8 ms·

Puzzling quantum scenario appears not to conserve energy

76 points by theafh 4y ago

rssoconnor 4y 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 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 4y 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?
- kgwgk 4y 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 4y 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.
    - kgwgk 4y ago
      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.
    - JBits 4y ago
      What makes these quantities conserved in QM/QFT?
ajuc 4y 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_rider 4y 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.
  - ajuc 4y 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.
    - MockObject 4y ago
      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 4y ago
        I'm not sure. Wouldn't the introduced waves cancel out then?
        MockObject 4y ago
        Only if it lead to abnormally cool photons as much as anomalously hot ones.
  - kgwgk 4y ago
peteradio 4y 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 4y 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...
- bowsamic 4y 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
  - spaetzleesser 4y 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.
    - PartiallyTyped 4y ago
      Plenty of people have come. Gödel 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 4y ago
        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
        4y ago
snarfy 4y 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 4y ago
  Neither do sinusoidal oscillations exist, since they would have to be eternal.
bee_rider 4y 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 4y 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 4y 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 4y ago
  My understanding is that at the beginning of the experiment there is only one red photon in the box.
  - bee_rider 4y ago
    Oh wow, that is a crucial aspect that I totally missed, which makes the result much more surprising!
Strilanc 4y 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.
deleted 4y ago
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potiuper 4y 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 4y 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.
  - potiuper 4y 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.
deleted 4y ago
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mikewarot 4y 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.
8bitsrule 4y ago
Sometimes when people 'shut up and calculate' [0] they find surprises. [0][https://aeon.co/essays/shut-up-and-calculate-does-a-disservice-to-quantum-mechanics 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."

76 points by theafh 4y 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 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 4y 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?
kgwgk 4y 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 4y 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.
  - kgwgk 4y ago
    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.
  - JBits 4y ago
    What makes these quantities conserved in QM/QFT?

ajuc 4y 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_rider 4y 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.
- ajuc 4y 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.
  - MockObject 4y ago
    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 4y ago
      I'm not sure. Wouldn't the introduced waves cancel out then?
      - MockObject 4y ago
        Only if it lead to abnormally cool photons as much as anomalously hot ones.
- kgwgk 4y ago

peteradio 4y 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 4y 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...

bowsamic 4y 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
- spaetzleesser 4y 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.
  - PartiallyTyped 4y ago
    Plenty of people have come. Gödel 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 4y ago
      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
      - 4y ago

snarfy 4y 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 4y ago
Neither do sinusoidal oscillations exist, since they would have to be eternal.

bee_rider 4y 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 4y 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 4y 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 4y ago
My understanding is that at the beginning of the experiment there is only one red photon in the box.
- bee_rider 4y ago
  Oh wow, that is a crucial aspect that I totally missed, which makes the result much more surprising!

Strilanc 4y 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.

deleted 4y ago

[deleted]

potiuper 4y 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 4y 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.
- potiuper 4y 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.

deleted 4y ago

[deleted]

deleted 4y ago

[deleted]

mikewarot 4y 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.

8bitsrule 4y ago

Sometimes when people 'shut up and calculate' [0] they find surprises. [0][https://aeon.co/essays/shut-up-and-calculate-does-a-disservice-to-quantum-mechanics 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."