There are no coincidences...

[natski]

Hello, I'm a third year physics student and we've recently touched on some of the Grand Unified Theories, well just mentioned that they exist really. The real problem appears to be uniting gravity with the other 3.

Surely someone has noticed before, that if you let a variable V = 1/(4*pi*G) where G = Gravitational constant, the analogy between electrostatics and gravitation is even clearer. They have exactly the same potential and Poisson's equation where charge and mass become analagous. V would be like a gravitational permeability or something. This can't be coincidence and surely this is a strong hint towards how EM & gravity are linked?

Natski

[ZapperZ]

Hello, I'm a third year physics student and we've recently touched on some of the Grand Unified Theories, well just mentioned that they exist really. The real problem appears to be uniting gravity with the other 3.

Surely someone has noticed before, that if you let a variable V = 1/(4*pi*G) where G = Gravitational constant, the analogy between electrostatics and gravitation is even clearer. They have exactly the same potential and Poisson's equation where charge and mass become analagous. V would be like a gravitational permeability or something. This can't be coincidence and surely this is a strong hint towards how EM & gravity are linked?

Natski

But you are ignoring one important aspect - electrostatic is a small subset of a LARGER encompassing theory of electromagnetism.

While the field equation for electrostatic looks similar to the field equation for classical gravity, electrostatic is part of a larger theoretical development of classical E&M. You are forgetting the "magnetic" part that is so intrinsically linked to the "electro" part. So now, when you look at the magnetic field equation, and the Maxwell equation as a whole, you'll see where the similarty ends.

Moral of the story: you can't just say that since the tails of two different animals look similar, then it must be the same type of animal.

Zz.

[natski]

I see your point, but I also would argue that although indeed electrostatics is a special case of electromagnetism, so gravity could also be a special case of a wider theory. If all the forces can be combined through one of the GUTs, then gravity and electromagnetism will indeed be the same 'animal' anyway.

[natski]

Also just to add to my previous comment, I know there is an asymmetry in the fact there are no negative masses which correspond to negative charge, but in EM there are no magnetic monopoles to correspond to electric monopoles.

[ZapperZ]

I see your point, but I also would argue that although indeed electrostatics is a special case of electromagnetism, so gravity could also be a special case of a wider theory. If all the forces can be combined through one of the GUTs, then gravity and electromagnetism will indeed be the same 'animal' anyway.

Again, except you are missing the bigger picture. Classically, they are not of the same animal already. Gravity is the ONLY "force" out of the 4 in which it DIRECTLY either modify, or a manifestation of the "frame" that we use to define things. Gravity affects spacetime per General Relativity. The "frame" that you use to define the field of the other forces does not get modified by them. Gravity does!

Besides, if it were THAT easy and THAT transparent, String, LQG, etc. would have made progressed faster than what we have seen.

However, it is still besides the original point that I wanted to make, in which the starting impetus for your argument (that the field equation looks similar) isn't that valid to deduce that they are the same. That is insufficient in light of the larger amount of differences between those two.

Zz.