Negative Energy in Particles: A Conundrum

[GravitatisVis]

I'm kind of struggling with the concept of energy. A particle in a conservative field has kinetic and potential energy (E=T+U), but I can always choose an inertial frame where the motion of the particle is zero, which means I can change the the particle's kinetic energy by just switching frames. I can Simultaneously change the zero point of the potential energy arbitrarily. So In one inertial frame the particle has E>0, in another E=0, and still E<0 elsewhere. I used to think that a negative total energy meant that the particle was in a bound state and vice versa, but now I'm not sure sure. Is it more of a bookeeping device for ultimately calculating the trajectory of the particle? Whats going on?

 

[zhermes]

Great question. Energy is (generally*) arbitrary up to a constant---which is reference frame dependent, as you point out. Differences in energy are reference frame independent (i.e. invariant).

Generally the arbitrary constant is defined such that E=0 corresponds to the border between a bound and unbound system----e.g. a projectile escaping a planet. This is convention, and is useful only as much as it is used consistently.
*Always for practical purposes---but technically there are situations in quantum mechanics and field theories where I think it might be less arbitrary...

 

[chrisbaird]

No, energy is very real. It is more than a book-keeping device. Just because a property changes value depending on which frame of reference you choose does not make it any less real. It just has to change in the right way when you switch frames (Lorentz transform between inertial frames. For instance, the speed of a baseball will depend on which frame you choose to measure it in. This does not make the speed an unreal property, the ball is obviously moving in all frames except its rest frame. So then you may ask, what is its real speed. The while point of Einstein's relativity is that there is no single real speed - there is no preferred frame. Everything depends on how you measure it. Likewise, there is no single real energy of an object (the rest energy is helpful). But this does not make it any less real.

Perhaps your problem is that mentally it is very easy to switch frames, and yet the energy of the observed object changes upon frame change, so you feel like you are creating energy out of nothing. But the object has not actually gained any energy, its just being measured differently because you are in a different frame. If you were to actually make a measurement in practice (say the kinetic energy of an asteroid), then change frames and retake the measurement, you would have to expend energy to accelerate your spaceship lab.

 

[A.T.]

Is it more of a bookeeping device for ultimately calculating the trajectory of the particle?

Yes, energy is just a numerical value, which happens to be conserved. And that makes it useful for calculating stuff. Feynman on energy:
http://www.phy.davidson.edu/fachome/swp/courses/PHY110/Feynman.html