Superposition and Quantum Collapse in Halakha – A Further Look (Column 689)

With God’s help

Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.

In the series of columns 322 – 327 I discussed the distinction between an ontic doubt (that is, indeterminacy in reality itself) and an epistemic doubt (that is, a lack of information on our part—what is usually called “doubt”). Among other things, I explained there the notion of superposition in quantum theory as a basis for understanding the notion of indeterminacy (as opposed to doubt). In column 324 I addressed the phenomenon of quantum collapse and its applications in Halakha. Using the double-slit experiment, I explained that quantum theory contains two innovations that appear, at first glance, independent: (1) the very existence of superposed states (for example, a particle in a wave-like state); (2) the collapse of such a state to a particle-like state in quantum measurement theory. We saw halakhic appearances of both innovations, and I also discussed the relation between them. In one of my recent classes, the matter became clearer to me, and therefore I thought to continue the engagement with physics (from the column before last) and dedicate a column to sharpening this topic. I will not repeat in detail everything written in those columns except what we need here; whoever wants more detail is referred there.

The Law of “Bererah”

Our starting point is the law of “bererah.” In Gittin 25a and onward there is an extensive discussion of this law, including a baraita cited in many places in the Talmud:

It was taught: One who purchases wine from among the Samaritans says, “Two log that I will in the future separate shall be terumah, ten log shall be ma’aser rishon, and nine log shall be ma’aser sheni,” and he redeems [the ma’aser sheni] and may drink immediately—these are the words of R. Meir. R. Yehudah, R. Yose, and R. Shimon forbid.

This is a tannaitic dispute regarding the following case: Someone bought a cask with one hundred log of wine that is tevel. As is known, tevel may not be consumed; separations of terumot and ma’asrot are required to render it permitted. For simplicity, I will focus here only on separating the large terumah (with an average eye, one separates 1/50 of the total tevel—i.e., in our case, two log). The purchaser wishes to separate the terumah in the following way: he declares that the two log that will remain at the end, after all the wine in the cask is consumed, will be the terumah and will be given to a kohen. The question is whether, based on this, he may drink the wine now and later transfer to the kohen the two log that remain at the end. R. Meir says yes, while his three colleagues disagree and forbid.

The various sugyot present several approaches to explaining this dispute. Here I will assume they disagree about “bererah,” i.e., whether a future event can be considered to clarify the present status. R. Meir holds there is bererah, so the two log that will only be determined in the future are already now considered terumah and immediately permit drinking the wine; his colleagues hold there is no bererah and therefore forbid. In their view the future event cannot be considered to have already fixed the wine now, and one must separate the terumah before drinking.

On the face of it, at the moment of the declaration a state of doubt is created: there are two log of wine in the mixture (namely, those that will remain at the end), but we cannot now point to them (since they are mixed in the cask), so for any amount we drink there is doubt lest part of it is terumah wine. Yet that picture, taken simply, is difficult to accept, since the two log that are terumah already now are precisely the two that will remain at the end. If so, there should be no bar to drinking the wine now: any quantity we drink is certainly not the wine that will remain at the end and therefore cannot be the terumah. Note that in this view, the separation takes effect immediately and confers the status of terumah on specific two log, and thus the tevel is rectified from the first moment. I indeed cannot yet identify the terumah log, but the future will reveal which they are. Note, too, that in this view there is no need to invoke any retroactive clarification; the terumah becomes terumah at the outset, and the transfer to the kohen takes place when we already know what the terumah is. So why can’t we drink the wine? What, exactly, is the core of the dispute? Why won’t the Tannaim accept such a separation? Some sugyot link this to the requirement of “its remainder is recognizable” (i.e., terumah cannot be separated if it is not distinguished from the rest of the tevel), which itself appears explicitly in the sources. Others link it to the concern that the skin will burst (i.e., that the wine will spill and in the end no two log will remain to be terumah), which is also explicit. But plainly these are other explanations not tied to bererah. The explanation via bererah stands even without those two principles. If so, we must understand and explain the law of bererah even if we do not require recognizable remainder and even if we do not fear the skin may burst.

Dispute Among the Rishonim

The Rishonim disagreed about the initial status of the wine according to the view that there is no bererah (or even, according to the view that there is bererah, up to the point of clarification). Rashi, in several places in the Talmud, repeats the claim that even for those who hold there is no bererah, already now there are two log of terumah in the cask. For example, in Hullin 14b s.v. “osrin,” he writes:

“They forbid”—it follows that according to R. Yehudah there is no bererah, and he fears lest he drank terumah.

