Let us assume Feynman was wrong.

[Ilja]

well, at least there are some good news: I mean, the relatively recent discovery of the Quantum Decoherence. It demonstrated that most or all 'classical' behavior can be derived directly from the 'pure' (interpretation-less) QM

It cannot. Decoherence needs some "decomposition of the universe into systems", which is not part of pure QM. http://arxiv.org/abs/arXiv:0903.4657"

 

[Dmitry67]

Copenhagen: equations AND observers

Many world: equations AND "frogs" who somehow see only a tiny part of the solutions of these equations

Bohm: equations AND some additional equations (that remove the need for observers and frogs)

MUH: equations AND additional equations AND more additional equations AND more and more additional equations ... until you exhaust the infinite set of all possible equations

I almost agree, except

1. MUH does not imply that the number of equations is limited. It is a well-justified HOPE. In fact, if the number of equations is infinite then MUH would lose all its charm for me.

So your claim (that the number of equations is infinite) is just your thought and not a part of MUH.

2. it does not contradict your description of MWI, but I was not absolutely confinced by MWI before I learned MUH. MUH implies that interpretation must be NULL - it can talk, however, about 'how the observers inside would percieve such universe' - but it does not change the basics.

So, if we forget about the frogs (imagine that in an Universe carbon syntesis was impossible and no life is created, or let's talk about our early universe) then what is left:

Copenhagen: ***FATAL ERROR*** can't not continue without any observers
Many minds: ***FATAL ERROR*** for the same reason
Many world: core QM equations
Bohm: core QM equations AND some additional equations
+ for example Objective collapse theories: core QM equations + objective collapse equations

Thank you for your patience :) Now apply the Occams razor. What is left? :)

So I imply that:
1. MUH + Occam = MWI
2. MWI = Null interpratation (shut up and calculate) + wordy stuff about 'what observers would see' derived from core QM.

 

[Ilja]

Copenhagen: ***FATAL ERROR*** can't not continue without any observers
Many minds: ***FATAL ERROR*** for the same reason
Many world: core QM equations
Bohm: core QM equations AND some additional equations
+ for example Objective collapse theories: core QM equations + objective collapse equations

Thank you for your patience :) Now apply the Occams razor. What is left? :)

So I imply that:
1. MUH + Occam = MWI
2. MWI = Null interpratation (shut up and calculate) + wordy stuff about 'what observers would see' derived from core QM.

Many worlds is core QM equations + unspecified "decomposition into systems" + some strange "containment"-relation between points in Hilbert spaces.

 

[Dmitry67]

Many worlds is core QM equations + unspecified "decomposition into systems" + some strange "containment"-relation between points in Hilbert spaces.

It is true that quantum decoherence is defined in terms of some degrees of freedom system, while that system is arbitrary.

But QD itself is used to define how the 'universe' looks like to that system X. So think about the QD as a function of a system.

If you don't care about the observers, then you don't care about it.

So your claim is true but it is a pure tautologie: to talk about what systems see we need to define systems somehow.

 

[Demystifier]

1. MUH does not imply that the number of equations is limited. It is a well-justified HOPE. In fact, if the number of equations is infinite then MUH would lose all its charm for me.

But according to Tegmark, MUH says that ANY logically consistent mathematical structure exists. There is certainly an infinite number of such structures.

But of course, you don't need to agree with Tegmark.

 

[Dmitry67]

But according to Tegmark, MUH says that ANY logically consistent mathematical structure exists. There is certainly an infinite number of such structures.

Yes, but (I HOPE) the number of equations of our particular Universe is finite

 

[friend]

Fra,

Einstein said in one of his essays, "Physics constitutes a logical system, whose basis cannot be distilled, as it were, from experience by an inductive method, but can only be arrived at by free invention. The justification (truth content) of the system rests in the verification of the derived propositions by sense experiences, whereby the relations of the latter to the former can only be comprehended intuitively."

This is because the scientific method used is to conjure up equations to fit the data collected by experiments. After we have what we think is an adequate equation that predicts the data, we see if we can find more fundamental structure in the equations and assign physical meaning to them. By this process we will never know if we've got the most fundamental theory.

But if a theory can be derived on principle of reason alone, and it results in equations that we are accustomed to, how could anyone object to it? How could they then after deny that physics is derived from logic?

 

[dx]

This is because the scientific method used is to conjure up equations to fit the data collected by experiments. After we have what we think is an adequate equation that predicts the data, we see if we can find more fundamental structure in the equations and assign physical meaning to them. By this process we will never know if we've got the most fundamental theory.

