# Q: Does anti-matter really move backward through time?

Physicist: The very short answer is: yes, but not in time-traveler-kind-of-way.

There is a “symmetry” in physics implied by our most fundamental understanding of physical law, and is never violated by any known process, that’s called the “CPT symmetry“.  It says that if you take the universe and everything in it and flip the electrical charge (C), invert everything as though through a mirror (P), and reverse the direction of time (T), then the base laws of physics all continue to work the same.

Together, the PT amount to  putting a negative on the spacetime position, $(t,x,y,z)\to(-t,-x,-y,-z)$.  In addition to time this reflects all three spacial directions, and since each of these reflections reverses parity (flips left and right), these three reflections amount to just one P.  You find, when you do this (PT) in quantum field theory, that if you then flip the charge of the particles involved (C), then overall nothing really changes.  In literally every known interaction and phenomena (on the particle level), flipping all of the coordinates (PT) and the charge (C) leaves the base laws of physics unchanged.  It’s worth considering these flips one at a time.

Charge Conjugation Flip all the charges in the universe.  Most important for us, protons become negatively charged and electrons become positively charged.  Charge conjugation keeps all of the laws of electromagnetism unchanged.  Basically, after reversing all of the charges, likes are still likes (and repel) and opposites are still opposites (and attract).

Time Reversal If you watch a movie in reverse a lot of nearly impossible things happen.  Meals are uneaten, robots are unexploded, words are unsaid, and hearts are unbroken.  The big difference between the before and after in each situation is entropy, which almost always increases with time.  This is a “statistical law” which means that it only describes what “tends” to happen.  On scales-big-enough-to-be-seen entropy “doesn’t tend” to decrease in the sense that fire “doesn’t tend” to change ash into paper; it is a law as absolute as any other.  But on a very small scale entropy becomes more suggestion than law.  Interactions between individual particles play forward just as well as they play backwards, including particle creation and annihilation.

Left: An electron and a positron annihilate producing two photons. Right: Two photons interact creating an electron and a positron.  We see both of these events in nature routinely and they are literally time-reverses of each other.

Parity If you watch the world through a mirror, you’ll never notice anything amiss.  If you build a car, for example, and then build another that is the exact mirror opposite, then both cars will function just as well as the other.  It wasn’t until 1956 that we finally had an example of something that behaves differently from its mirror twin.  By putting ultra-cold radioactive cobalt-60 in a strong magnetic field the nuclei, and the decaying neutrons, were more or less aligned and we found that the electrons shot out (β radiation) in one direction preferentially.

Chien-Shiung Wu in 1956 demonstrating how difficult it is to build something that behaves differently than its mirror image.

The way matter interacts through the weak force has handedness in the sense that you can genuinely tell the difference between left and right.  During β (“beta minus”) decay a neutron turns into a proton while ejecting an electron, an anti-electron neutrino, and a photon or two (usually) out of the nucleus.  Neutrons have spin, so defining a “north” and “south” in analogy to the way Earth rotates, it turns out that the electron emitted during β decay is always shot out of the neutron’s “south pole”.  But mirror images spin in the opposite direction (try it!) so their “north-south-ness” is flipped.  The mirror image of the way neutrons decay is impossible.  Just flat out never seen in nature.  Isn’t that weird?  There doesn’t have to be a “parity violation” in the universe, but there is.

Matter’s interaction with the weak force is “handed”.  When emitting beta radiation (a weak interaction) matter and anti-matter are mirrors of each other.

Parity and charge are how anti-matter is different from matter.  All anti-matter particles have the opposite charge of their matter counterparts and their parity is flipped in the sense that when anti-particles interact using the weak force, they do so like matter’s image in a mirror.  When an anti-neutron decays into an anti-proton, a positron, and an electron-neutrino, the positron pops out of its “north pole”.

CPT is why physicists will sometimes say crazy sounding things like “an anti-particle (CP) is like the normal particle traveling back in time (T)”.  In physics, whenever you’re trying to figure out how an anti-particle will behave in a situation you can always reverse time and consider how a normal particle traveling into the past would act.

“Anti-matter acts like matter traveling backward in time”. Technically true, but not in a way that’s useful or particularly enlightening for almost anyone to know.