That is, every wine he drinks is possibly terumah. We see that, in his view, even for the Tannaim who forbid drinking, the prohibition is not due to tevel. The prohibition is despite the fact that there is already terumah mixed in the cask; we just have doubt which two log are the terumah, so there is concern that he will drink terumah. Rashi understood that according to these three Tannaim, drinking is forbidden due to doubtful terumah, not due to tevel.[1]

By contrast, in Tosafot, Eruvin 37b s.v. “ela me’ata,” two views are cited:

“But then, if two pomegranates were before him… If you will ask, let us challenge likewise if the reason is because there is no bererah; and one may answer that if the reason is because there is no bererah, indeed it would not be terumah. But if the reason is that we require ‘first’ whose remainder is recognizable, then here too with two pomegranates it would not be terumah… And Mahar”i explains that if R. Shimon’s reason is because there is no bererah, it works well: indeed one of them was terumah, and the kohen may eat them, even though there is no bererah, for one of them is certainly terumah. But on the reason of ‘first/remainder recognizable’ the challenge stands: then there would be no terumah at all and a kohen would be forbidden. And likewise regarding calling a name for the pile…”

The first view holds that on the no-bererah approach, terumah does not take effect at all and there are presently no terumah log in the cask—everything is tevel. Mahar”i, whose words follow, agrees with Rashi that from the outset there are two log of terumah mixed in the cask (there the case is two pomegranates, one of which is terumah—but it is the same idea), and the state is one of doubt.

Clarifying the Nature of the Doubt According to Rashi

It is fairly clear that Rashi and Mahar”i do not mean that there are specific two log in the cask that are terumah, and our doubt is merely that we do not know which they are (an epistemic doubt). I explained above why that is implausible. In that picture, even according to R. Meir there would be no need for retroactive clarification to permit drinking, and then it would not be clear what his colleagues dispute. It appears, rather, that Rashi means that a status of terumah rests (lightly) on every possible pair of log in the cask—an ontic indeterminacy—and the debate over bererah is whether we may regard what remains at the end as clarifying retroactively that these were the two log sanctified from the outset, or whether there is no retroactive clarification and everything remains indeterminate.

It is important to understand that Rashi does not mean that the entire cask is terumah—after all, only two log were separated. Nor does he mean that there are two particular log and we merely lack knowledge which they are. He means that a tenuous terumah status hovers over each possible pair of log; the tannaitic dispute is whether this can be clarified retroactively (i.e., fixing that the two log left at the end were those sanctified from the beginning) or not. Now it is clear that we are speaking of retroactive clarification and not a simple doubt; and here it makes sense to dispute whether such a move is possible. According to Rashi, we are dealing with an ontic indeterminacy and not an epistemic doubt—that is, the uncertainty is not due to our lack of knowledge (as it would be if there were fixed two log of terumah but we do not know which); rather, reality itself is indeterminate (even the Holy One could not point to which log are sanctified).

We can now also understand why those Rishonim who disagree with Rashi hold that there is no terumah at all (again, not because of “recognizable remainder” or fear of bursting). They apparently do not accept a picture of “tenuous effect” (which is not a doubt) i.e., an indeterminate reality. Therefore, according to the no-bererah approach—i.e., no retroactive clarification—the separation simply did not work. Note that according to Rashi it did work in some manner; that is precisely what his disputants reject. For them there is no ontic doubt, only epistemic.

Still, it is hard to accept, even on Rashi’s terms, that every pair of log is terumah—even tenuously. After all, only two log can be terumah, since he separated one-fiftieth of the quantity, not the entire amount. From here one may even say that in the indeterminate state there is a logical contradiction: if these two log are the terumah then those are not, and vice versa. How can both this pair and that pair be terumah?! It is important to see that a regular (epistemic) doubt is coherent, since there really are just two log of terumah and we merely lack knowledge of which they are; ignorance is possible. But an ontic doubt—indeterminacy in reality—is a contradictory state. And yet, as I explained, the epistemic reading (there are specific two log and we don’t know which) is implausible here. In sum, we seem to be at an impasse.

“Kiddushin That Are Not Capable of Consummation”

This doubtful state recalls the law of “kiddushin she’einan mesurin lebi’ah” discussed in column 323 in that same series. The Gemara in Kiddushin 51a cites a dispute between Abaye and Rava:

It was stated: Kiddushin that are not capable of consummation—Abaye said: they take effect; Rava said: they do not take effect. Rava said: Bar Ahina explained to me: “When a man takes a woman and comes to her” (Deut. 24)—kiddushin capable of consummation take effect; kiddushin not capable of consummation do not take effect.

The case is of a man who gave a perutah to a father and betrothed one of his two daughters, Rachel or Leah, without specifying which. These are kiddushin not capable of consummation, since he may not have relations with either lest she be his wife’s sister. The assumption is that either Rachel is betrothed (and Leah is his wife’s sister) or Leah is betrothed (and Rachel is his wife’s sister). Because of the doubt, he is prohibited from relations with both; thus the kiddushin are “not capable of consummation.” The dispute is whether such kiddushin take effect (and the halakha follows Abaye that they do—the letter “kof” in the mnemonic Ya’al Kegam), but for us what matters is the shared assertion that they are not capable of consummation.

