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Eddington once gave the following quote:

The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations—then so much the worse for Maxwell's equations. If it is found to be contradicted by observation—well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics, I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

What did Eddington mean by this? Why did he give a special status to the Second Law of Thermodynamics?

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    $\begingroup$ When did Einstein or Eddington actually say this ? In what context did they say this ? Can you actually cite the whole context of what they said ? $\endgroup$
    – silverrahul
    Commented Apr 14, 2021 at 7:31

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While the other answers brought important clarifications about the context and what exactly was meant, this is a rather interesting question to ponder in its own right.

In this case we have to make a distinction between thermodynamics, which is a theory based on the empirical facts, and statistical physics, which is a result of logical reasoning. In other words, we have to make distinction between a law of nature and a human-made theory. It is very likely that the authors of the quote meant the latter.

While an empirical theory is always at risk of being contradicted by an experiment, undermining mathematical proofs is much more difficult - unless there are errors in the proofs, this requires questioning the underlying axioms. Indeed, relativity and QM came into existence by questioning the underlying assumptions of Newtonian mechanics. Statistical physics is built essentially around counting the number of available states and some general assumptions about the accessibility of the states (such as ergodicity). Specifically:

  • We know exactly what these assumptions are and where the conclusions of statistical physics would not hold
  • Within the range of applicability of these assumptions, the theory is as good as our logical reasoning.

In other words: it is okay, if something contradicts known facts, it is not okay, if it contradicts logical reasoning. (From the point of view of physics, obviously.)

Update
It is worth adding the Einstein's full original quote which makes the same point:

A theory is more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended its area of applicability.

Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.

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    $\begingroup$ "rhermodynamics, which is a collection of empirical facts, " this is not correct, thermodynamics has its laws, as extra axioms in interpreting equations, and is very predictive still, in engineering applications, and even used in cosmology where appropriate. It is continuously valid in its specific phase space. Mathematics does not mold reality as far as physics goes, it is observations and data fitted to mathematical models and validated predictions that make a physics theory. valid. $\endgroup$
    – anna v
    Commented Apr 14, 2021 at 10:34
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    $\begingroup$ @annav yes, sure. And uf a theory contradicts experimental facts, it will be disproved. Math cannot be disproved, as long as we don't doubt the logical reasoning behind it. $\endgroup$
    – Roger V.
    Commented Apr 14, 2021 at 11:09
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    $\begingroup$ @annav I think "the collection of empirical facts" was an unfortunate (and possibly misleading) figure of speech. I have corrected it. $\endgroup$
    – Roger V.
    Commented Apr 14, 2021 at 11:37
  • $\begingroup$ There are of course other areas of applied maths which are just logical reasoning from a minimal set of assumption, such as fluid dynamics, which have a similar status to thermodynamics. $\endgroup$
    – isometry
    Commented Apr 15, 2021 at 13:22
  • $\begingroup$ @duality True. Perhaps, fluid dynamics has a much narrower area of applicability. $\endgroup$
    – Roger V.
    Commented Apr 15, 2021 at 13:25
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They said this in a certain context , and the statement you are making has been taken out of context.

As a general principle, ALL physics can be doubted . There are not many holy cows in physics. But, what it means to "doubt" something in physics is different than the colloquial usage of the word "doubt" that is often used by crackpot theorists.

Some theories have more levels of "credence" attached to them than others, which is a direct result of being able to describe and predict observations, better than other theories, in their domain of the natural world.

During the time of Eddington and Einstein, thermodynamics definitely had more "credence" than some other branches of Physics.

Also remember Einstein is just one scientist among many others. He was great in his topic of expertise, but he was not necessarily correct about everything.

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    $\begingroup$ "A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.", Albert Einstein, see for instance here. $\endgroup$
    – Yvan Velenik
    Commented Apr 14, 2021 at 8:02
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    $\begingroup$ Note that the question has been revised to include the exact quote from Eddington. $\endgroup$
    – Michael Seifert
    Commented Apr 14, 2021 at 20:49
  • $\begingroup$ @MichaelSeifert Okay, i removed the part asking to cite the quote. Also , i think it will be helpful , if you include the quote from Einstein in the question as well. You can copy the quote from the above comment by Yvan Velenik $\endgroup$
    – silverrahul
    Commented Apr 15, 2021 at 5:19
  • $\begingroup$ Ok I could not help but laugh at the "holy cows in physics" part $\endgroup$
    – Cantor Dust Drachen
    Commented Apr 15, 2021 at 12:24
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Why thermodynamics is beyond doubt?

Because it fits experimental data and is predictive , i.e. new data and systems are predicted for experiments, with small errors. Within its mathematical domain of applicability.

Einstein is not the Pope, neither is Eddington. For example Einstein is is quoted

Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice.

At present, mainstream physics posits that the underlying layer of physics is quantum mechanical. Physicists still exploring deterministic underlying theories are in a small minority. Still, even if they are proven right, the theory they come up with must embed the quantum mechanical observations at the phase space quantum mechanics has been found valid. (actually I should say"if new deterministic theories are validated by data and observations, "proof" has no meaning in physics, only in mathematics)

The real criterion for "credence" discussed in the other answer, is: reproducing data and predictivity of new.

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  • $\begingroup$ What’s a “phase space of validity”? Domain of applicability? $\endgroup$
    – Prof. Legolasov
    Commented Apr 14, 2021 at 12:42
  • $\begingroup$ The range of variables where the theoretical model , within errors, validly. For example Newtonian physics describes validly gravitation for small masses and space dimensions larger than micrometers and smaller than kilometers ( not to fall in the quantum or GR and SR range), I would be glad if you know a better way of describing this. $\endgroup$
    – anna v
    Commented Apr 14, 2021 at 13:13
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    $\begingroup$ @annav I agree with legolasov. Domain of applicability indeed seems a better description. It is less confusing and more intuitive . Atleast to us mortals, who are not retired experimental physicists. $\endgroup$
    – silverrahul
    Commented Apr 15, 2021 at 5:22
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    $\begingroup$ @silverrahul thanks for the suggestion. I edited $\endgroup$
    – anna v
    Commented Apr 15, 2021 at 5:44
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    $\begingroup$ Both thermodynamics and Maxwell's equations fit experimental data and are predictive. But the special status is given only to the former. So your explanation doesn't appear to explain anything. $\endgroup$
    – Ruslan
    Commented Apr 15, 2021 at 12:15

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