Is the Second Law of Thermodynamics Falsifiable?

[Dale]

When a theory Σ is said to be falsifiable what is usually meant is that there is a set of singular observation sentences which falsifies (i.e., is inconsistent with) Σ

With this definition the second law of thermodynamics is clearly falsifiable. If we take an isolated system and a clock and measure it’s entropy $S(t_0)$ and $S(t_1)$ with $t_0<t_1$ then the observation sentence $S(t_0)>S(t_1)$ is inconsistent with the second law of thermodynamics

 

[madness]

With this definition the second law of thermodynamics is clearly falsifiable. If we take an isolated system and a clock and measure it’s entropy $S(t_0)$ and $S(t_1)$ with $t_0<t_1$ then the observation sentence $S(t_0)>S(t_1)$ is inconsistent with the second law of thermodynamics

In the same way that the law "all squares have 4 sides" is clearly falsifiable according to sentence you selected. However, once you take into account the bold-faced part of the quote I posted you see it's not so simple.

 

[PeterDonis]

In the same way that the law "all squares have 4 sides" is clearly falsifiable

No, it isn't, because it's a tautology. The second law of thermodynamics is not a tautology.

Using "logical possibility" modal logic, the second law is falsifiable because there are logically possible worlds in which it is not true. There are no logically possible worlds in which there is a square that does not have 4 sides. See below.

I can point to an observation which would falsify it (finding a square with 3 sides)

There is no such observation; "a square with 3 sides" is a meaningless string of words, not a description of a possible observation. A plane figure with 3 sides is a triangle, not a square.

 

[Dale]

In the same way that the law "all squares have 4 sides" is clearly falsifiable according to sentence you selected.

What observation would falsify it?

If you see a three sided object then that is a triangle, so observation of a three sided object does not falsify it. So what observation would falsify it?

 

[madness]

Using "logical possibility" modal logic, the second law is falsifiable because there are logically possible worlds in which it is not true.

This was the question I've been trying to get answered and justified throughout the whole thread. You have simply asserted it without any evidence.

 

[PeterDonis]

You have simply asserted it without any evidence.

You already have a description of a logically possible observation that would falsify the second law (in post #61, and earlier ones in this thread as well). What more do you need?

 

[madness]

You already have a description of a logically possible observation that would falsify the second law (in post #61, and earlier ones in this thread as well). What more do you need?

A justification for the assertion that such the observation suggested in post #61 is logically possible.

 

[PeterDonis]

A justification that such the observation suggested in post #61 is logically possible.

The description of it is logically consistent. What more do you need?

 

[madness]

The description of it is logically consistent. What more do you need?

Others have claimed that the 2nd law of thermodynamics can be derived from probability alone. I would like to understand how that can be reconciled with the possibility that it might not hold in our universe.

 

[PeterDonis]

Others have claimed that the 2nd law of thermodynamics can be derived from probability alone. I would like to understand how that can be reconciled with the possibility that it might not hold in our universe.

Logical possibility has nothing whatever to do with the possibility that the second law might not hold in our universe. Our universe is not the only logically possible universe; plenty of things that are logically possible are impossible in our universe.

 

[madness]

Logical possibility has nothing whatever to do with the possibility that the second law might not hold in our universe. Our universe is not the only logically possible universe; plenty of things that are logically possible are impossible in our universe.

I don't follow your argument. My claim is that logical possibility constrains the facts which can be falsified (in any universe). Facts which hold in all logically possible worlds are called necessary truths, and are not generally considered falsifiable.

 

[PeterDonis]

My claim is that logical possibility constrains the facts which can be falsified

Yes, tautologies cannot be falsified because they are true in all logically possible worlds. But, as has already been pointed out, the second law is not a tautology. Tautologies are statements that are derivable from the laws of logic and the definitions of terms alone. "All squares have 4 sides" is such a statement, because having 4 sides is part of the definition of a square. Any tautology must therefore be consistent with all other logically possible statements. But the second law is not: it is inconsistent with the logically possible observation statement described in post #61. So the second law is not a tautology, and there are logically possible worlds in which it is not true.

