by Tim James
Virtual photons do not exist for long and do not have to follow the normal rules of physics, so we can assign them all sorts of properties we would not normally see, to account for any phenomenon we wish.
A virtual photon can transfer energy between electrons forcing them apart, but if one of the particles is oppositely charged, we can give the virtual photon a ‘negative energy’, which sucks the particles together like a whirlpool.5
The diagram for two like-charged particles repelling is shown opposite on the left, and attraction for oppositely charged particles is shown on the right. The calculations are a little trickier for these diagrams because we need to include two coupling constants (vertexes in the diagrams) and five propagators (for each particle line), but the answers generated by QED are bang on.
Electric charge turns out to be a measure of how strongly a particle interacts with the photon field and which way the virtual photons are behaving.
The physicist Julian Schwinger (who shared the Nobel with Feynman) said we should therefore imagine an electron emitting and absorbing virtual photons with itself constantly, like a person juggling as they run, thus creating a virtual photon cloud around itself as it moves, and other particles can bump into this cloud. QED explains the very nature of electric charge.
BREAKING THE LAW
One of the things we have been counting on since the beginning of the book is that cause always leads to effect and effect does not happen without cause. You never get something out of nothing nor can you extinguish something into nothing. This principle, laid out by Émilie du Châtelet in 1759, is often stated as ‘energy cannot be created or destroyed’, the first law of thermodynamics. And it is a law virtual photons are allowed to break.
Heisenberg uncertainty tells us that we cannot take precise measurements on a particle. Momentum and location are never fixed simultaneously so a particle cannot sit still. Quantum field theory extends this and says that whatever is true of particles must be true of their underlying fields, which means a field cannot have fixed values either.
Quantum fields have to jitter constantly and since these jitters are virtual particles, that means every empty field is constantly creating and destroying countless virtual particles every second. Every point of space around you is foaming and frothing with virtual particles sparkling into and out of existence in less than the blink of an eye. Empty space is not really empty.
Feynman calculated that if you take the energy of all the virtual particles appearing inside the volume of a single light bulb, you would have enough energy within them to boil the entire Earth’s oceans. We just do not notice all that energy because it disappears almost as quickly as it appears.
This realisation means that in quantum field theories you can get something for nothing because ‘nothing’ is unstable and the uncertainty principle will not allow it to stay put. If you have emptiness for a long enough time, energy will appear without a cause. It might sound like a crazy suggestion but we have to swallow it because QED has something weighty in its favour.
IT IS THE MOST ACCURATE THEORY IN ALL OF SCIENCE
To give credit where it is due, Feynman was not the only person to devise a fully working quantum field theory for electrons and photons. He shared his Nobel Prize with Shinichiro Tomonaga and the aforementioned Julian Schwinger, who had their own methods for calculating QED predictions.
Schwinger and Tomonaga’s versions were much beefier though and included a lot of excess work which Feynman showed was not necessary. (Feynman and Schwinger’s approaches were so radically different, nobody even realised they were working on the same problem until their mutual friend Freeman Dyson made the connection one afternoon while sitting at the back of a hot bus on his way to Ithaca.)6
Feynman diagrams are elegant, but you do not get a Nobel Prize just for drawing pretty pictures. Believe me, I have submitted dozens of my book illustrations to the Nobel committee and have heard nothing. QED did a little better though, because Feynman diagrams are not just fanciful sketches. They have serious predictive power.
One example of QED’s strength is the value it calculates for how strongly the photon and electron fields couple to each other (exchange quanta). The most exhaustive calculation of this number was performed in 2012 by Makiko Nio and his team, who computed the outcome of 12,672 Feynman diagrams each containing ten vertexes between photon and electron fields.
Their value of the coupling constant for the fields was 0.00729735256. The value measured in experiments is 0.00729735257. That is an agreement between theory and data to ten decimal places.7
Feynman described this kind of accuracy as like measuring the distance from New York to Los Angeles and getting it right to within the width of a single human hair. No other prediction in science even comes close.
If you accept any scientific theory, anything at all from what causes warm air to rise to how viruses work, you should probably accept QED too because its evidence is stronger. And if the numbers do not convince you, there is another prediction QED makes which matters. Or rather, antimatters.
SOUNDS LIKE SOMETHING FROM A MOVIE
When Dirac talked about particles appearing out of fields he pointed out that doing so should leave behind a hole in the field. Going back to the ice-cream analogy, each scoop we make from our ice-cream tub creates an ice-cream particle but also an equal-sized crater in the surface.
We can cancel it out by putting the particle back into the void, but it looks like generating a particle generates an inverted particle-hole simultaneously. An anti-particle.
Feynman’s QED predicts anti-particles as well, but they arise in a different way. Rather than one electron field out of which we make an electron and a hole, there are two fields: one for electrons and one for anti-electrons, with the photon field coupling to both.
Let us revisit our Feynman diagram for an electron absorbing (or spitting out) a photon.
