Day Six – the State of Superposition

And God saw all that He had made, and behold it was very good, and it was evening and it was morning, the sixth day. (Gen. 1:31)


The Biblical narrative of creation concludes with the above verse. Rabbi Shlomo Yitzchaki (a.k.a. Rashi) comments on this verse:

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the sixth day: Scripture added a “hey” on the sixth [day], at the completion of the Creation, to tell us that He stipulated with them, [“you were created] on the condition that Israel accept the Five Books of the Torah.” [The numerical value of the “hey” is five.] (Tanchuma Bereishith 1). Another explanation for “the sixth day”: They [the works of creation] were all suspended until the “sixth day,” referring to the sixth day of Sivan, which was prepared for the giving of the Torah (Shab. 88a). [The letter “hey” is the definite article, alluding to the definitive sixth day, the sixth day of Sivan, when the Torah was given]

What Rashi is saying here is that the world was suspended in the state of superposition of being created and not being created depending on the future choice to be made by Jewish people – to accept the Torah or not. Until that moment – the sixth day of Sivan – the world existed in a quantum-mechanical state of superposition of existence and not existence, as it were, just as a Schrödinger cat.

In quantum mechanics, a system (say, a particle) is described by a wave function (or wavefunction), that describes the distribution of probabilities to find the system (e.g., particle) in a particular area of space. The wavefunction obeys the Schrödinger equation that predicts the evolution of the wavefunction in time. Why the evolution of the wavefunction is deterministic, the predictions based on this equation are not deterministic. All we can predict is the probability of finding a particle in a particular area of space. However, when we conduct an experiment, we always get a definitive result for the measured property. This paradox is called the Measurement Paradox, which different competing interpretations of quantum mechanics strive to explain.

The Everett’s many-worlds interpretation of quantum mechanics postulates that a choice splits the universe into branches, where each of the possible outcomes is realized. In the orthodox Copenhagen interpretation of quantum mechanics, the choice causes the collapse of the wavefunction, whereby the plurality of possibilities is collapsed into a single actuality. Until such collapse, the system (e.g., particle) is in a state of superposition of all possible states. Thus, a Schrödinger cat exists in a state of superposition of being alive and dead at the same time, until its state is collapsed by the act of observation, whereby the observer “chooses,” albeit subconsciously, between two possible states.

According to Rashi, until the Sinaitic revelation, the world existed in a superposition of two states – existence and non-existence. “[The works of creation] were all suspended until the “sixth day.” It was the choice of the Jewish people who accepted the Torah that collapsed the wavefunction and broad the world into existence.

I don’t know if Rashi knew quantum mechanics, but his logic is clearly quantum-mechanical. This commentary is one of the most explicit examples of the quantum-mechanical concept of superposition and the collapsed the wavefunction as it is used in the Torah.


It gives me a great pleasure to thank our son, Elie, who pointed out to me this fascinating parallel. May the Almighty send him, Eliyahu Chaim Yitzchak ben Leah, refuah shaleimah!


Shabbat Bereshit – Past, Present, and Future

In the last post, Tishrei—Past, Present, and Future, we discussed how all Tishrei holidays – Rosh HaShanah, Yom Kippur, Sukkot, and Simchat Torah – are connected by the same thread of time and, more specifically, the unification of past, present, and future. This cluster of Tishrei holidays is culminated and concluded with Shabbat Bereshit, when we start the new annual cycle of reading the Torah. Not surprisingly, Shabbat Bereshit follows the same pattern of unification of past, present, and future.

The Torah starts with the creation of the world. The story of Creation, obviously, relates to the past.

The word “bereshit,” means, in the beginning. The root of “bereshit” is “reshit” – beginning. Beginning, however, points into the future – to something that will follow the beginning in the future.


The Lubavitcher Rebbe

Thus far, we easily identified the themes of past and future in the first chapter of the Torah. But where is the present?

The Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, in his speech on Shabbat Bereshit, explained that on that day we should focus on the notion that Bereshit – the beginning – is not something that happened thousands of years ago, but something that happens every moment.

The Psalmist wrote,

“Forever, O Lord, Thy word standeth fast in heaven.” (Psalms 119:89)

As it is explained at length in Tanya, the founder of the Chassidic movement, the Baal Shem Tov, interpreted this verse to mean that the word of God that created the universe in the first place forever stands in heaven continuing to recreate the universe at every moment. Every moment is a new creation. And this is the missing piece of the puzzle – the present moment.

There is a saying, wherever I go, I have to drag myself along, and that spoils all the fun. Indeed, wherever we go, we bring along our baggage, and not all of it is positive. Although we just began a new year, we come to it with our old habits, prejudices, misconceptions, and limitations. Every year, on Rosh HaShanah, we are given a new beginning, a new chance but, if we remain our old selves, what good is it? Every year, the slate is wiped clean for us on Yom Kippur, but what if we continue to make the same mistakes pursuing our old habits? Every New Year, people make resolutions to start exercising, to lose weight… It doesn’t take even a few weeks for most of us to slide back to our old habits, to our old selves.

Alan Lightman, in his wonderful book, “Einstein’s Dreams,” writes that time is sticky like glue, and one can get stuck in it:

“But in this world, the texture of time happens to be sticky… individual people become stuck in some point of their lives and do not get free.”

People who dwell too much on the past, get glued to it, and, as time moves on, get swept with it into the past.

As the Lubavitcher Rebbe suggested, the solution to this problem is to meditate on the profound concept of continuous recreation of the world. If every moment is a new creation, we are being recreated anew. There is no need to drag our old self with all the baggage along. Let old habits, old limitations, all weaknesses remain in the past and allow yourself to be created anew. We may have a choice of what we want to bring along into each new moment. Let us bring to each new moment the blessing of Rosh HaShanah, the forgiveness of Yom Kippur, the joy of Sukkot and Simchat Torah. If we could only internalize this concept, we could be free from all negativity of the past. This is a powerful message of the present moment, the lesson of Shabbat Bereshit.


Tishrei—Past, Present, and Future

The months of Tishrei is full of holidays, and they all share a common theme—the unification of time—past, present, and future.


Picart, Blowing of the Shofars on Rosh Hashanah

It all starts with Rosh HaShanah. Traditionally translates as the New Year, it literally means the Head of the Year. The word shanah has the same letters as the word shinui — “change.” As Aristotle famously wrote, time is change. The sages of Kabbalah agree—time in its essence is change. Thus, Rosh HaShanah can be translated as the Head of Time, or Beginning of Time (since a related Hebrew word, reshit means “beginning”). Indeed, it is all about time. Rosh HaShanah has three main themes—Zichronot (remembrances), Shofrot (Sounds of the Shofar), and Kabalat Ol Malchut Shamayim (acceptance of the yoke of the Heavenly Kingdom). It occurred to me this year, that these three themes represent respectively past, present, and future: remembrances relate to the past; one can only hear the sounds of the shofar in the present; and acceptance of the yoke of the Heavenly Kingdom is done for the future. Thus, from this point of view, Rosh HaShanah brings together past, present, and future.

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The Gates of Repentance

Rosh HaShanah is followed by Aseret Yemei Teshuvah—Ten Days of Repentance—the days between Rosh HaShanah and Yom Kippur. Teshuvah-penitence, which is the main mitzvah (precept) of the Ten Days of Repentance, also has three themes: charota—regret for the past (past), vidui—confession (present), and kabalat l’osid—resolution for the future (future). Once again, we are bringing together past, present, and future.


                                                                                  Isidor Kaufmann, Yom Kippur, c. 1900

Yom Kippur that concludes Aseret Yemei Teshuvah also has teshuvah-repentance as its main theme. We repent for the past misdeeds. Teshuvah, therefore, mainly relates to the past. Yom Kippur literally means the Day of Atonement. Indeed, the main purpose of the day is to atone the Jewish People. Atonement happens on Yom Kippur in the present time. But it comes with the judgment for the coming year, for which we all are inscribed and sealed in the Book of Life—this is related to the future. Which is why the service of Yom Kippur is concluded with a cheerful exclamation, Next Year in Jerusalem! As we see, Yom Kippur also brings together past, present, and future.

