Karl Popper on brownian motion and the 2. law of thermodynamics

[LTP]

I'm reading an old, maybe outdated, paper by Karl Popper about the 2. law of thermodynamics, brownian motion and perpetual motion.

Popper writes:

According to Einstein's theory we are forced to say that in the Brownian
movement, observable heavy particles are sometimes lifted against the
gravitational field of the earth, at the expense of a (slight) cooling down of
the liquid. Of course, just as many particles are sinking, thus restoring the
lost heat. But this does not matter : the letter of Planck's law is undoubtedly
violated, as Einstein in fact stated.
This situation is a little more serious than is usually seen. For the now
generally accepted theory of the Brownian movement clearly implies
that, precisely as small fluctuations affect small suspended bodies, big
fluctuations will affect big suspended bodies ; and it implies, moreover,
that big fluctuations, although very improbable and therefore very rare,
must occur, precisely as small fluctuations must occur.
All this is of course very well known to every physicist ; and I believe
that most physicists will accordingly agree that the entropy law, in Planck's
formulation, is simply falsfied by the Brownian movement, as interpreted
by Einstein. However, they may say, perhaps, that the Maxwell-Boltzmann
law is certainly not falsified but supported by Einstein. This is quite correct.
But the following consequences have not, apparently, been drawn from
the situation which I have described.

Before that, Popper has described Planck's law as:

There does not exist a perpetual motion machine, of the second
order, that is to say, a physical system, immersed in a heat bath, which,
by cooling down (or, which is the same, by absorbing heat from the
surrounding heat bath), can move a heavy body against a force, thus
increasing its potential energy ; or in terrestrial terms, a machine which,
by cooling down, can lift a weight.

So, my question is: Is brownian motion considered to be a violation to the 2. law of thermodynamics today? To me, it sounds like Popper is doing a lot of hand waving; and not so much with content in it.

Se the attachment for the full article.

 

[Andy Resnick]

No, Browian motion is not incompatable with entropy increase. Feynman invented a nice puzzle- a brownian ratchet which can appear to raise a macroscopic weight, driven by brownian motion. The resolution to this puzzle is interesting, and the groups trying to understand actin polymerization in terms of a Brownian ratchet would do well to read it.

The Second law of thermodynamics is a law of thermodynamics, and thus is a macroscopic, time-independant formulation. It has been experimentally demonstrated that entropy can decrease spontaneously for short times in out-of-equilibrium systems, in accordance with the fluctuation-dissipation theorem.

 

[astrokreng]

I would like to provide a response to your question about Karl Popper's views on brownian motion and the second law of thermodynamics.

Firstly, it is important to note that Popper's paper was written in the early 20th century and therefore may not reflect the current understanding and advancements in these areas. Science is a constantly evolving field, and our understanding of concepts and theories can change as we gather new evidence and data.

Regarding brownian motion, it is now widely accepted that this phenomenon is not a violation of the second law of thermodynamics. In fact, it can be explained by the principles of statistical mechanics, which are based on the second law. The random movements of particles in a fluid are a result of the thermal energy present in the system, and the overall trend is towards an increase in entropy, in line with the second law.

Additionally, Popper's statement about small fluctuations affecting small suspended bodies and big fluctuations affecting big suspended bodies is not entirely accurate. The size of the suspended body is not the determining factor in the occurrence of fluctuations. Rather, it is the number of particles in the system and their interactions that influence the occurrence of fluctuations.

Furthermore, Popper's argument that the Maxwell-Boltzmann law is supported by Einstein's theory is also not entirely true. While Einstein's theory does provide a theoretical explanation for brownian motion, it does not necessarily support the Maxwell-Boltzmann law. The two are separate concepts that can coexist and do not contradict each other.

In summary, while Popper's paper may have raised some interesting points and discussions at the time it was written, it is important to recognize that our understanding of these concepts has evolved since then. Brownian motion is no longer considered a violation of the second law of thermodynamics, and it can be explained within the framework of statistical mechanics. As scientists, it is important for us to constantly evaluate and update our understanding of the natural world based on new evidence and data.