[HN Gopher] Puzzling quantum scenario appears not to conserve en...
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Puzzling quantum scenario appears not to conserve energy
Author : theafh
Score : 69 points
Date : 2022-05-16 13:47 UTC (9 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| [deleted]
| ajuc wrote:
| Isn't this like the Maxwell's demon? Deciding what to do on micro
| level can create macro level changes that break physics, but it's
| not actually possible, so there's no paradox.
| bee_rider wrote:
| There's nothing really "not actually possible" about Maxwell's
| Demon. It is maybe impractical from an engineering point of
| view to create the demon, but this doesn't resolve the problem,
| which is based in the more fundamental physics. I think a more
| accurate description of the resolution is that this "deciding
| what to do on the micro level" must itself have an energy cost
| -- making it a great example of the link between information
| and thermodynamic entropy.
| shaded-enmity wrote:
| How do you build a mechanism that has a perfect knowledge
| about a system while being part of said system?
| bee_rider wrote:
| I'm not sure I see the link here (although it is definitely
| possible that I'm jsut missing something, I'm no
| physicist). I don't think Maxwell's demon needs perfect
| knowledge of the whole system -- it is just locally
| deciding to let through "fast" molecules and block "slow"
| ones.
| shaded-enmity wrote:
| I'm no physicist either, I just like to ask questions :)
|
| How does the demon attain the knowledge of what is "fast"
| and "slow" without continuous observation (and thus
| interaction) with the particles. Velocity is just
| function of position over time, so the demon needs at
| least 2 samples to make the most basic approximation.
| Where is the entropy for doing that coming from? How does
| the interference of the measuring apparatus factor into
| the whole process - what if the sole act of measurement
| changes the state of the particle from "fast" to "slow"
| or vice versa? Do we need to measure twice? But what if
| the second measurement causes the transition it was meant
| to detect?
| ajuc wrote:
| Yes, that's what I meant. This is similar - because you have
| to put a mirror at "just the right time" and you ignore the
| energetic cost of that.
| MockObject wrote:
| What if we have a mirror moving randomly around the box?
| That would lead to the same effect, whereas a randomized
| Maxwell's Demon would not.
| ajuc wrote:
| I'm not sure. Wouldn't the introduced waves cancel out
| then?
| MockObject wrote:
| Only if it lead to abnormally cool photons as much as
| anomalously hot ones.
| lamontcg wrote:
| Yeah these though experiments all seem to depend on some kind
| of very tiny perfect subatomic process which has no energy
| input. Flip it around and the violation of conservation of
| energy should place a minimum requirement on the energy
| required to run a real Maxwell's Demon, or the mirror in this
| experiment (and real mirrors aren't infinitely thin
| mathematical abstractions).
| bee_rider wrote:
| I think this is exactly the point.
|
| A good way to ask "what does our model mean, exactly" is to
| imagine the perfect processes with no unnecessary energy
| losses. Real mirrors might not be infinitely thin
| mathematical abstractions, but if there isn't an actual,
| physically defined fundamental limit to how thin a mirror
| can be, then it would be weird if we could violate
| fundamental laws of the universe, but for want of such a
| mirror.
|
| Maxwell's Demon is neat because we can whittle things down
| and eventually get to needing to account for the physical
| cost of the bits in the thing's 'brain.' An interesting
| example of the fact that information is actually a physical
| quantity.
| [deleted]
| davesque wrote:
| Yes, computation "costs" energy and increases entropy. The
| demon must compute its decisions before it can carry them
| out.
| kgwgk wrote:
| If there is nothing "not actually possible" what's the
| problem that needs to be solved?
| unholiness wrote:
| At the time it was proposed, it was thought that a thermal
| reservoir on its own could never do useful work. This is
| always what's observed in practice and laws of heat were
| based around it e.g. U = Q - W.
|
| In order to derive those heat equations from the second
| law, we now know it requires an assumption: that you (or
| any entropy-containing component not modeled in the system)
| cannot have specific knowledge of the microstate of the
| system, only its macroscopic properties. For a long time it
| seemed absurd that such an assumption would necessary at
| all, for these seemingly universal laws, and there was no
| clear way to thermodynamically model the knowledge of the
| actor _inside_ this system such that you wouldn 't need
| such an assumption.
| kgwgk wrote:
| > For a long time it seemed absurd that such an
| assumption would necessary at all, for these seemingly
| universal laws,
|
| Not so long. The second law dates from 1850 and the
| requirement of such an assumption is what Maxwell's demon
| illustrated less than forty years later.
