Killing Schrodinger's Cat

Currently, this page is a placeholder for a work-in-progress describing in detail why Schrodinger's Cat, Wigner's Friend, and macroscopic quantum superpositions in general cannot be experimentally demonstrated, even in principle.  

Existing preprints can be found here: "Killing Schrodinger’s Cat: Why Macroscopic Quantum Superpositions Are Impossible In Principle" and "Macroscopic Quantum Superpositions Cannot Be Measured,Even in Principle."

Here is a rough outline of this work-in-progress:

What I know and can write about:

·         QM as facts/correlations/history... transitivity of correlation... explaining “spooky action at a distance”... superposition = no fact... universal entanglement

o   Should I discuss that new correlations are new information? 

·         Deriving the same conclusion in terms of facts (like I did in the original paper and my original thought experiment) without need for relativity of quantum superpositions

o   Original idea: double-slit experiment done by measuring device in deep space on an object on which “there is no fact” (relative to universe) about its location... that “lack of fact” (i.e., superposition) can only continue when measured by the device if there is “no fact” about the device’s position (relative to the universe).

o   Try to use the notion of |A>_M + |B>_M, etc., in Powerpoint presentation?

o   Explain how I figured out the relativity of quantum superpositions in this post?

·         Implications:

o   QM not verifiably universal; MWI; CCCH; all the papers that depend on SC/WF, etc.

o   This solves the measurement problem because if it is impossible to measure a particular system in superposition, then whether QM applies to that system is not a scientific question, so that apparent collapse of the wave function, from a scientific perspective, is actual collapse.

·         There is only one cat.  If an “interesting” superposition could actually exist, then either configuration (alive or dead) is possible... e.g., measuring location of particle on its head in dead state would instantly “change” the location of a particle on its tail to correlate to a dead cat... vice versa for alive.  No wonder people keep talking about nonlocal “effects” in which measuring particle X in one place causes particle Y to be in another place... and also people talking about problems with energy conservation... but if instead there is only one cat (i.e., one set of correlation facts) then measuring the particle on its head just instantiates for the universe the set of correlations that already exists.

o   Note... if we’re only talking about a superposition over a shift (see below), then obviously it’s just one cat having one experience, and its position relative to the rest of the universe is irrelevant to (and can have no effect on) what it experiences.  See note in “SC-WF” document that includes statement “If they could evolve differently based on location relative to the rest of the universe, then it’s because of a dependency that can’t possibly exist if a superposition exists.”  The only way to get an “interesting” superposition is through amplification... but that’s not possible (see below).

·         “Interesting” superpositions: There is a huge difference between a superposition of a cat “shifted” over two locations (it’s the same cat and when a correlation event occurs, nothing changes about the cat... instead the cat and the universe just become better correlated (and they will both agree))... VERSUS a superposition of a cat in entirely different configurations (live vs. dead).

o   The first case is already impossible because amplification does not speed up natural quantum dispersion... it would take 3 quadrillion years for a cat to disperse adequately for a double-slit experiment assuming no decoherence... preventing decoherence over that time is impossible even in principle... and shielding doesn’t help (see my 9/24 email to Scott).  Further even if it could be “blurry” relative to the universe, the cat doesn’t see itself as blurry!

o   But even if all this were possible, that’s not what we mean by SC!!  What we mean is creating a superposition of interesting/different configurations of the cat’s matter, and the cat can’t “blur” into alive vs. dead states!  The key to my argument about amplification is that even though each of the subsequent subsystems evolves over time to different macroscopic pointer states, the superposition disappears (for the whole system) with the initial correlation (before subsequent evolutions) so that there CAN’T be superpositions of these entirely different states.

o   Also, if such an “interesting” superposition could exist, but the cat’s perspective is as valid as that of the universe, then if the cat is alive in its own frame but the universe measures it as dead, then imagine how fucked up the universe would have to appear to the cat.  (Better description on p.5 of “Gravitational Decoherence” document... also here)

 Addressing objections:

·         This is really about showing that amplification cannot make possible the impossible.  Also elaborate on the problem of shielding and why it’s a logical nonstarter.  Also be clear about “macroscopic” and “superposition.”  Also may not apply to “quantum computer” SC (but see my other papers for why conscious states can’t be copied), etc.  See 9/24 emails to Scott.

·         “A priori” armchair philosophy

·         Random stuff that I’m not clear on but I don’t think matters:

o   Monogamy of entanglement

§  No, this is irrelevant... see my 9/30/20 email to Yosi... also this and this

o   What’s special about the position operator... also how spin enters the picture.  Ultimately, if I discuss states in terms of position eigenstates, then the measurements CAN be done in the position basis and all my conclusions are correct... shouldn’t make any difference if these states are actually measured in a different basis (even though no one ever explains how, and it may not even be possible).

·         If I want to be comprehensive, make sure to address:

o   Superposition vs. mixture (quantum vs. classical probabilities) and how measuring a superposition usually requires lots of trials in a measurement basis that may be prohibitively difficult

 Ideas to explore:

·         Implications for (scalable) quantum computing

·         Time travel... if correlations embed facts/history...

·         Penrose’s gravitational collapse (assumes there are two “lumps”)

·         Black hole information paradox

·         Testability

·         If new correlations implies new information, what does this say about Rovelli’s idea of information and/or the possibility that ℏ is decreasing?

Here's my progress as of 10/19/20

Introduction

Just as logicians are bound by the laws of physics, physicists are bound by the rules of logic.

Contradictions, logically, are false statements.  Contradictions don’t exist physically or otherwise. 

Many physicists don’t realize that SC is, prima facie, nearly a contradiction.  For instance, if SC is characterized as, “A cat in state |live> + |dead> is simultaneously dead and alive,” then SC is inherently impossible because “dead” and “alive” are mutually exclusive.  Indeed, the characterization of any object in a quantum superposition of eigenstates of some observable that as being simultaneously in those eigenstates is equally problematic, so either quantum superpositions don’t exist or the characterization is wrong.

This paper is about SC, WF, the extent to which macroscopic quantum superpositions can be empirically demonstrated in principle, and the measurement problem.  This paper makes some potentially revolutionary claims about the foundations of quantum mechanics, and the typical physicist thumbing through it may summarily dismiss it on account of its lack of equations and quantum mechanical mathematical formalism.  To do so would be a mistake.  The failure in the past century to solve the measurement problem is not due to a dearth of mathematical formalism but instead, quite ironically, to a failure to fully recognize that the measurement problem is a product of, and logically cannot be solved by, the mathematical formalism.  What is lack in physics is not math, but logic, which is where I’ll begin.

The purpose of this paper is to show that SC/WF are impossible in principle.

·         Arguing about size of MQS, type of experiment, measurement basis, etc.

o   All I need to show is ONE counterexample to the claim that QM is universal.

·         Don’t need to... this already shows that QM is not, as a scientific matter, universal... also solves measurement problem...

·         QS can only be created by tiny quantum effects, like dispersion; and/or their amplification.  SC can’t be created by dispersion, and typical amplification equation is wrong.

·         This is not really a physics or math problem, which is why over the past century the physicists and mathematicians have failed to solve it.  It’s a logic problem.

Bad Logic in Physics

            Afshar

In ??, researchers performed a clever experiment that seemed to demonstrate a violation of BPC – that is, that an object displayed, to an impermissible extent, both wave-like and particle-like characteristics. 

