Can a particle have 0 energy?

[Severian]

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).

[5614]

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?

[Tom Mattson]

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.

[Tom Mattson]

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.

[zelcon]

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!!!

[5614]

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?

[zelcon]

5614:

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

[charm quark]

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!

[DQW]

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.