LHC - the last chance for all theories of everything?

[RUTA]

You know, there are some naïve questions like “what is space?”. People tend to ask such questions because of the intuitive conception that if something is not made of something then it is void and collapses. So the most satisfactory answer would be “space is made of spacions”. “Ah, yes, it makes sense”. Of course, after a while they would start wondering what spacions are made of.

We always had a situation that something was made of something: molecules of atoms, atoms of elementary particles, then came quarks, now we expect them to be made of strings. We so got used to it that we are not psychologically ready to the fact that in TOE that infinite reduction MUST END.

We make exactly this point in the Conclusion of arXiv 0908.4348. Our answer is to put a self-consistency criterion at bottom, i.e., a mathematical co-definition of space, time and divergence-free sources (QFT parlance), that underwrites a discrete action for the path integral in the transition amplitude.

 

[tom.stoer]

First of all I don't think that you responded to reason 2 and 3. Regarding Ockham's razor and reason 1 we should not waste too much time.

Some clarifications and remarks:

Each removal adds new information... contains MORE information than a list of ALL integers), so each removal must be justified.

I do not want to create selection rules by hand - I expect them to arise automatically. The idea regarding lifetime (see below) is one example.

It is not CONVERTED. It IS WORLD.

I do not mean "converted during a process", but "converted during our philosophical discourse". It's not the description that's converted into something but our understanding about the mathematical framework. So forget about this.

... there are some naïve questions like “what is space?”

That's not naive, that's a question which drives the whole scientific progress! w/o the question "what are atoms" we would not know anything about quantum mechanics.

... if something is not made of something ...

That's not my intention. I do not want to reduce the entities of the ToE to some more fundamental entity. This can happen, of course, but it's not required. In philosophy you can ask "what is goodness?" or "why does something exist instead of nothing?" or "what is time?" These questions do not automatically imply reductionism.

... he insists that there is nothing behind the curtain – no spoons, no realityons, no supercomputers. Fundamental notions are fundamental only if they do not consist of anything. Fundamental notions do not need any agents to be “incarnated”. Otherwise they are not fundamental and the theory is not a TOE.

But a mathematical framework consists of "something"; it consists of fundamental entities like an alphabet, definitions, rules and axioms. How do you "create" a mathematical framework out of nothing? You can only "create" it out of these constituents. But as I said above, that's not my basic concern here.

You are mixing 2 things:
(A)“eternal” as “lasting for eternity of time” = “being infinite in time”
(B) “eternal” as “existing independently of time” = “something to which a concept of time is not applicable”

Maybe I was not so accurate here, so I try again.

My basic intention is INDEED to mix these two "categories of existence", simple because the theory you are describing FORCES me to do this.

I start with my statement that each mathematical framework is eternal; there seems to be no meta-mathematics which "creates" or "kills" mathematics. So as mathematics has not been "created" at some "time", all mathematical frameworks are eternal, too.

The mathematical frameworks in question do not exist "in physical time" because time (and space) are entities "emerging" from these framework (not necessarily from all frameworks, as the ToE may allow for universes where physical time does not exist.

Up to now I do not mix these to "categories of existence". No my reasoning is as follows:

If some specific mathematical framework DESCRIBES a universe, the existence of the framework and the existence of the universe are two different "categories of existence"; therefore their "lifetimes" are independent. Whereas the description of the universe exists "before" the universe is "created" and after it "dies", the universe itself has a finite (physical) lifetime.

If a universe with finite "physical existence" IS IDENTICAL WITH the corresponding mathematical framework, you are in trouble. Either you have to forbid by some selection rule universes=frameworks with finite lifetime, or you have to lift the framework to some meta-level where its existence and "lifetimes" is again independent.

You are telling me that the universe and the framework are identical. So there must be a one-to-one correspondence of all entities, structures and aspects including EXISTENCE; especially you have to specify, what it means on the level of the framework that "the univeses dies" = "its existence comes to an end" = "the mathematical framework dies".
Either the existence of the framework comes to an end, too, then you have to explain what that means in pure mathematics, or the theory rules out universes with finite lifetime, or the framework does not die, but then its not identical to the universe in all aspects which contradicts your theory.
You have to explain how these sentences correspond to each other and how they can be formulated in a mathematically well-defined way.

Assume you are right and we are living in a universe=framework created by a big bang from nothing. What was the mode of existence of the framework before the big bang and how has it been created?