I wrote an article aiming to refute their conclusion simply by pointing out that it rested on a logical contradiction, specifically that ...

My intended contribution to the field was not the refutation of Afshar, which had already been more-or-less refuted by [references], but rather demonstrating that refuting Afshar required only the identification of a contradiction and did not need the hundreds of pages of analysis and dozens of equations of other articles. 

Afshar has been cited by over 100 publications, many of which cite it to support incorrect conclusions.  Among those that debate its correctness, not all of them refute it, and among those that refute it, many of them refute it incorrectly!  Why so much confusion in the foundations of quantum mechanics.  After all, Afshar’s conclusion that their experiment demonstrated a violation of BPC was incorrect for much the same reason that “An object is simultaneously a wave and not a wave” is incorrect.  However, this kind of logical contradiction may not be so obvious to those who are led to believe that SC is simultaneously dead and alive.[Footnote about Yu/Annalen?]

SC is both a cause and effect of bad logic in physics.  Initially, Schrodinger proposed SC as a means to demonstrate, at least superficially, that QM cannot be universal because that implied the absurd (read: contradictory) possibility of SC.  However, over time, the in-principle possibility of demonstrating a SC state has been more seriously considered by the physics and philosophy academies.  If SC is characterized as simultaneously dead and alive, then

As a result, physics students are primed for illogical thinking by superficial explanations of SC (or quantum superpositions in general) as “simultaneously X and not X.”  Perhaps the most dangerous feature of SC is that it primes physics students (and future physicists) to accept, or at least intentionally ignore, contradictions.

The Measurement Problem

The measurement problem is inextricably related to SC, WF, etc., and might be colloquially phrased as, “If a cat can exist as a superposition over macroscopically distinct eigenstates |dead> and |alive>, then why do we always see either a dead or a live cat?”  Or: “If quantum mechanics applies universally at all scales, then why do we never observe quantum superpositions?”  Or even better: “Why don’t we see quantum superpositions?”  The MP has been formally characterized many ways, but my favorite (for its simplicity) is Shan’s:

[Shan’s MP here]

As Penrose points out, the MP is actually a paradox and any solution to it requires showing that at least one of its assumptions is incorrect.  Of course, the MP would be solved if it were shown that the mathematics of QM was indeed not always correct (such as above certain scales).  After 100 years, why has this not yet been shown?  Among others, two reasons stand out, both attributable to bad logic.

First, modern physicists, who rely heavily on mathematics to proceed, demand rigorous mathematical treatment in addressing and solving physics problems.  Ordinarily, such demands are appropriate.  However, the MP arises directly as a result of the mathematics of QM, in which the Schrodinger equation evolves linearly and universally.  Because the MP is itself a product of the mathematics of QM, its solution is inherently inaccessible via the symbolic representations and manipulations that produced it.  You cannot use the math of QM to show that the math of QM is incorrect.  You can, however, use empirical evidence.  In fact, Penrose suggests that the fact that we always observe measurement results is excellent empirical evidence that the QM wave function cannot always evolve linearly, which brings me to my second point.

It is often claimed that no violation of the linearity of QM has ever been observed, or that no experiment has ever shown the non-universality of QM.  In fact, this is the only empirical scientific evidence that physicists can cite for the universality of QM.  However, if we only include experiments that, by their nature, cannot show non-universality, or exclude observations that are inconsistent with the linearity of QM, then the claims are inherently circular.

(As will be discussed in more detail later,) The mathematics of QM depends on interference between wave functions, which is why interference experiments are used to measure and demonstrate quantum phenomena. 

Consider the claim, probably supported by the vast majority of physics, that “The mathematics of QM applies to every object subjected to a double-slit interference experiment, no matter how massive, because no experiment has ever demonstrated a violation.”  Indeed, such experiments have been successfully performed on larger and larger (though still microscopic) objects, such as a C60 molecule.  However, performing a double-slit interference experiment by passing an object through slits A and B separated by some distance d first requires making the object spatially coherent over a distance exceeding d.  To get the object in the superposition |A>+|B> to subsequently show interference effects, you have to provide the object in a form that is adequately quantum mechanically “fuzzy,” a state that would already demonstrate interference effects.  In other words, to do a double-slit interference experiment on an object to show that it does not violate the linearity of QM, all you have to do is provide an object prepared so that an interference experiment would not violate the linearity of QM.  [This same kind of problem was in Afshar...]

Thus, no double-slit interference experiment can show a violation of QM, because if it is set up properly, the experiment is performed on objects that already cannot show a violation of QM. [Note: the irony that it becomes more and more difficult to do double-slit interference experiments on larger and larger objects is lost on the physics community.  If they already believe that there is no limit on the size of an object that can be made spatially coherent over a width that would distinguish slits A and B, then...]  The experimental difficulty is not in showing interference effects from an object prepared to show interference effects; the difficulty is in preparing the object to show interference effects. 

Therefore, evidence for violation of the linearity of QM does not include lack of interference effects by an object prepared to show interference effects; such evidence cannot exist.  Rather, the inability to prepare an object to show interference effects is evidence for violation of the linearity of QM.  The practical impossibility of preparing a cat to show quantum interference effects is, as Penrose points out, this very kind of empirical evidence.  

“No interference experiment has ever shown a violation of the linearity of QM” is logically circular – and therefore invalid as evidence – because any properly prepared interference experiment cannot show such a violation.  Indeed, if linearity appears broken, it is because, for example, some pesky photon decohered the object’s superposition coherence; the interference experiment cannot succeed until the object is properly isolated to prevent such decoherence mechanisms.  Therefore, by disqualifying as circular the only “evidence” for the universality of QM, all existing empirical evidence – e.g., our failure to prepare a cat to show quantum interference effects, to observe cats in macroscopic quantum superpositions, etc. – confirms that QM is in fact not universally applicable. 

For this reason alone, from a scientific standpoint, the MP should be dismissed – not because it has been solved, but because it should never have arisen in the first place.  [To elaborate further, consider the Santa Claus problem: Santa exists; his sleigh violates the laws of physics, etc... but there’s no evidence he exists!]  A person is no more scientifically justified in believing that QM is universal than that unicorns exist.  Now, it may very well be that unicorns actually do exist, but since there is no empirical evidence for their existence and lots against, no problems arise from the in-principle possibility of unicorns.  We are scientifically justified in stating that unicorns do not exist, full well understanding that a unicorn might someday be discovered, which might result in problematic implications about our current understanding of the world, but not worrying about such problems until then.  Having said that, what do you say to the child who, despite contrary evidence, firmly believes that unicorns exist and worries about the implications?  Is there a way to show that unicorns actually cannot exist? 

The MP depends on the truth of two statements, one of which is the universality of QM.  It should be enough to show that the best (and only valid) evidence regarding that statement shows that it is false.  However, given that the vast majority of physicists believe in the universality of QM, is there a way to prove that it cannot, even in principle, be empirically shown to be true?  For example, is there a way to show that there are at least some quantum superpositions that cannot, even in principle, be demonstrated?  Is there a way to show, for example, that no experiment could possibly demonstrate a cat in state |dead>+|alive>?  Is there a limit on the ability to prepare an object to show interference effects?  [If so, then that would solve the MP from a scientific standpoint... but philosophers can still fart around and waste everyone’s time with the useless bullshit.]

