**Entanglement is nothing else than correlation described in the quantum language**

Quantum entanglement is arguably the most "sexy" feature of quantum mechanics when it comes to the exploitation and abuse of quantum mechanics by popular books and TV programs. When I talk to the laymen and wannabe physicists who are excited about quantum mechanics, they are often excited about the entanglement.

Entanglement is the ultimate justification of the New Age memes that everything is connected with everything else, that quantum mechanics endorses souls that can separate themselves from the matter and that bring physics closer to religion, and that the laws of relativity have been abolished by quantum mechanics.

Don't get me wrong. Quantum entanglement is cool. It probably sounds bizarre to almost everyone who is starting to learn quantum mechanics. However, it's also completely mundane, generic, ordinary, and typical. All the supernatural implications of entanglement in the previous paragraph are bogus. And whoever keeps on thinking that "entanglement can't be true" or "it must be challenged and tested all the time" hasn't yet completed the learning of the basics of quantum mechanics. He or she hasn't reconciled himself or herself with the fact that classical physics died about a century ago.

I was directly led to write this blog entry by the question about an entangled electron-positron pair at the Physics Stack Exchange. Pipsi asked:

Usually when we talk about entanglement, we mean entangled spin states (of electrons) or polarizations (of photons). My questions are:You may see that the spirit of the question is the following: Quantum entanglement is such an unbelievable thing. Could it be possible that even particle physics is capable of achieving something so amazing and supernatural that the wonderful atomic physicists are doing in their labs of scientific witchcraft?

Does pair production guarantee the product electron and positron entangled?

If there's no observer measuring either particle, can we say the types, or charge, of the particles are also entangled, with a wavefunction like:\[

\frac{1}{\sqrt{2}} \zav{ \ket{+e} \pm \ket{-e} } ?

\]

Kostya gave this appropriate answer:

I've already quite a long time ago noticed that in particle physics we usually do stuff that quantum-computing people will call an "entanglement". We just don't phrase it like that, because we are used to it and we aren't much(Below the answer, you may read some violent exchanges between your humble correspondent and Emilio Pisanty, a man who is in awe about entanglement.)"in awe" about it.

So the "entanglement" you are talking about is long known in particle physics. The earliest reference I know is this:

“Pion-Pion Correlations in Antiproton Annihilation Events”,Phys. Rev. Lett. 3(1959),no. 4, 181–183.

As you see, it is for pions (charged, actually).

The more "modern" review is this:

“Bose–Einstein and Fermi–Dirac interferometry in particle physics”,Rep. Prog. Phys 66(2003)481.

Exactly, Kostya. Quantum entanglement is completely common and omnipresent in particle physics – and any other discipline of science that routinely observes quantum processes – and if particle physicists were in constant awe about it, they couldn't really focus on their work because quantum entanglement belongs among the basics.

In particular, whenever we create or recoil particles whose information is undetermined, they are always entangled. For example, if the angular momentum of the initial state is zero, the final state of spinning particles has to be proportional to\[

\eq{

\ket\psi &= \frac{ \ket{{\rm part.}\, 1\uparrow,{\rm part.}\, 2 \downarrow} - \ket{{\rm part.}\, 1\uparrow,{\rm part.}\, 2 \downarrow} }{\sqrt{2}}=\\

&=\frac{\ket{\uparrow\downarrow}-\ket{\downarrow\uparrow}}{\sqrt{2}}

}

\] If you re-express the spin to the basis "up" and "down" relatively to any other axis, you get the same form of the state (up to an overall normalization constant which is unmeasurable).

It's the standard Einstein-Podolsky-Rosen entangled state (EPR). Instead of these complicated terms suggesting a link with the supernatural world, particle physicists just call it "a singlet". It's a damn ordinary singlet, a rotationally invariant \(j=0\) state constructed out of two \(j=1/2\) degrees of freedom. Similar entangled states appear if you have two \(j=1\) particles and if you start with more complicated states or end up with more complicated states, the detailed form of the final state will differ but you may be sure that it will be an entangled state in almost all cases. Quantum entanglement is pretty much unavoidable once you get to the level of elementary particles (and even atoms).

**What is so new about quantum entanglement?**

In classical physics, especially when the laws of the classical theory are local (as required by special relativity), objects possess "objective and independent properties". For example, if you have two 4 GB Flash cards, each of them is classified by 30+ billion classical bits of information at each moment. The content of the other card must be independent from the first one. So you have 60+ billion classical bits.

However, if you're not sure what the state of all the bits is, but you still assume that classical physics is applicable, you have to describe your knowledge about the state of the two Flash cards by a probability distribution. There are 60+ billion bits whose values \(0,1\) may be combined in \(2^{60,000,000,000}\) ways or classical configurations (these configurations get generalized to points in the phase space if you consider continuous variables and not just bits). For each of these configurations, you must decide about the probability that the configuration is realized, so you end up with a rather large number of real numbers, the probabilities of each configuration:\[

p_i, \quad i\in \{1,2,3,\dots, 2^{60,000,000,000} \}.

\] The most general description of what you think about the memory chips involves this exponentially insanely high number of real parameters \(p_i\). Now, these numbers \(p_i\) may remember many patterns. For example, you may be sure that one of the Flash cards contains \(000\dots 000\) and the other one contains \(111\dots 111\) and you just don't know which one is which. Chances may be 64% and 36% that the Flash card with \(111\dots 111\) is the red one or the blue one, respectively. So the Flash cards are correlated. All these patterns, and many more complicated patterns, may be encoded to the probability distribution, in this case given by the probabilities \(\{p_i\}\).

**Going quantum**

The key fact one must understand when she is switching to quantum mechanics – the right fundamental theoretical framework to describe our Universe – is that quantum mechanics generalizes the latter, the probability distributions, and not the former, the objective state of bits.

In classical physics, the "objective independent state of the bits" could have been unknown but such ignorance could have been considered to be "just a personal disadvantage". You could always believe that there exists a "real state of the bits" – something that God, or at least the Big Brother, may know or does know. The fundamental description of Nature would be given by the knowledge of the Big Brother himself, so the usage of probabilities was a sign that someone was using a non-fundamental description of the fallible humans who are ignorant about certain things which is why they have to use the sinful concept of probabilities.

However, quantum mechanics tells you that there is no Big Brother. There is no objective state of the bits that someone could in principle know with certainty. The probabilities are completely essential. So according to quantum mechanics, even if our knowledge about the chips is "maximized", the state of the two Flash cards is given by the pure state\[

\ket\psi = \sum_{i=1}^{2^{60,000,000,000}} c_i \ket{i},\quad c_i\in\CC.

