Sunday, June 28, 2020

Is COVID there before you measure it?

Today I want to talk about a peculiar aspect of quantum measurements that you may have heard of. It’s that the measurement does not merely reveal a property that previously existed, but that the act of measuring makes that property real. So when Donald Trump claims that not testing people for COVID means there will be fewer cases, rather than just fewer cases you know about, then that demonstrates his deep knowledge of quantum mechanics.

This special role of the measurement process is an aspect of quantum mechanics that Einstein worried about profoundly. He thought it could not possibly be correct. He reportedly summed up the question by asking whether the moon is there when nobody looks, implying that, certainly, the question is absurd. Common sense says “yes” because what does the moon care if someone looks at it. But quantum mechanics says “no”.



In quantum mechanics, the act of observation has special relevance. As long as you don’t look, you don’t know if something is there or just exactly what its properties are. Quantum mechanics, therefore, requires us to rethink what we even mean by “reality”. And that’s why they say it’s strange and weird and you can’t understand it and so on.

Now, Einstein’s remark about the moon is frequently quoted but it’s somewhat misleading because there are other ways of telling whether the moon is there that do not require looking at it in the sense of actually seeing it with our own eyes. We know that the moon is there, for example, because its gravitational pull causes tides. So the word “looking” actually refers to any act of observation.

You could say, but well, we know that quantum mechanics is a theory that is relevant only for small things, so it does not apply to viruses and certainly not to the moon. But well, it’s not so simple. Think of Schrödinger’s cat.

Erwin Schrödinger’s thought experiment with the cat demonstrates that quantum effects for single particles can have macroscopic consequences. Schrödinger said, let us take a single atom which can undergo nuclear decay. Nuclear decay is a real quantum effect. You cannot predict just exactly when it happens, you can only say it happens with a certain probability in a certain amount of time. Before you measure the decay, according to quantum mechanics, the atom is both decayed and not decayed. Physicists say, it is in a “superposition” of these states. Please watch my earlier video for more details about what superpositions are.

But then, Schrödinger says, you can take the information from the nuclear decay and amplify it. He suggested that the nuclear decay could releases a toxic substance. So if you put the cat in a box with the toxin device triggered by nuclear decay, is the cat alive or is it dead if you have not opened the box?

Well, it seems that the cat is somehow both, dead and alive, just like the atom is both decayed and not decayed. And, oddly enough, getting an answer to the question seems to depend on the very human act of making an observation. It is for this reason that people used to think consciousness has something to do with quantum mechanics.

This was something which confused physicists a lot in the early days of quantum mechanics, but this confusion has luckily been resolved, at least almost. First, we now understand that it is irrelevant whether a person does the observation in quantum mechanics. It could as well be an apparatus. So, consciousness is out of the picture. And we also understand that it is really not the observation that is the relevant part but the measurement itself. Things happen when the particle hits the detector, not when the detector spits out a number.

But that brings up the question what is a measurement in quantum mechanics? A measurement is the very act of amplifying the subtle quantum signal and creating a definite outcome. It happens because if the particle hits the detector it has to interact with a lot of other particles. Once this happens, the quantum effects are destroyed.

And here is the important thing. A measurement is not the only way that the quantum system can interact with many particles. Indeed, most particles interact with other particles all the time, just because there is air and radiation around us and there are constantly particles banging into each other. And this also destroys quantum effects, regardless of whether anyone actually measures any of it.

This process in which many particles lose their quantum effects is called “decoherence” because quantum effects come from the “coherence” of states in a superposition. Coherence just means these state which are in a superposition are all alike. But if the superposition interacts with a lot of other particles, this alikeness is screwed up, and with that the quantum effects disappear.

