Talk given at San Jose State University, San Jose, CA October 26, 1994.
Let us look first at the Name of the Divine. In Hebrew, this is represented as Yud, Heh, Vav, Heh. This is traditionally never pronounced. Instead, other words are used: HaShem, The Name, Shaddai, The Breast etc. In particle physics there are four fundamental forces which govern the world. I will make some connections now between these four forces and the four aspects of the Divine mentioned above, a first such correlation, as far as I know.
Let me associate the weak force, with its internal symmetry of SU(2), with the Yud, the Father, Elohim, the alchemical Fire. The first Heh is the Mother aspect of the Divine, and I want to associate the electromagnetic force with its U(1) internal symmetry. This aspect corresponds to the alchemical Water. In the Near-Eastern/West Asian family Pantheon of the divine , She is Shaddai. I will associate then the Vav with the strong force, with its SU(3) internal symmetry. This is the Son - Ba'al of the pantheon of the Middle-East, the alchemical Air. Finally there is gravity, the force which keeps the Earth in orbit about the Sun. This force, like electromagnetism, has an infinite range, acting forever. Due to their long range, these forces have been known since antiquity. I will associate this with the final Heh, the Shekhinah , The Presence, the alchemical Earth, the Daughter in the divine family. Note the interesting connection between alchemical Earth and gravity, which rules our Earth!
Now the strong interaction is what holds the nucleus, the nucleons together. The electro-magnetic interaction is the familiar force of electricity between charges, or the magnetic force due to a current-carrying wire. Both SU(2) and SU(3) are very short range forces, of the size of the atom or nucleus, respectively. This means that effectively, they act only over a length of the size of a nucleus, about 1 Fermi or 10^-10 cm. Only in this century have we been able to probe matter at this scale. No wonder then that only in this century were we able to observe these forces.
Regarding the forces with the internal symmetries SU(2), SU(3), we also found that we needed to develop a new way of doing physics, quantum physics. This is very different from classical physics. At atomic scales, of the order of tens of Fermis or 10^-9 cm, classical mechanics fails. New rules are required. These are the quantum rules, which were constructed over 25 years, between 1900 and 1925, with the work continuing to this day. We can predict and explain many things with quantum mechanics, but we can't explain what's happening. We use words of classical physics like wave, particle, spin, charge, but we mean different things by these terms than we do in classical physics!
According to Jewish mysticism, part of our problem, why we are not one with the Divine is that the Shekhinah pays us only weekly visits, on Shabbat. It is interesting that in parallel with this situation in Kabbalah, in physics the theory of gravitation is also not among us at the quantum level: we have been able to construct quantum theories of the other three types of interaction, but a quantum theory of gravity has eluded us so far, and have only a classical theory of gravity.
Newton was the first to write down a theory of gravitation, but it had several limitations. In this century, Einstein extended Newton's work and was able to construct a general theory of gravitation. In this formulation, matter is intricately connected with the fabric of space-time. The amount of matter, the type of matter present affects the very shape of space-time. Likewise, the structure of space-time affects the matter which can exist! Imagine that we , in this room, are connected to the walls. Any motion of the walls, of ourselves, will distort the shape of the room, according to general relativity! This is a classical theory, with no quantum objects, operators, etc. Even so , it is hard to solve, and only a few exact solutions are known. If we want to quantize this theory, we have to re-interpret these classical solutions by some quantum rules. This is quite hard and so far we have no such theory of quantum gravity in 4 space-time dimensions.
We have achieved some unification of forces, namely that of weak and electro-magnetic, known now as electro-weak. This was done by A. Salaam, S. Glashow and S. Weinberg. References for much of the ideas presented here are:
So far I have drawn a parallel between the four fundamental forces and the TetraGrammaton, the four-letter name of the Divine. Sefer Yetzirah tells us that the Hebrew letters are holy and that they have specific characteristics. Particle physics tells us that there are only a few fundamental particles. There is an interesting parallel here between the building blocks of the kabbalistic creation , the 22 Hebrew letters, and the building blocks of Big Bang creation, the 24 fundamental particle and fields.
Let us start with the W^+-, Z and gamma - the particles which mediate the electro-weak force: W^+- and Z mediate the weak force, gamma (or the photon) mediates the electro-magnetic force. What do we mean by mediate ? Imagine two children on a beach, throwing a beach ball back and forth. The ball mediates their interaction. Similarly, two electrons throw back and forth a photon or a Z. The photon or the Z mediates the electro-magnetic force or the weak neutral force between. This exchange is what we mean by the force between the children, or the two electrons.
We will associate the 8 gluons g_1, g_2, ..., g_8 with the 7 double letters: Bet, Gimmel, Dalet, Kaph, Peh, Resh and Tav. Each of the gluons comes in 3 kinds, R, G, B (red, green, blue.) This is just a label, with no connection to the usual colors red, green or blue. The double letters are called such because they can have two different sounds depending on whether they have the dot, the Dagesh inside or not. Thus, Bet with the Dagesh is pronounced Bet. Without, it is Vet . The gluons mediate the strong force. As we have mentioned, we don't have a quantum theory of gravity, so we have no quantum field/particle associated with that force.
Besides these particles which carry the fundamental forces there are particles/fields which make up matter. The electron is such a particle. It has several cousins: the mu-electron and the tav-electron in increasing order of mass. There are also corresponding siblings: the electron neutrino, the mu-neutrino and the tav-neutrino. These fields interact weakly only, so their presence is a signature of the weak interaction. Protons are not fundamental. Rather, they are made up of particles called quarks. So far we have observed 5 of them: up, down, charm, strange and bottom. Recently the D0 and CDF collaborations at FermiLab have seen signatures for the top quark, the last one to be observed. But what do we see really ? We don't see the quarks. Rather, we do scattering experiments and observe indirectly the effects the electron interacting with the proton. How do we create a new particle( because we can do that )? Well, matter and anti-matter annihilation is the most common method. Electron+ anti-electron go into pure energy which goes into some other form of matter, since energy = mass x speed of light ^2. We can arrange so that the electron and positron have the right or desired energy so that we produce a particle of say 3.1 GeV. We can literally tune the beams . This is easy when we know the energy/mass of the desired particle. But what if we are looking for something new ? It is like going to a new town and we are looking for interesting radio stations on the dial. We can change one form of matter into another, like the the olde alchemists dreamed of doing! Even lead into gold, though this gold would be very expensive. So let us look a bit at e^+ + e^- ->J/Psi ->mu^+ mu^- at or near 3.1 GeV. How do we measure this ? e^+ + e^- goes into pure energy, then into J/Psi, then into mu^+ + mu^-. These particle then pass through detectors, interacting with them and leaving some signal that they went through. That's how we know what came out of the reaction.
The words particle, wave are a bit arbitrary. An electron can be a particle or a wave. Thus, in Compton scattering, the electron is a particle, in crystal diffraction it is a wave! We can't pin electron in either particle or wave category. Can we ignore gravity ? No, but we don't know how to think about it, quantum mechanically.
To finish our parallel construction, to the 12 matter fields introduced above we associate the remaining Hebrew letters: Qoph, Tzaddi, Ayin, Samekh, Nun, Lamed, Yud, Tet, Het, Zayin, Vav and He. Note that this organization of the Hebrew letters into these groups was done in the 1200's CE, while the physical particles were discovered this century!
Some things left out: the Hebrew vowels (ten of them) as well as the Higgs sector in particle physics, and gravity. The Bahir deals with the vowels. So the parallels are not perfect. It would have been suspicious if it had been, nu ?