\] In the classical probabilistic description, we used to have the super-insane exponentially large number of probabilities \(p_i\). In quantum mechanics, we have the same number of probability amplitudes \(c_i\). The only difference here is that \(c_i\) are complex, not real. The squared absolute values of these complex numbers play the very same role as the probabilities,\[

p_i = |c_i|^2,

\] however, the complex phase of each \(c_i\) is actually as important as the absolute value and it will show up when you try to calculate the probabilities of different measurements, measurements of "whether the state is found in a linear superposition", questions that are not just trying to emulate some classical questions about the bits.

And be sure that these questions are not contrived or unnecessary; they are exactly as natural as the "classical ones". For example, if you talk about the spin, the measurement of \(j_z\) may look like the measurement of the "classical bits" but in this basis, the measurement of \(j_x\) and \(j_y\) or any combination of the components (which are exactly as important as \(j_z\), due to the rotational symmetry) will look like a measurement "whether the state is in a particular complex superposition". This boils down to the fact that \(j_x,j_y,j_z\) don't commute with each other – the nonzero commutators (and not any non-locality or something like that!) are the real primary fact that logically distinguishes quantum mechanics from classical physics and that is behind the ability of quantum mechanics to circumvent Bell's inequalities and similar restrictions of classical physics.

I mentioned that \(\{p_i\}\) could remember various correlations between the two Flash cards. Because \(\{c_i\}\) produces its own \(\{p_i\}\) as well, it also remembers correlations. Again, if you decide to measure the values of individual bits and you never measure the value of observables that "don't commute with these bits" – and most observables don't commute with these bits, so it's a big sacrifice – the pure quantum state will behave exactly in the same way as the classical probabilistic distribution.

The only difference is that in quantum mechanics, there is no Big Brother. The probabilistic description optimized for the knowledge of an observer is the most fundamental description one may ever get. Even in classical physics, the belief in the Big Brother was useless, to say the least, because you were not the Big Brother so you never knew "everything". The Big Brother was a philosophical dogma, a tooth fairy, that you rarely used in strict predictions of messy systems. Quantum mechanics is telling you that this tooth fairy doesn't exist at all.

If you think about it rationally, it can't cause any paradox because the tooth fairy was just an unsubstantiated belief of your childhood. What you were actually doing since you became a "self-sufficient child" was to use the laws of physics and your probabilistic knowledge whether or not certain propositions are right to deduce whether or not other propositions are true. Quantum mechanics allows you to do exactly the same thing. It is just no longer compatible with the Big Brother or a tooth fairy.

**Anti-quantum zealots are like children**

The more I interact with them, the more I feel that the people who keep on talking about hidden variables, many worlds, pilot waves, mechanisms of collapses etc. – people who refuse to understand that the most fundamental description of the Universe is intrinsically probabilistic in character – resemble children who just can't live with the insight that the tooth fairy was just an illusion, a trick, an approximation in which playful parents are equated with the most divine layer of the Cosmos.

For example, take this Emilio Pisanty guy, a Mexican currently in London who studies some "quantum dynamics". He was feeling uncomfortable with Kostya's answer that entanglement has been mundane for more than half a century. So he wrote:

It's important to note, though, that there's an extra step to go from correlations to entanglement. From a brief look at the references it looks like they measure correlations that are well described by an entangled state, but they do not make efforts to prove they do not admit classical-correlations models. This is fine, but it is spooky how many "quantum" effects admit hidden-variable explanations.You see he is an immature child who just needs to listen to stories about "spooky" things (much like the climate alarmists?) – they're a part of his neverending childhood – and about hidden-variable models that try to create the illusion of a tooth fairy after he has clearly seen that there can't be any tooth fairy but he refused to believe his own eyes.

I told him that the desire to make things "spooky" was exactly what Kostya described by the words that "these people are in awe about entanglement". One may be "in awe" about "spooky" things but one doesn't have to be. More materially, I told him that almost all states in quantum mechanics are entangled. Recall that by definition, the only non-entangled states are the states of the form\[

\ket\psi = \ket{\psi_{A,i}} \otimes \ket{\psi_{B,j}}.

\] They're tensor products of particular states describing the subsystems. But you see that this state only depends on \(\dim\HH_A\) complex numbers describing the Hilbert space of the system \(A\) and \(\dim\HH_B\) complex numbers describing the Hilbert space of the system \(B\). Well, subtract one because if you scale the first factor \(A\) up by a factor and reduce the second factor \(B\) by the same factor, a complex number, you get the same \(\ket\psi\). So allowing an arbitrary normalization and unphysical phase, we need a certain number of complex numbers (the sum of the dimensions minus one).

On the other hand, the full Hilbert space for the \(AB\) system has the dimension that is the product of the dimensions. However,\[

\dim \HH_A + \dim \HH_B -1 \ll \dim \HH_A \cdot \dim \HH_B.

\] Well, for small dimensions, I should have written \(\lt\) and not \(\ll\) but at least the modest inequality is satisfied already for \(A,B\) describing two qubits (two-level systems). The non-entangled state represent a small-dimension submanifold in a greater manifold, so they're a measure-zero subset of the Hilbert space. Almost all states in the Hilbert space are entangled; they are nontrivial complex linear superpositions of different tensor product states. If the two subsystems \(A,B\) have interacted sometime in the past, it's pretty much guaranteed that they emerged in an entangled state.

Also, if the final particles are in any entangled state which may be as simple as the singlet, it's trivial to experimentally verify that the correlation will affect the measurements of the spins relatively to any axis – exactly like in the EPR measurements of "the" entanglement that is presented almost supernaturally. It's so well-known, trivial, and rudimentary – both experimentally and theoretically – that particle physicists just don't even talk about it.

(Note that once you "fully" measure \(A\) or \(B\), i.e. acquire a complete set of commuting observables that describe it, the entanglement disappears because after the measurement, you know that e.g. \(A\) has to be in a particular known state \(\ket{\psi_A}\) and therefore the full system \(AB\) must be in \(\ket{\psi_A}\otimes \ket{\psi_{B}}\) where \(\ket{\psi_B}\) is unknown before you measure \(B\) as well. So the entanglement only exists prior to the full measurement, and as you measure things, it goes away. Quantum entanglement is the "charge of correlation" that the subsystems acquired by their mutual contact in the past and that they "discharge" as they live and expose their independent lives later.)

