electron-positron question

[byron178]

Is the electron-positron interpretation traveling backwards in time really time travel backwards or is it a trick or an aid?

[mathman]

To me it is an aid or a mathematical trick.

[byron178]

To me it is an aid or a mathematical trick.

so in no situation does the electron or positron travel backwards in time to the past?

[Bill_K]

The short answer is, That's right - nothing ever travels backwards in time. The long answer combines an unfortunate historical misunderstanding with what is a really deep property of quantum fields.

When quantum field theory was first being developed, the description anticipated was in terms of a wavefunction ψ(x,t) a relativistic generalization of the Schrodinger wavefunction. But as the Klein-Gordon equation and the Dirac equation made clear, relativistic invariance implied the existence of negative energy (or at least negative frequency) solutions. And these solutions seemed to represent particles traveling backwards in time.

Second quantization put things in an entirely different light. ψ was not a wavefunction after all, but an operator. And furthermore, what that operator stood for hinged on the choice of Hilbert space. Resolution: the Hilbert space we had been assuming all along was the wrong one. The 'negative energy states' needed to be replaced by positive energy states of a second particle, the antiparticle. And the interpretation required of the field operator ψ was a hybrid. Part of ψ created particles, while the other part destroyed antiparticles.

Now here's what's deep about the thing. In any interaction, it's the combination ψ that always appears. That means the amplitude for the creation of a particle is closely tied to the destruction of an antiparticle. An antiparticle interacts "as if" it was a particle that had been twisted around to point into the past. The fact that this works consistently may seem like a trick, but it is much more than that!

[byron178]

The short answer is, That's right - nothing ever travels backwards in time. The long answer combines an unfortunate historical misunderstanding with what is a really deep property of quantum fields.

When quantum field theory was first being developed, the description anticipated was in terms of a wavefunction ψ(x,t) a relativistic generalization of the Schrodinger wavefunction. But as the Klein-Gordon equation and the Dirac equation made clear, relativistic invariance implied the existence of negative energy (or at least negative frequency) solutions. And these solutions seemed to represent particles traveling backwards in time.

Second quantization put things in an entirely different light. ψ was not a wavefunction after all, but an operator. And furthermore, what that operator stood for hinged on the choice of Hilbert space. Resolution: the Hilbert space we had been assuming all along was the wrong one. The 'negative energy states' needed to be replaced by positive energy states of a second particle, the antiparticle. And the interpretation required of the field operator ψ was a hybrid. Part of ψ created particles, while the other part destroyed antiparticles.

Now here's what's deep about the thing. In any interaction, it's the combination ψ that always appears. That means the amplitude for the creation of a particle is closely tied to the destruction of an antiparticle. An antiparticle interacts "as if" it was a particle that had been twisted around to point into the past. The fact that this works consistently may seem like a trick, but it is much more than that!

how about when an electron travels backwards in time in equivelent to a positron traveling forwards in time view? so what your saying is in no view does any of the particles travel backwards in time just forwards in time?

[clem]

Feynman diagrams are in 4-momentum space,so there is not even any time to speak about.
Feynman just liked to be whimsical in his descriptions.

[byron178]

Feynman diagrams are in 4-momentum space,so there is not even any time to speak about.
Feynman just liked to be whimsical in his descriptions.

So your saying that he like to play around? and that we should not take the travel backwards in time litteraly?