Elegant Universe: No fundamental physical laws beyond strings?

[JustStudent]

I've just read in the first pages of The Elegant Universe that Greene believes that all fundamental laws should be contained in the microscopic domain, all other laws are derived.

Is it really so evident that the laws of thermodynamics are derived and not fundamental? The second law, is it clear that it is not fundamental?

Also, what would be the definition of a fundamental physical law? Is it one not derivable from others? Is this definition free of loopholes? Again, is it completely clear that the second law is solely derived from others? I am pretty sure that it has an almost fundamental status, doesn't it?

 

[Fra]

reflection

Regardless of guesses in any direction, for sure I'd say nothing is "evident".

> Also, what would be the definition of a fundamental physical law?

I think this is a good question to ask.

Another question is what you mean by "derivable laws". None of the so called laws of physics has been derived in a deductive sense.

At best in some theories, that has been axiomatized, some laws may be like theorems, but that's still only within an system of choice, the choice and physical meaning/interpretation making up the premise is still an open wire.

I'm not sure there is a scientific answer to what fundamental physical law is, it sounds like something open for philosophical discussion, choice of both. But one might ask if fundamental laws are "inducable" from experience, in line with a scientific method? Then one might certainly say the these fundamental laws are derived from a more fundamental law - "law of learning" or the logic of science, whatever that is.

Or if you consider that the fundamental laws are not inducable from experience, they just "are", then it sounds like some hidden old style realism, and it doesn't sound like science.

I think the whole thing with string theory, and the quest for unification has put the focus on the question what the heck the fundamental laws of physics really mean - from a scientific viewpoint, in the context of some choice of scientific method.

My personal view is to focus more on the logic of science itself, and what the meaning of physical law is, in the context of science. What justification is there for physical laws, and what distinguishes a statement of physical law from any other statement?

I think some objections to these points is that this supposedly takes us into some cognitive or psychological sciences, and not physics. But that is too easy eascape IMO. If we take the relational thinking to heart, it might suggest that there are physical analogies to these admittedly "human philosophy points".

Then perhaps there might not be such a thing as "fundamental law", in the sense of universal and everlasting verifiable truth.

So before we decide to look for the universal fundamental laws, perhaps a second thought should be given to that this might be a inefficient focus point. Even IF there was such laws, there is STILL IMHO a more fundamental point, and that would be howto FIND these laws.

So there is this odd thought that maybe, the supposedly fundamental laws of physics, are "inducable" from some still yet unknown law of inference. And so on. The common critic to this is that this is circular reasoning. But is that really so?

It sure is not evident.

/Fredrik

 

[Fra]

2nd law of thermodynamics

If we disregard the semantics of what fundamental law means, the second law is certainly interesting.

On one hand, it's very easy to get a feeling that it's almost an tautology, in particular the statistical definition of entropy. With this I mean, that in the context where the concepts of microstructure, microstate and the measure we call entropy are defined, it is somehow natural to expect that the a priori expectation of change is that of increased entropy of the total system.

But that's deceptive, what's missing in the construct is the logic behind the choice and construction of the entropy measure itself, as well as how to distinguish a unique microstructure. If we choose a equiprobable set of microstates, or a set of microstates with an a priori given "preference distribution", then the deceptive part is the CHOICE of the premise, from with one might make conclusions almost tautologically.

But this way is not down to Earth IMO. In reality, the choice of measure and what to be measured (microstates) are part of the problem. Clearly, by choosing a microstructure we
are choosing the equilibrium. There is no innocence in choosing a microstructure, since the microstructure (partioning) implicitly singles out a prior distribution. So IMHO, there is physics missing here... yet to be supplied. This as I see it touches the foundations of probability theory and statistics, and it's applicability to science and inductive reasoning. This is the non-trivial part, though at first sight the second law looks like a tautology, but that is only after making non-trivial choices.

/Fredrik

 

[starkind]

One might begin with the definition of fundamental units.

