Is the Second Law of Thermodynamics Falsifiable?

[madness]

That is not even remotely what it means. Falsifiable means that there exists a possible experiment in this universe where a specific outcome would mean the law is false.

That's not correct. If there is an experiment in which a specific outcome would mean the law is false, yet there is no possible universe in which the experiment could yield that outcome, then the law is unfalsifiable.

 

[atyy]

If I'm not mistaken, the 2nd law is expected to hold regardless of the initial conditions. Entropy can never decrease according to the 2nd law (statistically speaking), and the fact that the initial conditions had low entropy then implies that we expect it to increase steadily over time. If the universe started at equilibrium state, entropy still wouldn't increase (statistically speaking again), which would again be in accordance with the 2nd law.

The second law of thermodynamics is not a fundamental law in the sense that we expect Newton's laws (or the Schroedinger equation) to be the fundamental equations governing the dynamics of systems in the universe. Newton's laws and the Schroedinger equation do not have an arrow of time, and we can set up situations using Newton's laws and the Schroedinger equation in which the second law of thermodynamics is violated. Thus we believe that the second law of thermodynamics arises because of how our universe was set up.

In addition to how the universe was set up, the second law of thermodynamics only applies to the "coarse-grained" entropy. It depends on our inability to observe all microscopic dynamics, as the "fined-grained" entropy does not decrease, due to the time-reversibility of the fundamental dynamical equations.

These points are in the same spirit as those made by @kith in post #22.

 

[DaveC426913]

No it isn't/doesn't. Finding out that we're wrong about how this universe works tells us nothing whatsoever about the possible existence of another universe or what its laws might be. It's just a self-contained logical construct. Similarly, writing 1+1=3 does not suggest the possibility that another universe exists where putting two apples in a basket yields three apples.

At the risk of going even further down the lock-this-thread rabbit hole:

If one is to grant the possibility of other universes with their own laws, then the very idea of falsifiability ceases to mean anything.

One need merely state that 'condition X' could exist in some alternate universe and is therefore unfalsifiable.

No. Falsifiability is constrained to our universe. It must be.

 

[atyy]

Maybe the 2nd law (entropy increases as time passes) is more a tautology, since we could say "the future is the direction in time having a higher entropy"

Yes, the labels of "past" and "future" are convention. However we can state the second law of thermodynamics without using that convention. A better way of stating the second law of thermodynamics is that there is an arrow of time that points in one direction (as opposed to multiple arrows pointing in different directions). By convention the end of the arrow that is lower in entropy is labelled the "past".

 

[Dale]

If there is an experiment in which a specific outcome would mean the law is false, yet there is no possible universe in which the experiment could yield that outcome, then the law is unfalsifiable.

The concept of falsifiability has no relation to other universes. It has only to do with possible experiments in this universe.

We don’t have any list or information describing other possible universes, but we can certainly describe possible experiments in this universe. A definition based on completely unknowable other universes is a scientifically vacuous definition.

 

[Drakkith]

That's not correct. If there is an experiment in which a specific outcome would mean the law is false, yet there is no possible universe in which the experiment could yield that outcome, then the law is unfalsifiable.

I don't agree with your idea of what falsifiable means. We are inherently limited to our own universe, so invoking definitions or arguments based on the existence of alternate universes is beyond wrong in my opinion.

 

[atyy]

I don't agree with your idea of what falsifiable means. We are inherently limited to our own universe, so invoking definitions or arguments based on the existence of alternate universes is beyond wrong in my opinion.

It is fine as the alternate universes are imagined universes.

 

[Dale]

@madness please provide a professional scientific reference using your other-universe definition of “falsifiable” or cease using it here.

 

[Dale]

It is fine as the alternate universes are imagined universes.

What indication do we have that imagined universes are possible? We have no basis to claim that.

 

[atyy]

What indication do we have that imagined universes are possible? We have no basis to claim that.

It's standard procedure. In the example you gave of the experiment with an egg, the outcome that did not happen is what you imagined might happen in an alternative universe.

 

[Dale]

It's standard procedure

Do you have a reference for that?

 

[russ_watters]

No. Falsifiability is constrained to our universe. It must be.

...and @Dale per what I think @atyy is saying:

It appears to me that the OP may be misunderstanding/overusing the "possible worlds" concept that he linked/cited. The way I read the link/concept, the "possible worlds" are strictly imaginary logical constructs, whereas it appears to me that the OP thinks they are potentially real. To me, this is a pointless "so what?". E.G. Gravity doesn't necessarily apply in the Matrix. So what; The Matrix isn't real, so that doesn't tell us anything about how gravity works in this universe.