Brief History of QM

To understand SC, WF, the MP, and the source of all this bad logic, etc., we need to understand what a quantum superposition is, and to do that we need to consider the history of quantum mechanics, particularly how the notion of quantum superposition first arose.

            Treatise decription

Facts vs. Knowledge (etc. from paper)

How much of this should be in an appendix?

What is a Superposition?

Let’s consider first what the state |A> + |B> means.  |A> represents the state the particle would be in if it were localized in slit A, while |B> represents the state the particle would be in if it were localized in slit B.  If the particle had been in state |A>, for example, then a future detection of that particle would be consistent with its having been localized in slit A.  [Note... also true of the superposition for a single measurement!]

However, superposition state |A> + |B> is not the same as |A>.  In other words, state |A> + |B> is not the state of the particle localized in slit A, nor is it the state of the particle localized in slit B.  However, it is also not the state of the particle not localized in slit A (because if it were not in A, it would be in B), nor is it the state of the particle not localized in slit B.  Therefore, for a particle in state |A> + |B>, none of the following statements is true:

·         The particle is in slit A;

·         The particle is not in slit A;

·         The particle is in slit B;

·         The particle is not in slit B.

While these statements may seem contradictory, the problem is in assuming that there is some fact about the particle’s location in slit A or B.  Imagine two unrelated descriptions, like redness and hardness.  “Red is hard” and “red is soft” might seem like mutually incompatible statements, one of which must be true and the other false, but of course they are nonsensical because there just is no fact about the hardness of red, or the redness of soft, etc.  Analogously, for a particle in state |A> + |B>, there just is no fact about its being localized in slit A or B.  The problem is in assuming that “The particle is in slit A” is a factual statement – that there exists a fact about whether or not the particle is in slit A.  Unfortunately, the assertion that there exists such a fact is itself incompatible with the particle being in state |A> + |B>.

Facts versus knowledge... Note also that state |A> + |B> is not an issue of knowledge: it does not mean that the state is actually |A> or |B> but we don’t know which, nor does it have anything to do with later discovering, via measurement, which of state |A> or |B> was correct.  Indeed, this was the very mistake that I addressed in my paper refuting Afshar.  If an object is in fact in a superposition state now, a future measurement does not retroactively change the fact of the superposition now.  [Maybe the facts vs. knowledge part should go here instead.]

The notion that an object in state |A> + |B> implies there just is no fact about its being in state |A> or |B> -- not that we don’t know, not that it is unknowable, but that such a fact simply does not exist in the universe – inevitably leads many to confusion.  After all, if a cat could exist in state |alive> + |dead>, and if that state is properly interpreted as there being no fact about its being alive or dead... what does that say about the cat?  Wouldn’t the cat disagree?  And how might the cat view you?  [Getting ahead of myself... these are just rhetorical questions right now.]

Relativity of quantum superpositions

In the above example, |A> represented the state the particle would be in if it were localized in slit A.  To be more technical, |A> is an eigenstate of the position operator corresponding to a semiclassical localization at position A.  But where the hell is position A?  If there is one thing that Galileo and Einstein collectively taught us, it’s that positions (among other measurables) are relative.  Already that instructs us that state |A> + |B> is meaningless without considering that the locations of positions A and B are relative to other objects in the universe; that is, quantum superpositions are inherently relative.  There are two types of relativity of quantum superpositions I’ll mention:

·         Weak Relativity of Quantum Superpositions: Measurement outcomes (eigenstates of an observable) are relative to other measurement outcomes. 

·         Strong Relativity of Quantum Superpositions: Essentially an extension of Galilean and Einsteinian Equivalence Principles, strong relativity suggests that if a first system (such as a molecule) is in a superposition from the perspective of a second system (such as a laboratory), then the second system is in a corresponding superposition from the perspective of the first system.  For instance, if a tiny object is in a superposition of ten distinct momentum eigenstates relative to a measuring device, then the measuring device is also in a superposition of ten distinct momentum eigenstates relative to the tiny object. 

While the notion of “quantum reference frames” is not new [cite], the above notion of Strong Relativity has only recently been discussed in the academic literature [cite].  If it is true, then it’s relatively easy to show, as I did in this paper [cite], that SC is a myth and that MQS cannot be demonstrated in principle.  In a sense, the truth of Strong Relativity excludes the possibility of SC nearly as tautology, since if a lab from whose perspective a cat is in state |alive> + |dead> can equivalently be viewed from the perspective of the cat, then which cat?  And what would the (presumably live) cat see? 

Perhaps it would view the lab in the superposition state |lab that would measure me as live> + |lab that would measure me as dead>.  And if we think that cat states |alive> and |dead> are interestingly distinct, can you imagine how incredibly distinct those eigenstates would seem from the perspective of the live cat?  From the live cat’s perspective, the lab would be in a superposition of:

|lab that would measure me as live, which isn’t surprising, because I am alive>

|lab that is so distorted, whose measuring devices are so defective, whose scientists are so incompetent, that it would measure me as dead>

The second state is actually far worse than described.  Every single measurement made by that lab would have to correspond, from their perspective, to a dead cat; the scientists in it, when looking at the cat, when receiving and processing trillions of photons bouncing off the cat, would see a dead cat!  And it’s worse than that.  Even when the scientists leave the lab, the universe requires that the story stays consistent; no future fact about the lab, its measuring devices, or its scientists – or anything they interact with in the future – can conflict with their observation of a dead cat, even though that second eigenstate (of the lab) is from the perspective of a live cat!  [Footnote: We view the world as eigenstates of observables, so if Strong Relativity is correct, then so must the cat.  There is nothing special in this example about the choosing the live cat’s perspective.  From the perspective of the dead cat, the lab is in the following equally ridiculous superposition: |lab that would measure a dead cat, which isn’t surprising, because it is dead> +

|lab that is so distorted, whose measuring devices are so defective, whose scientists are so incompetent, that it would measure a dead cat as alive>.  The point of this example is to show that the impossibility of SC follows almost tautologically from the Strong Relativity of Quantum Superpositions.]

I figured out Strong Relativity independently through a thought experiment ... [describe?].  Therefore, I regard it as nearly obviously true.  Further, my hunch is that it logically follows from Weak Relativity.  Nevertheless, because it is by no means universally accepted (or even known) by physicists or philosophers, I won’t depend on it in this paper.

Instead, I’ll use Weak Relativity, which was one of my assumptions when I first realized that SC/MQS are impossible.  Weak Relativity is obviously and necessarily true.  For instance, a particle is only vaguely specified by state |A> + |B>.  We should really be asking whether position A is localized relative to the measuring device M, the lab L, the scientist S, etc.  In other words, is the particle in state |A>_M + |B>_M, |A>_L + |B>_L, or |A>_S + |B>_S?

Why does this matter?  Surely position A is the same position relative to the measuring device, lab, and scientist.  And for essentially all practical purposes, that’s true, which is probably why the following analysis is absent from the academic literature.  After all, how could the device, scientist, etc., disagree about the location of position A?  Short answer (which will be analyzed further): quantum uncertainty disperses a wave packet, so over time a well-localized object tends to get “fuzzy” (or less well localized).  Why don’t we notice this effect in our ordinary world?  What keeps the scientist from becoming delocalized relative to the lab and measuring device?  First, the effect is inversely related to mass.  We barely notice the effect on individual molecules, so we certainly won’t notice it with anything we encounter on a daily basis.  Second, events, such as impacts with photons, air molecules, etc., are constantly correlating objects to each other.  In the words of decoherence theory, events are constantly decohering (coherent) superpositions.  Colloquially, we might say that every time an air molecule bumps into the scientist (which happens at an astronomical rate in his lab), it “measures” his position and thus prevents his quantum wave packet from dispersing. 