 

[tom.stoer]

Not to forget - what do you think about my ideas:

... I would like add an idea how ToEs could be categorized:
- first requirement is that the ToE incorporates all known interactions in some way, e.g. as low-energy effective theories
- second requirement is that the ToE is a consistent mathematical framework, i.e. it must be mathematically well-defined
- third requirement is that the theory must post-dict at least some known facts like the standard model gauge symmetries, number of generations, number of space-time dimensions etc.
- forth requirement is that the theory must predict new phenomena which should be (at least in principle) falsifiable by experiment
A (meta) requirement) for a (meta) ToE is that the theory in question can at least support why she is the ToE. That means if the ToE contains a certain mathematical structure, there should be an explanation in terms of deeper structures or insights why this structure MUST be contained. This is subtle, of course. Example: if the ToE is grounded on local gauge symmetries, I would like to know WHY.

 

[Dmitry67]

First of all I don't think that you responded to reason 2 and 3. Regarding Ockham's razor and reason 1 we should not waste too much time.

Reason 2: All discussions regarding the multiverse idea (many-worlds interpretation, landscape) I ever participated in came sooner or later to a point which I would describe like "I cannot explain why it's this way or that way - and therefore it's both ways!" That's not a sientific argument but an excuse only.

Reason 3 - and this is the most important one: even if you insist on the multiverse idea, it is by no means clear why ALL logically consistent ToEs should be physically real - why not only a certain subset? Compare it to evolution: not ALL possible species are alive, but only a certain subset. Why is this? Simply because there are selection rules (not hand made, but external to the species' ToE framework = the DNA, namely the environment) which suppress or constrain the evolution. In our case this could be some meta-theory, but nevertheless it must not be excluded.

No, it is exactly about the occams razor. Reason 2- I DID explain. The burden of proof is yours. Not I should explain why other universes exist, but you must proof that they don’t. See may explanation about justification of addition and removal. You can not agree with my reasoning, then let's discuss it. But your ‘Reason 2’ is just variation of Reason 1. The same for Reason 3 – again, it is variation of the same question, don’t you see? Yes, I insist that ALL Toes are physically real and there is no selection rule.

 

[Dmitry67]

If a universe with finite "physical existence" IS IDENTICAL WITH the corresponding mathematical framework, you are in trouble. Either you have to forbid by some selection rule universes=frameworks with finite lifetime, or you have to lift the framework to some meta-level where its existence and "lifetimes" is again independent.

You are telling me that the universe and the framework are identical. So there must be a one-to-one correspondence of all entities, structures and aspects including EXISTENCE

I recommend you checking the concept of Block Time:
http://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time )

Time does not "move". Universe is not a "movie". It does not "dies". "NOW" is just an illusion. Past is as real as future.

You are claiming that video tape turns to dust as soon as observers see "THE END" title, or Videogame self-destroys on your computer as soon as you go thru it to the very end.

Mathematical frameworkd is an analog of a program or a videotape.

If you have a universe which exists limited time (say from Big Bang to Big Rip) then the mathematical system describes it completely, from the very beginning, to the very end. it is a tape. You can look at it over and over. You can move at any direction.

As you know from SR, time is dimension (slightly special). Now replace time with space and repeat your reasoning. So, if universe is finite (limited volume) and say is only 100 meters long, the you say, I am in trouble, because my formulas disappear to the left or to the right from the universe :)

 

[Dmitry67]

Not to forget - what do you think about my ideas:

- first requirement is that the ToE incorporates all known interactions in some way, e.g. as low-energy effective theories
Agreed

- second requirement is that the ToE is a consistent mathematical framework, i.e. it must be mathematically well-defined
Definitely

- third requirement is that the theory must post-dict at least some known facts like the standard model gauge symmetries, number of generations, number of space-time dimensions etc.
Yes

- forth requirement is that the theory must predict new phenomena which should be (at least in principle) falsifiable by experiment
It would be good, but I am not sure.

A (meta) requirement) for a (meta) ToE is that the theory in question can at least support why she is the ToE. That means if the ToE contains a certain mathematical structure, there should be an explanation in terms of deeper structures or insights why this structure MUST be contained. This is subtle, of course. Example: if the ToE is grounded on local gauge symmetries, I would like to know WHY.
- Ha Ha.
I can not help you with it.
At first you violate occamz Razor and invent an unneeded notion - "selection rule"
They you ask: what properties does that rule have?
I don't have a selection rule, then I don't need to answer that question

 

[tom.stoer]

No, it is exactly about the occams razor. Reason 2- I DID explain. The burden of proof is yours ...