But if a theory can be derived on principle of reason alone, and it results in equations that we are accustomed to, how could anyone object to it? How could they then after deny that physics is derived from logic?

That's not quite what Einstein meant. He was talking about the conceptual foundations of physical theories. Like the concept of force. That is not something that is uniquely determined by experience, but is a creation of the mind.

 

[p764rds]

Since this is a free, argumentative thread, I will share my thoughts accordingly.

This is the same thing people have said for a while now. This is a problem with modern physicists. They think in equations, and they neglect what the equations mean. Eventually, they lose the notion of a picture, or a conceptual idea. Numbers are what we use to represent nature. They are not nature itself.

I am not sure where you are coming from, but IMO numbers are able to implement mathematical equations. For example the computer we are on now is doing all its 'thinking' and data retrieval using numbers (well, binary numbers - 0s and 1s in effect). But the numbers are only the cogs in the machine, as you know.

(I would say that 'nature', and us, are totally in numbers, its just we think its a 3 Dimensional space - I think you do not agree with that though - yet )

 

[benk99nenm312]

I am not sure where you are coming from, but IMO numbers are able to implement mathematical equations. For example the computer we are on now is doing all its 'thinking' and data retrieval using numbers (well, binary numbers - 0s and 1s in effect). But the numbers are only the cogs in the machine, as you know.

(I would say that 'nature', and us, are totally in numbers, its just we think its a 3 Dimensional space - I think you do not agree with that though - yet )

Yet? I'm so very sorry, but you will find that I am one of the most stubborn people on the planet. I do not change my views. I think I actually posted this because I misinterpereted one of the other posts, but since we are on the subject, I will keep going.

You say that nature is totally in numbers. You say that we just think that it is 3 dimensional space. You seem to harbor a view where numbers are the truth, and the concept of space and time is a creation of man. This is flat out wrong. I am very sorry to be the one to tell you this, but it is the exact opposite. Numbers are a creation of man, to represent what we see. When we look at the universe at a whole, we don't see a set of equations. We see a star, or a galaxy, that follows laws that we can represent with equations.

If you are not totally convinced, then you will be thinking of QFT, and how it regards particles to be excitations in a field. And by the way, a field is just an equation too. If you look beyond its mathematical interpretation, it is no different from the word ether. Obviously, QFT is not perfect. This tells us that, thankfully, we are not governed completely by numbers. Concepts have to be considered when you deal with physics.

This discussion is a popular one. I'm sorry, but I regard this as a very basic, yet imortant subject. How hard is it to see why I'm right? Is it hard to admit that? Do you really think you are sitting on the number 7? The universe is represented with math. It is not math itself.

 

[Dmitry67]

My opinion is that you're absolutely wrong.
I assume you had read Max Tegmark's 'Mathematical Universe Hypotesis'. If not search arxiv. He claims exactly is opposite: our universe IS math.

His article was much more convincing then your post, may be because he proided some arguments instead of saying "How hard is it to see why I'm right" :)

 

[Demystifier]

Yes, but (I HOPE) the number of equations of our particular Universe is finite

I hope that too.

But to hope that we already know all these equations would be too much. On the other hand, MWI arises from a desire that we do already know them, that there are no other equations behind those of standard quantum theory.

 

[Dmitry67]

On the other hand, MWI arises from a desire that we do already know them, that there are no other equations behind those of standard quantum theory.

On some level, yes, but of course QM equations are not final - we'll get something like QLG or strings or something else that makes GR and QM mutually consistent.

However I don't expect TOE to explain the quantum phenomena more 'classically'. So we should forever abandon realism or single history (we don't know yet what exactly should be abandoned) loike we had forever abandoned the euclidean 3d space and we don't expect euclidean 3d space appear again in TOE

Personally I expect TOE to be even more weird then QM. So far the theories we have are not crazy enough - like Stabdard Model does not provide anything more fundamental then we have in QFT. That is why there is no significant progress.

So even TOE would change the equations I don't think it would remove or explain the 'QM weirdeness'

 

[Fra]

we should forever abandon realism or single history
...
Personally I expect TOE to be even more weird then QM. So far the theories we have are not crazy enough

I agree.

So even TOE would change the equations I don't think it would remove or explain the 'QM weirdeness'

What if the QM weirdness is simply the result of our still realist-mode brains trying to make sense of our "not crazy enough theories"?

In no way do I think we will recover realism at any level, but I do think that some of the "weirdness" in QM could be partly reduced if the take the abanoning of realist thinking fully.