So while the scientist might in principle be delocalized from the measuring device by some miniscule amount, that amount is much, much, much smaller than could ever be measured, and is therefore irrelevant to whether position A is located relative to him or the measuring device or the lab.  Therefore, it’s usually fine to write state |A> + |B> instead of |A>_M + |B>_M, etc., because |A>_M + |B>_M ≈ |A>_L + |B>_L ≈ |A>_S + |B>_S.

However, the whole point of SC, MQS, etc., is that these kinds of macroscopic delocalizations are actually possible, if perhaps very difficult or impossible to achieve in practice.  If we’re going to talk about cat state |alive> + |dead> [Footnote: explain why this cat state represents a delocalization (e.g., his head, his tail, his blood cells, etc.), or a superposition of a massive object in position eigenstates so separated that they would produce distinct gravitational fields [Penrose], or macroscopic quantum superpositions in general, then we can no longer be sloppy about how (i.e., in relation to what) we specify a superposition of eigenstates.  That said, I’ll now show how keeping track of these relations between systems implies the impossibility of SC, etc.

My Proof

(Seems like I introduce two notions... Weak Relativity discussed above... but also the notion that state A_M of the object implies state M^OA of the measuring device.  Might not need that until the “math” proof but it’s interesting and new.)

In some sense, the argument is largely based on realizing that we must keep track of what we mean by eigenstates... from whose perspective... look how sloppy the typical von Neumann equation is... no accounting for who is measuring what, what correlates to what, etc.

(Note: In the following analysis, when I refer to “superposition,” I am referring in general to a superposition of distinct semiclassical position eigenstates.)

A scientist S wants to measure the position of a tiny object O.  The object O is in a superposition of position eigenstates corresponding to locations A and B, separated by some distance d, relative to the scientist S.  Thus, neglecting normalization constants, |O> = |A>_S + |B>_S.  To measure it, he uses a measuring device M configured so that a measurement of the position of object O will correlate M and O so that M will then evolve over (some brief but certainly nonzero) time to a corresponding macroscopic pointer state, denoted |M_A> or |M_B>.  In other words, M is designed/configured so that if M measures O at location A, then M will, through a causal chain that amplifies the measurement, evolve to some state that is very obviously different to the scientist S than the state to which it would evolve had it measured object O at location B.  The problem, of course, is that device M measures the location of O relative to it.  Relative to device M, the object O is in state |A>_M + |B>_M, which means that a correlating event between O and M will cause M to evolve into a state in which indicating A (such as an arrow pointing at the letter “A”) correlates to its measurement of the object at position A relative to M, and vice versa for position B.

Of course, this doesn’t typically matter in the real world.  The scientist S is already well localized relative to device M.  Because |A>_M + |B>_M ≈ |A>_S + |B>_S, measurement of the object O at A relative to M is effectively the same as its measurement relative to S, so the device’s macroscopic pointer state will properly correlate to the object’s location at position A or B relative to S, which was exactly what the scientist wanted to measure.  However, under what circumstances would it matter whether |A>_M + |B>_M ≠ |A>_S + |B>_S, and how could this situation come to pass?

Let’s say that the experiment is set up at time t0; then at time t1 the device M “measures” the object O via some initial correlation event, after which M then evolves in some time Δt to a correlated macroscopic pointer state; and then at t2 the scientist S reads the device’s pointer.

Under these normal circumstances, at time t0, object O is in a superposition relative to both M and S.  (Said another way, relative to M and S, there is no fact at t0 about the location of O at A or B.)  Its being in a superposition is what makes possible an interference experiment on O to demonstrate its superposition state.  At time t2, the scientist S is correlated to M and O – i.e., the object’s position at B, for example, is correlated with the device’s pointer indicating “B” and the scientist’s observation of the device indicating “B.”  At time t2, object O is no longer in a superposition relative to either M or S.  (Said another way, relative to M and S, there is a fact at t2 about the location of O at position A or B.)  Consequently, at t2 it is not possible, even in principle, for the scientist S to do an interference experiment on object O or device M to demonstrate a superposition, because they aren’t.  It is not a question of difficulty; I am simply noting the uncontroversial claim that by time t2, the position of object O is already correlated to that of the scientist S, so he now cannot physically demonstrate, via an interference experiment, that there is no fact about O’s location at A or B relative to him.

Let me summarize.  At t0, object O is in a superposition relative to S, so scientist S could in principle demonstrate that with a properly designed interference experiment.  Device M, however, is well localized relative to S, so scientist S would be incapable at t0 of showing M to be in a superposition.  At t2, neither O nor M is in a superposition relative to S, so S obviously cannot perform an interference experiment to prove what is false.  The only question remaining is: what is the state of affairs at time t1 (or t1+Δt)?  The standard narrative in quantum mechanics is the following von Neumann chain: [Footnote: The standard narrative does not really distinguish between the state at t1 and t1+Δt so I’ll treat them as the same time in the following equation.] 

Equation 1:

t0:                    |O> |M> |S>

                        = (|A> + |B>) |M> |S>

t1 (or t1+Δt):   (|A> |M_A> + |B> |M_B>) |S>

t2:                    |A> |M_A> |S_A> + |B> |M_B> |S_B>

According to Eq. 1, at time t1 object O and device M are correlated to each other but scientist S is uncorrelated to O and M.  Said another way, O and M are well localized relative to each other (i.e., there is a fact about O’s location relative to M) but S is not well localized to O or M (i.e., there is not a fact about the location of O or M relative to S).  If that is true, then scientist S would be able, at least in principle, in an appropriate interference experiment, to demonstrate that object O and device M are in a superposition relative to him.  No one claims that such an experiment would be easy, but as long as there is some nonzero time period (in this case, t2 - t1) in which such an experiment could be done, then maybe it’s just a question of technology.  The problem, as I will explain below, is that there is no such time period.  The appearance of a nonzero time period (t2 – t1) in Eq. 1 is an illusion caused by failure to keep track of what the letters “A” and “B” actually refer to in each of the terms.

Let’s assume Eq. 1 is correct: that at time t1, the location of O is correlated to M but is not correlated to S.  That means that the location at which M measured O, which is what determines the macroscopic pointer state to which M will evolve, is not correlated to the location of O relative to S.  Consequently, the macroscopic pointer state to which M will evolve will correlate to the location of O relative to M at t1, but because that location of O (relative to M) is not correlated to its location relative to S, the macroscopic pointer state of M will itself be uncorrelated to O’s location relative to S.  Then, at t2, S’s observation of M’s pointer will therefore be uncorrelated to O’s location relative to him. 

