# "Rest is a special case of motion" ?

1. Aug 9, 2014

### Helmoltz

Im currently researching momentum, kinetic energy and potential energy. I came across the idea
that potential energy or an object at mechanical rest is still however in motion/ or a form of motion. The ideas are very dated however. 19th century.
Tait - "potential energy is subsequently resolved into a form of actual motion"
Kirchhoff - "Rest is a special case of motion"

I think in general, and in principal it is correct. But lacking a physics background im looking for further information.

my thoughts so far are, that an object would still be technically moving at rest on the macro scale as the earth is spinning and in orbit, galaxy moves etc. And also on a micro scale, there will be subtle chemical changes on a molecular and quantum level. But i don't think this is the point that is being made.

My only guess is towards relativity. In which rest is merely a relative position between objects. And there is no absolute rest.

I''ll be much obliged if you can put me straight on this one.

2. Aug 9, 2014

### Staff: Mentor

I'd go with relativity's answer in that whether an object is at rest or at motion depends on the frame of reference.

3. Aug 9, 2014

### Staff: Mentor

Right. "At rest" always implies "for the observer". That also means kinetic energy depends on the observer.

That is called "heat".

4. Aug 10, 2014

### Helmoltz

Thanks, i think this is the right line of inquiry.
Ill have a read on special and general relativity.

A question that arises for me however, is that it appears that rest "for the observer" implies a subjective standpoint. Which can make sense since everything is in motion, however things can "appear" to be at rest relatively. But how can kinetic energy also be relative to the observing subject?
Surely if we for example throw a stone in a body of water, there is an objective transference of kinetic energy, a definite change of motion into different forms ?

5. Aug 10, 2014

### Helmoltz

Slight update to my last question.
Kinetic energy is relative, right ?
because, in my example. the stone and myself and the body of water are all travelling at the speed of the earths rotation. however its kinetic energy which we would measure would not be in reference to that speed/velocity, it would be in relation to the velocity of the stone and the ground - which would appear at rest. So the quantity of motion measured regarding its kinetic energy would be relative to what we reference we chose being in the normal case the ground.

Am i getting close ?

6. Aug 10, 2014

### Staff: Mentor

It might be better to say that kinetic energy is "frame-dependent" instead of "relative", but either way the answer is yes.

7. Aug 10, 2014

### Staff: Mentor

The conversion of energy types is objective, but the sources are not.

In the frame of the water, the stone has kinetic energy that gets dissipated to heat.
In the frame of the original motion of the stone, the water (and the whole earth) has kinetic energy, the stone does not. The water gets slowed down a bit when it its the resting stone, so the whole earth loses a bit kinetic energy to (a) the acceleration of the stone and (b) heat.
In every frame (including those not discussed here), the energy transfers look a bit different, but the amount of heat stays the same and energy conservation is valid everywhere.