Lecture 4

We can certainly say that the driving force of science since Einstein has been the quest for unity. As we said before, in his theory of special relativity, Einstein unified energy and matter with space and time, by bringing space-time into the context of events that involve energy and matter, all with the equation: E=mc². But then, for the rest of his life, Einstein tried to unify gravity—as he had described it in the general theory of relativity—with electromagnetism. But, he was unsuccessful. After his death, two more forces were found that work at the sub-atomic level, the strong and the weak forces. So once more, a grand unified field theory is what everyone is looking for.

The fact that science is seeking unity is a very Jewish thing. Even though we said before that scientists are wrong in seeking a totally encompassing theory, because it can never fully be found, nonetheless, the quest for unity is the real reason that scientists continue to do so. Indeed, every step is a step forward. God makes it so that the scientists believe that they might find the ultimate theory, all in order to get them to progress and move higher and higher in their understanding.

Three methods for attaining unity

As we said, the quest for unity is a very Jewish thing, as the essence of our faith is unity. As in the verse, “Hear O’ Israel, Havayah is our God, Havayah is one.”[1] There are actually three different ways to attain unity. These three themselves correspond to the mind, heart, and action of the individual (i.e., the intellectual, the emotional, and the habitual faculties of the soul).

The first way to attain unity is when two entities that seem to be opposite nullify themselves to something that is above them. The classic example for this is a king who has two opposing ministers. When they are in the king’s presence, because they both nullify themselves before him, they can bow down together. As soon as they rise up and go home, they return to their adversity. But, in the presence of the king they are null, and because of their nullification they become one. This is called hitbatlut (הִתְבַּטְּלוּת), or nullification.

There is a second way to attain unity, and this is very appropriate to our lives. Take for example a couple that wants to achieve greater unity. One way is to have common nullification to someone, for instance the Rebbe. But, then you have to be with the Rebbe (in your mind’s eye) all the time, otherwise you fall back into disparity. The second approach is inter-inclusion, or hitkalelut (הִתְכָּלְלוּת). In inter-inclusion each one has to reveal in himself an aspect of the other. This is something like charge symmetry—that each has the other in him.

The third approach is to undertake a project together. Even if we are different, a common objective that we are working on together will unite us. This can be thought of as cooperation (shituf pe’ulah, in Hebrew).

Let’s try to think about these three types of unity.

Nullification is what can be achieved by the mind. But if you do not remain at a very high level of consciousness, you can readily fall from this type of unity, meaning that the mind is not everything. It’s important to realize that the mind, chabad, is not everything, as far as unity is concerned. To this end, the Mittler Rebbe explained in Kuntras Hahitpa’alut (An Essay on Excitation) that the heart is the real essence of our service, and a person should not think that to pursue the Divine is solely an intellectual endeavor. Our purpose on earth is to rectify the heart by means of the intellect. So the mind is important, but it is not the whole objective.

To have maximum unity, one has to have all three types of unity. We have to have nullification, and inter-inclusion, and cooperation. Cooperation means that by having a common objective we will be unified. Inter-inclusion means realizing that you are in me and I am in you. Inter-inclusion allows us to exchange roles in a sense, allowing me to become you and you to become me. It’s just a question of which side of my personality I manifest.

Physics pursues unity through nullification

Of all the approaches to achieve a unified field theory, before string theory, the only approach was through nullification. The model for this was extremely high temperatures at which the different forces become one. At very high temperatures, it is as if the different forces melt together, and they just become the same thing. This was demonstrated for the weak force and the electromagnetic force, which at very high temperatures are the same. Raising the temperature to such a great degree is like nullifying each until they can combine. It is a little like melting things together. So this is just nullification. At very high temperatures, even the forces of nature melt into one plasma. But, at lower temperatures they divide, which in our metaphor is similar to when the two ministers leave the king’s presence.

So the theory went that at earlier times, at the very first instance of creation, at extremely high temperatures, the strong nuclear force would also combine with the weak force and electromagnetism, giving one unified force. Nonetheless, it is clear that even at higher temperatures, the gravitational force cannot be united as well. So this method is only good for the non-gravitational forces. Regardless of the height of the temperature, gravity could not be “melted” into the other three forces.

String theory and unity through cooperation

How did string theory help in this respect. String theory posits that by adding spatial dimensions, in actuality the forces merge together. Merging is like working together, like cooperation, they work together. This is what we described before as unity that corresponds to nehi, the habitual, action-oriented sefirot, netzach (victory), hod (thanksgiving), and yesod (foundation). Science has not yet discovered at all the intermediate level of unity through inter-inclusion. There is no theory that tries to surmise that perhaps within gravity there is some inter-inclusion of the strong or weak or the electromagnetic forces. Meaning, that there is some trace of these forces within gravity.

The future is in unity through inter-inclusion

Spiritually and psychologically these are three essential types of unity. Until science discovers a form of unity based on inter-inclusion the picture will not be complete. All the GUTs (Grand Unifying Theories) before string theory were based on melting the forces together. But, this does not work for gravity, and has not even been proven for the strong force. It has only been proven in regard to the weak and the electromagnetic forces. What remains open is unity based on inter-inclusion. On the spiritual level, inter-inclusion is the most important. By seeing that I am in you and you are in me, we can go on to do things together (as in cooperation).

Going back to our example of a married couple and their quest for unity, they first need a common commitment to one authority, like the Rebbe, then they have to find themselves in one another, and finally they have to work together. Because science does not have all three types of unity, the quest for unity is still incomplete.

The divide between general relativity and quantum mechanics

Before we conclude this lecture, let us say one more thing. The problem with 20^th century science is that general relativity does not get along with quantum mechanics. At very small scales, the foam, or claustrophobia of the subatomic particles does not work with the laws of gravity which are relatively very gentle and not frantic.

General relativity says that space is curved, but it is a relatively gentle curve. There are no extreme and frantic events that affect spacetime. But, quantum mechanics claims that the smaller things get the more frantic they become. That wildness of the extremely small is caused by putting a particle, which is like a soul, into a small box, and then it goes mad. The more you try to confine an elementary particle to a determined space, the more crazy it becomes and because of that strange things happen, for example, the fabric of spacetime begins to tear apart, as well as other strange topological changes.

Relatively, general relativity is the world of rectification (tikun) while quantum mechanics is an example of the world of chaos (tohu). The two do not get along. General relativity is excellent at describing the cosmos, the very large, the macro. But, it cannot explain the very small. Quantum mechanics is just the opposite. They especially do not agree at the micro level.

This disagreement comes to the fore in special cases like a black hole, which occupies a very small space (on the scale of a particle), but has a huge mass (on the scale of many, many stars). Another place is in cosmology, at the moment of the Big Bang, when all the mass of the universe was confined to a single point. We will discuss more about this later on.

The need to unify tikun and tohu

But, what we now see is that the ultimate quest for unity revolves around getting rectification (tikun) and chaos (tohu) to unify. This is why inter-inclusion is the missing link. Because tohu and tikun will not cooperate together without inter-inclusion. They will not become good partners doing the same thing without inter-inclusion. Even at the level of nullification, which we likened to their being melted together, they will not work together on a common project.

The example of chaos and rectification in the Torah is that of Jacob, who is like general relativity and Esau, who is like quantum mechanics (as we mentioned earlier, Noah discovered special relativity. Then came Jacob and Esau). And they are not going to jive unless some inter-inclusion will be found to connect them. This is something that the Rashash teaches, that even extreme opposites like tohu and tikun do possess some inter-inclusion and that is the only way to unify them.

Unifying determinism and free-will

One last topic that we need to address is that of determinism. It is well known that Einstein preferred determinism, he did not like to think that God was playing dice with the universe. Again, Einstein did not like quantum mechanics’ seeming allowance of free-will due to probability. But, the Torah tells us that free-will is one of its most basic and fundamental tenets. Quantum mechanics allows a lot more freedom. General relativity, on the other hand, follows Einstein’s preference for determinism. So deep down, unifying general relativity and quantum mechanics also depends on our ability to solve the paradox of God’s omniscience (determinism) versus man’s free-will. General relativity is like God’s omniscience. Quantum mechanics is like our freedom of choice.

Ultimately this goes back to the right and the left. Right is omniscience, while the left represents free-will. The angel of Esau is called the samech mem (alef lamed), which is a variant spelling of the Hebrew word for “left” (שְׂמֹאל). In the weak interaction (force) the left remains the left, it does not interchange with the right. In other words, because the weak force does not preserve parity, the samech mem, the left there, remains the samech mem, Esau’s angel. Nonetheless, he too has to do teshuvah, meaning he has to change. Until, as the prophet says, finally, “Death will be swallowed up, forever,”[2] meaning that Esau’s angel, the samech mem, will eventually be swallowed up in a black hole.

We will explore black holes and how they swallow things later. We will then also better understand how to achieve unity between quantum mechanics and general relativity.

Lecture 5

Back to symmetry

We will now continue to talk about symmetry. Symmetry is one of the most important concepts in modern science. Last time we spoke about CPT symmetry, which stands for Charge, Parity, Time. Symmetry in modern science is used in the sense that if you interchange or reverse two complementary concepts, then the end result will be the same, meaning that you will not be able to distinguish between the universe that you began with and the universe that you arrived at after your interchange.

If all the electrons in the world would suddenly change into positrons, and all the positrons would change into electrons, then you would not be able to tell the difference. Parity symmetry means that if right and left reverse, which is basically that you would be looking at the universe through a mirror, then everything would remain the same, you would not be able to tell the difference. Time symmetry is the most difficult to understand because it says that if you reversed the order of things, everything would still remain the same. Time symmetry is the most counter-intuitive of the three and it is very difficult to understand what it means.

But, as we mentioned before, none of these symmetries is complete by itself. Instead they are complete only in conjunction. Meaning, that if all the charges would reverse, and all the directions, the spatial extensions, and time would reverse, only then would you still see the same universe that we have now.

We mentioned that time relates to the mind, the intellectual level of the soul, while charge relates to the emotional attributes of the soul, and parity relates to the habitual or behavioral faculties of the soul.

Now let us turn to two additional examples of symmetry that emerge from modern physics.

Size does not matter

There is a symmetry principle, which derives solely from string theory considerations, which is the most amazing type of equivalence that can be imagined and this principle is denoted by the simple equation R = 1/R, where R is the radius of the universe, which is very large, millions of light years. And yet, what this equation says is that our huge universe, which is billions of light years across, is no different from a universe that is so tiny that it is inconceivably small, much smaller than even a photon. A universe with radius R is equivalent to a universe with radius 1/R. In other words, there is no difference between big and small.

“He who is large is small (and large)”

Every thought which has any truth to it must have a source in the Torah. This very last thought, has a very explicit source in the Zohar which reads: “He who is very small is very big, and he who is very big is very small.”[1]

What this implies of course is that a person who in his own eyes[2] is very small—he is very humble—from the perspective of the Almighty, that person is actually very great. In this world, which is the world of deceit, he is small, but in the world of truth, he is very big. And the opposite is also true, a person who in this world considers himself to be very big, great, and outstanding, in the world of truth, from the true perspective of the Almighty, he is actually very small.

