What came first, the Schrödinger cat or the fig of Rabbi Akiva? You be the judge. Today we present a guest post by Rabbi Dr. David Kagan.

Fig of Rabbi Akiva

By Rabbi David Kagan, Ph.D.

If Trumah (Trumah is a tithe separated from produce and given to a priest (Kohen) to be eaten with strict laws of purity) is mixed into ordinary food (chulin), and if the ratio of trumah to chulin  is less than 1:100, the Trumah is nullified (batel) and the mixture may be eaten as ordinary food. (The law of nullification, bitul, applies to mixtures of two types of food – one being forbidden one allowed. With certain ratios, the minority is nullified and it has the same status as the majority. For example, if some non-kosher food was mixed with kosher food, if the ratio of kosher to non-kosher is more than 60:1 the whole mixture is allowed. We deem the non-kosher food to be nullified (batel). The whole concept of nullification only applies in a mixture which is not easily separable. If the non-kosher food is clearly recognizable it is not a real mixture so there can be no nullification.

The Mishnah Trumos 4:8 discusses the following situation.

If there is a mixture of roughly 50 white figs of chulin and roughly 50 black figs of chulin totaling more than 100, and one fig of trumah fell into this mixture. There are three opinions:

1. R. Yehoshua: The Trumah is batel.
2. R. Eliezer: Since there are two colors of ordinary figs (chulin), the trumah is not batel. For, if it was a white fig, it is only mixed with the white figs and hence a ratio of less than 1:100 is not achieved. Similarly, if it was a black fig, it is mixed only with the black figs, not the white ones, and a ratio of less than 1:100 is not achieved.
3. R. Akiva: If the color of the Trumah fig was known, it is not batel; if not, it is batel.

The Jerusalem Talmud explains that R. Yehoshua also agrees that, if the color is known, the fig is not batel. But R. Yehoshua says that, if the color of the Trumah fig was known when it fell in but subsequently forgotten, the Trumah is batel . R. Akiva says that if the color was known at time of falling in it will not be batel, even if is subsequently forgotten and unknown.

The opinions of R. Eliezer and R. Yehoshua are easily understood. According to R. Eliezer our state of knowledge is irrelevant. The fact is, that we do not have a true mixture of 100:1, because in reality we have two easily separable colors. So we have two separate mixtures. One of these mixtures will contain the Trumah fig and it is therefore not batel. The doubt is not according to our state of knowledge but according to the reality.

1. R. Yehoshua says that since we do not have knowledge of the color of the Trumah fig there is a question regarding the whole mixture of white and black figs and the Trumah is therefore batel. The doubt is fixed by our state of knowledge. In our mind, since we do not know the color of the Trumah fig, it is “mixed up” with all of the figs.
2. R. Akiva’s opinion is hard to explain. If the mixture’s status depends on our state of knowledge he should agree with R. Yehoshua. If at present we do not know the color of the Trumah (even if it was known before), it should be batel. If, on the other hand, he considers the reality there is never a true mixture of 100:1 figs.

Welcome to the world of Quantum Torah:

The “classic” quantum two-slit experiment has the following setup: If a single photon has the choice of two slits it will display an interference pattern – as if the wavefunctions originated from both slits. If an observer measures whether the photon is going through the slit, it will go through only one of the slits. The observer collapses the wave function. Once the observer has collapsed the wave function, it cannot jump to another state namely the second slit or back to the un-collapsed wave function of both slits. (In mathematical terms, the states are orthogonal eigenstates of the measurement operator, hence the probability of jumping from one state to another is zero. This has implications regarding time, or the imposing of an arrow of time, but that is another discussion.)

Now let us understand the case of Trumah according to R. Akiva.

1. R. Akiva opines that, if there is no observer at the time the fig falls into the chulin so its color is unknown, a mixture (interference pattern) is made and the Trumah is batel. If there is an observer who determines the color of the Trumah fig, there is no longer an interference pattern and it belongs either to the white figs or the black figs and it is therefore not batel. In the words of the Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson obm, “the knowledge of the observer creates the reality in the object.” [Likuutei Sichos Vol. 28, top of page 63] Subsequent forgetting of the color will not recreate the mixture just as subsequent forgetting of which slit the photon was OBSERVED to go through will not recreate an interference pattern. (See above reference, where the possibility of a person’s knowledge effecting (halachically) an object external to the observer is discussed.

To explain the analogy in a clearer way. Rabbi Akiva does not view the fig of Trumah as one with definite color. The fig to falling into the mixture is considered as being in a mixed state of both colors – the state of superposition.  When the observer sees the actual color of the Trumah fig he collapses the wavefunction and fixes the color of the fig. Now saying that the Trumah fig is in a mixed state is at first glance illogical. The fig is either white or black prior to falling in. However, R. Akiva is saying that the color has no halachic (i.e., legal from halachah–religious law) significance until it becomes part of a mixture. So it is in a mixed state of both colors until it falls in. (In the halachic literature figs are either “white” or “black”, obviously meaning light colored or colored.)Then, if observed, the wave function is collapsed and the halachic status of color is determined. There are other examples of a halachic status being only created after it is “observed”.  (The days of sefira become “sefira days” only after the act of counting them, even though the days exist there without the counting. The observation of the Kohen is needed to create the halachic status of leprosy.)

What we see here is an example of R. Akivah viewing the halachic reality as being created by the observer. In the above referenced Sicha, the Rebbe explains that specifically regarding Trumah the ability of the human to create the halachic reality is to be found. He references the verse Devarim (Deut.) 18:27 and the Rambam, Trumos 4:16, Shulchon Aruch, Yoreh Deah, 331:46, where it states that the thought of the man that creates the Trumah.

This is yet another example of how Quantum Logic fits very well with aspects of “Talmudic” thinking, as opposed to classical Logic.