If you look at the numbers you find that decoherence happens enormously quickly, and it happens more quickly the larger the system and the more it interacts. A few particles in vacuum can maintain their quantum effects for a long time. A cat in a box, however, decoheres so quickly there isn’t even a name for that tiny fraction of a second. For all practical purposes, therefore, you can say that cats do not exist in quantum superpositions. They are either dead or alive. In Schrödinger’s thought experiment, the decoherence actually happens already when the toxin is released, so the superposition is never passed on to the cat to begin with.

Now what’s with viruses? Viruses are not actually that large. In fact, some simple viruses have been brought into quantum superpositions. But these quantum superpositions disappear incredibly quickly. And again, that’s due to decoherence. That’s what makes these experiments so difficult. If it was easy to keep large systems in quantum states, we would already be using quantum computers!

So, to summarize. The moon is there regardless of whether you look, and Schrödinger’s cat is either dead or alive regardless of whether you open the box, because the moon and the cat are both large objects that constantly interact with many other particles. And people either have a virus or they don’t, regardless of whether you actually test them.

Having said that, quantum mechanics has left us with a problem that so far has not been resolved. The problem is that decoherence explains why quantum effects go away in a measurement. But it does not explain how to make sense of the probabilities in quantum mechanics for single particles. Because the probabilities seem to suddenly change once you measure the particle. Before measurement, quantum mechanics may have said it would be in the left detector with 50% probability. After measurement, the probability is either 0% of 100%. And decoherence does not explain how this happens. This is known as the measurement problem in quantum mechanics.

49 comments:

  1. Dr. S.,

    You may not be exactly correct about President Trump's deep understanding of QM, although I'd guess the gentleman has as much as Schrödinger's cat.

    In debating some other issues, he might have more significant support.

    Good Karma to all.



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    1. You have deeply insulted cats. Cats have considerable sense of spatial reasoning. They are able to work their way out of things, such as figuring out how to open a latched cage door. Dogs on the other hand have no spatial reasoning; just note that a single dog will get wound up in a chain and not figure if they just retraced their steps they would be free. Dogs though have a deep social intelligence and emotional basis.

      It is strange how cats become the butt of these sorts of things. Ambrose Bierce said a cat exists for us to kick when affairs went bad. Schrodinger seemed to extend this to the physics world. I mean, we do not talk about Schrodinger's dog.

      The Schrodinger cat argument was made to illustrate something that is absurd, the idea cats can be both alive and dead in a superposition.

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    2. well, Wolves can cooperate to pull on 2 separate ropes simultaneously, to pull a tray of food toward themselves.
      https://www.nytimes.com/2017/11/07/science/wolves-dogs-cooperation.html
      Unclear whether that implies any spatial reasoning. Perhaps it's no different than 4 wolves instinctively pulling at 4 legs of their prey, to tear apart the hapless victim.

      Delete
  2. Regarding the last paragraph, haven't you just reasoned a solution for the measurement problem? The time one can maintain a quantum state upon interaction with something (like a detector, or a double slit or anything) is extremely short. In fact, probably a lot shorter then any thinkable detector time-resolution. Hence, decoherence always occurs too quick to observe, and you get 0% or 100% - unless maybe one can build a slowly scaling detector, where a single particle affects really only two others, and so on until its finally measurable.

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    1. Rorokpal,

      The problem is that the outcome of a decoherence process is *not* 0 or 100%. Instead, it's (generally) something in between, which makes no sense for single particles.

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    2. Decoherence establishes decoherence sets, where we can in a coarse grained setting think of the density matrix of our system stripped from off-diagonal terms corresponding tow quantum phases. The remaining diagonal terms just give what amount to classical-like probabilities. This does not give a formalism for predicting an actual outcome. How outcomes of decoherence or measurements happen is unknown.

      The stripping away of off diagonal terms in a density matrix means that Tr(ρ) = Tr(ρ^n) no longer applies, for Tr(ρ) = sum of probabilities = 1. As a funny sideline, when I think of stripping away off-diagonal terms from the density matrix the Frank Zappa song Montana Dental Floss Ranching comes to mind with the part about waxing them down. Decoherence "waxes" the density matrix.

