What Drives the Quest for Quantum Gravity?

[Pjpic]

Are the differences between relativity and quantum mechanics due to the difference between gravity and electromagnatism?

 

[tiny-tim]

Are the differences between relativity and quantum mechanics due to the difference between gravity and electromagnatism?

Hi Pjpic!

From the PF Library on geodesic deviation (between world-lines free-falling under gravity) …

Geodesic deviation equation:

[tex]\frac{D^2\,\delta x^{\alpha}}{D\tau^2}\ =\ -\,R^{\alpha}_{\ \mu\beta\sigma}\,V^{\mu}\,V^{\sigma}\,\delta x^{\beta}[/tex]

for 4-velocity [itex]V[/itex] and gap [itex]\delta x[/itex]

where [itex]\tau[/itex] is proper time and [itex]R[/itex] is the Riemann curvature tensor

Electromagnetic comparison:

By comparison, the world-line deviation equation between world-lines followed by two charged particles with the same charge/mass ratio freely moving (in flat Minkowski spacetime) in an electromagnetic field is:

[tex]\frac{D^2\,\delta x^{\alpha}}{D\tau^2}\ =\ \frac{q}{m}\,F^{\alpha}_{\ \mu\,;\,\beta}\,V^{\mu}\,\delta x^{\beta}[/tex]

where [itex]q[/itex] is charge, [itex]m[/itex] is mass, and [itex]F[/itex] is the electromagnetic tensor

 

[Kaizer6]

Are the differences between relativity and quantum mechanics due to the difference between gravity and electromagnatism?

I'm not sure what you mean by "differences" between these two theories, because they are afterall entirely different from one another. You're quite correct when you mention gravity and electromagnetism because they are intrinsically linked to relativity and quantum mechanics.

The differences between gravity and electromagnetism are obvious when looking at the Coulomb force or the gravitatonal force. The differences between relativity and quantum mechanics are a little more subtle. The main idea behind general relativity is to link the gravitational field in curved space to the results of special relativity. Quantum mechanics is about looking at the probabilistic uncertainties involved in measuring quantum phenomena. They are two different fields of investigation.

However, my research involves looking at gravitational waves. A very current topic is "quantum gravity", which tries to bring ideas together from both theories.

Hope this helps.

 

[Pjpic]

Hope this helps.[/QUOTE]

Yes, it does help; well written.

Why is it thought that there will be quantum gravity (if up to now gravity seems to be more of a geometric thing than a probability thing)?

Would a quantum gravity theory have the particle/wave duality element?

 

[Kaizer6]

[/QUOTE]

Why is it thought that there will be quantum gravity (if up to now gravity seems to be more of a geometric thing than a probability thing)? [/QUOTE]

Well the whole idea of quantum gravity came about when people were trying to apply the ideas of quantum mechanics to general relativity. Contrary to popular belief, these two theories are comptiable, it is possible to show that the structure of general relativity follows from the quantum mechanics of a theoretical particle known as a graviton.

No one knows for sure whether this graviton exists or not but if we have a look at other other fundamental forcesin nature we find that they have one or more messenger particles. Gravity is the only one that doesn't, this leads people tobelieve it must be there in the form of this graviton.

You bring up an interesting point when you mention probability. I'm not sure about this but I'm guessing it would be probabilistic.