 

[PeterDonis]

Others have claimed that the 2nd law of thermodynamics can be derived from probability alone.

I haven't claimed that, and I'm not sure that "can be derived from probability alone" is equivalent to "is a tautology" anyway.

 

[Ibix]

I don't follow your argument. My claim is that logical possibility constrains the facts which can be falsified (in any universe). Facts which hold in all logically possible worlds are called necessary truths, and are not generally considered falsifiable.

If the second law follows directly from the statistics of random motions of atoms, then your assumption is that the motions of atoms are random. The second law would be falsified if atomic motions were found not to be random.

 

[madness]

Yes, tautologies cannot be falsified because they are true in all logically possible worlds. But, as has already been pointed out, the second law is not a tautology. Tautologies are statements that are derivable from the laws of logic and the definitions of terms alone. "All squares have 4 sides" is such a statement, because having 4 sides is part of the definition of a square. Any tautology must therefore be consistent with all other logically possible statements. But the second law is not: it is inconsistent with the logically possible observation statement described in post #61. So the second law is not a tautology, and there are logically possible worlds in which it is not true.

I did mention in my earlier reply that I have more or less been convinced already by the arguments in this thread that the 2nd law is falsifiable. In particular that there appears to exist logically consistent physical theories that would violate it. Rather than continuing to argue over that point, I was hoping to refine the question to get a better understanding of what kinds of logically possible worlds might violate the 2nd law. It seems to me that the 2nd law does logically follow from a very minimal set of quite general assumptions (as suggested by a previous post regarding its derivation from probability). What are the assumptions needed to derive the 2nd law from pure probability theory? If it is not a tautology, is that because probability theory is not tautological, or because something else is required in addition to the laws of probability?

 

[PeterDonis]

What are the assumptions needed to derive the 2nd law from pure probability theory?

Basically, that the system is closed, that all microstates of the system are equally probable, and that we are using a coarse-graining of microstates into macrostates that leads to the existence of a thermodynamic equilibrium state which has so many more microstates than any other macrostate that the probability is overwhelming that a randomly chosen microstate of the system will be in the thermodynamic equilibrium macrostate.

If it is not a tautology, is that because probability theory is not tautological, or because something else is required in addition to the laws of probability?

Probability theory as a piece of pure math is tautological (since any piece of pure math is), but as a piece of pure math it doesn't apply to anything.

Probability theory as applied to any actual physical system is not tautological, because it must be supplemented with propositions describing the actual physical system that can be logically linked to probability theory.

 

[Dale]

Others have claimed that the 2nd law of thermodynamics can be derived from probability alone.

So what? Who cares how it is derived in determining falsifiability. It is logically possible that the world does not obey the laws of probability. I don’t see how the method of derivation matters to falsifiability. Per the definition of falsifiable it is falsifiable, as described above.

Furthermore, I disagree that the second law of thermo can be derived from statistical mechanics. Statistical mechanics can derive that the second law is asymptotically correct over long times and for large systems. The second law itself does not say “entropy doesn’t decrease in the long run for large systems” it just says “entropy doesn’t decrease”. So in fact the “derivations” you suggest actually indicate that the second law will occasionally be falsified for sufficiently small systems over sufficiently short time scales. In this sense, statistical mechanics supersedes and generalizes the second law of thermo, just like relativity supersedes and generalizes Newtonian mechanics.

In the same way that the law "all squares have 4 sides" is clearly falsifiable according to sentence you selected.

I am still interested in hearing how you think this is falsifiable. What observation would be inconsistent? I think you are misapplying the definition.

If you observe a three sided object, then that is a triangle, so observation of a three sided object does not falsify it. So what observation would falsify it?

 

[atyy]

Basically, that the system is closed, that all microstates of the system are equally probable, and that we are using a coarse-graining of microstates into macrostates that leads to the existence of a thermodynamic equilibrium state which has so many more microstates than any other macrostate that the probability is overwhelming that a randomly chosen microstate of the system will be in the thermodynamic equilibrium macrostate.

Depending on how one defines things, this need not be considered "pure" probability, since the assumption that all microstates of the system are equally probable need not hold for all dynamical systems. For example, it is not clear if the assumption holds when the dynamical system is not ergodic. It may be possible that the second law holds without ergodicity, but that possibility seems not yet well understood. I found an interesting discussion in Ergodic hypothesis in classical statistical mechanics by César R. de OliveiraI and Thiago Werlang.

Here are some other interesting discussions:
http://www.cgogolin.de/downloads/absthermalization.beamer.pdf
https://arxiv.org/abs/1503.07538 (see Chapter 7 and Appendix A)
p56: "We have seen that the ETH as defined in Definition 3 is by construction essentially sufficient and, in a certain sense, necessary for thermalisation. The necessary part, however, only holds if one is willing to call a system thermalising only if it thermalises for a given set of POVMs for all initial states with a sufficiently narrow energy distribution for which it also apparently equilibrates. Hence, there is the possibility to show thermalisation in systems that do not fulfil the ETH, if one is willing to restrict the class of allowed initial states. As we will see in the following this can indeed be done."

 

[madness]

I am still interested in hearing how you think this is falsifiable. What observation would be inconsistent? I think you are misapplying the definition.

If you observe a three sided object, then that is a triangle, so observation of a three sided object does not falsify it. So what observation would falsify it?

It is only falsifiable according to your own mistaken definition that " there is a set of singular observation sentences which falsifies (i.e., is inconsistent with) Σ " which you subselected without including the broader requirement of logical possibility. According to my own definition the statement is not falsifiable because one has to not only name a possible observation but has also to verify whether the observation is logically possible. You seem to have no problem applying the correct definition, and you just did so in this post.

 

[Lord Jestocost]

My question is which kind of "law" is the 2nd law of the thermodynamics? And pointing out a case in which we can imagine the 2nd law being falsified won't work, as we can apply the same logic to other statistical laws, including the law of large numbers.

Sir Arthur Stanley Eddington in “THE NATURE OF THE PHYSICAL WORLD” (Cambridge, At the University Press (1929)):

Primary and Secondary Law. I have called the laws controlling the behaviour of single individuals "primary laws”, implying that the second law of thermodynamics, although a recognised law of Nature, is in some sense a secondary law. This distinction can now be placed on a regular footing. Some things never happen in the physical world because they are impossible; others because they are too improbable. The laws which forbid the first are the primary laws; the laws which forbid the second are the secondary laws…..

….But for all its completeness primary law does not answer every question about Nature which we might reasonably wish to put. Can a universe evolve backwards, i.e. develop in the opposite way to our own system? Primary law, being indifferent to a time direction, replies, "Yes, it is not impossible". Secondary law replies, "No, it is too improbable". The answers are not really in conflict; but the first, though true, rather misses the point.

 

[Dale]

It is only falsifiable according to your own mistaken definition

I don’t think it is falsifiable even with that definition (which isn’t mine, it is Hempel and Popper’s according to your source). What observation can be made to falsify it? You can write down the sentence “square with three sides” but the definition requires an “observation sentence” not merely a “sentence”. There is no observation you can make which corresponds to that sentence, so it isn’t an observation sentence.

If you disagree then spell out the actual observation. What combination of observed lengths and angles leads to a falsification?

 

[madness]

I don’t think it is falsifiable even with that definition (which isn’t mine, it is Hempel and Popper’s according to your source). What observation can be made to falsify it? You can write down the sentence “square with three sides” but the definition requires an “observation sentence” not merely a “sentence”. There is no observation you can make which corresponds to that sentence, so it isn’t an observation sentence.