What string theory adds to the regular interpretation of this statement from the Zohar, is that both sides of the statement are true—simultaneously! The usual interpretation is that if you consider yourself to be small, in truth you are big, and if you consider yourself to be big, in truth you are small, or insignificant. But, now we are saying that to be very small is to be very big. Both are true simultaneously. So symmetry is telling me that I cannot tell the difference between the two things. Big and small are entirely equivalent. It is not just a question of perspective; they really are exactly the same. Again, this is the most counterintuitive result of modern physics. We usually think that we can tell the difference between big and small. Yet, here comes string theory and teaches us that we really cannot tell the difference between the two.

So we have just presented in short a symmetry principle, an equivalence principle, which is entirely different from CPT. It is much more than CPT symmetry.

Super-symmetry

Let us turn to super-symmetry. What super-symmetry says is that fermions and bosons can be interchanged. In this lecture we will begin talking about all the different types of elementary particles and what they have to teach us about our lives.

In general, in physics today we recognize two types of elementary particles: real particles and virtual particles. Real elementary particles divide into two categories: the fermions are the matter particles, and the bosons are the messenger, or force particles, which cause interactions. Examples of fermions are electrons and quarks, which make up the protons and the neutrons out of which matter is made.

The simple difference between bosons and fermions is in their spin. Elementary particles that have a half (or multiple of a half) spin are matter particles, or fermions. Elementary particles that have a whole (or a multiple of a whole number) spin are messenger particles, or bosons.

The concept of “whole” and “half” is straight out of the teachings of the 12^th century Kabbalist, Rabbi Avraham Abulafia. Abulafia explains that the world has to simultaneously have both whole and half. In Kabbalistic terminology, this refers to the masculine and feminine aspects of reality, where the “whole” represents the masculine and the “half” represents the feminine. In modern physics, these two aspects, whole and half, appear in the context of the spin of an elementary particle.

Spin

What is particle spin? You can think of spin as being the number of times that you have to rotate a particle in order to bring it back to its starting position, so essentially spin is a symmetry consideration, because we are asking, under what kind of rotation will the particle return to its initial state?

Particles can take on spin values of either half-integers (1/2, 3/2, ...) or whole integers (1, 2, ...). Matter particles (fermions) have 1/2 spin while messenger particles have whole integer spin. Strangely, this means that electrons (fermions) for instance have to be spun twice to return to their initial state. Following the Kabbalistic terminology noted above, we can relate matter particles, which have spin values of half integers, to the feminine aspect of reality and messenger particles, which have multiples of whole spin, to the masculine aspect of reality.

Super-symmetry is fairly simple to express: if you would exchange all the fermions for bosons and all the bosons for fermions, the universe would stay the same and you would not know the difference. In our spiritual language, you could say that if all the men were exchanged for women and all the women were exchanged for men, then the universe would stay the same and you would not be able to tell the difference.

Super-partners

What super-symmetry implies is that every particle has a super-partner. The partner of every elementary particle that we know of has spin exactly ½ less than that particle. This means that every matter particle has a messenger-particle partner lurking somewhere in the quantum world, but these super-partners have yet to be found.[3] The same is true for every messenger particle with whole spin. It too has a super-partner, with spin ½ less, which identifies it as a matter particle.

It is important to stress the difference between anti-particles and super-partners. These are not the same at all. Every particle has an anti-particle, which has negative the amount of electrical charge that the particle has. But, with respect to super-symmetry and super-partners we are dealing with the particles’ spin and claiming that every particle has a super-partner with ½ less spin than it has. If these super-partners would be found, it would prove super-symmetry. This would not yet prove that super-string theory is correct, but it would support it.

Why is it so difficult to find these super-partners? The problem with observing these super-partners is that they are very heavy, which means that you need a lot of energy to create them and they exist for a very short amount of time. This is also a counter-intuitive notion, because we would think that the bigger something is, the easier it should be to observe it. But the bigger the elementary particle is, the less time it exists, giving you less time to find it. One of the objectives of building bigger and bigger particle accelerators is to be able to create heavier particles. One of the hopes is that in these new, more powerful accelerators we will be able to observe the conjectured super-partners of super-symmetry.

Super-symmetry and the sanctification of marriage

The Torah allusion to super-symmetry, which states that the two basic types of particles, bosons and fermions, can be interchanged, is to be found in the beginning of the second chapter of the tractate of Kidushin, the Talmudic tractate that deals with marriage and the sanctification of a woman by a man. The mishnah states that the husband can sanctify a woman in marriage either himself or by messenger, and the woman can accept the sanctification of marriage from a man either herself or by messenger. In other words, the groom can give the wedding ring (or an amount of money) to a messenger to take to a woman, who perhaps lives far away, in order to sanctify her to be betrothed to him. The messenger can then go to the woman and sanctify her on behalf of the person who sent him. The same is true of the woman. She can receive the ring directly, or she can send a messenger to receive the ring.

The Hebrew wording of the mishnah leaves it open to a simple misunderstanding. In the original Hebrew, the conjunction connecting “himself” with “by messenger” is what is usually understood as the “and” conjunction.[4] Nonetheless, this is not the simple, literal meaning of the mishnah, for sometimes the conjunctive “and” is understood to mean “either/or.” So though one might conclude that both forms of sanctification—in person and by messenger—are needed in order to get married, but this is not the case. A man can sanctify his wife either himself, in person, or by messenger. He does not have to do both.

Virtual particles and literal readings of the Mishnah

Nonetheless, many times, a Kabbalistic interpretation can reveal how the literal meaning is also correct. In this case, the Kabbalistic interpretation would be that the mishnah is also alluding to our subject of matter and messenger particles.

The man sanctifying a woman symbolizes the matter particle. His messenger sent to sanctify the bride symbolizes the messenger particle. What modern quantum mechanics has revealed is that every direct interaction between particles involves both matter and messenger particles, which are actually virtual particles.

In order to describe this process one needs to use diagrams developed by Richard Feynman, a Jewish physicist from Caltech, and considered by some to be the greatest physicist after Einstein. Feynman diagrams reveal how whenever there is a quantum interaction, even a direct interaction like an electromagnetic interaction between two electrons, both sides actually exchange messenger photons, which are virtual particles.

Going back to the mishnah. First let us say that perhaps the greatest example of interaction in the Torah is that of a man sanctifying a woman in marriage. Whenever there is an interaction, at some level, there are either actual or virtual messengers that are being passed back and forth to facilitate the interaction.

Two fires

Let us see another example of this. In Hebrew, “man” is אִישׁ, and “woman” is אִשָּׁה. They share the two letters alef and shin (אש). The two remaining letters from the two words are yud (י) and hei (ה), whose values are 10 and 5, respectively. So, in terms of their gematria, yud and hei have a relationship of a whole and a half. The combination yud-hei (י־ה) is also one of God’s Names. Thus, Rabbi Akiva says that if a man and a woman merit to manifest the yud of the man and the hei of the woman and to unite them into a holy Name, then the Divine Presence dwells between them. If they do not merit to manifest and unite these two letters, the two left-over letters in each word alef and shin, which together spell “fire” (אֵשׁ) will consume them. This fire is either the fire of unholy passion, or the fire of anger. If the yud and hei are united, then the fire becomes holy fire, the fire that consumes the sacrifices in the Tabernacle.

Everything the Torah describes regarding the service that takes place in the Tabernacle alludes to secrets of both creation and the secrets of the Divine chariot. So now, based on this particular reading of the mishnah, both the man and the woman have a messenger in addition to being able to sanctify in person. These messengers are like angels. In fact, we usually explain that everything in the world of quantum mechanics, all the elementary particles can be understood as angelic “entities.” This is especially true of the force particles, which act as messengers. So, if the male and the female both have messengers, then the male fire represents both the male and his messenger, and the same goes for the woman.

In the beginning of the Song of Songs, we find the phrase: “…support me with fires”[5] (סַמְּכוּנִי בָּאֲשִׁישׁוֹת). In the Temple there were two fires that simultaneously burned on the altar and consumed the sacrifices that were placed on it. The first was a fire that came from below, meaning that it was lit by the priests. That was the feminine fire. In direct response to the fire brought from below, fire would descend from heaven. That was the masculine fire. These are the two fires that are referred to in this phrase.

So, as we said, both the man and the woman have the two letters alef and shin in common. The shin, the initial letter in the word “messenger” (שָׁלִיחַ), is common to both the male and female.

There is a question raised in the Talmud about what happens if the messenger has “second thoughts.” I send him to sanctify a woman, but when he meets her he decides to sanctify her for himself. This creates all kinds of problems, but in quantum mechanics this corresponds to an example of super-symmetry, because the boson (the messenger) has decided to become a fermion (a matter particle). The messenger has transformed into the person sanctifying. The same is also true for the woman.

Three symmetries and three aspects of love

We have now seen three different examples of symmetry:

• CPT (Charge Parity Time)
• Size equivalency
• Super-symmetry

Each of these is totally different from the others. To give these three a model, we refer to the three parts of the second verse of the Shema: “And you will love God with all of your heart, with all of your soul, and with all of your might.” The three aspects of the love of the Almighty are thus:

• Love with all of your heart
• Love with all of your soul
• Love with all of your might

CPT and the heart

The sages say that to love with all of one’s heart means to love God with both the positive and negative inclinations. Meaning, that one has to reach in one’s consciousness an equivalency, a symmetry, or parity between the left and right sides of the heart (which are explained in the Tanya to harbor the negative and positive inclinations, respectively). As explained earlier, parity symmetry must come together with time and charge symmetry. Earlier, we saw how CPT correspond with the intellectual, emotional, and habitual faculties (in the order of time, charge, and parity). Now we are saying that as a whole, since they must go together, they correspond to the intellectual, emotive, and habitual faculties within the heart in itself.

Meaning, that from whatever angle of your heart, whether it be the habitual, the emotive, or even the innermost aspect of the heart, its intellect, you should have parity between the good and evil inclinations. Practically, this means that we have to be flexible enough to change the way in which we serve God, as explained before in relation to the Akeidah (the Binding) of Isaac. Even if my primary way of serving God is through fear (or awe), being flexible enough to also serve through love opens up the same possibility for someone who serves out of love.

Super-symmetry and the soul

Super-symmetry corresponds to loving God with all of one’s soul. Why? One’s soul represents one’s function or role in life.

Feynman’s explanation for the paradox inherent in the quantum world was that in reality all possible paths are taken simultaneously. In order to figure out why a particle reaches a certain destination, you have to sum over all the possible paths that lead to that destination. Sometimes, there could be an infinite number of possible paths. Nonetheless, we have to take the sum over all of these possibilities in order to fully describe what happened.

