# Is anti-matter matter going backwards in time?

Some sources describe antimatter as just like normal matter, but "going backwards in time". What does that really mean? Is that a good analogy in general, and can it be made mathematically precise? Physically, how could something move backwards in time?

To the best of my knowledge, most physicists don't believe that antimatter is actually matter moving backwards in time. It's not even entirely clear what would it really mean to move backwards in time, from the popular viewpoint.

If I'm remembering correctly, this idea all comes from a story that probably originated with Richard Feynman. At the time, one of the big puzzles of physics was why all instances of a particular elementary particle (all electrons, for example) are apparently identical. Feynman had a very hand-wavy idea that all electrons could in fact be the same electron, just bouncing back and forth between the beginning of time and the end. As far as I know, that idea never developed into anything mathematically grounded, but it did inspire Feynman and others to calculate what the properties of an electron moving backwards in time would be, in a certain precise sense that emerges from quantum field theory. What they came up with was a particle that matched the known properties of the positron.

Just to give you a rough idea of what it means for a particle to "move backwards in time" in the technical sense: in quantum field theory, particles carry with them amounts of various conserved quantities as they move. These quantities may include energy, momentum, electric charge, "flavor," and others. As the particles move, these conserved quantities produce "currents," which have a direction based on the motion and sign of the conserved quantity. If you apply the time reversal operator (which is a purely mathematical concept, not something that actually reverses time), you reverse the direction of the current flow, which is equivalent to reversing the sign of the conserved quantity, thus (roughly speaking) turning the particle into its antiparticle.

For example, consider electric current: it arises from the movement of electric charge, and the direction of the current is a product of the direction of motion of the charge and the sign of the charge.

$$\vec{I} = q\vec{v}$$

Positive charge moving left ($+q\times -v$) is equivalent to negative charge moving right ($-q\times +v$). If you have a current of electrons moving to the right, and you apply the time reversal operator, it converts the rightward velocity to leftward velocity ($-q\times -v$). But you would get the exact same result by instead converting the electrons into positrons and letting them continue to move to the right ($+q\times +v$); either way, you wind up with the net positive charge flow moving to the right.

By the way, optional reading if you're interested: there is a very basic (though hard to prove) theorem in quantum field theory, the TCP theorem, that says that if you apply the three operations of time reversal, charge conjugation (switch particles and antiparticles), and parity inversion (mirroring space), the result should be exactly equivalent to what you started with. We know from experimental data that, under certain exotic circumstances, the combination of charge conjugation and parity inversion does not leave all physical processes unchanged, which means that the same must be true of time reversal: physics is not time-reversal invariant. Of course, since we can't actually reverse time, we can't test in exactly what manner this is true.

• I read somewhere that the "one electron going back and forth in time" idea was Wheeler's, not Feynman's originally. (Wheeler was Fenyman's thesis advisor.) Unfortunately I forgot where I heard this, but it was probably in one of Feyman's lectures/writings. – Nathan Reed Feb 10 '15 at 22:31
• Just a note: If Freymann's view (a single electron bouncing back and forth in time) is true, then we would have exactly the same amount of electrons and positrons... Don't we? – Calmarius Feb 18 '15 at 13:21
• @Tobia antimatter has been used for many things, and nobody has ever seen any evidence of it carrying information backwards in time. If anyone had an idea of how antimatter could be capable of carrying information back in time, in a way that would not have been noticed, someone would certainly do an experiment to test it, but that's never happened as far as I know. – David Z Jun 22 '15 at 8:53
• Yes @Calmarius , that's why Feynman gave up the idea I seem to remember. – Andrea Mar 22 '16 at 9:41
• I'm pretty sure it was Wheeler who originated the idea of there being one electron, just crossing our timeline a collossal number of times. IIRC Feynman talks about this in his Nobel Speech, saying that he "stole" the idea from Wheeler to spawn many of his own. – Selene Routley Jun 20 '17 at 23:53

Antimatter is in every precise meaningful sense matter moving backward in time. The notion of "moving backward in time" is nonsensical in a Hamiltonian formulation, because the whole description can only go forward in time. That's the definition of what the Hamiltonian does--- it takes you forward in time a little bit. So if you formulate quantum mechanics the Hamiltonian way, this idea is difficult to understand (still it can be done--- Stueckelberg discovered this connection before the path integral, when field Hamiltonians were the only tool).

But in Feynman's particle path-integral picture, when you parametrize particles by their worldline proper time, and you renounce a global causal picture in favor of particles splitting and joining, the particle trajectories are consistent with relativity, but only if the trajectories include back-in-time trajectories, where coordinate time ticks in the opposite sense to proper time.