So if someone has a problem with the entangled states, he has a problem with 99.99999...% of the Hilbert space. The Hilbert space describes what the world may look like according to quantum mechanics. So if you have a problem with entanglement, you have a problem with 99.99999...% of what quantum mechanics may be saying about the world!

It's completely irrational – a form of a self-confusing propaganda – to try to hype non-entangled states or other states that are more compatible with a classical description. Most states (almost all states, both in the informal sense and in the strict sense of measures) in quantum mechanics are entangled. Most experiments (in both senses) are incompatible with a hidden-variable or otherwise "intrinsically classical" description, too. What's the point of using the completely invalid classical description (in the context of atomic experiments) as a zeroth approximation, of discussing the violation of this zeroth approximation? When you get to the level of individual spins or individual qubits or other pieces of quantum information, our Universe violates the basic assumptions of classical physics almost entirely. Any agreement with the classical intuition is a coincidence, an artifact of very special and uninteresting assumptions about the state, and someone's desire to focus on these special cases means that he wants to use an arbitrarily weak noise or infinitesimal glimpse of classicality to resuscitate his old belief in a tooth fairy.

But there's clearly no tooth fairy.

Those old children don't want to hear anything of the sort. So Emilio Pisanty wrote another reply:

Yes. Nevertheless, one must keep in mind that there is an extra step from correlations to entanglement. This is not crucial here, but the distinction can be quite important: for a strong example, in quantum cryptography, any improvement over classical protocols must come from nonclassical correlations. I wouldn't call this a lack of will to accept QM is right, but rather a cautiousness in scientific adventuring as well as a precise, quantitative understanding of how quantum an actual experiment is.You see that it's still the same rubbish, just using slightly different words so that the refutation must use different words, too. However, the beef in these wrong claims is still the same.

It is not true that there is an "extra step from correlations to entanglement". Entanglement is just the generic, typical, and universal relationship between two (or more) physical systems that is, according to quantum mechanics, synonymous with correlation. There is no extra step from correlations to entanglement. Within the framework of quantum mechanics, they are the same thing. Every time you construct a pure state of a composite physical system in which the subsystems are correlated, this pure state will be inevitably "entangled". And vice versa. Entangled states predict correlated probabilities of measurements of \(A,B\). In quantum mechanics, entanglement and correlation is the very same thing.

When we deal with "classical information", the only reason why the quantum aspects of the correlation may be unimportant is that the value of each qubit is "copied many times", i.e. to many qubits (the number of copies moreover grows with time, due to decoherence), and the classical system (or computer) is constructed to preserve the agreement between all the copies. This assumption – implied by keeping the voltage at each place at 0 V or 5 V or something like that – effectively bans all the observables that don't commute with the "classical bit" operators. It bans superpositions, allows one to reinterpret the quantum probabilities as classical observables, and when the computer is healthy and digital, it even keeps these observables in a discrete set in the course of the evolution.

A way to make Emilio's sentence about the "extra step" valid is to say that there is an "extra step" from classical correlations to quantum correlations i.e. entanglement. But this shouldn't be shocking. After all, there is an "extra step" from classical physics to quantum physics which affects pretty much everything. It affects how they describe Nature. They describe correlations differently, too. After all, as mentioned in the "inequality for dimensions" above, almost all the information carried by the state vector in quantum mechanics is about correlations. And yes, most of what quantum mechanics says is "new" so it follows that most of what quantum mechanics says about correlations must be different than in classical physics, too.

There is no room in 2012 for "cautiousness in scientific adventuring" of accepting quantum mechanics as the right language. Such discussions may have been OK 80 years ago but they are not OK today. People who try to stick to the classical intuition in 2012 are on par with the people who keep on believing in geocentrism. Classical physics doesn't work for anything in the world of spins and elementary particles, so of course it doesn't work for correlations, either.

Entanglement is being particularly assaulted and challenged and retested etc. because it's a particular indisputable way to show the incompatibility of our quantum world (and its quantum mechanical theoretical description) with the classical framework. But even if you don't talk about entanglement, this incompatibility may be easily demonstrated. In the Physics Stack Exchange discussion, people talked about entangled spins – because spins are the most convenient discrete quantum numbers where such a discussion makes sense.

But another thing that these overaged children believing tooth fairies overlook is that the spin itself is incompatible with classical physics, too. Even if you only consider one spin-1/2 particle which can't be entangled with anything else because you assume there is nothing else, it's still a system that is totally incompatible with classical physics. First of all, the spin may be carried by point-like particles but classically, such particles would have to spin at an infinite angular speed to have a finite angular momentum which would violate the laws of relativity.

Of course, it's not a real problem for the classical limit because in the classical limit, the whole spin disappears. Its magnitude is a small multiple of \(\hbar\), the reduced Planck's constant, and the classical limit is defined by \(\hbar\to 0\). There's just no spin left in the classical limit. That's a good thing because if such a discrete quantum number survived in classical physics, it would be a catastrophe. The electron spin may be\[

s_z\in\{ +\frac \hbar 2, -\frac\hbar 2 \}

\] and if a particular component of a vector were constrained to belong to a discrete set, the symmetry under continuous rotations would be manifestly violated: discrete numbers such as \(\pm 1/2\) cannot be transformed to each other by continuous rotations from \(SO(3)\). Quantum mechanics avoids this conclusion because it fundamentally rejects the existence of any objective \(s_z=\pm \hbar /2\). Instead, it says that the most fundamental description is given by complex probability amplitudes \(c_\uparrow\) and \(c_\downarrow\) and these complex probability amplitudes are continuous which means that they nicely transform under \(SU(2)\approx SO(3)\) (the isomorphism holds locally on the group manifold).

Another crazy thing is that the wave function doesn't return to itself after a rotation by 360 degrees (it changes the sign whenever the spin is half-integer). Everything we know in the classical world should return to itself. (Well, there could also be classical spinor fields in classical physics but no one has thought about them before the birth of quantum mechanics and they couldn't describe the measurements of individual particles' spins, anyway.)

This point is much more general. Nature crucially depends on "basic descriptive numbers" that are continuous. Classical physics needs observables such as \(\vec x, \vec p, \vec E(\vec x)\) etc. that are continuous because it says how they evolve as functions of a continuous time \(t\) and if the degrees of freedom were discrete, they couldn't really ever controllably change. Quantum mechanics changes it: it allows objects (e.g. the spin of an electron) to "discontinuously change" but that's because it doesn't describe the "objective state of objects" itself; it describes the probabilities (more precisely probability amplitudes) and those change continuously with time. In classical physics, there was only one explanation of a "weak influence": the observable properties changed by a small amount due to this influence. In quantum mechanics, there's a new type of a "weak influence": the observable properties may change by a finite (or even large) amount but the probability of this happening may be tiny.