Why are they prohibited? I explained there that this is not a conventional (epistemic) doubt. If it were, then at least according to Rambam—who holds that a biblical doubt is lenient biblically—it would be permitted to have relations with each one. Beyond that, the nature of the case makes it clear: there isn’t some determinate woman who is betrothed with only our knowledge lacking. Here, even the Holy One cannot point to the betrothed woman, for there is no such determinate woman. This is not epistemic doubt but ontic indeterminacy. Briefly: not a doubt but an indeterminacy. What happens in such a case? We cannot say that either Rachel is betrothed or Leah is, and I am in doubt. Yet something happened: there is in some sense one woman who is betrothed. It is customary to explain (following R. Shimon Shkop) that according to Abaye both are betrothed with a tenuous kiddushin—just as we saw in Rashi’s approach to bererah. According to Rava such kiddushin cannot take effect—but he too agrees that if they did, relations with either would be prohibited (that is precisely why, in his view, they do not take effect).

The major problem is that even here such an account is hard to accept, perhaps even more than in the wine case. Even if we say that both Rachel and Leah are betrothed with tenuous kiddushin, we would still have a state where two sisters are betrothed to me—a logical contradiction. Again: in an epistemic doubt there is no problem—only one is actually betrothed, and I simply do not know which. But a state where both sisters are simultaneously betrothed to me (ontic indeterminacy) is contradictory. The tenuousness does not help; at best one has a “tenuous contradiction.” Analogously, even if it were rabbinic it would still be a contradiction; rabbinic contradiction is still contradiction. Thus it seems implausible that both sisters are betrothed to me at once. So what then? We are back at the same impasse.

The Wavefunction in a Nutshell

In column 322 in the series I described the double-slit experiment in quantum theory. Briefly: when an electron is sent toward a barrier with two slits, it turns out that it passes through both, just like a light wave, and interferes with itself as recorded on the screen placed beyond the barrier. This is a wave-like state (like light passing through the two slits, which of course goes through both). But if we place a detector at one slit (which lights up if the electron passed through that slit; if not, then it passed through the other), then the electron passes through only one slit (one of the two: either the one with the detector or the other); that is, placing the detector yields particle-like behavior (a particle can pass through only one slit, not both).

I noted there that there are two independent innovations: (1) a particle can behave like a wave (so long as it is not measured). Its behavior is described by a wavefunction (like a light wave dispersed in space). (2) If one measures (places a detector), its wavefunction “collapses” to a particle-like state. These two innovations are independent. In principle, we could have discovered that the particle behaves wave-like without there being any collapse phenomenon. Collapse is not a consequence of wave-like behavior; it is an additional empirically discovered phenomenon (it belongs to measurement theory, not quantum theory per se). One cannot infer it from wave-likeness alone.

Here too a logical problem arises, similar to what we saw above. If it is a particle, how can it pass through both slits? Apparently this is a contradiction: if it passed through slit A then it did not pass through B, and vice versa. One cannot say a particle passes through both simultaneously. Here too, people say that it passes through each slit “tenuously.” Note: according to quantum theory this is not a doubt as to which slit it passed; the claim is that it passed through both. What confuses many is that if we place a detector and check which slit it passed, we find it passes through only one, and the probability of A or B is given by the wavefunction. In that case the wavefunction indeed encodes probabilities. But absent measurement, the assertion that the particle passed through both slits is not probabilistic. It passes through both, like a wave. The “doubt” in the double-slit experiment is ontic (indeterminacy), not epistemic.

But saying “it is a wave” is not precise; otherwise the mystery of quantum mechanics would be easily resolved. What is the problem with a wave passing through both slits? That is what waves do. Our case concerns a particle that passes through both slits—that is what creates the difficulty. How do we remove the logical problem? We must realize that we cannot maintain a scientific (or any) theory that contains a logical contradiction. Such a theory is empty, for from a contradiction one can derive any conclusion (and its negation). If there is a contradiction, we must remove it; the theory must be coherent.

In quantum theory we remove the contradiction by the concept of superposition. The particle’s wavefunction is described as a sum of two particle-states, in one it passes through slit A and in the other through slit B. Note that this is not a statement that it passes through both slits. The “particle” (not really a classical particle) is in a superposition—i.e., a sum or combination of two states, each of which on its own is logically coherent:

α[0,1> + β[1,0>

Each of the two states is coherent, since it describes the particle’s status relative to the two slits: state <1,0] describes a particle that passes through slit A and not through slit B; state <0,1] describes passage through slit B and not slit A. The coefficients α, β indicate how much of the “particle” is in each of these particle-states. They describe the “smearing” of the “particle” across these states. As mentioned, if we place a detector, the function suddenly acquires a probabilistic meaning: these coefficients then give the chance that the particle will pass through slit A (probability ) or B (probability ). Each addend above is a particle-state, but each is coherent because in each there is passage through only one slit. So what is the entity described by their sum? It is not a wave but a particle—in a superposition.

