10 Essentials of Quantum MechanicsI won't marking her because that's non what Gentlemen practise to Ladies but if I were grading her, she would acquire a B today – a much improve marking than the D of Mark Alford too Steve Hsu who believe that the EPR correlations are due to some form of nonlocality – or at to the lowest degree that it's (pedagogically etc.) useful to invent novel awkward phrases whose destination is to maintain this telephone commutation misconception alive.
But let's furnish to the text at Backreaction (and Starts With a Bang). Let me verbalise over those 10 assertions i past times i (Alford's too Hsu's error is addressed inward the item #4).
1. Everything is quantum.
Evaluation: Exactly.
This is a seemingly trivial betoken for a practicing physicist but an of import i inward these discussions too I scream upwards it's in all likelihood right that it appeared at the real top. The betoken is that you lot can't sympathise quantum mechanics every bit some "extreme rules" that solely grip inward some limited situations piece most of the globe follows "different laws". In principle, the whole Universe follows the quantum mechanical laws. However, "large enough" or "macroscopic" or otherwise special systems also approximately concur alongside laws of some other type, classical physics, because classical physics too quantum mechanics move indistinguishable. That's why it was difficult to notice the quantum effects too the people waited upwards to 1925. But quantum mechanics was born too it applies everywhere.
2. Quantization doesn’t necessarily imply discreteness
Evaluation: Exactly.
Linguistically, the price "quantum theory" (1900) too "quantum mechanics" (1925) were chosen because some quantities that were continuous inward classical physics – well, peculiarly liberate energy but also the angular momentum etc. – turned out to live discrete. Electromagnetic waves came inward quanta (later named photons) too those quanta were also emitted or absorbed when the atoms were jumping from i liberate energy aeroplane to another. Using the quantum mechanical jargon, some observables may or must receive got a discrete spectrum inward quantum mechanics. \(E=N\hbar \omega\) for a grouping of photons of frequency \(\omega\). \(E=-E_0/n^2\) for the bound state of the hydrogen atom, too thence on. This discreteness was a novel aspect which is why it could receive got given the scream to "quantum mechanics".
But other quantities may withal receive got a continuous spectrum – or a mixed spectrum alongside a continuous and discrete portion (the hydrogen atom's liberate energy is continuous – all positive eigenvalues are OK – for the situations when the atom is ionized). Even for continuous spectra (e.g. those of \(x\) too \(p\) inward infinite space), quantum mechanics plant too has implications which are by too large new.
It's first-class that Hossenfelder at nowadays acknowledges that for the same reason, the chore of understanding "quantum gravity" doesn't hateful that observables receive got to receive got discrete spectra. Kashyap asked Hossenfelder:
Then, what is the motivation for trying to discretize space-time? Does it assist inward whatever other situation?Sorry but the solely motivation to discretize spacetime is the stupidity of the people who practise so. Some physically unrealistic models of quantum gravity may display discretized geometry (noncommutative geometry is basically equivalent to the infinite divided to cells every bit a stage space; quantum foam has quantized areas, too thence on) but the 3+1 spacetime dimensions nosotros know receive got to acknowledge a telephone commutation description that makes them continuous, otherwise the Lorentz invariance would live broken. In the next comment, Hossenfelder replied to Kashyap:
Yes, exactly. Discretization is a skilful way to tame infinities. As long every bit you lot amount upwards a finite amount of finite things, you lot volition acquire a finite answer.Sorry but this is naive bullšit (which I generously won't consider to the grading of Hossenfelder's "main point"). Discretization of the spacetime doesn't assist i at all alongside the actual work manifesting itself every bit the infinities, namely alongside the non-renormalizability. It's just a "cutoff" but all the infinities just redress themselves every bit the cutoff-dependence of all the terms, too it's the infinite collection of unknown values of these constants that is the actual problem. See e.g. the 2005 newspaper past times Nicolai, Peeters, too Zamaklar (which is past times the way i of the most cited papers nigh loop quantum gravity).
3. Entanglement non the same every bit superposition
Evaluation: ambiguous, betoken is foggy.
