# A seemingly naive question

1. Nov 1, 2004

### siddharth

I learnt that when we accelerate a charge we get EM radiation. If I have a universe with only 1 electron in it so that no other Electric Field exists, and I then procced to accelerate the charge, will I still get EM waves?

(Neglecting mass of charge)

Since there is no other force on this charge, because the Electric field cannot act on iteself, I need no external force to accelerate it. Therefore i can keep producing energy in form of em waves.

If yes, then is the energy conservation not violated?

2. Nov 1, 2004

### Garth

How do you propose accelerating the charge?
Garth

3. Nov 1, 2004

Staff Emeritus
If the charge were massless it would move at the speed of light (special relativity) so then you couldn't accelerate it. Therefore it has mass. If you accelerate its mass it gets increasing kinetic energy, but it also radiates, losing energy. Energy is conserved, and the radiated energy is subtracted from the kinetic energy, slowing the acceleration down.

4. Nov 1, 2004

### Garth

In what frame of reference is the lone electron accelerating or decelerating?

Garth

5. Nov 1, 2004

### siddharth

Lets say I use a spring to accelerate the charge in SHM. Now i have only the spring and the charge in the universe. Now what would happen. Would the E-fields due to spring affect the situation in anyway?

6. Nov 1, 2004

### siddharth

Also, Because of the fact that the charge is alone in the universe and there is no other field (In my first post). There is no external force which can act on the charge. Therefore how can it lose energy and slow down without an external force?

Modifying my last post let us assume that the spring is made of a particle which does not have charge but exhibits, say strong interactions.

7. Nov 1, 2004

### HallsofIvy

You can't have it both ways! You can't say "accelerate a charge" and then say "there is no which can act on the charge". If there is no external force, then you can't accelerate it.

You said before "Lets say I use a spring to accelerate the charge in SHM." Okay, the spring is exerting an external force. In order to do that, the spring has to be attached to something or at least stationary in some frame of reference.

8. Nov 1, 2004

### Garth

Then its not alone in the universe! My questions are centred on Mach's principle and the thought that if a particle were alone in the universe then it could not move or accelerate because there would be no way of measuring what it is moving with respect to.

If you had two particles, they could be two electrons, then they would repel each other and would accelerate away from each other. You could tie a non-inertial frame of reference to either particle, or an inertial frame of reference to an imaginary spot in the middle at the centre of mass.

Garth

9. Nov 1, 2004

### siddharth

I am sorry for not making my question clearer. I hope this clarifies it.

My spring system is made of two particles which exhibit the same type properties except for charge. The particle on the left end of the spring system does not possess the property of charge. The spring itself is made of particles which does not posses the property of charge. The particle on the right end of the system has charge.

Now, when the spring undergoes SHM the center of mass of the system is at rest. Therefore I have a non-inertial frame. Furthermore I can accelerate the charge by forces other than coulumbic forces.

Therefore i ensure that the only electric field is due to the charge. Now my question is will the oscillating charge produce EM waves. If yes, then does it not violate the conservation of energy?

10. Nov 2, 2004

### siddharth

Read as: Therefore I have an inertial frame

11. Nov 2, 2004

### Garth

Yes and No. Yes the charge will emit EM radiation, and No energy conservation is not violated as the energy of the spring's oscillations will be used up.
Both two particles will also radiate gravitational waves, (very weakly) and the system will loose 'kinetic' mass as these two forms of radiation leak energy into empty space.

Garth