|
| > and there was no clear way to thermodynamically model
| the knowledge of the actor inside this system such that
| you wouldn't need such an assumption.
|
| There is still no way to model an actor inside a
| thermodynamical system in equilibrium - by definition.
| bee_rider wrote:
| There isn't a problem.
|
| The initially apparent problem is that the demon appears to
| be generating a temperature gradient "for free" by just
| swinging a gate open (for fast molecules) or closed (for
| slow ones) (because there's no fundamental physical cost
| for gate-swinging).
|
| It is resolved by taking into account the fact that the
| demon must use _at least_ a bit of memory, while acquiring
| the 'status' of the molecule (let through or don't). So,
| we can at least say that the demon, no matter how slow and
| lazy (efficient) it wants to be, must pay the information-
| theory based cost of erasing that bit.
| kgwgk wrote:
| > There isn't a problem.
|
| I agree.
|
| > The initially apparent problem is [...]
|
| Why would that be a problem? If it's because the second
| law of thermodynamics says that it cannot happen
| spontaneously in a thermodynamical system in equilibrium
| why would that be applicable when we're not considering
| just a system in thermodynamical equilibrium?
|
| As Maxwell wrote: "This is only one of the instances in
| which conclusions which we have drawn from our experience
| of bodies consisting of an immense number of molecules
| may be found not to be applicable to the more delicate
| observations and experiments which we may suppose made by
| one who can perceive and handle the individual molecules
| which we deal with only in large masses."
| jp57 wrote:
| Is it merely impractical though? In the thought experiement
| the demon needs to be able to know the state of the impending
| particle before it arrives, so it can decide whether to open
| the door. It can't do that without interacting with them and
| changing their state.
| bee_rider wrote:
| I think it depends on how you define the demon. I first
| heard of it in the final, resolved version, so I see it as
| just impractical (because the solution is baked in).
|
| The interaction between the demon and the particles is the
| key. The final version, at least as far as I'm concerned,
| comes from Landauer and Bennett [https://en.wikipedia.org/w
| iki/Maxwell%27s_demon#Criticism_an...] -- the demon must
| accumulate information (which it can only do finitely) or
| erase it. Erasing information has a real physical cost,
| resolving the issue.
|
| When the demon was first invented, information theory
| hadn't been developed yet. So the mystery to Maxwell was
| that it looked like it was violating energy conservation,
| but that's just because there's a sneaky place we can store
| entropy temporarily or finitely.
|
| So, I think I was imprecise (or... wrong). A demon that
| does what we really want (generates free energy) is
| impossible. But it is impossible for weird reasons that
| Maxwell wouldn't have been aware of, and I don't think he
| explicitly explored them.
| throwawaymaths wrote:
| This was my first gut instinct, except even simpler than
| Maxwell's demon: by partitioning the apparatus with the mirror,
| you're altering the statistical ensemble of possible wave
| states (increasing the relative information entropy) and that's
| where your energy comes from.
|
| That's just my gut though, I'm not a professional physicist.
| potiuper wrote:
| Non-inertial reference frames do not abide by the special
| principle of relativity or global Lorentz covariance. From the
| article: "energy isn't conserved in situations where gravity
| warps the fabric of space-time, since this warping changes the
| physics in different places and times, nor is it conserved on
| cosmological scales, where the expansion of space introduces
| time-dependence". The principle of covariance (see General
| covariance) in GR implies "local" Lorentz covariance such that
| the Lie group GL4(R) is a fundamental "external" symmetry of the
| world. But, the fluctuation theorem has no such requirement and
| does not imply or require that the distribution of time averaged
| dissipation be Gaussian. FT (together with the universal
| causation proposition) gives a generalization of the second law
| of thermodynamics which includes as a special case, the
| conventional second law. When combined with the central limit
| theorem, the FT also implies the Green-Kubo relations for linear
| transport coefficients, close to equilibrium. Given general
| covariance along with the differentiable notion of time and space
| geometry requires linear transport, then its validity would be
| dependent on the applicability central limit theorem. In
| addition, the Gallavotti-Cohen fluctuation relation is limited to
| chaotic dynamical systems with microscopic reversibility when the
| fluctuations of a suitably defined function of the phase space
| trajectories, taken as a measure of violation of the detailed
| balance, i.e. of entropy production, are measured.
| im3w1l wrote:
| That doesn't seem to be what's going on in this thought
| experiment, as it's not using GR.
