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Re: The Reference Frame: Franson's "breakthrough" concerning the speed of light

Edwin Steiner — Mon, 30 Jun 2014 11:50:41 -0000

You are missing that the states of well-defined energy are just a basis
of the Hilbert space, they are not the full set of physical states.
There's plenty of other states available which can be written as
superpositions of energy eigenstates. In an introduction to
time-dependent perturbation theory you will see how the physical state
of the electron can change smoothly due to a perturbation of the
Hamiltonian.

The transition is definitely not instantaneous, otherwise spectral lines could not be so sharp, for example.

Re: The Reference Frame: Franson's "breakthrough" concerning the speed of light

Edwin Steiner — Mon, 30 Jun 2014 14:43:00 -0000

In order to take relativity fully into account you need to step up to quantum field theory, i.e. QED in this case. This is not needed to counter the original argument, however: The reasoning that due to the discreetness of the energy levels the electron's state must change discontinuously is wrong. One would make the same mistake with the argument: The independent spatial directions are discreet (3), thus an object can only rotate in instantaneous jolts of 90 degrees. Obviously continuous rotations are possible and in the Hilbert space of QM the situation is mathematically analogous (roughly replacing directions with physical states and rotations with unitary transformations).

Re: The Reference Frame: Franson's "breakthrough" concerning the speed of light

Edwin Steiner — Tue, 01 Jul 2014 04:53:12 -0000

I think you still have the mental picture of a classical electron somehow hidden behind quantum mechanics. There is no such thing. There are no orbits. You can estimate the time the transition takes from the width of the spectral line, but there is no fixed "distance". To speak of a distance covered by the electron only makes sense if you make at least two measurements of the electron position. When you are observing spectral lines, i.e. energy differences, you make no (precise) position measurements at all. You cannot make them, because any position measurement of enough precision would completely ruin your energy measurements. The operators of energy (Hamiltonian) and position do not commute, so it makes no sense to speak of their eigenvalues (well-defined values of energy or position, resp.) at the same time.

Re: The Reference Frame: CMS "sees" \(650\GeV\) leptoquarks

Edwin Steiner — Fri, 11 Jul 2014 16:17:15 -0000

One of the properties of a leptoquark that Lubos mentions is "transforms as a color triplet". A hydrogen atom does not transform like that - it is a color singlet, i.e. it is "colorless", which means it carries no charge with respect to the strong force. Due to confinement everything you can see at low energy is colorless.

Re: The Reference Frame: Non-orthogonal quantum states are not mutually exclusive

Edwin Steiner — Mon, 21 Jul 2014 09:13:55 -0000

The friend cannot repeat the whole experiment (the elaborate one that Wigner uses to verify his 100% prediction of the measurement of O_Wigner) because the friend is himself part of this experiment. He would need to prepare his own brain in exactly the same state each time, for example. The friend could run his own private series of little experiments inside the box, but then we are no longer talking about the same experiment that Wigner meant when he calculated the 100%.

Re: The Reference Frame: Non-orthogonal quantum states are not mutually exclusive

Edwin Steiner — Mon, 21 Jul 2014 10:38:38 -0000

If I may, I recommend as an intermediate book "The Principles of Quantum Mechanics" by Dirac. It is by far the clearest QM book I have found so far - written by a true master. (I'm a bit shocked that someone gave this excellent book 1 star on amazon.de) Whether it will help you with the mentioned theory is another question altogether.

Re: The Reference Frame: Non-orthogonal quantum states are not mutually exclusive

Edwin Steiner — Tue, 22 Jul 2014 05:44:19 -0000

Which part you call the "box" is not important. The point is that the friend is part of the state that Wigner prepares for the experiment (by doing some initial measurements). This is very clear to me from Luboš' article:
"In that experiment, Eugene Wigner confines a killing machine containing a
hammer, Schrödinger's cat, and his friend to an isolated box." (my emphasis)
and
"Eugene Wigner is the master of the whole box so he may be sure that the whole system is prepared in a specific state."

Re: The Reference Frame: Non-orthogonal quantum states are not mutually exclusive

Edwin Steiner — Tue, 22 Jul 2014 05:50:38 -0000

I don't know what you mean. Neither in the article nor in my post I see any point where a significant difference is made between humans and machines in a way that would affect the argument.

Re: The Reference Frame: Non-orthogonal quantum states are not mutually exclusive

Edwin Steiner — Tue, 22 Jul 2014 05:56:23 -0000

Re: "There is a world of fun and **sex** out there"
Dang, I think I hit the wrong spot in the landscape! Must be a false vacuum around here or something. ;)

Re: The Reference Frame: Non-orthogonal quantum states are not mutually exclusive

Edwin Steiner — Tue, 22 Jul 2014 06:06:27 -0000

Yes, there are nice anecdotes about Dirac. There is a long interview with him online, which among other things gives some glimpses of the childhood that shaped the personality of this strange and great man. I found it almost heart-breaking in places: http://www.aip.org/history/...