Looked at in the Hamiltonian formalism, the coordinate time is the only notion of time. So those paths where the proper time ticks in the reverse direction look like a different type of particle, and these are the antiparticles.

Sometimes there is an idenification, so that a particle is its own antiparticle.

### Precise consequence: CPT theorem

The "C" operator changes all particles to antiparticles, the P operator reflects all spatial directions, and the T operator reflects all motions (and does so by doing complex conjugation). It is important to understand that T is an operator on physical states, it does not abstractly flip time, it concretely flips all momenta and angular momenta (a spinning disk is spinning the other way), so that things are going backwards. The parity operator flips all directions, but not angular momenta.

The CPT theorem says that any process involving matter happens exactly the same when done in reverse motion, in a mirror, to antimatter.

The CPT operator is never the identity, aside from the case of a real scalar field. CPT acting on an electron produces a positron state, for example. CPT acting on a photon produces a photon going in the same direction with opposite polarization (if P is chosen to reflect all spatial coordinate axes, this is a bad convention outside of 3+1 dimensions).

This theorem is proved by noting that a CPT operator corresponds to a rotation by 180 degrees in the Euclidean theory, as described on Wikipedia.

### Precise consequence: crossing

Any amplitude involving particles A(k_1,k_2,...,k_n) is analytic in the incoming and outgoing momenta, aside from pole and cut singularities caused by producing intermediate states. In tree-level perturbation theory, these amplitudes are analytic except when creating physical particles, where you find poles. So the scattering amplitudes make sense for any complex value of the momenta, since going around poles is not a problem.

In terms of mandelstam variables for 2-2 scattering, s,t,u (s is the CM energy, t is the momentum transfer and u the other momentum transfer, to the other created particle), the amplitude is an analytic function of s and t. The regions where the particles are on the mass shell are given by mandelstam plot, and there are three different regions, corresponding to A+B goes to C+D , Cbar + B goes to Abar+ D, and A + Dbar goes to C+Bbar. These three regimes are described by the exact same function of s,t,u, in three disconnected regions.

In starker terms, if you start with pure particle scattering, and analyticaly continue the amplitudes with particles with incoming momentum k's (with positive energy) to negative k's, you find the amplitude for the antiparticle process. The antiparticle amplitude is uniquely determined by the analytic contination of the particle amplitude for the energy-momentum reversed.

This corresponds to taking the outgoing particle with positive energy and momentum, and flipping the energy and momentum to negative values, so that it goes out the other way with negative energy. If you identify the lines in Feynman diagrams with particle trajectories, this region of the amplitude gives the contribution of paths that go back in time.

So crossing is the other precise statement of "Antimatter is matter going back in time".

### Causal pictures

The notion of going back in time is acausal, meaning it is excluded automatically in a Hamiltonian formulation. For this reason, it took a long time for this approach to be appreciated and accepted. Stueckelberg proposed this interpretation of antiparticles in the late 1930s, but Feynman's presentation made it stick.

In Feynman diagrams, the future is not determined from the past by stepping forward timestep by timestep, it is determined by tracing particle paths proper-time by proper-time. The diagram formalism therefore is philosophically very different from the Hamiltonian field theory formalism, so much so Feynman was somewhat disappointed that they were equivalent.

They are not as easily equivalent when you go to string theory, because string theory is an S-matrix theory formulated entirely in Feynman language, not in Hamiltonian language. The Hamiltonian formulation of strings requires a special slicing of space time, and even then, it is less clear and elegant than the Feynman formulation, which is just as acausal and strange. The strings backtrack in time just like particles do, since they reproduce point particles at infinite tension.

If you philosophically dislike acausal formalisms, you can say (in field theory) that the Hamiltonian formalism is fundamental, and that you believe in crossing and CPT, and then you don't have to talk about going back in time. Since crossing and CPT are the precise manifestations of the statement that antimatter is matter going back in time, you really aren't saying anything different, except philosophically. But the philosophy motivates crossing and CPT.

This refers to Feynman's 1949 theory.

From there: "Feynman's Theory of Antimatter

In 1949 Richard Feynman devised another theory of antimatter.

The spacetime diagram for pair production and annihilation appears to the right. An electron is travelling along from the lower right, interacts with some light energy and starts travelling backwards in time. An electron travelling backwards in time is what we call a positron. In the diagram, the electron travelling backwards in time interacts with some other light energy and starts travelling forwards in time again. Note that throughout, there is only one electron.

A friend of mine finds the image of an electron travelling backwards in time, interpreted by us as a positron, to be scary.

Feynman in his original paper proposing this theory wrote:

"It is as though a bombardier flying low over a road suddenly sees three roads and it is only when two of them come together and disappear again that he realizes that he has simply passed over a long switchback in a single road." (Physical Review 76, (1949), 749.)