 

[Drakkith]

@russ_watters Exactly my thoughts, though I couldn't put it into words like you could.

 

[hmmm27]

"In the philosophy of science, falsifiability or refutability is the capacity for a statement, theory or hypothesis to be contradicted by evidence." - ex Wikipedia

I think that the center of each black hole is occupied by a little green man. Since we can't see into black holes to possibly prove otherwise, that is not a falsifiable statement.

 

[PeterDonis]

They are essentially introduced in a system of formal logic (modal logic) to rigorously define notions of "possibility" and "necessity"

And one of the key points of this system is that there is no unique definition of those notions. There are different modal logics that correspond to what kinds of constraints you want to impose. For example, logical possibility is a less restrictive constraint that physical possibility: it is logically possible that a universe could exist that is governed exactly by the laws of Newtonian physics, but it is not physically possible, because "physically possible" means "consistent with the laws of physics of our actual universe", and our actual universe is not governed exactly by the laws of Newtonian physics. But there are many other physically possible universes than ours, since there are many sets of initial conditions other than those of our actual universe that are consistent with our actual universe's laws of physics--or, to put it another way, there are many other solutions of the equations of our actual universe's laws of physics, besides the solution that our actual universe realizes.

So if you are going to involve modal logic with respect to the question of whether the second law of thermodynamics is falsifiable, you need to first tell us which modal logic you are using, and convince us that that is the right modal logic to use to address the question.

 

[atyy]

Do you have a reference for that?

Yes, you did it yourself as standard procedure. It's a matter of semantics what you call the alternative "possibility" or "outcome" or "universe". We shouldn't let semantics distract from the physics of the question, which is a good one.

 

[Dale]

Yes, you did it yourself as standard procedure. It's a matter of semantics what you call the alternative "possibility" or "outcome" or "universe". We shouldn't let semantics distract from the physics of the question, which is a good one.

Sorry, misrepresenting a physics forum post is not a professional scientific reference. This thread is closed. If an actual suitable reference defining falsifiability in terms of other universes is sent to me by PM then I will reopen the thread. Otherwise I would encourage you and the OP to use less objectionable semantics.

 

[Dale]

The OP has found a reference from the professional philosophical literature that uses slightly different terminology than previously proposed. While we normally don’t go into philosophy, since the concept of falsifiability was originally developed by a philosopher and is used by professional scientists I felt that it was appropriate in this context. Please allow the OP to post the reference and from thence we will stick strictly to the language therein.

 

[Grossglockner]

1) The mathematical model of Nature, the Second Law of Thermodynamics, can be derived from basic Probability. I derived it in my book "Mathematical Models of Information and Stochastic Systems"(2008) by Philipp Kornreich CRC Press Taylor Francis Group ISBN 978

 

[shjacks45]

But we can take that reasoning to absurd limits, for example by applying the same logic to the laws of arithmetic. It's an empirical fact that if I put one apple and then another apple in a bowl then there are two apples in the bowl. We could imagine that I put one apple and then another in the bowl and there are three apples in the bowl, but that doesn't happen because the universe appears to obey the laws of arithmetic. Most wouldn't claim that the laws of arithmetic are scientific or falsifiable laws.

If I'm not mistaken, the 2nd law is expected to hold regardless of the initial conditions. Entropy can never decrease according to the 2nd law (statistically speaking), and the fact that the initial conditions had low entropy then implies that we expect it to increase steadily over time. If the universe started at equilibrium state, entropy still wouldn't increase (statistically speaking again), which would again be in accordance with the 2nd law.

A misreading. There are many reactions (specific cases) where entropy decreases. The Second Law only promises that the average total system entropy will increase.

 

[PeterDonis]

There are many reactions (specific cases) where entropy decreases.

More precisely, where entropy of one part of the reacting system decreases, compensated for by a greater increase of entropy in another part.

 

[atyy]

If I'm not mistaken, the 2nd law is expected to hold regardless of the initial conditions. Entropy can never decrease according to the 2nd law (statistically speaking), and the fact that the initial conditions had low entropy then implies that we expect it to increase steadily over time. If the universe started at equilibrium state, entropy still wouldn't increase (statistically speaking again), which would again be in accordance with the 2nd law.

