Classic Physics: Exploring Symmetry of E&M & Gravity

[michael879]

"classical" physics is completely defined by three basic theories. It starts with the basic theory, F=dp/dt, p = mv, etc. (sorry, I'm blanking on what its called). The forces, E&M and gravity, are then defined by Maxwells equations and the GEM equations. You could include special relativity here but its really just a consequence of those three theories. Light and gravity waves are just massless, energyless waves in the two sets of fields (E&M and GEM). As far as I know, this classical theory is completely self-consistent, and very closely describes the world. In addition, its a very elegant theory with just two forces that are almost identical.

My question is: knowing this theory does NOT accurately describe the world at large and small scales, how can you explain the symmetry between the only two forces in it? Gravity, described by GR, deviates from GEM at large scales and E&M, described by QED, deviates from maxwells equations at small scales. Photons and gravitons have both energy and mass, and the two forces act nothing alike when described with modern theories. In addition, there's the strong force and the weak interaction that deviate even further from gravity and E&M. Why does the world appear to be so simple and elegant at human scales, when its actually much more complex? Is there any kind of explanation given as to why gravity and E&M are almost identical at these scales or is it just generally thought of as a coincidence?

P.S. I realize GEM is not generally thought of as classical physics, but Einstein was really ahead of his time in formulating GR. In order for Newtonian gravity to be lorentz invariant, there must be a magnetic component to it. GEM comes straight from special relativity, and is necessary for a consistent classical theory.

 

[Creator]

" Is there any kind of explanation given as to why gravity and E&M are almost identical at these scales or is it just generally thought of as a coincidence?

.

Sure.
E & M is a linear theory, and actually GEM (as you refer to it) is simply Gen. Relativity in linearized form, an aprroximation of GR in the low velocity, low mass limit. Basically GEM removes the nonlinear terms of Gen Rel.
Other than that the question becomes almost philosophical.

Creator

 

[quZz]

Is there any kind of explanation given as to why gravity and E&M are almost identical at these scales or is it just generally thought of as a coincidence?

What do you mean by identical? I find them quite different =)

 

[Bob_for_short]

In addition, its a very elegant theory with just two forces that are almost identical.

The both operate with average quantities, that is why they are simple. Any massive body is not point-like and we observe it with help of photons. We obtain an average picture and we content ourselves with only three (center inertia or geometric center) coordinates.

The gravity is different by its low intensity and lack of graviton radiation (never observed, only assumed). Electromagnetic interactions are always accompanied with radiation (and absorption), and sometimes it is very essential difference.

 

[michael879]

What do you mean by identical? I find them quite different =)

in geometrized units the only difference is a sign in one of the equations..

 

[michael879]

The both operate with average quantities, that is why they are simple. Any massive body is not point-like and we observe it with help of photons. We obtain an average picture and we content ourselves with only three (center inertia or geometric center) coordinates.

The gravity is different by its low intensity and lack of graviton radiation (never observed, only assumed). Electromagnetic interactions are always accompanied with radiation (and absorption), and sometimes it is very essential difference.

gravity waves have been observed, just not directly. If you accept conservation of momentum, gravity waves pretty much have to exist.. The only reason gravity and E&M appear so different to us, is because of their different strengths. Gravity is weak, and we NEVER observe the "magnetic" component in every day life (and because of this gravitational waves too). But mathematically, they're both described by the same set of differential equations (classically).

*edit: sorry, that would be conservation of energy. If I recall it right, they observed two stars (probably neutron stars) orbiting each other. Their orbit was observed shrinking, which suggests a significant loss of energy. The generally accepted conclusion (last I heard at least), was that this was caused by the radiation of gravitational waves.

 

[michael879]

Sure.
E & M is a linear theory, and actually GEM (as you refer to it) is simply Gen. Relativity in linearized form, an aprroximation of GR in the low velocity, low mass limit. Basically GEM removes the nonlinear terms of Gen Rel.
Other than that the question becomes almost philosophical.

Creator

yea, you could call it philosophical if you just want to dismiss it, but unless there is some explanation for this "coincidence" in the current theories, I think it suggests some broader, unknown theory. There are plenty of forms a linear theory could take.. I don't see how that explains their similarities.

Also, like I said before, I'd really call GR the generalization of GEM. GEM really should have come first, because if you apply SR to Newtonian gravity you can very easily derive the GEM equations (just assume Newtonian gravity is correct in the static case, and that gravity is lorentz invariant). Yea, it didn't play out like that but that's only because Einstein was a profound genius.

 

[Hermit]

Light and gravity waves are just massless, energyless waves in the two sets of fields (E&M and GEM).

Energyless ? Is it right ?

And what do GEM means ?

 

[Lambda3]

I think GEM stands for gravitoelectrodynamics or something close to that.
Photons and Gravitons may seem similar at first, but unlike photons, gravitons cannot superimpose.

 

[michael879]

Energyless ? Is it right ?

And what do GEM means ?

GEM stands for GravitoElectroMagnetism. It was formulated by linearizing GR in the low field limit. However, like I said above, the order in which these two theories were discovered was kindof backwards. It is really the correct "classical' (semi-classical, w/e) theory of gravity. Newton's theory of gravity is not lorentz invariant and is not consistent with SR.

By linearizing GR, or by making Newtonian gravity consistent with special relativity, you arrive at the GEM equations. These equations are very similar to maxwells equations (even more so once u get rid of all the natural constants by using geometrized units). The two distinguishing differences are the relative strengths of the forces and the signs in the equations (The "Gauss's law" equation has an opposite sign in GEM from maxwell's equations).

No, sorry, I misspoke. Photons and gravitons have energy in the classical theories. They just don't have mass. The point I was trying to make is that classically, electric charge is the charge of E&M and gravitational mass is the charge of gravity. Massless energy does not interact gravitationally and inertial mass is not the same as gravitational mass.

 

[michael879]

I think GEM stands for gravitoelectrodynamics or something close to that.
Photons and Gravitons may seem similar at first, but unlike photons, gravitons cannot superimpose.

All waves can superimpose.. I'm not sure exactly what you mean by that. Regardless, photons and gravitons do not exist classically. They are E&M waves and gravity waves, and act just like any kind of wave (more or less). Photons and gravitons are the quantum mechanical explanation of these apparent waves.

 

[quZz]

in geometrized units the only difference is a sign in one of the equations..

So you're talking about electrostatic, magnetostatic and Newtonian gravity: $$\nabla^2 X= Y$$. I believe this coincidence in equations comes from the properties of the space: $$\nabla^2$$ is the simplest second-order derivative operator that is isotropic and homogeneous. =)

 

[michael879]

So you're talking about electrostatic, magnetostatic and Newtonian gravity: $$\nabla^2 X= Y$$. I believe this coincidence in equations comes from the properties of the space: $$\nabla^2$$ is the simplest second-order derivative operator that is isotropic and homogeneous. =)

umm no... I think you misunderstood me (although that is the kind of answer I'm looking for). I'm talking about the general case, not the static case. I was saying that one way to derive the GEM equations is to assume that Newton's equation is correct in the static "gravitoelectric" electric case. By using SR you can derive the rest of the GEM equations (Newtons equation is essentially the first one of four).

Here:
http://en.wikipedia.org/wiki/Gravitomagnetism#Equations
The comparison is actually written out. The coincidence is more than just in the magnetostatic or electrostatic case. The equations are identical except that a negative sign is placed in front of the two charge terms in the GEM equations (see the representation in Planck units on that page).