So the consistency requires that all real or complex numbers describing possible outcomes of measurements that constitute a "discrete set" are inevitably just probability amplitudes. If they were an "objective reality", the rotational symmetry, other continuous symmetries, and the ability of the system to evolve in (continuous) time would be invalidated.

The overaged children must suffer when they read such rudimentary comments. They will look for another contrived setup that will re-energize their belief that there must exist a classical or hidden-variable tooth fairy. And they will use any new, perhaps more detailed or more convoluted, proof that there can't be any tooth fairy and the world is intrinsically quantum and probabilistic as a reason to believe in the Big Brother anyway – and to believe that the Big Brother must be even bigger than previously thought because He is able to imitate all these blasphemous quantum, non-realist laws. That will always strengthen, and not weaken, their search for the Big Brother.

These folks are analogous to hopeless religious bigots.

And that's the memo.

## snail feedback (41) :

"There is no objective state of the bits before the measurement"

----

It logically follows that the objective state of bits must be created by the act of measurement (collapse of the wave function, in other words). But if the blue flash disk on Mars collapses to some particular objective state of bits, how does the red flesh disk on earh 'know' that it should collapse to such an objective state of bits that is correlated with the objective state of bits on Mars? I do not try to deny quantum mechanics or entanglement, I am just trying to find some logical explanation for how nature works and I know that just asking such questions can make you angry. Many people miss some kind of explanatory mechanism for these quantum correlations, that is why they come up with FTL transmission of information and similar stuff

----

Classical correlations and quantum correlations are not exactly the same, because the predictions of quantum correlations cannot be reproduced by ordinary correlations

http://www.mathpages.com/home/kmath521/kmath521.htm

"It logically follows that the objective state of bits must be created by the act of measurement (collapse of the wave function, in other words)."

If one wants to be accurate, your statement is just invalid. The act of measurement isn't "creating" any reality; it is *learning* something about the reality. Learning is a sort of change of the subjective knowledge, and the change of the wave function we do after the measurement is learning, so it is a change of the subjective knowledge, too. Nothing is objectively collapsing, ever. Collapse as a real physical process is a crackpottery.

"The act of measurement isn't "creating" any reality; it is *learning* something about the reality."

---

But this statement of yours implies that there is some kind of objective reality to learn about and that is in contradiction to your statement that there is no objective reality prior to measurement

----

I will not continue because I do not want to make you angry. One of the problems in these discussions is that words like 'reality', 'objective', 'subjective', 'ontologic', 'exist' etc are rather vague. The mathematics works, that is beyond dispute. So have a nice weekend :-)

"But this statement of yours implies that there is some kind of objective reality"

No, it doesn't. You fraudulently added the word "objective" and then you pretended I said. I have never said something like that because it is wrong. Quantum mechanics shows that reality is fundamentally always subjective.

Two questions for you, Lubos:

1) What about gravitational entanglement? That is, what about entanglement of gravitons with other particles?

2) If a non-linear generalization of QM were built, could we define the notion of entanglement as some effective stuff?

PS: From an unbiased reader...Take care and keep you up with all your stuff ;).

Lubos, aside from how you demonstrate your grasp of QM, I getting more and more impressed with how you interprete the psychology of those who possibly would experience primal panic if suddenly deprived of their de facto non-accepting attitude to your kind of consistent/conservative understanding of the (to me awsome) QM aspect of What Is going on.

Dear Lubos, this question is likely not even wrong since I'm just a layman and half senile at that [ ): ] but do the results of the famous 2-slit experiment Feynman describes in his famous lectures on physics have anything to do with entanglement? I remember he said the whole essence (or words to that effect) that was contained in that experiment. Momentum and position can be entangled, correct? As can spin up and spin down. What other quantum numbers can be entangled? All of them?

Also I remember Feynman praising somewhere an explanation of entanglement for laymen that used the example of colored triangles and squares arranged as the corners of a triangle, each corner a possible measurement, or something like that. Do you know the link?

Thanks so much for your blog. Of the several I visit daily yours is the only one I always anticipate with pleasure.

Hello Lubos,

Really great post. What a profound knowledge of QM you have!

I can understand Mephisto's problem with measurements.

Does this Gedanken experiment make any sense?

Suppose in the center of a train two entangled photons are transmitted

to two observers A en B. A is a little closer to the machine that sends

the photons and makes the spin measurement on the photon first. So in

Mephisto's view A creates the state of his photon (say clockwise) and B

just observes the result (anti-clockwise) of the instantaneous

wave-function collapse. But for someone standing outside of the train

(and if the train moves almost with the speed of light in the direction

of A) B makes the first measurement and causes the collapse of the

wave-function.

So "creating/causing" the instantaneous collapse of the wavefunction is not Lorentz invariant and so makes no sense.

This example is very elementary and I have never heard it before. Am I missing something?

Thanks in Advance

Hi Lubos, nice article.

I think it will help many that you use the word correlation and not just entanglement. Nothing could be related to anything without correlations, which in a world of probability would imply entanglement. I guess you can think of the wavelength of a particle of definite momentum as a "correlation length" as different paths can be both "positively" and "negatively" (and anything in between) correlated depending on path difference.

I was wondering how you think about such matters. I mean, I am very curious about your thought experience. Like for instance, in this world of subjective reality how do you think about a phase transition. I am trying to ask, when you reach a new "level" in physics where new degrees of freedom become relevant and the old ones become invisible or irrelevant, can the old ones be said to exist at all. Often when you look closely you can rediscover (features of) the old or more fundamental ones but then you were doing just that; looking closely.

Does the world have stringy dynamics, for example, when the strings can't be felt by experiment? Or do we create this reality (in the future :-)) at high enough energies? Or is this a meaningless philosophical question and should one view string theory as simply a (possibly) better or more consistent mathematical picture of how to do calculations?

Also, entanglement (correlation) between systems is necessary in some sense for a relation (a reality) between them, which means they must have interacted at some point, can system which have never interacted even be expected to obey the same laws (live in the same universe)? You sometimes hear this 10^500 number as a number of the different possible vacua in string theory. I am trying to ask; does it in any way make sense to say that it is the constant interactions between systems which ensures consistent laws of nature. The supposed presence of the fields everywhere in field theory have this vacuum background of fields on which the probabilities are computed, can it change?

