and seventh dimension just in order to account for the weak and strong nuclear forces, too.

My question can re-worded: Why is 4-D spacetime thought to be insufficient, according to Kaluza and Klein, in order to account for gravity and the EM force qua geometrical distortions of 4-D spacetime?
 
  • #6
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Thank you all for your responses. I'm sure that the links you've supplied me will themselves supply me with a wealth of information.

Forgive me, but, is there a simple answer to the following question: Why must there be a one-to-one correspondence between forces and dimensions?

That is to say, if four dimensional spacetime wasn't postulated in order to explain gravity, but rather, in order to explain the propagation of light (an EM phenomenon, I might add), then why must an additional dimension be postulated just in order to account for an additional force (the EM force, I might add)? Along this line of reasoning, it (seems like it) would be necessary to posit a sixth and seventh dimension just in order to account for the weak and strong nuclear forces, too.

My question can re-worded: Why is 4-D spacetime thought to be insufficient, according to Kaluza and Klein, in order to account for gravity and the EM force qua geometrical distortions of 4-D spacetime?
I believe the same issue that plagues String Theory: "Why is gravity so 'weak' compared to the other fundamental forces?" In essence, extra dimensions are places to preserve or break symmetries, or have gravity "leak" into them. Note, that is about as non-technical as it can be, others will have better answers.
 
  • #7
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Forgive me, but, is there a simple answer to the following question: Why must there be a one-to-one correspondence between forces and dimensions?
There doesn't have to. The standard model has just the four.

My question can re-worded: Why is 4-D spacetime thought to be insufficient, according to Kaluza and Klein, in order to account for gravity and the EM force qua geometrical distortions of 4-D spacetime?
Hang on - just because K and K came up with this model don't assume it's the only way. K-K theory is not widely accepted in fact.

If you're interested in attempts to unify gravity and EM you should start with Feynman ( I need a reference - in which book does Feyman look at unifying EM and gravity ?). There have been many attempts and some are better than others.

A lot of current 'unifications' are near the cracked-pot level.
 
  • #8
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Hang on - just because K and K came up with this model don't assume it's the only way. K-K theory is not widely accepted in fact.
Totally understood. I wish I had asked "What were K and K's motives for insisting on this 1-to-1 force-to-dimension correspondence?" or "What are the motives of K-K theorists for insisitng...?"
"Why is gravity so 'weak' compared to the other fundamental forces?" In essence, extra dimensions are places to preserve or break symmetries, or have gravity "leak" into them.
Gotcha. I've heard that the strength of gravity is dwarfed by the strength of the nuclear forces, but is the same true about the EM force? In fact, somebody please correct the following statements if they are wrong and please tell me what I should replace the variables X and Y with.

1) Gravity is the weakest force, but its range is enormous. It's determined by mass, which is something that all 6 types of individual quarks possess, and something that both types of quark pairings; i.e., protons and neutrons, possess.

2) The EM force is the 2nd weakest, and its range is also enormous. It's determined by charge, which is something that not all 6 types of individual quarks possess; i.e., only 1 type: electrons, and something that not both types of quark pairings; i.e., only 1 type: protons, possess.

3) The weak nuclear force is the 2nd strongest, but its range is tiny. It's determined by X, which is something that no type of individual quark possesses, but something that both types of quark pairings; i.e., protons and neutrons, possess.

4) The strong nuclear force is the strongest, but its range is also tiny. It's determined by Y, which is something that all 6 types of individual quarks possess, but something that no type of quark pairing possesses.
 
  • #9
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Ontophile,

I'm not sure I can comment on K-K motivation. It seems like a good idea to me.

I'll take your list as true, with one exception.

...It's determined by mass, ...
Gravity is not generated by mass alone, but also by energy, and momentum and energy flow. The amount of momentum going through a unit area in unit time is called 'pressure' in GR and also gravitates.
 
  • #10
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Gravity is not generated by mass alone, but also by energy, and momentum and energy flow. The amount of momentum going through a unit area in unit time is called 'pressure' in GR and also gravitates.
With this in mind (plus the fact that between two bodies of equal mass but different density, the denser of the two will gravitate more strongly) why do we still say that gravity is determined by only two factors, the masses of the bodies and the distance separating them?
 
  • #11
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The amount of momentum going through a unit area in unit time is called 'pressure' in GR and also gravitates.
Can energy flow through "empty" spacetime, or is some sort of material vehicle or conduit necessary? I'm imagining regions of "empty" space which are gravity-wells nonetheless because the momentum of the energy flowing through them is so high. But if energy can only flow through regions of spacetime that happen to be occupied by matter, then the momentum of the energy flowing through any material body (and therefore, that particular region of spacetime) will only add to the strength of the gravity already exerted as a result of the body's mass. Now, since EM radiation travels through empty space, and EM radiation is a form of energy, I gonna guess that empty regions of space, in which there is no actual matter, can be gravity wells, so long as the momentum of the energy flowing through them is appreciable. But, if the speed of light is fixed, as is the mass of the photon, then its momentum must be fixed as well. Hence, EM radiation cannot be the sort of energy-flow that you are talking about. Now I'm back to square-one. Can energy flow through empty spacetime or only through corpuscular matter?
 
  • #12
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We see that the galaxies within clusters move faster than their combined masses dictate. We also see gravitational lensing going on in "empty" intergalactic space (with the exception of a few hydrogen atoms here and there). We do not infer that the momentum of energy flowing through those regions of empty space must be enormous in order to generate that much gravity. Instead, we infer that there must be a new kind of matter out there. On the basis of this, I'm gonna guess that the kind of energy-flow that you are talking about cannot, in fact, happen in empty space, but rather, must take place inside material bodies (even though material bodies are mostly empty space). If material bodies are mostly empty space, then we're back to the claim that energy must be able to flow (in gravity-producing ways) through empty space, otherwise it wouldn't even be able to flow through matter. But then why do we infer the existence of dark matter?! I am thoroughly confused.
 
  • #13
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plus the fact that between two bodies of equal mass but different density, the denser of the two will gravitate more strongly
I don't think this is always true. The internal state of the bodies has to be taken into account. Look up 'energy-momentum tensor' (EMT). This structure contains the gravitational sources that could arise as a result of rotation or flows, pressure, energy and mass.

why do we still say that gravity is determined by only two factors, the masses of the bodies and the distance separating them?
That is Newtonian gravity, which works well in weak gravitational fields with slowly moving or rotating bodies.

I just saw your last 2 posts.

I am thoroughly confused.
Yes.

Hence, EM radiation cannot be the sort of energy-flow that you are talking about.
Why not ?
Now I'm back to square-one. Can energy flow through empty spacetime or only through corpuscular matter?
Electromagnetic waves are energetic and 'flow' through empty space.

The logic in your #11 is not right. I have to go now.
 
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