Puzzling quantum scenario appears not to conserve energy
quantamagazine.org
quantamagazine.org
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.
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.
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.
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.
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.
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.
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.”
This quote seems more compelling in cases where the statistics are known, but and we just need to have enough samples, such that the expected values, etc, show themselves.
It's the very example that he was discussing, which he had described just before: "Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A."
Another interesting quote of his: "Available energy is energy which we can direct into any desired channel. Dissipated energy is energy we cannot lay hold of and direct at pleasure, such as the energy of the confused agitation of molecules which we call heat. Now, confusion, like the correlative term order, is not a property of material things in themselves, but only in relation to the mind which perceives them. A memorandum-book does not, provided it is neatly written, appear confused to an illiterate person, or to the owner who understands thoroughly, but to any other person able to read it appears to be inextricably confused. Similarly the notion of dissipated energy could not occur to a being who could not turn any of the energies of nature to his own account, or to one who could trace the motion of every molecule and seize it at the right moment. It is only to a being in the intermediate stage, who can lay hold of some forms of energy while others elude his grasp, that energy appears to be passing inevitably from the available to the dissipated state."
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?
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.
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/wiki/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.
That's just my gut though, I'm not a professional physicist.
But while we are on the topic I'm curious if the physics you describe make it possible to build a perpetuum mobile.
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.
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.
“Physicists discover limits of simplifying assumptions, pretend to be surprised ignoring things leads to inaccurate results in extreme circumstances.”
[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."
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.
But it's also worth remembering that some of the smartest people in our society are optimizing ad serving.
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]