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Perpetual motion describes hypothetical machines that operate or produce useful work indefinitely and, more generally, hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not.

(Source:Wikipedia)

With this definition in mind, particularly the "operates indefinitely" (I don't care about producing work), won't quantum mechanics allow perpetual motion due to energy quantization?

For example, an electron in hydrogen can be thought of as perpetual motion. It's indefinite(I think so); unlike gravitational orbits (which slowly release energy). This is due to the quantization of energy. Without it, the electron would have fallen into the nucleus.

More generally, if we energy is quantized in a system, dissipative forces of lesser magnitude cannot act on it, due to quantization.

For example, if a block can have only an integer value of energy in Joules, then frictional forces of power $P<\frac{1 J}{\text{planck time}}$ cannot act. Or something like that.

So does quantum mechanics permit an infinitely advanced civilization to build a machine which operated indefinitely without doing work?

I'm not well versed in quantum mechanics, so I may be making a mistake here, or I may just be confused. Refer to equations if you want, but try not to use them too heavily unless the answer depends on it. It's OK if they're explained a bit.

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  • $\begingroup$ i guess energy is free until you don't spent it in doing some work!! the gravitational forces, does work against the dust particles, hence the orbit gradually collapses...but other than that there's no point in talking about a perpetual motion machine which doesn't perform any work!! $\endgroup$
    – Vineet Menon
    Commented Feb 28, 2012 at 8:40
  • $\begingroup$ @VineetMenon The reason gravity isn't perpetual isn't only the dust particles. The (I think dominant) reason is that, even in a perfectly circular orbit, energy is radiated in the form of gravitational waves. Perpetual motion machines that don't do work are still supposed to be impossible due to dissipative forces, which can be minimized but never removed completely. It can also be seen as a consequence of the Second law of thermodynamics, that Entropy must increase (or stay constant in reversible cases--which are impossible). $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 8:47
  • $\begingroup$ @VineetMenon I don't want the machine to do work, I'm just curious as to whether or not the concept of "perpetual motion machines are impossible" applies to QM. Though a PMM which does work would be pretty useful =D. $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 8:48
  • $\begingroup$ It should be mentioned that there are different kinds of perpetual motion machines, cf. the classification $\endgroup$
    – Qmechanic ♦
    Commented Feb 28, 2012 at 15:40
  • $\begingroup$ @Qmechanic Yep, which is why I specified what I was referring to in the beginning of the qn. But I didn't know that they had names corresponding to the thermoD laws. Thanks! $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 15:58

3 Answers 3

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Yes, perpetual motion that does not work is possible, and has been done in a famous Soviet experiment. You put a superfluid in the interior of a macroscopic donut-shaped tube in the normal state, and let the tube spin along the donut axis, fluid plus pipe, then cool the thing down so that it becomes a superfluid. Then you stop the tube from spinning.

The superfluid will spin with no measurable loss essentially forever, even in imperfect conditions. It spun for many years without measurable loss in the actual experiment. This is quantum perpetual motion in your sense, and it doesn't require such an advanced civilization, just mid 20th century humans.

The statement that perpetual motion is impossible is nowadays always interpreted to mean energy producing machine, not a motion that does not decay by friction.

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  • $\begingroup$ what about my quantum fluctuations point below? $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 14:41
  • $\begingroup$ @Manishearth: The motion is not completely perpetual, in principle it can decay. But the decay at zero temperature requires a macroscopic quantum fluctuation, which has probability exponentially small in the size of the system, so it will never happen in real life. This is analogous to an excited state that is prevented from decay by coupling to an environment (Zeno effect), but in this case, the environment and the system are one and the same. $\endgroup$
    – Ron Maimon
    Commented Feb 28, 2012 at 14:48
  • $\begingroup$ So here we have PMM which is not perpetual in theory but is, for all practical intents, a true PMM. Strange, but interesting. I'll look up the superfluid later. Thanks! $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 14:58
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    $\begingroup$ This is interesting. Do you have a ref for the experiment? $\endgroup$
    – qubyte
    Commented Feb 28, 2012 at 15:11
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I guess the operative question here (no pun intended) is, what does it mean for a machine to "operate"? If you consider a particle that just sits there and doesn't do anything to be an operating machine, then yes, it is theoretically possible to build one. Just put an atom somewhere isolated and leave it there. In reality, of course, you can't do this because there's no place in space that is truly isolated, and even if you did manage to cut off a box from all external influences, you would have virtual particle pairs popping out of the vacuum. But in a theoretical empty universe with no quantum fluctuations, assuming that the constituent particles are stable, an atom would just sit there forever.

But I don't think anyone would seriously consider a static system to be a machine. That's really all that an electron in an undisturbed atom is. It's just like a particle sitting in space, except that instead of sitting at one location, it probabilistically "sits" at every location.

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  • $\begingroup$ The atom was just an example. Could an infinitely adv civilization use quantization of energy to create a PMM? $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 9:03
  • $\begingroup$ Hmm, virtual particle antiparticle pairs reminded me about Heisenberg's. Then would such a PMM would be slowed by 'borrowing' of energy by other regions of space? Or would it come back to original speed since the energy comes back? $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 9:08
  • $\begingroup$ I guess that QM fluctuations would eventually stop any PMM. They have equal probabilities of giving and taking energy from a system, and we have infinite time to consider, so it's stop at some point. If that's correct, please edit it into your answer. If it's not, let me know where I'm going wrong... $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 9:16
  • $\begingroup$ @Manishearth Think of the mechanisms designed to get energy out of the waves in the ocean ocsenergy.anl.gov/guide/wave/index.cfm . One of the reasons I am keeping an open mind on LENR proposals is that I think that by serendipity the crystals that are involved might be tapping gravitational wave energies from the sea :). $\endgroup$
    – anna v
    Commented Feb 28, 2012 at 11:08
  • $\begingroup$ @annav Gravitational wave energy from the sea? Strange =P. I didn't exactly get the correlations with waves.. Were you referring to the wave fluctuations in comparison with QM fluctuations? $\endgroup$
    – Manishearth
    Commented Feb 28, 2012 at 11:15
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It seems that a PMM is impossible even if energy levels are quantized.

As @DavidZaslavsky pointed out, the electron example is sort of invalid, as there's no motion involved.

In QM, even if we manage to lower the effectiveness of dissipative forces to below the quantum of energy of the PMM in question, we will still have vacuum fluctuations, which can both give and take any amount of extra energy from the system at random. Now, there is a finite probability that it ends up taking all of the energy away (it can have some 'gives' interspersed as well). Note that after this it may go back in motion after recieving some energy from the surroundings). Obviously, it is no longer in motion, so in such a case, the PMM ceases to be perpetual. Since we have infinite time to consider the motion of the machine, this event becomes compulsory at some point in the infinite lifetime of the PMM. And thus, no PMM constructed on the basis of quantization of energy will work.

In fact, this seems to put an extra barrier for PMM enthusiasts. Even if you manage to remove all dissipative forces, quantum mechanics will bring the machine to an instantaneous standstill at some point in time. So it's no longer 'perpetual motion'

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