Let me reiterate.  Object O is in a superposition of position eigenstates |A>_S and |B>_S relative to him.  He asks a simple question: “Will I measure it in position A or B?”  To answer the question, he uses a measuring device M that is designed to measure the object’s position and indicate either output “A” or “B.”  But if Eq. 1 is correct, then when he looks at the device’s output, a reading of “A” does not tell him where the object was measured relative to him, which is what he was trying to find out!  Rather, the device’s output tells him where the object was measured relative to the device, to which, at t1, he was uncorrelated.

If Eq. 1 is correct at t1 that M is in a superposition relative to S (by virtue of its entanglement with object O), then the device’s measurement and subsequent evolution are uncorrelated to the location of object O relative to scientist S.  In other words, if Eq. 1 is correct, then as far as scientist S is concerned, measuring device M didn’t measure anything at all!  Instead, the output of the device M would only correlate to the object’s location relative to S if M was well correlated to S at time t1, in which case Eq. 1 is wrong.

I should stress that the current narrative in physics is not just that Eq. 1 is possible, but that it is true in every quantum mechanical measurement, big or small.  At t1, device M, but not scientist S, is correlated to the position of object O.  But what I’ve just shown is that if that’s true, then the position of O to which M is correlated is a different position of O than the scientist S intended to measure, such that the device’s output will necessarily be uncorrelated to – and thus irrelevant to – the scientist’s inquiry.  If Eq. 1 is correct – if macroscopic device M, which is correlated to object O, can be in a superposition relative to science S – then measuring devices aren’t necessarily measuring devices and the very foundations of science are threatened.

Conundrum as this may be, it’s not even the whole problem with Eq. 1.  We have to ask how could it be that the measuring device failed.  Remember that what the scientist wants to measure is the object in state |A>_S or |B>_S, but the device M is only capable of measuring in state |A>_M or |B>_M.  When he starts the experiment at t0, he and device M are already well correlated, the idea being that a measurement by the device of |A>_M, when observed by S, will correlate to |A>_S.  But if Eq. 1 is correct, then the correlation event at t1 is one that guarantees that this can’t happen, which means that at t1, |A>_M ≠ |A>_S.  So even though |A>_M ≈ |A>_S at t0, Eq. 1 implies that |A>_M ≠ |A>_S at t1 (and obviously by a significant amount), which is impossible in principle.  [This is what was shown by my analysis with coherence lengths and wave packet dispersion.]

Think about it this way.  At t1, device M has measured object O relative to it, so there is a fact about O’s location relative to M.  But if we stipulate that there is not a fact about O’s location relative to S (by claiming that it’s still in a superposition relative to S), then what M has measured as position A (|A>_M) could correspond to what S would measure as position B (|B>_S) – or more generally, M’s indicator pointer will not correlate to O’s location relative to S.  That just means that, at t1, M did not measure the location of O relative to S.  The only way this could have happened is if |A>_M and |A>_S, which were well correlated at time t0, had already become uncorrelated via quantum dispersion by time t1.  Impossible.  Therefore Eq. 1 is incorrect... at no point can scientist S measure device M in a superposition.

Proof with drawings

Here is another relatively simple explanation.  With reference to Fig. 1a, at time t0, object O is in a superposition of position eigenstates corresponding to locations at A_S and B_S relative to scientist S, where the object O is shown crosshatched to represent its superposition, relative to S, over two locations.  A measuring device M is also set up at t0, the device M having slots (a) and (b) and configured so that detection of object O in slot (a) will, due to a semi-deterministic causal amplification chain, cause device M to evolve over some nonzero time Δt to a macroscopic pointer state in which a large arrow indicator points to the letter “A,” and vice versa for detection of object O in slot (b).  Because the device’s detection of object O in slot (a) actually corresponds to measurement of the object O at location A_M relative to M (and vice versa for slot (b)), the device M is placed at t0 so that A_M ≈ A_S and B_M ≈ B_S for the obvious reason that the scientist S intends to measure the object’s location relative to him and therefore wants the device’s indicator to correlate to that measurement.  Finally, the experiment is designed so that the initial correlation event between object O and device M occurs at time t1, device M evolves to its macroscopic pointer state at t1+Δt, and scientist S reads the device’s pointer at t2.

Fig. 1a

Figs. 1b and 1c show how the scientist might expect (and would certainly want) the system to evolve.  In Fig. 1b, the locations of O relative to M and S are still well correlated (i.e., A_M ≈ A_S and B_M ≈ B_S), so the device’s detection of object O in slot (a) correlates to the object’s location at A_S.  [Footnote: No collapse or reduction of the wave function is assumed in this example or anywhere else in this paper.  Fig. 1b simply shows the correlation between detection in slot (a) and location A_S; there would also be a correlation between detection in slot (b) and location in B_S.]  Then, in Fig. 1c, device M has evolved so that the indicator now points to letter “A,” correlated to the device’s detection of object O in slot (a).  Then, when scientist S looks at the indicator at time t2, he will observe the indicator pointing at “A” if the object O was localized at A_S and “B” if it was localized at B_S, which was exactly his intention in using device M to measure the object’s position.

               

Fig. 1b                                                             Fig. 1c

Notice, however, that at time t1 the object O is not in a superposition relative to S, nor is device M (which is correlated to object O).  At t1, object O is indeed localized relative to device M, and since A_M ≈ A_S and B_M ≈ B_S, it is localized relative to S.  We don’t know, of course, whether object O was detected in slot (a) or (b), and Fig. 1b only shows the first possibility, but it is in slot (a) or (b) (with probabilities that we can calculate using the Born rule), with slot (a) correlated to A_S (which is localized relative to S) and slot (b) correlated to B_S (which is also localized relative to S).  If that weren’t the case, then object O’s position would still be uncorrelated to device M, which negates the correlation event at t1.  In other words, at time t1 in Fig. 1b, object O is localized at A_S or B_S – i.e., there is a fact about its location relative to S – whether or not S knows this.  [Footnote: Actually, he can’t know this.  Whether or not S is “isolated” from M, which I’ll discuss more later, the speed of light still limits the rate at which S might learn about O’s localization.]  Because object O is localized relative to S at t1, S cannot do an interference experiment to show O in superposition, nor can S show device M, which is correlated to O, in superposition.

Now, suppose we demand, consistent with Eq. 1 (the standard narrative about amplification and the universality of QM), that at time t1, scientist S can, in principle, with an appropriately designed interference experiment, demonstrate that object O and device M are in a superposition (relative to S).  That requirement implies that the object’s location, as measured by M via the correlation event at t1, does not correlate to the object’s location relative to S. 

For example, the device’s detection of the object O in slot (a), which corresponds to its measurement of the object at A_M, cannot correlate to the location of the object at A_S – otherwise S would be incapable of demonstrating O (or M, to which O is correlated) in superposition.  Thus, to ensure that object O remains unlocalized relative to S when the correlation event at t1 localizes object O relative to M, that location which M measures as A by detection of object O in slot (a) cannot correlate to A_S. 

Fig. 2a

This example is shown in Fig. 2a in which both object O and device M are shown in a superposition of position eigenstates relative to S.  The object’s crosshatching, as in Fig. 1a, refers to its lack of correlation to locations A_S and B_S.  Analogously (but without crosshatching), device M localized at M_A is shown superimposed on device localized at M_B.  Importantly, M_A is the position of device M that would measure the position of object O at A_M as A_S, while M_B is the position of device M that would measure the position of object O at A_M as B_S.  Because O remains uncorrelated to S at t1, the measuring device M that detects O in slot (a) must also be uncorrelated to S at t1.  Again, the same is true for device M that detects O in slot (b), which is not shown in Fig. 2a.  The point is that the correlation between M and the localization of O relative to M requires, in Fig. 2a, that M is not correlated to S, thus allowing S to demonstrate M in a superposition.  Then, in Fig. 2b, at time t1+Δt, device M has evolved so that the indicator now points to letter “A,” correlated to the device’s detection of object O in slot (a). 