|
| But while we are on the topic I'm curious if the physics you
| describe make it possible to build a perpetuum mobile.
| potiuper wrote:
| GC used in GR implies conservation of energy due to the GL4
| symmetry with respect to the time dimension in its
| differentiable geometry along with Noether's theorem. A
| breakage of GR on the cosmic scale might be with the super
| oscillatory phenomenon appearing around an isolated and
| fairly inactive dark star ("black hole") when a star passes
| in line behind it and the corresponding frequency bump in the
| spectrum as light is "mirrored" or trapped around the dark
| star is observed. Systems that do not adhere to the
| requirements of the FT could show perpetual motion while the
| causality proposition seems less likely to find violations,
| although a duality is "rough"ly around those two.
| mikewarot wrote:
| So this experiment seems to create a virtual atom (the box with
| the mirrors), yet unlike a real atom, this system isn't quantized
| internally, so it's possible that you could get quanta of any
| energy up to the sum of all photons inside the box.
|
| Alternatively, it could be that the language used by physicists
| has overloaded too many conventional words, and the impedance
| mismatch between them and the public can not be overcome.
| peteradio wrote:
| Energy conservation seems to be a sleuthing tool for our pitiful
| existence to find some god damn consistency. If quantum mechanics
| is fundamentally formulated around statistics then energy
| conservation shouldn't surprise us to become statistical either.
| snarfy wrote:
| I was under the impression there is no such thing as an isolated
| wave function. They are all part of a larger wave function. If
| the isolated wave function is missing energy, it's in the larger
| wave function.
| HelloNurse wrote:
| Neither do sinusoidal oscillations exist, since they would have
| to be eternal.
| [deleted]
| Strilanc wrote:
| > _Quickly put a mirror in the photon's path right where the wave
| function superoscillates, keeping the mirror there for a short
| time._
|
| Varying things quickly in space or in time requires a lot of
| energy. The energy could be coming from moving the mirror too
| quickly. For example, if you modeled the mirror's movement as
| being driven by a force then you might find the mirror's motion
| is damped by reflecting the photon; losing energy.
|
| Instantaneously switching the driving Hamiltonian can easily
| spread energy around, unless they commute. The Hamiltonians for
| "no mirror" (H1) and "yes mirror" (H2) won't commute. It sounds
| like they've arranged for the eigenstates of H1 to overlap with a
| huge range of eigenvalues of H2, and vice versa. So when you
| switch from H1 to H2 you end up in a superposition of all kinds
| of different energies. Evolve there for a bit so switching back
| won't destructively interfere you back down to exactly where you
| started, and voila.
|
| I think if they account for these kinds of "changing the
| Hamiltonian ain't free" effects, they'll find where the energy
| came from.
| [deleted]
| rssoconnor wrote:
| I'm just an armchair physicist, but I thought we had already
| established that in quantum mechanics conservation laws only hold
| on average and not on a per run basis.
|
| In https://news.ycombinator.com/item?id=24762436,
| @HackOfAllTrades notes that angular momentum is not preserved on
| a per run basis.
|
| In a Mermin Device a pair of entangled spin particles is set to
| two Stern-Gerlach experiments. The two particles has net (spin)
| angular momentum of 0 because that's was the net angular momentum
| of starting material. But if you measure the angular momentum of
| the two particles in two non-parallel directions, and if we also
| require that the only answers you are allowed to get are +hbar/2
| or -hbar/2, then the sum of the angular momentum you get by
| adding +/-hbar/2 times one direction plus +/-hbar/2 times a
| different direction can never be 0.
| tooltower wrote:
| But couldn't the missing angular momentum still be imparted
| onto the measurement device? I.e. maybe our Stern-Gerlach
| apparatus will start spinning ever so slightly if they were
| floating in space?
| kgwgk wrote:
| What does starting with an entangled pair add to that argument?
|
| You could say simply that if you have prepared a (half) spin
| state |z+> the angular momentum along the x axis is zero but if
| you measure the spin along the x axis you will find a non-zero
| value.
| prof-dr-ir wrote:
| This is not correct. The _expectation value_ of the angular
| momentum along the x-axis might be zero, but the state itself
| simply does not have a definite angular momentum.
|
| I like your example because it clearly shows the subtlety
| that the original comment by rssoconnor also misses. Energy,
| momentum, and angular momentum absolutely _are_ conserved
| quantities. But if you prepare your initial state such that
| it does not have a definite value of these quantities then
| you cannot with certainty predict the measured value, either.
