# B Understanding the force between two objects

1. Jan 6, 2017

### bwana

When we calculate the gravitational or electrical or magnetic potential energy difference between two objects, the equation includes the the distance between the objects and some measure of the intrinsic field strength generated by each object.
For gravity for example, two objects with mass M and m separated by distance,r
W= mMG/r
For electrical charges q and Q
U=qQ/4πer

These energy calculations are the abstract summation of the difference of the force 'experienced' by each particle over the distance separating them.

Is it fair to say that force between two objects interacting through a field is mediated by photons?

2. Jan 6, 2017

### phinds

EM is mediated by VIRTUAL photons. Gravity is not.

In GR, gravity isn't even a force. I'm not sure how that ties to the theory that gravity may be mediated by virtual gravitons but it may be that all this mediation by virtual particles is just a calculating aid.

3. Jan 6, 2017

### Staff: Mentor

Only if the field is the electromagnetic field. (Also, the photons are virtual photons, and the whole concept of forces being mediated by particles this way is really an approximation, but that's probably beyond the scope of this discussion.)

4. Jan 6, 2017

### newjerseyrunner

You're equation is incorrect. The force of gravity is relative to the inverse of the distance squared.

5. Jan 6, 2017

### Staff: Mentor

No, it isn't. His equation is for the potential energy, not the force. The potential energy goes like $1 / r$.

6. Jan 6, 2017

### newjerseyrunner

Oh shoot, I didn't see that.

7. Jan 6, 2017

### bwana

what is the difference between a virtual photon and a real photon? reference please?
and why do you say that gravity is not? Nothing in my question references relativity so I don't know why you mentioned it.

8. Jan 6, 2017

### Staff: Mentor

That's too complicated for a "B" level thread. You will need a basic background in quantum mechanics and quantum field theory, at least at the undergraduate ("I") level (and graduate, "A", level would be better). You can also try searching the Quantum Physics forum for threads on the topic.

Because gravity is not mediated by photons. Only the electromagnetic force is mediated by photons.

Yes, it does; the whole concept of forces being mediated by exchange particles (photons or anything else) comes from quantum field theory, i.e., our best current theory that combines quantum mechanics and relativity. So you were referencing relativity even if you didn't realize it.

9. Jan 6, 2017

### phinds

@PeterDonis can answer that better than I can
You said "For gravity for example, two objects with mass M and m separated by distance,r" so why would you, or I for that matter, not think your statement involved gravity?

EDIT: I see Peter beat me to it. Again. He keeps DOING that

10. Jan 6, 2017

### Staff: Mentor

He was asking why we thought his statement involved relativity, not gravity.

11. Jan 6, 2017

### phinds

OK. I just mentioned it because he was talking about gravity (among other things) and force mediation and I am personally curious how the fact that gravity is not a force in GR ties to the concept of gravity being mediated by virtual gravitons.

12. Jan 6, 2017

### newjerseyrunner

Your original question mentioned "force," and only force. There are also more forces that just EM and gravity, and those do not follow the same curve. These forces also do not interact through the EM field, the strong force below happens in the gluon field.

In the Standard model, EM, and the strong and weak nuclear forces are mediated by particles called bosons. There is a different boson for each force (photon is the electromagnetic boson, the strong boson is called a gluon.) Gravity is not included in this model, but there are modifications of it which include a graviton, which mediates force similar to photons, but it's got some problems, which is why it's not part of the standard model.

13. Jan 6, 2017

### Staff: Mentor

It doesn't. In GR, gravity is not a force because it's spacetime curvature--i.e., geometry. In the "field theory" view of gravity, gravity is a spin-2 interaction, and the graviton is the gauge boson associated with this interaction (just as the photon is the gauge boson associated with the spin-1 electromagnetic interaction). But the latter view assumes that we have a fixed background spacetime (usually flat Minkowski spacetime although it doesn't have to be), i.e., its geometry isn't affected by the presence of stress-energy, so this view is inconsistent on its face with GR, which says that the spacetime geometry is determined by the stress-energy that is present.

In other words, what we have here are two different, and apparently incompatible, views of what "gravity" is. And yet each view makes sense when taken on its own--GR's model of gravity as spacetime curvature seems obvious once you understand the equivalence principle, and the field theory view of gravity as a spin-2 interaction seems obvious once you understand quantum field theory. Part of the challenge of finding a theory of quantum gravity is how to resolve this dilemma.

14. Jan 6, 2017

### Staff: Mentor

The only times the word "force" appears in the OP are in the phrase "summation of the difference of force", and in the next (and final) paragraph. And it is obvious from context that by the quoted phrase he means potential energy, which is what he wrote equations for and which is what he talked about in the first paragraph of the OP. Please read carefully.

(I note, btw, that the diagram you give, which is very useful, is also a diagram of potential energy vs. distance, not force vs. distance. So evidently you understood what was really being asked about.)

15. Jan 6, 2017

### phinds

Thanks Peter

16. Jan 6, 2017

### Staff: Mentor

17. Jan 6, 2017

### newjerseyrunner

I don't understand QFT, so maybe you can explain why? The spin-2 and how it would act as a force to push something I understand (well enouh.) What I don't understand how to get to is how would a graviton affect time? Does time not move slower in gravitational fields in QFT? Google was unhelpful with this.

18. Jan 6, 2017

### Staff: Mentor

This should probably be a new thread in the Quantum Physics forum, but I'll try to give a brief answer here. There are two ways of looking at this, at least to a first approximation:

(1) To a first approximation, gravity as a spin-2 interaction does not affect time. We can use the spin-2 interaction model to obtain what looks like a Newtonian force, with some small corrections (like perihelion precession of planets), with no effects on time at all. (Of course if we carry the model out to higher orders of approximation, we will see effects on time, but we can just choose not to do that because the higher order terms are too small to matter.)

(2) Whether gravity as a spin-2 interaction "affects time" is coordinate-dependent. It certainly affects physical distances--for example, in a gravitational wave detector, which is standardly modeled in a way that is equivalent to the spin-2 interaction model. And in relativity, there is no way to affect distances without affecting time, because "distance" and "time" are coordinate-dependent; if you're affecting distances, then you're affecting time in at least some local inertial frames as well.