There are item claims she wrote that are just wrong, e.g. the disceptation that "superpositions are non fundamental". I am lamentable but the beingness or reality or admissability of superposition states is absolutely telephone commutation inward quantum mechanics – it's the universal "superposition postulate" that says that for whatever allowed states \(\ket\psi\) too \(\ket\chi\), the states \(a\ket\psi + b\ket\chi\) are also allowed for \(a,b\in \CC\). In other words, the telephone commutation infinite of pure states is a linear complex Hilbert space. This for certain is telephone commutation inward quantum mechanics, right? And a key axiom of linear spaces is that alongside all pairs of vectors, they also comprise the amount – the superposition. So this axiom is undoubtedly telephone commutation inward quantum mechanics.
The linear grapheme of the infinite of states – too of the operators – is a "simplifying rule" repeatedly emphasized e.g. inward Dirac's textbook – which guarantees that quantum mechanical theories are at to the lowest degree every bit constrained every bit their classical limits.
Entanglement is unambiguous, she writes. It's truthful inward some feel – if nosotros create upwards one's hear nigh a way to carve upwards the organisation into subsystems, a selection that the notion of entanglement depends upon. And she's right that entanglement may live viewed "just every bit a correlation". On the other hand, the claim inward the championship that "entanglement isn't superposition" is murky and, from some viewpoint, totally wrong. An entangled state is "also" exactly the same thing every bit a superposition of 2 or to a greater extent than tensor products that can't live written every bit a unmarried tensor production of states from the 2 subsystems. The entangled state is the same thing as\[
\ket\Psi = \sum_i c_i \ket{\alpha_i} \otimes \ket{\beta_i}
\] where the letters \(\alpha,\beta\) are reserved for the 2 subsystems, respectively, too the tensor production sign \(\otimes\) may live omitted. If it's needed to brand at to the lowest degree 2 of the coefficients \(c_i\) nonzero to write \(\ket\Psi\) inward this form, too then the subsystems \(\alpha,\beta\) are entangled. The "entangled grapheme of the state" is just the same thing every bit "the demand to usage a superposition to describe" the state. I am non sure whether she realizes that but her text seems to live "softly inward conflict" alongside this possible Definition of entanglement.
4. There is no spooky activeness at a distance
Evaluation: Exactly.
As Steve Hsu too his friend (not to advert Bill Nye too others) should move notice, the correlations seen inward the "entanglement" experiment are non due to whatever "action at a distance" that would receive got house at the minute of the measurement(s). It's a correlation implied past times the laws of quantum mechanics applied to the initial state that has already existed (=was the most precise way for an observer to depict his state of knowledge) from the minute when the 2 subsystems (e.g. 2 EPR photons from a positronium) were inward contact. If at that topographic point were an "action at a distance", it would live spooky, indeed, because it would actually conflict alongside Einstein's relativity, but no such activeness exists inward Nature and, if i embraces the framework of quantum mechanics, no such activeness at a distance is needed.
An activeness at a distance would live needed inward a classical model that would endeavour to mimic the predictions of quantum mechanics. But such a model would demand many other things too no such feasible classical model actually exists – too it's just fundamentally incorrect to assume that to sympathise physics, i should search for a classical model. The fact that a classical model would receive got to ship signals faster than low-cal actually way that all such models are basically inward conflict alongside special relativity which is a huge work for this shape given the flawless evidence inward favor of relativity.
5. It’s an active enquiry area
Evaluation: It depends.
There is for certain some interesting, serious, exciting contemporary enquiry that is closed to the "foundations of quantum mechanics", similar the recent "entanglement minirevolution inward quantum gravity" or some serious piece of work inward quantum computation. At the same moment, all the basic conceptual questions nigh the full general rules underlying quantum mechanics receive got been understood since the 1920s too aught whatever has changed nigh them.
6. Einstein didn’t deny it
Evaluation: Partially correct, partially wrong.
This betoken is i nigh the history too Hossenfelder's history is solely partially correct. The reality is that at the beginning, Einstein did deny quantum mechanics inward the strongest possible sense. It's referred to every bit the first stage of the post-revolution Einstein-Bohr debates. Einstein believed that the uncertainty regulation was sharply incorrect too demonstrably incorrect too he looked for experiments, gedanken too existent ones, that would demonstrate it. These proposals were shot downwards past times Bohr.
After a long sequence of failures, Einstein softened his rhetoric too started to enjoin that quantum mechanics described all these experiments correctly but it wasn't the deepest or most consummate possible theory to practise so. It was plenty for him to lose almost all contacts alongside the best active theoretical physics research. Because he was interested primarily inward the telephone commutation laws too he believed that the quantum laws weren't actually telephone commutation (although he made no progress inward constructing a hypothetical option theory that could also explicate the phenomena ordinarily explained past times quantum mechanics), he was but non interested inward the enquiry of these quantum laws.
