Monday, November 05, 2012

Why subjective quantum mechanics allows objective science

Short answer: Because subjective knowledge (and ignorance) is and has always been compatible with objective science and quantum mechanics simply transmutes all of science to a novel treatment of fundamentally subjective knowledge.

I've had an exchange about the subjective/objective nature of the observation in quantum mechanics with Arnold Neumaier, a mathematician in Vienna.

In my answer, I clarified that what is sometimes called the "collapse of the wave function" is actually a subjective process – it's a change of someone's knowledge because he or she or it or they is/are learning about the value of an observable. This "collapse" is the change of the subjective probabilistic distributions which is also why it may occur "faster than light". The collapse "only occurs in your head".

This basic principle – which I consider absolutely essential for the right understanding of the basics of quantum mechanics – is too counterintuitive for most people and Arnold Neumaier isn't an exception. So he protested:
If this were really true, one still had to explain why we get objective science out of our subjective measurements. Therefore, there may not be more subjectivity than is in the error bars.
But this widespread "argument" is a childish logical fallacy. The objective character of the reality – as assumed by any theory of classical physics and even the "pre-scientific classical reasoning" – is (or would be) a sufficient condition to enable objective science.

However, that doesn't mean that it is a necessary condition. Since the 1920s, physicists have known that it is neither a necessary condition nor the correct way to protect the world against contradictions that could result from a generic conglomerate of "subjective viewpoints". Many processes, especially the macroscopic ones, are predicted by quantum mechanics to proceed in a way that admits a classical description with an objective reality.

But what's at least equally important, many others don't. At the fundamental level, quantum mechanics authoritatively and indisputably states that there exists no objective reality that would explain all subjective viewpoints as its reflections. Arnold Neumaier asks what's the quantum mechanics' explanation for the absence of contradictions despite the non-existence of objective reality; but his question is phrased as a rhetorical one because he isn't really interested in the answer even though the answer is arguably the most important finding of the 20th century science.

Let me discuss a few manifestations of the subjective character of existence implied by the basic postulates of quantum mechanics and explain why it leads to no contradictions.

Wigner's friend: "collapse" isn't objective

Wigner's friend is a guy closed in a lab with Schrödinger's cat. The cat dies if and when some radioactive nucleus decays – its fate is decided by a quantum-style microscopic process that may only be predicted probabilistically. Wigner is outside the lab and may still describe the whole lab, including his friend, in terms of the linear superpositions of all, including those macroscopically distinct, states that follows from Schrödinger's equation.

The question is whether the fate of the cat was decided already when Wigner's friend looked at the cat, or only when Wigner himself looked at the whole lab including the cat and his friend.

Wigner's friend may be certain that he has already made a measurement so the fate of the cat was determined rather early. However, Wigner himself only learns about the fate when he does his own measurements, so the state of the cat is determined much later.

The answer to the question "When the fate of the cat became decided and ceased to be murky?" is therefore subjective. Note that with macroscopic processes that admit a classical description, you could claim that the state of the cat was decided "immediately" and this assumption won't drive you into contradictions. But if you considered smaller, more inherently quantum objects and processes, any assumption that the system already had some particular values of observables is enough for you to be driven to wrong predictions. It's very important that quantum mechanics only describes the state of the physical systems as a "murky probabilistic superposition" of different possibilities.

Let me repeat it differently: You are allowed to assume that the observed quantities have already been facts since the moment when the information carried by them got imprinted to the environment many times and "irreversibly" decohered. If you assume that the observation became a "fact" before it decohered, you will be driven to contradictions with experiments.

However, it's also important to notice that decoherence, while extremely fast as soon as it kicks in, is never perfect. The off-diagonal elements of the density matrix in a particular basis never go to zero exactly. (Well, they are zero in some basis because every Hermitian matrix may be diagonalized but in general, it will be a basis that mixes macroscopically distinct states to a comparable extent.)

Decoherence is one of the "irreversible" processes, much like the growth of entropy in thermodynamics. But the microscopic description of this irreversibility – whether we mean the statistical physics description of the increasing entropy, or the quantum mechanical description of the origin of decoherence – shows that the "impossibility to reverse things" is never absolute. In statistical physics, it's just unlikely that the entropy will go down; it is not impossible. Analogously, in quantum mechanics, the loss of the information about the relative phase of two complex probability amplitudes is a problem that may be "reverted" to some extent.

But once the increase of the entropy becomes macroscopic, the chances of returning the entropy to the original low value become exponentially tiny and negligible. We say that it's impossible. Similarly, the entanglement of the measured system with the environment quickly becomes so complex that we give up all the hopes to "disentangle" this entanglement.

There's no objective moment at which we may say that it has become impossible to reverse the processes. In practice, people will agree whether it's possible or not but in principle, one may imagine a more accurate extraterrestrial engineer who is capable of reversing processes we consider hopelessly irreversible.

Returning to Wigner's friend, there can't be any contradiction between Wigner and Wigner's friend because the question "When the fate of the cat became decided?" must be answered by an operational procedure and everyone understands that there's no "canonical" procedure to do so, so the result of any procedure will reflect the particular idiosyncrasies of the procedure. Wigner's friend may prepare records of the dead/alive cat taken well before Wigner returned to the lab. But Wigner may always disagree and say that these photographs have been in a linear superposition of macroscopically different states up to the moment when he returned to the lab.