Now, in life, sometimes I am trying to reach some goal and then all of a sudden I realize that perhaps I have to take the completely opposite direction to get to that destination. CPT symmetries mean that possible paths that involve opposite directions along parity, charge, and time also have to be summed in order to get the final outcome. Sometimes I have to change my left with my right to reach the goal, or change charge, or go backwards in time.

But, super-symmetry is not just a change of path to get to the same outcome; it represents a complete change in one’s “goal,” as it were. CPT symmetry is a change of path, but not a change of goal.

One way to see this is in Rebbe Nachman’s story of the Seven Beggars.[6] People were trying to reach the Tree of Life, but each one thought that there is a different path to reach it. It was impossible to make peace between these people because each had a different idea on how to reach the goal. Rebbe Nachman explained that the difference in directions is a consequence of the different goals that they have. Each person in essence possesses characteristics that suit the goal that he or she is trying to achieve.

We see this same problem in politics. Take for instance the politics of the Jewish people today. We have many groups, each with good intentions, all striving to reach peace on earth, but they do not agree with one another, because they each have a different path. So, people will never really agree on the path to take unless they find someone who can already embody the goal that they are trying to achieve. If we see someone living already with the goal that we are looking for, someone who is already experiencing this reality, then we might be able to agree on the path. This is like the Rebbe teaching us that to get to the revelation of the Mashiach we have to first live with Mashiach, we have to embody the very goal that we are seeking. Only then can we come to agree on a common path.

But, now returning to super-symmetry, we say that it is not just about changing one’s direction, one’s path, but changing the goal, changing one’s “mission statement.” In the language of physics, are you a boson or a fermion? Super-symmetry is thus about changing one’s purpose in life, one’s very identity. Super-symmetry implies that if all the goals were interchanged, the world would stay the same.

To be able to change one’s mission in life requires sacrifice. In a sense, it requires dying in order to become something else. To reach your super-partner you have to sacrifice your life, your very purpose. This is what is meant by the words “with all of your soul,” which the sages explain means, “Even if He [God] claims [takes] your soul.” The Arizal says about this that if a person has fulfilled his mission in life, the night following that day on which the function was fulfilled is very dangerous. Every night when a person is asleep, the soul goes above. On this night, it will be told that it has finished its work. The only way to remain alive and come back down is by assuming a completely new function, a completely new purpose for one’s life. This is one of the simplest intentions of the verse: “My soul, I long for you at night.”[7] The only way to claim my soul back is by sacrificing myself, sacrificing my identity. This is the only way to make it through that night. This is like a fermion becoming a boson. So much for the second level and aspect of loving the Almighty.

Size symmetry and one’s infinite nature

The third level of love is above even self-sacrifice and is described in the verse as “with all of your might.” How can something be more than sacrifice? One reading that is given by the sages, which is difficult to understand, is that “with all of your might” means “with all of your money.” It is sometimes more difficult for a person to give up all of his money, to give up his bank account, than it is for him to give up his life. How can we understand this?

One simple explanation is that giving up one’s bank account is like giving up what one will bequeath as an inheritance to one’s offspring, to coming generations. Spiritually, this is like giving up one’s power to procreate, which in Chassidut is a manifestation of the power of the infinite in each person, because the power of procreation, the power to give birth and to sustain one’s self through one’s offspring, is an infinite power, the most powerful of all human abilities. Thus, giving up all of one’s possessions, all of one’s might, all of one’s money, is like giving up all of one’s future generations; all that one would have bequeathed to the coming generations. So giving up one’s continuity is definitely more difficult than giving up one’s present identity.

But, let us see another explanation. Literally, the word that we usually translate as “with [all of] your might” (מְאֹדֶךָ) does not mean “might,” rather it means “very much.” This is one’s most extreme being. What is this “very muchness”? For many people this is indeed their bank account. This is exactly the idea behind the final form of symmetry derived directly from string theory. Being able to accept that size does not matter; that being small is exactly the same as being big. Translated into wealth this means that even if you are very wealthy it is exactly the same as being very poor.

In reference to money, the sages use a metaphor to capture the idea of the big being equivalent to the small. They state that wealth is like a wheel that revolves in the world—a wheel of fortune. Normally, the symbol of the wheel is meant to give a person the understanding that even if right now you are at the very top of the wheel and you have wealth, nonetheless, the wheel revolves and either you or your children will someday find yourselves at the bottom of the wheel. And likewise, even if now you are at the bottom of the wheel and poor, at some later time, either you or your children will find yourselves on top.

But now, what size symmetry, as derived directly from string theory, is saying is that there is no time-dependence, as it were. Being big and being small, being rich and being poor, being on top and being on bottom, they are exactly the same.[8] Not only that, they are happening simultaneously. Even if you are at the very top right now, you are really also at the very bottom, on a wheel there is no difference between top and bottom. If you are very, very big, you are also very, very small. This is the ultimate realization in pursuing love of the Almighty. If a person can reach this consciousness then that is giving up his “very muchness.” Every person has an infinity to him, which is his “very muchness,” which is much more difficult to give than giving up one’s finite being.

“With all your heart” means being able to switch careers. Super-symmetry thus implies that we should, like the Lubavitcher Rebbe said, never retire. Always find some new goal to pursue. Even when you have finished one career, pick up a new one.

R=1/R means being able to surrender one’s sense of being infinite, be that infinity the infinitely small, or the infinitely great.

Lecture 6

Her path

The Book of Leviticus begins with the verse, “A man who sacrifices from among you a sacrifice to God.” The sages state that the word “a man” (which in Hebrew is “Adam”) alludes to the rectification of Adam, the first man. As explained in Chassidut, the word “from you” means that the sacrifice has to be from one’s self. As the Alter Rebbe explains, this means that in order to properly bring a sacrifice, you first have to have the intent that you are bringing yourself (i.e., your own animal soul) and sacrificing it, and only then can you bring an actual animal sacrifice to place on the altar, where this animal then comes as a substitute for your own animal soul, which you are ready to sacrifice. This is similar to the second level of love, “with all of your soul,” which we discussed in an earlier lecture.

In Kabbalah, when considering the symmetry of words or phrases, we first count the number of letters in the word or phrase. When there is an odd number of letters, there is a letter in the middle, which can be seen as the axis of symmetry, and we say that this word or phrase exhibits masculine symmetry. But, if there is an even number of letters, there is no middle letter that can serve as an axis of symmetry, therefore the symmetry of the word or phrase reflects around an imaginary axis of symmetry (between the two middle letters). We say then that a word or phrase comprising an even number of letters exhibits feminine symmetry.

The phrase out of Leviticus we just quoted has 6 words in it (אָדָם כִּי יַקְרִיב מִכֶּם קָרְבָּן לי־הוה). Of these 6, four have an odd number of letters, so they have a middle letter. In Kabbalah, many times, when there are middle letters, we focus on these letters themselves.

The middle letter of “a man” (אָדָם) is ד.

The middle letter of “who sacrifices” (יַקְרִיב) is ר

The middle letter of “among you” (מִכֶּם) is כ.

Finally, the middle letter of “to God” (לי־הוה) is ה.

Together, these 4 letters spell the word, “her path” (דַּרְכָּהּ), where the word “way” (דֶּרֶךְ) here is in the feminine possessive form.

Wisdom’s path and location

In the language of the sages, this word, “her path” appears often, especially in the context of “the path of Torah.”[1] But, interestingly, this word appears only once in the entire Bible. It appears in a verse in the 28^th chapter of Job. The 28^th chapter of Job is such a unique and important chapter that the sages gave it a special name (there is no other chapter in the Bible that they gave a name to). They called it “the chapter of wisdom.”

Wisdom obviously refers to the wisdom of creation, as another verse states: “You created everything with wisdom.”[2] Even the first word of the Torah, “In the beginning,” alludes to wisdom, as in the verse “The beginning of wisdom….”[3] One of the most important and famous verses from the 28th chapter of Job is, “Wisdom is found from nothing and where is the place of understanding” (וְהַחָכְמָה מֵאַיִן תִּמָּצֵא וְאֵי זֶה מְקוֹם בִּינָה). Towards the end of this same chapter we find a verse, which contains the only appearance of the word “her path” in the entire Bible. This verse is, “God [and God alone] understood her path [the path of wisdom—wisdom has feminine gender in Hebrew], and He [and He alone] knows her location”[4] (אֱ־לֹהִים הֵבִין דַּרְכָּהּ וְהוּא יָדַע אֶת מְקוֹמָהּ).

There is a verse that describes wisdom as one’s sister, “Say to wisdom, You are my sister,”[5] meaning that a person should relate to wisdom as one relates to one’s sister, in a very close and intimate way. Even a man’s wife is sometimes called his sister.

Again, we came to this verse because of the middle letters, the letters that act as the axes of symmetry, in this phrase from the beginning of the Book of Leviticus.

Let us just for a moment give a numerical allusion here, which is very beautiful, in and of itself. The value of the entire phrase “A man who sacrifices from you a sacrifice to God [Havayah]” (אָדָם כִּי יַקְרִיב מִכֶּם קָרְבָּן לי־הוה) is 905. Subtracting the symmetry axes letters that spell “its way” (דַּרְכָּהּ) and whose numerical value is 229, we find that the numerical value of the remaining letters is 676, which is 26 squared. 26 is of course the value of Havayah, God’s essential Name.

Since this word “her path” (דַּרְכָּהּ) appears here in a very interesting way, when meditating and analyzing this phrase, we are motivated to find where else the Torah relates to this verse and how that helps us better understand its meaning. There is a simple principle that there is nothing that is not alluded to in the Torah. So again, the word “her path” (again, in the feminine form) appears only once in the entire Bible. As we have already said, we find it at the climax of the chapter of wisdom in Job.

God, the uncertainty principle, and Einstein

Now, let us look at this verse, “God understood her path, and He knows her location”[6] (אֱ־לֹהִים הֵבִין דַּרְכָּהּ וְהוּא יָדַע אֶת מְקוֹמָהּ). What is the first thing that comes to mind when relating this verse to our topic of modern science and its relationship to our service of God. This verse is talking about path and location. Quantum mechanics postulates that it is impossible to simultaneously know both the path (which implies the momentum and the velocity) and the position of a particle. This is called the uncertainty principle, the deepest principle of quantum mechanics and the bottom line of this whole theory. In an earlier lecture, we explained that this is not just a problem with the observer’s measuring capabilities, this is something inherent in nature. It is simply impossible to know simultaneously both the path (the trajectory) which implies the momentum and velocity vector of a particle and its position.

Now, what is this verse saying? Actually, it is saying exactly what Einstein said when he heard that the uncertainty principle was somehow inherent to nature: “God does not play dice with the universe.” It did not sit well with him that God cannot see beyond the uncertainty principle. Little did Einstein know that he had a verse in the Bible to support his intuition that God does know. This is the climactic verse of the chapter of wisdom that states exactly what he felt. Indeed, it says that God does know, indeed God is the only one who knows both the “path” and the “place,” i.e., the location.

