I understand this question has already been asked here, however, I don't have enough reputation points to place a comment (I suppose that's the reason) on a specific answer to request a reference.
A user has answered (I'm not sure I can cite his name here, so I won't):
There is one technical inaccuracy in saying that antimatter moves back
in time (whatever it might mean). In quantum field theory we get
positive energy solutions (usual particles) and negative energy
solutions. Negative energy solutions behave in time as if they were
propagating backward in time. But they are not the antiparticles, they
are just the "negative-energy particles". Antiparticles are positive
energy solutions, and they are obtained by acting with charge
conjugation operator on the negative-energy solutions. So,
antiparticles move forward in time, as usual particles.
and, even though someone else comments
This is interpreting "going back in time" differently than anyone else
does.
I'd like a reference for (or further clarification on) that, since I have already heard that before (also informally).
I understand this is a repost but if someone could at least give me some reference before closing it, I'd be thankful.
PS: My first intention was to ask how to proceed on this case in "meta", but I don't have reputation points to place a question there.
EDIT:
To clarify further my question: I had originally the same question as the OP from the post I quoted. At first, I thought that an explanation of what are anti-particles and the interpretation as particles going back in time could be found in quantum mechanics alone, without more advanced quantum field theory. The argument I knew is that anti-particles are really related to the originally negative-energy solutions, that can be reinterpreted as positive-energy solutions, as long as one invert the sign of time in the unitary time-evolution operator. This would hence lead to the reinterpretation of such states as positive-energy anti-particles going back in time or, at least, with anomalous time dependency.
The particular answer I quoted, seems to contradict this interpretation, saying that it is a mistake. I'd like a further clarification here. Is this interpretation really wrong?
From what is said on Wikipedia, looks like the Feynman–Stueckelberg interpretation relies on the fact that anti-particles are to be understood as particles going backwards in time and then related to the latter by charge conjugation.
Where does this interpretation primordially comes from? Where is it primordially needed if their association with the negative energy solutions of Dirac's equation (say) is a mistake? I understand that in quantum field theory one uses complex fields to describe both particles and anti-particles, relating them by charge conjugation. But isn't this done this way to accommodate Feynman–Stueckelberg's interpretation?
Best Answer
Please bear in mind that I am an experimentalist, therefore I treat theoretical ideas and models as dependent on experimental observations and not vice versa.
Facts:
elementary particles have measurable quantum numbers. These quantum numbers define the particle.
elementary particles have mass
there exist elementary and composite (from elementary) particles that have the same mass as others but opposite charge, as the electron vs positron, proton vs antiproton, called antiparticles because:
there is a very high probability that when scattered against each other, the particle and antiparticle disappear and the energy appears in a plethora of other particles. This is called annihilation because charge disappears, and in general the opposite quantum numbers are "annihilated".
On the theoretical side these experimental observations are fitted beautifully by the Dirac equation if one considers the negative energy solutions to describe the antiparticles.
One thing we can be sure of is that measured antiparticles travel forward in time.
The popular theoretical interpretation of antiparticles being particles traveling backwards in time mainly comes from the Feynman diagrams. These are a brilliant mathematical tool for fitting and predicting measurements representing particle interactions as incoming lines and outgoing lines and in between lines representing virtual particles that carry the quantum numbers but are off mass shell.
Due to the CPT theorem, once a Feynman diagram is drawn, one can interpret the lines consistently according to CPT and will get the corresponding cross sections and probabilities for the change in the quantum numbers consistent with CPT (charge conjugation, parity and time reversal). Identifying a positron as a backwards-in-time electron is an elegant interpretation that in the Feynman diagrams exhibits the CPT symmetry they must obey.
What I am saying is, the statement "positrons are backward-going electrons" is a convenient and accurate mathematical representation for calculation purposes. "As if". There has not been any indication, not even a tiny one, that in nature (as we study it experimentally) anything goes backwards in time, as we define time in the laboratory.
Edit replying to comment by Nathaniel:
In this bubble chamber picture we see the opposite to annihilation, the creation by a photon of an e+ e- pair. (This is an enlarged detail from the bubble chamber photo in the archives. The original web page with the letterings has disappeared, as of july2017)
The magnetic field that makes them go into helices is perpendicular to the plane of the photo. We identify the electron by the sign of its curvature as it leaves the vertex. The positron is the one going up to the left corner. We know it is not an electron that started its life before the vertex formed because as an electron/positron moves through the liquid it loses energy and the loss defines the time direction of the path. So the particle has to start at the vertex and end at the upper left, so it has the opposite curvature to the electron and it is a positron.
A Feynman diagram looks like a scattering in real space, or a pair production, but one cannot project the intricacies of the mathematics it represents onto real space. It is only the calculations of cross sections and probabilities that can be compared with measurements.