Note that Feynman's theory is yet another echo of the fact, noted above, that a negatively charged object moving from left to right in a magnetic field has the same curvature as a positive object moving from right to left.

Feynman's theory is mathematically equivalent to Dirac's, although the interpretations are quite different. Which formalism a physicist uses when dealing with antimatter is usually a matter of which form has the simplest structure for the particular problem being solved.

Note that in Feynman's theory, there is no pair production or annihilation. Instead the electron is just interacting with electromagnetic radiation, i.e. light. Thus the whole process is just another aspect of the fact that accelerating electric charges radiate electric and magnetic fields; here the radiation process is sufficiently violent to reverse the direction of the electron's travel in time.

Nambu commented on Feynman's theory in 1950:

"The time itself loses sense as the indicator of the development of phenomena; there are particles which flow down as well as up the stream of time; the eventual creation and annihilation of pairs that may occur now and then is no creation or annihilation, but only a change of direction of moving particles, from past to future, or from future to past." (Progress in Theoretical Physics 5, (1950) 82).

Then you mix in another very interesting problem, namely the origin of the apparent matter antimatter asymmetry in the observable universe (observed absence of annihilation radiation except in special circumstances) and point out that it may be related to a very very hard problem indeed, namely the origin of time asymmetry. One problem at a time, please. Maybe separate questions, but the answers will likely be more or less over your head since, to the extent that they are even partially understood, they are still being figured out.

• Why would your friend find electrons moving backwards in time scary when it is identical to positrons moving forward in time? – Gerard Nov 9 '10 at 18:28
• There is still an important aspect missing from that page and all the other explanations I have read. Has anybody ever tried to convey information using an antimatter particle, to see if that information is conveyed forwards or backwards in time? – Tobia Jun 21 '15 at 21:52
• @Gerard I imagine it could be scary for someone because, if it is true, it means that the matter that we are made of will need to turn back in time one day - annihilate with antimatter. – Pawel Welsberg Sep 23 '18 at 11:11

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.

• Note the subtile difference between backwards in time: from the future to the present, and back in time: from the present to the past. I feel that the mathematical formalism alone cannot decide on the issue. – Gerard Nov 9 '10 at 18:24
• This is interpreting "going back in time" differently than anyone else does. Going back in time, as it is usually meant, requires flipping the sign of the energy as measured along the proper time and the sign of the proper time as measured relative to coordinate time. This operation preserves the sign of the energy. – Ron Maimon Aug 12 '11 at 13:26

Anti matter is such a misleading term. It's not the opposite of "real" matter. It is made whenever particles are made. But it's just a function of the conservation of properties. Is like saying when one particle going left in pair production will go backwards in time but the one going right is going forward.

Anti matter and matter anihalite for similar reasons. A negatively charged particle that interacts with a positive cant have a charge. So... Boom. They go away and usually a photon comes out (this is being very simplistic. But that is the root issue).

If we called anti matter "opposite charge matter". No one would think it was so special.

Yes. According to the CPT theorem, antimatter is matter going backwards in time, but when viewed through a mirror. Correct me if I get this wrong.

No. If antimatter is going backwards in time, where did it go at the beginning of time (if indeed there is a beginning of time)?

• Maybe time is running in opposite directions simultaneously? – Len Loker Jun 25 '13 at 12:43
• That would answer the questions about what happened to the antimatter created at the beginning of time. We will never see it. But what we can see is antimatter created after the big bang running backwards in time. – Len Loker Jun 25 '13 at 12:49
• If we treat space and time on an equal footing then it would appear time running in both directions simultaneously would be consistent with space expanding simultaneously in all directions. I doubt Einstein understood all the consequences of his theories. – Len Loker Jun 30 '13 at 0:23
• Was the concept of the Dirac sea actually equivalent to the Higgs field? – Len Loker Jun 30 '13 at 16:12
• The Big Bang might be happening all time, in past present and future, adding to opposite time flowing matter and antimatter, expanding the universe, two perspectives of time in the same space time. Then we don't really need a start or an end, and space-time might even fold into a circle on a large scale. – Enos Oye Mar 7 '17 at 15:16

I have been investigating if tachyon faster than light speed is just an illusion of perspective. I used a hypothetical approach which avoids breaking both the speed of light boundary and causality. One of the solutions I got is that antimatter is tachyons. So it is great fun to find this question here, backed up by so many good answers.

It seems like antimatter indeed is going backwards in time, and according to my research I might state it even more accurately: Anti-matter particles carry a reversed arrow of time.

The reason why matter and antimatter can't coexist seems to be because they have oppositely directed arrows of time, and will upon interaction annihilate back into energy. We might say it so simple that that time itself nulls out for both particles and they both dissolve into pure energy.

