A good book that explains quantum physics like I'm an idiot?

Discussion in 'General Science & Technology' started by stateofmind, Feb 17, 2015.

  1. Schmelzer Valued Senior Member

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  3. arfa brane call me arf Valued Senior Member

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    Bear in mind that QM isn't about physical forces or say, the sizes or geometry of particles. Rather it's an extension of classical probability theory that treats quantum objects as probability amplitudes.

    We don't see these objects; what we see is the result of their interactions with "the" environment.
     
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  5. exchemist Valued Senior Member

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    Not sure I would agree with that. Physical forces are a critical part of QM. Without them, you would have no interaction between QM wave-particles and no physics.

    And I don't think it is true that QM is an extension of classical probability theory either. Most of it can be seen as the result of treating matter as wavelike. The square modulus of the amplitude of the wave corresponds to a probability density, sure, but you do not use the mathematics of probability in QM at all - or barely. What you use is the mathematics of waves, matrices and vectors.

    As for not seeing them but only their interactions, I know what you mean but one might argue that what we call "seeing" is merely one form of just such an interaction.

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  7. arfa brane call me arf Valued Senior Member

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    I don't think that's true. The Schrödinger equation doesn't describe forces.
    But, that's exactly what the Copenhagen interpretation is.
    --https://en.wikipedia.org/wiki/Schrödinger_equation

    If quantum particles (waves) have no exactly determined properties, it must be a problem defining forces acting on them (in fact, a problem with no solution).

    A good book that explains quantum physics would need to explain what "the Schrödinger equation" is, what it means physically. I don't know that I can say understanding it is something that comes easily, Schrödinger, Einstein, Bohr, Heisenberg et alia, all found it "troubling".
     
    Last edited: Feb 29, 2016
  8. arfa brane call me arf Valued Senior Member

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    I think doing experiments is probably the best way to start. So can you do quantum experiments at home?

    Today, laser pointers are cheap, polarising filters are too. You can make a double slit with three pencil leads (I've seen this done), or with an ordinary piece of paper and a safety pin (with which you make two holes close enough together so they lie inside the laser beam).

    With three polarising filters, ordinary light as an input you can see a quantum effect, quite a well-known one, and explaining it properly requires more than classical logic.
    Lastly, there is google, try "quantum experiments at home" . . .
     
  9. exchemist Valued Senior Member

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    Yes but the Hamiltonian in the Schroedinger equation does contain a term for potential, (usually denoted by the symbol V), right?

    And that potential is the potential energy of the QM entity, due to a force (in an atom, electrostatic force between the nucleus and the electron).

    For the electron, no force -> no potential -> no bound state -> no classical periodic motion -> no quantisation. Thus the states of a free electron, not subject to any force, are not quantised.

    If you do not know how the force behaves, you cannot construct V. So force is absolutely part of QM - it is just rather taken for granted as a precursor to the equations one normally sees.

    As for the probability issue, yes I understand what you are saying but my point was that you do not use probability theory (i.e. the branch of mathematics concerned with calculating probability) much, if at all, in QM. You use some basic probability ideas, such as the concept of the square modulus of the wavefunction as a probability density, and the idea of a probability distribution, but you do not in general spend much time using the mathematics of probability theory. An expert on the maths of probability will not find it gets them very far at all in mastering QM. Whereas somebody good at the maths of waves (all those second partial derivatives, Fourier transforms and so forth), matrices and vectors will find that very helpful indeed.

    You raise an interesting point about calculating the force on a fuzzy wave-particle. But in fact Schroedinger's equation treats the electron as a particle in motion, in order to construct the wavefunction, which is then interpreted as a sort of square root of a probability density. If you read texts that describe the QM treatment of a harmonic oscillator or a particle in a box, it is the same story. The QM entity is in all cases treated mathematically as a particle: it is just that (as per our friend Heisenberg) you can only know approximately where it is and/or how fast it is going, hence the fuzziness.
     