Fig. 2b

However, now we have a problem.  In Fig. 2b, the pointer indicating “A,” which is correlated to the device’s localization of object O at A_M, is not correlated to the object’s localization at A_S.  When the scientist S reads the device’s indicator at time t2, it’s not that the output is guaranteed to be wrong, but rather that the output is guaranteed to be uncorrelated to the measurement he intended to make.  Worse, it’s not just that the output is unreliable – sometimes being right and sometimes being wrong – it’s that the desired measurement simply did not occur.  The correlation event at t1 did not correlate the scientist to the object’s location relative to him.

Therefore, to guarantee that object O (and device M, to which it is correlated) is in superposition relative to scientist S at t1, the location A_M as measured by device M cannot correlate to location A_S relative to scientist S, thus there is no fact at t1 about whether the measurement at A_M (which will ultimately cause device M to indicate “A”) will ultimately correlate to either of localizations A_S or B_S relative to S.  (Similarly, there is no fact at t1 about whether location B_M will correlate to either A_S or B_S.)  That is only possible if that which device M would measure at t1 as location A_M could be measured by S as either A_S or B_S, and that is only possible if A_M ≠ A_S.

To recap: At t0 the scientist S sets up the experiment so that A_M ≈ A_S and B_M ≈ B_S, which is what S requires so that measuring device M actually measures what it is designed to measure.  Eq. 1 implies that at time t1, A_M ≠ A_S and B_M ≠ B_S.

This has two consequences.  First, we need to explain how (and whether) device M could become adequately delocalized relative to scientist S (so that A_M ≠ A_S and B_M ≠ B_S) in the time period from t0 to t1.  Remember, we are not talking about relative motion or shifts – we are talking about A_M and A_S becoming decorrelated from each other so that they are in a location superposition relative to each other.  In other words, how do A_M and A_S, which were well localized relative to each other at time t0, become so “fuzzy” relative to each other via quantum wave packet dispersion that A_M ≠ A_S at time t1?  They don’t.  To show that, I have shown (Appendix?) that as long as the relative coherence length between two objects is small relative to the distance d separating distinct location eigenstates, then the situation in which A_M ≠ A_S cannot happen over any time period.  But on retrospect, I realize that this doesn’t matter, as Eq. 1 is claimed to be true for any arbitrary measurement time t1, so if it’s false for some times, which it clearly is, then it’s false in general.

Second, it doesn’t matter.  The quantum amplification in a von Neumann chain depends on the ability of measuring devices to measure what they are supposed to measure.  A state |A>_S + |B>_S can only be amplified through entanglement with intermediary devices if those terms actually become correlated to states |A>_S and |B>_S, respectively.  But if Eq. 1 is correct, then that inherently cannot be the case, meaning that the assumption underlying Eq. 1 is wrong.  Eq. 1 is internally inconsistent and is therefore false.

Proof with math

Let me discuss a little more about states, facts, and superpositions.  By state |A>_S, I mean the object O is located at position A relative to the scientist S, by which I mean there is a fact about that location, whether or not S knows it.  And what does that mean?  It means that S won’t make any measurements, have any experiences, etc., that are inconsistent with that fact or even, more importantly, any of its consequences. 

And that certainly includes interference experiments.  Because |A>_S is a state of object O located at position A relative to scientist S, it implies a state of the scientist S that is correlated to the location of O at A relative to him.  The scientist in that state, which I’ll write |S^OA>, may or may not ever measure the location of object O, but if he does, he will with certainty find object O at position A.  Said differently, |A>_S is a state of object O in which scientist S would be incapable of measuring O in state |B>_S, |A>_S + |B>_S, or any other state inconsistent with |A>_S.

For instance, imagine if whether it rains today hinges on some quantum event that is heavily amplified, such as by chaos.  (Indeed, there are some who argue that all probabilistic effects, certainly including weather, are fundamentally quantum.  CITE)  Specifically, imagine that a tiny object, located in Asia and in superposition |up> + |down>, was “measured” by the environment in the {|up>,|down>} basis by an initial correlating interaction or event, followed by an amplification whose definite outcomes, correlated to the object’s measurement as “up” or “down,” are that it either will or will not rain today in Europe.  If that object were in fact in state |up>, then an observer would make no measurements and have no observations that are inconsistent with that fact.  Of course, the observer in Europe would not immediately observe the fact or its consequences, but now that the fact has begun to manifest itself in the world, that observer will eventually observe its effects – notably rain.  That observer – the one correlated to observing rain – now lives in a universe in which he will not and cannot make a contradictory observation (i.e., one logically inconsistent with the fact of |up> or its consequences).

Of course, a superposition is fundamentally different.  For an object in state |A>_S + |B>_S, there is no fact about the object’s location at position A or B relative to scientist S.  While |A>_S is a state in which O is in fact located at A relative to S, which implies that S is in state |S^OA>, it is a mistake to assume that |S^OA> exists without |A>_S – i.e., it is a mistake to assume that they are already correlated prior to a correlating event.  After all, prior to a correlation event, the state of S can mathematically be written in lots of different ways, most of which will be useless or irrelevant.  Even though it may be correct that an object O is in state |A>_S + |B>_S, that same superposition can be written in different bases, and the state in which O will be found will depend on the relevant measurement basis.  So just as O can be written in state |A>_S + |B>_S (among others) and S can be written in state |S^OA> + |S^OB> (among others), neither |A>_S nor |S^OA> come into being until a position measurement correlates them.  Before the correlation event, there is no object O in state |A>_S just as there is no scientist S in state |S^OA>, while after the correlation event there is.

Let me elaborate.  If object O is in state |A>_S + |B>_S, then it is in fact not in either state |A>_S or |B>_S, which also means that the scientist S is not in state |S^OA> or |S^OB>.  Remember that the scientist in state |S^OA>, if he measures object O, will with certainty find it at position A.  But if object O is in state |A>_S + |B>_S, there is no such scientist.  Instead, we can say that object O in state |A>_S + |B>_S implies scientist S in state |S^OA> + |S^OB>.  Just as object O is in neither |A>_S nor |B>_S (or, stated differently, there is no object O in state |A>_S or |B>_S) and there is no fact about its location at A or B relative to S, we can also say that scientist S is in neither state |S^OA> nor |S^OB> and there is no fact about whether he would with certainty find O at position A or B.  Until a measurement event occurs between O and S that correlates their relative positions, there is no scientist S that would with certainty find O at A (or B).  It’s not a question of not knowing which state the scientist is in, for if S were actually in |S^OA> or |S^OB>, then he was mistaken about being in state |S^OA> + |S^OB>.  [Again, this is the Afshar error.]  That is, before the correlation event, there is no scientist in state |S^OA> or |S^OB>.  Rather, what brings states |S^OA> and |S^OB> into existence is the event that correlates the relative positions of S and O:

t0: |O> |S> = (|A>_S + |B>_S) |S> = (|A>_S + |B>_S) (|S^OA> + |S^OB>)

t1: Event correlating their position: |A>_S|S^OA>  + |B>_S|S^OB>

[Footnote: I am assuming the universality of QM here and throughout this paper.  For clarity, a collapse theory of QM would say that after the correlation event, the scientist assumes either state |S^OA> or |S^OB> -- that is, after the measurement, he will observe that the state of object O has collapsed into either |A>_S or |B>_S.  On the other hand, MWI would say that after the event, both scientists exist, one correlated to localization of object O at A and the other at B.  But until the correlation event, no theory or interpretation of QM claims that there are any scientists in states |S^OA> or |S^OB>.]