There can't be any sharp contradiction because the question is an ill-defined question about philosophy, the kind of question you should avoid according to the "shut up and calculate" dictum. Moreover, no one really cares about "when the fate of the cat got decided". We may mathematically derive that if a nucleus decays, the engine will immediately kill the cat. But we don't know whether the nucleus was "objectively" in the decayed state or a linear superposition and we don't really care. What we really care about is what the fate is. Is the cat alive, or dead?

Concerning the latter question, there won't be any contradictions. The evolution in quantum mechanics \[

\ket{\text{dead cat}} \to \ket{\text{dead cat}}\otimes \ket{\text{sad Wigner's friend}} \otimes \ket{\text{sad Wigner}}

\] and similarly for "alive cat" and "happy men" guarantees correlations – using the most general quantum description, it guarantees entanglement – between the state of the cat, the state of the Wigner's friend's brain, and the state of Wigner's own brain. We may show – by a simple calculation in quantum mechanics establishing the evolution above (not by classical dogmas about the objective reality!) – that if the cat dies, it will make the "same" impact on Wigner and Wigner's friend if both of their brains are measured. If the cat survives, the measurement of the two men's brains will yield compatible results, too.

So the two men will agree whether or not the cat is alive if both of them perform the measurement. But men – and other physical systems – don't have to agree about the question whether a measurement has taken place. A measurement is a process by which you are gaining the information and whether you are gaining the information – or you want to gain it – is a subjective matter. So people may disagree about the moment.

In classical physics, we were allowed to assume that there existed an objective world that someone could in principle know in the full entirety and accuracy. Individual people's knowledge reflected this objective reality and the ignorance (and statistical tools used to describe the imperfect knowledge) were just reflections of the individuals' imperfection that could have been avoided in principle.

Quantum mechanics shows that our world doesn't work in this way, however. The probabilistic character of the values of any observables is a fundamental property of the laws of physics in our Universe. It is inevitable that the value of most observables we can measure is uncertain and "probabilistically mixed" even a femtosecond before these observables are measured. There is no agent, not even God, who would know the state of the observables a moment before they're measured. The very assumption that such a perfect being exists mathematically contradicts the fact that the operators don't commute with each other; physically, such an assumption will either lead to predictions that disagree with the experimentally measured correlations, or with locality as demanded by the special theory of relativity.

So the question "whether some observation has already become a fact and when" doesn't have any objective, canonical answer – even though many people using the same conventions and models may usually agree. But this agreement only reflects their shared taste and social conventions (i.e. the same values of "tiny probabilities" that they're already willing to identify with zero when they discuss irreversibility of various processes). It doesn't reflect any objective reality that would exist in principle.

Purity of the "right state" is a subjective question, too

People often try to imagine that many other questions have "objective answers", too. One important example is the question:
Is a particular physical system described by a pure state, or a mixed state (density matrix)?
Different observers may have different answers to this question, too. And there are many reasons for that.

First of all, the subjective character of the answer directly follows from my previous point, namely the conclusion that "the moment when the measurement took place is a subjective matter". Imagine that Wigner and his friend study any physical system, for example the spin of an electron. Wigner and his friend agree that in the initial state, it is determined by a given density matrix \(\rho\). So it's mixed. But once Wigner's friend measures the spin with respect to the \(z\)-axis, he will find out it's either "up" or "down" and the state of the electron will inevitably become pure – for Wigner's friend. However, Wigner himself will continue to evolve the whole lab via Schrödinger's equation. That means that he will ignore any hypothetical "discontinuous change" associated with the spin measurement and his description will continue to build on a mixed state. The state will be mixed for Wigner but pure for Wigner's friend.

(Even if you appreciate the discontinuity of "purity" of a state, you won't be able to measure how much "mixed" it is because neither the state vector nor the density matrix are observables. Physically, they don't come with apparatuses that could spit out a particular eigenvalue after one measurement – and the state vector isn't even an operator in any sense. The density matrices and state vectors – up to the overall phase – may only be "measured" by many times repeated experiments with the same initial state but this can't be counted as a "measurement" of any property of a single repetition of the experiment.)

There is another reason why different observers will disagree about the purity of the state. This reason is simple: a basic justification of the "density matrix" formalism is to allow for people's individual ignorance. While a pure state describes a "maximally well-known state of a physical system" in quantum mechanics, a density matrix allows you to "add the same kind of ignorance that already existed in classical physics".

Take the electron's spin. The density matrix \(\rho\) is a Hermitian \(2\times 2\) matrix with non-negative eigenvalues \(p, 1-p\). Their sum equals \(1\) because of the "total probability" normalization for the trace. If \(p=0\) or \(p=1\), the density matrix describes a pure state and may be written as \(\ket\psi\bra\psi\) for some pure state \(\ket\psi\). Moreover, for the particular state of the electron's spin, each pure state \(\ket\psi\) may be identified with the "up-spin" state with respect to a particular axis in \(\RR^3\).

If you choose both eigenvalues to be \(p=1/2\), the density matrix is one-half times the identity matrix (which is why it has this form in any basis) and it describes the "maximum ignorance" about the spin. Such a density matrix is "maximally mixed". If you don't know anything about the spin of an electron, you should assume that its state is given by this particular density matrix – a highly mixed state. However, someone else may be aware of some previous measurement of the spin that was conserved etc. So he may actually know that the spin was "up", for example. He will use a pure state to describe the electron's spin.