  10. arfa brane call me arf Valued Senior Member

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    In the particle in a box scenario, V can be infinite. The wave equation for such a particle depends on its energy and the dimensions of the box, there are no forces involved.

    It's confusing I guess, because an electron in a hydrogen atom is also a particle in a potential box, and the electron and proton each see a Coulomb force.
     
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  11. exchemist Valued Senior Member

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    Yes there are, actually. The infinite potential at the boundaries implies an infinite force acting on the particle once it reaches the boundary. That is what the square box potential means.

    With the harmonic oscillator, there is the classic SHM restoring force, proportional to displacement from the centre, which results in a parabolic potential.

    In the real scenario of the electron in the atom, there is a 1/r Coulomb potential which is determined by the inverse square-dependent force of electrostatic attraction between electron and nucleus.

    In the real scenario of vibration of the bond of a molecule, there is a more complex force pattern that attracts at longer distances and repels at short ones, sometimes approximated by a Lennard-Jones (6-12) potential or similar.

    All these situation involve a force acting on the QM entity. It is true that QM treatments focus on the potential resulting from these forces, rather than the forces themselves, but the forces are the source of the potential. Without considering the forces, how do you explain where these potentials come from?

    Rotation (say the Rigid Rotor) is the odd one out, as this is a form of what classically would be periodic motion that does not depend on a force, and so there is no potential involved - the Hamiltonian contains only a kinetic energy term.
     
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  12. arfa brane call me arf Valued Senior Member

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    Ok, well, I should reframe that statement: quantum mechanics isn't about forces, because a stationary state is fixed by all the forces acting on it, as a particle in a potential box.

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    Say you set up a quantum eraser experiment. The results: whether or not an interference pattern is observed and whether or not which-path information is known, depend on what happens in an abstract space, a Hilbert space which is \( \mathbb C^{2n} \), for n 'particles' (actually qubits). Forces aren't a part of the outcome, because these are all fixed in the experiment, so we know what they are without having to measure any of them.

    So, forces exist in a classical context, but not when you plug 'energy' into the Schrodinger eqn. If you can make sense of the diagram above and note that one of the states is not stationary, this could be a clue. It's the square of a probability amplitude, and it's oscillating.
     
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  13. Syne Sine qua non Valued Senior Member

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    A Brief History of Time, Stephen Hawking. There's even an illustrated version.
     
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  14. exchemist Valued Senior Member

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    Well, I know it's labouring the point, but I'd still love to hear your explanation of how the potentials I have been describing can be constructed, without reference to the force that gives rise to them.

    Your use of the quantum eraser example does not address this, since nobody is saying QM is ALL about forces. These electrons are not in a bound state so they are an example of QM in the absence of a constraining force. As is the Rigid Rotor example. Neither of these examples demonstrates that force is irrelevant to QM.
     
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  15. arfa brane call me arf Valued Senior Member

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    I think the reason quantum mechanics isn't about forces (which doesn't say forces are irrelevant), is that the Schrodinger equation can't be derived from Newton's Laws, or from Maxwell's equations. At least that's what Kenneth Krane, Modern Physics 3rd ed. says.

    Otherwise you could explain the photoelectric effect, say, starting with Newton or Maxwell. Would you agree at least with that summary?
     
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  16. exchemist Valued Senior Member

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    Yes I suppose that much is fair enough. I guess what it boils down to is what one means by "about". (Starts to sound a bit like Bill Clinton, eh?)

    QM is really "about" the wavelike nature of matter at the atomic scale, the sq. mod of the wave amplitude denoting a probability density (which I suppose is what you have been getting at.). E=hν and λ=h/p are about the most fundamental concepts, it seems to me, so our thanks for Dr. Planck and duc Louis de Broglie for those. Once you have matter behaving like waves, Heisenberg's uncertainty principle and the various quantised systems we are so familiar with in atoms and molecules follow pretty naturally, via harmonics, superposition, Fourier transforms and so on.

