# Antiparticles are regular particles going backward in time?

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1. Apr 6, 2015

### Diggabyte

First I would like to say that I'm sorry if this question has been asked before- I'm new here. I was reading QED by Richard Feynman, and he mentioned that any given antiparticle is just it's regular particle counterpart moving backwards in time. How is this possible? I thought that it was only possible to go backward in time moving faster than the speed of light. Does this mean that antiparticles are moving faster than the speed of light and therefore have negative mass? Or is this idea of particles moving backward in time no longer accepted, as QED was published in the 80's. I'm sorry if these are stupid questions; I'm new to quantum theory, and I don't have the necessary mathematical background to fully grasp most of the theories.

2. Apr 6, 2015

### HallsofIvy

Feynman never said that anti-particles were "regular particles going back in time", he only pointed out that such a concept would explain several thing. Imagine a two-dimensional graph in which the horizontal axis is a single space coordinate, "x", and the vertical axis is a time coordinate, "t".

Now draw a zig-zag line across that graph, first going up to the right, to point "A", then down to the right to point B., but not as far down as the original line, then back up to the right. Look at that from a "time bound" perspective- cover the graph with a sheet of paper with a single horizontal slot with the slot at the bottom of the graph. Move the paper slowly upward- t is increasing so you are moving "forward" in time. At first you see only a small bit of the line coming in on the left- that's a "regular" particle. Slowly moving the slip upward, you will see that particle moving to the right on slit. Then suddenly you will reach the point "B". As you continue moving the slot upward you see two new "particles", one moving to the right, one to the left. As you continue moving the slot the initial "particle", still moving to the right, and the new one, moving to the left, will be getting closer and closer. Eventually you reach point "A" when those two "particles" merge and disappear, leaving just the particle that appeared at point "B" and moved to the right.

From a "time bound" perspective, we could explain that as a "regular" particle coming in from the right, a "regular" particle and anti-particle being created at point "B", the anti-particle eventually hitting the original "regular" particle and both being annihilated.

Feynman also pointed out that this would explain why all electrons are identical- there is really only one electron, zipping back and forth in time!

(Relativity doe NOT say that an object moving faster than light goes back in time- it says it is impossible to go faster than light.)

3. Apr 6, 2015

Staff Emeritus
We have also known since 1964 that antiparticles are not particles going back in time.

4. Apr 6, 2015

### Diggabyte

I'm still a bit confused. If an antiparticle isn't a particle moving backwards in time, then what is the fundamental difference between a particle and it's antiparticle? Is there an actual link between these particles, or are they just arbitrary values that happen to line up a certain way?

5. Apr 7, 2015

### e.bar.goum

Antiparticles and particles have opposite electric charge. The other properties (mass, spin) are identical. Not arbitrary at all.

6. Apr 7, 2015

### vanhees71

It's very misleading to say an antiparticle is "going backward in time". The opposite is the case!

Antiparticles where predicted by Dirac in a very complicated and peculiar way. The space-time structure of special relativity (Minkowski space) implies the possible wave equations, which were taken as candidates for equation for single-particle wave functions for relativistic particles in analogy to the Schrödinger equation in non-relativistic quantum theory. In the latter case, of course, one has to use the space-time structure of Newtonian physics (Galilei space, if you wish to give it a name). Then the Born interpretation of the wave function, i.e., the definition of a conserved probability current with a positive definite probability distribution is straight forward. Also for the free-particle case the Hamiltonian has only positive eigenvalues, i.e., there's always a stable ground state.

In relativistic physics, the restriction to positive energies leads to very complicated "non-local" solutions, which also do not obey microcausality, i.e., although the wave equation is relativistically covariant there's signal propagation faster than light. Thus you have to admit solutions with negative frequencies, but if interpreted in a naive single-particle way this implies negative energies, and the Hamiltonian is not bounded from below, and there's no stable ground state. Dirac's idea now was to declare all negative-energy states occupied ("Dirac sea") and this state to represent the "vacuum" (which is a contradiction). Now, switching on interactions, enables transitions of a particle in the Dirac sea to the positive-energy states, leaving behind a hole, which behaves as an oppositely charged particle with the same mass as the particles. Such a hole can be reinterpreted as representing a such defined anti-particle with positive energy moving in the opposite direction.