Re: The Reference Frame: Non-orthogonal quantum states are not mutually exclusive

Edwin Steiner — Tue, 22 Jul 2014 13:10:56 -0000

Dear Luboš,

Thank you for this excellent article! I think it has improved my understanding of QM. To check: Textbooks always say that the state of a system can be represented by a unit vector |a> and that any normalized multiple of |a> will give the same predictions with 100%, so they are physically the same. What they could (and should) add is that generally any unit vector |b> will give the same predictions as |a> with |<a|b>|^2 probability, so |a> and |b> are physically the same to |<a|b>|^2 - a relation which cannot be expressed well in human languages. ("Probability" IMHO still gives the wrong mental picture that it is secretly either the same or not the same).

This also beautifully explains the under-determination of an ensemble of state vectors by the density matrix, which turns out to be a necessity. It also means that the change proposed by Weinberg in http://arxiv.org/abs/1405.3483 is actually a non-change. There is no physical distinction between ensembles of state vectors and density matrices in the first place, correct?

Re: The Reference Frame: Non-orthogonal quantum states are not mutually exclusive

Edwin Steiner — Tue, 22 Jul 2014 14:23:04 -0000

I am always impressed by the sheer amount of luck that you find in the biographies of very successful people. By no means I want to diminish their achievements, but luck is always an additional factor. Fortes fortuna adiuvat. (Not showing off ;} - I googled that looking for a similar German saying.)

Re: The Reference Frame: Do stringy electrons spin faster than light?

Edwin Steiner — Sat, 02 Aug 2014 08:56:38 -0000

See also this nice article by Terry Tao on this kind of "impossible" sums: http://terrytao.wordpress.c...

Re: The Reference Frame: Climate disagreements: do PR firms matter?

Edwin Steiner — Wed, 06 Aug 2014 05:13:07 -0000

To promote the likes of a psychopathic mass murderer who killed dozens of helpless children as something "healthy" is utterly disgusting, to say the least.

Re: The Reference Frame: An overlooked paper discovering axions gets published

Edwin Steiner — Fri, 17 Oct 2014 15:09:58 -0000

I guess it would, but I think the contribution from the solar field should be at least very roughly axially symmetric and thus not detectable as a seasonal signal, shouldn't it?

One point that worries me in the paper: The measured north/south ratio seems to match the predicted values very badly, if I'm not totally confused. The prediction (Fig 6) has the highest ratio around April, while the measured ratio has its minimum at this time (~A2 in Fig 19). The presentation is quite confusing, however, as they use different ranges and labelling for the time axis for model prediction and data.

Re: The Reference Frame: The very meaning of "probability" violates the time-reversal symmetry

Edwin Steiner — Fri, 17 Oct 2014 17:59:03 -0000

I just found a recording of a QM lecture by Sidney Coleman that may be interesting for other readers, too: http://media.physics.harvar...

The title is "Quantum Mechanics in your Face". :) I have watched half of it now, and it's very nice. Coleman's statements about QM are practically word for word identical to Luboš' statements in recent QM articles. For example that classical mechanics should be interpreted in terms of QM, and not the other way round, or that people get confused about what they call the "nonlocality" of QM because they secretly still think classically.

BTW: The great Coleman lectures on QFT are also online: https://www.physics.harvard...

Re: The Reference Frame: Naturalness is fuzzy, subjective, model-dependent, and uncertain, too

Edwin Steiner — Fri, 11 Sep 2015 14:39:48 -0000

You might want to reread the first few paragraphs of the article above. They explain very clearly why it is logical to worry about naturalness exactly when you consider the Standard Model as an effective theory.

Re: The Reference Frame: Harvard faculty obliged to call selected students "ze, e, they"

Edwin Steiner — Sun, 20 Sep 2015 09:30:00 -0000

Actually it should be "..., Sie haben recht". The German pronoun in the "Höflichkeitsform" is written in upper case (also its declinations like "Ihr", "Ihnen", etc.). In all other aspects, including pronunciation and grammatical use, it is exactly the same as the lower case "sie" (= they).

Re: The Reference Frame: No-transmission principle, antiholographic LQG

Edwin Steiner — Mon, 28 Sep 2015 03:49:26 -0000

Regarding "two lines that happen to contradict" - Did you mean "intersect"?