Here are I am referring to IMO realist remnants such as bird views etc. Here I am not with Tegemark. There is one way in which I can see a close connection between mathematics and reality, and that is that the physical makeup of say an observer, is the basis on which mathematics, such as counting, real numbers, transformations are based. But then, that is still almsot an opposite view of Tegemark, Tegemark seems to think of mathematics as existing in some transendent sense. I take the exact opposite view, that the fact that IF mathematics is supposedly one-2-one with physical reality, then this constrains the mathematics, rather than frees up reality. This is why I object to the use of continuum abstractions.

Smolin also made the correlation between realist thinking, and the idea of universal timeless law. The problem is that even with current QM, it still contains realist elements - which is why I think it's almsot conceptually inconsistent.

So I agree it's not mad enough.

/Fredrik

 

[Dmitry67]

We have agreed on the first part.
But regarding the second, I wanted to ask you, did Mandelbrot set exist before it was discovered?

 

[Fra]

But regarding the second, I wanted to ask you, did Mandelbrot set exist before it was discovered?

To make sense out of this question, the key is what do you mean with exist.

Sure, it's easy to imagine that yes of course it did exist before, it's just that we didn't discover it until then. But there is something wrong with that way of reasoning when you put reasoning in a sort of scientific context, where the justification of a conjecture lies in what implications it has.

If we by exists, mean the only reaonsonable thing, that someone (the one saying it exists) has the information, then clearly before it was first observed, it didn't exists in the sense that it had any predictable impact on reality.

But certainly, two observers here could disagree. Someone who discovers it first, would think the second observer is "crazy" to suggest that it didn't exists just because he didn't know about it.

But m point is that from the point of view of measurable differences. The realist-sense of "EXIST" that I think you have in mind, doesn't make sense.

What I am focusing on, is how different observes interact with each other. And each observer, acts in line with his information, not in line with "some reality" to which he is indifferent. It's a form of locality in terms of information, that an observer responds and acts only upon the information he has, this is so even if the information is wrong!

This relates to my comments in this thread.
https://www.physicsforums.com/showthread.php?p=2130382

I don't expect you to agree, but I present to you my incomplete arguments.

So to repeat my point.

To put your question in context, there must be a way in which the observer is not indifferent to the existence of non-existence of the mandelbroth. If not, the answer
is not yes it did exist or it did not exist, the resolution is that this question would
never appear physically.

If it appears, then it's asked by an observer who already found the mandelbroth, and then this observers QUESTIONING of othre observers would quality as a physical interaction, and this indirectly informs the first observer (originally indifferent to this) about the mandelbroth.

So I really do not see any contradictions here. The one point of confusion is this strange realist-view that something exists independent of observation. That applies IMHO to mandelbroth as much as it applies to electron spin.

But as always I would up my rear on this (I have no proof). But I have to say I'm comfortable.

/Fredrik

 

[Dmitry67]

I see your point.

There are 2 observers, A and B very far from each other so they can't communicate, until they lightcones intersect. When they finally meet together, is it possible that for A number 11 is prime while for B it is not? let's say thay examine together their list of primes and the value of pi. What a coincidence! They are identical!

How do you explain it, if the 'list of primes' did not exist before they discovered it?

 

[Fra]

If you will say that then the two observers view are inconsistent, then my response is that, this is exactly why we predict an interaction between these observers! Their different "view of reality", is what causes them to interact, and the result of the interaction is that both of them are updating their information! And loosely speaking, the consistency you seek is reasearched only asymptotically as an equilibrium condition.

Analogies of how such differing leads to interaction is common in human society. For whaterver reasons (culture, religion, history, personcal experiences etc) different people have different opinon on what is right and wrong and howto act according to that. Sometimes this leads to conflicts. The result of the conflict is that they are fighting each other, and there are different possible outcomes. One possibility is that they reach an compromise, based on a mutual understanding. It may not mean they agree, but they have agreed to disagree and coexist in a steady state.

Similary, the physical information, may lead to physical inteactions. And think classification of these, will help us understand the standard model, and it's place in a larger evolving scenario (the two persons interacting above, still both exist in a larger context, a cirty, or even a country, a planet, or galaxy, etc)

/Fredrik

 

[Fra]

There are 2 observers, A and B very far from each other so they can't communicate, until they lightcones intersect. When they finally meet together, is it possible that for A number 11 is prime while for B it is not? let's say thay examine together their list of primes and the value of pi. What a coincidence! They are identical!

How do you explain it, if the 'list of primes' did not exist before they discovered it?