One of the nifty features of Feynman diagrams is that they are valid from any angle, meaning we can rotate them and get an equally correct answer. If we flip the above diagram by ninety degrees we end up with this…
When read from the bottom upward, a quantum in the photon field is propagating through space, then randomly decides to die, transferring its energy into the electron field (a photon turns into an electron). But if we look closer we can see something odd. One of the electrons has its propagator arrow pointing backward.
The propagator on the right is representing the electron, but the particle on the left must be some sort of reverse electron generated at the same time. And we can flip the whole thing again…
The two arrowed lines now show an electron (on the right) and an anti-electron (on the left) approaching each other and annihilating to produce a photon. (NB: for mathemagical reasons, the collision actually produces two photons rather than one but it does not make any difference to our picture.8)
‘What would an anti-electron be like?’ I hear you ask. Well, something like a normal electron but with the charge reversed. A positive electron rather than a negative. But, if an electron gets its charge from juggling photons in one direction, is the opposite charge the result of juggling photons the other way? Feynman, rather cryptically, said yes.
In 1949 he showed that if you take the propagator for a normal electron and flip the direction of time in your equation (reverse the diagram arrow) you get the propagator for an anti-electron. Anti-particles are, according to Feynman, regular particles moving backwards in time.9
This idea of a backwards-time electron is scalded by some modern physicists because you cannot seriously claim an electron can time travel. To me, this feels a little like Einstein objecting to superposition. He did not like what it implied but it is not possible to determine if it is right or wrong yet; all we can say is that the equations work. What this means is a matter of taste. Antimatter particles do exist and they behave exactly the way Feynman said they would.
BUILD YOUR OWN PARTICLE DETECTOR
Antimatter
was discovered by Carl Anderson using a device called a cloud chamber. The design is so straightforward anyone can build one. I have made several and I am as useless in a lab as Heisenberg, although I do know how to change the battery in a smoke alarm (funnily enough, a smoke alarm is crucial for any lab I am working in).
Here is how you do it. Get a transparent tank and line the edge all the way round with a strip of felt soaked in alcohol (propan-2-ol/rubbing alcohol works best). Seal it back up and stand the whole thing on a layer of ice to cool the bottom surface. This will establish a thin atmosphere of alcohol vapour inside the tank and any particles which zip through the plastic walls will leave a vapour trail in their wake, showing up as pale whispery lines, seemingly out of nowhere.
You can also put a magnet inside and charged particles will move in a curved path around it, charge and magnetism being characteristics of the same field.
Carl Anderson was studying cosmic rays – particle debris that rains down on us constantly from space – and counting the electrons that reach the surface of the planet. When he did so, most behaved exactly as expected, but fifteen of the tracks moved the wrong way around the magnet. Anderson was observing positively charged electrons. Antimatter from space.10
Anti-electrons were named ‘positrons’. A reverse-charged proton was disappointingly called an anti-proton, however, and a reverse-neutron is similarly called an anti-neutron, although you might be wondering how it is possible to have a reverse-charge neutron – famously a neutral particle. We will get to that in the next chapter.
Thanks to QED, our picture of reality became a lot more complicated because there are now seven particles/fields to deal with: protons, antiprotons, neutrons, anti-neutrons, electrons, positrons and photons.
Photons do not have antimatter counterparts, which actually makes perfect sense in the Feynman time-reversal view. If antimatter really is regular matter going backwards in time, photons should be their own anti-particle because they do not experience time.
As we have already seen in special relativity, time slows down until you hit the universal speed limit and, since photons are already moving at that limit, their notion of time is non-existent. Photons do not age forwards which means they do not age backwards either.
THE WEAPON OF CHOICE FOR COMIC-BOOK VILLAINS
Antimatter particles have a short life expectancy because as soon as they meet regular matter (most of the universe) they cancel out producing photons. But worry not, you can make your very own antimatter particles right here on Earth for the low, low price of $62 trillion per gram!11
Obviously, because it is so difficult and expensive to produce, antimatter is only ever generated in tiny amounts by particle physicists with a lot of patience. The record for keeping the most antimatter alive at the time of writing is a whopping sixteen and a half minutes for 309 atoms of anti-hydrogen (an anti-proton with an orbiting positron), which was achieved in 2011.12
The main reason it might be worth looking into antimatter as a technology is that the energy you get from matter-antimatter collisions is so great you could power a rocket to Alpha Centauri with little more than a teaspoon of the stuff. It could also accelerate a medium-sized spaceship to about a quarter the speed of light, allowing you to make the trip in a matter of years rather than centuries.
That kind of energy does make it ripe for weapons manufacture, of course, and the notion of antimatter bombs has been occasionally discussed by military officials. Depending on how we play it, antimatter could become the most destructive thing on our planet or the very means by which we escape it.