Re: The Reference Frame: Anti-diesel hysteria emulates witch hunts in Salem, MA

Edwin Steiner — Fri, 02 Oct 2015 04:18:25 -0000

Dear Luboš,

I agree with practically all assertions you make about the VW issue. There is just one point that bothers me: As you I'm convinced that all modern engines continuously optimize different parameters depending on the "driving" situation, etc. So it is no surprise when cars exhibit non-optimal emissions in many real-world situations. However, this is surely common knowledge also in VW, and there has to be something qualitatively different in their case which in the end forced them to officially admit to manipulations, etc. I could imagine that there is some text in the laws which explicitly bans detection of the test cycles and that either insider information or the structure of the VW code gives away that they specifically checked for that, or so. So far I am missing a discussion of this point in the media. You are the first commenter I saw to question these aspects at all, actually.

Re: The Reference Frame: No-transmission principle, antiholographic LQG

Edwin Steiner — Fri, 02 Oct 2015 05:09:01 -0000

BTW, I wondered if this was a case of some Czech semantics peeking through. In German we literally say that the lines "cut each other", so that would be closer to "intersect", but I can imagine that other languages use different, perhaps more civilized, metaphors ;)

Regarding your point "the right Hilbert space shouldn't actually contain separate basis vectors for [...]", there is one thing I'm a bit confused about: e.g. in gauge theories two states differing by a gauge transformations are physically the same, but if I understand correctly they are often represented by vectors |a> and |a> + |d>, where |d> != 0 is orthogonal to any vector in the "Hilbert" space, i.e. |d> is invisible for the "inner product" (which of course makes the quotes necessary in a mathematically pedantic sense). Does your statement mean that in the right Hilbert space "8" and "oo" would actually be the same vector |a>, or would equivalence with respect to the inner product be enough? Or would you disregard the zero norm vectors when speaking about basis vectors? Or am I totally confused? :)

Re: The Reference Frame: Quantum field theory obeys all postulates of quantum mechanics

Edwin Steiner — Wed, 21 Oct 2015 05:10:43 -0000

The problem is that so many popular accounts sell superpositions as something "strange" or extra. I think every popular introduction to superpositions should immediately add that, for example, the most "natural" states of electrons in the atoms we are made out of and that we touch every day are very complex superpositions of eigenstates of position (or momentum). So if a reader considers the "position of an electron" to be a natural notion, *e must at the same time accept superpositions as completely natural in order to get anything resembling a real atom. The explanation should also add that - vice versa - the position eigenstates are complex superpositions of the energy eigenstates, to emphasize the symmetry of this relation. It might also help to point out that giving coordinates on the surface of the Earth in terms of longitude and latitude does not limit our directions of motion to strictly North/South or East/West ;)

Re: The Reference Frame: New painful hype on "spooky nonlocalities"

Edwin Steiner — Thu, 22 Oct 2015 11:50:16 -0000

I sometimes think that people who study physics (in the traditional pseudo-chronological order) might have a harder time accepting quantum mechanics than someone from the "general public". Because if you study physics you typically go through an intense phase of reasoning about and quantifying the world classically, first. Classical physics works extremely well - up to a point -, much better than non-scientifically minded people realize, I think. So you fall in love with this kind of objective classical reasoning and it is not easy to let go. On the other hand, "generic" people have little trouble to accept that statements about the world are subjective and that one can only predict probabilities, etc. However, their acceptance of the "fuzziness" is superficial. I think the truly miraculous thing about quantum mechanics is that it is in fact crystal clear and very precise. And it tells us in a quantitative way that e.g. of two observables A and B either can have a well-defined value, but not both at the same time. This complementarity and that "complete knowledge" does not imply "complete predictability" is the main shocking and wonderful realization in quantum mechanics. How cool is it to find out something like that about the world? For me this is the number one achievement of the human mind ever, so far.

Re: The Reference Frame: Physics problems cannot be undecidable

Edwin Steiner — Thu, 10 Dec 2015 05:43:30 -0000

Dear Luboš, thank you for this interesting discussion! It reminds me of a point I have often wondered about: One often hears statements that phenomena like dimensional transmutation can only occur due to divergences in QFTs which in turn are linked to the infinite number of degrees of freedom. I found this somehow unsatisfying because I felt that for something that has measurable consequences like the proton mass, it should not make a difference if there is truly an infinity of DOFs or just a number that is much larger than the number of DOFs that are practically observable. The same goes for the Ising model, for example: A finite Ising model cannot have phase transitions in the strict sense, because its partition function is holomorphic. However, for a very large lattice, the behavior should be indistinguishable from a true phase transition within the accuracy of "measurement", right? (The Wikipedia entry on "Ising model" seems to confirm that: "The convergence to the thermodynamic limit is fast, so that the phase behavior is apparent already on a relatively small lattice, even though the singularities are smoothed out by the system's finite size.") I would expect that e.g. a lattice QCD then shows the appearance of the QCD scale in an approximate sense also on a large but finite lattice with a small but finite spacing. Does this make sense?

Re: The Reference Frame: Physics problems cannot be undecidable

Edwin Steiner — Thu, 10 Dec 2015 06:09:25 -0000

Thanks, a spectacularly clear answer!