Sorry, but that's demonstrably false!

We see, observe and live in exactly one universe. All other universes (frameworks, ToEs, ...) are speculations and not accessible experimentally. Therefore they are metaphysical ballast - as long as you cannot show that they MUST exist.

 

[RUTA]

No, it is exactly about the occams razor. Reason 2- I DID explain. The burden of proof is yours. Not I should explain why other universes exist, but you must proof that they don’t. See may explanation about justification of addition and removal.

In general, the burden of proof is always on the positive claim. For example, if I claim ghosts exist, it's incumbent upon me to prove they exist, not you to prove they don't. If you claim QM entails multiple worlds, then that's something you must prove and in this case, since there are interpretations of QM without MW, the proof/evidence would have to be experimental.

 

[tom.stoer]

Mathematical framework is an analog of a program or a videotape.

If you have a universe which exists limited time ..then the mathematical system describes it completely ... it is a tape.

You do not understand my point.

In my opinion there are two "categories of existence", a) the video tape and b) the movie (I do not have a problem with this point you view)

In our opinion these two categories have to be identified, the video tape (framework) and the movie (universe) are identical. But then you have to identify all aspects, entities and structures of the tape and the movie as well. If you can't do that, you failed to identify these concepts.

My impression is that you (partially) still refer to the framewortk as something that is external to the universe, something that is "only" its description. If you idea is right, then it provides not only a MAPPING between structures of the tape and structures of the movie, it provides an IDENTIFICATION.

Let me ask one easy question: do you think that the word "apple", the meaning of "apple" in the english language, the representation of an apple as picture, as "entity" on your retina / in your brain and as wiki article are identical? You do you think they are different aspects of one ontological nucleus?

 

[tom.stoer]

Agreed ... Definitely ... Yes ... It would be good, but I am not sure.

Thanks!

Ha Ha.

Of course I expected this answer :-)
Are there other opninions as well?

 

[tom.stoer]

... if I claim ghosts exist, it's incumbent upon me to prove they exist, not you to prove they don't...

Thanks!

 

[Dmitry67]

In general, the burden of proof is always on the positive claim. For example, if I claim ghosts exist, it's incumbent upon me to prove they exist, not you to prove they don't. If you claim QM entails multiple worlds, then that's something you must prove and in this case, since there are interpretations of QM without MW, the proof/evidence would have to be experimental.

Yes, and the positive claim is in this case is "selection rule exists"
"Positive" is what is adding new information
Burden of proof is on the party which is adding new information

I copy what I said before, if you don't agree with the logic please tell me where:

Occams razor. In informational sense, “information should not be multiplied unnecessarily”. When we build something, we add building blocks, adding new information an every step. That is why every new stone you put in the building must be well justified. However, using this method you can add only finite number of stones/entities. You can’t define integers by providing a complete list, right?

When we manipulate with infinite numbers of entities we go in the opposite direction: we start from the Universum, and then remove something. Each removal adds new information (and list {12438, 59859599, 858585, 77} contains MORE information than a list of ALL integers), so each removal must be justified.

It seems you understand it and for that reason you call a “selection” rule (selection – taking one from many = removing others). Again, you are not asking how to justify the creation of OUR universe( that would be natural for one going from nothing to the Universum), you seek the justification of removal for the others. So we are on the same page.

But: if we go in the opposite direction, from the Universum, then any REMOVAL adds new information and hence is a subject of Occams razor. Going from nothing to the Universum we must justify any addition, going back we must justify any removal. You mentioned Occams razor and on the very next step started inventing NEW entity which you call a “selection rule”. Do you agree with my logic?

So Occams razor is the very reason I believe other Universes exist.

 

[Dmitry67]

Sorry, but that's demonstrably false!

We see, observe and live in exactly one universe. All other universes (frameworks, ToEs, ...) are speculations and not accessible experimentally. Therefore they are metaphysical ballast - as long as you cannot show that they MUST exist.

Please also tell me where exactly you don't agree with my logic about the Occams razor (above)

 

[tom.stoer]

I do not agree that the selection rule is the positive claim. My statement is that "other universes do exist" is the positive claim.

Maybe your proposal does not add information, but it adds an ONTOLOGICAL ENTITY for which you CLAIM existence w/o being able to PROVE existence. Either you can prove it experimentally or you have to demontrate it by other means. Otherwise these entities (universes) are metaphysical speculations.

 

[RUTA]

Yes, and the positive claim is in this case is "selection rule exists"
"Positive" is what is adding new information
Burden of proof is on the party which is adding new information

I copy what I said before, if you don't agree with the logic please tell me where:

I'm talking about ontology, you're talking about methodology. Ontologically speaking, you're claiming MW so you need an experimental result consistent with MW and inconsistent with a single universe.

For example, suppose you start methodologically with "Everything imaginable exists." According to you, qualifiers such as "A thing must have empirical consequences" would be a negative, so that it is incumbent upon your skeptics to prove unicorns don't exist.

 

[Dmitry67]

Lets talk about integer numbers.

Empty set, like a set of ALL integers is only one. It is, physically speaking, in the lowest entropy state.

Now I add a number, say, 34553. I add new information. There are mnay different lists which contain only one n umber, right? Interestingly enough, the set of all integers minus one number has the same property.

Now I add a second number, second entity. Now I have a combination of 2 numbers, and I have even more information. Adding more and more numbers to my list I add more and more information.

But this is true only if I add a finite number of integers. I can add an infinite number of integers, filling all voids, thus making my list a full list of integers. So adding an infinite number of integers I had reduced information!

So give an example,

{} - empty set - 0 bits.
{n} - one number - info about 1 number
{n,m} - 2 numbers - info about 2 numbers
...
{all except n,m} - info about 2 numbers
{all except n} - info about 1 number
{all integers} - universum - no info

I attract your attention to the fact that information at first increases and then decreases.

Maybe your proposal does not add information, but it adds an ONTOLOGICAL ENTITY for which you CLAIM existence w/o being able to PROVE existence.

No. I don't add AN ENTITY. If I would be adding ONE entity you would be absolutely right.

I am adding an infinite number of entities to a list with one element (only our universe). The list I add in complementary to that list and union becomes a Universum - a list of all possible universes.

Hence I decrease an information, and occams razor is on MY side.

 

[RUTA]

Lets talk about integer numbers.

So give an example,

{} - empty set - 0 bits.
{n} - one number - info about 1 number
{n,m} - 2 numbers - info about 2 numbers
...
{all except n,m} - info about 2 numbers
{all except n} - info about 1 number
{all integers} - universum - no info

I attract your attention to the fact that information at first increases and then decreases.

This has nothing to do my claim about methodology and ontology, but I believe your claim is false. In fact, I would argue that the set of all integers contains an infinite amount of information. To make my point, produce the set -- not the words "all integers" but the elements themselves.

 

[Dmitry67]

"You are wrong"
These 13 characters gives you some information.
Now I provide you a list of all 26**13 combinations of characters. Beginning from AAAAAAAAAAAAA to ZZZZZZZZZZZZZ. Somewhere in the middle you will find "YOU ARE WRONG" and "YOU ARE RIGHT". What information you have now? Nothing!

And asking me to write all integers... Science would end if we stop at the level of "2 apples plus 3 apples makes 5 apples". How do we suppose to work with infinite sets if we need to write all the elements?

 

[RUTA]

And asking me to write all integers... Science would end if we stop at the level of "2 apples plus 3 apples makes 5 apples". How do we suppose to work with infinite sets if we need to write all the elements?

This has nothing to do with the progress of science, we're talking about how much information is contained in the set of all integers. I say it's infinite and you say it's zero. To argue my point, all I have to do is "play dumb" and require you to give me the information explicitly, i.e., list the elements of the set. If you're correct, you have nothing to send me. If I'm correct, you have an infinite number of numbers to send me. That's my argument.

How does this bear on the original post for this thread? I've lost track.

 

[tom.stoer]

... and occams razor is on MY side.

No it isn't.

From a ontological point of view we can be sure that one universe exists; everything else is speculation.

From a computational-complexity point of view there is no difference between the two statements
a) one universe exists
or
b) all possible universes exist - except one
Of course specifying the one in both cases should require the same amount of information.

Similarly computationally the statements
a') no universe exists
and
b') all possible universes exist
have the same complexity.