It is crucial to understand that the composite (superposed) state described by the sum above does not describe a particle passing through both slits, which might be denoted [1,1>.[2] Such a state is not logically coherent. Our case is a sum of two states each of which is coherent, and therefore the sum is coherent. It is a sum of states, not of “the same particle going through both slits.” When I write this sum, I mean that the “particle” is in a superposition of the two particle-states. Note that the “particle” here is not a classical little ball, but an abstract entity that may be in various particle-like or wave-like states. It is indeed a “particle,” but it has particle-like properties only when it is in one of the particle-states, not when it is in superposition. When we speak of an electron, we are not speaking of a particle in the classical sense but of some abstract entity. When that entity is in a state like <0,1] and its like, only then may we speak of a classical particle.

The logical significance is critical. The presence of such an abstract entity as a sum of two different particle-states (a superposition) is not a logical contradiction because the sum describes the state of an abstract entity, not a particle. A single state (each of the addends) does describe a particle state, in which the particle truly passes through only one slit—hence coherent. This description is logically consistent—and precisely thereby quantum theory is purged of contradictions (and may have factual-scientific content).

Back to Halakha: Kiddushin in Superposition

Returning to our two halakhic topics—kiddushin not capable of consummation and the wine in the bererah sugya—we saw that the declaration that both sisters are betrothed is not logically consistent (Halakha does not allow marrying two sisters: if one is wife, the other is wife’s sister). The same seems to be true for the wine (with a reservation below). On the other hand, we saw that these are not ordinary doubts (there is one woman and we do not know which; or there are specific two log of terumah and we do not know which). The only way to produce a logically coherent description is to use the logic of quantum superposition. The coherent description says that the women-state is described by the sum in the formula above. It is a superposition of two states, each coherent. For the women: “Rachel is betrothed to me and Leah is my wife’s sister” together with the state “Leah is betrothed to me and Rachel is my wife’s sister.”

Note that this is not equivalent to the claim that both are betrothed to me—which is contradictory. Even the claim that both are betrothed with “tenuous kiddushin” is contradictory; it parallels the [1,1] state above. But that is not our case. It seems the only way to present this coherently is via quantum superposition. The implication is that the kiddushin do not address the two women but some abstract entity (a wavefunction), which may be described as the sum of the two women. Such an entity may be in a superposition of states of a single woman; that sum is not contradictory. This means the odd kiddushin here make the two sisters into one abstract composite object upon which the kiddushin fall (the abstract entity is what is “betrothed” to the husband). Put differently: we are speaking about the kiddushin, not about the women. The superposition says the kiddushin that arose are one kiddushin spread over two women; but it is a single kiddushin, so there is no contradiction.

It is important to understand that even Halakha cannot live with contradictions, lest it be drained of content. This demand is not limited to scientific theory but to any theory. The only way to present this contradiction-free is by quantum superposition. I do not mean to claim that our sages knew quantum theory. Moreover, had you asked them they might have told you that both are betrothed with tenuous kiddushin (as R. Shimon Shkop writes). Such descriptions are not correct formulations of a correct intuition; the logically coherent description is that offered here. A person may have an intuition, while not being aware of its problems or of its precise formulation; the later interpreter understands and explains him better than he himself (see examples and elaboration on this phenomenon in the series 622 – 626).

Quantum Collapse in Halakha

So far we have seen superposition or indeterminacy in Halakha. But we saw above that quantum theory adds another novelty: collapse. Can that, too, be found in Halakha? Here we must return to the bererah sugya.

Seemingly everything I have described applies as well to the wine (though I will later qualify this). If so, according to the view that there is bererah, we encounter precisely a case of quantum collapse. When two specific log remain, the prior superposition that had hovered over all pairs is shed, and it is clarified retroactively that these were the terumah log from the outset. This is quantum collapse of the superposition that applied to all pairs in the cask. If so, apparently we have found quantum collapse in Halakha as well. What about kiddushin not capable of consummation—can one speak of collapse there? Seemingly not. What distinguishes this case from bererah? This is addressed by the following dispute among the Rishonim.

Ritva vs. Tosafot Rid

In column 324 I cited the dispute among the Rishonim regarding collapse in Halakha; I now wish to revisit it and sharpen it further in light of the account here.

