Puzzling quantum scenario appears not to conserve energy

https://www.quantamagazine.org/puzzling-quantum-scenario-appears-not-to-conserve-energy-20220516/

by theafh • 4 years ago

76 60 4 years ago

rssoconnor• 4 years ago

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• 4 years ago

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?

kgwgk6• 4 years ago

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• 4 years ago

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.

ajuc3• 4 years ago

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_rider8• 4 years ago

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.

ajuc3• 4 years ago

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.

kgwgk6• 4 years ago

If there is nothing "not actually possible" what's the problem that needs to be solved?

shaded-enmity2• 4 years ago

How do you build a mechanism that has a perfect knowledge about a system while being part of said system?

lamontcg• 4 years ago

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).

jp57• 4 years ago

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.

davesque• 4 years ago

Yes, computation "costs" energy and increases entropy. The demon must compute its decisions before it can carry them out.

throwawaymaths• 4 years ago

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.

peteradio• 4 years ago

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.

RappingBoomer• 4 years ago

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...

bowsamic6• 4 years ago

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

spaetzleesser3• 4 years ago

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.

snarfy• 4 years ago

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• 4 years ago

Neither do sinusoidal oscillations exist, since they would have to be eternal.

bee_rider8• 4 years ago

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.

zmgsabst• 4 years ago

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.”

ziddoap• 4 years ago

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.

QuadmasterXLII• 4 years ago

My understanding is that at the beginning of the experiment there is only one red photon in the box.

bee_rider8• 4 years ago

Oh wow, that is a crucial aspect that I totally missed, which makes the result much more surprising!

Strilanc• 4 years ago

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.

potiuper2• 4 years ago

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• 4 years ago

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.

potiuper2• 4 years ago

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• 4 years ago

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.

8bitsrule2• 4 years ago

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."

Puzzling quantum scenario appears not to conserve energy

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