Should a stationary charge on the earth radiate?

[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?

 

[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.

 

[GRDixon]

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?

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.

 

[starthaus]

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?

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

 

[Dale]

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

 

[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.

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

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.

 

[Dale]

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.

Here is one:
http://wwwphy.princeton.edu/~kirkmcd/examples/EM/almeida_ajp_74_154_06.pdf
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.

 

[atyy]

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

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

 

[bcrowell]

What the OP is asking about is a special case of a more general issue, which is whether or not the equivalence principle applies to charged objects. Here are some papers on this topic:
C. Morette-DeWitt and B.S. DeWitt, "Falling Charges," Physics, 1,3-20 (1964)
http://arxiv.org/abs/gr-qc/9303025
http://arxiv.org/abs/physics/9910019
http://arxiv.org/abs/0905.2391
http://arxiv.org/abs/0806.0464

 

[abhi2005singh]

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

C. Morette-DeWitt and B.S. DeWitt, "Falling Charges," Physics, 1,3-20 (1964)

 

[Antiphon]

There is an extensive discussion of this in the thread here:
https://www.physicsforums.com/showthread.php?t=65767

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.

 

[bcrowell]

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.

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.

 

[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.