Again, this disagreement between the people when it comes to the state's purity can lead to no contradictions. The person who uses the mixed state will predict (twice) lower probabilities for the outcomes that depend on the spin's being up. But his predicted probabilities will be nonzero so they won't be incompatible with these events. Moreover, he will understand that the lower predicted probabilities – relatively to the guy who knew the spin was "up" – were just due to his ignorance about the "lucky" initial conditions "up". The mixed nature of the state may be said to be due to some "extra ignorance" and it's not too shocking that ignorance is subjective.

This discussion about the purity is quantum mechanics' complete counterpart of a similar discussion in classical physics. We may either describe a mechanical system by its coordinates and momenta \(x_i(t)\) and \(p_i(t)\), or we may specify a probabilistic distribution on the phase space, \(\rho(x_i,p_j;t)\). The latter may be interpreted as a tool to deal with the imperfect subjective knowledge by some people but it's possible to imagine that some "right" configuration of \(x_i(t)\) and \(p_i(t)\) exists at each moment. In quantum mechanics, density matrices play the role of the probabilistic distributions on the phase space.

However, there's still a fundamental difference between classical physics and quantum mechanics.

In classical physics, it was possible to know the positions and momenta, at least in principle, and if we knew them, everything was unambiguously determined. The state of "maximum knowledge" in classical physics implied unambiguous predictions for everything. In quantum mechanics, the state of a "maximum knowledge" is any pure state. And even if we know that the system is in a pure state, we are only able to make probabilistic predictions for most observables.

Imagine that you use the density matrices for everything and substitute \(\rho=\ket\psi\bra\psi\) if you had a pure state instead. Then the "pure density matrices" will only differ from others by their list of eigenvalues – all of them are zero except for one that equals one. My point is that these "special density matrices" may look qualitatively similar to all other density matrices (especially in a random basis) and we have universal formulae of the type \({\rm Tr}(\rho P)\) to calculate the probabilities of \(P\) (a proposition represented by a projection operator) out of any density matrix \(\rho\), whether it is pure or mixed.

This trace formula therefore unifies the treatment of the "probability-distribution-on-phase-space-like" aspect of the probability in quantum mechanics – which already existed in classical physics and you may think that it's avoidable – with the "unavoidable" probabilistic character of the predictions that follow even from the pure state. This unification really tells you that the "probabilistic nature of the pure states" is exactly as natural and obeying the same mathematical rules as the "probabilistic nature artificially incorporated via the density matrix formalism". But it's unavoidable, too.

Physically meaningful questions have to be associated with a linear operator on the Hilbert space

In this text, I argued that many philosophical questions such as "what may count as an observation", "when did an observation exactly take place", "is the state of the physical system pure or mixed" are questions that depend on the particular observer and his description of the reality, his standards of "how much of irreversible phenomena is really irreversible" and "how small probabilities may be practically identified with zero", among other things.

These questions are not really "practically relevant" for the working of the world. What is "practically relevant" are the questions associated with actual observables and all observables are, according to the basic postulates of quantum mechanics, represented by linear Hermitian (or, in some special cases, unitary or normal) operators. Such observables include positions and momenta and angular momenta and spins of particles, numbers of particles in a given state, intensities of fields, and so on.

For these observables, the evolution equations of quantum mechanics guarantee correlations or "entanglement" that is the ultimate reason why observers will never disagree about "hardcore practical questions" whenever they are known to agree from the experience. All these correlations are analogous to the evolution that I have already mentioned,\[

\ket{\text{alive cat}} \to \ket{\text{alive cat}}\otimes \ket{\text{happy Wigner's friend}} \otimes \ket{\text{happy Wigner}}.

\] This derived fact about the evolution of an initial state of the cat-friend-Wigner physical system allows you to conclusively prove that "if the cat stays alive, both Wigner and his friend will be happy".

On the other hand, there is no rule that the observers must agree about the philosophical questions mentioned three paragraphs above, beneath the title of the section. These are not true physical questions: they're unphysical gibberish you should avoid while you "shut up and calculate". There is no linear operator on the Hilbert space that would have eigenvalues \(0\) for pure states and \(1\) for mixed states, i.e. that would answer the question "Is the state pure?". An "unpure" admixture qualitatively changes the answer to the question whether a density matrix is pure so of course, such an operator would have to be discontinuous on the space of density matrices and discontinuous operators can't be linear. So indeed, quantum mechanics doesn't imply the objective character of the answers to these unphysical questions – they actually do depend on the observer and there's no empirical evidence that there's anything wrong about the fact. The only thing that contradicts the subjective nature of these answers is people's stubbornness, bigotry, and psychological obstacles preventing people from abandoning classical physics.

It's one of the basic principles of quantum mechanics – or "shut up and calculate" quantum mechanics – that all physically meaningful questions about the Universe may be expressed by a linear Hermitian operator, an observable. Quantum mechanics gives you the universal rule to predict the probability of different answers and nothing else can be predicted. If your question isn't talking about the value of any observable, then it is unphysical gibberish. Way too many people – including people considered to be physicists – still haven't learned to think in the quantum way. They keep on trying to "reduce" important questions about our world into a language of philosophers and other cranks, a language that implicitly makes many totally wrong assumptions such as the assumption that there fundamentally exists an objective reality in the classical sense.

Instead of specifying observables (linear operators on the Hilbert space) and calculating their eigenvalues and their probabilities of individual eigenvalues given some knowledge about the state, they keep on asking whether some "cloud here" affects another "cloud there" or whether it "collapses", assuming that the clouds objectively exist in the classical sense. That's not a good starting point to understand the essence of modern physics.