A tachyon is said to have greater than light speed velocity, and then it has according to special relativity faster than light backwards time travel. Every tachyon is then constantly traveling backwards in time. And as our arrow of time propagates forward in time, the tachyons arrow of time propagates backwards in time. Normally we should then not be able to observe tachyons, as they are in an opposite time perspective with a reversed arrow of time.

This led me to wonder if there could be time symmetry in the universe, where tachyons are existing in a backwards time perspective, while we exist in a forwards time perspective. Two perspectives of space-time with oppositely directed arrows of time. With such a time symmetry a tachyon with infinite speed will not really have infinite speed, as this is just an illusion of perspective, in reversed time a tachyon will instead have the opposite of infinite speed, which is being at rest. And tachyon theory already state that a tachyon with infinite speed have energy as it was at rest. Tachyon theory also state that a tachyon gains energy as it decelerate towards the speed of light boundary, but seen from a reversed time perspective the tachyon actually gains energy as it accelerates towards the speed of light boundary, which is just like normal particles in our time perspective.

So the calculated faster than light speeds of tachyons might be an illusion of perspective. The imaginary tachyon mass which is a result of faster than light speed, is then also an illusion of perspective. And tachyons neither breaks causality, as cause is happening before effect in their reversed time perspective. By adding symmetric time to super symmetry it seems like the physical problems of tachyons get solutions.

If a tachyon, in some way, comes into our observable reality, it is then likely to have a velocity corresponding to the velocity it had in reversed time. It will also carry with it a reversed arrow of time, and can't then coexist with the particles of this opposite time perspective. If two opposite time particles meet, time will null out, and they will both transform into pure energy. This is when it struck me, what if the reversed time particles actually are antimatter particles? I did not know much about antimatter, so I googled antimatter and backward time, and found this question, where many answers suggest there is a relation. Great fun!

And if there is a whole lot of tachyon antimatter existing in a reversed time perspective that could also resolve the antimatter asymmetry problem.

How these opposite time perspectives might interact is also fascinating. The instant speed of the quantum link, measured to be close to infinite speed, might for instance also be an illusion of reversed time. But interaction between the two time perspectives, if possible, may also create problems with causality.

So this hypothetical approach seems to make some sense, and does not seem to be in conflict with physics. We only have to add symmetric time to super symmetry, so everything can become more symmetrical. There might be some conflict with some theories, like the Big Bang theory, which again has problems to explain the antimatter asymmetry. With symmetric time there might even be a possibility that the Big Bang is sort of happening all the time, when energy transforms into matter and antimatter which end up in their opposite perspectives of time. That might again explain why the universe is expanding with an accelerating speed.

We might also wonder if matter that goes into a wormhole, might shift into antimatter. As in a one way wormhole we get faster than light time travel, which shift the arrow of time direction for matter, which may cause matter to shift into pure energy and then into antimatter. What comes out of such a wormhole through a white hole could then mostly be antimatter and/or pure energy. Maybe we can even talk about sort of a spectrum of matter, going between matter, pure energy and antimatter.

So there is a lot of possibilities here for being carried away with excitement, as if we can add symmetric time to super symmetry, this might open up a whole new avenue of physics, where we might find answers to many problems in physics and get a more fundamental understanding of our reality.

• $\sqrt{1-\frac{v^2}{c^2}}$ doesn't give a negative result for $v \gt c$, it gives imaginary result. – peterh - Reinstate Monica Sep 19 '18 at 19:16

It might boil down to the definition of time.

For example if time is a measure of change then by that definition for a particle that has only constant properties, including position and speed, time has stopped which cannot be achieved physically due to the Heisenberg uncertainty principle

By that same definition a particle evolving a certain way in spacetime would be "traveling in forwards time" And the same particle evolving that certain way but "backwards" in spacetime would be "traveling backwards in time"

for example as we grow up we mature from a baby to a kid to a teen and eventually to an adult or nicely said we evolve over the years from a baby to an full grown adult. Then "traveling backwards in time" would be an full grown adult devolving backwards to a baby, kinda like watching a video backwards. This would make traveling backwards in time impossible for humans but not for particles

That said if that definition were to be true then we'd be observing time dilation effects near absolute zero which I haven't heard of yet

• no comment on why i got a vote down? i'd love to improve my answer, if i knew where i went wrong....... – Fuseteam Nov 24 '17 at 22:26

It's not really that antiparticles are travelling backwards in time. But mathematically speaking, an antiparticle travelling forwards in time is indistinguishable from the corresponding particle travelling backwards in time. They're just different ways of understanding the same physical situation.

• -1 This was said several times in other answers already. You didn't even say anything about symmetry. – Brandon Enright Apr 25 '13 at 7:32