Whether Einstein was a "denier" inward this after stage depends on "what he was supposed to deny". He didn't deny that quantum mechanics was basically right to depict all these experiments. But he did deny that it's the to a greater extent than accurate too telephone commutation framework for physics than the classical or "realist" framework. Given the fact that at to the lowest degree today, nosotros tin to a greater extent than or less rigorously demonstrate that this watch of Einstein was flawed, nosotros should in all likelihood enjoin that he was a denier of an of import aspect of the quantum mechanical framework underlying physics.
7. It’s all nigh uncertainty
Evaluation: Exactly.
The refusal of \(x,p\) or other pairs (almost all pairs) of observables to commute alongside each other, \(xp-px\neq 0\), is actually the source of all the differences betwixt the quantum mechanical framework too its classical predecessor. As Feynman clearly stated at the halt of the Chapter III/20 of his lectures, after he emphasized that the average values don't depict what's actually going on:
Quantum mechanics has the essential divergence that \(px\) is non equal to \(xp\). They differ past times a footling bit—by the small-scale break \(i\hbar\). But the whole wondrous complications of interference, waves, too all, outcome from the footling fact that \(xp-px\) is non quite zero.The nonzero commutators are actually the essence. The whole novelty too arts of quantum mechanics is nigh one's might to brand feel out of the formalism where observables turn down to commute. Once you lot know how to practise it, you lot may derive all the interference, discrete spectra, entanglement, tunneling, too other things. And, every bit Hossenfelder correctly says, the uncertainty regulation is telephone commutation – it's non something i could correctly dismiss every bit a technical flaw of the measuring apparatuses. It's an unavoidable truth independent of all the apparatuses. Just similar the special relativity says that 2 observers inward the state of relative motion usually can't concur on the simultaneity of 2 events (it's non just due to their sloppy measuring of time), quantum mechanics says that pairs of complementary observables can't receive got well-defined values at the same moment.
8. Quantum effects are non necessarily small...
Evaluation: Exactly.
In general, quantum mechanics makes predictions that are fundamentally dissimilar from the predictions of classical physics. For large systems, nosotros may similar to enjoin that they are "small" because \(\hbar\) is much smaller than the angular momentum of objects nosotros run into alongside our naked eyes or than the activeness calculated for the development of macroscopic systems about us. But the qualitative or conceptual divergence of quantum mechanics is ever there. And that's why they may live manifested at macroscopic distances. The entanglement for certain continues to be fifty-fifty at huge separations.
And the ex-dean of my Alma Mater Prof Sedlák loved Hossenfelder's example every bit an explanation why he did physics of depression temperatures: quantum effects manifest themselves at macroscopic pieces of materials. The other thing he told me instantly afterwards was that my classmate Ms M.Z. had overnice legs. But you lot gave her a C, I responded. But that wasn't for the legs, he defended the grade. ;-)
It's all nice, you lot may derive the moving ridge functions every bit "reinterpreting" the Cooper pairs' moving ridge component subdivision every bit a classical field. But there's also something you lot should live aware of: If you lot receive got many Cooper pairs inward the same state, inward a Bose-Einstein condensate, their "shared" moving ridge component subdivision really becomes something that is closed to a classical field. If you lot receive got many (\(N\)) of these bosons inward the same state, the prediction for "their per centum that receive got a sure property" becomes rather accurately predictable – the relative error goes downwards similar \(1/\sqrt{N}\) past times the basic rules of statistics. In the \(N\to \infty\) limit, all these numbers move basically deterministic classical degrees of liberty without uncertainties too may live derived from novel classical fields.
So it's also right to enjoin that a macroscopic slice of a superconductor is described past times some other classical patch theory – but it's a classical patch theory whose construction is real similar to the construction of moving ridge functions inward quantum mechanics too that may almost straight "derived" from these moving ridge functions. So the patch theory describing a slice of a superconductor is a different classical theory than i you lot could receive got started with. This is a "lab" or "mundane" example of the fact that a quantum mechanical theory may receive got many dissimilar classical limits.
9. ...but they dominate the small-scale scales
Evaluation: Exactly.
