Saturday, September 26, 2020

Understanding Quantum Mechanics #6: It’s not just a theory for small things.

[This is a transcript of the video embedded below. Some parts of the text may not make sense without the graphics in the video.]

One of the most common misunderstandings about quantum mechanics that I encounter is that quantum mechanics is about small things and short distances. It’s about atomic spectral lines, electrons going through double slits, nuclear decay, and so on. There’s a realm of big things where stuff behaves like we’re used to, and then there’s a realm of small things, where quantum weirdness happens. It’s an understandable misunderstanding because we do not experience quantum effects in daily life. But it’s wrong and in this video I will explain why. Quantum mechanics applies to everything, regardless of size.

The best example of a big quantum thing is the sun. The sun shines thanks to nuclear fusion, which relies on quantum tunneling. You have to fuse two nuclei together even though they repel each other because they are both positively charged. Without tunneling, this would not work. And the sun certainly is not small.

Ah, you may say, that doesn’t count because the fusion itself only happens on short distances. It’s just that the sun contains a lot of matter so it’s big.

Ok. Here is another example. All that matter around you, air, walls, table, what have you, is only there because of quantum mechanics. Without quantum mechanics, atoms would not exist. Indeed, this was one of the major reasons for the invention of quantum mechanics in the first place.

You see, without quantum mechanics, an electron circling around the atomic nucleus would emit electromagnetic radiation, lose energy, and fall into the nucleus very quickly. So, atoms would be unstable. Quantum mechanics explains why this does not happen. It’s because the electrons are not particles that are localized at a specific point, they are instead described by wave-functions which merely tell you the probability for the electron to be at a particular point. And for atoms this probability distribution is focused on shells around the nucleus. These shells correspond to different energy levels and are also called the “orbitals” of the electron, but I find that somewhat misleading. It’s not like the electron is actually orbiting as in going around in a loop.

I get frequently asked why this is not a problem for the orbits of planets in the solar system. Why don’t the planets emit radiation and fall into the sun? The answer is: They do! But in the case of the solar system, the force which acts is not the electromagnetic force, as in the case of the atom, but the gravitational force. Correspondingly, the radiation that’s emitted when planets go around the sun is not electromagnetic radiation, but gravitational radiation, which means gravitational waves. These carry away energy. And this indeed causes planets to lose energy which gradually shrinks the radius of their orbits.

However, the gravitational force is much, much weaker than the electromagnetic force, so this effect is extremely small and it does not noticeably affect planetary orbits. The effect can become large enough to be observable if you have a system of two stars that circle each other at short distance. In this case the energy loss from gravitational radiation will cause the stars to spiral into each other. Indeed, this is how gravitational waves were first indirectly confirmed, for which a Nobel Prize was handed out in 1993.

But this brings up another question, doesn’t it. Why aren’t the orbits of planets quantized like the orbits of electrons around the atomic nucleus? Again the answer is: they are! It’s just that for such large objects the shells are so close together that the gaps between them are unmeasureably small and the wave-function of the planets is very well localized. So it is an excellent approximation to treat the planets as balls – or indeed points – moving on curves. For the electron in an atom, on the other hand, this approximation is terribly bad.

So, all the matter around us is evidence that quantum mechanics works because it’s necessary to make atoms stable. Does that finally convince you that quantum mechanics isn’t just about small things? Ah, you may say, but all this normal matter does not look like a quantum thing.

Well, then how about lasers? Lasers work by pumping energy into a crystal or gas that makes the electrons mostly populate unstable energy levels. This is called “population inversion.” If one of the electrons drops down to a stable state, that emits a photon which causes another electron to drop, and so on. This process is called “stimulated emission”. Lasers then amplify this signal by putting mirrors around the crystal or gas. The light that is emitted in this way is coherent and very strongly focused. And that’s thanks to quantum mechanics because if the atomic energy levels were not quantized this would not work.

Nah, you say, this still doesn’t count because it is not weird. Isn’t quantum theory supposed to be weird?