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  3. Sabine, thank you. Your essay provides a precise and beautifully clarifying explanation of how observation works in physics. I especially liked how you constructed a decoherence framework from which to make your final point: the deepest mystery is the source of the final decision that must occur during any given observation. Blaming it all on a naturally occurring quantum version of a random number generator is insufficient, and frankly uncomfortably akin to invoking angels to push planets around in precise orbits. I've written programs to emulate random number generation, and they are anything but trivial. More work, and more skepticism of the casual invocation of magic mathematical functions to "explain" randomness, is needed.

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  4. Covid-update. With myself I had a prolonged period of fatigue and back in April a funny feeling as if my brain had been rewired. With Don-the-Con t’Rump I figured you had to be kidding when you said this reflects a deep understanding of QM by him. I think there are species of flies that have a longer attention span than t’Rump has. Experiments have been done with Buckminsterfullerenes which show they can have quantum mechanical properties. Many viruses are similarly polytopes in the protein coats, which means that if cooled to supercold temperatures, as was done with Buckminsterfullerenes, they might actually have quantum properties. However, in a warm wet environment of a human body, not a chance.

    A quantum observer needs to be any conscious entity at all. All that is required for a system to act as a quantum observer is for the it to couple to a pure quantum state so the quantum phase of that pure state is completely transferred to the large N number of mixed quantum states composing this system. This serves as the collapse. Further this quantum system with frequency ν will enter this state of affairs on a time scale T << 1/ν and so the system never executes its quantum oscillations. The quantum properties or phase of a system is taken up into a measurement apparatus. The phase previously a superposition or entanglement phase of a small N-particle system is taken up into a very large N-particle system. This becomes intractable and we can say the wave function has collapsed within a coarse grained setting.

    There is no need for a mentally conscious being. A biological system, whether a purring cat or a person is a finite non-zero temperature entity filled with quantum noise due to its thermal properties. As such the Schrödinger cat is not possible. There is no way a cat can be in a superposition of states, or at least not the entire thing. A measurement or decoherent event is what converts a quantum eigenvalue into a classical variable. The old photomultiplier tube used in nuclear and particle physics amplifies the excitation of a grid element to convert the quantum state of that particle into a classical readout. There are pieces of flint with tracks of cosmic rays, usually secondary muons, from millions or even billions of years ago. The rock provided the measurement or decoherence of a quantum state. The geologist who finds the piece did not somehow collapse the flint wave function by looking at it under a microscope. There is no need for there to be any actual awareness or knowing of the measurement or decoherence outcome.

    I think it is possible the answer to the measurement problem is there is no answer. A measurement is a sort of quantum self-reference, where quantum states are encoded within qubits of a system. The system → system plus apparatus is a sort of Gödel numbering of quantum states and this has some level of undecidability. There may simply be no possible solution to the measurement problem.

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    1. I'm not a physicist, but I like the idea that if gravity is quantized, there is a minimum unit of gravity. Maybe superposition spontaneously collapses if the superposed gravitational fields differ by more than a gravitational unit; i.e. there is only so much "gravitational strain" that superposition can support.

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    2. Gravitons can have different wavelengths and thus different energy. The low energy weak interacting gravitons are approximately linear and may form superpositions more readily. High energy gravitons may not. Curvature in a cryptic representation are R ~ ∇Γ + ΓΓ, where the dependency on constants is Γ ~ G/c^2, and Γ varies with energy or momentum as E^2 or p^2, which means terms quadratic in Γ or Γ^2 are going to be smaller and contribute significantly only at high energy.

      This is where things get a bit odd. For physics should still function at high energy. In fact quantum gravitation, which largely occurs at high energy, should be dual to the source that generates them. In other words

      Quantum gravity at UV = Quantum fields at IR.