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The Kabbalah teaches that the four days between Yom Kippur and Sukkot correspond to the four letters of Tetragrammaton, YHWH. As the Sages teach, this Name means Hayah (He was), Hoveh (He is), and Yihieh (He will be). Once again, this period brings together past, present and future.


                                                                                                    Moritz Daniel Oppenheim, Sukkot

And now we come to Sukkot, Feast of Tabernacles.  Sukkot is all about time. In Biblical times, on Sukkot, the number of oxen brought for daily sacrifice in the Holy Temple, Bet HaMikdash, changed every day. As mentioned above, the change is the essence of time. This is the reason why every day of Sukkot we say full Halel. On Sukkot, we dwell in a sukka-booth (tabernacle) in remembrance of our travels in the Sinai desert after the Exodus from Egypt. Looking at the s’khakh (makeshift roof made of organic materials such as bamboo sticks or tree-branches) of the sukkah, we remember how God protected children of Israel in such booths in the desert. We also remember ananei hakavod—the clouds of glory that protected children of Israel from the desert sun. All that reminds us of our nation’s past. However, one can only sit in the sukkah-booth in the present time. S’khakh is etymologically related to the word iskah derived from the Aramaic root denoting seeing. Iscah (the spelling in Hebrew is the same as iskah) was of the names of Sarah, the prophetess, signifying her extraordinary prophetic powers. She had even greater prophetic power than Avraham, which why God told Avraham, “Listen to your wife Sarah!” By gazing at the skhakh of the sukkah, we draw the spirit of prophecy, the ability to predict the future. Generally, the Talmud states that Simchat Beit HaSho’evah, the water libation ceremony conducted in Biblical times every night of Sukkot was the source of prophetic power in Israel. Hence, we again have a combination of past, present, and future.


Solomon Alexander Hart. “The Feast of the Rejoicing of the Law at the Synagogue in Leghorn” (The Jewish Museum)

The holiday of Sukkot concludes with Simchat Torah. On this Holiday we do three things: we finish the annual cycle of reading the Torah, by reading its last portion, Vezot HaBrachah (this is related to the past year); we start the new annual cycle of reading the Torah, by reading its first portion, Bereshit (this relates to the coming year—the future); and we dance with Torah scrolls—one can only dance in the present. Once again, this Festival brings together past, present, and future.

May the future be bright and happy and may it bring us much joy, which we draw from Simchat Torah. Hag Same’ach!


Scientists are Clarifying Witnesses

Listen, O heavens, and I will speak! And let the earth hear the words of my mouth!

(Deut. 32:1)

In this Torah portion Haazinu, Moses appeals to heavens and earth as witnesses. However, a few verses later, he extorts the Jewish people:

“Ask your father, and he will tell you; your elders, and they will inform you” (Deut. 32:7)

as if to confirm the testimony of heavens and earth. Why wasn’t the testimony of heavens and earth enough? Why did their testimony need to be corroborated by “your father” and “your elders”?


The Lubavitcher Rebbe

The Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, in one of his talks (see R’ Schneerson, M.M. Likute Sihot (Brooklyn, NY: Vaad L’Hafotzas Sichos, 1998) v. XIX, Devorim, pp. 188-196) discusses the Talmudic concept of two types of witnesses: clarifying witnesses and establishing witnesses (see Talmud, tr. Kiddushin, 65b).  The first type of witnesses is called eidei birur, or clarifying witnesses.  These witnesses do not consummate the transaction that they witness, but they clarify the transaction if its terms are later disputed.  Witnesses to a business transaction are clarifying witnesses.  To be sure, a business transaction takes effect regardless of whether witnesses are present.