Ok, so you want weird. Enter Zeilinger. Anton Zeilinger is famous for, well, for many things actually. He’s been on the hotlist for a NobelPrize for some while. But one of his most famous experiments is showing that entanglement between photons persists for more than one-hundred kilometers. Zeilinger and his group did this experiment between two of the Canary Islands in 2008. They produced pairs of entangled photons on La Palma, sent one of each pair to Tenerife, which is one-hundred-forty-four kilometers away, and let the other photon do circles in an optical fibre on La Palma. When they measured the polarization on both photons, they could unambiguously demonstrate that they were still entangled.

So, quantum mechanics is most definitely not a theory for short distances. It’s just that the weird stuff that’s typical for quantum mechanics – entanglement and quantum uncertainty and the ability of particles to act like waves – are under normal circumstances really really tiny for big and warm objects. I am here using the words “big” and “warm” the way physicists do, so “warm” means anything more than a few degrees above absolute zero and “big” means anything exceeding the size of a molecule. As I explained in the previous video in this series, it’s decoherence that ruins quantum effects for big and warm objects just because they frequently interact with other things, air or radiation.

But if you control the environment of an object very closely, if you keep it cool and in an ultra-high vacuum, you can slow down decoherence. This way, physicists have been able to demonstrate quantum behavior for big molecules. The record holder is presently a molecule made of about 2000 atoms or about 40,000 protons, neutrons and electrons.

An entirely different type of “large” quantum states are Bose Einstein condensates. These are clouds of atoms cooled to very low temperature, where they combine to one coherent state that has quantum effects throughout. For Bose Einstein Condensates, the record is presently at a few hundred million atoms.

Now, you may still think that’s small, and I can’t blame you for it. But the relevant point is that there is no limit in size or weight or distance where quantum effects suddenly stop. In principle, everything has quantum effects, even you. It’s just that those effects are so small you don’t notice.

This video was brought to you by Brilliant, which is a website on which you can take interactive courses on a large variety of topics in science and mathematics, including quantum mechanics. Brilliant has courses covering both the mathematical basis of quantum mechanics, as well as quantum objects, quantum computing, quantum logics, and many of the key experiments in quantum mechanics. I have spent some time browsing the courses offered by Brilliant, and I think they are a great starting point if you want to really understand what I explained in this video.

To support my YouTube channel and learn more about Brilliant, go to brilliant.org/Sabine, and sign up for free. The first two-hundred people who go to that link will get 20 percent off the annual Premium subscription.

49 comments:

  1. "Ok, so you want weird. Enter Zeilinger. Anton Zeilinger is famous for..."
    Clever, yes. Weird, no?
    Clever to keep the photons entangled for so long.
    Weird? This is like my point in the quantum cryptography article in that, in order to test the photons, the photons need to be measured in their direction of polarisation? (I assume that is correct.) That makes it no more weird than Bertlmann's socks. Or you could use two gyroscopes with entangled spins, and later find that they are both still spinning along their common axis.

    The Penrose CCC universe ends (cycle) in a Bose Einstein Condensate so that is something apparently big, although the number of different states is small. And the next cycle starts at single state or point. I am losing track of whether this is big or small ... but in some respects it is small ...

    Austin Fearnley

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    Replies
    1. This was not a comment about Zeilinger, but about quantum effects!

      Delete
    2. I think the Penrose CCC universe is rooted more in ego and religion than fact. I wonder what systems of unified theory might be created if someone were brave enough (and popular/influential enough) to point out the lack of clothing on that emperor.

      Space-time is flat. Think about it. All that background radiation? We have less than one tenth of one percent of one frame in the movie some claim plays backwards to the big bang. Black holes don't work today the way they were thought to work last decade. They didn't work last decade the way they were thought to work the decade before. The QCRE has merit and should be explored and improved upon instead of attacked like a heretic defiling the sanctuary of the true science. We already know that quantum particles decay and that the universe is not a closed system.

      I do not have the time or leasure to fully vet or explore unified theory but what upsets me is I constantly see scientists treating weak and anomaly-filled theories with undue respect because they are supported by other scientists with power and not because they are sound science.

      Delete
  2. As a rule the ratio of action to the Planck or Dirac unit of action or S/ħ is a measure of quantum mechanics on the large For S = nħ, say the quantum rotator, if n is large the action unit spacings between quantum states becomes very small compared to the action of the system. This is as you point out with the Earth orbit. Now, if n is an index for a set of states things get strange when all of those quantum states are in the same state. This can happen with entanglements, condensates and over complete states. As a result we can have quantization on the large.

    A superconductor with a discrete set of magnetic fluxes Φ_0 = h/(2e) ≈ 2.0678×10^{−15}Wb, very analogous to the rotator, can be made with Josephson junction gaps. This permits a set states that tunneling can occur. Considering the lowest state this is a qubit. It is also a qubit quantized on the large.

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  3. "without quantum mechanics, an electron circling around the atomic nucleus would emit electromagnetic radiation, lose energy, and fall into the nucleus very quickly. So, atoms would be unstable. Quantum mechanics explains why this does not happen."

    Atoms were stable for billions of years before anyone knew that there were atoms and explained why they were stable.

    Quantum mechanics is a human creation the explains the natural world to humans. Quantum mechanics may not even be the final or only theory that does that. We know that there are holes in the theory and that it has limitations. Many scientists have labored, so far unsuccessfully, to create a theory that explains more than quantum mechanics does. Until such time, if ever, as they succeed, quantum mechanics will do. but, we should not confuse a theory with the phenomena that it explains.

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  4. @ Fat Man,

    "Atoms were stable for billions of years before anyone knew that there were atoms and explained why they were stable."

    is also a human creation that explains "the natural world" to humans.

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  5. nice of your production team to edit out all the profanity... i'm still recovering from the f****** last one!!

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    Replies
    1. That's funny, I found all that profanity refreshing!

      Delete
  6. 7:31 "When things get small, things get weird" - Seems to go against the message of the video :P

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  7. Hi Sabine,

    "But the relevant point is that there is no limit in size or weight or distance where quantum effects suddenly stop."

    The record experiment you quote (25000 AMU) is about 10^15 orders of magnitude below the Planck mass. In theory, what should happen to the wavelength of a molecule or a mono-crystal with enough atoms to reach that mass (or close)?

    Best,
    J.

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    Replies
    1. Nothing, because it has already happened in some restframe.

      Delete
    2. Thanks Sabine,

      so there can be a wavelength smaller than the Planck length?
      (either h/mc, or h/mv with the right choice of v). I am very surprised, I thought that was the big deal of quantum gravity.

      Best,
      J.

      Delete
    3. The Planck scale is just a cut-off in being able to isolate a qubit. You can have wavelengths that are enormously small, but one is not able to isolate a unit of quantum information with wavelengths smaller than ℓ_p = √(Għ/c^3). This is why we can cut-off or use the Planck scale as a regulator.

      Delete
    4. @ akidbelle,

      The Planck constants are just heuristics obtained using dimensional analysis! There are no rigorous conclusions from them.

      Delete
    5. That is not right. The Planck length can be derived by setting the wavelength of a black hole equal to its Schwarzschild radius. Another way is to think of a black hole changing its mass and Schwarzschild radius 2GM/c^2 by absorbing a particle of mass m. This particle has a Compton wavelength λ = ħ/mc. Since any particle entering a black hole or leaving by Hawking radiation gives no information about the interior or the horizon the wavelength is then spread over the black hole and so λ = R. This mass is then a unit of mass change for the black hole m = δM = ħ/Rc and the change in radius of the black hole is δR = Għ/Rc^3, The area A = 4πR^2 change is δA = 8πRδR that is a Planck area and so δR = Għ/c^3.

      This is a physical real quantity that gives a natural scale for QFT cut-off, which is applicable to quantum gravitation. The scale means this is the smallest region one can localize a qubit. We can think of the above argument as a sort of Heisenberg microscope where any attempt to find a region on a horizon a particle enters or exist results in a wild uncertainty in position.