This is not so mystical I think, but I'll have to get back to this later due to time. There are several levels here, such as the uniqueness of mathematics and logic etc. But also language.

The two observers, must first learn howto communicate to make a comparasion even. If observer A asks B : "gimme your list of primes" :), B would not understand anything, only hear noise. however, if as they met, agree upong a definition of "primes", sure they would agree upon their lists.

Is it possible though that one observer never even developed the notion of primes, or a different list of whatever that aren't A:s primes. Yes sure. But the disagreement on the lists is no contradiction because have not relation.

However, from my point of view as a human, pondering about a theory of the universe and other observers, then in my abstracion of an observer, there is a starting point of distinguishable states, which ultimately can label states, and further construct measures by counting, which indirectly leads to ordered sets. So I picture a mathematical abstraction of observers. But that is only MY view, as a human. But then it's my free choice. Someone else doing what I do, can do it differently, but I still suspect that while our descirptions would be different both of us would successfully be able to make sense of what we see.

To repeat rovelli, the only way to compare what I see with "what I think" you see is to interact with you, and try to interpret the response according to MY view. This applies also to my information about physical law. This is why I think we need an abstraction where physical law evolves.

/Fredrik

 

[Phrak]

I see your point.

There are 2 observers, A and B very far from each other so they can't communicate, until they lightcones intersect. When they finally meet together, is it possible that for A number 11 is prime while for B it is not? let's say thay examine together their list of primes and the value of pi. What a coincidence! They are identical!

How do you explain it, if the 'list of primes' did not exist before they discovered it?

You keep asking the interesting questions, Dmitry.

I don't think you have to get so invloved. Numbers don't exist. The counting numbers 1, 2, three... They don't exist. Show me the number 12.

 

[Demystifier]

However I don't expect TOE to explain the quantum phenomena more 'classically'.

But this is merely your prejudice without a sufficiently strong argument, just as my expectation that the opposite is the case is my prejudice without a sufficiently strong argument too. Hopefully, one day we will know who was right. But at least we should agree that both options are possible, and consequently that researches in both directions should be encouraged.

For example, in
http://xxx.lanl.gov/abs/hep-th/0407228 [Eur. Phys. J. C 42, 365 (2005)]
http://xxx.lanl.gov/abs/hep-th/0601027 [Int. J. Mod. Phys. D 15, 2171 (2006)]
I have attempted to DERIVE the Bohmian equations of motion from the requirement of general covariance.

 

[Dmitry67]

You keep asking the interesting questions, Dmitry.

I don't think you have to get so invloved. Numbers don't exist. The counting numbers 1, 2, three... They don't exist. Show me the number 12.

1. Thank you
2. But what exists then? Do you exist?
All your atoms are normally replaced every 2 years, and as particles are indistinguishable then they even can exchange their positions sometimes with each other and the environment. So you can not define "YOU" based on what you consist of, an absence of any barcodes on atoms and particles makes it impossible.

The only way to define "YOU" is to write some complicated predicate IsPhrak(physical data) which returns true or false. So you are a function, a mathematical equation, not matter as matter in QM is not really 'traceble'. (for example, any real particle can be replaced by the virtual one if the 'original' one dissapears, leaving the virtual one on its place)

 

[p764rds]

Yet? I'm so very sorry, but you will find that I am one of the most stubborn people on the planet. I do not change my views. I think I actually posted this because I misinterpereted one of the other posts, but since we are on the subject, I will keep going.

You say that nature is totally in numbers. You say that we just think that it is 3 dimensional space. You seem to harbor a view where numbers are the truth, and the concept of space and time is a creation of man. This is flat out wrong. I am very sorry to be the one to tell you this, but it is the exact opposite. Numbers are a creation of man, to represent what we see. When we look at the universe at a whole, we don't see a set of equations. We see a star, or a galaxy, that follows laws that we can represent with equations.

If you are not totally convinced, then you will be thinking of QFT, and how it regards particles to be excitations in a field. And by the way, a field is just an equation too. If you look beyond its mathematical interpretation, it is no different from the word ether. Obviously, QFT is not perfect. This tells us that, thankfully, we are not governed completely by numbers. Concepts have to be considered when you deal with physics.

This discussion is a popular one. I'm sorry, but I regard this as a very basic, yet imortant subject. How hard is it to see why I'm right? Is it hard to admit that? Do you really think you are sitting on the number 7? The universe is represented with math. It is not math itself.

I like your attitude - "stubbornest person on the planet" it made me laugh.
In reply I can say that the numbers/information solution which I believe is depressing to say the least!
I am just forced that way after studying QM, programming and philosphies. I would rather have MWI at a personal level but information as the key is what I think is the truth (I know, its a cold and spiritless solution).
I suppose entanglement issues was the final blow to it all for me.

 

[camboy]

That's an over simplification. Read this for a discussion of the many problems with Bohm theory: http://motls.blogspot.com/2009/01/bohmists-segregation-of-primitive-and.html

Schmelzer has now put in the (boringly considerable) time and effort and has produced a nice discussion showing up most of the multiple problems with Motl's rant.

See http://ilja-schmelzer.de/realism/Motl.php"

 

[Fra]

http://xxx.lanl.gov/abs/hep-th/0601027 [Int. J. Mod. Phys. D 15, 2171 (2006)]
I have attempted to DERIVE the Bohmian equations of motion from the requirement of general covariance.

What I find to be an interesting observation, while I do not believe in realist models, is that it touches relates to a view I hold, which is that there is a dual standard in physics when it comes to realism, in particular when we discuss symmetries.

Usually realism suggests that reality must be definite even without an interaction by an observer, and the other camp suggest that without such interactions the observer is indifferent to this "hidden reality", which suggest that even the notion of a definite hidde reality microstructure, whose microstate is unkonwn isn't consistent.

For some reason, many who pick on realist models, don't seem to realize that even the notion of definite symmetries is also a realist type of idea. I personally think that the only solution, to at least have a reasonable consistent reasoning is to put symmetries in a evolving context.

Demystifier somehow here argues that the existence of diffeomorphism symmetry, implies also a realism in the sense of hidden variables. Set aside the arguments given, I think that in a general sense that makes sense to me. Because in my opinon, the notion of diff.invariance is in itself a realist type of statement. I've noted this before, but the reason is that symmetries are not directly observable. They are rather infered by risky arguments, and then used as a basis for further interactions.

So I have a question for Demystifier, would you agree that one possible conclusion from your reasoning is that instead of our argument supporting realist models, you argument might in fact be an indication that we do not yet understand that physical meaning of symmetries in physics?

/Fredrik

 

[Fra]

Also not that in a certain sense, an evolving model, might be partly in line some of the bohmian objections to standard interpretations. I think it's not correct to say that just be cause we can not predict a particular event, we will never even in the future. some bohmians has argued that this is somehow to throw in the towel. In the evolving scheme, this is not so. IT just acknowledges our de facto inability to predict the specific outcome and how our actions follows from this uncertainty, it does not deny that future interactions my provide us with more information that changes this picture.

This suggest that we can never predict the future. All we can do is GUESS the future. Even in physics, down at the levle of law. What is wrong with thinking of the laws of physics as the ultimate scientific construction of a guess? That for many purposes are indistiniguishable from a definite prediction.

As I see it, the problem with hidden variables is that it does not make sense to picture a definitie microstructure, with a total lack of knowledge of the microstate, because without the latter, the microstructure itself is also uncertain. Most bell stuff arguments assumes a definite microstructure of the hidden variable. If you instead considers tht all microstructures are evolving, new opportunities open up, that can I think also satisfy at least part of the bohmian objections. (But not old style hard realism, but at least make clear that abandoning iold style realism does NOT mean we are throwing in the towel)

/Fredrik

 

[Demystifier]

What I find to be an interesting observation, while I do not believe in realist models, is that it touches relates to a view I hold, which is that there is a dual standard in physics when it comes to realism, in particular when we discuss symmetries.

Usually realism suggests that reality must be definite even without an interaction by an observer, and the other camp suggest that without such interactions the observer is indifferent to this "hidden reality", which suggest that even the notion of a definite hidde reality microstructure, whose microstate is unkonwn isn't consistent.

For some reason, many who pick on realist models, don't seem to realize that even the notion of definite symmetries is also a realist type of idea. I personally think that the only solution, to at least have a reasonable consistent reasoning is to put symmetries in a evolving context.

Demystifier somehow here argues that the existence of diffeomorphism symmetry, implies also a realism in the sense of hidden variables. Set aside the arguments given, I think that in a general sense that makes sense to me. Because in my opinon, the notion of diff.invariance is in itself a realist type of statement. I've noted this before, but the reason is that symmetries are not directly observable. They are rather infered by risky arguments, and then used as a basis for further interactions.

So I have a question for Demystifier, would you agree that one possible conclusion from your reasoning is that instead of our argument supporting realist models, you argument might in fact be an indication that we do not yet understand that physical meaning of symmetries in physics?

Well, I would not interpret my results in that way. In particular, I do not think that I have really derived realism from diffeomorphism symmetry. Instead, I have derived some new EQUATIONS from diffeomorphism symmetry. Equations, by themselves, do not necessarily refer to realism. However, the equations that I obtain this way are mathematically the same equations that Bohmians postulate with intention to recover realism. Thus, even though the equations I obtain do not necessarily need to refer to realism, such a realistic interpretation of these equations seems to be the most natural one.

I can also put it this way. Even if you do not believe in realism, there is a theoretical reason to accept the Bohmian equations of motion.

 

[Fra]

Thanks for your response. I figured you don't interpret it as I do, but do you see any principal difference between the notion of "hidden variables" and "hidden/broken symmetry".

Can one defend the reality of the latter but not the first by observability arguments and still be somewhat coherent?

It's not quite the point you tried to made, but I couldn't making this association when I noticed your paper.

The way I see the apparent realism that is more or less a fact in classical domains, is explained by that different observers simply are tuned to their expectations. And even though in principle their reality could a priori be all different, the result of evolution/interaction has tuned them as it wouldn't be an even quasi-stable situation that interacting observers have drastically diverging opinon of reality.

/Fredrik

 

[Demystifier]

Thanks for your response. I figured you don't interpret it as I do, but do you see any principal difference between the notion of "hidden variables" and "hidden/broken symmetry".

I view the notions of reality and symmetry as somehow opposite, in the sense that more symmetry implies less reality. Namely, if some quantity changes under some symmetry transformation, than this quantity is not real. Conversely, if some quantity is real, then a transformation of this quantity is not a symmetry transformation.

Hidden variables are, by definition, quantities that are real even when measurements are not performed. Thus, more hidden variables may induce more broken symmetries. Hence hidden variables and broken symmetries are related, but they are certainly not the same.

 

[Fra]

It's interesting how we seem to take so opposite views.

But I think it it is that you have a totally different view of what's fundamental. It seems you somehow start with some requirement of the existence of a "consistent realist birds view", and argue always from that point. Which means that single observations are not fundamental, they are only arbitrary projections of this presumed real birds view? And arbitrary projections that are generated by symmetry transformations doesn't carry information about reality?

I start from a totally different point, from the inside view. How can I, knowing noting, by means of physical inquiry and observation, learn to know what possible symmetries, or approximate symmetries that exists in my environment? And how does the emerging knowledge of that influence my own interaction pattern? (and of course how does a particles emergent knowledge of it's own environment, influence it's interaction properties)

Hidden variables are, by definition, quantities that are real even when measurements are not performed.

My perspective is the operative one, everything justifies itself in the sense whereby it makes a potential difference.

Since I think that the constructive reading of "measurement" in a measurement theory is = physical interaction, your notion of "real" here has no justification from my perspective.

OTOH, the usual idea that there is a (hidden) variable (a microstructure) whose value (microstate) is not known, and IF it was know *would make a difference* is ambigous in the sense that the mere definition of the microstructure implies information by means of an ergodic hypothesis.

If the inference of the microstructure of the hidden variable is described as a physical process, this could be justified. But until then it's a catch 22.

I think the ergodic hypothesis is manifested physically as an emergent microstructure, which would imply that "objective reality" is emergent.

So paradoxally, it's the breaking of symmetry, that justifies it. From the point of view of observations, I think differing views comes first, as that's how they distinguish themselves. A never broken symmetry would not be distinguished, and thus meaningless.

This is why I think there are no stable unbroken symmetries.

I suspect I didn't convey the message very well but I maintain the idea that the notion of symmetry in physics is not put in a proper interaction context. To understand what a symmetry is from the point of view of mathematics is I think quite distinct from to see it's value as a constructing principle in physics.

They are constraints for sure, but the point is that they are not god-given constraints, they are infered from a history of physical interactions, and a limited one at that.

/Fredrik

 

[Demystifier]

But I think it it is that you have a totally different view of what's fundamental. It seems you somehow start with some requirement of the existence of a "consistent realist birds view", and argue always from that point. Which means that single observations are not fundamental, they are only arbitrary projections of this presumed real birds view?

Essentially, yes that is how I look at it.

 

[AUMathTutor]

First off, to whomever said that "physics was fundamentally math", I disagree but would like to discuss. Also, anyone believing that the universe is mathematical can feel free to discuss this with me as well; I don't necessarily believe that mathematics has anything to do with how reality actually is.