Now, in this verse, God is referred to by the Name Elokim, which we know refers to nature, because it is the Name used in the account of creation appearing in Genesis. Elokim refers to the Divinity that is inherent within nature. And what this verse says is that Elokim, and only Elokim, understands the path and knows the position of wisdom (every elementary particle of nature is a point of Divine wisdom) simultaneously.

What causes the uncertainty principle?

Let us say something further about the implications of Elokim knowing the path and position simultaneously. Before the primordial sin, Adam was likened to Elokim. Mankind was destined to reach the level of consciousness of Elokim, as the verse in Psalms states: “I said [i.e., I desired] that you [mankind] be Elokim.”[7] But, because you ate from the Tree of Knowledge of Good and Evil prematurely, you fell to the level of just being a mortal man. Had you waited a mere three hours until the beginning of Shabbat Kodesh, then it would have been permissible for you to eat from the Tree of Knowledge. That is what it says in Kabbalah. It would have been the “oneg Shabbat” (the special pleasure of Shabbat) to eat from the Tree of Knowledge then. (Even though now in the Shulchan Aruch it says that there is a special mitzvah to taste the Shabbat dishes before Shabbat, when it came to the Tree of Knowledge, God explicitly forbade this.) But because man (Adam and Eve) ate from the tree prematurely, it resulted in the fall of mankind. The continuation of the same verse from Psalms, which refers to this fall says: “Yet, like a man you shall be mortal.” Meaning, again that God had in mind that we should attain the level of Elokim, but because of the sin we became mortal. This is referring to the human condition.

Now, Heisenberg said that the inability to know the path and velocity of an elementary particle is not just a problem with the observer, with the “human condition,” if you will, but it is a limitation within nature itself. In Kabbalah, we learn that when Adam fell from his original state, not only did his human psyche fall, but all of reality, all of nature, collapsed and descended 14 degrees. It is as if there was a wave collapse of all reality when Adam sinned, and this introduced a mortal consciousness into nature, one that does not allow path and position to be known together. Again, originally, before the primordial sin, nature did not limit the observation of a particle’s path and position simultaneously.

Now it is even more interesting that this verse is not just telling us that there exists a potential state of consciousness where one can know both path and position simultaneously, it is also telling us how to reach that state. As we shall explain in a moment, symmetry plays a key role in achieving this state of consciousness. If one is perfectly symmetric, one indeed becomes like Elokim (as God had initially intended).

Verses with perfect symmetry

To see this we first have to look at the Masoretic note on this verse, a note that was left to us by the final editors of the Bible who lived in the Land of Israel some 1200 years ago, in the time of the Ge’onim. They are known as ba’alei hemesorah, the masters of the Masoretic tradition. They finalized the Bible in regard to every word’s vocalization (nikud, in Hebrew) and cantillation marks (trope, in Yiddish, or ta’amim, in Hebrew). These sages also wrote notes regarding the text of the Bible. These notes are mostly about the frequency of rare words in the Bible. But, on a few occasions they alert us to some very unique phenomena in the Bible, phenomena that no one would ever think of pointing out.

One such example, perhaps the most beautiful, is found on this verse. The Masoretic sages noted that there is a phenomenon in this verse that is repeated three times in the Bible, once in each part of the Bible: once in the Five Books of Moses, once in the eight books of the Prophets, and once in the eleven books of the Writings. What is the special phenomenon? It is that these three verses comprise 7 words each and all three are symmetric around the same middle word, “and he” (וְהוּא). So the structure of these three verses is “word₁ word₂ word₃ וְהוּא word₅ word₆ word₇.” What these three verses possess is perfect symmetry. The verse that we have been looking at is the last, the one from the Writings.

The verse from the Prophets is: “A generous person advises generosity and he will stand on his generosity,”[8] or in Hebrew:

וְנָדִיב נְדִיבוֹת יָעָץ וְהוּא עַל נְדִיבוֹת יָקוּם

The generous person is the description of a person who donated to the construction of the Tabernacle. This verse contains another rare phenomenon: the root for “generosity” (נדב) appears three times. A person who is generous himself gives others the advice that they too should be generous. The root for the word “advice” (יעץ) is related to the word for “tree” (עֵץ).

Now, the Mashiach is called one who gives wondrous advice (פֶּלֶא יוֹעֵץ). People are always looking for counseling. Today some counselors are called coaches. The purpose of a good counselor is to rectify your tree. The word for “counsel” or “advice” in Hebrew comes from the word for “tree.” The most wondrous counsel, the Messianic counsel, is to be generous. The only one who can give this type of advice is a person who is essentially altruistic and generous. Every person has to have a counselor today, which in Chassidut is called a mashpia. Every person today should himself strive to become a mashpia. To be a counselor you have to be a generous soul. It is best to have both physical and spiritual affluence from which to be generous. In any case, in virtue of his generosity and his advice to others that they too be generous, the generous soul will stand up.

“Standing up” here also alludes to the resurrection of the dead (תְּחִיַּת הַמֵּתִים). Rashi says that his “stand” is his ability to “stand up” in the national sense, the entire Jewish people standing up, as in the phrase, “I [God] will lead you erect”[9] (וָאוֹלֵךְ אֶתְכֶם קוֹמֲמִיּוּת). Interestingly, in Modern Hebrew, the word for “universe” is יְקוּם (yekum), like the last word in this phrase. In Modern Hebrew “world” is translated as עוֹלָם (olam), whereas “universe” is translated as this word, יְקוּם. Because yekum comes from the word קַיָּם, which means “exists,” so “universe” is taken to mean “everything that exists.” When Adam sinned, he fell, and he will stand up to eternal life in virtue of generosity. So this is the verse from the Prophets.

The verse from the Five Books of Moses that exhibits this symmetry is: “From Asher, his bread is fat, and he will give the delicacies of the king,” or, in Hebrew:

מֵאָשֵׁר שְׁמֵנָה לַחְמוֹ וְהוּא יִתֵּן מַעֲדַנֵּי מֶלֶךְ

This is the verse with which Jacob blessed his son Asher. The Lubavitcher Rebbe was very fond of this verse because he was born on the day the prince of the tribe of Asher, (which means “happiness”), brought his communal sacrifice to the Tabernacle—the 11^th day of Nisan. The Rebbe explained that the name Asher specifically relates to “commitment with happiness,” meaning that accepting the yoke of heaven leads to the greatest happiness.

Jacob, who spoke this verse, is also known as “Israel” (יִשְׂרָאֵל) whose value is 541, and so is the value of first word, “From Asher” (מֵאָשֵׁר). Thus, the name Asher is seen to reflect the entire Jewish people. The verse’s second word, “is fat” (שְׁמֵנָה), has the same letters as the word for “soul” (נְשָׁמָה). So these are the three perfectly symmetric Shabbat-like verses with the word “and he” (וְהוּא) in the middle.

Symmetry hidden in the verses

Now let us make a very beautiful numerical observation. The symmetry axis word is “and he” (וְהוּא), and its gematria equals 18. But, what happens if we calculate the value of this word's four letters using what is called mispar keedmee (מִסְפַּר קִדְמִי), which literally means the “primordial numbering.” In number theory, this is what is called a “triangular number.” The n^th triangular number is the sum of integers from 1 to n. To calculate the triangular value of an entire word we sum the triangular values of each of its letters.[10]

In this case: the first letter vav (ו) equals 6, and the triangle of 6 [written: △6] is equal to 21. The next letter is hei (ה). It equals 5 and the triangle of 5 [△5] is 15. The third letter is vav again and its triangular value is once again 21. The fourth and final letter is alef (א), its value is 1 and the triangle of 1 [△1] is just 1. Finally, the sum of all four triangular values is: 21 + 15 + 21 + 1 = 58.

As we saw in a previous lecture, the Hebrew word for “symmetry” is חֵן, and its numerical value is 58. So the numerical value of the axis of symmetry of these three uniquely symmetrical verses in the Bible is the same as the numerical value for the word for “symmetry,” in Hebrew! We have here a beautiful allusion, and self-reference, to the symmetry inherent in these three verses. In more depth, we might contemplate how these three verses correspond to the three general types of symmetry that we talked about in our previous lectures.

One of the special Names of God discussed in Kabbalah is the Name of 72, which is actually made up of 72 triplets of letters (216 letters in all). One of these triplets is אום. You might note that these three letters are the initial letters of our three verses. So this meditation is an expansion of that Name. So we can now say that this special Name is an allusion to the three different types of symmetry.

Path mentality, position mentality

The Divinity within nature does simultaneously know the position and path of an elementary particle. This is the rectified state of the Tree of Knowledge. What does it mean that there is a Tree of Knowledge of Good and Evil. Why did Adam lust after this tree? The literal understanding is that if you eat from this tree you can know good and evil, simultaneously. As we will explain, to know good and evil simultaneously opens up a third type of dimension that science is not yet aware of. If science would know about this dimension it would most probably solve many, if not all, of the outstanding problems in science.

But for our purposes here, what is the difference between the path that something is taking (a particle, or the path of wisdom) and its position? Path implies velocity and momentum, and place implies position. Above, we talked about the difference between messenger consciousness and matter consciousness; about whether you are a fermion or a boson. Now we will apply this to something similar. There is a person whose consciousness in his life focuses on a path. He is always on the go towards some objective. He is a “walker.” A Jewish soul is supposed to be a “go-er,” one who is always moving towards a certain goal. This is one of the reasons why halachah is called by this name, because just as much as the law seems to be a fixed statute, there is always some inherent flexibility within the law because a law is not static. So this is one type of mentality that people have, being on the go and moving towards a goal.

There is another different type of mentality connected with being static, with having a space. A person wants to have his space, and he is happy in his space. The Rebbe Rashab explained that if a person wants no one else to enter his space, this type of mentality becomes baseless hatred (שִׂנְאַת חִנָּם) and is the reason for the destruction of the Temple and for our remaining in exile for so long.

So here we have a simple way of understanding why these two, movement and space do not go together. When a person is moving, really on the go, he does not ask himself where he is. Either you’re on the go or you’re stationary. This is a very simple way of understanding the uncertainty principle. To think about where I am requires a feeling of self. When a person is on the move he cannot ask himself, “Where am I?” So you cannot really be moving and ask yourself at the same time, “Where am I?” Only God can have both attitudes at the same time.

These two attitudes are actually the same as “good” and “evil.” Good is a good path. To be “good” is to be on the path, to be going somewhere. If you are really on the way, you are really not in any particular place. As soon as you are “someplace,” you have stopped. To continually be on the move is the “good news” of the one side of the uncertainty principle. If you are on the go, you do not know where you’re at. So not having a place is actually a good thing.

But, if you are concerned about where you are at, you are no longer moving, no longer on the way and do not know where you are going. You have lost awareness of your way. To know your way is good, to know where you are at is bad. So, in this sense, the primordial tree is about knowing “good” and “evil,” knowing both where you are at (evil) and still knowing where you are going (good).