      In some ways this is the Einstein field equation. With the AdS/CFT duality we have nonlocal field theoretic gravitation in the anti-de Sitter (AdS) bulk equivalent to the local quantum field theory on the boundary as the conformal field theory (CFT). The nonlocal bulk q-gravity by some mechanism then must encode quantum information corresponding to the IR local CFT on the boundary.

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  5. @ Sabine,

    You write: "A measurement is the very act of amplifying the subtle quantum signal and creating a definite outcome. It happens because if the particle hits the detector it has to interact with a lot of other particles. Once this happens, the quantum effects are destroyed."

    This is a view from the old quantum theory (1900-1925)! In the new quantum theory (1925+) observables are fundamental and not defined. Your approach doesn't take into account the Kochen-Specker Theorem!   

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    1. It's not "my approach" it's a summary of decoherence theory, and if you think KS disagrees with it, you misunderstood KS.

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    2. @ Sabine,

      You're right! You were presenting the standard theoretical physicists approach. That approach doesn't require coherence or consistency; these are traded-off for visualizability and computational ease and power. This is proved by the continued lack of satisfaction of even theoretical physicists for the meaning of quantum theory. (For example, Feynman's statement that no one understands quantum theory.) My approach is a synthesis of Bohr and von Neumann without all their confusions.

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    3. Bohr and von Neumann, eh? Well good for you, at least it's less tired than the kinship claims to Galileo, Einstein and Feynman.

      Delete
  6. Quantum Mechanics is the anthropocentric view of a world where humans possibly mean nothing. People that write computing code used to say that a binary variable is undefined, null, or set to 1 or 0. A variable is undefined when its name is not present in the code script. A variable is null when its name, although present, has not assigned any value, so its content is empty. A variable is set when its name exists and you let it be certain value. In quantum computing, you can set a qubit into certain binary probability, but classically that binary variable is seen just as null, although may be stochastically biased. The probability that the Moon does not exist when you eventually look at it equals the probability that you are dead when the Moon doesn't cast its shadow on you in a summer night. Antianthropocentric models tell us that you are dead when nature can't apply (observation) its laws on you. So you, as a dead, are now disolving yourself (undefining) and homecoming to the Nothing Sea you were into before you were born. An atom in not decayed and not decayed before its decay measurement, it is just its decay state is anthropocentrically null. That atom already exist as an undefined entity, although with a null decay status. The measurement problem becomes a non existing problem if your code is correctly written.
    ..

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    1. Albert,
      QM does seem anthropocentric in concept, but not the relevance of the application you give.
      For me, the value a variable is assigned is usually less significant than its allowable range, particularly when combined probabilistically in groups of variables.
      When I write my codes correctly, as (hopefully) when doing Monte Carlo analysis of possible configurations, the measurement problem not only exists, its result, or optimal assignments of all values, is what I try to predict.
      Best Regards, Bert




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  7. Sabine,

    In regards to photons have we entirely ruled out there being a basic asymmetry between emission and absorption processes; with emission being the true quantum process and absorption being more of a integral process, perhaps integrating photonic wave energy that has spread out classically with distance or even simultaneously integrating wave energy (of the same frequency) from two separate sources that combine somehow to produce singular emitted photons.

    There is no known mechanism to allow photons of a particular frequency to spread out like classical waves and to be reabsorbed over time with emission taking place once the stored energy reaches hv. However there have been some quantum noise experiments documented on-line where asymmetries between emission and absorption have been observed; these may tentatively show that absorbed energy only could have been simultaneously integrated (my interpretation) from more than one source prior to emission.

    Are you aware of any recent or historical published theoretical investigations investigating such a possibility?

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  8. Some years back I read a biophysics book, Life's Ratchet. It described how cellular machinery, myosin in particular, introduces a time asymmetry which enables cellular metabolism. Myosins carry other chemicals on tracks inside of cells. The chemical storm within a cell can drive reactions forward or backward with more or less equal probability. It is only an asymmetric reaction, one with high forward probability but low backward probability, a toggle reaction, that lets life move forward. In the case of myosins, it is the conversion of ATP to ADP at an effective temperature, according to biophysicists, of about 7000K that ratchets life forward.