And that's the memo.


  1. Ha ha, I recently had an issue too with Arnold Neumaier at Physics SE, see his answer to a question asking about how the universe is created and the comments below:

    He thinks that mythology and theology are much better suited to answer fundamental questions, whereas fundamental physics is just "scientific speculation" and of not much value compared to the two first mentioned approaches ... :-D

    I will read about your exchange at Physics SE with Arnold later this evening :-)


  2. Yup, I noticed he's kind of deeply religious and mythical:

  3. Once I wrote half-assed answer to one of the zillion questions inspired by Schrodinger cat "problem":
    (even mentioned in the comments where I learned about it)

    People didn't like it. They vigorously protect ways to sneak religion and superstition into physics, and this, it seems is a prefect backdoor.

  4. Dear Marko, I agree with your answer, too.

    The point you and Dilaton mentioned is interesting - how does religion affect people's attitudes. I am not sure. On one hand, classical physics is the ultimate "non-religious" attitude and quantum mechanics was viewed by "dogmatic atheists" to be a partial loss, so they didn't like it.

    On the other hand, religious people tend to advocate the classical framework as well. Like Neumaier. Perhaps it's because they believe that there has to be an omniscient God who knows everything, so there can't be anything fundamental that depends on the subject's knowledge.

    To summarize, everyone (from the previously defined groups) - atheists and theologians alike - are against quantum mechanics. ;-)

  5. "if you considered smaller, more inherently quantum objects and
    processes, any assumption that the system already had some particular
    values of observables is enough for you to be driven to wrong

    This fact actually suggests a way to restore objectivity! You can use consistent histories formalism and think in terms of a maximal set of consistent histories. Because it is maximal, you can't make it more "fine-grained" by adding more projectors. So you should think of the maximal set of projectors as the complete and objective description of physical reality.

    The main problem here is that we don't have a good principle to choose one maximal set over another maximal set. So maybe we could never know which one is right, and the "subjective" framework is the best you can do *scientifically*. But there's no need to say that reality is "objectively subjective".

  6. Dear Mitchell, you may try to find a maximally fine-grained set of consistent histories but they won't ever be "exactly consistent" so the "obstacle from taking an even finer one" will always be "tolerance to larger inaccuracies". Moreover, even aside from this problem, the "maximal set" won't be unique. There can be totally different maximal sets.

  7. my non-Wigner's friend recently sent me an interesting short video (created by physicists from the Centre for Quantum Technologies in Singapore) on the same topic as your post:

    Life, death, and collapse (Quantum Lightness of Being).

  8. Dear Lubos, I've always liked Popper's definition of a scientific fact: an intersubjective observation about which there is agreement between observers. The objective world is composed of those observations about which there intersubjective agreement (among qualified observers). Is there anything wrong with this definition?

  9. "The answer to the question "When the fate of the cat became decided and ceased to be murky?" is therefore subjective."

    Is there a linear Hermitian operator, an observable that could tell us when the cat lived/died - NO.

    Is this then a viable (sensible) question? - NO

    Bohr - 'It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.'

  10. I don't agree with Neumaier (he promotes a classical inspired 'thermal interpretation' of QM at various places on the web), but I wonder if your complete dismissal of an objective world does not itself have problems. Suppose humans never evolved after the dinosaurs were wiped out - does that mean the dinosaurs never existed "objectively"? What about if aliens visited out planet and discovered the fossil record, does that suddenly create the dinosaurs "objectively".

    What's wrong with assuming the universe evolves probabilistically BUT objectively - ie it always exists but we can't know definite facts, even in principle, without making an observation.

  11. Dear Luke, I can't point out any disagreement between the philosophical thesis you reproduced and the known scientific facts and methods that have already been established.

    However, it doesn't guarantee that this philosophical thesis will remain an adequate description of science in an arbitrary future. Quite generally, similar philosophical "straitjackets" have repeatedly proved to be wrong.

    As this very blog entry emphasizes. there should be an intersubjective agreement about the laws of physics but there will inevitably be disagreement about many things such as "when the state vector changed discontinuously" even though such changes are used in a legitimate scientific description of Nature.

  12. "Perhaps it's because they believe that there has to be an omniscient God who knows everything, so there can't be anything fundamental that depends on the subject's knowledge."

    How about we ditch omniscience and omnipotence and merely stick with the possibility that there might be a kind of rough justice built into the biology of all sentient organisms: that the sum total of pleasurable and painful experiences over the lifetime of the organism balance out, any residual "balances" being canceled in the moment of dissolution. Of course whether such a possibility is actual is both subjective and unanswerable, especially the final canceling out of any residual balances.

    I submit that the mere possibility of such a "symmetry" between pleasure and pain would be enough to give people pause -- in particular that they would be less likely to lead decadent lives of parasitism on the sufferings of others. It might also give those trapped in suffering some hope for the future.

    Indeed, the mere belief in the possibility might do the trick.

  13. Good questions James, I, too, ask myself that.

  14. Hi Lubos,

    Nice article.

    Of course you know this inside out, but if a system is entangled with another - and the complete system is in a pure state - one must use a mixed state if on "chooses" to only consider one of the smaller subsystems and ignore the other. The subsystems by themselves cannot be described correctly by a pure state, but correct probabilistic predictions for one may be done by using the density matrix. The reason I write this is just because you don't necessarily use a mixed state because of ignorance, but maybe just for convenience, because even though the larger system is a pure state, you only wish to focus on the subsystem, which is not. Its just to highlight that mixed states can in this sense be real unlike in classical mechanics, so I thought the analogy with the classical might be a little confusing to some, even though you definitely can use the density matrix in the same sense.