      Delete
    6. "This is a physical real quantity that gives a natural scale for QFT cut-off, which is applicable to quantum gravitation. The scale means this is the smallest region one can localize a qubit. "

      This is incorrect. The former is a distance *scale* (correct) the latter is a distance (incorrect). The former is Lorentz-invariant, the latter Lorentz-covariant, meaning it cannot be a minimal distance. I explain this in detail in my review".

      Delete
    7. I am saying that one can not do an experiment to localize a quantum bit on a smaller scale than ℓ_p. I am not saying this is some minimal length, which is what the LQG tend or tended to impose. A string has an infinite set of modes, and most of these waves have wavelength below the Planck scale. If an experimenter tries to localize a qubit on a smaller scale this requires a Planck energy or more and they only produce quantum units of black holes. If they try to go to even higher energy they may produce quantum black holes with several or even many Planck units of mass.

      Delete
  8. You left out superfluids and superconductivity. These are both quantum effects that are very much on a macroscopic scale.

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  9. Sabine, you say:

    “You see, without quantum mechanics, an electron circling around the atomic nucleus would emit electromagnetic radiation, lose energy, and fall into the nucleus very quickly. So, atoms would be unstable. Quantum mechanics explains why this does not happen.”

    I think that this is the typical treatment of quantum mechanics. Something physical happens, which is not understood, and it gets the label “QM”; and this is meant as a kind of understanding.

    QM does in general not mean understanding and should not be taken as that. We do not understand everything in physics, of course not. But we should not give up to try it.

    If we want to understand why an electron does not radiate in the atomic orbit, we should first understand why it radiates in the normal case of acceleration. Maxwell has once said that an “accelerated charge” radiates. But Maxwell could not give us an explanation at his stage of physics. Maxwell did not know relativity and he did not know anything about the structure of particles as we have got it from de Broglie, Schrödinger, and Dirac.

    Now, with this knowledge, it is possible to understand the phenomenon, even without QM. It's not really complicated. But then the question, why not radiating in an atomic orbit, is more complicated.

    This is not the place to explain this process. But I find it necessary to emphasize that we should not stop to find solutions. And particularly we should not feel satisfied by answering a question with a pseudo explanation like the mention of QM.

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  10. In video at 5:15 you are showing Gran Canaria, not La Plama

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    1. metju,

      Yes, sorry, someone else already pointed out this blunder to me. I have added a correction in the info below the video.

      Delete
    2. aha ok, sorry then for repeating ..
      I have looked a bit and didn't find it .. but there are many comments here .. that's because your chanell, blog, book, you ;-) .. are fantastic! I hope you can continue for some time in the future. Thanks for sharing this knowledge and good luck!

      Delete
  11. @ antooneo,

    QT is just a form of generalized probability theory. Empirically it turns out to correctly predict certain phenomena. One should simply be gratful for such successes!

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    Replies
    1. @Prof. David Edwards:

      Yes, I agree. But I have referred to the saying: “Quantum mechanics explains why this does not happen.” The WHY is generally not the matter of QT, but QT is often treated like having this.

      I have a lecture of Feynman about QED where he says: “The laws of quantum electrodynamics are at present given in the following way without a justification: xxx “. – Is there any new state of this?

      Delete
    2. @ antooneo,

      In spacetime dimensions 2&3 there are some rigorous models; in particular, (phi^4)2 has all the properties physicists hope for. (The Feynman perturbation expansion is an asymptotic expansion for the scattering matrix!) But for QED, the electo-weak theory, and the standard model all one has are bits and pieces of theory.

      Delete
    3. Hello Antooneo,

      construct an object that
      - is larger than a double slit
      - is able to fly through it
      - is absorbed from time to time
      - comes through from time to time and then is still essentially the same object
      What we can exclude are:
      - particles, because they cannot see both slits.
      - waves, there is no object that contracts waves again, which is necessary for absorption
      - With a wave function you end up in the dead end of the "collapse of the wave function".
      This sounds scientific, but it is only a word and does not explain anything.

      You will probably have to think of something new...

      Have fun
      Stefan

      Delete
    4. Stefan Freundt,

      "What we can exclude are:
      - particles, because they cannot see both slits."

      Of course they can. The concept is well known in classical physics and it is called "field". An electron can "see" both slits because the barrier consists on charged particles (electrons and nuclei) and the field configuration depends on the distribution of those charges. The electron interacts differently with a one-slit barrier than with a two-slit barrier because the fields associated with those geometries are different.

      Delete
    5. @Prof. David Edwards:

      I have mentioned Richard Feynman because he says in the lecture that there is a theory of QED on the one hand but on the other hand there is no justification for this theory – which I find typical for QM. You say that there is a further development of bits and pieces of the theory; thank you.

      @Andrei9 and Stefan Freundt:

      If we take the electron model of Louis de Broglie, then we are close to a solution without the weirdness of QM: In de Broglie’s view, the electron is a particle, a bullet, accompanied by a field. - Physically better is a pair of bullets, which are mass-less each. The mass of the electron is caused by the interaction of the bullets. - The field guides the particle, the bullets are the actors in particle reactions like absorption.

      The field builds an interference pattern at and beyond the double slit. This field guides the bullets to the screen behind. And as the bullets do not have any individual mass, they follow the field exactly. So the absorption events on the screen show the well-known pattern.

      The model which derives the inertial mass of the electron from the internal field interaction yields the mass of the electron with a precision of better than 10^-5 without any use of free parameters to be adapted. And without any use of QM.

      So, I’m having fun indeed.

      Delete
    6. antooneo,

      de Broglie's theory is non-local, right? Can you point me to the paper where the electron model of Louis de Broglie is presented?

      Delete
    7. Andrei:

      Sorry, I have at first overlooked your question.

      De Broglie first described his electron model in his thesis for which he received the Nobel prize:

      'Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis, Paris, 1924, Ann. de Physique (10) 3, 22 (1925)'
      An English translation of the paper by A. F. Kracklauer can be found at:
      https://aflb.minesparis.psl.eu/LDB-oeuvres/De_Broglie_Kracklauer.pdf

      Later de Broglie did not continue with his model of the electron because he could not get an employment at a French university unless he fully converted to the QM of Heisenberg. This will also have affected his position to non-locality.

      Delete
  12. Kind of suprised you don't mention white dwarf stars as an example of a thing that's "cold" enough to be quantum i.e. a bose einstein condensate. Is it because there's some debate as to whether that's true? If so, it still seems worth mentioning. A pretty cool idea.

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  13. When doing experiments to see quantum effects that particles are subject to, the experiential results look like probing only the micro world of particles, but they also depend on the validity of quantum mechanics of the macroscopic measurement device used.

    Take e.g. a Mach-Zehnder interferometer. The photons bounce off mirrors in the interferometer. One can then ask why the recoils of the photons when they collide with the mirrors, don't destroy the interference. Momentum is indeed transferred to the device and it depends on the path taken by the photon.

    The reason why interference is nevertheless not destroyed, is because quantum mechanics also applies to the device. The quantum state of the device (plus environment) does not have a precisely enough defined momentum for the different recoils for the different paths to be well distinguishable.

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  14. Hello Andrei,
    but in this picture you will not see any interference stripes, but only the classic two stripes, one behind each slit. The particles then behave like shot balls. Whether the second slit is there or not is negligible for the particles.
    Have Fun
    Stefan

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    Replies
    1. Stefan Freundt,

      "Whether the second slit is there or not is negligible for the particles."

      Can you point me to a paper where the fields are computed and found negligible in regards to electron's trajectory?

      Delete
  15. Hello Andrei,

    the negative and positive charges neutralize each other.
    Correspondingly, there is no electric field and thus no deflection.
    There will be no paper.
    Do you expect an electrically neutral object to deflect an electron?

    But well.
    Let us assume for the moment that the electron - as a particle - flies through the right slit.
    Does the left slit have an attracting or repelling effect?

    But good.
    Let's assume for the moment that the second slit is attractive.
    Then the electron's trajectory would be deflected towards the second slit.

    Now many electrons fly sometimes right and sometimes through the left slit,
    you would see a main maximum in the middle behind both slits,
    with intensities decreasing to the side.

    In the experiment, however, we see a main maximum and secondary maxima on both sides,
    whose intensity continues to decrease.
    And between the maxima there are minima.
    And these minima have the intensity zero !!
    How do you want to get them in the particle image by classical means?
    You cannot add intensities to zero!!

    Therefore you need waves for the interference stripes and
    particles for absorption and jumps from one model to another as required.
    I personally dislike this kind of ingenious thinking.

    But to explain it all in one piece,
    you will have to come up with something new,
    something really new.

    Have fun
    Stefan

    ReplyDelete
  16. Stefan Freundt,

    "the negative and positive charges neutralize each other."

    No, they do not. The electrons and nuclei do not share the same position, therefore it will be a field. An electric dipole, even if "neutral" does produce an electromagnetic field of infinite range.

    "Correspondingly, there is no electric field and thus no deflection."

    See above! Also, if there is no electric field why do you think the electron doesn't just pass through the barrier like a neutrino? Do you think it just "bumps" into other electrons, like a billiard ball?

    "There will be no paper."

    I've expected that.

    "Do you expect an electrically neutral object to deflect an electron?"

    Yes, I do! The object is not neutral in the sense a neutrino is neutral. It's neutral on average. The main value of the field far away from a macroscopic "neutral" object is null. But the electron does not experience the mean value of the field, but the actual value the field has when the electron is there.

    "Let us assume for the moment that the electron - as a particle - flies through the right slit.
    Does the left slit have an attracting or repelling effect?"

    In order to calculate the field you need to model the system on a computer. The system is dynamic, so I expect the field to change. But is difficult to say without calculating it.

    "Let's assume for the moment that the second slit is attractive.
    Then the electron's trajectory would be deflected towards the second slit."

    No, it's not that easy. You need to model the thing on a computer.

    "Therefore you need waves for the interference stripes and
    particles for absorption and jumps from one model to another as required."

    "In the experiment, however, we see a main maximum and secondary maxima on both sides,
    whose intensity continues to decrease.
    And between the maxima there are minima.
    And these minima have the intensity zero !!
    How do you want to get them in the particle image by classical means?
    You cannot add intensities to zero!!"

    In order to determine where the electrons go you need to know:

    1. The initial state of the electron as it leaves the source.
    2. The electric/magnetic fields associated with the electrons/nuclei in the barrier.

    Of course, the electron might also have an effect on the charge distribution of the barrier.

    Then, you determine the electron's trajectory using Newton's laws and the Lorentz force law and see what you get. Until this calculation is done you cannot conclude anything, the system is too complex to intuitively grasp it. It's basically a N-body electromagnetic problem where N is about 10^26.

    "But to explain it all in one piece,
    you will have to come up with something new,
    something really new."

    There is no need to invent something new. We know how the electron interacts with the barrier. It's by electric, magnetic and gravitational fields. One needs to somehow calculate this. If the result is inconsistent with the experimental results, only then, we would need something new.

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    Replies
    1. Assume there are equal number of positive and negative charges spaced around in a region with a mutual distance from each other around d. For a distance r >> d the electric field is going to appear as E ~ qd^{n-1}/r^{n+1}, which if n is very large is a very small field.

      Delete
    2. Lawrence Crowell,

      1. No matter how small the field is it has to be the cause of the electron's change in trajectory because there is nothing else that could do it. Gravity is even weaker.

      2. How strong the field needs to be so that it accounts for the change in electron's trajectory?

      3. Charged particles in a solid do not move at random, independently of one another, so even if the field associated with the distant slit is too weak to deflect the electron, the existence of a second slit could alter the charge distribution around the first. It's not just the incoming electron interacting with the charges in the barrier, but also charges in the barrier interacting with each other.

      Delete
    3. The 2-slit experiment works for a range of particles, the easiest being photons and it has been done with neutrons. If this were done with neutrinos there would be no interference pattern for neutrinos pass through most ordinary matter. You would have to use, but some unknown means, material in a neutron star to do a 2-slit experiment with neutrinos. The fact this matter in the slit interacts is though a form of boundary condition, so the wave function of the particle we set to it, of course as a wave, conforms itself nonlocally to this configuration. It is not about a particle being rattled around by interactions with the mask.

