Julian Barbour presented his essay "Bit from It" at the FQXi essay contest Is Reality Digital or Analog?.

The essay is beautiful and I agree with the conclusion "Bit from It", in a way I will try to make clear. But I disagree with the way the conclusion was reached - it seems to me that the central part of Wheeler's 'ontology' "It from Bit" was overlooked, and this makes it look naive, while it is in fact very profound.

In a classical world, Wheeler's "It from Bit" would be obviously silly. When we measure something, we can write down the outcome as a string of digits, and by collecting all these digits we can determine the state. In such a world, "bit" would indeed originate from "it".

But Wheeler is discussing the quantum world. And for Wheeler, the quantum world is not just "classical world" plus "probability". Julian Barbour said: "Crucially, even if individual quantum outcomes are unpredictable, the probabilities for them are beautifully determined by a theory based on 'its'", but this is not the whole story. If this would be all, then he would indeed be right to say "I see nothing in Wheeler's arguments to suggest that we should reverse the mode of explanation that has so far served science so well". Julian Barbour tries to understand how Wheeler could do so trivial mistakes: "Wheeler's thesis mistakes abstraction for reality", and "A 'bit' has no meaning except in the context of the universe". Yet, there is no such a gross mistake.

Wheeler's "It from Bit" can be understood in the context of the "delayed choice experiment". He realizes that it is not enough to specify the outcome, but also what we measure - for example "which way" or "both ways" in the Mach-Zehnder experiment. But he realizes that our choice of what to measure determines how the state was (yes, in the past). This is the key problem of quantum mechanics, and this is the fundamental obstacle of all realistic interpretations of quantum mechanics: we choose "now" what to measure, and our present choice dictates how the state was, long time before we made our choice. We can think that there is an ontology behind the outcomes of our measurements, as in the classical world. But the "delayed choice experiment" shows that the "elements of reality" depend of the future choice of our measurements. And the outcomes depend of these choices too. So, it is in fact "the choice of what to measure" (Hermitian operator) plus "the outcome" (eigenvalue) that forms the "Bit" from Wheeler's "It from Bit". And the "It" is in fact the eigenstate corresponding to the obtained eigenvalue, given that the observable was that particular Hermitian operator. Wheeler was not that naive to think that eigenvalues determine eigenstates by themselves, without considering the Hermitian operator, so he accounted well for the prescription "A 'bit' has no meaning except in the context of the universe".

The central point of Wheeler's "It from Bit" is that the reality of today depends on the choices we make tomorrow, when we decide what to observe, and of the outcomes of the observations. He compares this with the game of 20 questions, when we try to guess a word by asking 20 yes/no questions, under the prescription that the choice of the word is not done at the beginning. The person who "knows" the word changes it by wish, so long as it remains consistent with the answer she already gave to our question. Wheeler wants to emphasize by this the similarity with the quantum state we try to determine, but which depends on what we choose to observe. This is why he was led to the idea that the state of the universe (it) results from the observations (bit).

I give more credit than Julian Barbour to the "It from Bit" philosophy - I view it as a way to present a central problem of quantum mechanics. I think, nevertheless, that it is exaggerated to conclude from this, as many do, that the world is digital. It may be or it may be not, but we should not force the conclusion. After all, the "It from Bit" philosophy is intended to clarify some points of a theory based on continuum - Quantum Mechanics.

My viewpoint on "It from Bit" is that we should regard the outcomes of measurements as "delayed initial conditions" for the Schrödinger's equation. I presented my view in this article, and this video. A solution of a partial differential equation like Schrödinger's is determined by a set of initial conditions. Classically, the initial conditions can be determined from future observations. In Quantum Mechanics, the future observations determine the state in the two meanings of the word "determine": passive - "find out what it is" (by the selection of an eigenvalue of the observable), and active - "choose what it is" (by the choice of that observable). Another central problem is that two consecutive observations of the same quantum system are incompatible, if the observables do not commute. That is, they impose incompatible initial conditions to the wavefunction. But, the second measurement is not, in fact, a measurement of the same system. The system interacted with the first measurement device, and this measurement device has many degrees of freedom which are not determined yet. So, the second observation measures in fact the composed system - the observed system plus the apparatuses used for the previous observations, and all the past interactions of the observed system. This may offer enough degrees of freedom to maintain the unitary evolution and to avoid a discontinuous collapse of the wavefunction.

My interpretation comes with a realistic wavefunction, which is not yet determined among the possible wavefunctions, but whose "delayed initial conditions" are determined by all future and past observations. I think that we cannot avoid the idea of "delayed initial conditions", no matter what "It" we choose to consider as the underlying ontology.

My view is therefore that "It from Bit" and "Bit from It" are reciprocal: a set of possible "It"s (solutions to the Schrödinger's equation), a set of possible "Bit"s (observations, delayed initial conditions) and the Universe is a pair (It, Bit), so that the "It" and the "Bit"s are compatible.

On the other hand, the "Bit" itself is part of the solution of the Schrödinger's equation, that is, of the "It". This is why I said at the beginning that I agree with "Bit from It". But if we have some "delayed initial conditions" - the "Bit"s - the "It" that satisfies to them is not necessarily unique. So, in fact, what we have is not a pair (It, Bit), but a pair ("It"s that satisfy to the observed "Bit", the observed "Bit"). There is a relation "one-to-many" between the "Bit" and the "It"s. The "Bit" appears to be discrete, but the "It" may very well be continuous. So, although "It from Bit" reflects an important aspect of Quantum Mechanics, it should not be taken too far.