The second type of witnesses is called eidei kiyum, or establishing witnesses.  These witnesses are an integral part of the transaction that they view, and in their absence, the transaction has no effect.  Witnesses to the ceremony of Jewish betrothal (Kidushin) are establishing witnesses, and their testimony establishes the marriage in Jewish law (see ibid.). Without their presence, the marriage does not take effect. Establishing witnesses can also be called upon to clarify the transaction at some later point, but that is not their primary function.

Image result for rogatchover gaonThe Rogatchover Gaon explains that the distinction between clarifying witnesses and establishing witnesses is also apparent in the laws of interrogation (see Responsa Tzafnat Paneach, Dvinsk, Volume 1, 69). As clarifying witnesses perform their primary function when they clarify a matter through testimony in court, they are not technically considered “witnesses” until they testify, and they attain the status of witnesses in beth din (Ecclesiastic court). The Torah requires beth din to interrogate witnesses before allowing them to attain the status of witnesses.  On the other hand, establishing witnesses perform their primary function by simply viewing the transaction, and their status as witnesses is not conferred by beth din.  Therefore, beth din does not interrogate establishing witnesses.

The Rebbe draws the parallel with two interpretations in the Zohar (III, 86), of the verse:

“You are my witnesses, says God.” (Isaiah 43:10)

One interpretation is (the simple interpretation of the verse) that it refers to the Jewish people. The second interpretation is that the verse alludes to the sky and earth as witnesses, as another verse states:

“I call heaven and earth as witnesses.” (Deut., 30:19)

According to the Rebbe, the latter interpretation suggests that heaven and earth are clarifying witnesses, whereas the former interpretation, referring to the Jewish People, considers them establishing witnesses, whose testimony establishes the act of creation.  The parallel between the Talmudic “establishing witness” and Wheeler’s “participating observer” is remarkable.

This discussion sheds light on the question of the interplay between science and faith. Both play important but different roles as respectively clarifying and establishing testimonies to the creation. Recall that in Talmudic law the clarifying witnesses are subjected to interrogation to clarify their fitness as witnessed and the veracity of their testimony. Heaven and earth, which are called “witnesses” by Moses and which, according to the Rebbe, are clarifying witness, need to be thoroughly examined. This is the role of science which seeks to clarify the nature and the laws of the creation by probing and examining heaven and earth, figuratively speaking. Once the clarifying witnesses are examined they can testify. This will happen, according to the Jewish tradition, in the Messianic era when heaven and earth will offer their testimony of the creation and instead of concealing Godliness they will bespeak it. The first human observers, Adam and Eve, on the other hand, established the very existence of the world as the establishing witnesses or, in the language of quantum physics, as participating observers, the moment that they ‘witnessed’ its existence.

Jewish people continue this process today by declaring each Friday night on the eve of Shabbat a testimony to the creation of the world (see prayer Vaihulu HaShamaym… in the Liturgy for Kabalat Shabbat).  Chasidic philosophy maintains that the world is recreated by God every moment (See Tanya, Shaar Yihud VeHaEmuna). Therefore, just as at the time of Adam and Eve, there is a continuous need for establishing witnesses to reaffirm and establish the act of creation. This role is played today by Jewish people who are the quintessential participating observers in the language of quantum mechanics.

Ultimately, science and faith do not contradict each other but play a complementary role of respectfully clarifying and establishing witnesses to the creation. As Niels Bohr put it, contraria sunt complimenta—the opposites are complementary.

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Brit Milah in Six Dimensions

Sefer Yetzira speaks of three dimensions: OlamShanah, and NefeshOlam literally means “world” and signifies space. Shanah literally means “year” and signifies the dimension of time. Nefesh literally means “soul” and signifies the spiritual dimension. In another place, recognizing the space itself is three dimensional, Sefer Yetzira speaks of five-dimensional space which is a Minkowski spacetime with an addition of the fifth spiritual dimension. This construct is very similar to the Kaluza-Klein five-dimensional generalization of the General Theory of Relativity (a theory that is near and dear to my heart, because, unaware of its existence, I independently rediscovered it as a teenager.) Kaluza-Klein, first forgotten, is now experiencing a revival as a special case of the string theory.