This whole construct is not only pretty inconsistent but also very complicated to deal with. However, it leads to the correct predictions (at least for QED). It's also inconsistent from a fundamental point of view, because you start with a single-particle description and end up with infinitely many particles in the Dirac sea. Such a system should, however, be described as a many-body system to begin with. The above discribed particle-antiparticle pair-creation process also implies that particle number is not conserved (but charge is). The most convenient way to describe such a system is quantum field theory with an empty vacuum and creation and annihilation operators with respect to a well-defined single-particle basis (for free particles these are the momentum-polarization eigenstates). Then the only trick needed to reinterpret the negative-frequency modes as positive-energy excitations is that you have to put a creation operator in the mode expansion of the field operator and flip three-momentum. For the positive-frequency modes you put an annihilation operator as in non-relativistic many-body theory (where you have only annihilation operators in that expansion). This superposition of negative and positive-frequency modes, together with the canonical equal-time commutatation/anticommutation relations also leads to a microcausal local quantum system with a stable ground state.

Together with this assumptions, you can derive the correct QFT's systematically from the group theory of the Poincare group, implying the spin-statistics and CPT theorem, both of which are confirmed by all observations so far.

7. Apr 7, 2015

Staff Emeritus
Vanhees71, I don't think the OP is quite at that level. Maybe a simplified version would help him?

8. Apr 10, 2015

### Diggabyte

Vanhees71, thank you for explaining such a difficult concept. Unfortunately I'd have to agree with Vanadium 50; you use a lot of terms that I'm not familiar with, and I don't even know where to start looking to learn the rest of quantum physics that I'm missing.

Last edited: Apr 10, 2015
9. Apr 11, 2015

### stevendaryl

Staff Emeritus
What happened in 1964? (Besides the Beatles coming to America?)

10. Apr 11, 2015

### DaveC426913

Me.

Though I'm not sure that is directly bearing on the question.

11. Apr 11, 2015

Staff Emeritus
CP violation, which implies time-reversal violation, was discovered in 1964 by Jim Christianson, Val Fitch, Rene Turley and Jim Cronin.

12. Apr 11, 2015

### stevendaryl

Staff Emeritus
Okay, that's what I guessed you were hinting at. But that doesn't seriously impact the hypothesis that antiparticles are particles moving back in time. Instead, it would be modified to something like: antiparticles are parity-flipped particles moving back in time.

13. Apr 11, 2015

### stevendaryl

Staff Emeritus
To me, a serious attempt to make sense of "antiparticles are particles moving back in time" would require a lot of mathematical machinery that maybe doesn't exist.

One could imagine starting with single-particle quantum mechanics, but in the Feynman path-integral formulation in 4-D spacetime, instead of 3-D space. A path is then a function $\mathcal{P}(s) : R \rightarrow R^4$. So instead of considering a path to be a spatial location as a function of time, we consider it a spacetime location as a function of a path parameter $s$ (which might be proper time, but that's not necessary). If the path is differentiable, then we can identify a 4-velocity: $U = \frac{d}{ds} \mathcal{P}$. We can say that it is traveling "forward in time" if $U^0 > 0$, and "backwards in time" if $U^0 < 0$. If the sign of $U^0$ is always constant, then we can just re-parametrize, by replacing $s$ by $-s$. However, we could also consider paths for which $U^0$ changes.

The mathematics of such a path integral would be incredibly complex (making path integrals give a well-defined value is difficult enough even for nonrelativistic quantum mechanics). In particular, if the particle is allowed to take an arbitrary path, then the path would be allowed to double-back, so that the particle collides with itself, at an earlier value of the path parameter, $s$.

It seems conceivable to me that such a path-integral formulation could be developed to be equivalent (in some sense) to QED, but it would be incredibly complicated to do so. Does anybody know whether this line of research has been pursued?

14. Apr 11, 2015

### vanhees71

I don't know, when precisely Stueckelberg wrote his idea in a paper at first, but I guess it's in the late 1930ies beginning 1940ies. Many of these papers are in French, and I must admit, I've not read the original publication, containing this idea. Later Feynman used the same idea (not independent from Stueckelberg, because he cited one of Stueckelberg's papers) in 1949 in one of his famous papers on QED.

The very point of the Stueckelberg-Feynman trick is, brought in modern QFT language to associate a creation operator with the negative-frequency-mode solutions of relativistic free-particle wave equations (be it Klein-Gordon, Dirac, the em. field, or any other relativistic field). Then you have automatically the interpretation of the negative-frequency modes as antiparticles with positive energy moving forward in time and at the same time microcausality and positive definiteness of the Hamiltonian, provided you quantize the fields with the "matching" statistics, namely half-integer-spin particles as fermions and integer-spin-particles as bosons. This constraints (microcausality, boundedness of the Hamiltonian) imply, besides this spin-statistics relation also that the "grand reflection" CPT is necessarily always a symmetry (Pauli-Lueders theorem).