 

[Demystifier]

I think the second law is not fundamental. It cannot be derived that this law must be obeyed, but this law can be viewed as a special solution of fundamental equations that are symmetric under the time inversion. In other words, the second law is merely an accidental property of the (part of the) universe in which we happen to live. (By the way, in a (part of the) universe in which the second law were not valid, life probably could not exist.)

 

[Fra]

I think the funny part is that the whole notion of probability and measures in general is unavoidably conditional to several premises, and so is entropy. Ie. I have a hard time to figure out what those two sometimes think about universal measures of disorder are really talking about. Disorder as as far as I see it a relational notion, and partly in the eyes of the beholder.

I think the reason why statistical mechanics applied to ordinary statistical physics works so well is that the problem ignored, has minimal effects. Human to human, comparing molecular dynamics, there is a large environment to serve as a kind of information sink that provides at least locally an effective "locally universal" reference.

The idea that everything follows from the microstructure of the universe, smells from this IMO. The problem is the CHOICE of the microstructure. And the point would in my eyes at least be that there is no foolproof way to reason from arbitrary premises towards a unique conclusion.

This is why I think that the better way is to analyse the logic and dynamics of information exchange at a deeper level. It is what to me is taking the relational ideas seriously. Then one might argue that there is no conincidence that nearby observers tend to agree, simply because we have equilibrated and evolved in interaction.

The only common reference we, that I can make sense of, is our interactions with our environment. Should the laws of nature if anything, be encoded in these interactions? And therefore also must live there. I find it troublesome to reason about these things, using fictive references that themselves are not defined in terms of interactions.

I see two issues with the second law.

1) The first is wether one thinks of this deterministically or probabilsitically. If we think that "entropy of the universe" will never decrease, that seems to fall because we still need statistics to establish that to a reasonable level of confidence. That leads us to the probabilistic and almsot tautological meaning, that the entropy is unlikely to decrease. This is almost to say that the "probability of the state of the universe" are unlikely to decrease. So one can simply say that statistically the second law is expected.

2) But the other issues is the meaning of statistics or probability. If this is going to be realistic, I think the statistics must be real physics. Ie real observers "living this statistics". And it might suggest that even beyond the statisticsl expecation of a 2nd law, the two views might not arrive at a consistent probability. There might arise contradictions between the two views. And I think of these "contradictions" as the basis for physical interactions. And the classification of physical interactions, might possibly relate to classification of relational contradictions.

I think this is deep foundatioanl questions yet open, that touches probability in scientific methods, and many others things. Clearly action principles and max ent principles are related, and are also corners of this same buried dog.

I personally sense that this is too often simplified and it bugs me. I sure don't have any answers but I think it's worth pointing out that there might be a real problem here, that could make a difference if resolved, although it is clear that a lot of people for one reason or the other chooses to ignore this, and seems to hold the opinion that it is of no relevance to science.

/Fredrik

 

[JustStudent]

I think the second law is not fundamental. It cannot be derived that this law must be obeyed, but this law can be viewed as a special solution of fundamental equations that are symmetric under the time inversion. In other words, the second law is merely an accidental property of the (part of the) universe in which we happen to live. (By the way, in a (part of the) universe in which the second law were not valid, life probably could not exist.)

There is something I still don't understand. You are saying that we can derive that fundamental laws must be obeyed. I thought a fundamental law would be something that would arise just by observation or some kind of
consistence. For example, general covariance is a fundamental law, isn't it? Or should I do a distinction between "fundamental principles" and "fundamental laws"?

In any case, consider my doubts being about fundamental something. The second law is analogous to energy conservation, in the sense that it's a principle that is not violated, right?

Can't I argue in the same way that energy conservation is just an accidental property of our part of the universe?

Sorry if the question seems silly, but that's just because I'm still confused.

 

[Demystifier]

TThe second law is analogous to energy conservation, in the sense that it's a principle that is not violated, right?

Wrong! The first law is a variant of energy conservation and cannot be violated. However, the second law CAN be violated. The probability for violation is very small for a large number of particles, but it is violated every day for systems with only a few particles.