The Arizal explains that if Adam would have waited three hours before eating from the Tree of Knowledge, it would have been Shabbat already, and it would have become permissible to eat from the Tree of Knowledge. It would have been a mitzvah to eat from this tree. This is because on Shabbat we have Divine consciousness and knowing where you are at (I'm here, but not yet where I should be) actually gives you additional momentum to follow your path in life. In this state, the evil becomes a seat, a foundation for good.

Adding dimensions

Let us now discuss the fact that the three symmetrical verses we mentioned earlier each contains 7 words. The first thing that comes to mind when contemplating the number seven in the context of modern physics and all our considerations of time and space is that most of mankind has set the week for some seemingly arbitrary reason as 7 days. Arbitrary, because nobody actually imagines that nature possesses some kind of phenomenon that corresponds to this cycle of seven days that make up each week. A year corresponds to some phenomenon in the natural world (the revolution of the earth once around the sun), so it is not arbitrary. But, going one step further, even a year is arbitrarily man-made, because it is a cycle that has meaning only on Earth. Outside the Earth, if you were living on Jupiter for instance, one revolution around the sun takes a much longer period of time. So in short, we can generalize and say that all our time cycles, days, weeks, months, and years are not considered by scientists to be inherent cycles in the dimension of time. Instead, they record or measure some local phenomena, such as the movement of the earth, etc.

Above, we noted that when string theorists today add dimensions in order to unify the forces in nature, they only add space dimensions. Nobody today entertains the notion of adding time dimensions. What science knows for sure is that in our world there are three space dimensions and one time dimension.

Now, why do scientists not add time dimensions, only spatial ones? One scientific text even questions this supposition, and indeed asks, why not add time dimensions? The simple answer is that to try to imagine another time dimension is very counter-intuitive—much more so than imagining additional spatial dimensions. Since we already have three space dimensions, it does not seem so strange to add a few more!

Curled-up space dimensions

In order to explain why we do not experience more than three space dimensions, string theorists explain that the additional dimensions are curled up. There is a simple analogy given in books on string theory in order to help us imagine what a curled up dimension might be like. This is called the garden hose analogy. Imagine a garden hose that is strung out between two buildings. If we look at it from a great distance, it seems like a one-dimensional line. But, from the perspective of an ant walking on the hose, there is of course another circular dimension on which it can walk. Now what happens if the ant decides to walk around the hose? From my perspective, from afar, the ant would seem to suddenly disappear; it is as if it went out of existence, because I cannot see that the hose has another dimension. This is the conceptual way that curled up dimensions are described. This is a very simple, balebateshe (layman’s) explanation.

But now let's think of our garden hose as the dimension of time, not of space. What would it mean to have a curled up time dimension? It would mean that there is some inherent cycle that is running around (or inside) the straight coordinate of time. Maybe this cycle is the week, maybe this is the secret of Shabbat.

Additional dimensions in Kabbalah

Interestingly, the Arizal does not speak explicitly of additional spatial dimensions. However, in the later Kabbalistic writings of the Rashash (who lived in the 18^th century), he explains that in order to solve some inherent contradictions that come about because of spatial contradictions in the Arizal’s writings, you have to assume that there are indeed more than three spatial dimensions. So the Rashash says explicitly that we have to add spatial dimensions to the Arizal’s Kabbalah in order to understand it. But, what about time dimensions, the Rashash does not say this explicitly, but actually adding time dimensions in the Arizal’s system is much more obvious and natural. This is because the Arizal himself explained that there are different cycles of times, which in the higher worlds are represented by totally different partzufim (personas) and it is only natural to attribute a separate time dimension to each of these cycles.

Let us stress that in a certain sense, it is much easier to understand that the curled up dimensions required by string theory are time dimensions and not spatial dimensions. Once more, according to string theory, there are 3 extended spatial dimensions that we experience normally, and an additional 6 curled-up dimensions. Exactly what it means that these curled up dimensions are spatial, is very difficult to understand. They are so small that you cannot detect them, which is why the garden hose analogy is introduced.

The most important thing about time is that there are cycles of 7; e.g., the seven days of the week, the seven years of the Shmitah cycle, etc. This was all parenthetical to our main topic, and we could have dedicated an entire lecture just to this subject of additional time dimensions curled up. It can mean something very obvious: that there are inherent, not just man-made, cycles of time, the most important of which is the Shabbat, which is how the world was created. So there is something about time that is based on the number 7.

Shabbat and the symmetrical verses

Usually, Shabbat is considered the seventh day. Sometimes it is considered to be the first of the seven days, from whose holiness all the other days of the week are blessed. But, most often in the writings of the Arizal, Shabbat is considered to be the 4^th day of the week. How is this?

From Wednesday to Friday we ascend from the World of Action, to the World of Formation, to the World of Creation. Finally, on Shabbat we ascend to the World of Emanation, the highest plane of consciousness (pure Divine consciousness). Then from Sunday to Tuesday, we bring the Divine consciousness of the World of Emanation (Shabbat consciousness) back down into reality. So on Sunday we descend back to the World of Creation, with the blessing received from the Shabbat. On Monday we descend to the World of Formation, again with the blessing of the Shabbat. Finally, on Tuesday, we descend into the World of Action with the blessing of the Shabbat. For which reason, the Arizal explains that a person who is engaged in work in the physical world should, if he can, limit his work to Tuesday and Wednesday. This would thus endow him with an extended weekend, beginning on Thursday and ending on Monday (with the reading of the Torah on the first, middle, and last day of the weekend). Tuesday and Wednesday (the two days that we are in the World of Action) would remain for devoting oneself to work in this world.

Now, we notice that this order of 3 days, followed by the highpoint that is Shabbat, followed by three more days, has the same structure as that underlying the three verses we discussed earlier: three words, then the word “and he” (וְהוּא), and then three more words.

Lecture 7

In this lecture we will continue our study of elementary particles in light of Torah.

There are three types of elementary particles. Two are referred to as real particles, and the third type is called virtual. As we will describe, these three types of particles correspond to the three Worlds of Creation, Formation, and Action. Virtual particles correspond to the World of Creation. The two other types of particles are bosons (force particles) and fermions (matter particles). Fermions—matter particles—clearly correspond to the World of Action, which is where matter exists, and bosons—force particles—most of which have 0 rest mass[1] (except for the particles of the weak interaction, the W and Z particles, which do have mass) clearly correspond to the World of Formation.

Let us summarize this in a table:

type of particle	World
virtual	Creation
bosons	Formation
fermions	Action

Virtual particles and the World of Creation

Virtual particles are not called that because they are unreal. All physicists agree that they exist. It is because they exist for such a short time that it is virtually impossible to identify and observe them. There are four types of virtual particles. They can be virtual bosons (virtual force particles) or virtual fermions (virtual matter particles). They appear in pairs, of positive and negative, as if out of nowhere, and immediately annihilate one another.

There are four sources of virtual particles. Three of these sources are a direct result of the uncertainty principle. These three consequences of the uncertainty principle are:

1)      any real particle can spontaneously emit any virtual particle,

2)      outer space (which is wrongly considered to be a vacuum) can also spontaneously erupt into virtual particles, which immediately annihilate one another,

3)      an electromagnetic field gives rise to virtual particles.

The fourth source of virtual particles comes from Feynman diagrams, where virtual particles are exchanged when an interaction takes place. Quantum mechanics posits that when there is an electromagnetic interaction, two virtual photons, which are messengers, make the interaction take place. A real photon is a particle of light. A virtual photon is “created out of nothing.” This is why they are related to the World of Creation. A “vacuum,” like space, is continuously creating virtual particles. Another reason virtual particles correspond to the World of Creation is that three of the four sources for virtual particles are a direct result of the uncertainty principle, which we have already identified with the counter-intuition of the World of Creation.

Based on the verse, “The concealed is for Havayah our God, and the revealed is for us and our children, forever,” Kabbalah teaches that the two higher Worlds, the Worlds of Emanation and Creation, are relatively concealed, whereas the two lower Worlds, Formation and Action, are relatively revealed. So, given that virtual particles are relatively hard to detect and observe, we understand them to correspond to the World of Creation, while force and matter particles, which can be detected, therefore correspond to the Worlds of Formation and Action, the revealed dimensions of reality. Only that the World of Formation is composed of forces, whereas matter exists in the World of Action. So we have here our three types of elementary particles.

Virtual particles and consciousness

Let us repeat that the virtual particles can be either virtual force or virtual matter particles. A very interesting thing is that there are some scientists who believe that conscious systems correspond to the level of virtual particles, or, put another way, that conscious thought is a result of virtual elementary particles, which once more are created ex nihilo. This is an amazing relationship. This is another reason to relate virtual particles to the World of Creation, which corresponds to the mind. Conscious systems in nature correspond to the World of Creation.

Now, we said before that with the primordial sin, when Adam ate from the Tree of Knowledge, all of these three worlds fell into a state of uncertainty. So that means that the conscious systems also fell 14 levels. Or, as we said before, that the very consciousness inherent within nature became mortal, which means that it became subject to existential uncertainty. Thus, these three types of particles exist in our three lower Worlds.

Three visions of the Divine Chariot

Now let us look at a more detailed chart based upon the previous one:

prophet	consciousness in World of	type of particles		type of angels
Isaiah	Creation	virtual	consciousness	Seraphim
Ezekiel	Formation	force (bosons)	Real	Living beings	strong	lion
weak	ox
e/m	eagle
gravity	man
Zachariah	Action	matter (fermions)	Horses

To understand the chart above, we have to know that Kabbalah teaches that there were three prophets who in their prophecy experienced the Workings of the Divine Chariot. They were Isaiah, Ezekiel, and Zachariah.

There are two secret subjects in the Torah: the Workings of Creation and the Workings of the Divine Chariot. “Workings of the Divine Chariot” refers to the purpose of creation. Three prophets had a vision of the Chariot, the purpose of creation. Each of them saw the Chariot from a different perspective.

The highest vision was Isaiah’s, whose consciousness was in the World of Creation. Ezekiel’s consciousness was in the World of Formation. Zachariah saw his vision in the World of Action. Because their consciousness was at a different level, each saw a different image of the Divine Chariot. The components of these Chariots are angels, and in each image the angels were of different types. We already mentioned in one of our previous lectures that angels can be understood as elementary particles. In each vision they saw the Chariot driven by different angelic beings. Of course, the most well-known is Ezekiel’s vision, appearing in the first chapter of his book.

We will start from the bottom. Zachariah saw the Chariot as a chariot driven by horses (מֶרְכֶּבֶת סוּסִים).[2] To see the purpose of creation at the level of matter is seeing horses. In the world of Action, it is all just one big horse-race. And the matter particles appear as horses on the run.

