This is such a self-evident slice of rubbish that I am amazed how whatever physics PhD may ever neglect to run into it.
In the v5 arXiv version of the paper, the paradox is described as an experiment inward bullets on page 12-of-15. In the morning, they stair out some spins weakly, inward the evening, they gain so strongly, together with some alleged understanding betwixt the 2 types of measurements is said to bear witness that the "later randomly generated numbers" were already known inward the morning.
Before I volition beak over that their beak most this materials is non just incorrect but pretty much every judgement inward their flush is wrong, I desire to remind you lot how extremely simple, unambiguous, together with self-evidently consistent the full general rules of quantum mechanics are.
As the 17th century "father of liberalism" John Locke already knew, all noesis most the solid seat down of Nature comes from sensory reception. I just mentioned Locke, a darling of the US of America founding fathers (who came later), to emphasize that the basic "quantum mechanical philosophy" was already appreciated yesteryear wise men to a greater extent than than 200 years before so the excuse that the quantum mechanical agency of thinking is "too new" just doesn't deal much water.
In quantum mechanics, all of one's noesis most the physical organization is encoded inward the density matrix \(\rho\) which reduces to \(\rho=\ket\psi \bra\psi\) inward the special instance of the pure states (maximum noesis allowed yesteryear quantum mechanics).
The observer has determined \(\rho\) from his previous observations – from previous sensory reception, if I work Locke's synonym. And he may work it to predict the probabilities of his subsequent or time to come observations. If he observes the condition of a Yes-No query determined yesteryear the projection operator \(P^2=P\), the probability of getting Yes is \({\rm Tr}(P\rho) = {\rm Tr}(P\rho P)\) – which reduces to \(\bra \psi P \ket \psi\) for pure states. And 1 time the respond Yes or No is known, the density matrix changes to\[
\rho \to P\rho P \quad {\rm or}\quad \rho \to (1-P)\rho (1-P)
\] inward the instance of Yes or No, respectively, or the pure solid seat down changes to the projection\[
\ket\psi \to P \ket\psi \quad {\rm or}\quad \ket\psi\to (1-P) \ket\psi
\] which may endure used for subsequent predictions.
These projections play exactly the same role as Bayesian inference has ever played inward the probability calculus. You acquire novel information (evidence) so you lot must conform your subjective beliefs (probabilities) most everything inward Nature. In particular, you lot "erase" all the possibilities that receive got been ruled out etc.
The entirely novel aspect of quantum mechanics is that all the probability distributions are encoded inward the density matrix amongst off-diagonal, generically complex, entries (or inward the corresponding solid seat down vectors). But this complex-matrix-generalized probability calculus yet plant perfectly.
Well, the projection should endure followed yesteryear the "renormalization" of \(\rho\) or \(\ket\psi\) to croak on their describe or norm (the total probability) at one, i.e. by\[
\rho \to \frac{\rho}{{\rm Tr} \,\rho}\quad {\rm or} \quad \ket\psi\to \frac{\ket\psi}{\sqrt{\langle\psi\ket\psi}}.
\] No segmentation yesteryear null may ever occur because the probability that "the denominator is zero" is equal to null – the probability of the particular final result is the denominator! ;-)
Now, all measurements – everything nosotros tin ever acquire most Nature – may endure reduced to Yes/No observations. Is \(x\gt 0\)? Is \(x\gt 5\)? And so on. I could receive got discussed to a greater extent than full general measurements that gain the eigenvalue of a full general Hermitian operator \(L\) but I wanted to endure genuinely simple together with Yes/No questions are sufficient as simple edifice blocks for all measurements.
The projection operators may endure written inward damage of other observables. Influenza A virus subtype H5N1 total quantum mechanical theory has an algebra (a non-commuting algebra) of observables. Their fourth dimension dependence is determined yesteryear the Heisenberg equations of motion; that development inward fourth dimension may endure replaced yesteryear the fourth dimension dependence of \(\rho\) or \(\ket\psi\) if you lot prefer the Schrödinger motion painting where the operators don't depend on time.
So the rules higher upwards are complete. They enjoin us how quantum mechanics allows us to determine novel truths from sometime truths: It calculates probabilities that arguing most the time to come observations are right according to the well-defined formula. Once a particular consequence is produced yesteryear the measurement, the \(\rho\) or \(\ket\psi\) changes according to a well-defined prescription, the projection, together with that novel \(\rho\) or \(\ket\psi\) may endure used to predict additional observations, together with so on.
Once you lot know how Hilbert spaces together with operators on them piece of work together with 1 time you lot acquire the relevant mathematics – which contains no physics together with cannot endure physically controversial – you lot entirely demand to sympathise 2 things: How the matrix elements of operators or traces predict the probabilities of outcomes yesteryear Born's rule, together with what you lot demand to gain amongst \(\rho\) or \(\ket\psi\) 1 time you lot acquire the consequence of some other measurement.