The Ritva, on the sugya of kiddushin not capable of consummation (Kiddushin 51a), asks:

“In the margin of the manuscript it says: There is great difficulty, for if we say bererah, then the kiddushin were capable of consummation from the outset.”

He assumes that for the view that accepts bererah (as with the wine), even in the case of one who betrothed one of two sisters he could, the next day, choose one of them to be his wife, and this would clarify retroactively that she was his wife from the outset. In doing so the betrother disperses the quantum indeterminacy and selects a classical state (only one wife)—precisely as in collapse in quantum theory. In light of that, he asks: such kiddushin should be capable of consummation. Why then do Abaye and Rava both agree that if they take effect, relations with either are prohibited?

The matter is stated even more explicitly by the Ritva in Yevamot 23b:

“If you will ask: Why are they not capable of consummation from the outset? For since he said ‘one of them,’ he can clarify which, and it will be clarified that this is whom he betrothed retroactively for one who accepts bererah; and Abaye and Rava accept bererah in Perek Kol haGet.”

The Tosafot Rid in Kiddushin there asks the same question regarding consecrating 40 loaves of a thanksgiving offering out of 80:

“All agree that where he said, ‘Forty out of eighty shall be consecrated,’ they are consecrated. I saw people ask: R. Yochanan holds everywhere that there is no bererah.”

He wonders why we say all are consecrated; if there is bererah we should take this as a case where 40 are consecrated and only later clarified which.

The Tosafot Rid resolves this by comparison with kiddushin not capable of consummation:

“These words are nonsense. When we say ‘forty out of eighty are consecrated’ because of bererah, this is comparable to one who betroths one of five women and did not specify which—where all require a get. So here, for each and every loaf one can say ‘this one he consecrated,’ and therefore they are all consecrated out of doubt, and they are eaten with the stringencies of thanksgiving loaves. Surely, if he had said, ‘I will select forty of them and say: these shall be holy and the rest chullin,’ then it would be appropriate to say there is bererah. But this cannot be said, even according to one who accepts bererah—that we would release consecrated items to chullin by bererah—for there is nothing to clarify here: since he did not designate which he consecrated, they are all in doubt. And similarly with the five women, one cannot rely on bererah and say, ‘This one I desire,’ and it is clarified she was the one betrothed—for since at the time of kiddushin it was in doubt, what bererah is there? Surely, if he had said, ‘Whichever I wish today or tomorrow,’ and likewise with the loaves, then he could rely on bererah since he hung it on his will. But this, that he betrothed initially in doubt without designating which—one cannot speak of bererah there.”

He argues that the linkage between kiddushin not capable of consummation and bererah is mistaken. If the betrother had said, “I betroth whichever I choose tomorrow,” then certainly, on the view that accepts bererah, he could come tomorrow, choose one, and it would be clarified retroactively that she had been betrothed from the outset and the other not. Such kiddushin would indeed be capable of consummation (because this is an epistemic doubt—the particular woman is fixed even if the betrother has not yet chosen). But in our sugya he betrothed “one of two sisters” without adding that he intends the one he will choose tomorrow. In such a case, an ontic indeterminacy arises in the kiddushin (according to Rashi and Mahar”i; perhaps Tosafot, who disagree, follow Rava about bererah). Since that is so, one cannot come tomorrow and choose one. His claim is that the ability to choose tomorrow is contingent on having stipulated this at the time; without such a stipulation, once an ontic indeterminacy arose, it cannot really be altered. Therefore, if a man betrothed one of two sisters without a condition, he cannot add it after the fact. The die is cast. He compares this to the impossibility of redeeming consecrated items into chullin after consecration.

Indeed, in most examples where bererah is applied, the doer says in advance (at the time of the act—divorce, separation of terumah, etc.) that he is doing this on whatever will be chosen later. If the statement accompanies the act, it can qualify it and hang it on the future choice. But if one simply creates an indeterminate effect, that is what took effect; what has already taken effect cannot be casually altered later. This, it seems, is true even for the view that accepts bererah.

In that column I suggested that the Ritva and the Tosafot Rid disagree whether bererah can apply where there is ontic indeterminacy—i.e., when the doer did not explicitly hang his act on a future clarifying event. The Ritva assumes that nevertheless the mechanism of bererah can be applied, while the Tosafot Rid says no. But on further thought, that seems unlikely. We saw that the whole discussion of bererah concerns ontic indeterminacy. In an epistemic doubt there is no need for bererah, since there is already now a particular betrothed woman (or two terumah log), and our ignorance of which is no different from any halakhic doubt. And if I myself can choose a woman later, why prevent me from choosing one now and having relations?