Also, camboy:
I'm not sure I follow your logic. So if Feynman says that nobody knows the machinery of QM, but Bohm says he knows, how do you know Bohm is right? Your argument seems to rest on the fact that it's not fair to say Bohm is wrong since he can't be proven wrong, but then you go on to say that he's right. I don't think it's fair to draw this conclusion either... in fact, science is such that we'll never know if any of it is right, or just works by some strange coincidence.

 

[Dmitry67]

First off, to whomever said that "physics was fundamentally math", I disagree but would like to discuss.

To begin with, did you read this:
http://arxiv.org/abs/0704.0646
?

 

[AUMathTutor]

Oh, well, I'm glad I started reading that. It turns out I don't agree with the ERH, so I guess the MUH says nothing about what I should believe or not.

Is it reasonable to believe in the ERH?

 

[Dmitry67]

Max Tegmark has completely convinced me (except some minor things). Now I don't ask 'is space real? what is reality? what time is made of?' etc - all these questions are gone. Equations, and nothing more.

P.S
Sorry, I was thinking you were asking about MUH
What is ERH?

 

[AUMathTutor]

Have you read the document you sent me?

External Reality Hypothesis (ERH):
There exists an external physical reality completely
independent of us humans.

That's the assumption that his MUH is based on. Therefore, since I don't necessarily accept that, it's natural that his conclusion regarding the MUH is something I shouldn't believe in either.

 

[Dmitry67]

Well, if you want to check the other side of the spectrum, then Fra has some ideas I can not accept, but they are very interesting.

 

[AUMathTutor]

Yeah, I read the previous page, it's very interesting stuff.

I wonder where the idea that math corresponds to physical reality began? I guess it's clear that in a very general sense, it does correspond to it, but the other way around... math is a product of reality, a subset of it. In my mind's eye, though, math is no different than language, and as such, we must keep a clear distinction between the things we're talking about and the language we use to do the talking.

 

[Dmitry67]

I wonder where the idea that math corresponds to physical reality began?

Where? In Greece. Check Platonism.

 

[Fra]

science is such that we'll never know if any of it is right, or just works by some strange coincidence.

This is an important observation IMO. Yet we are constantly left with no choice but to act upon whatever incomplete information we have.

A major part of the reason for my own views is that a lot of these pretty fundamental physics questions we elaborate here, really can not be separated from fundamental questions of science itself.

What is science? what is knowledge, how is knowledge acquired? Alot of these questions are somehow apparently ignored by some of the realist view, including tegemark.

Is there a "reality" independent of my interactions? Well if so, I sure want to learn about it ;-) If there is a reality I can not learn about, one certainly might ask - then what's the utility of these abstractions? So the question is still how can I inform myself about this mysterious "reality", or these mysterious "equations". Apparently Tegemark has not written down his equations yet, neither do I see that he has a strategy of how to infer them from future experiments.

I mean, if he pictures some birds view equations that predicts everything, that is fine, but it still doesn't adress (IMHO) the correct question: How a inside observer can learn about this and make predictions? He seems to somehow have an idea that someone performing calculations of these birds view questions, could predict any inside view, but who is actually making these predictions? God? Again, as I see it, it is perhaps a good answer, but to the wrong question.

Even - given that tegemark is right, the question still remains, how does that help us? does Tegemarks idea suggest to us a rational methodology on howto find and actually make use of these equations? And how does we described the world UNTIL we have nailed these equations? I think we keep doing exactly would nature would do, we keep acting based upon incomplete information at hand. It's the only choice we have, and I think it's the only choice nature has.

Many of the fundamental questions in physics, unavoidably reflects back to the foundations of science, and the scientific method. There are many examples of this. The symmetry arguments is one. Ergodic hypothesis in the foundations of statistics is one. The actual sense in the probability formalism, in cases where it's bleeding obvious that the physical realisation of repeated experiments does not make sense. For some more notes on this see http://math.ucr.edu/home/baez/bayes.html. Some of these things are so basic, that it's hard to imagine how to do science if we question them. But I think we have to. A good example is Rovelli which avoids some of this discussions in his RQM paper. Unfortunately the parts he avoid, are important. I don't know if he avoids them because he sincerely think they aren't important, or if we just doesn't know how to go on when these are questioned. From an apparently wise man like rovelli I think it is the latter.

/Fredrik

 

[jefswat]

Where? In Greece. Check Platonism.

I think the pythagoreans came first. I assume you mean applying math to problems like finding the hypotenuse of a triangle or other geometry. Or do you mean applying math to explain why things happen like all our theories do now?