 

[mhill]

this is depending your point of view :)

if the 'fractal ¡ theory of universe is true (universe would have a fractional dimension between 3 and 4) then the scale is not important, at any scale the universe would be self-similar and physical laws would be valid all the time, a fractal universe would be boring though .

 

[Coin]

Hm, that is an interesting question that I would like to see a string theorist answer-- when doing string theory, is the second law something which is a condition imposed on string theory? Or something which is derived from string theory?

Does Greene state an opinion one way or the other?

I think the second law is not fundamental. It cannot be derived that this law must be obeyed, but this law can be viewed as a special solution of fundamental equations that are symmetric under the time inversion. In other words, the second law is merely an accidental property of the (part of the) universe in which we happen to live.

Hm, I'm not sure I understand this. You're suggesting that this "property" (that the second law is followed) is something which was imposed on this section of the universe due to some initial condition which might have varied elsewhere?

What form does this property take? What enforces it?

 

[JustStudent]

Wrong! The first law is a variant of energy conservation and cannot be violated. However, the second law CAN be violated. The probability for violation is very small for a large number of particles, but it is violated every day for systems with only a few particles.

Hmmm... I was already thinking in the statistical version. Is there a microscopic version of the second law? It seems to me that, by what you said, it is not to be used for a small number of particles, is it?

Also, I thought energy coservation could be violated for small amounts of time compatible with the energy/time uncertainty relation.

Another thing: I thought that energy conservation was an experimental principle. Of course you can deduce it by time translation invariance of the lagrangean using Noether theorem, but the universe does not have this time translation invariance, does it?

 

[friend]

Also, I thought energy coservation could be violated for small amounts of time compatible with the energy/time uncertainty relation.

Another thing: I thought that energy conservation was an experimental principle. Of course you can deduce it by time translation invariance of the lagrangean using Noether theorem, but the universe does not have this time translation invariance, does it?

I understand that energy conservation is not guaranteed in General Relativity - that it holds only in flat spacetimes. Is this right?

 

[Fra]

Hmmm... I was already thinking in the statistical version. Is there a microscopic version of the second law?

The statement is a relation between two decriptions: macrostructure vs microstructure.

Usually the macrostate is defined statistically in terms of distributions over the microstates. And implicit in that is that we are dealing with limits, and this makes no sense where the approximation of "large numbers" are invalid.

The construct is that the a priori probability of decreased total entropy is lower than than of the reverse. This follows from the construction and the choice of the equiprobable microstructure.

This probability depends on the samples size, and goes to zero as system comlpexity goes to infinity. So one might say that there is an uncertainty in the second law, that depends on the complexity scale.

At the limit of minimum complexity the law is so uncertain that it makes no sense - the arrow of time has no confidently preferred direction.

This may give a deja vu to other uncertainty relations. There seems to be a relation between complexity scale (large vs small numbers) and confidence in constructed measures - such as entropy. So that any constraints on the values of the meaures themselves, become weaker as the confidence in the mesure themselves decrease. In a certain sense I personally associate here a sort of "inertia" to measures.

A very superficial but simple analogy.

Think of a measuring stick (meter stick if you want). You use this stick to measure with, but cleary if the actual stick becomes too thin, the measurements becomes unreliable, becuase you can hardly distinguish the stick itself from a fluctuation in the environment.

So instead of saying the the second law is violated in case of few microstates, one can say that the concept of entropy itself starts to become poorly distinguishable.

Here there are I think analogies to energy too. After all, energy is also a measure. But a measure of something else.

About energy, there are two questions. Before one asks, what is the value of the energy (ie how many joules). The first question is what is the MEASURE of energy, and how confident are we in the "energy-meter-stick".

Same with time.

Usually in statistical mechanics, these questions aren't asked like this, and it's non standard indeed, but given that the question is fired in the beyond standard model I thought this was what you were after?

I'm sorry if I brought only fuzz to this.

/Fredrik

 

[arivero]

Real fundamental principles are invariance, preservation, symmetry etc. String theory is still there because it survives, apparently, to the restrictions imposed by fundamental principles.

It seems more easy to get fundamental laws out of the fundamental principles when we are in the microscopic, few bodies and few degrees of freedom, case.

 

[Fra]

I do agree with Arivero to an effective extent, but one can go one step further and question the nature of these fundamental principles.

As far as I see it, either

1) they are metaphysical statements, somehow providing a starting point for science, and serve like a premise of reasoning or hypothesis generation. Ie. any hypothesis that fails to be in line with the fundamental principles can be ruled out on logical grounds - without need for experimental feedback. And a theory violating the basic principles aren't even worthy of beeing tested.

2) or they are seen as theoretical frameworks in the context of the scientific method, meaning they are not proven, but rather seen as the framework subject to further scientific test, but more importantly also subject to possible revision. Suggesting that some element of humbleness might be worthwhile before by means of various no go theorems (coming from a choice of fundamental principles) to in a deductive manner irreversibly rejecting possibilities. The mistake could be in assigning too much confidence (inifinite confidence) in the induction of these so called "consistency tests".

The metaphysical view is I think not attractive, so the latter view is more plausible. Still it is quite obvious that the current framework does suggest a plausability to various hypothesis. Hypothesis that are not very plausbile (although theoreticall possible) will rightfully be given less "investment" - there is certainly plausible reasoning here. But this still leaves room for analysis, on the nature of not only law but of fundamental principles.

As I see it, there are not clear candidates for fundamental principles at all - of the rank that could never ever possibly be revised in the light of any evidence.

/Fredrik

 

[friend]

As I see it, there are not clear candidates for fundamental principles at all - of the rank that could never ever possibly be revised in the light of any evidence.

Perhaps I can suggest an undeniable fundamental principle: that all facts are consistent with each other, none proves that another does not exist. Suppose fact A proves fact B, but fact C proves that fact B can not exist. We would then question our certainty of the facts because our more fundamental belief about reality is that all facts are consistent with each other. Right?

 

[Fra]

Perhaps I can suggest an undeniable fundamental principle: that all facts are consistent with each other, none proves that another does not exist. Suppose fact A proves fact B, but fact C proves that fact B can not exist. We would then question our certainty of the facts because our more fundamental belief about reality is that all facts are consistent with each other. Right?

Yes, that sounds like a good principle on a constructive reasoning, but I notice here what I consider to be a interesting point.

You come with two suggestions here.

(1) Facts must not exist in contradiction.
(2) If rule (1) is violated then we must resolve it, by revising the supposed facts.

If rule 2 is to be necessary, it means rule 1 does not say that "facts does never contradict" - ie we do not exclude inconsistencies, consistency (1) is more of an "ambition", and whenever inconsistencies are observed they should be resolved to recover consistency.

I think this can be seen in at least two ways.

- either you think at a human level and think that if we run into a "inconsistency", then we have been mistaken about some of the facts in the sense that we have somehow comitted an "error" in arriving at the inconsistency. But maintaining the vision that nature itself is never inconsistent and there are meaning in talking about universal facts, it's is only the human understanding that sometimes get into inconsistecies because we "get the facts wrong".

- or you try to extend the meaning of consistency to nature itself, and try to find in the rules of constructive reasoning and logic, the fundamental rules that leads to the laws of physics, and hold the opinion that any relations in nature are uncertain by it's nature, and that consistenct is more to be interpreted as a sort of equilibrium condition. A system can be perturbed away from consistency, but as per rule 2, there is a tendency of nature to try to recover a new consistency.

I subscribe to the second point of view and I seek what I like to call a new logic, to be applied to physical theories. I think one new focus becomes that of the physics of resolving a contradiction when/if it is "thrown in our face" and what the physical basis of this is, and this I think gives a new abstraction of the meaning of fact and law. I think there are no observable certain universal facts, observer independent laws or truths.

I think what most of us call fundamental principles and laws is more something like expectations that guides our actions, and rightfully so. But sometimes things happens that was simply unexpected.

/Fredrik

 

[friend]

I subscribe to the second point of view and I seek what I like to call a new logic, to be applied to physical theories. I think one new focus becomes that of the physics of resolving a contradiction when/if it is "thrown in our face" and what the physical basis of this is, and this I think gives a new abstraction of the meaning of fact and law. I think there are no observable certain universal facts, observer independent laws or truths.

I am more of the opinion that the uncertainties we observe are derived from a more underlying requirement of consistency. Though you might be right that we cannot formally prove by observation this absolute consistency because of the inaccuracies and uncertainty of our measurements.

It's probably more of a faith issue on my part to believe that the most fundamental facts are absolutely logically consistent with each other. I can't even imagine how to proceed if such consistency is not the case. I don't know of any sort of reasoning process that doesn't rely on consistency.

There have been attempts to derive the laws of physics starting from the consistency between facts. But these efforts are not complete yet and are not on the arXiv and are not peer reviewed yet. So what are we to make of the situation if it turns out that we can indeed derive the Standard Model and General Relativity from this consistency between facts that we now only take on faith. Would observation then prove this underlying consistency? Or would this derivation only be a coincidence?

 

[Fra]

Hello Friend, I just got back from a trip and didn't have much time before that.

It's probably more of a faith issue on my part to believe that the most fundamental facts
are absolutely logically consistent with each other. I can't even imagine how to proceed
if such consistency is not the case. I don't know of any sort of reasoning process that
doesn't rely on consistency.

Of course a set of facts that isn't consistent isn't satisfactory, no question about that - we agree on that. But the question I ask is if we should focus on possible states of perfection, or on the PROCESS of improvement?

Ie. which choice of question are likely to be of highest utility to us?

I neither rule out consistency, nor presume it's unique existence (in the sense of realism). I simply suggest a different focus, where the question is making the "best choice" in a case where the "perfect choice" isn't at hand, or identified - it's a game.

But for me the focus is as much on the reasoning process itself rather than the state of reason, because the state of reason changes, and I consider a connection where the lack of perfect consistency in any state of reason, is the basis for expecting change.

I take the lesson to be to try to treat processes and states on the same basis. So that while we might never find perfect consistency in the ordinary sense, one might hope to find a process of increasing the consistency.

I guess I picture something like degrees of consistency, or it might be better called degrees of constructivity - an inconsistent observer will "not survive", so when perturbed it better get back on track, or face destruction. This aims to bring the question of consistency into an evolutionary context.

Since to my understanding all information, knowledge and measures are relative to a context, and I equate this concept to an observer. This means that in my view of things the question of consistency is the question of survival and persistence. As I see it the laws of nature, are implicit in the makeup of observers and matter. So it makes no sense (I think) to separate the two, except for hte case where you have single out an observer of course. But then the "consistency" of thta observer relative to other observer translates into interactions and ultimately the evolution of hte observer (matter).

This way of reasoning really does put the notion of law, method on an edge as I see it.

There have been attempts to derive the laws of physics starting from the consistency
between facts. But these efforts are not complete yet and are not on the arXiv and
are not peer reviewed yet. So what are we to make of the situation if it turns out
that we can indeed derive the Standard Model and General Relativity from this
consistency between facts that we now only take on faith. Would observation then prove
this underlying consistency? Or would this derivation only be a coincidence?

Do I think it is possible to find a choice of statements from which the standard model of particle physics and GR follows from consistency? I think that might well be. But I still think that isn't the best question to ask. It's not the type of questions I want to ask.

Ok, the question is how can all this be turned into constructive mathematics?

I look at the basic notions of distinguishability, and the construction of measures (probability beeing one). I think an analysis of this, will introduce relative measures that come with natural measures such as rating states (entropy) and rating processes (actions) that are more well founded in the foundations of a new logic of probability that what one is feed with from standard physics textbooks. I think out of this a new relation between the continuum and discreteness will follow.

/Fredrik