Either way, the Ritva asks why, for the view that accepts bererah, there exist kiddushin not capable of consummation at all; the Tosafot Rid disagrees. In that column I brought three answers that the Ritva offers in Yevamot (the second of which is essentially the Tosafot Rid’s view), but that is not our concern. For us what matters is that in the Ritva there is a conception (in his question and his first and third answers) that bererah applies even in kiddushin not capable of consummation.

Comparison to Collapse in Quantum Theory

Above I explained that the indeterminate effect created by betrothing one of several women parallels ontic indeterminacy in quantum theory. According to this, we saw that one might continue and argue that the view accepting bererah posits collapse of the wavefunction. If so, the later choice that the Ritva posits in kiddushin not capable of consummation corresponds to measurement-induced collapse in quantum theory: choosing one woman transforms an ontically indeterminate effect into a sharp (classical) effect—kiddushin on a specific woman (though unknown until the decision). The no-bererah view holds that there is indeed an indeterminate effect but no collapse. This is apparently also the Tosafot Rid’s view even for those who generally accept bererah: he holds that collapse is possible only if it was set by a prior stipulation; then it is not really “collapse” but a condition (creating a state of doubtful effect rather than ontic indeterminacy). But without prior stipulation, as in kiddushin not capable of consummation, where the indeterminacy is ontic and not doubt, collapse is impossible. According to this, even in the Ritva the claim for collapse of the halakhic “wavefunction” is proven only from kiddushin not capable of consummation, not from bererah cases, where there is prior stipulation—though the Ritva himself says there is no difference.

In that column I explained that, for the Ritva, the very existence of an indeterminate effect compels a mechanism of collapse; lacking any source and against the simple reading of the sugyot, he assumes there cannot be an ontically indeterminate effect without a mechanism to collapse it to a sharp ontic state. He pushes this so far that he even challenges the Gemara based on that assumption. In his view, even without an explicit stipulation by the doer, the very emergence of ontic indeterminacy compels collapse (for the view that accepts bererah). He is unwilling to accept ontic indeterminacy as a free-standing state. Note that this contrasts with quantum theory: there we saw that collapse is an additional assumption (of measurement theory), not dependent on quantum dynamics and ontic indeterminacy itself. In physics the conclusion of a collapse mechanism emerges from experiments that forced physicists to accept it; it is not a necessary consequence of indeterminacy alone. The Ritva seems to say that we should have expected likewise in quantum theory (before experiments) that if there is an indeterminate state, a collapse mechanism must exist (some claim it must be a human choice—i.e., measurement. Elsewhere I have noted that this is likely a popular residue, and experiments have meanwhile refuted it; even a detector whose output is discarded causes collapse). This is a large novelty.

The “Avnei Milu’im”’s Distinction

In Shulchan Aruch, Even ha-Ezer 41:2, the ruling follows Abaye that kiddushin not capable of consummation are kiddushin:

“One who betroths two women at once, whom he may not marry together due to forbidden relations, they are not betrothed. How so? If he betrothed a woman and her daughter, or two sisters at once, saying: ‘Behold you both are betrothed to me,’ they are not betrothed and none requires a get. But if he betrothed only one of them and did not specify which—e.g., he said to the father: ‘One of your daughters is betrothed to me,’ and the father accepted the kiddushin—or if two or three sisters had one act as agent to accept kiddushin for her fellow, and he placed [the perutah] in her hand and said: ‘One of you is betrothed to me’—all require a get from him, and he is prohibited from relations with any of them, lest she be his wife’s sister.”

The Avnei Milu’im there (s.k. 2) cites the dispute between the Tosafot Rid and the Ritva:

“‘And he is prohibited from relations with any of them’—the Ritva (Kiddushin 51a) writes: ‘There is great difficulty, for if we say bererah, then kiddushin capable from the outset…’ And the Tosafot Rid (ibid.): ‘Surely, if he had said ‘whichever I desire today or tomorrow,’ then he could rely on bererah since he hung it on his will; but this, that he betrothed initially in doubt—one cannot speak of bererah.’”

He now challenges the Tosafot Rid:

“His words are not clarified, for indeed according to one who holds bererah, even where he did not hang it on his will, we say bererah.”

He indeed understands the Ritva as I did above: according to him, there is bererah even without stipulation (irrespective of intention or implied choice), and he claims the Ritva is surely correct (flatly against the Tosafot Rid’s contrary assumption). His claim is that from the bererah sugyot it follows that for the view accepting bererah, one may select a woman even if the betrother said nothing at the time. This contradicts the common assumption (that the Ritva is the novelty opposing the simple reading, which deals only with cases of stipulation).

The Avnei Milu’im brings proof from Yoma:

“As we say in Yoma 55 regarding two women who bought their bird offerings jointly and one died—let us take four zuz and throw them away, and the other will be permitted, because of bererah.”