You may also want to look at the Poincare recurrence time, which would lead to a violation of the second law of thermodynamics in some universes. In our universe, the recurrence time is far longer than the age of the universe, as mentioned in eg. Time's arrow and Boltzmann's entropy.

There is also discussion as to whether big crunch scenarios or cyclic cosmologies would lead to violations of the second law of thermodynamics, as mentioned in eg. Universe bounces back from the brink which refers to Turnaround in Cyclic Cosmology.

Another interesting read is Wald's amusing personal account of the events leading to Bekenstein and Hawking's discovery of black hole entropy. He states that at one point he thought it would be fine if the second law of thermodynamics is violated, since it is not a fundamental law. In a classical universe, it can be argued that black holes will lead to a violation of the second law of thermodynamics. In a quantum universe, black holes radiate and have a temperature, saving the second law of thermodynamics.

 

[Dale]

Please wait for the OP to post their reference before continuing

 

[zinq]

The "2nd law of thermodynamics" is not really a law, in that unlike other laws of physics, it does not always hold. Rather it is a statistical law, which is different. Simple models of entropy show that (on a given experimental trial) it is overwhelmingly likely that entropy will increase, but with a very small positive probability, it will not increase.

 

[madness]

Apologies all for the delay in responding to this thread. The reference I found for the "logically possible worlds" definition of falsifiability was this one https://www.jstor.org/stable/pdf/687321.pdf?casa_token=pqL-ZTfdrUwAAAAA:8w6gGfAMqSueO1bQbf2p1pn_tu1SfSQxQM6u_SRNVdB1FSG-nXkrG43C14cbwunQnj5fwqsKGUZMZfL0igb2AKa-7yC2EIn5nBsFIFTByJ1pk6YUiu8 , from which I quote:

"Falsifiability in the strong sense demands that there be a refutation of the theory in every logically possible world in which the theory is empirically inadequate "

"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. Essentially this is the classical analysis given by Hempel and Popper. Semantically, it requires that in some observation structure there exists a set of observations which refutes Σ. In a much stronger sense we might say that Σ is falsifiable just in case in every observation structure not expandable to a model of Σ there exists a falsifying set of observations. Let us distinguish these two senses by calling the first the weak sense and the second the strong sense. The difference is this. The weak sense requires only that an empirical refutation of Σ be a logical possibility. The strong sense stipulates in addition that no matter how Σ is empirically inadequate it is susceptible to empirical refutation. For example, an observation sentence of the form 'VxFx' is strongly falsifiable, but the conjunction of 'VxFx' with another observation sentence of the form '3xGx' is only weakly falsifiable" [boldface my own]

The first quote justifies my usage of logically possible worlds (I used universes, as I felt it was a better choice at the time). Technically, however, their "strong definition" in the first quote doesn't exactly correspond to my own definition, where I required the existence of a logically possible world in which the a falsifying observation could occur. To see this discrepancy, note that if the set of logically possible worlds were the empty set, falsiability would trivially hold according to their "strong" definition but would fail according to my own definition. Nevertheless, on reading both the weak and strong definition put forward in the second quote I believe that my definition is actually consistent with their "weak" definition (see boldfaced text). One might quibble that they used "logical possibility" rather than "logically possible world" as I used, but on comparing the strong definition across the two quotes it looks as though the two terms are used interchangeably by the author.

Now aside from that, I've become reasonably convinced from certain posts in this thread that the 2nd law is falsifiable (in the sense of the study I linked as well as the more naive sense that several posters in this thread argued for). In particular, if atyy is correct in post #57 that there are already logically consistent physical theories that violate the 2nd law, then that would effectively answer the question. Grossgnlockner in post #54 appears to suggest otherwise - I would like to get to the bottom of that if possible. Does the derivation from probability assume some basic physics that is not present in the theories mentioned by atyy? Do the theories mentioned by atyy violate the basic laws of probability used in the derivation mentioned by Grossgnlockner?

Footnote:

As an aside (I left this as a footnote as I am not sure how well non peer reviewed sources will be taken here). There was a discussion on a similar topic on falsifiability here . They found better examples than my case of arithmetic (which was quite fairly critiqued in this thread). Specifically, is the statement that all squares have four sides falsifiable? I would argue not, and yet I can point to an observation which would falsify it (finding a square with 3 sides). The only way I can see to evade this problem is to add the condition that falsifying observations have to be logically possible in the definition of falsifiability! PS: if the moderators don't like my including this link, I'll be happy to remove it, but I thought some posters did a better job at framing the issue than I did.

 

[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.