A free particle cannot have 0 energy. E² = m²c⁴+p²c², where E is energy, p is (three-)momentum and m is mass. To have E=0, you would have to have m=0. But a massless particle such as a photon have E=hf where f is the frequency of the wave, so E=0 implies a wave with zero frequency, which is unphysical (actually it can be subtracted off).

OK, so free particles cannot have e=0 but we can always add a potential energy allowing e=0

 

So is ZPE always zero because you can always apply a potential?

A free particle cannot have 0 energy. E² = m²c⁴+p²c²' date=' where E is energy, p is (three-)momentum and m is mass.

[/quote']

 

But that relation has the potential V set equal to zero by hand, does it not? The same dynamics of a free particle follow from V=(constant). So if I replace E with E+V, V=constant, and put it into the relation above I obtain:

 

E²+2EV+V²=m²c⁴+p²c²

E²=m²c⁴+p²c²-2EV-V²

 

If I set E=0 then I have:

 

V²-(m²c⁴+p²c²)=0,

 

which has 2 real solutions for V.

Oops, never mind. The solutions to the above equation will indeed make E=0, but E is not the energy of the particle anymore. E^*=E+V is the energy, and that is not zero.

Dude,

Particles have mass. According to Einstein's theory of general relativity, mass and energy are interchangable aspects. Hence, there is no such thing as a 0 energy particle.

 

P.S.: Sorry, I didn't read all the other posts, they say just what I said!!!

Can I re-ask these two questions from post #27:

 

OK, so free particles cannot have e=0 but we can always add a potential energy allowing e=0

 

So is ZPE always zero because you can always apply a potential?

5614:

I would say yes, but don't take my word for it.

This is such a great topic and I only can put my one piece of information mass-energy sequence.This among other topics show great simplistic abscurity! I love science!

Can I re-ask these two questions from post #27:

 

OK' date=' so free particles cannot have e=0 but we can always add a potential energy allowing e=0 [/quote']Yes, though this would make little "sense" and really, serve no purpose. And it would be quite confusing - non-interacting particles would have negative potential energy (put in by hand).

 

So is ZPE always zero because you can always apply a potential?

See above.