    At this scale, it is chemical probabilities, not quantum effects that enforce a forward arrow of time, but I'm wondering if this kind and perhaps scale of asymmetry is close to where the quantum world meets the macroscopic world.

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  9. P.S. I forgot to point out that in quantum computing, it takes energy to erase information. That ATP->ADP energy release lets the myosin forget its reversible state.

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  10. Sabine,

    “This special role of the measurement process it an aspect of quantum mechanics that Einstein worried about profoundly. He thought it could not possibly be correct. He reportedly summed up the question by asking whether the moon is there when nobody looks, implying that, certainly, the question is absurd.”

    Einstein didn’t just “worry” about this, he proved that unless one rejects locality, the measurement results are predetermined. Given the large body of evidence for locality we can conclude that we knew since 1935 that the moon is there when nobody looks.

    “Schrödinger says, you can take the information from the nuclear decay and amplify it. He suggested that the nuclear decay could releases a toxic substance. So if you put the cat in a box with the toxin device triggered by nuclear decay, is the cat alive or is it dead if you have not opened the box?”

    Just like we “observe” the moon by observing the effects of its gravitational field we also “observe” the cat inside the box by observing the effects of its gravitational field. So, the assumption that you can put large objects such as cats into superpositions by using a box is false. The only superpositions that can be created are those based on the uncertainty limit. And that limit is the same with or without a box. For large objects, the uncertainty in position is practically 0. There is no box that can shield a gravitational field, or even an electric or magnetic field, so all those experiments based on Schrödinger’s cat or Wigner’s friend are undoable, even in principle, so they can teach us nothing.

    “The moon is there regardless of whether you look, and Schrödinger’s cat is either dead or alive regardless of whether you open the box, because the moon and the cat are both large objects that constantly interact with many other particles.”

    This is also true for an electron. An electron always interacts with all other electrons and quarks in our universe by electric and magnetic fields. There is no way to “switch-off” the field of an electron, there is no way to “isolate” an electron. The reason the so-called “quantum effects” can be noticed for an electron is that, giving its low mass, the associated uncertainty is large.

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  11. I am wondering, if in large objects, the moon for example, if the universe, is itself, taking measurements constantly, with gravitational forces, and making the moon real. So the moon comparison of quantum mechanics isn't a real valid comparison.

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    1. The problem with this argument is that we don't have a theory of quantum gravity, so no one knows how to make this formally precise.

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    2. Roger Penrose in his Road to Reality states something of this form. Penrose favors the idea of what he calls an R-process, where gravitation demolishes quantum information. His idea is interesting, though I think is is possible that gravitation may not so much demolish quantum information as to convert it to another form. That form might be in the form of IR gravitons or BMS symmetries. Which ever is the case Penrose argues that gravitation couples to a quantum wave to induce a collapse. It is an interesting idea. If this is not fundamental it might have some phenomenology with weak or emergent quantum gravitation.

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    3. I think even short of full quantum gravity, there are some interesting things we can wonder about it. My understanding was that there's an interesting question on whether or not, once we can get the coldness and noise under control to get a system of order Plank mass into a coherent quantum state, its gravitation would cause it to decohere. Though I'm fuzzy on the specifics of what we'd hope to observationally distinguish in this regime - I have a vague sense that we have interesting things to experimentally discover, but it's largely a 'grass is greener with more imminent results in fields I did not go into' sort of feeling.

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    4. Quantum gravitation in the UV limit is in a funny way "self-decohering," and is then not quantum in the standard meaning of the term. See above with my comment to Castaldo ( Dr. A.M. Castaldo1:56 PM, June 29, 2020 ) about some of this. Gravitation is no unitary in the usual meaning because as a gauge-like theory it is not Lorentzian. By some means quantum gravitation is a quantum error correction system if qubits are conserved.