    All I suppose I am really trying to get across is that it still deals in familiar concepts from mechanics, including force, momentum, moment of inertia etc. As someone who read chemistry, I am always suspicious of the tendency for some people to stress the "otherness" of QM, imbuing it with an air of mystery (double slit experiment, entanglement and all that shit), when in fact its huge successes have been in explaining things we all rather take for granted today, such as atomic and molecular spectra, chemical bonding and the properties of chemical compounds.
     
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  17. arfa brane call me arf Valued Senior Member

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    Well, as it happens, there are two ways to explain a double slit experiment and one is classical. Essentially you treat two rectangular slits mathematically as two rect functions and do a Fourier transform.

    What I wanted to stress about quantum experiments is that forces are part of the classical setup--there are forces keeping all the apparatus together--but they are not part of the Schrodinger picture. Potentials in this picture are boundaries at which the wavefunction, or say a deBroglie matter-wave, is continuous. Particles can tunnel through potential barriers if the barrier width is less than their wavelength, which can't be explained by forces. The explanation is that the wavefunction decays exponentially inside the barrier, and will have a lower amplitude after it tunnels through it, but it can't if it decays to zero, i.e. if the barrier is too wide.
     
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  18. exchemist Valued Senior Member

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    In that case I'd still like you to explain to me how the 1/r Coulomb potential is arrived at.
     
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  19. danshawen Valued Senior Member

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    This thread is easily a contender for one of the finest I have ever seen discussed here, or anywhere else.

    Of course, Schroedinger's wave equation was not derived, but it is equivalent to Planck's matrix methodology. Bohr grilled poor Schroedinger literally to tears about his differential wave equation method before this was fully realized or appreciated however.

    The rotational (bound) energy propagation mode of fundamental particles like electrons SHOULD represent potential energy in the Hamiltonian (summation of kinetic, potential energies) as well. The reason it doesn't is because for over 50 years, no one believed in the spin zero boson that is the only means for getting potential energy in or out of quantum spin states, other than by means of nuclear fission or fusion, that is.

    You can see how this might be an important physical detail. Whenever and wherever energy does not appear to be immediately conserved in particle interaction, that is where the energy goes or is derived.

    We are living in a universe of energy transfer events. That is literally all there is, or ever was, to account for.

    And when Newton appeared to be the best human being ever born to do math related to physics, they mistook his talent for that of an accountant and put him in charge of the treasury, and also requested that he calculate the precise date of creation from Greek translations of Hebrew scripture, for the first edition of the King James Bible. He never rendered a single calculation associated with that task, and also took issue (in his posthumously discovered writings) with an explicit mistranslation of the Greek word for trinity, which he saw as responsible for changing monotheistic Christendom into a derivative of a Greek polytheistic culture.

    Most abrhamic religions are big on counting commandments from G-d, but what used to number 613 was pared down to only 10 in derivative traditions, and the first one of those commandments clearly states the monotheistic basis of the original tradition. It's like humanity has been afflicted with discalcula as well as comprehension issues for longer than anyone can even remember. So you can imagine the frustration of someone like Newton.

    Too heavy a reliance on ancient Greek inspired static geometry mistakenly applied to inertialess relativistic space to formulate physics is a big concern of mine also. More realistic math is sorely needed, and as capable as he was, Hilbert's falls far short of the mark.

    One of the finest engineer/scientists I ever knew started out his accomplished career as an accountant. It took me most of my life to understand the connection. Do you see it yet? It is altogether fitting that a book about physics should treat us all as the idiots we manifestly are.
     
    Last edited: Mar 3, 2016
  20. PhysBang Valued Senior Member

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    It took the development of both methodologies before they were equivalent, as initially neither could be applied to the same quantum states.
    Ah, yes, the danshawen conspiracy theory that, somehow, contemporary mathematics doesn't actually work in science and the entire scientific community is fooling everyone into thinking that their results are accurate. I know the weird anger and inability to work through the math would come up in this post eventually.
     