Concerning this question about how you think, I know it is really difficult to explain to others how one experience thoughts. But it would be really interesting to hear something about this. Like when you do physics do you quickly reduce complexity and extract whats relevant (as many physicists apparently do) or do you consider a lot simultaneously and then "sense" what makes "sense" (as "right brain thinkers seem to).

Thanks for your kind words, Marcel, and exactly - your thought experiment is the full and complete reason why it is invalid to say that the "reduction of the wave function" is caused by the first measurement: which measurement is first depends on the inertial system so different observers in the sense of special relativity won't agree which of the experimenters is responsible for the "reduction of the wave function". The fact that different observers disagree "when" and "why" the collapse occurred is enough for a similar statement that the "collapse" is no objective process.

Thanks for your questions, ∂³Σx² - Θ³Σx² - ΘΣ .

1) Well, gravitons may be entangled much like any other particles. Gravity is a part of the world so it must be fully subject to its laws. In particular, one may create linear superpositions of states with different numbers of gravitons, different gravitational fields, different black holes, and so on.

There is one more comment to mention. The black hole complementarity says that the Hawking radiation is also "correlated" with the black hole interior in some way - they're not independent degrees of freedom. But that's a different type of correlation than one discussed in the normal discussions of entanglement and correlations. In the case of black hole complementarity, the correlation between the interior and the Hawking radiation is a *law of physics*, not a property of a particular state. So *all* the states in which certain (complicated, scrambled) correlations between the black hole interior and the Hawking radiation are not respected are prohibited. These states don't exist in the physical Hilbert space at all.

2) I think it is impossible to build a "nonlinear generalization of QM" and the behavior of the entangled states is one way to see what would be wrong about such a nonlinear generalization. Probabilities of independent, uncorrelated independent events always factorize as

P (A = a_i, B = b_j) = P (A = a_i) * P (B = B_j)

This is pure maths, pure probability theory. One can't "nonlinearly deform it" in any way. However, this also says that the probability of the combined proposition is "linear" in the probabilities for A and B separately. This must be true if the probabilities are computed from the wave functions, too. It follows that the wave function for the combination of two uncorrelated = unentangled subsystems must also be a tensor product - bilinear, linear in each subsystems' wave function. If these subsystems continue to be independent, the evolution of the wave function must be linear in each, otherwise the tensor factorization will also be violated. In this sense, locality - and the very existence of objects independent from other objects - requires the evolution of the wave function to be linear.

A "nonlinear generalization of QM" wouldn't allow unentangled states at all - even if you started with unentangled ones, the evolution would inevitably make them entangled. This would make it impossible to produce relativistic laws of physics, invariant under the Lorentz transformations, and other things. Physics really holds tightly together and the postulates of QM including linearity are the "least deformable" ones i.e. the most safely established laws in the 20th and 21st century science.

Tx. ;-)

Off-topic, congratulations on reaching 50,000 reputation points on Stackexchange! Maybe the owners could let you put your fingers in their cookie jar, after all you are the main draw on physics.SE....

Yes, Luke, one may learn everything about entanglement from the double slit experiment, too. Feynman was surely right even if you apply his "admiration for the double slit experiment" to the case of entanglement. Entanglement is omnipresent although some people fail to see it.

The double slit experiment describes entanglement because one may verify that when one particle is shot to the double slit, the state of the two slits is entangled. It's because it is

| psi (double slit) › = 1/sqrt(2) [ | particle in slit A, nothing in slit B › + | nothing in A, particle in slit B › ]

This may look different than the "singlet entangled state" of the two spins but it is actually completely isomorphic mathematically, with two slits playing the role of the two spins, and "0 and 1 photon state of a slit" playing the role of "up and down" for the spin, respectively.

One may verify that the particle never appears in both slits at the same moment - a sort of a position measurement. But one may also verify that the state of the double slit has zero probability to be, for example, in the "difference state" (the same psi, but with the relative minus sign). This may be verified by seeing some interference minima on the photographic plate, a sort of the measurement of the "momentum" or the "wavelength of the interference pattern". So the field in the two slits is entangled with the other slit when it comes to the position but also when it comes to the momentum.

Exactly the same fantasies that people say about entanglement - e.g. the wrong claim that the first measurement "objectively collapses the wave function" - could be said here, and one would also run to the same conflicts with locality and special relativity.

Dear Eugene, thanks for the wishes. I made an experiment with full-sugar food today and if I will feel tomorrow as well as I feel now, I will return to things like their M&M's within days. ;-) But today, I am not going to actively work on algorithms to get any sweet things from Stack Exchange yet. :-)

Dear Michael, thanks for your interesting thoughts. First, I made the transition to "quantum thinking" when I was between 16 and 17. It's a long time ago. I only partially remember what it means to think about the world classically. Of course, this is an overstatement because for most things in everyday life and not only everyday life, classical reasoning is enough - and I understand why quantum mechanics actually reduces to classical physics whenever does.

So I don't understand what's the precise importance of phase transitions. Phase transitions are physical effects just like others. One may think about the state of a physical system before the transition and calculate the odds that it will undergo a transition - i.e. it will have some properties or others at the end of the experiment. Quantum mechanics is just the "logical reasoning about the natural phenomena done right". What you know is inserted, what you want to know is extracted using a combination of the rules of logic (and postulates of quantum mechanics) and the dynamical laws to evolve the state vector or operators.

The world always has stringy dynamics, whether or not they can be seen - it's just that for almost all situations we can achieve, string theory simplifies to theories that are more accessible to people with a reduced training in physics or reduced intelligence. So in those cases, both string theory and its "simplified parodies" do an equally good job in practice. But that doesn't mean that string theory isn't right or that it isn't more right than the parodies. Of course it is right and it is more right.

However, this fact is still independent from the foundations of quantum mechanics. String theory is "just another theory" running within the system of the general and universal rules we call the postulates of quantum mechanics. It just differs by a more sophisticated "Hamiltonian" or whatever plays its role.

I am gradually getting lost in your comment. But yes, the laws for the whole multiverse, regardless how large it is (maybe it's just our Universe), are universal and they hold for everyone, even if someone hasn't interacted with anyone else yet. One doesn't need to interact with others to have the same laws. If the laws themselves were evolving or depending on location or anything like that, it would just mean that these laws aren't quite fundamental. There would have to be laws that dictate how the "non-fundamental, variable laws" may change and do change, and we would soon or later switch to the research of these "meta laws". We don't have to do that because there's no indication that the laws of physics are changing with time or location at this point. So they hold in this visible Universe, for 13.7 billion years, and these laws/equations actually also admit solutions that look like totally different worlds, the landscape of string theory (and excited histories on each of its vacua). Whether all of them are equally "realizable" as our point in the landscape, within a cosmology etc., is an open question.

