Can you break it down in more detail instead of just saying “he’s an idiot”

I wrote to you to present his argument with premises and a conclusion, and if you don’t see it on your own I’ll try to address it.
All the best

He says that if A=A
and in two completely identical universes, even at the quantum level,
will there be a difference between them after some time?
If yes, then A≠A
If not, then there is no free choice

That’s still too general and doesn’t sharpen the point. Now try to sharpen the argument further. A logical argument has to be formulated precisely, clarifying exactly what each line means (each claim) and exactly how one moves from line to line, and in the process one sees that there are several premises and transitional steps missing from his “formalization.” When you do this, it will be an excellent exercise for you in examining arguments (that’s the main point of logic), and you’ll immediately see that this is nonsense suited to someone who completely lacks skill in critical and logical thinking.

Can you answer?
Or at least phrase it better

No. I insist, for didactic reasons, that you do the work and present the argument properly. Only afterward (if necessary) will I respond. The reason is that my goal is not to answer this specific argument (it isn’t worth that), but to teach you how arguments should be analyzed in general. You’re an intelligent guy, and precisely because of that I think this is the right way to do it. I promise you that you’ll learn quite a bit from this (and you’ll also stop looking down on philosophy and believing only in science, as you declared in our meeting. You’ll see here why it’s important for a scientist to be skilled in philosophy, and why Kaku—who is probably a successful scientist—suffers from not being skilled in it).
Still, to help you, I’ll give you a few hints for your work:
1. What does A=A mean? Is it equality or identity? For example, there are two raindrops that look exactly the same—are they one drop or two? You can look online for Leibniz’s “identity of indiscernibles” principle, which deals with this (and is mistaken).
2. Can two identical/equal universes (note that!) really produce two different outcomes? Even according to quantum theory, this is not at all certain. On the contrary, I tend to think not (though I’m not sure)—and if so, why? How does this relate to the principle of causality? Is the difference due to randomness or due to freedom (like freedom of the will)?
3. If two different outcomes emerge and the universes are now different, is the assumption A=A violated? In other words, assuming the initial universe is A, is the later and different universe also A? After all, it is different from the earlier universe, so how is it itself considered A (even before you compare it to its counterpart, the second universe—compare it to itself at an earlier time)?
4. According to the religious view, who created the difference between the universes? God? Kaku assumes so. Is he right?
5. Does the difference between the universes contradict the laws of logic?
6. How would Kaku himself, according to his own assumptions (the deterministic ones), explain this process of change in two identical universes?
7. Even according to his own assumptions, how does he prove from all this that either logic is violated or God has no choice? In other words: how is God’s free will connected to everything he says?
These are only some of the questions, because I don’t want to complicate the matter too much. But now think about these questions, and then try to formulate a valid argument that derives his conclusion from his premises. I’m sure that now you’ll easily see that he’s a babbler.

If you want, at the end of the process you can/we can write a systematic critical article on this argument, and maybe publish it on my site (or anywhere else you’d like). There is value in this, because again and again it becomes clear to me that intelligent people (important scientists, like Dawkins, Hawking, and others, as well as their readers) fail on ridiculous arguments like these, which nevertheless seem very deep and brilliant to those who read them. I’m interested in improving the public’s ability to think (that is my main goal on my site), so they won’t be taken captive or misled by this nonsense (both in the secular direction and in the religious direction. Both sides usually don’t know how to think systematically and therefore suffer from many fallacies).

1) Identical in space-time and in matter-energy
2) The same thing will lead to the same thing, I don’t see a problem here
3) I didn’t understand
4) If there is a difference then there is an extra-universal factor; you can call it God
5) Yes
6) Breaking the law that a thing is equal to itself
7) Are you basically claiming that it could be that God chooses not to change anything?

And I agree
There are idiots everywhere

A., you answered my questions. I sent them to you so that, on their basis, you would build a systematic presentation of Kaku’s argument. Can you present a constructed argument?
By the way, the expression “identical in space-time and in matter-energy” is not sufficiently defined. Are two completely identical photons that are in the same place and at the same time the very same photon? They have no matter, and they are identical in all their properties—in energy and in their place and time.

The same location, both at the quantum level and the same thing in quantum precision.
The argument goes like this:
Two worlds that are completely identical, even at the quantum level—will there be a difference between them after some time?
If yes, then there is no causality, because there is no reason there should be a difference
If not, then there is no choice, because there is no way to change what was predetermined

Hello A.,

Again, you didn’t answer my question about identity and equality, but let’s examine the formulation you sent.