If you argue strictly based on computational complexity and with Ockams razor, then you cannot distinguish between a') and b') nor can you distinguish between a) or b). So in order to do that you have to refer to some experimental result, i.e you have to enlarge your reasoning beyond computational complexity.

You do that by taking into account "known facts" and by going from a mathematical to an ontological reasoning. Of course you can rule out a') immediately. You can trust in a least one universe which means that ontologically and based on Ockams razor you should not add more assumptions than strictly necessary. So you add the assumption that one universe exists and - wow - it agrees with the known facts. If you would instead add an uncountable set of universes it would still agree with the known facts, but you have to explain why "they are there but invisible". Therefore you add assumptions which you cannot prove.

And don't forget: you cannot use your "mathematical multiverse hypothesis" as starting point for your proof as your quest is just to prove exactly this "mathematical multiverse hypothesis".

 

[Vanadium 50]

If you have a link handy to some particular abstract from the conference you were talking about, I'd be glad to give a look.

Sorry - it wasn't exactly handy. See http://www.auger.org/technical_info/ICRC2009/arxiv_astrophysics.pdf" for the Auger view: "The evidence for anisotropy has not strengthened since the analysis reported in [1]. The degree of correlation with objects in the VCV catalog appears to be weaker than suggested by the earliest data."

As you know, HiRes sees no such correlation.

Nature's http://blogs.nature.com/news/blog/2009/05/aps_2009_pierre_auger_backs_of.html" says "And now, today, Stefan Westerhoff, an Auger scientist from the University of Wisconsin at Madison, said that, based on new particle detections -- they have more than 50 now -- the correlation no longer holds. "The signal strength is certainly considerably weaker now," he told his audience. "This is certainly a disappointment."

The proceedings of that conference (APS 2009) unfortunately seem not to be available yet.

 

[marcus]

Fantastic!
this makes UHECR more of a mystery.
Maybe we should have a separate thread to keep track of this, but for now I will continue in context. Here is more of the 3 May quote about the Auger news at APS meeting:

==quote Nature.com==
APS 2009: Pierre Auger backs off claims for cosmic ray source

The mysterious origin of ultra-high energy cosmic rays is, it seems, still a mystery. Two years ago, scientists at the Pierre Auger Observatory in Argentina thought they had it solved. They published a paper in Science, based on two dozen particles, that there was a correlation with the location of Active Galactic Nuclei -- supermassive black holes that accelerate jets of material at near-light speed throughout the universe. At the time of the announcment, there was some doubt: The Hi-Res project, which scans the northern sky like Auger does the south, found no such correlation.
And now, today, Stefan Westerhoff, an Auger scientist from the University of Wisconsin at Madison, said that, based on new particle detections -- they have more than 50 now -- the correlation no longer holds. "The signal strength is certainly considerably weaker now," he told his audience. "This is certainly a disappointment."
But the correlation isn't so weak that they can give up. The 70% correlation between the cosmic rays and the AGN at the time of the Science publication has now dropped to about 40% -- considerably less, but not enough to support the null hypothesis. What could cause some particles to come from AGN, but not others? Westerhoff says it might have something to do with their composition. Maybe the protons come from the AGN, whereas higher mass cosmic rays, say iron nuclei, do not...
==endquote==

Here's a link to my post #66
https://www.physicsforums.com/showthread.php?p=2330554#post2330554
which had the abstract of an April 2009 paper by Glennys Farrar et al. They seemed to think there was some correlation too, but not complete.

 

[Vanadium 50]

The thing that's not being said is that if you split the data into the "early" and "late" phases, the correlation is almost entirely in the early set. You can sort of see it yourself - if with half the data you have a 70% correlation, and with two halves it's 40%, what's the correlation in the second half?

 

[tom.stoer]

How does this bear on the original post for this thread? I've lost track.

I think I started the trouble in post #17 saying that ... the LHC will be absolutely mute about any "ToE". It can support theories with respect to their low energy regime, but nothing else.

Then we started to discuss what a ToE could be, what the requirements are etc.

If we agree that a good candidate for a ToE must incorporate all known interactions, must be predictive up to arbitrary high energies and must be mathematically consistent (e.g. free of singularities, non-renormalizability, certain anomalies, ...) - and if we forget about all metaphysical speculations - then it's time to remember that we currently do not know a single candidate ToE.

 

[RUTA]

I think I started the trouble in post #17 saying that ... the LHC will be absolutely mute about any "ToE". It can support theories with respect to their low energy regime, but nothing else.

Then we started to discuss what a ToE could be, what the requirements are etc.

If we agree that a good candidate for a ToE must incorporate all known interactions, must be predictive up to arbitrary high energies and must be mathematically consistent (e.g. free of singularities, non-renormalizability, certain anomalies, ...) - and if we forget about all metaphysical speculations - then it's time to remember that we currently do not know a single candidate ToE.

Thanks. I can't think of a theory or pseudo-theory (e.g., strings) that meets your requirements for a candidate ToE. And, I agree that any such theory would not be confirmed by low energy tests alone, unless that is the realm where it is deemed fundamental. One really has to produce definitive experimental confirmation of its most fundamental aspects and the fundamental realm of all ToE-wanna-be programs today resides at high energy (I think strings would require an accelerator as big as the galaxy, and GUTs an accelerator as big as the solar system). Do you know of any exceptions, i.e., any programs where unification doesn't involve high energy realms? I asked this question before (maybe on this thread) and no one responded with any.

 

[tom.stoer]

I can't think of a theory ... that meets your requirements for a candidate ToE. ... Do you know of any exceptions, i.e., any programs where unification doesn't involve high energy realms? I asked this question before (maybe on this thread) and no one responded with any.

I am not sure but I think I remeber. I didn't respond because unfortunately I do not have anything to say about it. I do not know any candidate ToE.

Remark: should we have a look at strings and why they fail to be a candidate ToE?

 

[friend]

I am not sure but I think I remeber. I didn't respond because unfortunately I do not have anything to say about it. I do not know any candidate ToE.

Then perhaps we should start from principle alone to develop a TOE. It doesn't seem likely that we will ever be able to generate the energies necessary to confirm a TOE that is derived from curve fitting the data from experiment; we can't experiment with other possible universes. So we have no choice but to try to rely on some overriding, underpinning principle. But what principle could explain absolutely everything? The only thing that could explain absolutely everything is logic. Otherwise, you are left with something in nature, particles, strings, or spacetime structures, that need further explanation... Where did those things come from? But all explanations stop and you have a TOE if physics is derived from logic itself. So I wonder how the theoretical physics community looks upon any attempt to derive physics from logic. Do they dismiss such attempts out of hand? Are they skeptical and wait to see the theory? Would they gladdy welcome such a derivation if one were presented?

 

[Fra]

So I wonder how the theoretical physics community looks upon any attempt to derive physics from logic. Do they dismiss such attempts out of hand? Are they skeptical and wait to see the theory? Would they gladdy welcome such a derivation if one were presented?

How would you derive physics from logic? If we consider a pure axiomatic approach to physics from which things are deduced, then the question is WHAT axioms? Then it becomes the question of finding axioms. It doesn't solve anything in itself. It just moves the problem around. Then the status of the axioms is the same as the status of physical law.

If you then, like I do, think it's best to see laws as evolved, and evolving, then the same would apply to axiomatic approaches. The set of axioms would be subject to constant negotation and thus in principle, evovling, and there would not exists a universal timeless objective measure of the validity of axioms. They could be judged exlusively by their fitness only.

In this latter sense, I think physics could be done that way, but in this dynamical axiom vision, the problems are the same, it's just that we relabeled the words. Law -> axiom. Without solving any of the core issues.

/Fredrik

 

[Fra]

we will ever be able to generate the energies necessary to confirm a TOE that is derived from curve fitting the data from experiment; we can't experiment with other possible universes. So we have no choice but to try to rely on some overriding, underpinning principle. But what principle could explain absolutely everything?

I thought about this again, and in specific sense I think this might be an idea. As I see it, scientific process has two components it's

1) the production and construction of inferences, and there appears to be a kind of logic to this.
2) the feedback from the environment (~experiment)

A complete picture can not grow without (2) I think, but otoh I think we have not even close to exhauset the power of (1). I also think it's an almost exaggerated interest in the high energy experiments as the only place to get things. Some others point to cosmology, but I would like to add another more obvious and more accesible scale, which is the complex system physics, which would have to deal/explain behaviour that emerge only in complex systems.

Ariel Caticha going the tradition of Jaynes attempts to derive the laws of physics from general principles of inferece, such as rationality and honesty. This might partially be said to be in this direction.

You asked for "physics from logic", and Ariel, Jaynes and those working in that tradition view probability theory as an "extension to logic".
But while his idea is to derive the laws of physics from more or less standard probability and an Max Ent principle for information processing. I think one can go one level deeper and ask if standard probability and maximal entropy are really the only rational premises? I think here is a lot one can do without high energy accelerators.

And maybe this can ultimately produce more specific and more confident predictions for future high energy experiments or astronomical observations.

About my objection to the axiomatic approach - this is actually also what Ariel is doing and is where I disagree with them, since he is starting with some key axioms that leads to a unique formalism (which is of course probability theory, and it's no coincidence) and a unique rule for information entropic processing by a specific choice of entropy measure.

How about if we instead consider that the axioms are say mutating, could different systems of inference, in some situations be more fit? I think so. This is as far as I konw very poorly investigated. And to investigate this, one does not at least immediately need any LHC data. So I think there is a lot of progress that could be done still on point (1)

/Fredrik

 

[Dmitry67]

This has nothing to do with the progress of science, we're talking about how much information is contained in the set of all integers. I say it's infinite and you say it's zero. To argue my point, all I have to do is "play dumb" and require you to give me the information explicitly, i.e., list the elements of the set. If you're correct, you have nothing to send me. If I'm correct, you have an infinite number of numbers to send me. That's my argument.

How does this bear on the original post for this thread? I've lost track.

ok. Alice sends Bob 2 messages:
* first contains the length of a list
* second message contining a list.

For example:
* 3
* {39449, 545959, 6969}

As information can not travel faster then light, Bob has to wait the arrival of the second message until he is able to reproduce a list.

Except: except 0 and inf. Receiving "inf" Bob already knows what Alice is going to send him. Hence, inf and 0 does not contain any information.

 

[Dmitry67]

From a computational-complexity point of view there is no difference between the two statements
a) one universe exists
or
b) all possible universes exist - except one
Of course specifying the one in both cases should require the same amount of information.

Similarly computationally the statements
a') no universe exists
and
b') all possible universes exist
have the same complexity.

If you argue strictly based on computational complexity and with Ockams razor, then you cannot distinguish between a') and b') nor can you distinguish between a) or b). So in order to do that you have to refer to some experimental result, i.e you have to enlarge your reasoning beyond computational complexity.

You do that by taking into account "known facts" and by going from a mathematical to an ontological reasoning. Of course you can rule out a') immediately. You can trust in a least one universe which means that ontologically and based on Ockams razor you should not add more assumptions than strictly necessary. So you add the assumption that one universe exists and - wow - it agrees with the known facts. If you would instead add an uncountable set of universes it would still agree with the known facts, but you have to explain why "they are there but invisible". Therefore you add assumptions which you cannot prove.

And don't forget: you cannot use your "mathematical multiverse hypothesis" as starting point for your proof as your quest is just to prove exactly this "mathematical multiverse hypothesis".

We have almost agreed :)

Yes, empty set and universum contain the same amount of information - ZERO
So our multiverse contains NO information (of course not for "frogs") as it is Universum and it always exists in one and only one possible state.

And yes, my reasoning is:
2 possible options: NOTHING or EVERYTHING, we observe SOMETHING, hence the second option is valid. Note that "assumption that one universe exists" is not an assumption - it is an experimental fact :)

Your last point is valid: I use MUH as an axiom, because I don't see any choice.

I have 2 questions if you have time:
1. Do the inner regions of black holes (inside their horizons) exist? Are any claims of what is going on there falsifable?
2. Do you think that TOE would use only formulas or it would need to use some words? In another words, do you expect TOE to be interpretation-less? What do you expect TOE to do with the interpretations? (give a new one, tell us what is a right one, making the whole notion of interpretation a nonsense)?

 

[tom.stoer]

1. Do the inner regions of black holes (inside their horizons) exist? Are any claims of what is going on there falsifable?

Yes, inner regions do exist and in principle they are accessible for an experiment.

Think about a brave colleague (an expert in theory, experiments and results regarding GR and QG). His last project (together with his students) is to travel into a gigantic black hole and to spend the rest of his life in order to complete the knowledge regarding black holes. Within this large black hole he will - besides his experimental activity - publish research papers, create an own arxiv repository, organize conferences etc. Of course he has to hurry up, but in principle nothing will be in conflict with his objective.

2. Do you think that TOE would use only formulas or it would need to use some words? In another words, do you expect TOE to be interpretation-less? What do you expect TOE to do with the interpretations? (give a new one, tell us what is a right one, making the whole notion of interpretation a nonsense)?

I am not so sure.

A short-term candidate will certainly not be free of interpretation and non-mathematical rules ("if X ... then apply rule Y"). Even the basics of that theory may be easier to formulate in english language ("the speed of light is constant in all reference frames").

A long-term candidate may exist on the "next stage"; it could be some kind of meta-theory that addresses these formalization-issues; but perhaps it will aim for something totally different - today we do not know.

I expect that a candidate ToE will be based on few (hopefully :-) mathematical and non-mathematical "axioms". It will be able to address questkions like:
- what is the structure of space-time
- how does space-time, local gauge-symmetry, ... arise from X (where X is a more fundamental structure)
- why do we live in 3+1 dimensions
- why do we observe U(1)*SU(2)*SU(3)
- why do we observe three fermion generations, ...
- what is the origin of the cosmological constant
- what replaces the black hole and big banhg singularity, ...
- ...

After we are able to study one candidate ToE, of course new questions will arise, especially regarding the mathematicsl structure(s) X. Perhaps there will be competing structures X, X', ... (strings, loops, non-commutative geometry, ...). I do not know if this will be an iterative process (just as it was the last centuries) or if there will eventually be a paradigm shift which allows us to go the meta-theory level.

I agree that we need some deeper insights regarding development of physical theories, especially as we will have less new experimental facts - just because of the required energy scale. That means we must focus more on abstract ideas, mathematical justifications, completeness, consistency etc.

As you say, something like MUH will be an axiom (you could even say dogma, doctrine) and will therefore belong to / be related to the philosophical realm. I am pretty sure that physics and philosophy will again come closer together has they are today (there was an intensive dialog in the early twenties when QM was developed; in the following decades "shut up and calculate" became the major guideline.

 

[Dmitry67]

1 I expect that a candidate ToE will be based on few (hopefully :-) mathematical and non-mathematical "axioms".

2
- why do we live in 3+1 dimensions
- why do we observe U(1)*SU(2)*SU(3)
- why do we observe three fermion generations, ...

1 I always asked - but never got an answer - for an example of a "non-mathematical" axiom. An example of an axiom which can not be expressed in mathematical terms. Could you provide any examples (even not realistic, not about our universe)?

2 What kind of "why" do you mean?
a. anthropological principle
b. cosmic darwinism
c. proof of mathematical inconsistency of other possible universes

 

[tom.stoer]

Regarding a non-mathematical axiom: take constant c in GR as an example: as long as you do not have the full developed GR based on manifolds it's hard to write this as a mathematical axiom; of course you can start with a local description which will eventually correspond to the tangent space, but you don't know this in advance. So take this as a an example.

Regarding "why": the basic problem is that it's easy to ask these why-questions, but it's hard to answer them; therefore I don't think that it's a good idea to exclude ideas at this early stage. So right now I am trying to be open-minded to all three directions. My problem with
a) is that it appears to me as self-immunization against falsification
b) is that it sounds nice but nobody can tell me how evolution, mutation and evolutionary pressure could work; what is the DNA of the physical laws?

Of course I cannot prove that other universes do not exist; nevertheless I would take c) as starting point and search for
i) a theory that describes this specific universe and
ii) a selection principle (could be consistency or something else)
[this would be MY research program - I don't want to force anybody to abandon other lines of research]

 

[tom.stoer]

@friend & fra: I think you are trying to do something like "finding the DNA for physical law".

I have no idea how I would start and I am not familiar with the ideas and research programs you are mentioning. However, it becomes clear that even if you want to avoid axioms and rules but try to let physical laws emerge from something "deeper", you need a set of rules. Logic is perhaps the simplest mathematical structure, but I am afraid that logic alone will do the job. And negotiation must follow some logic, too. So it's at least logic that serves as a basis for you.

One remark: I am still not sure if we all understand what Tegmark wants to say. What does the small word "IS" mean? Is it absolute identity, not only isomorphism? Are the U(1) and the SUO(2) identical - or just isomorphic? Do they become strictly identical if I remove all "human baggage"? Is it correct, sufficient and reasonable to assume that there IS NOTHING ELSE but a relation between mathematical entities? He is not very explicit when it comes to relations to different philosophical schools ...