we should be able to come up with a one line description of it.

Take this equation: y=2x+7. In English it would be y is equal to twice x increased by 7. — TheMadFool

Do something similar with the equation for superposition (Schrödinger's?). — TheMadFool

I'm not satisfied with your answer. Thank you for taking the trouble to explain it though. G'day. — TheMadFool

Can you please write that in the usual bra–ket notation?
Especially the minus sign in R2 is strange. — SolarWind

However, the equation is just one line. — TheMadFool

What I see is the problem how, math is a language, a perfectly sensible expression (equation of quantum superposition) in math when translated into another language (natural languages like English), most who do so end up with a contradiction? I can't wrap my head around that, sir/madam, as the case may be. — TheMadFool

Suppose this :point: E is the equation for the superposition of spin states of a particle.

Your task: Translate E into English. — TheMadFool

Contradictions are about statements or propositions, reality itself is not contradictory. Contradictions only occur in language, i.e., when using concepts. — Sam26

The traditional source of the law of non-contradiction is Aristotle's Metaphysics where he gives three different versions.[14]

1. ontological: "It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect." (1005b19-20)
2. psychological: "No one can believe that the same thing can (at the same time) be and not be." (1005b23-24)[15]
3. logical (aka the medieval Lex Contradictoriarum):[16] "The most certain of all basic principles is that contradictory propositions are not true simultaneously." (1011b13-14) — Law of non-contradiction - Wikipedia

That's what I was getting at. What about Schrödinger's cat thought experiment? I suppose it's a veiled criticism of the Copenhagen interpretation which is open to so-called quantum weirdness. — TheMadFool

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks. — The Present Situation in Quantum Mechanics, 5. Are the Variables Really Blurred? - Erwin Schrodinger

Yes, despite my math illiteracy, I can tell, it's safe to assume, that there's no mathematical contradiction. The question then is, why do people, scientists, Schrödinger himself for example, resort to analogies that are frank contradictions (the cat is both dead and alive)? — TheMadFool

Then why all the hullabaloo about Schrödinger's cat? There's something odd about quantum mechanics, that's for sure. — TheMadFool

Why? Using only the axioms of math, whatever they are, we've arrived at a contradiction. What's the next step? — TheMadFool

1. How on earth does math state, as a mathematical equation probably, the contradiction referred to above (bolded/underlined) without itself being contradictory? This is diabolical sorcery: Here is a mathematical equation :point: Schrodinger's equation perhaps and it's not a contradiction BUT when translated into English, :point: both up AND down, it is a contradiction. — TheMadFool

2. Is it possible that quantum mechanics reveals that math is inconsistent? — TheMadFool

I mean the non-unitary collapse of the wave function. — DeScheleSchilder

The MWI of Everett does away with this. But at the points where a split into two worlds finds place, it seems that a comparable thing to collapse happens. — DeScheleSchilder

Bell constrains but not forbids. There even has been proposed an experiment to distiguish between pure, clean chance and dterminism. — DeScheleSchilder

Why are these undesirebale? — DeScheleSchilder

Isn't the unitarity problem, in the MWI, shifted to the branching points? — DeScheleSchilder

To put it differently, why do almost all think that Einstein (inherent determinism) was wrong and Bohr (inherent probability) was right? — Prishon

Call these strategies "change the philosophy" and "change the physics", respectively.

Famous examples of the change-the-philosophy strategy are the original Copenhagen interpretation, as espoused by Niels Bohr, and its various more-or-less operationalist descendents. Many physicists are attracted to this strategy: they recognise the virtues of leaving quantum mechanics — a profoundly successful scientific theory — unmodified at the mathematical level. Few philosophers share the attraction: mostly they see the philosophical difficulties of the strategy as prohibitive. In particular, attempts to promote terms like “observer” or “measurement” to some privileged position in the formulation of a scientific theory are widely held to have proved untenable.

Famous examples of the change-the-physics strategy are de Broglie and Bohm’s pilot-wave hidden variable theory, and Ghirardi, Rimini and Weber’s dynamical-collapse theory (see the discussions in chapters X and X of the current volume). Many philosophers are attracted to this strategy: they recognise the virtue of holding on to our standard picture of scientific theories as representations of an objective reality. Few physicists share the attraction: mostly they see the scientific difficulties of the strategy as prohibitive. In particular, the task of constructing alternative theories which can reproduce the empirical successes not just of non-relativistic particle mechanics but of Lorentz-covariant quantum field theory has proved extremely challenging.[5] — The Everett Interpretation - David Wallace, 2010

I'll have a re-read when I get a mo, but iirc the friend records that a measurement had taken place but remains unentangled with Wigner because no communication occurs. — Kenosha Kid

But in particular, the record that the N-S value of the spin was known to the observer at time t''' is preserved.