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  12. Oh boy, Trump ... I hope he goes a way soon and we do not have to talk about him.

    But meanwhile, I found a typo:
    "it an aspect" -> "is an aspect".

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    1. Ugis,

      Thanks for spotting this, I have fixed it!

      Delete
    2. Ugis,

      Be careful what you hope for.

      Best regards to all, Bert

      Delete
    3. This comment has been removed by the author.

      Delete
  13. I'm happy to learn that Trump has such a deep understanding of quantum phenomena. I suppose that gives fodder for long deep conversations with Merkel.

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  14. Sabine wrote: "In quantum mechanics, the act of observation has special relevance."

    Why should anybody accept this? If you believe that quantum mechanics is about "measurements", then it cannot be a fundamental theory. John Bell wrote:

    "And does not any analysis of measurement require concepts more fundamental than measurement? And should not the fundamental theory be about these more fundamental concepts?"
    (Quantum mechanics for cosmologists)

    Rather than dismissing QM as not fundamental, shouldn't we search for Bell's more fundamental concepts? The last century witnessed a hunt for ever more fundamental particles. But "particle" is a classical idea (even if shrouded in uncertainty relations). At bottom, couldn't there be something more fundamental than ever smaller particles?

    > "explain how to make sense of the probabilities"

    Why is it so difficult to accept quantum theory as the statistical theory that it obviously is? Quantum theory is the most successful theory that we have. It is painful to see it badly caricatured as a theory of "quantum particles" with unreal properties, and its statistical character hidden behind an entirely fictitious process: the "collapse of the wave function". I think it is a serious misrepresentation of quantum theory (even if it mostly echoes textbook wisdom!) and a disservice to your audience. There is a deep problem here, but it is not quite where you suspect it to be. Please, carry on!

    Best wishes,

    Werner

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    1. "Why is it so difficult to accept quantum theory as the statistical theory that it obviously is?"

      Statistics of what do you think it is?

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    2. @ Werner,

      You write:

      "If you believe that quantum mechanics is about "measurements", then it cannot be a fundamental theory."

      This depends upon a metaphysical assumption prioritizing physicalism over perspectivism! But Quantum Theory is best understood as a form of perspectivism not physicalism.

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    3. Prof. Edwards,

      of course you can define "measurement" (or "perspective")
      as "fundamental". Nice if it helps you to understand quantum theory better. For me it has the opposite effect.

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    4. Sabine asked: "Statistics of what do you think [quantum theory] is?"

      Statistics of events, i.e. points in spacetime. Or in a higher-dimensional manifold. For example, in QED each event would not only be characterized by its space and time coordinates, but also by a phase factor (a la Kaluza-Klein). Fields describe correlations between events, and QFT is a machinery for calculating correlation functions.

      One must not think of the absorption of a photon as happening in an instant. It is a composite event (a pattern). A glance at the Kubo formula for absorption coefficients indicates that there are two parts separated in time on the order of femtoseconds (for visible light).

      [I'm sending this again, because my previous reply, which was sent before the reply to Prof. Edwards, was apparently lost.]

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  15. "... we now understand that it is irrelevant whether a person does the observation in quantum mechanics. It could as well be an apparatus."

    When, and how, has this been convincingly shown to be true?

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    1. Well then, Jim.
      If we remove your term 'convincingly ',
      and replace it with the
      term. 'scientifically',

      Then , no.
      It hasn't been proved.
      .
      My question is where did you come up with the term
      ' We Now understand '

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    2. I quoted the blog post.

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    3. I'm sorry that I didn't keep the reference where I can find it, but some years ago I saw an article about a two-slit experiment run completely by computer, with no human observer involved in either detection, choice of whether to detect or not detect which slit a photon passed through, or analysis of results. In fact, the original observations were erased before any human had access to them. According to that article, the computer found the same results that humans do in such experiments.