  21. exchemist Valued Senior Member

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    A few points:

    1) I think the matrix methodology was Heisenberg's, not Planck's: https://en.wikipedia.org/wiki/Matrix_mechanics

    2) Your statement: "The rotational (bound) energy propagation mode of fundamental particles like electrons SHOULD represent potential energy in the Hamiltonian (summation of kinetic, potential energies) as well." appears confused. There is a varying mixture of kinetic and potential energy associated with an electron in an orbital, just as there is in simple harmonic motion. As with SHM, it is the sum of the two forms of energy that is conserved. But no energy is being "propagated", at least, not in a stable state. It is being conserved within the electron orbital.

    3) I'm not sure what you mean by not being able to get energy in or out of quantum spin states without this zero spin boson you speak of that "no one believed in". There is of course the photon, which has a spin of 1

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    . After all, in NMR for example, energy is emitted and absorbed by changes in quantum spin states, by means of radio-frequency photons. ESR is similar, except that the photons are in the microwave range. Both are well-established phenomena and important analytical techniques. So photons seem fine for such a job.

    4) Or, alternatively, is this something to do with trying to change the intrinsic spin of a particle? That intrinsic spin is treated as invariant, like charge - and so it is, to all intents and purposes, surely?

    As for the rest, well, er, it's a good job this thread is in the General section.

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    Your animus against poor old Hilbert seems undiminished, I notice. I am mystified as to its cause. I wonder if that means you've also got in for Dirac: after all, his bra-ket notation represents wave functions as vectors in a Hilbert space, doesn't it?
     
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  22. danshawen Valued Senior Member

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    Yes. My mistake.

    AND E=mc^2 is not a statement of potential energy for bound energy/matter? Be consistent.

    E=mc^2 is also not a complete statement. It shows matter-energy equivalence, but does not specify how or by what mechanism this occurs. Eventually, relativity comes up with two uniquely invariant reference frames; the speed of light for unbound energy, and "at rest" for the invariant rest energy of the bound energy state that is matter.

    Reflect for just a moment to imagine, Mach's formulation of spinning relative to the rest of the universe must also have at least one invariant state, and that would be quantum spin of zero. An equivalent invariant reference frame for bulk matter doesn't exist, because atomic structure is a dynamic that is the superposition of many spin states, and the same could be said of fundamental particles like quarks and electrons.

    But the spin zero state is unique for the same reason that "at rest" is unique for the bound energy that is matter. Although vector addition generally does not work as you might expect in relativistic space, one vector addition DOES work, and that would be +/- c (the superposition of +c in one direction, vector summed with -c in the diametric opposite direction is the best definition of "at rest" for ANY inertial reference frame in which matter exists. In the same manner, a quantum spin of +1 combined with a quantum spin of -1 vector sum to a vector spin of zero, the spin invariant state populated uniquely by the boson that is an excitation of the Higgs field.

    Your understanding of a universe composed entirely of energy transfer events is now complete. The hierarchy problem is resolved because the spin potential energy of matter can only be given inertia by something that couples to both the unbound energy of photons as well as the spin states of fermions. Electrons, quarks, electroweak bosons, and their antiparticles all get their inertial "at rest" masses by the only boson that is capable of slowing them down by means of interacting directly with their spin states.

    Relativity is the lingua franca of both linear bulk energy propagation, and energy propagation that is a superposition of rotational quantum spin states. This would include both fundamental particles and atomic structure. Quantum spin in opposing directions only makes sense for Higgs. Static geometry will not be of great utility for this. Vectors don't add in the rotational mode of energy either, neither is there a "constant" equivalent of pi. It works by means of other principles, yet to be defined. The Ehrenfest paradox must first be resolved. I already solved it. Have you? The solution rather strongly suggests, it is the rotational mode of energy propagation that is the origin of both the arrow of time, and of time itself. In this domain, one thing we do understand since the 1990s is that instantaneous velocities are more meaningful to time dilation than accelerations, so you can leave calculus on the shelf. Boost matrices are probably OK.
     
  23. exchemist Valued Senior Member

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    Can you cite a reference for any of this stuff? I've never come across it and it sounds woolly to me. Or is your own idea and thus belongs in the Alternative section?
     
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