At this point, t'''', according to the Everett interpretation, all copies of the observer are once again identical though they had been different in two branches at time t''' (69): — Quantum Theory as a Universal Physical Theory - David Deutsch, p36

If there was truly zero entanglement prior to and throughout the experiment until Wigner made his own measurement, then he ought to see interference effects as Deutsche originally intended. However by communicating with his friend, e.g. by exchange of photons or electrons, directly or indirectly, after his friend had branched, he would see no such interference effects. It just isn't possible to separate Wigner out of the wavefunction the way you think we can. — Kenosha Kid

Yes, this is what I meant regarding separability. In reality, it's not that clean: if you have two atoms, say, correlated by exchange of a photon, you cannot evolve them independently: it's a single many-body wavefunction describing the whole system, and the exchange and correlation parts of that are not trivial. — Kenosha Kid

The formalism above necessarily neglects the fact that Wigner and his friend are entangled anyway. — Kenosha Kid

What we should see in MWI is each branch evolving independently as if it were the whole universe. — Kenosha Kid

I note the posit of a 'real, objectively existing world'. Presumably this is not regarded as an axiom? It would seem a philosophical pre-supposition, at least. — Wayfarer

I'm sorry, but I just find this really creepy. And I still would like to know what Deutsch would be obliged to admit if it were shown it could not be true. I mean, what's he frightened of? — Wayfarer

If this was just a story about the friend telling Wigner that the measurement has been done by, say, sending a photon, ignoring everything else, even that the measurement was a quantum one, would you say that this process of sending a photon from one system to another didn't entangle the two systems? — Kenosha Kid

The novelty of Deutsch’s proposal [10] lies in the possibility for Wigner to acquire direct knowledge on whether the friend has observed a definite outcome upon her measurement or not without revealing what outcome she has observed. The friend could open the laboratory in a manner that allowed communication (e.g., a specific message written on a piece of paper) to be passed outside to Wigner, keeping all other degrees of freedom fully isolated, as illustrated in Figure 1. Obviously, it is of central importance that the message does not contain any information concerning the specific observed outcome (which would destroy the coherence of state (1)), but merely an indication of the kind: “I have observed a definite outcome” or “I have not observed a definite outcome”. If the message is encoded in the state of system M, the overall state is:

$\small | \Phi \rangle _{S F M} = \frac{1}{\sqrt{2}} (| z + \rangle _{S} | F_{z +} \rangle _{F} + | z - \rangle _{S} | F_{z -} \rangle _{F}) | I've \space observed \space a \space definite \space outcome \rangle {_M}$ (2)

since the state of the message is factorized out from the total state (I leave the option for the message “I have not observed a definite outcome” out, as it conflicts with our experience of the situation that we refer to as measurement and it also can be used to violate the bound on quantum state discrimination [8]). — A No-Go Theorem for Observer-Independent Facts - Caslav Brukner

In Section 8 I describe a thought experiment whose main purpose is to show how the conventional and Everett interpretations are in principle experimentally distinguishable. — Quantum Theory as a Universal Physical Theory - David Deutsch, 1985

The interference phenomenon seen by our observer at the end of the experiment requires the presence of both spin values, though he accurately remembers having known at a previous time that only one of them was present. He must infer that there was more than one copy of himself (and the atom) in existence at that time, and that these copies merged to form his present self.

So the upshot is that the friend has made a definite measurement and reported that she has done so to Wigner, without telling him what the result was. At the same time the lab remains in superposition for Wigner, per your (B).
— Andrew M

But at this point at the very latest Wigner and his friend should be entangled as they are exchanging information, i.e. they are not two independently evolving systems. — Kenosha Kid

I’m getting the sense that this new evidence is of the possibility of SOME information from inside the box being communicated to the friend without it being enough of the right information to collapse the wavefunction
— Pfhorrest

Yes, and maybe this is what Andrew had in mind too. — Kenosha Kid

What you're describing art the start is two unentangled systems (B). That is not what the experiment is describing, in which Wigner and his friend are correlated (should be (C), but isn't).