| kgwgk wrote:
| Good point. Anyway, the original example reduces to this.
| After the first measurement [it doesn't really matter which
| one is considered as first] we have a couple of
| complementary states +/- for the measured axis but it's not
| well defined for other directions and in general a second
| measurement will break the symmetry.
| 8bitsrule wrote:
| Sometimes when people 'shut up and calculate' [0] they find
| surprises.
|
| [0][https://aeon.co/essays/shut-up-and-calculate-does-a-
| disservi...] (Baggott, 2021): (Revisited this earlier today,
| coincidentally)
|
| "a dogma of indifference to philosophical questions was at least
| as much to blame for the rejection of foundational enquiry as
| anything Bohr might have said."
| RappingBoomer wrote:
| science is great...love it....got a degree in it...but i never
| pretend that we are anything but children when it comes to
| understanding the universe...we got a loooooonnnnnggg way to
| go...
| bowsamic wrote:
| I have a PhD in theoretical quantum optics, currently doing
| postdoc and moving to experimental stuff, and I have to agree.
| We don't know how quantum mechanics works at a basic level,
| what is a measurement? Are wave functions real? Are we just
| ignorant or are things really inherently probabilistic? These
| (and others) are huge questions underpinning our basic reality,
| but we have only made very modest progress on them, if any.
| It's not clear that we will ever know, there's certainly not a
| clear path forward
| spaetzleesser wrote:
| A guy like Einstein or Newton comes along every few hundred
| years. I can't even imagine what we will find out if we keep
| doing science for a few thousand years more.
| PartiallyTyped wrote:
| Plenty of people have come. Godel was one, JVN was one,
| Terry Tao is likely one.
|
| But it's also worth remembering that some of the smartest
| people in our society are optimizing ad serving.
| bowsamic wrote:
| Physics and maths are both so specialised and large now
| that it's not really possible to have such great minds
| now. Einstein had a good grasp on almost all physics of
| his time, Newton did for literally all of it for his
| time. It isn't possible for any modern physicist to have
| a full grasp of even a single sub field
| 8bitsrule wrote:
| >Newton did for literally all of it for his time.
|
| Even Newton wasn't wary enough of prejudices that slowed
| useful insights. As a result: "Until the early 19th
| century, most scientists shared Isaac Newton's view that
| no small objects could exist in the interplanetary space
| - an assumption leaving no room for stones falling from
| the sky."
| [http://www.meteorite.fr/en/basics/meteoritics.htm]
| bowsamic wrote:
| I think there is a limit, and that progress is not linear
| spaetzleesser wrote:
| I don't think there is a reason to think that we are
| close to any limit. I agree that progress is not linear.
| tshaddox wrote:
| What would the limit look like? Like would we just
| suddenly discover some wall in physics that makes it
| impossible to pursue further inquiry?
| bowsamic wrote:
| Yeah, some noise wall that we can't surpass by our
| technology, not being able to measure to small enough
| precisions or with enough energy, etc.
| outworlder wrote:
| We would keep trying to chip at the wall regardless.
| spaetzleesser wrote:
| We may hit a wall in one area and make progress in others
| which then feeds back into the first area. I think it was
| always that way.
| bee_rider wrote:
| This seems confusing to me (although I am just an engineer so it
| isn't surprising if I've missed something). The photon is
| basically a packet energy. It bounces out of the box, I guess
| reducing the energy in the box (right?), which is just normal
| photons-bouncing-out-of-box behavior.
|
| In this case, they've managed to come up with a configuration,
| via superoscillation, that results in an unusually large packet
| of energy. But is this a conservation of energy issue? I don't
| see how this is any "worse" for conservation of energy than
| bouncing out multiple red photons.
|
| Is the inability of a red box to release higher energy photons
| actually a deep physical principle, or just a general trend
| because configurations that can generate superocillations are
| rare? I guess I don't see the link between "photon is too big"
| and "conservation of energy" -- probably it is an obvious link
| for the physicists here, though.
| ziddoap wrote:
| They have a photon with energy=x, and are detecting a photon
| with energy=x+y. The question is where the y comes from. Since
| they've ruled out the usual suspects, it _seems_ to be a
| violation of conservation of energy.
| zmgsabst wrote:
| My experience of this is generally:
|
| "Physicists discover limits of simplifying assumptions, pretend
| to be surprised ignoring things leads to inaccurate results in
| extreme circumstances."
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