      Delete
    4. Lawrence Crowell,

      " You would have to use, but some unknown means, material in a neutron star to do a 2-slit experiment with neutrinos."

      Sure, but my point was that it is a requirement for this experiment to work that the incoming particles interact with the barrier. If they do not interact with it (like in the case of neutrinos passing through a copper foil) no interference is observed. This is proof that the ultimate cause behind the observed pattern is the interaction between the particles and the barrier.

      "The fact this matter in the slit interacts is though a form of boundary condition, so the wave function of the particle we set to it, of course as a wave, conforms itself nonlocally to this configuration."

      The boundary conditions is an implicit assumption that the particles interact with the barrier. You could also make this interaction explicit by reformulating the problem in terms of the EM interaction of all the particles involved. Such an approach cannot be done in practice (too much computing power required) but it should work in principle.

      "It is not about a particle being rattled around by interactions with the mask."

      You can treat the barrier as a large molecule and ask how an electron is scattered by it. So, in this case, the electron is actually "rattled around". Sure, QM will not give you a trajectory, but it does not deny its existence either.

      Delete
    5. The surface of a material has a sort of quantum atmosphere. The quantum fields or states that compose a substance define a quantum wave region within around 10^{-8}cm or so. As a result the electron approaching the material of the mask destructively interferes with this wavy quantum atmosphere. Frank Wilczek wrote a paper on the quantum atmosphere a couple of years ago.

      Delete
  17. Stefan Freundt,

    Why so complicated? Your problems do not exist if we follow the model of de Broglie. The field which guides the electron is an alternating field. (Classically understandable as the electron rotates and so do its internal charges.) This field underlies of course also destructive interference which explains the minima.
    De Broglie has assumed that there is no fundamental difference between a photon and an electron regarding this field.

    So, all considerations which explain the deflection of photons at a double slit are also applicable to the electron. And this remains a classical explanation.

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  18. In my opinion, the most obvious topic in quantum mechanics is that it is purely a statistical theory. You can’t get the right results with enough accuracy without extensively comprehensive statistics, which usually mean macroscopic structures.

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    Replies
    1. I feel I agree, but it's quite significant that it can't simply statistics covering up our ignorance of something better behaved. There's a lot of statistics in the world but this is special.

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    2. All rough-levels of statistics of physics are emergencies of statistical behavior of quanta, ok?

      Delete
  19. Hi, Sabine! I just wanted to say that your videos (specially the one about bra-ket notation) and Matt's PBS space time channel took away my fear to dive deeper into the math of QM. It motivated me to watch the 10 lecture course from susskind and the plan now is to start the 3º feynman book.

    Thanks for all your work. You are a great educator.

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  20. Playing with high temperature superconductors, in recent years, it was always quite cool to observe the macroscopic quantum effect of flux pinning as a small neodymium magnet hovered above the YBCO chip immersed in liquid nitrogen.

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  21. Antooneo said on 5:07 PM, September 28, 2020

    “Now, with this knowledge, it is possible to understand the phenomenon, even without QM. It's not really complicated. But then the question, why not radiating in an atomic orbit, is more complicated.”

    Indeed, this is a situation where the QM rationale for the lack of radiative loss in an atom always seemed to be incomplete to me. Then, two decades ago I came upon an idea that seemed to be the missing piece in the QM chain of logic. It’s a layman level idea, so perhaps not to be taken too seriously. But I even wondered if (apparent) macroscopic quantum effects claimed by a Russian ceramics engineer could be connected to this concept. And, more recently, a connection to the Universe’s dark sector enigma occurred to me. Granted, it’s a pretty far out idea, but I’m hoping to post the paper in a few weeks at that repository where ideas range from crackpot to possibly quite sensible.

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  22. Hi Sabine, can wave function collapse be seen as a symmetry breaking, a symmetry that translates into conservation of behavior (or logical consistency given by some axioms)? This symmetry would conserve the probabilistic behavior and interference (quantum behavior) and when it breaks down we remain with particles and general relativity.

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