This isn’t as useful an insight as it might seem.  Honestly, this is useful for understanding beta decay and neutrinos and the fundamental nature of reality or whatever, but as far as your own personal understanding of anti-matter and time, this is a remarkably useless fact.  The “backward in time thing” is a useful way of describing individual particle interactions, but as you look at larger and larger scales entropy starts to play a more important role, and the usual milestones of passing time (e.g., ticking clocks, fading ink, growing trees) show up for both matter and anti-matter in exactly the same way.  It would be a logical and sociological goldmine if anti-matter people living on an anti-matter world were all Benjamin Buttons, but at the end of the day if you had a friend made of anti-matter (never mind how), you’d age and experience time in exactly the same way.  You just wouldn’t want to hang out in the same place.

The most important, defining characteristic of time is entropy and entropy treats matter and anti-matter in exactly the same way; the future is the future is the future for everything.

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### 5 Responses to Q: Does anti-matter really move backward through time?

1. David Martin says:

What you say seems to suggest experiments to test it, but my guess is it’s not going to work, as the effect would have been observed already.
“The most important, defining characteristic of time is entropy”.
As you say, locally entropy doesn’t always apply, though over a larger area it does. Where you get order over a small area, shouldn’t time lose its directionality? could that be tested for? we could even contrive things to make increasing order in one place for short time. so shouldn’t time run backwards there? we do that a lot in fact, and time runs forwards, or we wouldn’t be able to do it. Or are you saying that the link between entropy and time is only a vague one?

2. The Hilbert Book Test Model is a pure mathematical model of the lower levels of the structure of physical reality. It base consists of an infinite dimensional separable Hilbert space and its unique non-separable companion Hilbert space. Both Hilbert spaces use members of a version of the quaternionic number system to deliver the values of their inner products. Thus also the eigenvalues of the operators that map Hilbert spaces onto themselves are quaternions. A special reference operator applies the rational members of the selected quaternionic number system to enumerate an orthonormal base of the separable Hilbert space. It uses the base vectors as its eigenvectors and the enumerators as the corresponding eigenvectors. The eigenspace can be used as a parameter space of a set of quaternionic functions and these functions can be used to define a category of defined operators that reuse the eigenvectors of the reference operator and apply the corresponding target values of thev function as its eigenvalues. The same trick can be performed in the non-separable companion Hilbert space, but this time all members of the number system are used.
A scanning vane can be defined as a subspace of the separable Hilbert space that is spanned by the eigenvector of the selected reference operator that share the same real part of the corresponding eigenvalues. The real value can be interpreted as progression. The vane splits the Hilbert space in a historic part, a static status quo (the vane), and a future part.
The non-separable Hilbert space can be considered to embed its separable companion. And the vane can be interpreted as representing the ongoing embedding process.
This simple dynamic model offers two views. One is the creator’s view. The creator has access to all dynamic geometric data that are stored in the Hilbert spaces.
The other view is the observer’s view. Observers are constituted from elementary modules that travel with the vane. In the vane, rays represent them. Rays are one-dimensional subspaces. In the vane, each elementary module owns a private location that is presented by the imaginary part of a quaternion. A stochastic mechanism generates these locations. Therefore, the elementary modules appear to hop around in a stochastic hopping path. After a while, the hop landing locations have formed a coherent location swarm. The swarm and the hopping path represent the elementary module. A location density distribution describes the coherent swarm. This distribution equals the squared modulus of the wave function of the elementary module.
The observers have no access to the future part of the model. They get their information via information messengers that travel in the embedding continuum. The embedding continuum is the living space of the elementary modules. Thus, it is also the living space of all observers.

In the creator’s view the elementary modules live in a tube that zigzags through the living space. The tube may just cross the vane, but it may also happen that the tube reflects against the vane. The reflection can occur at the historic side of the vane, but it can also occur at the future side. With other words, the tube may cross the vane multiple times. This means that the same elementary module can exist multiple times at the same instant in the vane. These appearances are entangled in a way that must be mysterious to the observers.
The observers will interpret the reflection against the historic side of the vane as the annihilation of a pair of an elementary module and its anti-module. The observers interpret the reflection against the future side of the vane as the creation of a pair of an elementary module and its anti-module.

3. The way I think of the ‘direction of time’ is that while the equations are symmetric under CPT the solutions need not be. It’s kind of like a ferro-magnet which has no preferred direction, but based on initial condiitions ends up pointing in only one direction.

If you start with a bunch of particles confined to the corner of a box, they will spread out and fill the box whether you run the clock forward or backward.

-Arthur Snyder, SLAC

4. Rosy motta says:

I think that the violation of pt shows that the antiparticles travel backward in time,and the space is twisted in two opposed orientations:left handed and right handed in spacetime curves in the fourth dimension,explaining the constancy and the limit for the speed of light

5. Conundrum says: