Limitations of Physics | Seeking Feedback on Ideas

[ThudanBlunder]

During an interview I once had to write an essay about the aims of education and whether it allows us to pursue 'the truth'. It included the following passage:

In physics, the more we probe the nature of matter, the more it appears that mind and matter are one, in the sense that the entities we are forced to invent and describe are more mathematical abstraction than physical reality. Complemented by empirical methodologies as it is, theoretical quantum physics is subject to the limitations of the scientific method and in my opinion the search for the chimerical Theory of Everything is thus doomed to failure.

I would appreciate any feedback on my 'naive' ideas about physics.

 

[Kevin_Axion]

I'm not sure how you can make such a bold statement of a "theory of everything" is bound to fail on the assertion of lack of Scientific Method and Mathematical Abstractions. Especially since mathematical abstractions are the nature of reality. And what chimera exists in reason? A Theory of Everything is the extrapolation of knowledge and logic following the actions of predecessors (Electroweak, Electromagnetism, Space-time), a testament to reality not illusion.

 

[tom.stoer]

Let me comment on a few snatches:

I don't think that neither within physics nor within mathematics we are even touching the problem of mind. It's like driving a car: the robot mounting certain pieces of a car does not know anything regarding traffic jams.

It is true that we have to invent a lot of abstract entities; nevertheless some of these entities turned out to be physically real (antiparticles, neutrinos, quarks, entangled quanta, ...) Compare it with ordinary language: I guess we agree what we mean by "red" or "redness", but I think we should also agree that both "red" and "redness" are abstractions. The problem is not that we do not understand the abstract entities in physics (we do understand quite well and we can distinguish between pure abstract entities and physical reality); the problem could very well be that we erroneously believe in our understanding of abstract entities like "redness". The difference is not that "redness" is easier to understand than "entanglement", but that we are familiar with the concept redness in everyday life w/o ever thinking about its true nature.

It is true that theoretical quantum physics is subject to the limitations of the scientific method. It is also true that scientists know about the limitations and are even able to derive physical predictions based on some limitations. Quantums physics tells us a lot about concepts which are not realized in nature; Bells theorem for example tells us what is not realized in certain quantum objects and how one can derive predictions from these limitations which are testable by experiment!

Your last statement that the search for the chimerical Theory of Everything is thus doomed to failure seems to be at odds with the rules of this forum and with good scientific practice. What does chimerical mean (it has different meanings)? What do you think is a theory of everything? What shall it provide? How shall it look like? Do you know about a candidate for such a theory and why it is doomed to fail?

 

[Dmitry67]

I don't think that neither within physics nor within mathematics we are even touching the problem of mind.

Yes, and as an example, no physical theory explains (or at least tries to explain) a very special role of the moment called 'NOW'. On the contrary, current physics denies any special role of NOW assuming Block Time. Looks like some physical things, like NOW, should be waiting for theory of consciousness to be explained.

 

[tom.stoer]

The natural conclusion is that any physical theory of everything is a theory of "everything except mind" :-)

Honestly: of course a physical theory of everything will have certain limitations we are not always aware of. Let's assume we are able to derive the standard model (symmetries, particle content, free parameters like masses and coupling constants) plus gravity (and cc) from string theory and let's assume that our universe is somehow singled out by a new selection principle within the landscape (e.g. some kind of evolutionary mechanism based on microscopic mechanism in string theory; just like ordinary evolution is somehow based on the chemistry of DNA + "survival of the fittest"). This would be a fantastic breakthrough and nearly everybody would agree that the ToE has eventually been identified.

Nevertheless this theory would not answer the question why our universe is described by string theory (instead of number theory, for example). In addition this theory would not explain concepts or entities like "string", "red", "mind", "god", "love", "evil".

 

[Dmitry67]

The natural conclusion is that any physical theory of everything is a theory of "everything except mind" :-)

Nevertheless this theory would not answer the question why our universe is described by string theory (instead of number theory, for example). In addition this theory would not explain concepts or entities like "string", "red", "mind", "god", "love", "evil".

But at least TOE should explain the observed values of the parameters of the Standard Model. It is hard to believe that these dimensionless numbers (even there are some relationships, like Koide formula) have no degrees of freedom. So TOE (as sterile set of equations) will be not the last step - we will need to draw the exact shape of the island of consciousness-friendly universes in the space of degrees of freedom of TOE. Are we in the center of that island? Are there any other separated islands? I would give my right hand to get an answer.

 

[Hurkyl]

It is true that we have to invent a lot of abstract entities; nevertheless some of these entities turned out to be physically real (antiparticles, neutrinos, quarks, entangled quanta, ...) Compare it with ordinary language: I guess we agree what we mean by "red" or "redness", but I think we should also agree that both "red" and "redness" are abstractions.

Your example is not ambitious enough!

An apple is an abstract entity. And I don't mean some notion of "appleness" -- I mean that when I look at a table and assert there is an apple upon it, I am invoking an abstract concept to organize and interpret the visual data gathered by my eyes.

 

[tom.stoer]

@Hurkyl: yes, you right. The whole discussion goes back to Platon and Aristoleles (or even to the pre-socratic philosophers like Thales, Heraklit, Parmenides, ...). The ancient greeks called it "metaphysics" which means "beyond physics".

This "meta" is what I wanted to stress: the discussion regarding "mind" and "nature of a ToE" is (at least partially) metaphysics. But this is not a problem as long as we are aware of the fact that it is metaphysics and as long as we are able to talk about intrinsic limitations of physics.

One could argue that I am closing my eyes (or like Feynman said: "shut up and calculate"). But this is not true. I think it's more about the expectation what can be achieved within physics and what cannot be achieved. If an engineer working in the automotive industry fails to construct a perfect vehicle which is able to explain the theory "of all vehicles" (and which can swim and fly) that does not automatically mean that the automotive industry has a problem :-)

 

[GeorgCantor]

Your example is not ambitious enough!

An apple is an abstract entity. And I don't mean some notion of "appleness" -- I mean that when I look at a table and assert there is an apple upon it, I am invoking an abstract concept to organize and interpret the visual data gathered by my eyes.

haha... as long as those abstract wave-like forms taste good and juicy, i'll accept them to be approximations of apples.

 

[DevilsAvocado]

Looks like some physical things, like NOW, should be waiting for theory of consciousness to be explained.

The natural conclusion is that any physical theory of everything is a theory of "everything except mind" :-)

Honestly: of course a physical theory of everything will have certain limitations we are not always aware of.
...
Nevertheless this theory would not answer the question why our universe is described by string theory

So TOE (as sterile set of equations) will be not the last step - we will need to draw the exact shape of the island of consciousness-friendly universes in the space of degrees of freedom of TOE. Are we in the center of that island? Are there any other separated islands? I would give my right hand to get an answer.

The ancient greeks called it "metaphysics" which means "beyond physics".

This "meta" is what I wanted to stress: the discussion regarding "mind" and "nature of a ToE" is (at least partially) metaphysics. But this is not a problem as long as we are aware of the fact that it is metaphysics and as long as we are able to talk about intrinsic limitations of physics.

This reminds me of a lecture with a very respectable physicist. Suddenly one of the more "philosophical" spectators asked: "I have the strong impression that the REAL cause is mathematics... Mathematics determines what is happening in the world... WHERE is this mathematics in three-dimensional space!?"

And the respectable physicist (now with long face) answered: "Well... I don’t have a clear opinion on that..."

I see two options:

• TOEEM - Theory of Everything except Mind
• TOEEM - Theory of Everything except Mathematics

 

[tom.stoer]

• TOEEM - Theory of Everything except Mind

No, not only "except mind"; there are several other entities to be excluded (I listed a couple of them); even "redness" - which is somehow related to "mind" - cannot be explained; "rednes"s is something else but a certain wavelength.

• TOEEM - Theory of Everything except Mathematics

Of course a ToE is based on mathematical axioms and cannot explain (but has to use) mathematics.

 

[feld]

ThudanBlunder,

If I understand your post correctly, you are saying that the physics community is struggling to develop a consistent theory of matter because of:
(1) its propensity for inventing mathematical theories that are devoid of physical reality;
(2) dysfunction in the system developed by the community for conducting research.

Why is the community failing to deliver? Here are some possibilities that occur to me:

(a) The next theoretical advance doesn't have to be a hard thing. In principle, there is little preventing anyone in the community from discovering it. But debates open up, conclusions are formed, the work is declared "done", the community moves on, in a herdlike fashion. So any issue that was not treated comprehensively in the past is unlikely to be done so again within the community.

(b) What is it that motivates a person to become a professional physicist? Love of mathematics? Thirst for knowledge? Or the all-too-human lust for status and security? (I have tenure! I'll never have to endure insults again! My retirement is assured!)

(c) Pressure to conform to doctrine, and fear of being outcast from the community. (Crank! Heretic! It's the factories for you!)

(d) Pressure to publish means researchers have no time to investigate the larger, more time-consuming problems. The library shelves fill up, and in turn, workers must spend more time keeping up with all the literature.

(e) A superficial expertise, gained from reading work done by others, rather than doing the work oneself. Knowledge gained through trial and error is precious, although it is inevitably more time-consuming, and hard to justify.

(f) Separation from society. Who challenges the community? No-one else speaks the language, no-one else has the "expertise". The community is safe from criticism. This is the same false paradise that is enjoyed by the bully. If physicists aimed to serve society, rather than look down on society, and if they strove to address the scientific questions society has, in a language that society can understand, then physics would be in a much healthier place. This may be a hard one for a member of the community to understand.

Actually I love theoretical physics, but I am enfuriated by the mess that is presently being served up by the physics community and being called theory. I am waiting for change to come, like many others, but I am not expecting the change to come from within the community. The community has demonstrated amply that it is interested in serving little but itself. If the community doesn't clean up its act soon, it risks becoming yet another irrelevant institution, which started with promising beginnings but has lost its way.

"We demand some more. Nature is a whore."

 

[tom.stoer]

Actually I love theoretical physics, but I am enfuriated by the mess that is presently being served up by the physics community and being called theory. I am waiting for change to come, like many others, but I am not expecting the change to come from within the community. The community has demonstrated amply that it is interested in serving little but itself. If the community doesn't clean up its act soon, it risks becoming yet another irrelevant institution, which started with promising beginnings but has lost its way.

How do you come to this conclusion? To which specific "community" and to which specific "theories" are you referring to? It seems that you have a rather limited scope, that you are disappointed with some singular aspect of theoretical physics and that you now generalize this disproportionately or inadequately.

 

[feld]

tom.stoer,

I am talking about the worldwide "community" of professional physicists, engaged in the pursuit of a unified "theory" of quantum theory and general relativity. I hope this is a clear enough definition.

I am expressing concern about the speculative turn that fundamental physics research has taken in the last few decades. It seems that the community has run out of good ideas to pursue. There have been fewer genuine discoveries made in the last few decades than in any time since Newton. This is somewhat embarrassing, given the number of professional physicists on the planet at the moment.

Naturally the nature of mind is an important topic. However I think theory needs to progress one step at a time, and at the moment the most pressing problems are the need to tidy up quantum field theory, unify the forces, and develop a more consistent cosmological model. Once this is done, the answers to other bigger questions may become clearer.

 

[tom.stoer]

I am talking about the worldwide "community" of professional physicists, engaged in the pursuit of a unified "theory" of quantum theory and general relativity. I hope this is a clear enough definition.

I am expressing concern about the speculative turn that fundamental physics research has taken in the last few decades. It seems that the community has run out of good ideas to pursue. There have been fewer genuine discoveries made in the last few decades than in any time since Newton. This is somewhat embarrassing, given the number of professional physicists on the planet at the moment.

Your definition is clear.
The observation regarding a "speculative turn" is somehow correct.
But the reason is imho due to the fact that we have seen a paradigm shift in the last ~30 years = since the SM except for the Higgs has been "verified".

The paradigm shift is that all new ideas (candidates for physical theories beyond the standard model) lack phenomenological or experimental support by construction. A new theory (strings, NGC, LQG, ...) is always based on two basic principles:
1) it must reproduce known physics => no new results for experimentally accessable domain
2) it completes SM+gravity beyond the accessible domain => new results are not accessable

So you cannot blame professional physicists for constructing a theory which can be verifyied only in a domain where it is (strictly speaking) not needed, which cannot be falsified in this domain (as it is constructed in such a way that it reproduces known results), and which can only be falsified in a domain which is unfortunately not accessible experimentally.

You see what my conclusion will be: the very principle of experimental input and falsification a la Popper is to be questioned. So what is required is a new principle (that's why I call it a paradigm shift) that supports and guides the construction of new theories. As long as this new principle is not available, we have to face the speculative turn for a while.

So one should not blame the majority of physicists for working on speculative ideas, but one should try to focus (in a small community) on this paradigm shift and its consequences.

 

[GeorgCantor]

Shots in the dark, this is what it's about. The easy part of the development of physics is over, there are no clear cut ideas to unification, no path seems promising or nearby.

The LHC could break the deadlock by either confirming some of the existing speculations/shots-in-the-dark or through a new, not as yet observed phenomenon. Exciting times, but at the same times somewhat depressing and hopeless.

 

[apeiron]

So you cannot blame professional physicists for constructing a theory which can be verifyied only in a domain where it is (strictly speaking) not needed, which cannot be falsified in this domain (as it is constructed in such a way that it reproduces known results), and which can only be falsified in a domain which is unfortunately not accessible experimentally.

Are you suggesting that this paradigm has much acceptance? It sounds quite contrary in fact. I would say instead that some rather unlikely theories (such as ones that suggest variable g, cosmic strings, clashing branes, etc) get support precisely because they offer the hope of being still testable.

So there is a prejudice (in an attempt to remain traditionally scientific - and probably also to keep the funds rolling for colliders and space telescopes) that favours the plausibly testable ideas rather than the ones that seem worthwhile for intuitive or philosophical reasons.

Still, I agree that there is a general question of how to proceed once we hit the limits of measurement. We will be back to doing meta-physics. But it need not be metaphysics as traditionally known.

For a start, it could indeed be a program of exhaustive mathematical search as with string theory - searching for deep pattern in a systematic fashion.

It could be (allied to this) a turn towards computers and simulation. This has already created one revolution with fractals and deterministic chaos. So where instruments can't reach, simulation might (and Loll's work on CDT is an example of course).

Personally, I think we also probably already know most of what we need to know. We just haven't packaged it all together. So this would be an argument that we have assembled many bits of the jigsaw, but also created such a confusion of other bits that we just have to filter the signal from the noise. We have been so prolific with ideas that the view is temporarily obscured.

So I would say that I see little evidence of any widespread support for the idea that the future of physics lies in systematic metaphysics. But perhaps in private, you may be arguing, this acceptance is taking hold. And now the issue is how to spin it to the public and the funding agencies as a bold advance rather than a rueful retreat.

 

[tom.stoer]

I agree that this paradigm shift is not widely accepted; it is not even recognized that there is such a paradigm shift, perhaps because we are no longer in the driver seat as we are no longer able to design instruments and experiments to verify / falsify new ideas.

First we have to acknowledge that the situation has changed! Then we can discuss (as we do here) how to respond.

I agree that there are some phenomenologically interesting ideas like clashing branes / ekpyrotic scenario, large extra dimensions, variable g and c etc. BUT: they are neither forced nor supported by experiment. So they are not a way out of the situation but simply an indication of this new paradigm.

Strictly speaking theoretical physicists could relax and say "there is no single experimental result that cannot be explained by our theories; so our job is done!"; of course they know their job is not done, but not due to new experiments but due to inconsistencies, incompleteness, missing axioms and guiding principles etc. This is the new situation.

I have the feeling that this discussion conerges somehow with the rather long thread regarding string theory we started a couple of weeks ago. But we can keep things separate. We can observe that there is this new situation and we should accept the paradigm shift. Then we can discuss if the way we respond (ST, LQG, CDT, NCG) is adequate or not (in the ST thread we do just this for ST).

It could even be that the LHC fails to produce an indication for future research: assume for a moment that the LHC finds the Higgs, disproves SUSY within below 14 TeV and rules out large extra dimensions. All what can be deduced is that e.g. SUSY / ST may be correct but at higher energies; or that asymptotic safety + SM could be the right way to go; or that NCG could be correct. ****! Billions of dollars / Euro for the simple result that everything we (or our professors or professors of our professors) guessed, constructed and derived a quarter of a century ago is correct.

I agree with you that - from the perspecive of ordinary theoretical physics - we are start to do metaphysics, but that - from the perspective of philosphers doing metaphysics - this is not ordinary metaphysics :-)

If you read Heisenberg's and Weizsäcker's books you will see that they were aware of the fact that physics and meta-physics are closely related. It is due to the fact that QM and the SM are extraordinary successfull we (~ 100 years later!) are no longer aware of this! But we can't close our eyes for another 25 or 30 yeras, we can't wait for the third, forth and sixth superstring revolution, we can't wait for the next generation collider (whatever it may be and regardless what it will cost) just to observe that something has changed fundamentally.

I do not say that all phenomenological research directions are nonsense - far from it! I only say that in parallel to ordinary physics, ST, LQG, NCG, CDT etc.we have to think about a new way, new principles, new guidelines of doing physics w/o experimental input.

 

[apeiron]

Well, the key problem for this new era would seem to be that there are no constraints to force a convergence of views. In science, the experimental evidence becomes a sharply decisive constraint. But in metaphysics, human ingenuity can probably spin an endless number of equally plausible scenarios. And there would be nothing to force people to prefer one over another.

So as a society, the more we spent on an army of post-doc meta-physicians, the more confused noise we might generate. We might feel we are making a bad situation worse - and this is what some may be feeling right now about theoretical physics.

Therefore the field might have to be structured differently. At the moment, a proliferation of views is tolerated/funded because in science, a single good experiment will cut them all down. As is hoped for with the LHC. But a big science project in meta-physics would have to apply its own discipline, its own constraints, on free speculation. What might that look like?

 

[tom.stoer]

What you describe is meta-physics as known from philosophy, driven mostly by categories of thinking deeply rooted in the nature human mind. What I have in mind is meta-physics driven by physical and/or mathematical/logical principles, but not necessarily experimentally dominated.

Your last question "what might that look like?" is the most important question in that context; to be honest: I don't know the answer.

But remember we have Fra here whi is interested in "inference of physical laws"; I have never really understood how this could help, but it seems to be an interesting idea.

 

[apeiron]

Your last question "what might that look like?" is the most important question in that context; to be honest: I don't know the answer.

Ah, Dr Stoer, welcome to the CERN institute for mathematical physics. You will first be visiting out zatta-flop supercomputer room where our experimental team rigorously simulate our candidate final theories. Then our psych lab where we carry out fundamental research on the embedded prejudices which might be blinkering our conceptual abilities. Later you will see our futures market where we use wisdom of the crowd techniques to isolate the most promising research initiatives (as you know, all funding is according to these ratings).

 

[DevilsAvocado]

No, not only "except mind"; there are several other entities to be excluded (I listed a couple of them); even "redness" - which is somehow related to "mind" - cannot be explained; "rednes"s is something else but a certain wavelength.

Yes, of course you are right. Let me ask you an "antipodal speculative" question – Is there any law in physics or that mathematics that prohibit us from ever find the "Theory of Ourselves"...?

(Over-speculative note: Let’s say that one day in the future, computers are going to be many times smarter than humans, and we can tell them to tell us who we really are... kinda... )

Of course a ToE is based on mathematical axioms and cannot explain (but has to use) mathematics.

Will http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis" agree on this?

 

[tom.stoer]

@apeiron: enjoy your next beer :-)

 

[tom.stoer]

Will http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis" agree on this? I don't think so.

To make one thing clear: I am not talking about a "theory of everything" where "everything" literally means everything. It means something like "all physical phenomena". If string theory (just as an example) would come up with a a fundamental formulation, a magic vacuum selection principle and a rigorous derivation of SM+gravity this would be my "theory of everything". It still would not able to derive concepts like "mind", "redness" and "apple", but I would be happy with it; it still would not be able to select itself from the space of all Tegmark-compliant theories, but I wouldn't care.

 

[DevilsAvocado]

Exciting times, but at the same times somewhat depressing and hopeless.

Is the glass half empty or half full!?

As a layman (that don’t have to struggle with mathematics!), I say it’s wonderful times! Exciting times!

The situation to me is very similar to when the Michelson–Morley experiment was performed in 1887. And we all know what happened after that...

And today we have a technology that would look like true science fiction to those old guys. We have very good knowledge of the "basics" – It’s just a matter of "getting it all together"; The Standard Model + Quantum Mechanics + Gravity + General Relativity!

 

[DevilsAvocado]

Strictly speaking theoretical physicists could relax and say "there is no single experimental result that cannot be explained by our theories; so our job is done!"; of course they know their job is not done, but not due to new experiments

And how do we explain EPR-Bell experiments without "escaping" to MWI...?

 

[DevilsAvocado]

it still would not be able to select itself from the space of all Tegmark-compliant theories, but I wouldn't care.

Agree.

 

[tom.stoer]

And how do we explain EPR-Bell experiments without "escaping" to MWI...?

Sorry for the confusion: "explain" simply means "predict measurable phenomena", not "explain an ontological concept".

 

[DevilsAvocado]

Okay, I understand.

 

[Dmitry67]

To what extent you expect TOE to end the 'interpretation war'?
It would be quite dissapointing if TOE would be compatible with several existing interpretatios (or new ones). I hope that TOE will show that Bohmian particles can't satisfy some conditions, so "at the end there will be only one" (c) Highlander.

 

[tom.stoer]

Eventually a ToE should address these interpretation issues, but this depends on which level this ToE acts. Interpretation issues are definately meta-physics (from the prospect of ordinary physics as known today)!

Let's make some examples:

• SM + GR is a ToE w.r.t. to all observable phenomena
• string theory is expected to be a ToE w.r.t. a completion and unification of SM+GR
• string theory may be in addition a ToE which turns the "space of possible theories" into a "space of solutions / vacua"

The last achievement is somehow the next level of ToEs, a meta-theory.

ST could turn out to be a framework for consistent theories. Of course this is something like "gauge theory" which is not a theory but a construction principle. I don't want to discuss the details of ST here (we have another thread), it should serve only as an example (of course not a very good one, because there is no commonly agreed answer to "what string theory really is?", but afaik it's the only theory that comes close to a ToE is therefore the only example I can think about).

To solve the interpretation issues I would have to add another bullet point. This is difficult as a) I do not know what to write there (ST does not help here, neither does any other theory I have ever seen) and b) even the last achievement of ST is questioned to be a true progress.

Let's phrase it that way:
- gauge theory+SR is a consistent framework for all known interactions except gravity;
- ST is a consistent framework for all known interactions including gravity.
If this were correct (it is not as gauge theory + SRT still lacks a sound mathematical basis and as ST has not been proven to be a consistent framework!) and if this is all ST is, than it's not a step forward into the direction of a ToE, it's only a broadening of the mathematical framework.

So ST seems to add some interpretation issues instead of solving them (in ST it's the landscape instead of the wave function). Perhaps this is true for other approaches as well.

Another question whether the interpretation issues are the main focus in developing a ToE. If yes it must provide means to discuss the relation between mathematics, physics and reality (in the ontological sense). So it must be meta-physics!

Look at Newtonian mechanics which deals with point particles. Does an euqation like F=m*a really answer the question what a point particle IS? Does it provide a means to discuss space, time, force etc. in an ONTOLOGICAL sense? It doesn't! Look at Kantian philosophy which deals with categories of the human mind, nature of space and time etc. If Newtonian mechanics would solve these issues, Kant's reasoning would not have been necessary. So even the simple framework of Newtonian mechanics doesn't tell us anything regarding the relation between mathematics, physics and reality in this simple context.

The only solution I can think about goes into Tegmark's direction of the mathematical universe; but I still do not like his idea very much as I think it's too early to close the eyes and say "since we cannot exclude it, we accept it as ontologically real".

A last point: any theory I have seen so far which is able to unify certain aspects in physics introduces new mathematical entities with rather unclear ontological status. Look at Maxwells theory: what is the true nature of the gauge potential? (a question that becomes interesting again in the context of QM and the Aharonov-Bohm effect); look at QM: what is the true nature of the wave function? what is the true nature of a time-dependent operator in the Heisenberg picture? what is the true nature of the Lagrangian in the path integral formalism?

A theory dealing with these interpretation issues can't simply pick a specific mathematical entity and explain what it IS staying blind about other mathematical objects one doesn't ike to explain. The ToE would have to explain the ontological status of ALL mathematical entities one has introduced; and be careful: even a proof and a calculation are mathematical entities. So the theory must explain the ontological difference or relation between a calculation of a scattering process and the scattering process itself.

My impression is a) that we do not have the tools / language / mathematical framework to even address these ontological interpretation issues and b) that we currently need not care about them as there is still much worl left for ordinary physics in construction a ToE in the limited sense of the two or first three bullet points.

 

[ConradDJ]

What you describe is meta-physics as known from philosophy, driven mostly by categories of thinking deeply rooted in the nature human mind. What I have in mind is meta-physics driven by physical and/or mathematical/logical principles, but not necessarily experimentally dominated.

I think Tom makes a very good point above – when the current theories already explain essentially all observable phenomena, it may no longer make sense to hope for new experimental discoveries to guide the development of theory.

On the other hand, we have some very large outstanding questions left over from the early part of the last century, like what does Quantum Mechanics mean, and how do we reconcile its foundations with those of classical physics and Relativity? It seems very clear that the metaphysical framework we inherit – our basic ideas about physical objects with definite properties moving around in space over time – isn’t adequate. And my problem with the “new paradigm” in the physics of the past few decades is that it follows the lead of purely technical, mathematical discoveries while more or less giving up on resolving these foundational questions.

Despite the tremendous advances in mathematical technology over the past century, at the conceptual level physicists are still operating with pretty much the same notions that were available in the 19th century. If we ask, what have we learned about the physical world since then? – well, we’ve discovered there’s a deep connection between space and time and gravity, that we know how to describe mathematically, but not in any other way. And we’ve found that essentially all the properties of things, including what they are and where they are and even whether or not they exist, depend on how and whether those properties are measured... but as to what that actually means, we don’t know.

When we say that all observable phenomena are “explained” by current theory, that’s true and very important. But since the theories that explain them are not understood at all, on the basis of any non-technical fundamental concepts, we still have a lot to learn about the world without going beyond the range of what’s already been empirically established.

My impression is a) that we do not have the tools / language / mathematical framework to even address these ontological interpretation issues and b) that we currently need not care about them as there is still much work left for ordinary physics in construction a ToE in the limited sense of the two or first three bullet points.

I agree with (a). But as to (b), I think the technical problem of reconciling QM and GR – finding a single mathematical formulation from which these two can both be derived – is a very poor substitute for the new insight we need into the nature of the physical world. If such a technical reconciliation ever succeeded in explaining all the complexities of the Standard Model, that would be a very great achievement – even if it still left us in the dark at an “ontological” level. But I doubt this will happen.

The basic idea of physics since ancient times is that the world consists of a certain set of given facts, and an ultimate theory will show that they all form one beautiful and simple mathematical pattern. But the role of measurement in QM, and the connection of gravity with space and time, and the “fine-tuning” of the parameters of the Standard Model, are to me all strong indications that something else is going on in the physical world besides beautiful mathematical patterns. And if this is so, then the quest for mathematical “unification” may have gone as far as it can usefully go.

 

[tom.stoer]

@ConradDJ: first of all thanks for this post; I fully agree with you; I only have to clarify b) a little bit better.

We started this discussion with some ideas regarding ToEs and unification; by that we usually mean unification of forces = standard model + gravity => e.g. string theory; one could as well interpret unification as unification of quantum mechanics + gravity => quantum gravity => e.g. loop quantum gravity != string theory. The latter program does explicitly not address unification of forces.

Both approaches are somehow unifications, but with different scopes and ambitions. I am pretty sure that both ST and LQG are acting on the level of the second bullet point. Both seem to be mostly unrelated, partially contradictory, totally different regarding mathematics that is used and/or required etc. I don't want to present a comparison regarding status, achievements, obstacles, etc., I only want to stress that there are different promising but still incomplete (!) reserach programs on the level of bullet point two or perhaps three.

That's way I think we are not yet read to discuss b) which is bullet point N, N>3.

 

[DevilsAvocado]

Another question whether the interpretation issues are the main focus in developing a ToE. If yes it must provide means to discuss the relation between mathematics, physics and reality (in the ontological sense). So it must be meta-physics!

Look at Newtonian mechanics which deals with point particles. Does an euqation like F=m*a really answer the question what a point particle IS?

This is very interesting. As a layman I interpret physics and mathematics as tools to make a "framework of predictions" of nature. But many times I find myself "marveling" about physics and "the true nature of nature". And I’m pretty sure that many amateurs "marvel" all the time...

Could it be (to me very possible) that we are still in the very early "childhood" stage of what an intelligent civilization really can achieve? After all, it’s only approx 100,000 years since we left the jungle in Africa to colonize the rest of the planet. And most of the science and technology we have today was discovered the last 100 years.

Could it be that in 50 or 100 years or so, we will find a mathematical ToE that will provide a "coherent framework of predictions" for everything in nature, but it will not tell us "what a point particle IS", or the true physical nature of an electron?

This work will be handled over to the coming generations to wonder about for a couple of 1000 years or so... and coming generations may find other tools than mathematics to find the true nature of nature?

After all QM has (almost) proved that there must be something wrong with our current axioms, and that QM 1 + 1 = 3 ...

To me it seems very unreasonable that current generations will have discovered everything in just 100-200 years, and then there is nothing more "to do" for eons... it just doesn’t make sense...

look at QM: what is the true nature of the wave function? what is the true nature of a time-dependent operator in the Heisenberg picture? what is the true nature of the Lagrangian in the path integral formalism?

This of course changes the picture completely. If the founding fathers of QM (Bohr, Heisenberg, Pauli, Born, et al.) was right; there is no underlying reality, no true nature of nature, just abstract mathematics, and probably not much for physicist "to do" in 102010...

My impression is a) that we do not have the tools / language / mathematical framework to even address these ontological interpretation issues and b) that we currently need not care about them as there is still much worl left for ordinary physics in construction a ToE in the limited sense of the two or first three bullet points.

Agree completely. My silly "layman-intuition" tells me; either mathematics is the real foundation for everything, and since mathematics is abstract, and it all originates from simple (binary) addition 1 + 1 = 2, the "reality" is also abstract, a freaking holographic simulation run by a freaking hacker "somewhere".

Or, mathematics is not the answer to everything, and we need other tools to go deeper...

(I prefer the later.)

 

[DevilsAvocado]

and the “fine-tuning” of the parameters of the Standard Model, are to me all strong indications that something else is going on in the physical world besides beautiful mathematical patterns.

Great! This is exactly what I have been wondering about!

If logical (human) mathematics is the foundation of everything, how "logical" is the http://en.wikipedia.org/wiki/Fine_structure_constant" ...??

The coupling constant characterizing the strength of the electromagnetic interaction, absolute crucial for everything we regard as the "reality"...

And a more personal speculation: What is the most natural shape in the universe? A box?? No, it’s naturally a sphere.

And what "natural" tool does mathematics provide to calculate circles and spheres? Yes, ∏:

[URL]http://upload.wikimedia.org/math/3/f/f/3ff406029245989360a3c1e3baf69b3f.png[/URL] . . .

To me, this doesn’t look like the most "natural" tool for the most natural shape in nature, but I could be wrong...


Richard Feynman referred to the fine-structure constant in these terms:

There is a most profound and beautiful question associated with the observed coupling constant, e the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!

 

[apeiron]

But the role of measurement in QM, and the connection of gravity with space and time, and the “fine-tuning” of the parameters of the Standard Model, are to me all strong indications that something else is going on in the physical world besides beautiful mathematical patterns. And if this is so, then the quest for mathematical “unification” may have gone as far as it can usefully go.

I would suggest that what is missing here in all three cases is a way mathematically to model constraint. Maths is very good for modelling constuction (the atomistic, adding together, bottom-up, way of making things happen). But it is harder to model that other part of reality, downwards acting, globally restricting, constraint.

So the measurement issue in QM is all about what imposes the constraints on QM uncertainty (the conscious human, the thermalising environment, etc? - something does, but how do we model that factor?).

Likewise GR. Spacetime has the thermodynamic property of wanting to be flat - to dissipate all curvature and arrive at a heat death. Gravity fields are gradients of curvature created by clumping mass, but that is a secondary and passing story. So to complete GR as a story of spacetime, we would seem to need some model of why "spacetime wants to be flat" - what is the nature of that global constraint? (Dark energy is of course a further complication).

Same again with the fine-tuned constants most probably. Constants arise in dynamical systems as equilibrium balances. They self-organise via global expression of emergent constraints. OK, this is a bit hand-wavey. But I am thinking of examples like Feigenbaum's constant and universality. When periodicity goes to infinity, there is a convergence on a limit.

So I am arguing that there is a general unrecognised problem. We have been very good at modelling things using notions of bottom-up constructive action, but have not developed descriptions of the top-down down constraints that are also a shaping part of any system.

This is exactly the story for string theory for example. It started with a different kind of "atom" - a loop instead of a point. And it has generated a landscape of possible solutions. But there is no model of the constraints that might act upon that landscape to narrow it down to some particular choice.

Yet there is hope because there are many people now looking at condensed matter approaches to fundamental questions. And this is a constraints-based way of thinking. Particles as solitons and instantons. Wilzcek's condensates. Wen's string nets. I would say gauge symmetry breaking is generally a constraints-based idea still seeking a model of its constraints.

Condensed matter approaches also have that intuitive content you are seeking. It is easy to understand why a soliton looks and behaves like a particle.

So to me, a ToE is mostly about making that shift from a collection of partial bottom-up models like QM and GR to a single general model that puts together both construction and constraint, the parts and the whole, into a mathematical description.

 

[apeiron]

This of course changes the picture completely. If the founding fathers of QM (Bohr, Heisenberg, Pauli, Born, et al.) was right; there is no underlying reality, no true nature of nature, just abstract mathematics, and probably not much for physicist "to do" in 102010...

I think the situation has to be read the other way round. What QM showed was constraints must be applied to uncertainty for certain reality to exist.

OK, this now points to a further piece of mathematics that is needed - a model of indeterminancy or vagueness. Our current models of naked potential are probablistic - a set of crisply existent microstates. We know from QM that this does not work. There are no hidden variables, just an unformed potential awaiting measurement. But we don't have a model of raw indeterminancy - a state without definite microstates.

So we have good models of construction (and probability theory is constructed additively from crisply existing microstates). But poor models of constraint and hardly anyone modelling vagueness (states of unformed potential).

BTW, these are all very ancient metaphysical concepts. Which is the irony I guess.

 

[Hurkyl]

I would suggest that what is missing here in all three cases is a way mathematically to model constraint. Maths is very good for modelling constuction (the atomistic, adding together, bottom-up, way of making things happen). But it is harder to model that other part of reality, downwards acting, globally restricting, constraint.

I'm not sure where you got the idea that math doesn't work well for top-down -- that is one of the major strengths of the axiomatic method that is often used in mathematics, and two of the major activities of mathematicians are:

• Given a list of properties, find one/all objects that have those properties
• Given interesting objects of study, find "top-down" characterization of them

Maybe I'm just misinterpreting what you mean by "top-down"? *Shrug*

 

[GeorgCantor]

So we have good models of construction (and probability theory is constructed additively from crisply existing microstates). But poor models of constraint and hardly anyone modelling vagueness (states of unformed potential).

It's not just that. We have very poor understanding of matter(on top of space, time and motion). Given the wave nature of matter, the HUP and qm's indeterminancy, we have very little understanding of why some energy fields appear as stationary matter, while others are manifested as electromagnetic waves. Probabilities, interpretational games and "shut up and calculate" are a disservice to science. Hopefully, these 'what' questions will not remain meta-physical and philosophical for long.

Pretty much everyone in the field understands that the universe is quantum in nature(as opposed to being classically naive), but nobody understands what the heck is going on in the so-called reality. There are probably as many opinions on this as there are physicists on the planet, ha ha.


Abandoning realism is very heavy price to pay, but if one really thinks about it in a non-naive fashion...hmm...

 

[GeorgCantor]

I'm not sure where you got the idea that math doesn't work well for top-down -- that is one of the major strengths of the axiomatic method that is often used in mathematics, and two of the major activities of mathematicians are:

• Given a list of properties, find one/all objects that have those properties
• Given interesting objects of study, find "top-down" characterization of them

Maybe I'm just misinterpreting what you mean by "top-down"? *Shrug*

Did you, by any chance, have in mind the Schroedinger's equation as the top-down causative agent describer?

 

[Hurkyl]

"Top-down causative agent describer?"


I would certainly call Schrödinger's equation a fairly low-level detail, especially in partial differential equation form. (but admittedly, I am not a physicist, so take my opinion with a grain of salt)

 

[apeiron]

I'm not sure where you got the idea that math doesn't work well for top-down -- that is one of the major strengths of the axiomatic method that is often used in mathematics, and two of the major activities of mathematicians are:

• Given a list of properties, find one/all objects that have those properties
• Given interesting objects of study, find "top-down" characterization of them

Maybe I'm just misinterpreting what you mean by "top-down"? *Shrug*

You have got it right. Axioms are global constraints. But we don't then have a model about the formation of axioms themselves. We only have an informal (metaphysical) approach to the creation of axioms. They appeal to us via intuition. And then confirm themselves because they seem to work (good maths arises from using those axioms - allowing them to constrain our thinking). But we do not have an explicit model of how global constraints (axioms, and the laws of physics, being examples) arise in nature.

So you are saying maths uses constraints. I am talking about the mathematical modelling of the emergence of such constraints.

 

[tom.stoer]

then you are talking about meta-mathematics

 

[ConradDJ]

I would suggest that what is missing here in all three cases is a way mathematically to model constraint. Maths is very good for modelling construction (the atomistic, adding together, bottom-up, way of making things happen). But it is harder to model that other part of reality, downwards acting, globally restricting, constraint.
...
So I am arguing that there is a general unrecognised problem. We have been very good at modelling things using notions of bottom-up constructive action, but have not developed descriptions of the top-down constraints that are also a shaping part of any system.

I agree with you as regards “constraint” being what’s missing from current theory. That is, given all the structural possibilities we can describe mathematically, why is it that certain very specific structures are built in as the universal laws, principles and constants governing the world? What’s missing is a way of explaining why we have so many very different kinds of underlying structure, operating at different scales in different kinds of situations.

But what you’re looking for – in Tom’s words – is a meta-mathematics that will give you a purely logical / formal source of constraint, and that doesn’t seem promising to me.

If you look at the situation in biology, it’s clear where the constraints come from. Organisms have to survive and reproduce in a physical environment that makes these things very difficult to accomplish. So the source of all the myriad constraints involved in “natural selection” are already there, given what life-forms have to do, in order to exist.

I think the problem we have in understanding physics is that we take what it’s doing for granted. We don’t see it as a functional system, because we take it for granted that there exist real entities with intrinsically definite characteristics, that there is a well-defined structure of space and time for them to exist in, and that they interact with each other in ways that make all of this structure physically observable. Despite the lessons of QM, among many other things, we’re still treating the physical world as a body of given fact that just is whatever it is – it doesn’t have to “accomplish” anything. And therefore, where the constraints come from is a mystery.

If the world is just a body of given fact, then the only way to explain it is to show that all those facts can be derived from simpler, more general facts – ideally, from purely formal principles. For you, these would be systems-theoretic principles rather than, say, purely geometric ones.

So the measurement issue in QM is all about what imposes the constraints on QM uncertainty.

Just to take this one example – QM is quite clear about what “constrains” a system to be in a certain place or to have a certain spin-orientation, or whatever. Physically measuring the system does that – i.e. putting it in a context of interaction in which information about its state makes a specific difference to the state of another system which makes a difference to some other system, etc. What makes this hard to understand is that we usually take it for granted that information about systems can be physically determined and physically communicated – we don’t ask what the functional requirements are for a system of interaction to do these things. Now in fact physicists have a tremendous amount of practical knowledge about how to measure things... but it isn’t seen this as relevant to the foundational issues, because they’re still looking for a purely formal explanation rather than a functional one.

Many times your approach to systems structure seems very insightful to me... but I don’t follow you in this traditional quest for the formal / mathematical principles that explain why systems are as they are.

 

[apeiron]

then you are talking about meta-mathematics

I was certainly pointing out the generality of this issue concerning global constraints - the issue of modelling contextual causes.

In the philosophy of maths, there is a divide between those who are platonists and those who are constructionists. The platonists make the claim that maths (our models and the axioms they are founded on) are irreducibly real. The constructionists say they are just the free creations of the human mind.

Neither of these extreme positions are satisfactory, though each seems to have some truth. I would argue that maths is just modelling and so basically constructed. A human mind has to chose the axioms. But also certain axioms seem natural. Reality seems constrained in its patterns and we can follow that in our modelling. However, to be really satisfactory, we ought to have a better understand how such constraints arise in nature. And that would strengthen the whole business of axiom choice.

Now there seems a fairly straightforward answer here. It is something we have already long done. Metaphysics is based on dichotomies - definitions based on mutual constraint.

So we have the "axiomatic" dichotomies that became foundational in Greek metaphysics such as discrete~continuous, stasis~flux, chance~necessity, substance~form, atom~void, etc.

Discrete is defined by its lack of continuity, and continuity by its lack of discreteness. Each state acts as a constraint on the other. I know I have discreteness because I know I have the utter absence of its other, continuity. But continuity must also exist, otherwise how could I know it was absent?

(Louis Kauffman wrote a good paper on modern attempts by mathematicians/logicians like CS Peirce to create a notation which captures this relation...
"The first Peirce notation is the portmanteau (see below) Sign of illation. The second Peirce notation is the form of implication in the existential graphs (see below). The Nicod notation is a portmanteau of the Sheffer stroke and an (overbar) negation sign. The Spencer-Brown notation is in line with the Peirce Sign of illation."
http://www2.math.uic.edu/~kauffman/CHK.pdf)

Anyway, the point is that there is already a royal road to axiom-strength metaphysics (which in turn created the basic concepts of both science and maths). The dichotomy is a system of mutual constraint such that we are always left with two mutually exclusive alternatives (thesis and antithesis) and yet there is also the deepest connection between them (as each needs the other for it to be known to exist).

So in science, this is why atom~void, or signal~noise, have become foundational concepts. They divide reality into its mutually exclusive possibilities. A process of mutual constraint gives us no other possible choice but to arrive at these very notions!

The same has happened in maths with category theory. It has been agreed that the basis of mathematical thinking is the foundational dichotomy - structure~morphism. There has to be the bit that does not change, so that there can be the other that is "just the change".

So landscapes (as bedevil string theory, modal logic, multiverses, constructivism, etc) are the result of unconstrained possibility. If you say this, then why not that, this, and the other too? There are no limits to self-organise the terrain. We can get arbitrary and shout, well just choose one. But there is no strong reason to back us. We are imposing a constraint on choice in a way that does not deal with all the other possible choices.

But if instead we step back and say constraint operates freely, we will find that only dualities can emerge as constraint is maximised. Only dualities have mutually reinforcing stability. Each depends on the pure denial of the other, and not a collection of others.

It is so simple. If you presume a space of unlimited possibility (Anaximander called it the Apeiron, Peirce called in Vagueness) and insist it must self-organise through all its possible interactions, then all the conflicting interactions must act on each other in contextual, constraining fashion. It is a symmetry and symmetry-breaking story. And as this seething activity sorts itself out, it must arrive eventually at the maximally constrained state of an asymmetry - a pair of polar opposites that mutually define each other (and exclude all other possibilities in doing so).

Constraint has the power to organise possibility. And the most organised states are dichotomous. Mutually defining.

We see this already everywhere in philosophy, maths and science. Even string theory has discovered its dualities (why three of them is a bit harder to explain). But we are not recognising constraint as an epistemological principle (and so dualities are usually taken to be troubling and paradoxical rather than exactly what good theory should yield).

 

[GeorgCantor]

Now there seems a fairly straightforward answer here. It is something we have already long done. Metaphysics is based on dichotomies - definitions based on mutual constraint.

So we have the "axiomatic" dichotomies that became foundational in Greek metaphysics such as discrete~continuous, stasis~flux, chance~necessity, substance~form, atom~void, etc.

And the deeper we delve, the more clear it becomes that these are false dichotomies. Is the Mandelbrot set a discrete or a continuous example?

At a deeper level, both alternatives become one and the same.

Discrete is defined by its lack of continuity, and continuity by its lack of discreteness. Each state acts as a constraint on the other. I know I have discreteness because I know I have the utter absence of its other, continuity. But continuity must also exist, otherwise how could I know it was absent?

True, but how far can this reasoning take us?

I'd go so far as to say that at the deepest level, the distinction between the universe and the self is anything but clear.

 

[tom.stoer]

@apeiron: Remarkable post!

@GeorgCantor: the question is not if these entities exist is a "phenomenological" sense, but if they exist on a deeper level. I think apeiron has made a very good point in focussing on their existence in order to define two antithetic entities.

Let's make a simple example: Assume you go to a pub in order to meet a friend. You are late by 30 minutes, you step into the pub, look for you friend and observe that he/she is not there. In that case it's his/her ABSENCE that exists for you and that becomes (somehow) phenomenologically real (as mathematics itself has no phenomenological level the example does not aply directly).

Your objection that two antithetic entities may become more or less the same points into the direction of a synthesis (according to dialectics) which does not automatically mean that the dichotomy itself becomes useless or meaningless.

 

[GeorgCantor]

Your objection that two antithetic entities may become more or less the same points into the direction of a synthesis (according to dialectics) which does not automatically mean that the dichotomy itself becomes useless or meaningless.

I meant to push the dichotomies further and deeper, that's where the dichotomies break down. Of course your pub example is valid at the level of existence of macro objects.


The point is, these examples(the dichotomies) are not and cannot be a fundamental description(constituents) of reality. How about this dichotomy:

Is a fundamental particle a wave(continuous) or a particle(discrete)? Is it both, or is it neither? What happened to the dichotomy that we know from the macro world of pubs and people?

 

[tom.stoer]

Is a fundamental particle a wave or a particle? Is it both, or is it neither?

Neither! But we ca talk about this "neither" only because we know what waves and particles "are".

btw.: the pub example is not mine, it's Sarte's :-)

 

[GeorgCantor]

Neither! But we ca talk about this "neither" only because we know what waves and particles "are".

When you say "Neither!" you are confirming the false dichotomy of discrete-continuous(or you are remaining agnostic on the issue?).