## 19 December 2007

### What if gravity reversed itself?

A friend of mine, not long ago, noticed that it was snowing up outside her office window. (When I've seen this happening, it's usually due to something like an internal courtyard in a building, so the air currents get sufficiently weird to push the snow upwards. Don't worry, physics isn't broken.)

This raises the (somewhat silly, I must admit) question: what if gravity had actually reversed itself outside my friends' office? Three scenarios are possible:

• gravity instantaneously reverses itself;

• the downward-pointing vector of gravitational acceleration decreases in magnitude, goes through zero, and then becomes an upward-pointing vector;

• the gravitational acceleration vector always has the same magnitude, but swings around through different angles to point up instead of down.

I claim that the third of these is not reasonable. Basically, this is for reasons of symmetry. Imagine gravity that neither points straight down nor straight up. How would gravity know in which of the many possible "sideways" directions to point? There are only two points that could possibly have any effect on the direction of gravitational acceleration, namely the point that you are at and the center of the Earth. The direction of gravity must be invariant under any isometry which fixes those two points -- thus it must point straight towards the center of the Earth or straight away from it.

Apparently I am more attached to gravity being a central force than to its particular strength or even to the fact that it is attractive, not repulsive.

(I'm not sure whether the first or second of the models suggested above is reasonable. This post is silly enough as it is.)

Eldila said...

If you are changing gravity (in any way), according to general relativity, this would require warping the space-time continuum.

However, Could the space-time continuum warp into a Non-Isotropic manifold and wouldn't this cause gravity to be Non-Isotropic.

Note: I don't pretend to understand general relativity or manifolds well enough to answer this question.

Robbie said...

This is unrelated to gravity but could anyone give me an explanation of why, according to the Lorentz force, a positive charge moving in a magnetic field will accelerate in the direction given by the right-hand rule? It seems to me that due to the symmetry of the system, a force shouldn't favour either of the directions that are perpendicular to both the directions of the magnetic field and the particle's velocity.

mcherm said...

I'd say that the third scenario (where it rotates) is just as likely as the first. There's a principle in physics that I forget the name of... I think it's "symmetry breaking" or something like that.

Imagine that at at exactly 12:00 noon for some reason the "potential energy of the universe" changes so that gravity pointing UP is favored over gravity pointing DOWN, but imagine also that the magnitude of gravity is fixed, only the direction is free to rotate. That's not quite enough information to predict what will happen: we also need to know about all the other directions -- like what's the preference for pointing 0.001 degrees EAST of DOWN.

I'll agree that your symmetry argument tells us that the universe's preference for pointing 0.001 degrees EAST of down matches its preference for pointing 0.001 degrees WEST of down (or NORTH or SOUTH for that matter). If these directions are less preferable than straight DOWN then we're at a local minimum, and the snow continues to drift earthward.

But if the slight perturbations are _more_ preferable than straight down, then we are sitting at the top of a potential hill. Even the slightest perturbation -- just some quantum-mechanical fluxuation -- will cause us to "drift down the potential hill" and rotate the force of gravity toward a stable minimum at UP. By symmetry, we can't know WHICH way it will rotate, but rotation is still quite plausible.

Thanks for providing me with such a silly yet interesting topic to consider.

-- Michael Chermside (mcherm.com/blog)

Rettaw said...

I'm not sure what you mean with non-isotropic, if you mean that it looks the same in all directions then that isn't true in general, there exist physical systems that only have axial symmetry and thus aren't isotropic. The instantaneous reversal of gravity runs into trouble with the fundamental principles, particularily the one that demands space is always locally flat. If the change is instantaneous then space will stretch in all kinds of horrible ways...

Also for lorentz law you have the different sign on the charges making one direction special, but of course what direction you make special depends on your definition of charge

eldila said...

I might be using the words non-isotropic and manifolds incorrectly.

However, I will try to explain myself better.

If you are warping the space-time continuum (for some unknown reason), there is no restrictions on how it might warp. For all we know, the Topology of the universe could be warping as well. Considering all the possible factors, I don't see how we can guarantee that gravity will remain isotropic.

John Armstrong said...

rettaw: the laws of gravity are isotropic. You're confusing the symmetry of particular solutions with the symmetry of the class of solutions. Even under Newtonian gravitation, the force was spherically symmetric even though the orbit of the Earth around the Sun (obviously) wasn't.

Further, space isn't locally flat. If it were locally flat there would be no gravity. In fact, it's not even Ricci flat.

Anonymous said...

robbie:
The symmetry is already broken by the origin of the magnetic field. Magnetic fields don't exist all on their own, they arise due to the motion of charges. This charge motion already sets up a preferred direction of the system.

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