Note that at t0, the scientist in state |S> is still separable (i.e., unentangled) with |O> and can, in principle, demonstrate O in a superposition relative to him.  However, the correlation event at t1 entangles S with O so that so no scientist (whether in state |S^OA> or |S^OB>) can measure O in a superposition.

Let’s return to the original example in which scientist S utilizes device M to measure the position of object O relative to him, which is in state |A>_S + |B>_S.  Of course, device M is only capable of measuring positions relative to it, but scientist S has set up the experiment so that at time t0, |A>_M + |B>_M ≈ |A>_S + |B>_S.  In the following nomenclature, |M^OA> is a state of device M correlated to localization of object O at position A_M (relative to M).  M in state |M^OA> is incapable of measuring O at position B_M or of any other measurement or experience that is inconsistent with the location of O at A_M.  Note that |M^OA> is not itself a macroscopic pointer state; rather, assuming device M is designed correctly, |M^OA> is a state that cannot evolve to a pointer state correlated to O located at BM.  In other words, macroscopic pointer state of M indicating “A” will be correlated to |M^OA> and not |M^OB>.  Therefore, I’ll write that pointer state as |M_A^OA>.

t0: (|A>_S + |B>_S) |M> |S> ≈ (|A>_M + |B>_M) |M> |S>

= (|A>_M + |B>_M)(|M^OA> + |M^OB>)(|S^OA> + |S^OB>)

t1: (|A>_M|M^OA>  + |B>_M|M^OB>)(|S^OA> + |S^OB>)

            = |A>_M |M^OA> |S^OA> + |B>_M |M^OB> |S^OA> + |A>_M |M^OA> |S^OB> + |B>_M |M^OB> |S^OB>

t1+Δt: (|A>_M|M_A^OA>  + |B>_M|M_B^OB>)(|S^OA> + |S^OB>)

At t1, the event between O and M correlates their positions, thus eliminating incompatible terms and ultimately entangling O with M so that they are no longer separable.  At t1, there is no M that can show O in a superposition (of position eigenstates relative to M).

Let’s assume that Eq. 1 is correct: that at t1, |S> is “separable” (i.e., unentangled/uncorrelated) from M and O.  If that’s true, then while |S> can be written as |S^OA> + |S^OB> (as above), it can also be written in lots of incompatible ways whose mathematical relevance depends on the nature of the “measurement” event that correlates S to M and O.

However, for |S> to be separable, then there cannot have already been an event that correlates S to M and O.  Is that true?  We can see in the expansion of the total state at t1 that the second and third terms are interesting.  For instance, in the third term (|A>_M |M^OA> |S^OB>), the scientist S would be incapable of finding object O at A_S relative to him, even though it is located at A_M relative to M.  For this term to remain (and for |S> to remain separable), it must be the case that the event that correlated the positions of O and M could not have correlated the positions of O and S, and further that |A>_M ≠ |A>_S.

If, on the flip side, we accept that device M indeed tells S the location of O relative to him – or even just accept that there is no physical means, even in principle, by which states |A>_M + |B>_M and |A>_S + |B>_S, which were well correlated at t0, could become adequately uncorrelated by some arbitrary time t1 – then |A>_M ≈ |A>_S and  |B>_M ≈ |B>_S at t1.  If so, then the second and third terms disappear because the event at t1 is one in which device M measures the position of O relative to S.  In other words, where |A>_M ≈ |A>_S and  |B>_M ≈ |B>_S, the event that correlates the locations of O and M is also a measurement that correlates the locations of O and S.  It is the preexisting correlation between M and S – i.e., the fact that they were already well correlated at t0 – that then allows the correlation event between O and M to transitively correlate O and S.

t1: |A>_M |M^OA> |S^OA> + |B>_M |M^OB> |S^OA> + |A>_M |M^OA> |S^OB> + |B>_M |M^OB> |S^OB>

≈ |A>_S |M^OA> |S^OA> + |B>_S |M^OB> |S^OA> + |A>_S |M^OA> |S^OB> + |B>_S |M^OB> |S^OB>

= |A>_S |M^OA> |S^OA> + |B>_S |M^OB> |S^OB>

So what’s wrong with Eq. 1?  It’s simple.  It fails to consider preexisting correlations between systems.  By assuming that O does not correlate with S at t1 (allowing O and M to exist in superpositions relative to S until t2), it follows that M cannot correlate to S, which is possible only if |A>_M ≠ |A>_S at t1. But not only is this a physically impossible evolution if |A>_M ≈ |A>_S at t0, it implies that the measuring device M didn’t (and therefore cannot) succeed.  Said differently: If device M measures O relative to S, then Eq. 1 is wrong at t1 (because the correlation with S would be simultaneous and therefore S can’t show superposition), but if device M does NOT measure O relative to S, then Eq. 1 is wrong at t2 because S does not get correlated to O’s location relative to him (and the device M is useless). 

Said another way, the problem with Eq. 1 is that it assumes that S’s observation of M’s macroscopic pointer state is the event that correlates S with O.  That’s the very justification for SC.  If the observer remains uncorrelated to the outcome of the quantum event until after observing the cat is its “macroscopic pointer state” of |dead> or |alive>, then S can (in principle!) show SC in a superposition over these two states prior to his observation.  But as we can see in the above (corrected) equations, the event correlating the positions of O and S – which is the same one correlating the positions of O and M – is independent of M’s future macroscopic pointer state and whether or not S observes it.

Try this another way.  t0 is just an instant before t1.

Situation 1:

t0: |O> |M> |S> = (|A>_S + |B>_S) |M> |S>

= (|A>_S + |B>_S)(|M^OA> + |M^OB>)(|S^OA> + |S^OB>)

= (|A>_S |M^OA> + |B>_S |M^OA> + |A>_S |M^OB> + |B>_S |M^OB>) (|S^OA> + |S^OB>)... these are just meaningless symbols until a correlation event actually brings them into reality by eliminating terms.

t1: Assume a correlation event happens between O and M.  This implies that |A>_S = |A>_M (i.e., they are correlated).  The result: (|A>_S|M^OA>  + |B>_S|M^OB>)(|S^OA> + |S^OB>)

Assume that S is separable, which requires that in the expansion of the above, no terms disappear.   But clearly some do (e.g., |A>_S|M^OA> |S^OB>), which leads to a contradiction.