"Quantum mechanics shows that reality is fundamentally always subjective.” That says it all, doesn’t it?

Until these overaged children can manage to swallow this basic truth about the universe there is no hope for them, none at all.

You are a wonderful teacher, Lubos, but even you cannot teach the unwilling.

Dear Lumo,

I congratulate you too to the 50 000, in my opinion this should earn you a moderator-diamond which you can invoke whenever you want to ;-)

And I wish that your sugar-food experiment goes well.

Cheers

I don't know whether or not you agree with me that non-scientists should learn the basics of quantum mechanics, but I feel it is important (as well as fascinating). I agree with you that Lubos is a wonderful teacher but please consider that some of us may not be unwilling, but instead slow to wrap our heads around what is to us difficult and alien.

Usually I am too cowardly to ask a question myself, so I am secretly glad that Mephisto is foolhardy enough to take the bullet for me :)

Eventually, after the third or thirteenth repetition, even I am capable of finally "getting it" :)

Yeah, we should offer Mephisto a bullet proof vest for Christmas, such that he can take even more bullets out :-D

Thank you for a very nice answer. I envy you that your natural mode of reasoning is "quantum mechanical". I understand why you would get lost in the comment, it's not very precise or coherent. That the laws (or the size of the physical constants) are the same in the visible universe wasn't something I understood to be an indicator that this "need for prior contact" argument was wrong, since our universe have a common history, as evidenced, for example, by the microwave background. But I guess one have to buckle up and learn string theory to understand what the landscape thought truly means, and what the dynamics is like before a vacuum comparable to ours is "created", which sadly is probably beyond most of us. I like you point to the fact that the quantum principles are beneath string theory and that you clearly state that the stringy dynamics is always there even though it may be hidden and reduce to simpler (fortunately) mathematics (actually it is interesting that this always (?) is the case, things become very complicated, and then new parameters capture simpler dynamics). But if one reads about reductionism, emergence, and maybe hear that the world is really "top down" and not bottom up and that quantum mechanics actually implies this, it is indeed easy to become confused :-).

Eugene S,

Perhaps I have been too hard on non-scientists by describing them as simply unwilling. It is really difficult to grasp the essence of quantum mechanics and understand that reality is necessarily subjective (while not being the tiniest bit arbitrary), but that is the beauty of quantum mechanics. It is completely rigid and simply cannot be fudged or modified in any way.

At UC Berkeley I took an introductory QM course in 1956, which, unfortunately, used David Bohm’s textbook on the subject. I did not start to see the light for almost a decade, while working closely with Herb Kroemer (2000 physics Nobel).

I don’t know of any shortcuts but think as deeply as you can about the double-slit experiment. A detection screen placed behind and very near the slits shows that each photon goes either through the left slit or through the right slit; they do not go through both slits, not ever. Yet a distant screen exhibits the diffraction pattern even if the time interval between successive photons is billions of times longer than the total photon flight time. When you understand how this works you will get the basic idea.

In quantum mechanics, a measurement made on a given system, changes the state of this system, and this uncontrollably. More precisely, the physical state of the system, is changed by the measurement process.

The main reason is that the state of the system is represented by a non-trivial structure, and therefore the operators applying on this state (physical quantities), also have a non-trivial structure, and in particular usually do not commute.

In contrast, classical mechanics, synonymous of realism, corresponds to systems whose states are described by trivial structures, and the actions of "operators" are therefore also trivial, and in particular they commute.

Of course, to really compare the classical case and the quantum case, we have to consider probabilistic systems. But, in this case, making a measurement usually means obtaining more information on the system, but this will never change the physical state of the system.

However, in causal theories, quantum mechanics does not correspond to the maximum violation of classical limits (CHSH inequalities). The maximum limit are obtained with the Popescu-Rohrlich boxes. And so it is very interesting to see to which precise supplementary constraints obeys quantum mechanics.

Some recent progress, like a principle of Information Causality, have been made recently to explain this, and it's quite fascinating.

Maybe the characteristic of quantum mechanics, is that the Hilbert space of several particles, is the tensorial product of the Hilbert space of each particle. We may imagine more complicated theories (PR box) or less complicated theories. In fact, the notion of a particle, is due to the fact that QM fits very well with special relativity. So maybe QM is just the causal theory choosen by nature, because it's the best fit with special relativity.

Lubos, I hope you are just joking and have not just appeared (from what you wrote) to have stopped being 'a nutter' about your own intake of nutritients; and about the links between innate and/or because of readily available distress-dampening psychoactive ingestables behaviorally developed food addictions; and about our more or less limited capacity to "in the domain of alimentary tissue responses" mask or block inflammatory responses to ingested irritants that thus can extra insidiously irritate the linings of our intestines and/or thereby adversely interfere with the probiotic microflora - sometimes in addition to damages that may have been done (such as in your case) to these friendly bacteria by antibiotic medication.

Dear Lubos,

I agree that entanglement means quantum correlation. But it is more than classical correlation, because a separable density operator can contain classical correlations. It is not an easy task to determine if a density operator is separable or not. Entanglement measures are actively researched.

Thanks for this gem! As an interested layman I really appreciate lucid explanations like these.

Lubos: "and I understand why quantum mechanics actually reduces to classical physics whenever does"

Could you maybe elaborate a little more on that? I find it difficult to understand how "classical" / macro behavior emerges from the probablistic micro world. And as any measurement instrument is itself the result from the same probablistic quantum rules; how can exact measurement exist at all??

Thanks, Martijn.

The emergence of classical physics from quantum mechanics has many aspects, see e.g.

http://motls.blogspot.cz/2011/11/how-classical-fields-particles-emerge.html?m=1

for an article on exactly this question.

@Gene, do you really believe that reality is at some fundamental level subjective? I would expect similar statement from psychologists or from some postmodern thinkers but not from fundamental physicists. Reality is not neither subjective nor relative (theory or relativity is really a misnomer), but objective, that means independent of conscious observers. It is also coordinate-independent (reference system independent). Most, if not all, theories of physics are formulated in a coordinate independent way (general covariance, lorentz invariance). I do not understand what you mean by a subjective reality. Subjective means to be related to a conscious observer and I certainly believe in a reality independent of a conscious observer

Mephisto,

Lubos and I are using an old word, “subjective” to describe a new concept as often happens both in physics and in other disciplines. We could create a new word but that would not help your understanding either.