    But I have a question that maybe highlights some of my ignorance about the subjectivity of quantum measurements. I read an article by you where you explained whats wrong with the many worlds interpretation, so that interpretation is nonsense. But as you say we have subjective ways of describing the quantum probabilities depending on our current knowledge, but we agree with other macroscopic observers in the end. As you say Wigner and his friend cannot disagree about the state of the cat because different macroscopic stories are orthogonal and don't mix, so only one is "chosen". You wrote: "You could claim that the state of the cat was decided "immediately" and this assumption won't drive you into contradictions. But if you considered smaller more inherently quantum objects and processes, any assumption that the system has already had some particular values of observables is enough for you to be driven to wrong predictions". Okay, that's all good, but since we are allowed to assume the cat (a macroscopic object) dies "immediately" why can't we simply "believe" the "philosophical picture" that whenever systems decohere sufficiently an "outcome" is somehow chosen by the world and therefore become a historical fact, also for Wigner even though he has yet to check it out.

    By the way I've written a story for you that I hope you enjoy, but its not related to quantum mechanics. Will it be okay to post it as a comment.

  15. Thanks, I think Mitchel Porter made a similar point with more technical rigour below.

  16. Dear James, I have never said anything that would indicate that the existence of facts or reality depends on the subjects being "human". This is clearly a misunderstanding. Humans, dinosaurs, intelligent machines, or anyone else is able to "evaluate" information. One doesn't need any humans for logical propositions about dinosaurs to be considered well-defined, and for quantum mechanics to be able to predict probabilities of different final states depending on initial states. Even without a single human, one may calculate from quantum mechanics that there's a nonzero probability for dinosaurs to evolve from some primitive organisms, that there is a probability 85% that dinosaur from species XY eats dinosaur from species CD, and so on, and so on. All the knowledge about how Nature works would exist just like it exists now. The idea that anything in science depends on any particular characteristics of "humans" is wrong, and when used as a criticism against the fact that quantum mechanics is fundamentally subjective, it is a straw man. Subjective doesn't mean "human". Subjective means that the things need a particular logical framework of knowledge about facts which may depend on the subject, but the subject doesn't have to resemble any human in any detailed sense.

    What's wrong with assuming the universe evolves probabilistically BUT objectively - ie it always exists but we can't know definite facts, even in principle, without making an observation.

    What's wrong with it is that we may show that it disagrees with outcomes of direct experiments - not sure whether you care about this "small imperfection". One may easily show e.g. Bell's theorem - if there exist any data that objectively encode the state of the physical system, then the laws of physics must either violate the symmetry between inertial systems and break relativity, or the theory will predict "too small correlations" within the Bell's interval even though Nature - and quantum mechanics - is known to predict things outside the interval. The only wrong thing about your sentence is that it is wrong.

  17. Hmm, ok I agree the bit about humans, but the second part seems to be causing amisunderstanding. A violation of Bell Inequalities can't occur if local (deterministic) hidden variables exist. But I'm saying just the opposite! You can have an objective world that is fundamentally probabilistic.

    I think I know why you don't like this idea, because it requires a step-like global time evolution (eg with half-life for probabilistic jumps ~10^-43 secs), and almost exactly two years ago you (temporarily) banned my for suggesting such an idea

    So I'd better not go there again today :-)

  18. OK, fine, then I don't understand what you mean by the word "objective". By saying that the world cannot be objective, I am saying that the data that manifest themselves in the observations can't be obtained as reflections of a universally valid and canonical collection of "objective information" - that must be shared by anyone - as long as the evolution laws and the dictionary to derive the observational outcomes from the "objective data" is Lorentz-invariant. This is what Bell's theorem implies.

    Do you agree with that? If you do and if you still claim that something fundamental about the world is objective, what is it exactly? It's unphysical because it can't be responsible for the results of observations.

  19. Hi Lubos,

    sorry you already answered my question, sorry. Right here: "Let me repeat it differently: You are allowed to assume that the observed quantities have already been facts since the moment when the information carried by them got imprinted to the environment many times and "irreversibly" decohered. If you assume that the observation became a "fact" before it decohered, you will be driven to contradictions with experiments." Thanks and sorry.

  20. Yes I agree with that. What is fundamental about the world that is objective is the wave function of the universe. That is what exists objectively. You just want to say the the wave function/state vector only describes probabilities, so it can't be objective, whereas I'm saying it evolves objectively existing complex numbers (~10^100 of them say) which can randomly change every evolution step.

    You see why I need the idea of a discrete time-step (not constant like a computer cpu, instead I assume a half-life ~10^-43 secs for the random jumps and hence varying time steps at this resolution)

    So my wave function exists OBJECTIVELY for ~10-43 secs - whereas yours never exists objectively - mine still allows violation of Bell Inequalities so you can't dismiss it.

