# Absoloute inertial reference?

1. Oct 12, 2012

### JustinRyan

I have a small intuitive issue with the idea.

If you could humour me for a moment, imagine a particle moving at some velocity v.
An observer sitting on an armchair at rest wrt the background stars, but far enough away from them to negate any gravitational effects, sees the particle moving past at v and calulates it has an increase of momentum energy by virtue of its velocity wrt c.
A second observer, a microscopic cosmologist living on the particle (just humour me) looks through his telescope and sees the massive bodies (stars galaxies etc) all moving at relativistic velocities and he calculates that they have an astronomical amount of kinetic energy.
Where has that energy come from?
Would I be wrong to think that there is some reference frame of minimum energy?

2. Oct 12, 2012

### Mentz114

If you had a system of inertially moving bodies in flat spacetime, then the total energy of the system calculated from any frame will be the same. Otherwise there would be a 'special' frame. We have to use the relativistic definition of energy, which is invariant under Lorentz transformation.

I'm sticking my neck out because I haven't done a calculation, just a mental picture.

Edit : It is shown here* that the relativistic energy of a particle is invariant under Lorentz transformation. There is no preferred frame using this criterion.

*http://galileo.phys.virginia.edu/classes/252/energy_p_reln.html

Last edited: Oct 12, 2012
3. Oct 13, 2012

### Staff: Mentor

Welcome to PF.

The energy hasn't come from anywhere. Kinetic energy is frame dependent. And yes, it is wrong to say that there is a reference frame for minimum kinetic energy....except of course, the rest frame of the object, where kinetic energy is zero.

4. Oct 13, 2012

### JustinRyan

So just so I am clear, my microscopic cosmologist will see a lorentz contraction of every object in space AND the space between them along the axis of his velocity?
I am going to have to do some more sums.
Could there be a case where he would witness a large mass + extra energy create a black hole? Can black holes be frame dependant?

5. Oct 13, 2012

### lightarrow

Yes.

6. Oct 13, 2012

### JustinRyan

Thanks. And thanks for the welcome :)