BINARY LOGIC v QUANTUM THEORY?
Does QUANTUM THEORY (QM) contend that a physical thing (there are no non-physical things) can exist in more places than one place at the same time?
I’m trying to defend binary logic wherein a physical thing only exists at one place at a time and it either exists or it does not. The fact that binary logic works on every level (computer logic gates, etc.) argues against QM’s contrary view an example of which is that some things don’t exist until you measure them or that the existence of a physical thing is ambiguous.
A binary logic would be one with only two truth values. The kind of symbolic logic you learn as an undergraduate would almost certainly be a binary logic called Propositional Logic. Each statement in Propositional Logic is either (and only) true, or false.
Is this what you have in mind when you refer to “binary logic”?
To violate propositional logic in this sense, quantum mechanics would have to affirm both P and not-P for some single sentence P. What example do you think there is of such a P in quantum mechanics?
*(What I mean by this a little more technically is: quantum theory is a model of propositional logic. What that means is, the atoms of propositional logic can be interpreted as statements about quantum mechanics, the true QM statements assigned the value “true” in PL and the false ones assigned “false,” and the connectives of propositional logic can be interpreted as “and,” “or,” “if-then” and so on, and once you’ve done all this interpretation, every true statement in propositional logic turns out to be a true statement in quantum theory and every false PL statement turns out to be a false QT statement.)
It depends on what you mean by a physical thing. If you’re talking about something that exists on the macro level, then no, there’s no such claim coming out of QM. But if you’re talking about elementary particles, then the situation is much more complicated. Particles may be physical things at the coarsest level of classification, but they’re fundamentally unlike macro objects, and it’s a little tough to assign them properties like location that make sense for what you’re used to.
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Computers actually have a third state, called high impedance and represented by a Z, which is neither true nor false. It was first used for bidirectional I/O pins, which are used for input and output. When you are using the pin as an input, you set a tristate buffer driving the pin to Z, so the value on the output does not conflict with the value driving the pin from outside. Tristate gates are also used internally for tristate multiplexers, which are pretty much like regular ones but faster.
Closer to the quantum world, when simulating a circuit you use an X state, which means whether the line is 0 or 1 is unknown. That is not physical, though, it just represents inadequate information and is used to make the results always accurate. Dealing with Xs leads to all kinds of problems.
That’s a hardware state, not software, which I assumed the OP was talking about. But the high impedance state doesn’t really change the logic. It’s a simpler means of implementation that allows bi-directional signals and eliminates additional switching logic. I was just about to write that there’s nothing random or undetermined about it, but then I’ve dealt with circuits that had too many tristate devices on a single wire. They ain’t magical.
We’re going to have to wait for quantum computers to come out to see real uncertainty. I’m not sure what software states are, unless you think of the instruction set architecture. There you have the IBM 1620 which looked inherently decimal to assembly language.
You do get some degree of uncertainty with tristates when you have bus conflicts, but that isn’t quantum uncertainty either.
Since when does binary logic posit that? Binary logic just says that things are either true or false, and cannot be both true and false, nor can they be neither true nor false.
And besides, you don’t even need to get as advanced as quantum mechanics to show that physical things can exist in more than one place at a time. Just consider simple waves. Look at this picture. Does it have a single position? No, it exists over a range.
Well here is the Wiki page, which matches what I’ve read in somewhat more technical publications. But I’m far from being an expert. A qubit is a 1, a 0, or a quantum superposition of a 1 and a 0, and so the result is probabilistic. I’m just glad I’ll never have to worry about testing these things.
I never got to program one, but I did learn the principles of assemblers from reading various manuals. There was one in Cooper Union, and it was probably the major draw for me (it being free was the major draw for my parents) but I chose otherwise. Still a cool computer and a cool looking computer, but rather more modern than what I learned on.
I’m not sure what is meant by “defending” binary logic.
Binary logic is a handy reasoning tool. But even without QM there are situations where, say, tri-state or fuzzy logic are more appropriate. Many “paradoxes” can be blown away by observing this.
If the OP is hinting towards computers and computability, note that any Turing machine can emulate any other. A base-2 (binary) computer is simply one of the easiest to construct. But at the application level, it does not need to work in binary logic.
Generally, in quantum logic, distributivity doesn’t hold – otherwise, you could indeed construct statements of ‘ambiguous’ truth value.
IIRC (don’t have time to check right now) Reichenbach (and maybe Putnam?) proposed to use a ternary (three-valued) logic to use for reasoning about the quantum world, but I this ultimatively lost out against the von Neumann/Birkhoff approach.
Well, I’ve come across lots of examples, but two come to mind:
Evaluating “this statement is false”.
This might be considered a paradox by many who assume every statement can be classified as either true or false (a claim which boolean logic doesn’t make, but an awareness of tri-state logic can make this more obvious).
Incidentally, the issue with “this statement is false” is not so much the contradiction, it’s that it’s purely a self-reference and there’s nothing to evaluate.
Another is all the “heap” paradoxes: e.g. since we can’t identify a particular number of hairs at which someone transitions from being “non-balding” to “balding”, it is impossible to become balding (or bald).
This is one where the “right” solution is debatable, but most agree that fuzzy logic is one possible solution (i.e. the loss of every hair increases one’s “balding-ness” and something like fuzzy collapse happens in trying to classify someone as balding or not).
p: the particle is moving to the right (I think this would be better phrased as ‘the particle’s momentum is p’, or something like that)
q: the particle is in [-1, 1]
r: the particle is not in [-1, 1]
Clearly, q v r = T, the particle is somewhere – i.e. an experiment will find it at some location, to steer clear of hidden variable accusations – thus p ^ (q v r) = p; however, p ^ q and p ^ r are both false, since if the particle’s momentum is known well, there is some uncertainty to its position, and it will have nonvanishing amplitude to be found both in and out of the interval – thus, p ^ q v p ^ r is false.
Actually, if it’s of interest to anybody, one can view the entirety of quantum theory as a sort of generalized probability theory – like the latter is built on a Boolean lattice (or algebra) (i.e. a structure which has operations like meet (‘and’, ^), join (‘or’, v), complementation (‘not’, !), is associative, commutative, distributive and then some) the former is built on an orthocomplemented lattice, which is a generalization of the Boolean lattice that precisely lacks distributivity.