  21. Exactly!

    Concerning the "time when the cat died/was saved", one needs to give an operational definition how to measure it, for the proposition to be physical. However, one may give it an operational definition that the time of the decision is when a detector detected a particle and printed the time at the printer, or an assistant wrote it into the books, or when Wigner wrote the time of his observation to his notebook. These different operational definitions will yield different answers - and that's a reflection of the fact that "the time when the fate of the cat was decided" isn't a question with an objectively valid answer. And there's nothing wrong about it. One can't demonstrate any contradiction by the diversity of possible methods and answers to the "detailed realizations of this question" simply because there's nothing wrong about these detailed questions' having different answers.

    As Bohr said, physics is about the business of relating the logical value (true/false) of propositions about Nature, and the right ways to relate them are almost always of probabilistic character. Physics isn't an enterprise obsessed with defending the idea that something objectively exists - or that the truth about everything is objective. When it comes to the truth about the observed data, it's fundamentally subjective, and before the observations, even a single subject should realize that his or her idea about "what the system is doing before the observation" is unphysical.

  22. Dear Lubos,
    need to read and enjoy the full article still. But I would like to make a point already after reading the first lines. Living human beings are warm, macroscopic objects. So any subjective knowledge they aquire will be decohered enough so that the age of the universe will not be enough to experience a situtation where the subjectivity of quantum mechanics will make a difference for direct human experience. It is as probable as waiting for a human being to resurrect form the deaths. So for all practical purposes quantum mechanics predicts that there is an objective reality on the level of human experience. So the discussion appears a little bit like the discussion how many angels can stand on a needle.

  23. "Perhaps it's because they believe that there has to be an omniscient God who knows everything, so there can't be anything fundamental that depends on the subject's knowledge."

    How about we ditch omniscience and omnipotence and entertain the more modest possibility that there might be a kind of rough justice built into the biology of all sentient organisms: that the sum total of pleasurable and painful experiences over the lifetime of the organism balance out, any residual "balances" being canceled in the moment of dissolution. Of course whether such a possibility is actual is both subjective and unanswerable, especially the final canceling out of any residual balances.

    I submit that the mere possibility of such a "symmetry" between pleasure and pain would be enough to give people pause -- in particular that they would be less likely to lead decadent lives of parasitism on the sufferings of others. It might also give those trapped in suffering some hope for the future.

    Indeed, the mere belief in the possibility might do the trick (even for idiots and sociopaths). I would like to see more research into the neuroscience of pleasure and pain, in particular into the question of whether they are correlative or independent phenomena.

  24. Just like almost all popular presentations of Schrodinger's cat, it misinterprets what the "superposition state" is. It doesn't mean that one is dead AND alive at the same moment. It simply means the normal thing that one is dead OR alive and the probabilities of either outcome are nonzero - these are inevitably subjective probabilities as evaluated by anyone who uses proper mechanics to study what's going on - before a measurement of the result.

    It's not true that one is half-dead half-alive zombie if the probabilities are 50% and 50%. The eigenvalue of the "dead/alive" operator are just 0 or 1. There is no eigenvalue 1/2 of this operator which means that one CANNOT be half-dead, half-alive. One may only be alive OR dead and the mixture just indicates the probabilities of these two sharp extreme outcomes that are the only two possible ones.

  25. Philosophers should NEVER EVER be allowed to patronize physics by telling physicists what they are allowed to research, talk about, be interested in, etc ... :-(0) !!!

    It is not their business, they should put their nose into their own things.

    The same goes for religious leaders, Sean Carroll seams to get often some hassle and severe hostility from them ...

  26. Thanks for the explanations and clarifications, Lubos!

  27. When I worked as a deck hand on a small fishing boat, I had a fairly
    circumscribed list of tasks, not too complicated or hard to remember.
    Yet I managed to screw up the order or proper execution, time and again.
    One day the captain took me aside and said, "Eugene, I have explained
    this to you before and I will explain it to you again -- once, twice, a
    thousand times -- as many times as it takes until you 'get it'."
    have always admired the man's superhuman self-control that enabled him
    not only to suppress his surely justified impulse to have me keelhauled
    on the spot but also to remain outwardly calm, professional, and patient.

    And so it is with the Boss. With infinite patience, he tells us again, and again, and again... knowing that, eventually, we will start to "get it".

    N.B. I speak only for myself, of course, not for the august company of my co-commenters, all of whom are much smarter than me.

  28. Thanks for the answer. Your explanations should be more widespread. I understand (I hope :-) ) your objection to using the word "is chosen" that it is subjective acquiring of information, and that you are ignorant about some facts when you use the density matrix. Where you knew this when you were 15-16 some of us first learned classical physics late, then some quantum physics and was always told about collapse, "electron clouds" and so on. The problem is when you try to "feel" new knowledge that is so fundamental, wrong ideas which has been in the mind for a while are difficult to eradicate.

  29. Everything was fine, smooth and classical for the dinosaurs James, because:

    (a) Quantum mechanics had not yet been discovered back then.

    (b) There were no cats. Actually, (a) follows from (b).

  30. Great article. I wish Nature would cooperate sometimes :-)

  31. Dear Michael, thanks for your thoughts. What was extra in "is chosen" were the quotes, and what was missing was the subject. The measurement that produces a value of an observable is chosen by the subject himself - so he "chose" it, in an active sense. Not every observable may really be measured in a given context but if it may be measured, it's an "active decision of an subject" to find it out.

    I think that the "collapse" of the wave function was the dominant explanatory theme in popular books I encoutered 20 years ago, too, but I just ignored the popular gibberish rather early. When you get to actual serious attempts to explain how atoms work etc., you just develop your own scheme to think about it and you do prefer the mathematical portions of the QM books because the philosophical interpretations are seen as vacuous vague babbling.