A zavah woman must bring a “kin” offering (two birds). The Gemara there discusses a case where two zavot purchased four birds (two pairs—i.e., the money for them) jointly, without defining which pair belongs to whom. One of the women died, and now only one pair is to be sacrificed; the other is chullin. The Gemara says: take the amount for two birds and cast it into the Dead Sea, thereby redeeming the two birds (of the deceased woman); the remaining money is assigned to the other women’s offerings. We see that the choice of that amount clarifies that the money thrown was the deceased’s—despite the absence of prior stipulation. Hence: bererah even without stipulation, as the Ritva claimed and against the Tosafot Rid. (Note: there is a dispute among Rishonim there; Tosafot in Temurah, cited below, read it thus—see Chavruta ed., n. 205, that others disagree.)

The Avnei Milu’im offers further support from Tosafot in Temurah:

“And in Tosafot, Temurah 30a s.v. ‘ve’idach lishtri,’ they question: if so, when prohibition falls into permitted [pieces], let us cast one aside and permit the rest…”

Tosafot asks: Why, in a case where a prohibited piece of meat falls into a mixture of permitted pieces (and it is not a case of bittul), thereby prohibiting the whole mixture, can we not take one piece, clarify retroactively that it is the prohibited one, discard it, and leave the rest permitted? If indeed there is bererah without stipulation (as seen in Yoma), then this should be an option here as well.

Tosafot answers:

“My teacher R. Meir of Rothenburg says a great rule: whenever the prohibition was clarified at the outset and afterwards mixed into permitted matter, we cannot rely on bererah since the mixture is already in prohibition; but those mixtures where the prohibition was not clarified before the mixture and only after the mixture the prohibition is born—we rely on bererah. And so too here, in one who betrothed one of two sisters, since the prohibition was not known at the outset but only by virtue of the mixture, we should say bererah.”

R. Meir distinguishes between a piece that was known to be prohibited and then mixed (an epistemic doubt) and a case where the doubt arose ab initio in a mixed state (as with the bird offerings). Likely he means: where the prohibited piece existed beforehand and only then was mixed, this is an epistemic doubt, not ontic indeterminacy (like a woman who was betrothed and then we forgot who—i.e., the betrothed woman is among the others). For epistemic doubt, bererah has no place. But with the bird offerings, not only did the problem arise in a mixed state, but it is ontic indeterminacy (no pair truly belongs to a particular woman); hence, one may clarify via later choice.

Thus, also in Yoma (per the Avnei Milu’im’s reading), and according to Tosafot in Temurah, we see like the Ritva: whenever ontic indeterminacy arises, there must be a mechanism of retroactive clarification even absent explicit stipulation.

But now we face a difficulty. If the Ritva is right and any ontic indeterminacy must come with a mechanism of clarification, then why, in one who betroths one of two sisters, are these kiddushin not capable of consummation? The betrother could choose one and thereby clarify that she was betrothed from the outset, resolving the problem. I noted that in his Yevamot commentary the Ritva gives three answers, but the Avnei Milu’im offers another:

“It appears to me that since he did not say ‘whichever I desire today or tomorrow’ and instead betrothed at the outset in doubt, then at the time of kiddushin there were no kiddushin since they were not capable of consummation; and since they did not take effect then, even if he later clarifies one of them, we cannot say that this is that which he betrothed—since there were no kiddushin at the time. But if he says ‘whichever I desire’ then at the time of kiddushin he hung the matter on his will, and they are kiddushin.”

“We wrote similarly in Ketzot ha-Choshen 61:3 regarding ‘two log that I will separate’—that there, the remainder is recognizable at the time of separation since he hung the terumah on what he will separate, and what he will separate will be the remainder recognizable. But if he says ‘two log within it are terumah,’ although he may drink relying on bererah since the prohibition was not recognized (as Tosafot in Temurah say that in such a case we say bererah), nevertheless, at the time of the separation, since he did not say ‘that I will separate,’ it does not take effect because at the time the remainder was not recognizable; later bererah does not help.”

“So here: since they did not take effect at the time of kiddushin, as they were not capable of consummation, later bererah does not help. According to us that we rule kiddushin not capable of consummation are kiddushin, but relations are prohibited due to wife’s sister, then for the prohibition bererah does help (as Tosafot in Temurah say: where the prohibition was not recognized, bererah helps). But we hold that biblically there is no bererah—consider this well.”

His claim is that even if there is bererah in kiddushin not capable of consummation, it will not render them capable of consummation. The kiddushin did not take effect initially due to the internal contradiction (kiddushin of two sisters), and bererah cannot change a state that did not exist at the time bererah would act; the initial ontic indeterminacy cannot exist on its own, so when we arrive at the moment when one wants to collapse/clarify, there is nothing to collapse. The indeterminate state never arose. In such a case only a prior stipulation can allow and install bererah. Without it, the process cannot begin. By contrast, with the thanksgiving loaves, we can say that initially the effect fell upon all eighty loaves; in such a case retroactive clarification is possible even without stipulation. He may mean that in the first case (two sisters), absent an explicit statement, bererah helps only prospectively—i.e., collapse occurs but does not act retroactively.