The most famous vision of the chariot is Ezekiel’s vision. He sees what are called in the Bible “holy living beings” (חַיּוֹת הַקֹּדֶשׁ). His chariot is composed of four different kinds of living beings. Those exist in the World of Formation. How amazing is it that there are four forces in our physical world, which must naturally correspond to these four types of angels. The simple meaning of a “living being” is a being that gives life, or in other words, a life-force. These are of course the four force particles of the four forces in nature. The last of these is the living being which resembles a man. This is not the higher man that in Ezekiel’s vision sits on the throne being carried on the chariot. This living being is different from the four others. Living being (חַיָה) also means “animal,” in Hebrew (i.e., animation). So of these four living beings, three are represented by animals, a lion, an ox, and an eagle. So, this fourth one, resembling a man, is obviously different. In the text of Ezekiel, the living being that resembles a man appears first, but in Kabbalah it is ordered last. This living being that resembles a man corresponds to gravity, as we will see. The three others represent the three other forces of nature, which can be almost unified even without string theory. But, the one that is elusive and cannot as yet be connected with the others is gravity. In any case, we have here a beautiful allusion to the four forces in nature.

Finally, the highest vision of the Divine Chariot was experienced by Isaiah (chapter 6), which corresponds to the consciousness of the World of Creation.[3] In the Chariot as seen by Isaiah, there is only a pair of fiery angels (seraphim). As we noted, virtual particles appear in pairs. But, what is even more significant for correctly identifying which particles these angels correspond to is the word used to describe them: seraph. Seraph literally means “fiery angel,” which describes them as beings that appear and are then spontaneously burnt up. In other words, they appear and are immediately annihilated, which is the exact nature of virtual particles! Isaiah’s vision is of fiery angels that are created and then spontaneously burn away. To burn away, in the case of the seraphim, means that they return to their origin in Emanation.

Take the image that we gave above of the vacuum constantly erupting into virtual particles, which are then annihilated. This is an image of something being created (ex nihilo, like in the World of Creation) and subsequently returning back to its source. The very same process describes the creation of the seraphim out of the World of Emanation, which is the very nothingness that creation ex nihilo comes from.[4]

Three types of angels

So now we have three names of angels:

• the seraph: the virtual particles in the World of Creation
• the living being, or animal: the real force particles in the World of Formation
• the horse: corresponds to the real matter particles of the World of Action.

Now let us look at the significance of the numerical values, the gematrias of these names:

• The value of seraph (שָׂרָף) is 580, or 10 times 58, and we are all fully aware by now that 58 is the value of the Hebrew word for “symmetry” (חֵן), so the word seraph in Hebrew is a multiple of “symmetry.”
• The value of “living being” (חַיָה), or chayah as it is pronounced in Hebrew, is 23. Chayah is a very important word in Kabbalah. In the entire first account of creation there are 469 words. The middle word, the 235th word is chayah. It appears in the verse, “God said, ‘Let the waters swarm with living beings’” (וַיֹּאמֶר אֱלֹקִים יִשְׁרְצוּ הַמַּיִם שֶׁרֶץ נֶפֶשׁ חַיָּה). This is also the first appearance of this word in the Torah. So this word acts as the axis of symmetry for the entire story of creation. This alludes to the fact that while in Ezekiel’s vision there is no mention of fish, only land animals, in the Torah the first example of living beings specifically refers to fish.
• Finally, the value of “horse” (סוּס) is 126. The letters of this word are themselves symmetric. There is something very symmetric about a horse. (Apparently a horse can go back in time, retaining CPT symmetry).

So we have now seen that each of these three words exhibits a different form of symmetry.

The sum of all three types of angels, seraph (שָׂרָף), living-one (חַיָה), and horse (סוּס) is 729, which is also 27 squared, or 9 to the third power, or 3 to the sixth power. Whenever we have a number raised to a power, an expression in the form x^y, we are expressing a quality of inter-inclusion.

The Paschal lamb, matzah, and bitter herbs

We are taught in Kabbalah that there is another set of three very connected words whose sum is 729. In the Hagadah we quote from the Talmud that whomever does not experience three things on Passover has not performed the seder properly. These three words are: the “Paschal lamb” (פֶּסַח) whose value is 148, matzah (מַצָּה), whose value is 135, and “bitter herbs” (מָרוֹר), whose value is 446. Their sum, again, is 148 + 135 + 446 = 729! Obviously, this is a meditation to have on Passover.[5]

Let us see how these three components of Passover correspond to the three types of particles. Indeed, today the Paschal lamb remains at the virtual level for us, because we cannot offer the sacrifice. The mitzvah of the Paschal lamb is that it be eaten roasted, more burnt than anything else eaten in the Temple service. There is no other offering that is eaten so “burnt,” so seraph-like. This represents the level of consciousness attained by a tzadik who always feels how the world is coming into being out of nothing and instantaneously returning to nothingness.

Eating the matzah corresponds to the four force particles. Bread is what gives a person energy, or life-force. As the verse states: “Not on bread alone can man live, but on the word of God will man live.”[6] So it is not the physical matter that gives life, but the inner life-force. Matzah, which is a form of poor bread, reveals this—that it is not the physical but the spiritual within the physical that gives life. So eating matzah is to remind us that real force, real life, comes from the utterance of the Almighty.

The matter particles correspond to the bitter herbs, and remind us of the hardship that is inherent in the world of Action. Hardship is ultimately a good thing, because reward comes from the hardship that we experience. In the verse that lists the four Worlds, the World of Action is preceded by the word “even” (אַף), which also means “anger,” alluding to the difficulty and hardship inherent in the physical world. So once again, we see here a very nice correspondence of the three elements of Pesach with the three types of particles, with the three lower Worlds as the foundational frame of reference for all these correspondences.

Unifying the particles in each world

We mentioned in an earlier lecture that there are three methods for unification:

• in the World of Creation, the unifying principle is nullification (הִתְבַּטְּלוּת), we see this as the seraphim being burnt, that is nullified, in their return to nothingness.
• in the World of Formation, the unifying principle is inter-inclusion (הִתְכַּלְּלוּת).
• in the World of Action, the unifying principle is cooperation (הִשְׁתַּתְּפוּת).[7]

Corresponding these three methods with the three visions of the Chariot, we may now say that the horses (i.e., the fermions, the matter particles) of the World of Action need to cooperate, to act, or work together. The unification of matter is when it works together.

Unifying the four forces of nature

Let us now turn to the four forces in nature. As we have just said, all four are included within the World of Formation. The living beings (i.e., the bosons, the force particles) of the World of Formation are joined through inter-inclusion. In Ezekiel’s vision, each of the living beings exhibits perfect inter-inclusion, because each has four faces, with each one of the faces resembling one of the four living beings: a lion, an ox, an eagle, and a man. And furthermore, each of these faces inter-includes all four in itself (just that the predominant face is one of the four). Thus, the unifying principle for force particles is inter-inclusion.

The paradigmatic enigma today in physics is how to unify the four forces of nature. We mentioned in a previous lecture that this is what physics is still lacking: a model of unification based on inter-inclusion. This type of unification is readily apparent from a holographic image that is etched on a crystal. In other words, somehow in the strong force you should be able to see the weak force, the electromagnetic force and gravity, all reflected in it.

The Targum Yonatan, based on the sages says that together the four chayot, the living beings, had 256 wings. 256 is 4 to the fourth power (4⁴). This is a beautiful example of inter-inclusion, because, as mentioned, each of the four living beings had four sides to it, and each side had four faces, and each face had four wings. So altogether the four living beings had 4 to the fourth wings.

There is a particular type of symmetry known as angular symmetry, if you look at something from a different angle you will still see the same thing (like in a ball under rotation). Here, from whatever direction you looked at the living being, you saw the same thing. So in that sense, wings are like spin.

The seraphim, the fiery angels of Isaiah’s vision, each had 6 wings. The horse angels of Zachariah’s vision each had 2 wings. They are the most like how we usually image that angels have 2 wings (like physical birds).

Now we can draw the following correspondence:

particle	# of “wings”
virtual	6
force	4
matter	2

This correspondence and its scientific and spiritual implications need to be developed further. But, let us once more note that the living beings exhibit the greatest degree of inter-inclusion, where all four living beings reflect all four and each of these reflections itself reflects all four. And altogether they have 256 wings.[8]

Time reversal in Ezekiel: the dry bones

The book of Ezekiel,[9] begins with a vision that is related to the number 4 (four faces, four wings, etc. to each chayah, each living being). Close to its end there is another vision related to the number 4, known as the vision of the dry bones.[10] The dry bones represent the dried up state of the Jewish people while we are in exile. In his vision, Ezekiel sees the entire House of Israel as dry bones, which means that they resemble the dead. Not only has death set in, but the remaining bones are scattered apart, representing a state of maximum entropy where everything has fallen apart completely.

Then Ezekiel describes something which is an example of time-reversal: the dry bones come together and sinews, flesh, and skin grow on them. When scientists want to demonstrate the concept of the arrow of time—that time has a direction, from past to future—they tell us to imagine a shattering glass. Now if this shattering was filmed and played backwards, we could immediately tell that the film was playing in reverse as we would see the pieces coming together. This is an example of teshuvah.

It is also similar to the principle that in the Torah, in the Pentateuch, there is no chronological order,[11] in the normal sense of chronology. Sometimes, things that happened later are written as if they happened earlier. This concept is the foundation of teshuvah, which allows a person to go backwards and relive, and even take positive advantage of negative past events. In this manner, as already explained, evil becomes a seat for the good.

Ezekiel sees the film of “death” being played in reverse, the bones coming together and growing a human being as it were. This is the experience of resurrection. Ezekiel’s vision is an example of time reversal and a shattering of the law of entropy. From a state of high entropy (a later state, as death progresses) a state of lower entropy emerges (an earlier state, the energy of life). The arrow of time normally travels from low entropy to higher entropy. And here, in Ezekiel’s vision he sees the opposite occurring: a high entropy state (death)—a state with less order—develops into a low entropy state (resurrection), a state with more order.

In his vision, Ezekiel saw the body divided into four components: bones, sinews (blood vessels), flesh, and skin. As he saw the parts being added to the bones, entropy was decreasing, but at the end the body was still not alive—life-force was still missing. So if these four parts of the body represent the four forces of nature, then something more still had to be added in order to unify the forces together, to bring the body to life. This is what Ezekiel prophecies as: “From all four corners, the wind [spirit] shall come to enliven these dead corpses.”

Now, we cannot go into great detail for lack of time, but let us see how these four parts of the body correspond to the four forces:

• The bones correspond to the strong nuclear force, which holds the nucleus of the atom together, just as the bones (the skeleton) hold the entire body together.
• Blood vessels (sinews) correspond to the weak nuclear force. It is the weak force that is responsible for radioactivity, which bears an important relationship to blood, that we will not discuss right now.
• Flesh, or the muscular system, corresponds to the electromagnetic force. In principle, the nervous system corresponds most closely to the electromagnetic force, and it is most closely represented in Ezekiel’s model by the muscular system.
• Skin corresponds to gravity. The complexion of the skin represents the curvature of space. As we explained, according to Einstein, space is relatively gently curved and its curvature is equivalent to gravity. We mentioned that the biggest discrepancy between general relativity and quantum mechanics is that relativity speaks of gentle curvature while quantum mechanics speaks of frantic curvature. Einstein was into the World of Rectification, which is gentle, while Heisenberg was into the World of Chaos, which is frantic. In any event, it is a very beautiful image to see the skin as representing the gentle curvature of space. The skin is where you see the human features of the face (just as in the four faces of the living beings—the angels in Ezekiel’s vision of the Divine Chariot—the one that resembles a man, corresponds to gravity).