At curt plenty distances, the importance of quantum mechanical effects is basically unavoidable. The deeper into thing you lot endeavour to penetrate, the closer to the telephone commutation laws your involvement is focusing onto, the to a greater extent than essential it is for you lot to larn quantum mechanics too receive got it real seriously every bit the "fundamental form of a description".
10. Schrödinger’s truthful cat is dead. Or alive. But non both.
Evaluation: Exactly.
The moving ridge functions too their superpositions are oft presented every bit a "clearly bizarre" too actually "incompatible alongside our experience" prediction of quantum mechanics that when nosotros banking concern jibe whether a truthful cat is dead or live past times an observation, nosotros volition acquire some obscure mixture. We don't. When nosotros expect at a cat, it is almost ever either clearly dead or clearly alive. And quantum mechanics predicts just that. It doesn't predict whatever "foggy mixed too undetermined" results of the observations. If quantum mechanics were predicting something totally dissimilar than what nosotros observe, it would live a falsified theory too physicists would abandon it. But quantum mechanics predicts what's observed inward all experiments which is why physicists haven't abandoned it.
The moving ridge component subdivision \(0.6\ket{\rm alive}+0.8i\ket{\rm dead}\) describes a "dead too alive" superposition too you lot should notice that the price are connected past times the operator "plus". It way that the seem is a amount too the formalism of quantum mechanics says that it's interpreted analogously every bit the logical sum. And, brand no error nigh it, the logical amount refers to the operator "OR". So the truthful cat is either live "OR" dead, alongside the given probability amplitudes. If you lot needed the dead too live truthful cat to be at the same time, you lot would receive got to usage the logical operator "AND" which is also called the logical product. Note that the probability of 2 independent events "A AND B" is \(P(AB)=P(A)P(B)\), also a product. In price of the moving ridge functions, you lot would demand some production of moving ridge functions, namely the tensor product. So the state\[
\ket{\rm dead} \otimes \ket{\rm alive}
\] describes a state of 2 cats (a non-entangled state because i tensor production is plenty too at that topographic point are no superpositions). One of these cats is dead too the other i is alive. That's the state inward which the dead too live cat(s) be simultaneously. But inward the superposition states, they just don't because the improver of moving ridge functions way "OR", non "AND", because the improver of moving ridge functions is sort of similar to the "addition of the foursquare roots of probabilities", too the improver of probabilities clearly refers to "OR", too.
(Whenever the mixed bilinear price inward the probability amplitudes – those responsible for the quantum interference – drib out, the additive handling of the probability amplitudes becomes equivalent to the additive handling of the probabilities. Again, the improver of probabilities or amplitudes way "OR", non "AND". Also, I must emphasize that my usage of the words "OR" too "AND" doesn't hateful that you lot should restore your belief inward classical physics. It's withal truthful that the properties of objects can't live described past times "sharply true" or "sharply false" statements earlier you lot brand the relevant measurement. When I enjoin that "the superposition refers to OR", it way that the moving ridge component subdivision is aught else than the most consummate bundle of data usable to predict the next observations, too the predictions resulting from the superposition enjoin that either i OR some other outcome takes house – where "one" too "another" would refer to the interpretation of the 2 private price inward the superposition.)
When the observable is observed, e.g. when you lot expect whether the truthful cat is live or dead, you lot unavoidably alter the state of the physical organisation (the cat). The moving ridge component subdivision collapses into an eigenstate of the observable you lot receive got just measured. This collapse isn't a alter that should live explained past times some additional "mechanism". It straight follows from the quantum mechanical postulate that \(c_i\) are the probability amplitudes too \(|c_i|^2\) are probabilities. Whenever an observer learns novel information, his subjective probabilities abruptly change. In classical physics, the formula dictating this alter is the Bayes formula. We don't inquire what's "inside" this formula because it clearly follows from basic logic too probability calculus. The collapse of the moving ridge component subdivision is just analogous to Bayes' formula but it's written using the objects allowed inward quantum mechanics too inward understanding alongside the novel features of quantum mechanics that may live ultimately derived from the nonzero commutators, every bit nosotros said (and the implications include all the interference too other effects).
Verdict
Hossenfelder got seven "totally correct" ratings, iii "ambiguous" ones, too no "completely wrong" ones. This is improve than what 90% of the people calling themselves "researchers inward the quantum foundations" could ever achieve. ;-)