# Should a stationary charge on the earth radiate?

1. May 23, 2010

### abhi2005singh

There are actually two questions which I think are inter-related.

1. Consider an electron and Mr. A, both in a box. Let the box be accelerating with acceleration a. Will the charge radiate EM waves for Mr. A also?

2. Considering the fact that gravity and acceleration are equivalent, will a stationary (w. r. t. the earth) electron on the earth radiate?

2. May 23, 2010

### Tomsk

A charge on the surface of the earth doesn't radiate because it's not oscillating (assuming it's not orbiting), but its electromagnetic field is bent by gravity.

Have a look at this applet: http://www.its.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

if you click the arrow to increase the velocity you can simulate a constant acceleration. The field doesn't ripple at all, but you can see how it bends. Same thing in a gravitational field. Although the field seems to get more bent as you get faster in that applet, but I think for a charge on the surface of the earth its field would just have a constant curvature or something.

3. May 23, 2010

### GRDixon

Excellent question. In general, accelerating charges radiate, but with at least one notable exception: a charge subjected to a constant FORCE does not radiate. (But the same charge DOES radiate when its acceleration is constant.) This being the case, if Mr. A's box is being accelerated by a constant FORCE, then the charge will not radiate. And the charge being held at rest in earth's gravitational field, being subject to a constant FORCE, can also be expected not to radiate. As I recall, this conundrum was discussed here on PF in the past. The idea, that a charge subjected to a constant force does not radiate, could be tested by letting a charge accelerate between the plates of a large, parallel plate capacitor. Such a charge should not radiate, although it can be expected to accelerate while between the plates.

4. May 23, 2010

### starthaus

For a very good analysis, start reading here, post 11. It elaborates on the correct answer already given by Tomsk.

5. May 23, 2010

### Staff: Mentor

Also, note that the presence or absence of radiation is frame-variant when you are including non-inertial frames.

6. May 23, 2010

### abhi2005singh

Thank u all for the help.
Still have some doubt. Should an electron at rest wrt the earth radiate wrt to some fellow on the earth? And should it radiate wrt sun? (I think it should radiate in both frames of reference) Please also consider the rotation and revolution of the earth.

Well this is new to me. I was not knowing that even radiation can be frame dependent for non-inertial frames. Some link, reference or details will help a lot.

7. May 23, 2010

### Staff: Mentor

Here is one:
http://wwwphy.princeton.edu/~kirkmcd/examples/EM/almeida_ajp_74_154_06.pdf [Broken]
Note the key quote in the intro "the concept of radiation has no absolute meaning and depends
both on the radiation field and the state of motion of the observer".

Also, the Unruh effect is a well-known example of frame-dependent radiation:
http://en.wikipedia.org/wiki/Unruh_effect

And the Hawking radiation near an event horizon does not exist for a free-falling observer, but I don't have a good online reference for that.

Last edited by a moderator: May 4, 2017
8. May 23, 2010

### atyy

Gravity and acceleration are equivalent only in Newtonian gravity, for a uniform gravitational field. Gravity an acceleration are not fully equivalent in general relativity. They are equivalent only in the limited sense at a point in spacetime, and provided one does not examine spacetime curvature.

http://arxiv.org/abs/0806.0464

9. May 24, 2010

### bcrowell

Staff Emeritus
10. May 24, 2010

### abhi2005singh

Thank you all for ur answers and the references. These were very helpful.
However, I could not locate the reference

11. May 25, 2010

### Antiphon

There is an extensive discussion of this in the thread here:

The short answer is that a charge in gravity and an accelerating charge are on exactly the same footing. Whether or not any radiation is observed depends on the motion of the observer and not the charge.

12. May 25, 2010

### bcrowell

Staff Emeritus
I don't think that's correct. My #9 gives a sampling of the extensive literature that's been published on this topic, over a period of many decades. The answer isn't that simple.

13. May 29, 2010

### Antiphon

The first paper at least has it wrong. If their rocket were in my elevator working against the acceleration of my larger rocket, their test gives the same result as gravity.

That author seemed to have started with a false premise that radiation in any frame is radiation in all frames but they treated it correctly later in the paper. I'll try to get the other links you posted too but there is no "charged particle" exception to Einstein's equivalence principle.

Edit: on reading this paper more closely, the do agree with me that no radiation is seen in the elevator. Their understanding of equivalence may be flawed. There's no experiment you can do in the elevator that distinguishes between gravity and acceleration. Their assertion that it takes more fuel to accelerate the charge is true but tantamount to looking outside the elevator! As long as the elevator is accelerating at 1 g it doesntn matter how much fuel is used. The interior of the elevator including the charge is still indistingusable from gravity.

Last edited: May 29, 2010