The fact that then the spirit has to come in to unify these four forces, to make them into a living man, this is similar to the creation of man, where after Adam’s body had been formed physically, God breathed into him the breath of life,[12] which then animated him and made him alive.

Lecture 8

Wave-particle duality

The first topic that we will discuss in this lecture is the wave-particle duality of elementary particles. Einstein was the first to postulate that light, which at that time was considered to be a wave phenomenon, possessed a particle expression called a photon. Unlike an electron, a photon has no mass. It travels at the maximal speed, the speed of light (c) which for Einstein in his theory of relativity is considered to be the absolutely fastest speed physically possible in this world.

Later, another scientist discovered that particles, like electrons, also exhibit wave properties. In a certain sense, this was a greater innovation, but since Einstein had already said that a wave is also a particle, this is usually seen as just the other side of a single duality. This is an example of symmetry (in this case a duality). If what seems to behave like a wave also exhibits particle-like behavior, it is simply the next step to say that what seems to behave like a particle also has wave-like behavior.

The wave function is a probability function, which measures the probability that a particle be found in a particular position (or state) in the universe. Now it is agreed that all elementary particles, whether they are fermions or bosons, exhibit this duality, which is a paradoxical phenomenon. It only depends on whether the observer is concentrating on observing the wave or the particle-like characteristics.

Let us explain what this duality means in terms of Chassidic teachings. What does it mean to be a wave and a particle at the same time?

One important model in Kabbalah, which is an example of the principle of “a reversing seal” (חוֹתָם הַמִּתְהַפֵּךְ), the reversing seal (a principle of symmetry) which applies to every Kabbalistic model that makes use of the essential Name of God, Havayah. Whether it be the four letters as they correspond to wisdom, understanding, the emotive faculties, and kingdom, or whether it be the model of how they correspond to the four Worlds, the model always exhibits this property. Between them, the four letters of God’s essential Name exhibit the phenomenon of a reversing seal, where whatever corresponds to the first two letters, is duplicated in reverse in relation to the two last letters. The best example to illustrate this is how the four letters of God’s essential Name correspond to love and fear:

Yud – higher awe

Hei – higher love

Vav – lower love

Hei – lower awe

The metaphor for this is that when you have an embossed seal (the stamp sticks out) then when you push down on hot wax for instance, it will engrave an inverted image of itself.

In respect to elementary particles, let us first say that we can relate their particle and wave properties to two concepts that appear clearly in Kabbalah: matter and form. That the particle properties correspond to matter is clear, and here we are adding that the wave properties correspond to form. Now, the example here of how the reversing seal is used in a model relies on recognizing that in our revealed reality form informs matter and therefore is considered higher than matter. Revealed reality corresponds to the two lower/last letters of the Tetragrammaton, vav (ו) and hei (ה). In almost all discussion of these two concepts we find that form is like the soul of matter. So in our revealed reality, form is higher than matter. Form is like the male aspect and matter is the female aspect. But, in respect to their origins, the reverse is true: the origin of matter is higher than the origin of form.[1] The origins correspond to the two first/higher letters, yud (י) and hei (ה) of God’s essential Name, Havayah. These two levels are also called the father and mother principles. So the origin of matter, which is called by the sages hiyuli[2] matter, or primordial, ethereal matter, is like the father and the hidden origin of form is like the mother.[3]

So our complete model, which exhibits the reversing seal, looks like this:

Letter of Tetragrammaton
yud (י)	(origin of) matter
hei (ה)	(origin of) form
vav (ו)	form
hei (ה)	matter

Furthermore, we are taught that the subjective experience of matter arouses awe and fear, whereas the experience of form arouses love and attraction. Meaning, if we experience light as a wave, in some way, it arouses love. This is exactly what is said that in the two higher levels, the yud is called the higher fear, which is nullification of reality connecting it with the primordial matter, whereas, the hei (mother) is called higher love, which corresponds to the origin of form.

But in the revealed levels, form is the masculine, while matter is considered the feminine. So in direct experience, the masculine induces love, while the feminine awakens fear, or awe.

The sages say that innately a child fears and has awe of his father and loves his mother. But this needs to be balanced, so that he should also fear his mother and love his father. To this end, when the Torah commands us to fear our parents, it first mentions the mother: “A man should fear his mother and father.” But, when it commands us to honor our parents, and honor is considered to be an expression of love, then it first mentions the father: “Honor your father and mother….” Once more we see that the father represents awe and the mother represents love (these correspond to the two initial letters of the Tetragrammaton). But, in respect to the husband and wife relationship (corresponding to the two last letters of the Tetragrammaton), the husband becomes love and the wife represents awe (as in Proverbs, where the good wife is called a God-fearing woman[4]—because she assumes the simple duty of raising her children in accordance with the Torah). So, this is a very general principle throughout the entire Torah. The phrase most often used to describe this principle of the inverted seal is in Aramaic and it reads: “fear and love, love and fear.”[5] Often, before commandments that we perform we say, or have in mind, that we are performing this commandment “with fear and love, with love and fear.” This is just like saying: “matter and form, form and matter,” or “particle and wave, wave and particle.”

According to Kabbalah if there is a true state of unification, it must have both manifestations, both aspects. If it is the higher unification, then the particle comes before the wave. If it is the lower unification, then the wave is above the particle. But, each unification has to have both aspects to it. Especially, if it is a total consummate unification, it has to have all four aspects to it. Meaning that this would be an objective of science to try and distinguish between the concealed wave property, vs. the revealed wave property. And even harder: to distinguish between the concealed particle property vs. the revealed particle manifestation. The clue to understanding these distinctions is that the concealed property is “non-local” whereas the revealed property is “local.” And therefore, the concealed wave/particle property envisions each wave/particle as relating to and interacting with all others across the span of the entire universe simultaneously, while the revealed property does not. Locality vs. non-locality is a most important topic that we leave for later.

Einstein in the Bible?

In this context, let us mention that James Gleick, the author of Chaos, claims that the three most brilliant physicists of all time lived in the previous century. They were all Jewish and they all suffered from anti-Semitism in one way or another. They were, Albert Einstein, Lev Landau, and Richard Feynman.

Lev Landau was a Russian physicist. In addition to being a physicist he was an educator. Gleick mentions that when Lev Landau taught physics he created a system to rank the genius of a physicist. It was like a quantum system and went in increments of ½. The greater the physicist, the lower his number. Landau gave Planck, Bohr, and Dirac a ranking of 1 (as he did for Richard Feynman). He ranked himself initially as 2.5, but at the end of his life he ranked himself as a 2. According to Landau, in all of history, Einstein was the only physicist worthy of a ½ rank. This conceptualization of rank for physicists goes very well with what we discussed in an earlier lecture, that the smaller you are, the greater you are.

Apropos, let us say another thing. If Einstein is at a different level altogether than all the other physicists, so he too must be alluded to in the Torah. What we are trying to say is that everything is alluded to in the Torah. Nowadays, people look for celebrities and events in the Torah using equidistant letter skipping and the like. All those so-called Torah codes, which there is a lot to say about, but not right now, are not as significant or as serious as finding some explicit source in the Torah: a literal source in the Torah for a person or a concept. For Einstein there is a very explicit and beautiful such source.

In the previous lecture, we discussed Zachariah and his vision of the Divine Chariot. There is another important prophecy by Zachariah who lived in the time of the second Temple’s construction, after the Babylonian exile. In his prophecy, he sees the cornerstone of the Temple and the Menorah. About the cornerstone he writes: “On one stone are seven eyes”[6] (עַל אֶבֶן אַחַת שִׁבְעָה עֵינָיִם). This one stone that he is referring to is the cornerstone (or headstone) of the Temple. The end of the prophecy reads: “The headstone, grace, grace to it”[7] (הָאֶבֶן הָרֹאשָׁה תְּשֻׁאוֹת חֵן חֵן לָהּ). The word translated here as “grace” is the Hebrew word for “symmetry” (חֵן). Since here it says “grace, grace,” this even means double symmetry. Now, the name “Einstein,” in German and Yiddish literally means “one stone.” This idiom actually appears five times in the Bible. If we would like to give a lecture on Einstein we would have to go through all five times that the Bible speaks of “one stone”[8] (אֶבֶן אַחַת). But, now we will only mention the first and the last.

The first time is found in the Book of Joshua where it mentions that when the Jewish people were crossing the Jordan river, entering the land of Israel, each of the princes of the 12 tribes took one stone on their shoulder from the riverbed and carried it to the Jordan’s west bank.

The last time that this phrase “one stone” appears in the Bible is here in this prophecy of Zachariah. What does it mean here that the “one stone” has “seven eyes.” There are some commentaries who say that the seven eyes are a symbol for the guarding force watching over the “one stone.” But, in our opinion there is a much better explanation.

In another place in the Bible, we find that the phrase “seven eyes” symbolizes God’s Providence over every single aspect of creation (what we know as personal and individual Providence). So, what the verse is saying is that all of God’s Providence over the entire world is concentrated through the cornerstone of the Temple. It is like the “one stone” is the focusing lens of Divine Providence.

This concept also appears in two other verses in the Torah. The first is a verse in Deuteronomy, which states that “the eyes of God are upon the land of Israel, from the beginning of the year to the end of the year”. So here, the land of Israel is like the lens through which God sees the entire world. First His “gaze” is focused on the land of Israel, and from there it spreads out to the rest of the world.[9] The second verse is recited as part of the ceremony when bringing of the first fruit to the Temple: “Gaze down from Your holy abode in the heavens and bless Your people, Israel.” In that case, it is explained that “the heavens” are a metaphor for the Torah, thus the Torah acts like a lens through which all of Divine Providence passes.

In any case, what this means is that God’s Providence is first concentrated on the “one stone” of the Temple, and then spreads out to every minute detail of creation.

Seven space-time directions

But now, what do “seven eyes” have to do with Einstein. We mentioned earlier that Einstein united space and time. Normally, we consider space and time to be 4 dimensional: 3 dimensions of space and one dimension of time. But, the time dimension is not the same as the three space dimensions. What is the difference between them? When represented mathematically, as a complex field, the time dimension is described as the imaginary component (in terms of i, the square-root of negative 1, or √-1) in this complex plane, while the spatial dimensions make up the real component. But, more simply put, the difference between the time dimension and the space dimensions is obviously that in each of the spatial dimensions you can go in two directions—to two different extremities. I can go east and I can go west. I can go up and I can go down. There is no preference or dictation in which direction to go. But time is uni-directional. I cannot go in both directions. This is the arrow of time, which we have explained already as the law of entropy.

Another way to understand direction is as a vector, which is like the direction of sight. So each of the seven eyes is symbolic of sight in a given direction, like a vantage point from which something is being looked at. So in 4-dimensional space-time you can actually only go in seven directions.