The essay is beautiful and I agree with the conclusion "Bit from It", in a way I will try to make clear. But I disagree with the way the conclusion was reached - it seems to me that the central part of Wheeler's 'ontology' "It from Bit" was overlooked, and this makes it look naive, while it is in fact very profound.

In a classical world, Wheeler's "It from Bit" would be obviously silly. When we measure something, we can write down the outcome as a string of digits, and by collecting all these digits we can determine the state. In such a world, "bit" would indeed originate from "it".

But Wheeler is discussing the quantum world. And for Wheeler, the quantum world is not just "classical world" plus "probability". Julian Barbour said: "Crucially, even if individual quantum outcomes are unpredictable, the probabilities for them are beautifully determined by a theory based on 'its'", but this is not the whole story. If this would be all, then he would indeed be right to say "I see nothing in Wheeler's arguments to suggest that we should reverse the mode of explanation that has so far served science so well". Julian Barbour tries to understand how Wheeler could do so trivial mistakes: "Wheeler's thesis mistakes abstraction for reality", and "A 'bit' has no meaning except in the context of the universe". Yet, there is no such a gross mistake.

Wheeler's "It from Bit" can be understood in the context of the "delayed choice experiment". He realizes that it is not enough to specify the outcome, but also what we measure - for example "which way" or "both ways" in the Mach-Zehnder experiment. But he realizes that our choice of what to measure determines how the state was (yes, in the past). This is the key problem of quantum mechanics, and this is the fundamental obstacle of all realistic interpretations of quantum mechanics: we choose "now" what to measure, and our present choice dictates how the state was, long time before we made our choice. We can think that there is an ontology behind the outcomes of our measurements, as in the classical world. But the "delayed choice experiment" shows that the "elements of reality" depend of the future choice of our measurements. And the outcomes depend of these choices too. So, it is in fact "the choice of what to measure" (Hermitian operator) plus "the outcome" (eigenvalue) that forms the "Bit" from Wheeler's "It from Bit". And the "It" is in fact the eigenstate corresponding to the obtained eigenvalue, given that the observable was that particular Hermitian operator. Wheeler was not that naive to think that eigenvalues determine eigenstates by themselves, without considering the Hermitian operator, so he accounted well for the prescription "A 'bit' has no meaning except in the context of the universe".

The central point of Wheeler's "It from Bit" is that the reality of today depends on the choices we make tomorrow, when we decide what to observe, and of the outcomes of the observations. He compares this with the game of 20 questions, when we try to guess a word by asking 20 yes/no questions, under the prescription that the choice of the word is not done at the beginning. The person who "knows" the word changes it by wish, so long as it remains consistent with the answer she already gave to our question. Wheeler wants to emphasize by this the similarity with the quantum state we try to determine, but which depends on what we choose to observe. This is why he was led to the idea that the state of the universe (it) results from the observations (bit).

I give more credit than Julian Barbour to the "It from Bit" philosophy - I view it as a way to present a central problem of quantum mechanics. I think, nevertheless, that it is exaggerated to conclude from this, as many do, that the world is digital. It may be or it may be not, but we should not force the conclusion. After all, the "It from Bit" philosophy is intended to clarify some points of a theory based on continuum - Quantum Mechanics.

My viewpoint on "It from Bit" is that we should regard the outcomes of measurements as "delayed initial conditions" for the Schrödinger's equation. I presented my view in this article, and this video. A solution of a partial differential equation like Schrödinger's is determined by a set of initial conditions. Classically, the initial conditions can be determined from future observations. In Quantum Mechanics, the future observations determine the state in the two meanings of the word "determine": passive - "find out what it is" (by the selection of an eigenvalue of the observable), and active - "choose what it is" (by the choice of that observable). Another central problem is that two consecutive observations of the same quantum system are incompatible, if the observables do not commute. That is, they impose incompatible initial conditions to the wavefunction. But, the second measurement is not, in fact, a measurement of the same system. The system interacted with the first measurement device, and this measurement device has many degrees of freedom which are not determined yet. So, the second observation measures in fact the composed system - the observed system plus the apparatuses used for the previous observations, and all the past interactions of the observed system. This may offer enough degrees of freedom to maintain the unitary evolution and to avoid a discontinuous collapse of the wavefunction.

My interpretation comes with a realistic wavefunction, which is not yet determined among the possible wavefunctions, but whose "delayed initial conditions" are determined by all future and past observations. I think that we cannot avoid the idea of "delayed initial conditions", no matter what "It" we choose to consider as the underlying ontology.

My view is therefore that "It from Bit" and "Bit from It" are reciprocal: a set of possible "It"s (solutions to the Schrödinger's equation), a set of possible "Bit"s (observations, delayed initial conditions) and the Universe is a pair (It, Bit), so that the "It" and the "Bit"s are compatible.

On the other hand, the "Bit" itself is part of the solution of the Schrödinger's equation, that is, of the "It". This is why I said at the beginning that I agree with "Bit from It". But if we have some "delayed initial conditions" - the "Bit"s - the "It" that satisfies to them is not necessarily unique. So, in fact, what we have is not a pair (It, Bit), but a pair ("It"s that satisfy to the observed "Bit", the observed "Bit"). There is a relation "one-to-many" between the "Bit" and the "It"s. The "Bit" appears to be discrete, but the "It" may very well be continuous. So, although "It from Bit" reflects an important aspect of Quantum Mechanics, it should not be taken too far.