That's it.
My call for is that the people who write dozens or hundreds of pages most the "confusing things inward quantum mechanics" together with they still neglect to sympathise the simple together with self-evidently consistent together with consummate rules higher upwards are just incredibly stupid people. They may claim to endure just bigots who insist on classical physics ("realism" etc.) but inward that case, they're masking a large share of the truth. They're non just bigots, they are rattling stupid bigots.
The simple rules higher upwards may endure together with should endure applied to everything inward Nature – inward regulation non just spins or electrons inward the atoms but also to falling trees inward the forests, moons orbiting their planets, together with indeed, particular patterns seen inward the cosmic microwave background. If you lot desire to depict anything inward Nature fundamentally correctly, you lot demand to beak inward damage of density matrices together with observables, everything that you lot may know or seek most Nature must endure phrased inward damage of observables i.e. operators acting on the Hilbert space, together with all predictions most such testable things must endure made amongst the assist of Born's rule.
If you're trying to beak most some dissimilar "truth" most the solid seat down of Nature that is unrelated to your observations – together with hence unrelated to particular operators on the Hilbert infinite together with accompanied yesteryear the collapse of \(\rho\) or \(\ket\psi\) – so you lot are just non doing proper modern physics. If you lot think that anything most the rules higher upwards may endure paradoxical or that the random numbers may endure forecast inward advance, so you lot couldn't receive got peradventure understood the simple rules I receive got described.
Back to stupidities most the weak measurements
OK, permit me supply to the Aharonov et al. newspaper most acusality. On page 12, nosotros read:
1. On morning, several weak spin measurements were performed on \(N\) particles, resulting inward fifty-fifty \(\uparrow/\downarrow\) distributions. These outcomes were recorded, thereby becoming definite together with irreversible.This judgement implicitly claims that the results of a weak touchstone are either upwards or down, just similar for a regular potent measurement. But these people must receive got forgotten the rattling showtime newspaper inward which they joined the weak touchstone movement. The championship was How the final result of a touchstone of a element of the spin of a spin-1/2 particle tin plough out to endure 100.
So the results of the weak measurements may endure pretty much whatever number, non just "up" together with "down", together with the judgement (1) totally misrepresents what may genuinely happen.
Incidentally, those who speak English linguistic communication would say "in the morning", non "on morning".
2. Then on evening, all the particles underwent potent measurements, on spin orientations chosen randomly, hence unknown beforehand, fifty-fifty to the experimenter himself.Similarly, people say "in the evening", non "on evening". ;-)
In quantum mechanics, 1 can't ever know everything precisely, due to the doubt principle. But 1 knows something – the probabilities – beforehand. The previous weak measurements receive got brought the organization to a solid seat down together with this solid seat down may endure used to brand probabilistic predictions. Probabilistic predictions aren't completely sudden but they imply that the outcomes are non "completely" unknown.
So the judgement higher upwards is "partly misleading" together with "certainly fuzzy". When the predicted probabilities for the "strong" touchstone inward the eve are 0% together with 100%, together with this may happen, in that location is certainty together with the judgement higher upwards claiming that the final result was "unknown beforehand" becomes an unequivocal falsehood.
3. All these eve measurements exhibited Bell inequality violations inside each pair.This is consummate nonsense. The Bell inequality is an inequality obeyed yesteryear some statistical quantities, averages, probabilities, together with particularly correlations (degrees of correlation). So it just cannot peradventure endure "applied inside each pair"! Whether or non the Bell inequalities are violated may entirely endure decided when \(N\to \infty\) measurements are existence made!
And it goes on together with on together with on. These people just don't receive got a damn clue what they are talking about. At the end, the rattling "program" to divulge a novel acausal paradox amongst the assist of a "weak measurement" is just some other champaign idiocy. There can't endure whatever paradox similar that together with the "weak measurement" can't peradventure endure useful for anything similar that.
The argue is simple. Whenever the term "weak measurement" has a well-defined meaning, all stories that include this term may endure rephrased inward damage of something to a greater extent than commutation together with easier to understand, namely the regular ("strong") measurement. Why?
Just read e.g. this exposition on Wikipedia. You desire to stair out something you lot can't touching or stair out properly ("strongly"), permit me telephone outcry upwards it a baby B. It should endure tardily to call back because some babes don't desire to endure touched etc. But you lot may brand B interact amongst some other object, ancilla A, together with after Influenza A virus subtype H5N1 together with B acquire entangled a bit, you lot may stair out the ancilla A. The whole demagogy of the "weak measurement" is that this potent touchstone of Influenza A virus subtype H5N1 is sold as a weak touchstone of B.