As we saw in the previous lectures, in Kabbalah we always speak of the 6 extremities of space, not just 3 spatial dimensions. But, time only has one direction. These seven directions correspond to the seven attributes of the heart and to the seven days of the week. The Midrash tells us that each day of the week is paired with one another, just like the three spatial dimensions have two directions each. But, Shabbat complained to God that it was lacking a partner (exhibiting its uni-directional character). So, the Midrash says that the Almighty paired the Shabbat with the Jewish people. The six days, which correspond to the six extremities of space relative to Shabbat, are paired. But, Shabbat, which is the essence of time, does not have a pair, so that is why God paired it with the Jewish people.

What does this mean? It means that there is something about the congregation of Israel that can go backwards in time. Because if they are really going to be the Shabbat’s soul mate so, even though Shabbat is uni-directional, nonetheless, the Jewish people represent movement in the opposite time direction. How is this? Because the Jewish people exhibit the secret of teshuvah, they can go back in time. Indeed, Kabbalah stresses that the word Shabbat in Hebrew can also read as the word that means “[you shall] return” (שַׁבְתָּ), the literal meaning of teshuvah, to return. Teshuvah is capable of converting a transgression into a merit. But to do that you have to be able to go back in time. So teshuvah is like a time machine.

Shabbat: time travel and teleportation

In Hebrew, “time machine” is written מְכוֹנַת זְמַן, and has the numerical value of 613! This is of course the number of commandments in the Torah. If a person is complete in all 613 commandments then he has a time machine. There is a related concept called teleportation, which is the short form of tele-transportation. This is a phenomenon of quantum tunneling. The way to think of a teleporter is that it does with space what a time machine does with time, so a teleporter is actually a “space machine.” In Hebrew we would call a “space machine” מְכוֹנַת מָקוֹם, and its gematria is 702, the value of “Shabbat” (שַׁבָּת).

So here we have an example of the inter-inclusion of space and time within Shabbat. On the one hand the Shabbat complained to God that it has no partner, indicating that it is uni-directional, or time-like. On the other hand, we see here that Shabbat equals a space-machine, meaning that it is space-like.

This reminds us that the sages say that if the Jewish people would keep but two Shabbatot, they would immediately be redeemed. Sometimes it is explained that the two Shabbatot are the two Shabbatot before Pesach, Shabbat Parashat Hachodesh and Shabbat Hagadol, because Pesach is the time of redemption. But, in Kabbalah and Chassidut it is explained that these two Shabbatot occur together on the same Shabbat, meaning that every Shabbat has two aspects to it. This corresponds to our description of Shabbat having a potential of moving us freely both forward and backward in time. Shabbat is the seventh eye on the one stone that represents the uni-directional arrow of time. But, in order to be redeemed we have to pair it up with the Jewish people through teshuvah, specifically teshuvah out of love. Redemption is freedom. The ultimate prison that the world is in right now is time. The best you can do is to maximize your time. But, to get out of the uni-directional prison of time, to free yourself from aging, that is the ultimate form of redemption. Only the Jewish people can achieve this freedom and redemption through the power of teshuvah. Because the Jewish soul is the Shabbat’s partner, it is like the second extreme of the dimension of time.

One stone and seven eyes

So all of this came out of our searching in the Bible for an allusion to Einstein. The “one stone” is the lens through which all the personal Divine Providence goes through. We have 7 eyes peering or gazing through the one stone. The model here is 1:7 and the word that reflects this ratio is “then” (אָז), whose two letters, alef (א) and zayin (ז) equal 1 and 7, respectively. Now what is the sum of one “stone” (אֶבֶן) and 7 times “eye” (עָיִן)?

אֶבֶן עָיִן עָיִן עָיִן עָיִן עָיִן עָיִן עָיִן = 963

But, 963 is also the value of the phrase found in the beginning of creation: “And God saw that the light was good”[10] (וַיַּרְא אֱ־לֹהִים אֶת הָאוֹר כִּי טוֹב).

Recall that “time machine” equals 613. The first time there are adjacent words in the Torah whose numerical value is 613 is in this very phrase, specifically, “[And God saw] the light” (אֶת הָאוֹר). So, light is a “time machine,” as above. All this was in praise of Einstein. We hope that he appreciates it.

How do you say “wave-particle duality” in Hebrew?

Our motivation for going into this discussion about the allusion to Einstein in the Torah is that every concept in science must have an origin that can be identified in the Torah. One might think that a sophisticated idea like light being both a wave and a particle simultaneously would be beyond the Torah’s mind-set, that there could be no simple word to describe this. But, chas veshalom that this should be the case. This is a false thought. There must be a word in the Torah that expresses the wave-particle duality inherent in a photon. Why are we so sure of this? Because we are taught that God creates the world continuously through the letters of the holy language of the Torah, so if there is such a phenomenon it must be possible to find it in the Torah.

One of the foundations of teaching science in a 100% Torah context is that we need to rename many of the concepts and terminology that science uses today.

We now are looking for a word in the Bible that unites the concepts of wave and particle. And we would like this word to be directly related to light, which is the way that Einstein originally came upon this duality. So we turn to the Book of Job once more. Job is a man afflicted with terrible suffering. He has three very good friends who come to console him, but fail. Then a young man, who was listening quietly to the conversation, interjects. His name is Elihu ben Brachel (אֱלִיהוּא בֶּן בְּרָכְאֵל), whose numerical value is 358, the same as “Mashiach” (מָשִׁיחַ). After Elihu speaks, God himself addresses Job with 50 rhetorical questions dealing with the secrets of creation: “Do you know this?” “Do you know that?” God’s message to Job is that if you do not know the secrets of creation, you cannot understand the Divine Providence that governs your fate.

In the introduction to his commentary on Sefer Yetzirah, the Ra’avad explains that these 50 questions correspond to the Fifty Gates of Understanding. One of those 50 questions is: “Who gave birth to the drops of dew?”[11] (מִי הוֹלִיד אֶגְלֵי טָל). This is one of the most beautiful of these 50 questions. Drops of dew are very special because they do not fall from the sky like rain or snow. Instead, we wake up every morning to find these drops on the grass. Where did they come from? From our perception they came out of nothing. Earlier, we talked about virtual particles that just appear out of nowhere. Our experience of drops of dew is that they just come out of nothing. The word we are going to be focusing on is “drop” (אֵגֶל).

Every word in Hebrew has both a three-letter root, and an essential root, called a gate, which is its two-letter sub-root. Now, the first experience that we have of light is as a wave. “Wave” in Hebrew is a familiar word, גָל (pronounced “gal”). This is indeed the grammatical gate, or two-letter root, of the word “drop” (אֵגֶל). How so? There is a rule in Hebrew grammar that there are seven letters (האמנתי"ו) that do not change the essence of the essential two-letter root; they are the vowels (אהו"י) and the three letters מנ"ת, which tend to fall from a three-letter root leaving the two-letter gate, or essential sub-root.[12] So definitely the letter alef (א) that precedes the two letters gimel (ג) and lamed (ל) is an added letter to the two-letter sub-root גל. Some of the commentaries explain that drops of dew are related to waves, because when you look at an entire field full of grass and all the drops of dew on it, it looks like waves of dew.

Now, if you look in the Radak’s book of Hebrew roots, you will find that אגל is a root with only a single meaning, a drop of dew. It is never used in any other context. It is not a drop of rain, or a drop of oil, or a drop of anything else; only a drop of dew. What is special about this is that the sub-root by itself means “wave”, but as soon as you add an א to it, it becomes a “drop” (אֵגֶל).

A drop of dew is special because it just seems to appear out of nowhere. But more importantly, dew is a symbol in the Bible for light, as in the verse, “Your dew is the dew of light”[13] (טַל אוֹרֹת טַלֶּךָ). The reference in this verse is not just to regular dew or light, but to the dew, the light with which God resurrects the dead. This is a very special type of light called “Torah dew” (טַל תּוֹרָה), alluding to the hidden mysteries of the Torah, the deepest secrets of the Torah, that bring the dead back to life.[14] Thus, God is asking Job, do you know who gave birth to these drops of dew? We have here a most beautiful origin for the fact that photons have a dual property, a dual representation as a wave (גָל), and as a particle (אֵגֶל). For this reason, we can say that the best choice for a word for “photon” in the language of the Bible, is אֵגֶל, pronounced eigel.

This word should not be confused with the Hebrew word for “calf” (עֵגֶל), which is pronounced similarly but is written with an ayin (ע), not with an alef (א).[15]

The value of changing scientific nomenclature

Let’s return to a story we did not tell before about Richard Feynman. As a child he did not speak until he was three years old. Sometimes the greatest geniuses start speaking at a very late age, so do not worry if your child talks late. Sometime in grade school, Feynman taught himself trigonometry. He saw that trigonometry uses all these strange notations like sin(e), cos(ine), tan(gent), etc, which take three letters to write. At a very early age he came up with a much better notation. He decided to use his completely different and simpler notation. Much later in life he came up with diagrams to describe some of the most complex ideas in quantum mechanics. But, at this early age he was very frustrated that nobody adopted his notation, which he considered to be much better. At a certain point he matured enough to understand that he cannot change the world. Even though I could have done it much better, it is a lost cause.

So the question we have to ask is: should we too despair of changing the word used by all of science today to fit the Torah? We don’t think we should despair! One of our objectives in teaching science is to change words. It’s a very difficult objective. Feynman tried and failed. If it is already engraved in the psyche of the world it is difficult to change it.

But, here we are saying something else. We are looking for the correct Torah terminology for describing something that science has discovered. So we want to change “photon” into “eigel,” and “electron” into “ofan,”[16] and there are numerous other such examples. Now, the moment that science adopts the Torah word for these terms it itself will be resurrected. Scientific thinking will be given new life, like the dry bones we were talking about earlier. To resurrect science, it has to use the proper Torah terminology.

More waves

Now, the two-letter sub-root of the Hebrew word for photon (אֵגֶל), eigel, that means wave is as we said, גָל, pronounced gal. We explained that there are seven letters that you can add to the sub-root that do not significantly change its essential meaning. For example, we mentioned the word that means “calf” and is written with an ayin (ע) added to it. But, since ayin is not one of these seven letters, it significantly changes the essence of the sub-root. In our case, there is another letter, except for alef (א) that most easily fits in phonetically to this sub-root: the letter mem (מ). The mem can be added either before the two-letter root, in between the two letters, or after them. In each case, we have a new word that has meaning. They are

• Adding the mem before yields the word מַגַּל, which means “sickle”; if we have our high grass with the drops of dew on the top, then we take a sickle, it is a symbol for many things in the Torah.
• If you put the mem in the middle of the wave it turns into גָּמָל, which means “camel.”
• And if you put it at the end of the wave, you get גֹּלֶם, which means “golem.”

So all three of these words are variations of the two-letter root meaning “wave” (גל) with a letter mem.

In the next lecture we will see how camels are themselves symbols of photons.