      Of course, some people will probably conclude the computer was subconsciously controlled by human minds somehow, but the experiment sounded convincing to me at the time I read it. That is, the simplest assumption seemed to be that human minds are the product of physical laws, not the creator of them.

      Perhaps with some googling you can find the paper which the article cited, or a similar one. Good luck.

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  16. Sabine,

    The more I think the more I am sure that decoherence is just a neat - but very deceptive - way of sweeping the problem under the carpet. The problem is still alive and bites, as you seem to say in the last paragraph.

    ,,The moon is there regardless of whether you look, and Schrödinger’s cat is either dead or alive regardless of whether you open the box, because the moon and the cat are both large objects that constantly interact with many other particles.''

    There is more faith than physics in these statements (as always when we think about really deep problems, nothing wrong with that, even math needs some faith). You can not prove that using only mathematics of decoherence, at the end of the day you still need to make some very strong assumptions, philosophical ones, about consciousness etc.

    And even ,,single'' electron constantly interacts with many other particles - virtual ones but still. What is wrong with this counterargument?
    Here we have the same problem: what makes a/the particle real? A definite outcome in some mind, or interaction with other ,,real'' particles?

    BR,
    Wojciech

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  17. "So when Donald Trump claims that not testing people for COVID means there will be fewer cases, rather than just fewer cases you know about, then that demonstrates his deep knowledge of quantum mechanics."

    Just GOLD. Love your sense of humor.

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    1. "when Donald Trump claims that not testing people for COVID means there will be fewer cases,"

      Is it not true there will be fewer _REPORTED_ cases? That's what virtually all news media report, even if it's not explicitly stated.
      Epidemiologists will estimate & extrapolate the "number of infections", but majority of TV, web, and print reporters are too severely arithmetic-impaired to understand.

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    2. The likely reason he doesn't want to more tests is that fewer positive cases will be reported by the media, yes, I think you understood that correctly. In case you missed the point, people die regardless of whether you know what they died from.

      In any case, the situation in the USA looks so bad at this point I suspect they'll soon give up testing people other than those who are on an ICU, so they can write Covid in the death certificate.

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  18. Sabine, what do you think of the following critique (not mine, I think it's by Earman) of decoherence: it requires a limit in which time t must go to infinite in order to produce the desired result, which doesn't happen for any finite time, no matter how large. It's like the singularities in idealized situations like the Schwarzschild metric, you need more general theorems to prove that in physically meaningful situations the singularities still happen. An analogous theorem seems to be absent in the current mathematical framework of decoherence.

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    1. Aleask,

      That's just not correct. In the t-> infinity limit you get the off-diagonal elements to strictly zero, but fapp you can't tell exactly zero from 10^-200 anyway, so you don't need t -> infinity. Decoherence is all well and fine, really. There's nothing wrong it it. It just does not solve the measurement problem, as too many people erroneously think. (Though, oddly enough, philosophers tend to understand this point. Not sure how come.)

      Delete
  19. "measurement does not merely reveal a property that previously existed, but that the act of measuring makes that property real."

    Can this statement be empirically confirmed? Isn't it just a prejudice?

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    1. @ Greg Feild,

      There's a theorem that the standard quantum logic cannot be embedded in a Boolean Logic. (Corollary of Gleason's Theorem or the Kochen-Specker theorem.) Since QT is empirically highly confirmed, it is reasonable to conclude the above!

      Delete
  20. Sabine,

    besides physics, how interesting do you find viruses?

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  21. When we talk about Schrödinger’s cat, we should be aware of his motivation to create this thought experiment. It was not Schrödinger’s idea to give a lecture here about quantum mechanics. But his point was that he did not at all like the idea of superposition and he used this picture of a cat experiment to demonstrate how crazy he found this portion of quantum mechanics.

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