As I said above, the alternative is to insist that entanglement doesn't occur just when two systems exchange information, but when an observer makes a measurement, which is not justified by the experimental setup. — Kenosha Kid

The novelty of Deutsch’s proposal [9] lies in the possibility for Wigner to acquire direct
knowledge on whether the friend has observed a definite outcome upon her measurement or not without revealing what outcome she has observed. The friend could open the laboratory in a manner which allowed communication (e.g. a specific message written on a piece of paper) to be passed outside to Wigner, keeping all other degrees of freedom fully isolated. (italics mine)

Many Worlds is fully compatible with Wigner's Friend. It's just a situation where worlds not only can split but also merge again under the right conditions.
— Andrew M

That would be different to many worlds in itself. If you have to add a thing (merging criteria) that's a new theory. — Kenosha Kid

Copenhagen was originally epistemological, yes. Iirc Bohr himself went the ontological route in the end (I didn't know this until someone here found a relevant quote, should be able to dig it out if need be). — Kenosha Kid

But anyway there's a bunch of ontological Copenhagenists out there. — Kenosha Kid

Agreed, if 'reality' is left ambiguous between a unique realist objective ontology and many relativist subjective appearances. Philosophical disagreement and repeated failed attempts to discover some missing factor to make everything orthodox make all objectivist attempts suspect from the start. — magritte

I'd be interested in hearing both your thoughts on what kind of relativism this is. — Kenosha Kid

The essential idea behind RQM is that different observers may give different accurate accounts of the same system. For example, to one observer, a system is in a single, "collapsed" eigenstate. To a second observer, the same system is in a superposition of two or more states and the first observer is in a correlated superposition of two or more states. RQM argues that this is a complete picture of the world because the notion of "state" is always relative to some observer. There is no privileged, "real" account. — Relational quantum mechanics

Since the observer-dependence of collapse in these Wigner's friend experiments is essentially a disagreement between observers in their own frames as to whether something is in superposition or not, something like this might be the answer.

https://www.nature.com/articles/s41467-018-08155-0 — Kenosha Kid

What does this mean? Some interpretations of quantum mechanics would be less compelling. The ontological Copenhagen interpretation is out. Many worlds is out, but not it's curious variant 'many minds' (in which there's no universal branching, rather the mind remains branched). Bohm and the epistemological Copenhagen interpretation look unaffected to me. — Kenosha Kid

There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature. — Niels Bohr (as quoted by Aage Petersen)

More broadly, can it really be that reality is subjective? It looks objective enough, but that's the classical limit at work. — Kenosha Kid

That said, Wigner and his friend aren't people in these experiments... Consciousness does not appear to be a prerequisite for having a unique external reality. Is it nothing more than localism, another relativism with another kind of reference frame? — Kenosha Kid

↪TonesInDeepFreeze ↪Andrew M
Seems we have agreement that modus ponens is not invalidated by the argument in the OP; that the premises are true, the argument valid and the conclusion true, but incomplete. — Banno

And we can bring out even more clearly what is wrong with these supposed counterexamples by considering the following modification of (1) - (3):

(7) If a Republican wins, then if he is not Reagan he will be Anderson;
(8) A Republican will win;
(9) If he is not Reagan, he will be Anderson.

The antecedent of (7) restricts the possibilities for the interpretation of the pronoun in its consequent. The second assumption (8) does the same job for the conclusion (9), and it would be a transparent mistake to try to interpret 'he' in some other way, in an attempt to show that (7)-(9) is invalid. McGee would make a mistake of this type if he thought of (8) as a relatively long-lasting mental state of justified belief outside of the context of this inference. He would not then see (8) as an assumption in an inference, determining in that context which proposition is expressed by (9).

An inference should be defined in terms of a relationship between assumptions and a conclusion, as is standard in logic. We should remember that the assumptions can restrict the relevant set of possibilities and so affect the propositions expressed under them, just as the antecedents can affect the propositions expressed by the consequents of conditionals. We must therefore be careful about the propositions expressed in inferences, particularly ones containing conditionals, if we wish to question their validity. — Assumptions and the Supposed Counterexamples to Modus Ponens, D. E. Over, Analysis, 1987

1. Either Shakespeare or Hobbes wrote Hamlet.
2. If either Shakespeare or Hobbes wrote Hamlet, then if Shakespeare didn't do it, Hobbes did.
3. Therefore, if Shakespeare didn't write Hamlet, Hobbes did it.