The point is that you have to abandon the idea of a previously existing, "objective" reality that determines the result of a measurement. You seem unable or unwilling to do that.

Lubos has explained this many times and he has done it very well.

Gene, very true and an important point. The word "subjective" is just used as a placeholder for "something that isn't objective in the classical sense" and like other words, it may be overinterpreted, humiliated, caricatured, and so on, if someone has an agenda that encourages him to such humiliation. But some word has to be chosen - or created. The essence, as you say, is that the quantum frameworks works differently than classical physics, and the "objective character" of existence in classical physics (which could also be called differently) is the assumption that is (and must be) rejected by quantum mechanics. Mephisto is among those who are just unable or stubbornly unwilling to make this inevitable, scientifically unavoidable step.

Hey Lubos, I'm in awe of all of physics, including classical. So sue me! :-)

Hello Gene,

I am a layman when it comes to math & physics, and I believe this is one of the reasons why it is still hard for me to understand these points. But I am willing to put effort into it.

As I understand it, there are two points you (and Lubos) are trying to get across:

1) There is no objective pre-existing value for that which is being measured.

2) The act of measurement on a pair of entangled particles doesn't magically hard-code the values.

An interpretation I've heard from some science popularizers (probably the source of all this confusion) is that the act of measurement itself is what "sets in stone" a certain value.

Lubos has kindly explained that "But looking at the dice didn't "create" the information. We just learned about it.", but to the layman this looks as if there already was a pre-existing reality there for us to learn about.

Accepting that there is no pre-existing reality (specific values), but that the act of measurement is what changes the state of subjective knowledge for us seems like a contradiction.

What does it mean for us to find out the value of something, when there is no value? I'm sure this is the point where math would be useful, but whenever I read "math talk" I might as well hear Chinese. I am sorry, but this just is the situation for me and many laymen. We could simply accept that "it is this way", but I, at least, feel uncomfortable not knowing something which can be known.

"But looking at the dice didn't "create" the information. We just learned about it.", but to the layman this looks as if there already was a pre-existing reality there for us to learn about.

Dear Stantul, I probably lack some empathy but I just can't understand what can be so difficult about the simple point I am making (and physicists have been making for 85+ years) to the laymen – and not only those who admit they are laymen.

The layman - I mean you in this case but it is not just you - "deduces" that there has to be a pre-existing reality because you are *assuming* that there exists objective reality - some objective answers to some fundamental questions so that all observations are functions of these answers - at all times, so it was either there before the measurement or it was created by the measurement.

But both of these options are wrong because sharp objective reality does NOT exist at all times. The result of the measurement is the only information that exists, and even this result only exists subjectively although quantum mechanics guarantees that the subject's perception will be correlated with the perceptions of all other observers that depended on the same observation. Nothing objective exists before the measurement and nothing objective exists after the measurement.

If you don't assume any objective reality existing at all times, you won't be able to derive any contradiction. And you shouldn't assume such an objective reality before the measurement because it doesn't exist. What makes sense is to talk about the results of observations that have already been made; and the results of measurements that will be done. The latter may be probabilistically determined in advance. Once the measurement is done, a particular outcome becomes known to the subject so his knowledge has to be adjusted. But the subject knows that the physical system was in one of the possible states - he just didn't know which one it was, instead, the actual state was given by a quantum-generalized probability distribution.

Before an electron's spin is measured up or down, I can say that the spin is certainly up or down. But no answer to the question is right "objectively". The statement "it is either up or down" must be treated as a logical proposition whose true/false value is unknown. There can't exist anyone for whom the value is known before the measurement, not even in principle. Once the spin is measured, a single answer becomes known to the observer, so the question "where does the spin point" will get an answer, the proposition "the spin is up" will gain a well-defined value, either true or false. No sharp answer existed in advance and no object was "created": a subject just learn some damn bit of information. There is obviously no contradiction here. What the hell is so difficult about this simple point that some people just can't get it after dozens of articles that are written so clearly that, I believe, every kid in the kindergarten who is not technically retarded must get it.

Surely you can understand, Lubos, how even a non-retarded kindergarten patron can get confused by the use of the word "measurement", since that word has always been used, in his experience, to denote the act of extracting pre-existing information.

And in the quantum world, indeed, we have the measurment devices, we have the scientists recording everything, but what we don't have is that which is being measured.

I love the metaphor of the emperor with no clothes, but in this case, a more appropriate metaphor is the clothes with no emperor.

Anti-quantum zealots, as you might describe them, dislike this so profoundly that they imagine there is an emperor but he is so well-dressed that we are just failing to detect him properly. So in their view, we just have to undress him enough times until we find the emperor.

Some misguided QM popularizers view half of this scenario: they imagine the emperor is still picking his clothes, but when we open the door, he makes a decision, and from there on, he knows exactly what he's wearing.

The "non-realist" view is that there is no emperor, we just notice different clothes every time we look.

It is the second option which confuses people, because they view half the scenario: they have learned by rote that, ok, there is no pre-existing value, but surely there is one afterwards, no? And the answer has to be a resounding no. There is no objective value before or after what we call measurement.

What we call measurement is simply the effect of the quantum system influencing the classical measurement device in such a way that it registers a certain value. But the value is not a property of the quantum system, rather it is the effect the quantum system has on the classical one, as a result of the interaction between the two.

Perhaps a helpful analogy to understand the distinction would be the perception of color. The concept of color - take "red" for example - only makes sense for those organisms capable of processing visual information. There is no metaphysical "redness" (either as a property or as a substance) in a red flower. And there is a clear distinction between what we call redness and the fact that the molecules that compose the flower absorb and reflect certain electromagnetic waves through a medium which is transparent to them.

Dear Stantul, you are just trying to invent some verbal demagogy to say that everyone believes that the world fundamentally works within the classical framework. I knew this to be wrong already when I was a kid and I am surely not the only one so your suggestion that "everyone" assumes that the measurement has to obey the basic characteristics from classical physics is surely incorrect.

In fact, quantum mechanics is much less devastating for the preconceptions you mentioned. A retarded kindergarten patron may still rightfully think that the measurement is a process by which one finds out some pre-existing information. The only classical property that this pre-existing information doesn't have according to QM is "knowable". The information about the observable before the measurement is unknowable, even by an arbitrarily "omniscient" being. It's unknowable in principle.

