# How is relativity related to anti-particles? [duplicate]

I have heard that a positron is like an electron moving backward through time. Can someone elucidate this statement for me. I would like to hear a deeper explanation of what we believe anti-matter to be, why it annihilates with matter and how this relates to relativity.

## marked as duplicate by ACuriousMind♦, Gert, Prahar, user36790, John RennieNov 24 '15 at 7:57

• one approach to this would be deeply linked to relativistic quantum mechanics (say the dirac equation for electrons). Demanding Lorentz-Invariance (and little more) one can derive the equation of "motion" which inherently has two solutions (with positive and negative energy) with two "entries" (~ spin up/down). Very simply put: the relativistic dispersion $E^2=p^2+m^2$ has two solutions. $E=\pm \sqrt{\ldots}$. Re the propagation in time: the propagator in time is (cf. schrödinger eq.) ~$e^{iEt}$ changing the sign of energy or time does the same thing. (a real answer would take much time) – Bort Jul 27 '15 at 8:44
• Possible duplicate of Is anti-matter matter going backwards in time? – ACuriousMind Nov 23 '15 at 22:45
• @ACuriousMind I'm not sure that is a good duplicate. at least if the interpretation I answered is what the OP meant then it is not the same question. – dmckee Nov 23 '15 at 22:56
• @dmckee: Well...the question seems to consist of two disjoint pieces: "I have heard that a positron is like an electron moving backward through time. Can someone elucidate this statement for me." is a proper duplicate. "I would like to hear a deeper explanation of what we believe anti-matter to be, why it annihilates with matter and how this relates to relativity." is not, but it's also a completely different question. Yours and annav's answer seem to focus on that part, but that doesn't remove the first part. What do we do with questions that are "half-duplicates"? – ACuriousMind Nov 23 '15 at 22:59

I would like to hear a deeper explanation of what we believe anti-matter to be, why it annihilates with matter and how this relates to relativity.

This is the table of elementary particles deduced from innumerable measurements:

Each particle has a characteristic mass and several characteristic quantum numbers.

To each particle there corresponds an antiparticle which means : the antiparticle has the same mass as the particle but opposite in sign quantum numbers. Thus when particle meets antiparticle the quantum numbers become zero and the available energy ( minimum 2*m) can turn into other particles with quantum numbers that in total will add up to zero. Thus e+e- can annihilate to neutrino antineutrino, quark antiquark etc as long as the sum of the quantum numbers is zero.

The relationship to relativity comes from the famous equivalence of mass to energy .

The fanciful expression the positron is an electron moving backwards in time comes from the mathematics of calculating crossections, and particularly with Feynman diagrams. Just mathematics.

The statement that a positron is like an electron moving backwards in time is in itself perfectly explainable with classical physics. As the charge of the particles is opposite, the force caused by the electrical and the magnetic field i.e. q(E + v x B) will be opposite. So, fields accelerating electrons, will decelerate positrons at the same rate and vice versa. So, fields being equal, the movie of the positron will just be a reverse play of the electron movie. This is what is meant by moving backward in time.

The necessity of anti-particles was first noticed when trying to construct quantum mechanical descriptions of particles that obey the relativistic energy-momemntum-mass $m^2c^4 = E^2 - (\mathbf{p}c)^2$ relationship.

The Schrödinger equation is intuited from a combination of de Broglie's rules $E = hf$ and $p = h/\lambda$ and the classical Hamiltonian $E = p^2/2m + V(x)$. Accordingly this is a non-relativistic theory by construction.

Attempting to replicate the intuitive leap in a relativistically correct way leads to the Klein-Gorden equation $$\left[ \frac{\partial^2}{\partial x^2} - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} - \frac{m^2 c^2}{\hbar^2}\right] \Psi(x,t) = 0 \,,$$ and the Dirac equation both of which exhibit two sets of solution identical except for the sign of the energy. Antiparticle fall out of considerations of the meaning of the second set of particles.

When quantum mechanics is extended to form quantum field theories the meaning becomes even more clear, because the "destruction" operators for each particle are also the creation operators for the anti-particles.

So a very reasonable view here is that the nature of mass as a Lorentz scalar requires that massive particles exhibit anti-particle partners.

This answer is the short and incomplete version of the argument outlined by Bort in the comments to the question itself.

How is relativity related to anti-particles?

As far as I know relativity doesn't say anything about antiparticles. But particle physics does. Have a look at the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". An electron doesn't rotate like a planet, because as we know from atomic orbitals, electrons "exist as standing waves". And as we also know, they have a Dirac's belt "spinor" nature: "In this sense a Möbius strip is reminiscent of spin ½ particles in quantum mechanics, since such particles must be rotated through two complete rotations in order to be restored to their original state".

GNUFDL spinor depiction by Slawekb, see Wikipedia

Google on positron chirality, and you can read that the positron has the opposite chirality to the electron. IMHO you can appreciate this by making Möbius strips with different chiralities. One with an anticlockwise twist to the left represents the electron. The other with a clockwise twist to the right represents the positron. Or you can play around with something dynamical, such as Adrian Rossiter's torus animations. This gif represents the positron:

Now find a program to reverse the gif, and "play it backwards". If you also flip it horizontally it looks more like your left-handed Möbius strip. So this gif represents the electron:

Please note that the electron and positron aren't actually purple doughnuts. They "exist as standing waves" that look motionless, they have a spherical symmetry, and they don't have any kind of surface. It's quantum field theory, the electron isn't some solid torus or billiard-ball sphere that has a field, field is what it is. This field has spin ½ spinor nature, and these gifs are the best things I can find to get that across.

I have heard that a positron is like an electron moving backward through time.

It isn't. Like Anna said, that's just mathematics. The electron is only a "time-reversed positron" like the gifs above are reversed. Neither are going backwards in time. They just have the opposite chirality. And charge. They have the opposite quantum numbers. All of which cancel each other out in annihilation, which typically results in two gamma photons. For an analogy, if a cyclone met a anticyclone, all you'd be left with is wind. When an electron meets a positron, all you're left with is light.