Since Shakespeare did write Hamlet, the first premise is true. The second premise is also true, since starting with a set of possible authors limited to just Shakespeare and Hobbes and eliminating one of them leaves only the other. However, the conclusion may seem false since ruling out Shakespeare as the author of Hamlet would leave numerous possible candidates, many of them more plausible alternatives than Hobbes. — Modus Ponens - Alleged cases of failure - Wikipedia

(background assumption) 1 — TonesInDeepFreeze

So my solution is that there is good reason to believe both ~R -> A and ~R -> C.

Though it is counterintuitive to believe ~R -> A.

So there is good reason to believe something that is counterintuitive. And that is counterintuitive. (Is it paradoxical?) And modus ponens ponens is not invalid. And I think the problem has more to do with disjunction than with modus ponens. That aligns with you and fdrake in the sense that the puzzle results from leaving off Carter in the disjunction. — TonesInDeepFreeze

That's really good. It puts the puzzle in stark formal terms and takes out the background noise about the historical election facts. Thanks. — TonesInDeepFreeze

In the broader context of all the die faces, the inference would be invalid
— Andrew M

I don't get that. The logic is monotonic. So how can adding premises make the argument invalid? And how would we formalize the inclusion of a broader context? I surely see the point that not mentioning (2) relates to the problem, but I don't know how we would formulate that other than just mentioning it, and how it would overturn an argument in a monotonic logic. — TonesInDeepFreeze

Meanwhile, I'm inclined to think that a solution would center around problems with the notion of "good reason to believe". — TonesInDeepFreeze

I only have this example. Does anyone have more? — Banno

[odd]  1: 80%
[even] 2: 19%
[odd]  3: 1%

The issue of realness, which is my main interest, is not boarded, penetrated, or even significantly reach by the cultural use of language, not even by specialty uses of language of writers such as Wittgenstein, Ryle, Austin, etcetera because what is handled by them is logic. — Nelson E Garcia

So if you have a prejudice against dualities, — Nelson E Garcia

(Actually I'm reading a very interesting philosophy of physics book, Nature Loves to Hide, Shimon Malin, which attempts to situate quantum physics in the broader context of Western classical philosophy. Pity you're not nearby, I'd lend it to you.) — Wayfarer

Yes, quite. Although there's a danger here of giving the sense that QM is a bottom-up theory of ignorance: it isn't. The version of QM that encodes such ignorance (density matrix theories) is mathematically distinct from QM, and will yield different experimental predictions. — Kenosha Kid

Quantum superposition is experimentally verifiable, so the wavefunction captures something ontological. — Kenosha Kid

In principle, relativistic quantum mechanics does away with this. Instead of capturing all possible paths from a given initial state, we capture all possible paths between a given initial state and a given final state. There is no need to represent an outcome that will not happen, nor to represent interference between trajectories toward outcomes that are orthogonal. — Kenosha Kid

So what's the alternative to Copenhagen? — frank

I hold that all interpretations of QM are just crutches that are better or worse at helping you along to the Zen realization that QM is what it is and doesn’t need an interpretation. As Sidney Coleman famously argued, what needs reinterpretation is not QM itself, but all our pre-quantum philosophical baggage—the baggage that leads us to demand, for example, that a wavefunction |ψ⟩ either be “real” like a stubbed toe or else “unreal” like a dream.

...

You shouldn’t confuse the Zen Anti-Interpretation with “Shut Up And Calculate.” The latter phrase, mistakenly attributed to Feynman but really due to David Mermin, is something one might say at the beginning of the path, when one is as a baby. I’m talking here only about the endpoint of the path, which one can approach but never reach—the endpoint where you intuitively understand exactly what a Many-Worlder, Copenhagenist, or Bohmian would say about any given issue, and also how they’d respond to each other, and how they’d respond to the responses, etc. but after years of study and effort you’ve returned to the situation of the baby, who just sees the thing for what it is. — The Zen Anti-Interpretation of Quantum Mechanics - Scott Aaronson

Clear enough? — Nelson E Garcia

Ordinary language is not the last word: in principle it can everywhere be supplemented and improved upon and superseded. Only remember, it is the first word. — J. L. Austin

So with the Copenhagen Int., we can talk about superposition, but we aren't talking about reality. That's so weird. — frank