If you disagree then spell out the actual observation. What combination of observed lengths and angles leads to a falsification?

You quoted a small part of the definition attributed to Hempel and Popper but left out the part that stated the observation must also be logically possible. You now appear to have resorted to defining observation sentence to mean "sentence pertaining to an observation which is also logically possible", which is the same as my definition anyway. In fact, that isn't the definition of an observation sentence.

https://plato.stanford.edu/entries/quine/#ObseSent

 

[Dale]

In fact, that isn't the definition of an observation sentence.

So what is? I had encouraged you by PM to provide all of the definitions of the unfamiliar terms. I am not trying to cherry-pick a definition, but the one that I picked had the least unfamiliar terminology.

You quoted a small part of the definition attributed to Hempel and Popper but left out the part that stated the observation must also be logically possible.

I quoted the whole part you quoted. If you provided an incomplete reference that is on you.

 

[madness]

I quoted the whole part you quoted. If you provided an incomplete reference that is on you.

That's simply false. I boldfaced the statement on logical possibility in the quote I posted and you left it out.

 

[Dale]

That's simply false. I boldfaced the statement on logical possibility in the quote I posted and you left it out.

That wasn’t part of the definition. It was a subsequent explanatory paragraph! Look at it. There is the definition I quoted, then the statement that the previous sentence is the one used by Popper. Then the subsequent explanation. That is not part of the definition.

In any case, I just read the link on observation sentences and it completely corroborates my assertion. Your “observe a 3 sided square” is not an observation sentence. There is no set of sensory stimuli that correspond to it.

 

[madness]

In any case, I just read the link on observation sentences and it completely corroborates my assertion. Your “observe a 3 sided square” is not an observation sentence. There is no set of sensory stimuli that correspond to it.

And how did you arrive at that conclusion? Presumably by noting that the observation would be logically impossible. Or put another way, that there is no logically possible world in which the observation could occur.

 

[Paul Colby]

A justification for the assertion that such the observation suggested in post #61 is logically possible.

Logic is only as good as the assumptions or givens. A logical deduction about a proposed experiment on a system is only as good as the givens assumed. If the givens are garbage, so is the logical conclusion one has made. If the system in #61 doesn't conform to the assumptions one is making about it, then it's the assumptions which must be changed. Hence the experiment has falsified the assumptions or the model of said system.

 

[Dale]

And how did you arrive at that conclusion?

By noting that “I observe a three sided square” is not an observation sentence since it does not correspond to any sensory stimulus or combination of sensory stimuli. As I already said.

If you disagree then spell out the actual observation. What combination of observed lengths (ruler observations) and angles (protractor observations) leads to a falsification?

Purely by Poppers definition the second law is falsifiable and your straw man is not.

 

[madness]

By noting that “I observe a three sided square” is not an observation sentence since it does not correspond to any sensory stimulus or combination of sensory stimuli. As I already said.

And how did you come to know that “I observe a three sided square” "does not correspond to any sensory stimulus or combination of sensory stimuli"? Presumably you will admit that “I observe a four sided square” does correspond to a sensory stimulus? And yet the difference between the two sentences can only deduced from logical considerations.

 

[jbriggs444]

And how did you come to know that “I observe a three sided square” "does not correspond to any sensory stimulus or combination of sensory stimuli"? Presumably you will admit that “I observe a four sided square” does correspond to a sensory stimulus? And yet the difference between the two sentences can only deduced from logical considerations.

If we are arguing about the meaning of threeness or fourness then we are not arguing about universes. We are arguing about words.

If we are arguing about what it entails for an object to have three sides or four sides, we are not arguing about the problem at hand. We are arguing about definitions.

Once we have dispensed with details of interpretation, there is no physical problem remaining. All that remains is a dispute about whether three is equal to four. Or whether four is equal to four. We need not invoke universes to argue that. [In my view, "three" is part of the model, not part of the universe].