The Reason for Antiparticles.The Field Guide to Particle Physics : Season 3. Episode 8.
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ReferencesThe definitive resource for all data in particle physics is the Particle Data Group:
https://pdg.lbl.gov. This episode also pays tribute to
Richard Feynman’s 1986 Memorial Dirac Lecture.
Terrell-Penrose rotation can be viewed from a human perspective in at "
A Slower Speed of Light" by MIT's GameLab. That demo also includes the relativistic doppler effect. Some other great videos by Ute Kraus and Corvin Zahn at
spacetimetravel.org. See in particular their
dice demo.
The Reason for Antiparticles.Antimatter is uncommon, but it’s not exactly rare. Antiparticles - especially those generated by cosmic radiation - are all around us, all the time. But just what is it doing here?
Antimatter is just like MatterIn a lot of ways, antimatter behaves just like matter does. Quarks make up protons? Antiquarks make up antiprotons… and antineutrons, too!
Antiprotons and antielectrons - that is, positrons - combine to form antihydrogen atoms.
The Antihydrogen Laser PHysics Apparatus - the ALPHA Experiment at CERN - studies the spectroscopic properties of antihydrogen. That is, it uses photons to give a little extra energy boost to those positrons. As those positrons relax to their ground state, they emit distinct wavelengths of light.
Just like regular hydrogen atoms.
Photons, you see, are their own antiparticles. They interact with matter and antimatter in precisely the same way.
If there were any difference between hydrogen and antihydrogen - any difference in mass, spin or the magnitude of their electric charge - those wavelengths of emitted light would also be different. And the ALPHA experiment would be able to detect those differences.
But no such differences have been observed.
So again, what exactly is antimatter doing here in our physical reality?
Antimatter annihilates MatterThe one thing antimatter does *not* do is hang around.
Antimatter annihilates with ordinary matter. Electrons and positrons annihilate to form a pair of gamma rays, a pair of photons.
If the universe were balanced between matter and antimatter, we wouldn’t be here. Or… perhaps worse… we’d rapidly disintegrate into a bursts of gamma radiation as our particles and those antiparticle partners annihilated.
So if antimatter is so uncommon - why is it even here? What is the point, the reason for antimatter? Why does the universe need antimatter?
To understand that, we need to talk about time travel.
The Light ConeOur reality has four dimensions. Three space and one time. Famously, Einstein’s special theory of relativity tell us that these four dimensions are related.
That relationship is nature’s conspiracy to make sure that nothing travels faster than the speed of light.
One way to think about how this works is time travel. Literally traveling through time.
When we are still, we are traveling forward, through time. When we spring up to go for a run, we’re still traveling through time, but we *rotate* our perceived motion through time into space.
This is a four-dimensional sort of rotation. Sometimes this is called a Terrell rotation. There are some stunning visualizations of Terrell rotation linked in the show notes.
The amount of Terrell rotation varies without speed. In a sense, we exchange some of our speed in the time direction to travel through space. The faster we go through space, the slower we go through time.
There is a limit to this kind of rotation. We cannot rotate our motion so deep into space that we travel backwards in time. The most we can do is cause time to stand almost still, which happens when we travel just shy of the speed of light.
Light of course always and only travels at the speed of light, in the absence of matter anyway. And because everything that must travel slower than light - everything that has mass - like protons, electrons, atoms and US - is subject to the ultimate cosmic constraint: the light cone.
To visualize this four-dimensional cone, think of a camera flash. It’s a sphere of light moving outwards from a point. The tip of the cone is us snapping the photo, and the vertical part of the cone corresponds to the dimension of time.
At any moment, our reality can be cut into two regions: inside or outside the light cone. All those points that light can touch - and those that it can’t. Inside the light cone represents everything we can possibly hope to effect later in time. Outside the light cone is outside of our agency to do so.
The light cone - in other words - represents the boundary of causality.
Because we cannot travel faster than the speed of light, any Terrell rotation we experience inside our light cone retains a positive flow of time - however slow.
But outside the light cone, that same rotation can cause our perception of time to reverse. Outside our light cone, if we are traveling fast enough, we can perceive time as flowing backwards.
It’s a fun thought exercise to figure out how we might perceive an event outside our own light cone - I’ll leave that one for you to figure out - but here’s a hint: “wait and see”.
If you’re curious, check out our instagram account in the coming days for the answer.
Time flowing backwards might seem terrible for cause an effect. It would literally reverse the two! But time flowing backwards outside our light cone - outside our sphere of influence - has no bearing on our physical reality. As long as our causal influence is restricted to inside the light cone, the observable universe makes sense.
Now let’s tie this back to particle physics. You’d see, the relationship between the world inside and outside the light cone is intimately related to the relationship between matter and antimatter.
The Feynman-Stückelberg Interpretation of Negative EnergiesThe celebrated Dirac equation - the mathematics which describes particles likethe electron - suggests that positrons are just electrons with negative energy. But what is negative energy? This interpretation was confusing for quite some time.
But energy you see is intimately related to time. As time is to space, energy is to motion through space. Energy, in other words, can be thought of as motion through time.
So an antiparticle with negative energy can be thought of as a particle with positive energy moving backwards though time.
In his 1986 lecture commemorating Dirac, Feynman - who is credited with formalizing this interpretation - gave a concise, technical and frankly satisfying explanation for this phenomena.
It went something like this:
Quantum Theory also predicts that particles tend to smear out like a wave. In atoms, electrons smear out to form standing waves, which we call electron orbitals. In modern language, we say that these waves are really probability distributions for a particles position and momentum.
Left to their own devices, quantum mechanics tells us that these probability distributions spread out in space.
For example, when an alpha particle’s smeared probability distribution spreads outside the nucleus, there is a nonzero chance that it will tunnel through, and escape as radiation: alpha radiation.
So you might ask. Can the probability distribution of an electron spread outside the light cone?
Unfortunately, the answer is yes.
And if you’ve studied quantum mechanics, this is probably no surprise. The path integral formulation requires us to consider every conceivable motion of the electron - including those moving faster than the speed of light.
So it might seem that Quantum Mechanics and Einstein’s theory of special relativity are fundamentally incompatible.
If true, this would be a huge problem. Anything moving faster than the speed of light - even by means of quantum mechanics - could mess with our notion of cause and effect. Causality is central to our ability to perform experiments - to make sense of our physical world.
And yet. Quantum Mechanics is compatible with relativity.
You see, the smeared probability distribution for the positron can also leak through the light cone.
Taken together, fortunately, the probability amplitudes for particle and antiparticles to be outside the light cone cancel each other out exactly. Why exactly? Because matter and matter are identical - at least up to that overall minus sign.
It’s just that what we call reality - sometimes - occasionally splits into particle / antiparticle pairs - or not - depending on how fast we’re moving.
In short. The reason for antiparticles is causality.
The Alpha Experiment, RevistedThis is a simplification, to be sure. There are plenty of details to discuss about so-called virtual particles, parity and particle-antiparticle annihilation.
Perhaps another time.
If you’re interested in more of the details, a good place to start looking would be Feynman’s 1986 Dirac Lecture at Cambridge, linked in the show notes.
With any mature scientific theory, there are nuances and details that are exciting to explore. We’ll see more soon enough. But for now, let’s just say that the ALPHA experiment - that experiment at CERN looking for differences between Hydrogen and AntiHydrogen - has searched for violations in causality - that is, violations to the CPT theorem - and has excluded them at the level of 200 parts per trillion.
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