But the measurement never depended on the belief that there exists an "omniscient" being who could have known than pre-existing information even before it's measured. The process of measurement never depended on the existence of God or any other similar empirically unjustified belief and the belief that the state of the physical system is in principle "knowable" even before the measurement is just a belief, and a wrong one. It's actually a rather illogical one, even in classical physics, because "learning about something" pretty much tautologically requires a measurement, so no one can know things without such a measurement!

So a measurement is a process by which one finds the information about an observable, about a property of the physical system, and the property existed before the measurement in the sense that one may formulate logical propositions about these properties, even before the measurements. Howver, the false/true truth value of these propositions doesn't commute with the truth values of most other propositions one could think about which is why it's good news that the truth values can't be simultaneously well-defined, and can't be "knowable" or identified with true/false, before the measurement. One may talk about the truth values but they don't commute with each other in general which is why there can't exist any being, not even in principle, that would know the truth values - that would know the information about the very same things that may be found out by the measurement. At least not in the classical sense of the information.

Anti-quantum zealots may demagogically talk about the emperor's clothes but there's really no emperor according to quantum mechanics at all. Instead of searching for a non-existent nude emperor, they should pay some attention to the shit that is constantly being emitted by their stupid mouths.

Your comments about the color have absolutely nothing to do with these issues. You say that there's no "metaphysical redness". However, in this discussion on physics, there *is* metaphysical redness. Even without any eyes or humans or animals or anything of the sort, there exists a projection operator (on an interval of frequencies) that decides whether a particular photon is red. And there exist propositions about the color of the photons, represented by Hermitian projection operators. The eigenvalues of these projection operators are 0 and 1, i.e. false and true, just like for any other projection operators. The eigenstates with false eigenvalue are perpendicular to those with the true eigenvalue, due to the Hermiticity. The only thing that doesn't "metaphysically" exist is a knowable classical answer to what the truth value actually is before the measurement. The truth value exists in the logical sense but it is unknowable before the measurement.

Can we even imagine an experiment which would differentiate between the following two statements?

1) "The value exists but is unknowable before the measurement".

2) "The value never has sharp values, it is only our instruments which display such values. What we have is knowledge of the possible values - meaning a (calculable) expectation about what the values can be."

Are they not equivalent, since you can only get a value once you perform the measurement? I find the second formulation much more clear, but this might just be a bias.

Is this too solipsistic?

Yes, of course, the experiments have been done at the very beginning of the quantum era and millions of times after that.

And I am telling for the 1000th time to you - and millions of apparently totally deaf people - that the answer is that 1) is right and 2) is wrong. If 2) were right, there would have to be superluminal influences or loss of entanglement but experiments show that those don't occur, so 1) is right and 2) is wrong.

Do you realize that by writing similar elementary questions, you're *still* asking whether the uncertainty principle is a real limitation or just an illusion by which physicists with sloppy experimental apparatuses try to delude everyone else?

One may prove that a particle can't have a sharp X and P at the same moment because it would be an eigenstate of X and P but that's not possible because the eigenvalues would commute, xp-px = 0 acting on psi, while XP-PX acting on psi must give a nonzero vector, -i.hbar.psi.

That's a complete proof, without any loophole, just totally waterproof, that a particle can't *have* a sharp X and P at the same moment. Analogously, if a particle has a sharp anything, Y, then almost everything else, almost all other operators, must refuse to have sharp values.

The logical proposition is true in *general*. I didn't assume that the X of the particle or the P of the particle were fully and precisely known; indeed, that would make the situation singular. The principle is not true just "after a measurement", The only thing that changes after a measurement is that one learns what the X is or what the P is - and indeed, one of them may have an arbitrarily sharp value right after the measurement. But the value of the other quantity can't be sharp. Well, if X were almost accurate, then P is actually extremely inaccurate, and vice versa.

So the uncertainty principle is relevant after a particular measurement. But every moment of time is *after* a measurement (some preceding event). Every time we know something about a physical object, system, Nature, or the Universe, it's because we had done some previous measurement. There is no conceptual difference between different times. So the uncertainty principle holds totally universally.

"The second formulation" might be much more clear to you but it is totally and fundamentally wrong. You don't seem to care about whether things are true or false, about whether propositions about science are gold or stinky feces. You prefer clear lies, feces, and denial of fundamental insights of all modern science over the truth.

You wrote: "The value never has sharp values, it is only our instruments which display such values."

I thought you were saying that it is only our instruments which display non-sharp values. If you really meant that "it is only our instruments which display such values", and it wasn't a typo, then it is also a clear nonsense because if an apparatus measures an observable precisely, then the observable clearly has the value that was measured. If you repeat the measurement of the same observable by the same precise apparatus immediately after the first measurement, you will get exactly the same value once again. So the observable clearly *does* have a sharp value if it was just sharply measured by an apparatus!

@Sfantul Sisoe sheds a lot of light on non-locality. Motl gets everything 100% backwards (as did Coleman in his famous lecture Quantum Mechanics in Your Face). The fact that there is no objective reality prior to our observation implies that the observation was NOT simply learning information about the system. Before the measurement, an objective state didn't exist. After our measurement, an objective state did exist. Therefore, our measurement changed "something". Combine this with the fact that an entangled partner also experiences a change in something implies non-locality. Also, I highly suggest you read Quantum Non-locality and Relativity by Tim Maudlin, who is one of the only people other than Bohm, Bell, and Einstein to grasp what's going on.

No, Justin, your comments are just hogwash. The measurement found out something about a quantity but the values of all noncommuting quantities are completely uncertain even immediately after the measurement, in fact more uncertain than they were before. There is no objective reality before or after a measurement. After all, there's no qualitative difference between different moments. Every initial state is just a reflection of some measurements done previously.

Tim Maudlin is a nasty aggressive crackpot and even according to folks who don't always agree with me, he is an idiot.

The comment from Justin (a student of the unfortunately-surnamed Maudlin?) throws up so many red flags right away. The odds that both Sidney Coleman and Lubos Motl "get everything 100% backwards" on basic questions of quantum mechanics may not be zero exactly but have to be vanishingly small -- all the accomplished experts who view these two as accomplished experts would themselves have to be wrong. And the enumeration of "Bohm, Bell, and Einstein" is highly curious as well. All three names are frequently cited by proponents of hidden-variable theories.

My "bullshit meter" detects a common tactic employed by a certain type of individual -- those who cannot bring themselves to admit ignorance as they have such a high opinion of their intellect, hence they frame their question as an assertion. But it's obvious even to someone unschooled in the field that they are blowing smoke. I predict that even if Justin manages to learn something here, he will depart without a word of thanks. Maybe he needs to learn some humility first and foremost.

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