(In fact S is not separable and cannot be written arbitrarily, as writing S as |S^OA> + |S^OB> results in elimination of terms and therefore entanglement/correlation:

            = |A>_S |M^OA> |S^OA> + |B>_M |M^OB> |S^OB>)

Situation 2:

t0: |O> |M> |S> = (|A>_M + |B>_M) |M> |S>

= (|A>_M + |B>_M)(|M^OA> + |M^OB>)(|S^OA> + |S^OB>)

= (|A>_M |M^OA> + |B>_M |M^OA> + |A>_M |M^OB> + |B>_M |M^OB>) (|S^OA> + |S^OB>)

t1: Again, assume a correlation event happens between O and M (no requirement about relationship between |A>_S and |A>_M).  Result: (|A>_M|M^OA>  + |B>_M|M^OB>)(|S^OA> + |S^OB>)

This time, let’s also assume that S is separable, which requires that in the expansion of the above, no terms disappear.  (That would require, for example, |S^OA>, which is correlated to O at A_S, is correlated to |M^OA>, which is correlated to O at A_M, which implies that A_S ≠ A_M... i.e., that A_S and A_M are uncorrelated.)

But S being separable also means that |S^OA> doesn’t exist (since S can be written as a superposition over different bases) until it correlates to |A>_S, and S can still choose the measurement (i.e., correlation event) that brings into existence various states of S.  So S can, if he wants, do an experiment that will correlate |S^OA> to |A>_S.

Note that we’ve assumed O and M have correlated, so |M^OA> is correlated to O=|A>_M and |M^OB> is correlated to O=|B>_M but S would still report that O remains |A>_S + |B>_S.  Thus |M^OA> is correlated to O= |A>_S + |B>_S and |M^OB> is correlated to O= |A>_S + |B>_S.  Thus, by adding in the requirement that S is separable:

(|A>_M|M^OA>  + |B>_M|M^OB>)(|S^OA> + |S^OB>)

= ((|A>_S + |B>_S) |M^OA>  + (|A>_S + |B>_S) |M^OB>)(|S^OA> + |S^OB>)

= (|A>_S + |B>_S)(|M^OA> + |M^OB>)(|S^OA> + |S^OB>)... note that we can’t eliminate any terms between O and M precisely because, in Situation 2, |A>_S and |A>_M are uncorrelated.  This last line is one in which O and M have not correlated, contradicting the assumption.  Thus Situation 2 is not possible.

Summary of Situation 1: if O starts as (|A>_S + |B>_S) and a correlation event happens between O and M, then it must have been the case that M and S were already correlated |A>_S = |A>_M, resulting in a simultaneous correlation to S (because assuming S is separable leads to a contradiction).

Summary of Situation 2: if O starts as (|A>_M + |B>_M) and a correlation event happens between O and M, and if we assume that S is separable, then O and M did not correlate, leading to a contradiction.

In other words: It makes no difference if O starts as (|A>_S + |B>_S) or (|A>_M + |B>_M) at t1.  Either way, the assumption that an event at t1 correlates the positions of O and M and does not simultaneously correlate to S (so that S remains separable) leads to a contradiction and is false.  (In Situation 1, the fact that S and M are correlated leads to the result that S is not separable from O/M.  In situation 2, the fact that S and M are not correlated leads to the result that O and M cannot correlate.)

 Analysis

Of course, what this all shows is that because the positions of M and S are already well correlated to a tolerance (coherence length) that is effectively zero, the event that correlates O to M is the same one that (simultaneously) correlates O to S.  Notice that none of this analysis depends on the evolution over time to a macroscopic pointer state.  The point is that once a correlation event guarantees that the device M will not observe anything inconsistent with O being localized at A, scientist S also will not observe anything inconsistent with that.  (And note that that’s independent of whether M actually evolves to the “A” pointer state... if it doesn’t, it’s because it was designed wrong, and that indicating “B” is consistent with O being localized at A.)  This is the same conclusion as my other paper, but did not rely on Strong Relativity.

Other clear implications:

·         So if S and M are well correlated, then the event that brings |M^OA> into existence is the same one that brings |S^OA> into existence.  We can easily extend this logic to show why the analysis of my other paper (using Strong Relativity) is true.  (Not sure if this is a “proof” of Strong Relativity, but almost.) 

·         Correlation between two systems does not require a direct impact/interaction... rather, correlation passed through M to S because they were already well correlated (due to prior interactions)... i.e., implies transitivity of correlation.  Also implies systems can contain their own “internal” set of correlations/facts.  Further implies that SC can’t exist because the cat has its own set of correlations (corresponding to either dead or alive), and to the extent that they are not well correlated to some other system, an event can correlate them, but they can’t make a dead cat look alive, etc.

·         Since past correlations matter, correlations include a history of facts.  Also, this all seems to imply universal entanglement... the question is not whether everything is entangled, but to what extent.

·         Testability: Yes, there is a problem with QM equations... specifically, any notion of von Neumann chain or linearity that fails to include preexisting correlations.  What I have proven is that if M and S are adequately correlated (in the measurement basis), such as having a relative coherence length very small relative to the distance separating distinct position eigenstates, and they are large enough that QM dispersion is irrelevant, then S will be unable to show M in a superposition (independently of any efforts to isolate/shield).  If the morons want an experimental test to confirm what logically must be true, then here it is.

Isolation

When I first experienced the above insights, I had been imagining some measuring device that I had just set up somewhere out in deep intergalactic space.  Some tiny object was in a spatial superposition relative to the device and me, which were well correlated.  Then I asked myself under what conditions the device could measure the object relative to it that did not also localize it relative to me, and the answer was that, in the time period between my setting up the experiment and the measurement being made by the device, the device must have delocalized relative to me a distance comparable to the initial delocalization of the tiny object.  From that realization, I then realized that such a delocalization is limited by coherence length, which is ridiculously small for any object we might classify as “macroscopic.” 

Isolation or shielding doesn’t change this conclusion for reasons that I may discuss later in this paper.  After time t1, the only thing shielding could do is to delay the time at which S interacts with M, but if the relevant correlation event occurs simultaneously at t1, then such delay is irrelevant.  (It will only serve to delay S’s knowledge of M’s measurement, not the time in which S can demonstrate a superposition, which is zero.) 

Before time t1, it might be argued, isolation would allow the wave packet of the device to disperse (albeit very slowly) so that A_M ≠ A_S.  (This ignores the shielding the shield problem...)  Or, perhaps when we’re not looking, and we’re somehow able to completely “shield” the device, its location gets fuzzy quickly.  It doesn’t matter.  Either way, our ability to measure M in a superposition is already predicated on A_M ≠ A_S, which means that it cannot measure what it is designed to measure.  So it doesn’t really matter when, or by what mechanism, |A>_M came to be delocalized from |A>_S (to an extent adequate to allow S to demonstrate M, which is correlated to O, in a superposition)... the point is that if they are delocalized to that extent, then M’s macroscopic pointer states are uncorrelated to and irrelevant to the measurement S intended to make, in which case it failed as a measuring device. 

  

Ultimately this is about a logical contradiction.  If S and M are well correlated at t1, then M’s measurement of O (relative to it) is also a measurement relative to S... i.e., correlations are transitive.  If S and M are not well correlated at t1 (in which case M is in superposition relative to S), then M’s measurement of O is not a measurement relative to S, so S’s observation of M at t2 will be uncorrelated to the location of O relative to S (and actually may still be in superposition relative to S).

How might S and M not be well correlated at t1?

·         QM dispersion drift... impossible

·         Isolation/shielding... again impossible

·         Correlations are not transitive... this implies that there are no measuring devices!