    Quite generally, I think that everyone should try to find out how QM really works - it's new but it's not "complicated" in the sense of requiring too much time to learn. It's a couple of universal rules and principles. One should convince himself that it works, and then he should focus on actual explanations of particular effects, facts, observations, patterns which is rooted in the maths of operators. If someone continues to be dominated by philosophical babbling and especially nostalgia about classical explanations, he hasn't really started to work with quantum physics yet.

  32. As QM "knows no time" I don't think that we will ever be able to solve the problem within QM. Rather, I think it will take (at least) a QFT-generic effect. There's a lot of literature on things that point in this direction and therefore I will not go into details here. Just a few keywords: "Spontaneous symmetry breaking", "(quantum) phase transition", "unitary inequivalence", "dissipative brain model", ...

  33. I think what is interesting about Wigner's friend's cat is the joint distribution associated with the common observable of Wigner opening the door to the lab. Although Wigner must view a superposition of possible outcomes when he opens the door, Wigner's friend must view of possible outcomes of when the door will be open (and indeed if it is open by Wigner). However, there is no possible scenario where the door will open at different times for the two observers (neglecting potential clock differences due to relativity).

  34. Ha ha, so it is probably a good thing that I have implemented the "shut up and calculate" explicitely into my user profile at Physics SE by ignoring the "quantum-interpretations" and "epistemology" tags... Concerning the second one I always forget how to spell it, such that I always have to look it up when I want to mention it, LOL :-D

    In this way, I am not bothered by gibberish stuff and only take notice of such question if Lumo gives nice explanations and clarifications of things, such as in this article :-)

  35. I agree one should learn quantum mechanics and be careful with the philosophical babbling. But when you say you develop you own way of thinking about it, that's exactly right, and the thing is, many develop nonsensical interpretations but don't notice it. That only probabilities are calculated and the world around us is therefore non-deterministic, is not as difficult for most to grasp compared to the "quantum challenge" to the notion of what an event actually is, and it deserves careful thought. Quantum mechanics give you this technique for predicting probabilities, yes, but as you know better than most it tells us much more. For example time and space, continuous parameters in QFT and they apparently have to be because of Lorentz invariance, do not provide the world with infinite resolution, because quantum mechanics doesn't allow us to look infinitely precisely at positions, and if we try anyway we end up creating more particles, and its important and profound. The macroscopic world does at least appear to allow this straightforward interpretation, that macroscopic events take place quite literally, even though they never have infinite resolution or are infinitely well defined. They have to interact before they can be truly related to one another, so there descriptions or calculations of other systems can and do differ because their level of interaction with such systems differ. While shut up and calculate certainly is efficient, I think these articles as yours right here, do have a lot of merit.
    On a slightly other note, many also want to relate the quantum with consciousness and free will and I suspect your answer would be that this is futile and only represent more philosophical babbling, and I tend to believe that is probably correct. But the fact is quantum mechanics is almost certainly correct and consciousness and free will certainly also appear to exist. Some think consciousness is not part of science, and it may in a sense be inherently inaccessible to physics and maybe to science in general, but it is - perhaps ironically - where all scientific theories "live". Free will, to some the most important aspect of their conscious lives, certainly could not truly exist in a classical deterministic worldview, but the question is, can it finally exist in this quantum world of ours. Quantum mechanics describe probabilities, how may choice arise from such randomness. Maybe this subjective viewpoint of yours provide an open window. We claim the experimenter chooses what variable he want to measure. Does he want to measure the x or the y component of spin or does he simply want to go home and watch the big bang theory. While he surely chooses the latter and everyone know that :-), we can describe him and his lab (correctly) quantum mechanically from the outside with no regard for the fact that at least one "entity" in there is conscious and supposedly equipped with free will. It might be that quantum mechanics is sufficiently "non-limiting" that free will really can have its freedom, and not just freedom, but controlled choice that we truly choose, albeit limited by some physical (and mental :-) )limitations.

  36. And Thanks for all the impressively extensive answers. I look forward to re-reading and letting your more subjective - and yet more objectively correct - interpretation linger in the mind and hopefully do its work, so it come to where it "feels" right.

  37. I do not agree. First, If the lab is closed, Wigner is outside the lab, and Wigners' friend is inside the lab, you are not allowed to consider their states entangled together, because no present interaction is possible (we suppose here that there was no interaction between Wigner and Wigner's friend in the past, so no correlation coming from the past is possible). Second, if Wigner's friend make a measurement about cat or spin, after a measurement, the cat or spin is in a precise state (for Wigner's friend). For Wigner, it's a mixed density matrix, just because a lack of information (as in classical probems). Wigner's friend has more information than Wigner. If Wigner's friend measurement is a alive cat or a spin +1, be sure that, if Wigner opens the lab door, it will not find a dead cat or a spin -1. In opening the lab door, Wigner just acquire information on the system, and will have the same representation of the cat/spin as his friend. So, in fact, all that you describe seems a standard classical problem, where an observer has less information than an other.

  38. Prathyush ManchalaNov 8, 2012, 11:48:00 PM

    As far as I see, What appears to be missing in the Decoherence programme is clear understanding of what it means to record an observation? While Decoherence is correct on the level of what happen to system under observation, Its description of what happens to the experimental apparatus is rather murky. To me, concepts of free energy and entropy must play a vital role in the description of measurement apparatus. for example, To reset an experimental apparatus one must expend free energy.

