# Does time slow down in an electromagnetic field?

1. Jul 6, 2012

### TVI_1405

According to relativity, time rate differs in regions with different gravitational potentials, i.e. the closer we are to the source of gravitation the slower time passes. Does anyone know what happens to time in electromagnetic fields?

2. Jul 6, 2012

### Dickfore

Define what you mean by time.

3. Jul 6, 2012

4. Jul 6, 2012

### TVI_1405

The rate of change, whatever it may be (chemical reactions, radioactive decay, heat transfer). I guess I am interested if there is a difference between the time rate near the electromagnetic source and the time in any other place (similarly to when time is measured at the top and at the bottom of a high building).

5. Jul 6, 2012

### TVI_1405

Thanks jedishrfu! I have come across that article too...but I wonder if there is anything else on the topic?...My Google search was not that effective somehow...

6. Jul 6, 2012

### Dickfore

OK, what you are referring to is called local proper time. It is connected to the zeroth coordinate (so called coordinate time) via the relation:
$$d\tau = \frac{\sqrt{g_{00}}}{c} \, dx^{0}$$
Because the components of the metric tensor depend on space-time, this conversion factor may change from one point in space to another, as well as at different epochs at the same point in space

Also, the metric tensor components change if we change the choice of coordinates. We may always choose a system in which $g_{00} = 1$, as well as $g_{0 i} = 0, \ (i = 1, 2, 3)$. The first condition tells us that the proper time is the same always and everywhere. The second allows for synchronization of clocks everywhere in space.

Such a system is called a synchronous coordinate system, and the coordinate/globally proper time in it is called world time.

As you can see in such a system, time flows evenly, regardless of the curvature of space. The curvature, in turn, may be determined by the present electromagnetic field.

7. Jul 6, 2012

### TVI_1405

So, the answer is that the local proper time may flow at a different rate due to space-time curvature created by an electromagnetic field? And according to the previously referenced article, such a curvature will be very small (if you create an electromagnetic field in a laboratory), hence, the change in the local poper time may be so tiny that it could not be observed? Have I got it right?

8. Jul 6, 2012

### Dickfore

My point was that local proper time depends on your choice of curvilinear space-time coordinates. Furthermore, in a special (synchronous) coordinate system, you may make local proper time flow evenly at any point, regardless of the curvature.

However, there is a caveat. The metric in a synchronous system is necessarily non-stationary, i.e. depends on time. Think of the model of anexpanding Universe as an example.

9. Jul 8, 2012

### cosmik debris

Yes, pretty much. All energy gravitates.

10. Jul 12, 2012

### TVI_1405

Thank you Dickfore and Cosmik debris. And is it possible calculate what the gravitational effect of energy (say, an electromagnetic field) would be?

11. Jul 13, 2012

### Neandethal00

Interesting. But the article later has kind of side tracked.
I once had a thought motions of charges or magnets placed next to each other could be caused by distortion of space, just like what gravity does to objects.

Which in another word means 'gravity' is the main fundamental force.

12. Jul 14, 2012

### TVI_1405

It is very interesting, thank you Neandethal00. I guess more experiments are required...

13. Jul 15, 2012

### cosmik debris

There is an old 5D theory Kaluza-Klein I think, that attempted to unify EM and GR.