# Can an object that is producing radiation, have an acceleration but not move

1. Apr 6, 2012

### blastoise

Can an object that is producing radiation, have an acceleration but not move....

Hi,

I took a quiz today and one question was ,

"Which of these would produce radiation"
a) a moving particle
b) accelerating particle
c) DC current
d) a magnetic field (can't remember this)

The answer is B. But, I would argue that an accelerating particle must be moving hence the answer would be A and B. Was told no not true and the answer is B.

How is it possible for a particle to accelerate and not be moving in ℝ^3

position f during time t is

f(t) = location at time t
f'(t) = velocity
f''(t) = acceleration >> which produces radiation

if f'(t) = 0 or a, where a is a constant then then f''(t) = 0, so no radiation is produced if f'(t) = 0 or a.

But.... f''(t) =/= 0 => f'(t) = anti derivative f''(t)=> f'(t) =/= 0 hence it is moving

Can any one think of an example where particle in space has an acceleration not equal to 0, but does not have any movement?

2. Apr 6, 2012

### Matterwave

Re: Can an object that is producing radiation, have an acceleration but not move....

Motion is always frame dependent.

If you are in a reference frame accelerating along with the particle, then the particle is not moving in your reference frame.

We usually don't like to use accelerating reference frames because inertial reference frames are easy to deal with (and SR prohibits accelerating reference frames from being global like inertial ones), but they are not invalid frames of reference.

For example. I would say that me sitting in my chair is "not moving". But I am accelerating along with all the other objects on the Earth's surface due to both the rotation of the Earth, and the orbit of the Earth. It's simply that I am in a non-inertial reference frame.

3. Apr 6, 2012

### blastoise

Re: Can an object that is producing radiation, have an acceleration but not move....

If the particle was said to be in a vacuum would the frame of reference argument still hold?

What about if the particle is spinning would it still be moving?

4. Apr 6, 2012

### haruspex

Re: Can an object that is producing radiation, have an acceleration but not move....

You're missing the point. A particle can be moving but not accelerating. In that case it would not produce radiation. The question could be made clearer: "which will necessarily produce radiation", whereas you're reading it as "which could produce radiation".

However, the answer given is still not right. Only a net acceleration of charge will produce radiation.
Accelerating isolated proton or electron: yes.
Accelerating neutral atom or molecule: no.
Internally vibrating N2 or O2 molecule: no.
Internally vibrating electrovalent bond: yes.
Internally vibrating polar molecule (like CO2, H2O): yes.
DC: no.
AC: yes.
Etc.