Explanation

What is the difference between these two cases? Why does indeterminacy not arise initially in betrothing two sisters, but does with the loaves? Note that in betrothing one of two sisters there is a built-in contradiction, whereas in the thanksgiving loaves there is not. There is no principled bar to consecrating all eighty loaves, beyond his desire to consecrate only forty. But with two sisters, even if he wished kiddushin to fall on both it cannot work halakhically: there is a logical contradiction (Rachel’s kiddushin contradict Leah’s, and vice versa). Therefore, in kiddushin not capable of consummation, argues the Avnei Milu’im, the initial state is contradictory and cannot exist; thus bererah cannot help to choose one of two states when the initial state of both contradictory states cannot exist. In such a case a statement is needed to create the collapse: what does the statement do? It seems to convert the state into doubt, upon which bererah can act. If from the outset only one is betrothed, retroactive clarification merely identifies her; that is possible for the view that accepts bererah.

But the Ritva of course does not accept this distinction (he remains in difficulty). In his view, for the view that accepts bererah, bererah should work even there. What is the basis of their disagreement? We saw that to make such a state coherent at the moment of kiddushin one must split it into a superposition—i.e., construct it as a sum of two states, each coherent, as described above. The Avnei Milu’im can assume that such a state is impossible, for he sees a contradiction (he did not study quantum theory); or he may hold that even if it is possible, we have no source that collapse applies there, since bererah is stated only when there was an explicit statement. The two innovations in quantum theory are independent; thus even if one accepts the possibility of superposition, it does not follow that there is collapse. By contrast, the Ritva perhaps says such a state is coherent and therefore may exist—and, in his view, there can also be collapse there (either because the two innovations are not independent, or because bererah teaches the second innovation in such cases as well). Again, I do not mean that the Ritva was aware of quantum superposition logic; rather, he had the intuition that such a state can be coherent.

As noted, all this is said in the contradictory case like kiddushin not capable of consummation. But in the thanksgiving loaves, there is no contradiction in the initial state that all eighty are consecrated, even without bererah. There is no bar to saying that all eighty loaves are consecrated with a tenuous consecration (for there is no rule forbidding all to be holy). There the initial indeterminate state can indeed arise, and therefore there can be retroactive clarification even without a prior statement. This is indeterminacy (there are not forty consecrated loaves but eighty), yet it resembles an epistemic doubt more than a contradictory indeterminacy (as with kiddushin not capable of consummation).

Summary: The Role of Contradiction in Decomposing into Superposition

Thus, the contradiction present in the superposition state is essential for understanding the sugya and the varying views. This is the point I wished to sharpen here relative to the earlier columns. We saw that contradiction compels us to create a superposition (else we would face a logical contradiction), and that is what raises the difficulties and differing opinions. Where there is no contradiction between the options (as with the thanksgiving loaves) there remains indeterminacy in reality (which forty are consecrated), and we say all eighty are consecrated with a tenuous consecration—but there is no reason to posit superposition, since the [1,1] state in such a situation is itself coherent (even without decomposing into and summing coherent states). This is exactly like one who betroths one of five women who are not sisters without defining which; there is indeterminacy like the loaves, but no quantum superposition. This is unlike the case of betrothing one of two sisters, where the [1,1] state (both betrothed with tenuous kiddushin) is contradictory and therefore must be decomposed into a superposition of coherent states.

In the non-contradictory case, according to the Avnei Milu’im, the problem will not arise at all. Not only will we say that all are betrothed out of doubt and these are not kiddushin not capable of consummation (for there is no prohibition that all be betrothed to me—they are not sisters), but here one could also select one and resolve the matter retroactively. In a non-contradictory state from the outset, no superposition arises but something like an epistemic doubt (even though in truth it is also an ontic indeterminacy), and that can be clarified for the view that accepts bererah. Only contradiction generates the need for superposition.

[1] R. Yosef Engel, in his Atvan d’Orayta, rule 2, argues that there is a dispute among Rishonim whether the prohibition of tevel itself is due to the terumah mixed in the chullin, in which case tevel would itself be a doubt of terumah. I think this is not relevant to our issue, since he too agrees these are two distinct prohibitions (for at the tevel stage the terumah has not been separated); rather, in his view the reason for the tevel prohibition is the potential loss of terumah. In his own words it is unclear, and further discussion is warranted.

[2] More accurately: <α,β]. For simplicity I ignored this.