There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature. — Niels Bohr (as quoted by Aage Petersen)

the shut-up-and-calculate philosophy or the Copenhagen interpretation (which I think of as shut-up-and-calculate minus the shutting-up part)
— Get real - Scott Aaronson, Nature Physics, June 2012

Haha that's excellent! — Kenosha Kid

(Neo-)Copenhagen interpretations get around it by saying that you can't talk about the state of reality independent of measurement.
— Andrew M

That is the point that I was trying to make. I think it calls into question Kenosha Kid’s view that there is ‘one objective reality’ which all interpretations try to approximate or interpret. — Wayfarer

I agree that reality may be one, but that unity must necessarily transcend subject-object dualism, — Wayfarer

meaning that it’s out of scope for naturalism as such. — Wayfarer

We learn that things (objects) exist in their own, but in fact each time you sense-target there is only a substratum which requires mind to become an existent. — Nelson E Garcia

Such state of affairs does not affect logical facts such as the one you mentioned: “the Earth existed billions of years before the emergence of human beings (with minds).” — Nelson E Garcia

Therefore before you become acquainted with my whole frame of mind, all significant aspects of it, I suggest taking my initial explanation as a correction of misguided language. In metaphysical talk (perception metaphysics in particular) it is incorrect to refer to existence-in-its-own, there is no such thing in the universe. Existents become by act of mind. — Nelson E Garcia

I claim: Objects do not exist independently, there is no existence without mind actualizing it. — Nelson E Garcia

↪Kenosha Kid
Superposition is an epistemological situation, right? — frank

... if you adhere to the shut-up-and-calculate philosophy or the Copenhagen interpretation (which I think of as shut-up-and-calculate minus the shutting-up part) then the PBR result shouldn’t trouble you. You don’t have an ontology: you consider it uninteresting or unscientific to discuss reality before measurement. For you, ψ is indeed an encoding of human knowledge, but it’s merely knowledge about the probabilities of various measurement outcomes, not about the state of the world before someone measures. — Get real - Scott Aaronson, Nature Physics, June 2012

I favour the Platonist view. — Wayfarer

t since it was not possible for them [mathematical objects] to exist in sensibles either, it is plain that they either do not exist at all or exist in a special sense and therefore do not 'exist' without qualification. For 'exist' has many senses..
— Aristotle's Metaphysics 13.1077b-1078a [Book XIII, Part 2 - Part 3]

So, does a number, say the number 7, exist? You will say - of course, you just wrote it. — Wayfarer

But that's a symbol, which denotes a quantity, a numerical value. Different symbols can refer to the same number, but the quantity or count is what the number is, and that is something that only can be grasped by a mind capable of counting; hence, it's an 'intelligible object'.

Here is a Platonic rejoinder, consisting of a passage about Augustine's view of intelligible objects. — Wayfarer

Mathematics is true a priori and so empirical validation isn't relevant. — Wayfarer

For if attributes do not exist apart from the substances (e.g. a 'mobile' or a pale'), pale is prior to the pale man in definition, but not in substantiality. For it cannot exist separately, but is always along with the concrete thing; and by the concrete thing I mean the pale man. Therefore it is plain that neither is the result of abstraction prior nor that which is produced by adding determinants posterior; for it is by adding a determinant to pale that we speak of the pale man.

It has, then, been sufficiently pointed out that the objects of mathematics are not substances in a higher degree than bodies are, and that they are not prior to sensibles in being, but only in definition, and that they cannot exist somewhere apart. But since it was not possible for them to exist in sensibles either, it is plain that they either do not exist at all or exist in a special sense and therefore do not 'exist' without qualification. For 'exist' has many senses.

...

The same account may be given of harmonics and optics; for neither considers its objects qua sight or qua voice, but qua lines and numbers; but the latter are attributes proper to the former. And mechanics too proceeds in the same way. Therefore if we suppose attributes separated from their fellow attributes and make any inquiry concerning them as such, we shall not for this reason be in error, any more than when one draws a line on the ground and calls it a foot long when it is not; for the error is not included in the premisses.

Each question will be best investigated in this way - by setting up by an act of separation what is not separate, as the arithmetician and the geometer do. — Aristotle's Metaphysics 13.1077b-1078a [Book XIII, Part 2 - Part 3]

1. Some observer who already has information on the state of entangled particles. God??? — TheMadFool