Sefer Yetzirah

In every one of these dimensions, God created the domain of holy and the domain of profane; and He commanded us to separate between the two. This is part of being a holy nation—Am Kadosh, as kadosh literally means “separated.”

In the domain of space, we have reshut hayahid—the domain of one, and reshut harabim—the domain of many. The former signifies the One above, and the latter signifies the multiplicity of the mundane world. We separate between the two by affixing mezuzot on the doors of our houses creating a line of demarcation between the domain of one and the domain of many and separating the sanctity of a Jewish home and the mundane world outside it.

In the domain of time, we have Shabbat, which is the domain of holiness. We also have weekdays, which are mundane. We sanctify Shabbat by making a Kiddush at the start of the Shabbat and separate it from mundane weekdays by making Havdala at the conclusion of Shabbat.

In the dimension of spirituality, God chose the nation of Israel and made it holy. “You shall be holy because I am holy.” (Lev. 19:2) The separation between the Jews and other nations is expressed in the prohibition of intermarriage and the Brit Mila—circumcision—the sign of the Holy Covenant, which symbolizes this line of demarcation.

Thus far is explained in Kabbalah and Chasidic philosophy. I would like to suggest that each of these dimensions has, in turn, two subdimensions—external and internal—hitzoniut and pnimiut.

In physics, we also have concepts of external and internal aspects. For example, we have external symmetries, such as translational symmetry (that states that all laws of physics are valid in every point of space) and the corresponding law of momentum conservation, or time symmetry (that states that all laws of physics are valid every moment of time) and the corresponding law of energy conservation. But then, we have internal symmetries, such as the spin of elementary particles; charm, color, and the strangeness of quarks and their corresponded conservation laws. I think, similar inner symmetries exist in the Torah.

In the domain of space, we have mezuzot separating between the domain of one from the domain of many. However, this is the external aspect of space. Recall that mezuzot should be affixed not only at the front door, but on every doorpost inside the house with mezuzot separating one room from another room. The reason for this is that each room has its own unique purpose and mezuzah sublimates and dedicates this purpose to the service of God. This is the inner aspect of space.

In the dimension of time, we have Shabbat as the domain of Holiness. However, the book of Zohar speaks of two Shabbats—Shabat Eliyon (Higher Shabbat) and Shabbat Tachton (Lower Shabbat). The lower Shabbat is the regular Shabbat that we celebrate every seventh day. The higher Shabbat is celebrated in the higher worlds, when we fulfill the will of God. That is why Mishnah calls Pesach a “Shabbat” (see my essay on Passover). This higher Shabbat is the inner Shabbat, whereas the lower Shabbat is the external aspect of Shabbat.

Related imageIn the domain of spirituality, we have Brit Mila. However, physical circumcision is the external aspect of Brit Mila. There is also circumcision of the heart, which will be attained with the coming of Mashiach (Messiah). In Chabad communities, it is customary for the father to recite at the brit the ma’amar of the Admur Hazaken (the Alter Rebbe, the first Lubavitcher Rebbe), which discusses the circumcision of the heart. This is the inner aspect of spirituality.

Tonight is Yom Kippur. When the Holy Temple stood in Jerusalem, on the day of Yom Kippur, the three dimensions—Shanah, Makom, Nefesh—converged together: on the holiest day of the year (Yom Kippur), the holiest soul (High Priest-Kohen Gadol) would enter the holiest place (Holy of Holies—Kadosh Hakadoshim).

When the Third Temple, Bet HaMikdash HaShlishi, is rebuilt with the coming of Mashiach, not only three external dimensions will converge together but all internals dimensions as well (incidentally, bringing the total number of dimensions to ten—the same number of dimensions as in the string theory).  May this happen immediately!