CHAPTER THIRTEEN Particle Physics Gets Jacked
PARTY-CRASHER
The year is 1936. The atomic structure has been solved and quantum field theory is making accurate predictions. The last time we felt this confident was right before Max Planck began experimenting with light bulbs and surely that could not happen again. How could there be anything else?
Well, as the oft-quoted Robbie Burns poem says: ‘the best laid plans of mice and men, do not take into account the presence of the muon field’.
Carl Anderson had discovered antimatter by observing positron trails in a cloud chamber. That was awesome but it had not blown anyone away since antimatter was an expected prediction of QED. What did blow everyone away in 1936 was another trail, spotted in his cloud chamber, which behaved just like an electron… only two hundred times heavier.
This particle, christened the muon, has the same characteristics as an electron, couples to the photon field and follows Feynman’s diagram rules; it is just fat and, as far as we could tell, completely unnecessary for our theories to work.
No atom contains muons because they are short-lived particles, lasting for about two-millionths of a second, so they are present in the universe but have no apparent purpose, prompting the Nobel Laureate Isidor Rabi, to bellow ‘Who ordered that?’ in astonishment when he was told there was a new field none of our theories predicted or asked for.1
Because they are so heavy they are also high in energy and, in the same way an energetic guitar string dampens down to a softer vibration, fluctuations in the muon field rapidly transfer their energy to the electron field, decaying the heavier particle into the lighter one (a fancy way of saying muons turn into electrons).
Then it happened again in 1974 when Martin Perl discovered the tauon (often just called the tau), an even heavier electron, this time three and a half thousand times heavier with an even shorter lifetime.2
Electrons and positrons were not unique it turned out. They were the lightest of members of a particle family comprising electrons, muons, tauons and their antimatter twins. These six particles are collectively called ‘leptons’ from the Greek leptos, which means small, and their existence is a little unsettling.
There was once a time when we imagined every law of physics conspired in some way to permit or encourage life. The discovery of the muon and tauon challenges that view because it would appear nature sometimes does stuff that has nothing to do with us whatsoever. Life exists just fine without muons and tauons. Whatever they exist for, we apparently do not need them.
Muons and tauons have a few esoteric uses such as probing the interiors of pyramids (they are heavier and penetrate deeper than an electron beam would) but other than that, it would appear nature triplicated the electron for no reason. And it does not stop with leptons.
THE PARTICLE ZOO
Cosmic ray particles are hard to detect because most of them interact with our atmosphere and never reach the surface. To get a better view, Cecil Powell decided to stick a bunch of particle detectors at the top of the Andes Mountains and see what was coming down. At these great heights, in 1947, he discovered a particle he called the pion, which had the same charge as a neutron, but a lower mass.
A few months later, the kaon particle was discovered by Clifford Butler in a similar way. Then in 1950 we discovered the lambda particle, which acted like a heavy proton. Then we found xi particles, eta particles, omega particles and, by the early 1960s, there were over four hundred new particles to keep track of.3
Our neat collection was looking more like an unruly party, with new gate-crashers arriving every five minutes. Robert Oppenheimer remarked that they should just give a Nobel Prize to any physicist who managed to not discover a new particle4 and Enrico Fermi expressed his frustration by saying, ‘if I could remember all those names I would have become a botanist!’5
Quantum field theory was supposed to be an elegant, albeit mathematically complicated, description of the fundamental laws of physics. This ugly potion of particles was not painting such a portrait.
It was reminiscent of what happened in chemistry a century before. New chemical elements were being discovered with a variety of properties and the confusion was only brought to order when we realised atoms were made of smaller things – the protons, neutrons and electrons with which we are today familiar. Physicists began to hope that something similar would happen for particles.
Four hundred different species in the zoo looked too messy. Someone was going to have to find a pattern in the chaos, the way Feynman had brought order to our understanding of electrons and photons. Fittingly, or perhaps ironically, the person who achieved this monumental task was Feynman’s rival: Murray Gell-Mann.
Gell-Mann’s office was across the corridor from Feynman’s and there was often tension between them, perhaps worsened by the fact they both had Nobel Prizes.
Feynman was a partying entertainer who enjoyed the company of women (he married three times) and rarely bothered to read books. Gell-Mann was a distinguished academic who attended Yale at fifteen, spoke many languages and spent his time reading papers on linguistics and archaeology. Gell-Mann was about the quiet life whereas Feynman was about the bars and clubs (although it is worth noting that Feynman never drank alcohol and encouraged sobriety).
Despite their disagreements and different lifestyles, both men suspected that protons and neutrons were not fundamental after all. There were scores of known lighter particles, which implied a sub-structure of smaller things, and the race was on to come up with a new quantum field theory to describe them.
Feynman referred to these hypothetical sub-proton/neutrons as ‘partons’ and did a lot of work on how we might observe them. The theory that described them in detail, however, was laid out by Gell-Mann, who called them ‘kworks’ for no other reason than he liked the way the word sounded (if you’ve read about this topic before and are not sure about my spelling, hold on).