But if the interaction betwixt Influenza A virus subtype H5N1 together with B were non-existent, the touchstone of Influenza A virus subtype H5N1 would clearly enjoin you lot null most B whatsoever! And fifty-fifty if the interaction exists but is somewhat weak, you lot should yet realize that you're mainly measuring A, non B. The describing word "weak" totally distorts what's incorrect amongst your measurement. The job isn't that the "measurement of B is weak" inward some intrinsic way. The job is that what you're doing is a touchstone of A, non B! ;-) I've discussed this job inward related words in 2012 – the "weak measurement" genuinely depends on all the details of the touchstone protocol etc., it's non a pure touchstone of B but genuinely a touchstone of A+B – genuinely done as a "strong" touchstone of Influenza A virus subtype H5N1 only.
OK, accept the 2012 "paradoxical" newspaper yesteryear Aharonov et al. together with simply expand all the steps involving the "weak measurement" yesteryear substituting the Definition of the weak touchstone from the Wikipedia. OK, so they're non genuinely measuring the spins B (they are the "babe" here) only. They're measuring the organization A+B that includes the ancilla A. OK, you lot brand a sequence of measurements of some observables. Each possible consequence of such a touchstone is predicted yesteryear quantum mechanics according to Born's dominion I receive got explained above. Quantum mechanics says that the random selection is genuinely determined at the 2d of the touchstone together with is random – unless the predicted probabilities are 0 or 100 percent. And so quantum mechanics tells you lot how to update your density matrix.
That's it.
It's spectacularly obvious that there's no illegitimate influence on the future, reading the time to come random decisions inward advance, or anything of the sort. The add-on of "weak measurements" entirely adds room for mistakes together with stupidity. This terminology encourages you lot to forget most the subsystem Influenza A virus subtype H5N1 altogether. By doing so, you lot may forget e.g. that all the post-measurement states are yet unavoidably orthogonal to each other (because the Influenza A virus subtype H5N1 or ancilla-related factor of the post-measurement solid seat down vectors are orthogonal to each other). It is absolutely obvious that these "weak measurements" can't peradventure convey anything fundamentally interesting to this debate. Weak measurements aren't needed, they aren't fundamental, together with they aren't fifty-fifty useful inward practice. All the beak most "weak measurements" is just a misleading linguistic communication to brand gullible people think that they're doing something completely dissimilar than what they are doing.
In this spider web log post, I wanted you lot to sympathise that the quantum mechanical prescription for next together with predicting the demeanor of Nature is simple. It's a simple sequence of "predict probabilities from \(\rho\) yesteryear Born's rule", "update \(\rho\) yesteryear the projection when you lot acquire the actual outcome", "predict probabilities from \(\rho\) yesteryear Born's rule", "update \(\rho\) yesteryear the projection when you lot acquire the actual outcome", together with so forth. It's just 2 simple steps that are existence repeated all the time.
When you lot sympathise what these 2 steps do, you lot should apply it inward many situations because this is genuinely how quantum mechanics wants you lot to sympathise everything inward Nature, including the large objects etc. that were previously described yesteryear classical physics rather well. When you lot combine this noesis amongst some mathematical proofs, you lot should also endure able to sympathise
- why the predictions of quantum mechanics acquire basically equivalent amongst those of classical physics for "large" systems – why classical physics becomes an OK approximation inward sure regimes
- why in that location is never whatever non-local influence; inward quantum land theory, spacelike-separated operators (graded) commute amongst each other which is why the conclusion "what to measure" yesteryear a distant observer can't modify your local probabilistic predictions
Nothing tin peradventure endure contradictory or incomplete most quantum mechanics. For example, if you lot aren't sure whether you lot receive got observed/perceived/experienced/measured something or what it was (or if your sensory receptors or your encephalon is malfunctioning), so you lot won't endure able to calculate meaningful right predictions but it's non the fault of quantum mechanics. If you lot didn't know whether or what you lot observed inward a classical globe (or if your sensory receptor or encephalon were malfunctioning over there), you lot would receive got been unable to gain right meaningful predictions, too!
So quantum mechanics doesn't forestall you lot from making whatever predictions inward analogous situations inward which classical physics would receive got been capable to say something. Quantum mechanics is as consistent, as complete, together with as predictive as classical physics – it's just a dissimilar affair generating dissimilar predictions that can't endure imitated yesteryear whatever classical theory, a to a greater extent than empirically successful theory, together with arguably (from a pure theorist's viewpoint) a to a greater extent than general, natural, together with prettier sort of a physical theory.
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