This is the argument you put in Kaku’s mouth.
1. Two worlds are completely identical, even at the quantum level—will there be a difference between them after some time?
2. If yes, then there is no causality, because there is no reason there should be a difference
3. If not, then there is no choice, because there is no way to change what was predetermined

First, I’ll ask you what someone who doesn’t believe in God is supposed to do with this argument. According to your formulation, this whole business has nothing to do with God; what we have here is a logical proof in favor of determinism [by the way, that is only because of the very “thin” interpretation you gave the argument. There are many other possible interpretations, and that is because it is formulated so carelessly and amateurishly. For example, where in your interpretation do we need the logical law of identity, represented by A=A? He mentions it countless times in this video, but in your interpretive version it is not needed and does not appear at all. But for our didactic purposes, let’s go with your interpretation].

Second, this argument is problematic on its face, even before we start checking it (it is philosophers’ craft to identify problems in arguments a priori): after all, the thesis of determinism is a factual claim (= the world operates deterministically. That is a claim about the world, that is, a fact). Now we must examine whether this is a true or false fact. Kaku proposes a logical way to show that it is true. But there is no way to prove factual claims with an a priori argument (without observation). You, as someone who doesn’t think much of philosophy but only of science, should be the first to agree with that. This is what philosophers call the emptiness of the analytic (this is what is argued against logical proofs for the existence of God: that you cannot prove a fact with a priori tools without observation).

It is true that he also assumes that causality requires there be no difference, but causality itself is an a priori assumption (as David Hume showed, it has no empirical basis). Beyond that, your claim 2 is nothing but the result of a definition (of causality). In other words, Kaku proves determinism through a logical argument and conceptual analysis. That is what is called analytic analysis. But the analytic is empty. There is no way to prove factual claims analytically.

Good, so we understand that even before examining the argument, it is certainly wrong. Now all that remains is to inspect the argument and locate the mistake. Even in your “thin” version there are several basic errors (and in his words in the video there are many more). In brief:

A. Two worlds identical at the quantum level can develop in two different ways. Quantum theory allows different developments from the very same state, and that is the randomness in it.
One of the confusing components of quantum theory is randomness, meaning the departure from classical causality. If so, then the correct scientific conclusion is 2 (in your numbering). But what does that have to do with violating the laws of logic (the law of identity), or with the conclusion that God has no free choice? It only means that quantum theory is not causal. Hardly a great revelation.

B. Of course, in order to see whether the worlds are different or not, you need an external factor that measures the world, and its measurements and properties will yield different results. But that factor itself—is it part of the worlds or not? Is it subject to quantum theory or not? And perhaps that is God? My friend Professor Nadav Shnerb wrote an article arguing that applying quantum theory to the whole universe leads to a logical contradiction. Therefore, by definition, one cannot apply quantum theory to the whole of reality; that is, if these worlds are quantum, then at least the measurer must be outside them.
Put differently, the question whether there is or is not a difference between the worlds depends on the observer. Someone has to determine whether there is or is not a difference (to measure). In fact, before measurement there is no meaning to the question whether they are identical or different (they will probably be identical, because the quantum dynamics itself is apparently not random. From the same initial state, the wave function reaches the same state at every time. Only the measurement introduces the change).
Now ask yourself whether the observer itself is not subject to quantum theory. After all, the human being is part of the quantum world he is observing. He too develops quantum-mechanically over time, doesn’t he? And in general, does he belong to world A or to world B?

C. Even if, for some reason, someone decides that these two worlds will develop in the same way (contrary to the findings of quantum theory), that only means that the laws of nature are deterministic. Let us assume for the sake of discussion that God decided they would be that way (another unsupported assumption. Maybe they are simply that way because they are that way, as the atheist who does not believe in a creator of the laws thinks). But even if He is the one who created the laws (as I indeed think), why does that prove that He has no free will or free choice? It only means that He does not apply His free will to inanimate nature. But He still has free will in one of the following senses:
1. Maybe He chooses in other contexts/places.
2. Maybe He does not choose at all, but He can choose (He chooses not to choose).
3. Or maybe He chooses only in the contexts of human actions, where people have free will and are not completely subject to the laws of nature.
And that is only regarding your “thin” version. In the video and in Kaku’s formulations there are many more errors, nonsenses, and question-begging assumptions.