  39. Hi,

    are you the same Prathyush who uses to make completely dismissive comments about fundamental physics at Physics SE ;-) ?

    Such as in this answer for example:

    and in the comments below this question:


    I'm just curious and apologize if I'm wrong... :-P

  40. I think some of the confusion comes from the word "subjective", which (like all words) has multiple meanings. The wave function, and its collapse during measurement are subjective, in the sense that they are defined with respect to an observer, but *not* in the sense that beauty or fairness are subjective.

    During the middle ages, artists tried to depict things as they were, but it was impossible, you can't capture a 3D thing in a 2D paining. Renaissance artists gave up on how things are, and showed how they look (from a particular point of view), and the paintings were much more realistic. The collapse of the wave function is like the vanishing points in perspective. They are objective in the sense of not being optional, but subjective in the sense that they are observer dependant.

    The quantum (our) world has are rules that determine how things appear, the rules are mostly known, and are every bit as rigid as the rules of perspective, but the things "as they really are" don't even exist. There is no objective reality, except as an approximation, but for big complicated systems it is a *very* good approximation.

  41. Prathyush ManchalaNov 8, 2012, 11:53:00 PM

    I did post those on SE, I tend to dismiss ideas if I find them speculative.

  42. Prathyush, what you write is complete rubbish. There is nothing "murky" about what happens to an experimental apparatus. Experimental apparatuses obey the same laws of physics as any other physical objects and nothing that would contradict these laws ever happens to them. Also, it's nonsense that "free energy and entropy" should enter these discussions, as they're statistical emergent concepts describing different, thermodynamic features of large systems.

  43. Seems you have really no clue about the scientific method. It is completely legitimate and sometimes even needed for theoretical ideas to be ahead of experiments (and the technology needed to realize them). Consider for example how GR was first theoretically developped and later experimentally confirmed. You should not be allowed to use a GPS ...!

    You better stop trolling against legitimate fundamental physics the Milner prize

    is targeted at (and Lumo is working on too...), and stop attacking people who are interested in it or their questions and answers at Physics SE !

  44. Prathyush ManchalaNov 9, 2012, 12:12:00 AM

    I think there is some an important connection that between free energy and measurement that is yet to be unfolded, and due the the very uncertain nature of these ideas I will proceed with at most caution. I quote Niels Bohr "Observation must make use of some registering device, whether through a photographic plate or directly through the eye, which involves a process of amplification by which free energy is spent".

    Now I think he points to something very important here, you may disagree, But if you don't communicate your reasons and just brandish them I'm hardly interested.

    While I agree that Measurement apparatus must follow the same laws of physics. What it means to record information is not very clear to me, If you think you understand it please enlighten me.

    One more important reason I think thermodynamic concepts must play a role in measurement is Landauer's Principle which is accepted as correct by most physicists but as far as my understanding goes it is not on a very firm theoretical ground.

  45. It is not clear at all what you have any clue about. Ever.

    "sometimes necessary"?

    The scientific method is specifically the application of experiment to test theory.

    "Let's see what happens" is not experiment, and is not scientific. It is probing.

  46. Prathyush ManchalaNov 9, 2012, 12:12:00 AM

    I notice people have a tendency of imagining how nature works rather than looking at it. I am not trolling but I'm a rather interested party and I communicate if I find something to be misleading in direction.

  47. You have neither a clue about the scientific method, nor about fundamental physics.

    You should be banned from physics SE, if you dont stop harrasing people who are interested in fundamental physics and keep spitting and spatting on the work of serious physicists over there.

    And what you write in your profile is complete nonsense, you dont even understand what physics is about. It's purpose is NOT to "organize human experience into language", but to unravel how nature works by the scientific method which you dont understand.

    If you are really interested in physics as you claim (I dont believe you), you should at least read Prof. Strassler's explanation of the scientific method:

  48. Prathyush ManchalaNov 9, 2012, 12:13:00 AM

    talking to you is a waste of time.

  49. Go troll somewhere else!

    I'll not talk to you because I adhere to the the Eleventh Commandment which says:

  50. Dear Lumo,

    seems there is some clearing up to do in the comments above ;-).
    We obviously have an invasion of the armies of Mordor here ... :-/

  51. Dear Luke, well, the words "evidence" and "subjective" are surely not synonyma. For example, one of them is noun and the other is an adjective and their meanings have nothing directly to do with one another, either. ;-)

    There is evidence of dinosaurs and evidence of interactions that destroyed the interference pattern. But one first had to ask the question: what do I see at the [place where we found the dinosaur bones]? Where did a photon [coming from the slits] come from and what did it interact with?

    If no one had asked the questions, the propositions that the dinosaurs existed or that the photon came through the left slits would remain with a sharp truth value. Someone asked the question, subjectively, the person who discovered those things, so it was a subjective measurement. Quantum mechanics guarantees the correlations/entanglement so that other people who looked into the existence of dinosaurs or interactions in the left slit would find the same result, but it was a subjective issue for them, too.

    Of course, it makes little sense to discuss dinosaurs in quantum mechanics because the classical framework is a very good approximation to make basic propositions and for common sense. At most, dinosaurs reduce to the universal discussion that QM is compatible with classical reasoning in the classical limit. On the other hand, the double slit experiment is inherently quantum and, when properly analyzed, contains all the wisdom about quantum mechanics. Still, something coming from the interactions in the left slit - which destroyed the interference pattern - had to be observed.