 

[p764rds]

First off, to whomever said that "physics was fundamentally math", I disagree but would like to discuss. Also, anyone believing that the universe is mathematical can feel free to discuss this with me as well; I don't necessarily believe that mathematics has anything to do with how reality actually is.

Also, camboy:
I'm not sure I follow your logic. So if Feynman says that nobody knows the machinery of QM, but Bohm says he knows, how do you know Bohm is right? Your argument seems to rest on the fact that it's not fair to say Bohm is wrong since he can't be proven wrong, but then you go on to say that he's right. I don't think it's fair to draw this conclusion either... in fact, science is such that we'll never know if any of it is right, or just works by some strange coincidence.

Love your post - you appear to be totally rational (at this stage anyway!).

I too, now think that the universe is mathematical in essence - at least informational. I have a lot of reasons stemming from QM, QFT, philosophies, computing and classical physics.

Recently I realized how it could actually be achieved. The idea of particles made of mathematics or geometric shapes- platos triangles flying around did not make sense (how do they do it?), but particles made in von Neumann-like machines does make sense (to me at least). It explains a lot of quantum bizarreness easily.

It needs an 'information space' that feeds into physical space through, maybe, Heisenberg uncertainty regions at the quantum level. This space is outside physical space and creates it as an illusion. (this ties up nicely with many philosophies)

But to believe it one has to accept that we are all sitting next to each other and made of numbers! Thats hard to swallow! (well? so what? - a mobile telephone call is a stream of numbers flying through the air, and a 3d video game originates entirely in numbers!)

 

[AUMathTutor]

Here's something to think about, though... maybe it doesn't make a lot of sense, but perhaps you can unravel it for me.

First off, I would like to distinguish between the terms "mathematics" and "metamathematics".

By "mathematics" I will mean the (finite, or potentially infinite) set of truths derivable from logic and associated philosophies. "Mathematics" is what we write down, talk about, and use to solve problems.

By "metamathematics", I will mean the (actually infinite - see below) set of truths or principles upon which reality is based. "Metamathematics" includes those hidden processes and relationships which govern the nature of things, according to your (and others') belief in the MUH.

Therefore the problem boils down to whether or not there is really a "metamathematics" at all - you are convinced there is, and I am led to believe there is not.

In the ZFC set theory axioms, a set is not allowed to belong to itself. If the set of metamathematical truths were finite, then it would be possible (in theory) to list them all. However, such a list would contain a statement of all metamathematical truths, which would be semantically equivalent to metamathematics. So metamathematics would have to "contain itself", as it were, if there were only finitely many truths in it. Therefore, we can conclude that there are infinitely many metamathematical truths, given that the ZFC axioms, and the resolution to Russel's Paradox, are correct.

Another interesting note is that, if there is a metamathematics, I don't think our mathematics would have anything to do with it. Here's my reasoning: I'm not sure how any system can simultaneously encode its information along with a means for expressing that information, if the means for expressing it must also be included in the information. Let me try to come up with a concrete example.

Say you want to write a very simple, single program that saves a copy of itself to disk. Assume there is no OS to do it for you; the only thing you can do is write immediate data to the disk.

It's simple enough to copy the rest of the program, with the saving procedure excluded, and write that to disk. If your total program took 100 lines and the saving procedure took 20 lines, you would write 80 lines to disk and be done.

However, you want to write a program that's also capable of copying itself; one which can not only provide a representation of itself, but which can do so in such a way that the representation can also represent itself, and so on ad infinitum.

I think that with a little thought you'll agree that it's not possible to do this unless you have a third party come in and act on the whole program without the program's intervention.

So what does this all have to do with us? Well, if metamathematics really existed, it would have to encode in itself a way in which to represent it, that is, mathematics. Remember, mathematics (if it has anything to do with metamathematics) *is* the way to encode metamathematics. Anyway, I think you'll also agree it's reasonable to say that we have ways of encoding mathematics (notations, conventions, etc.) Ergo, metamathematics must be capable of representing not only a non-empty subset of itself, but also the rules for encoding this non-empty subset of rules.

And herein lies the rub: even if you assume metamathematics, there must be a higher level of abstraction - a manager - if our mathematics is to have anything to do with metamathematics. And if metamathematics is completely unrelated to mathematics, then why think of it like mathematics at all?

 

[p764rds]

Here's something to think about, though... maybe it doesn't make a lot of sense, but perhaps you can unravel it for me.

First off, I would like to distinguish between the terms "mathematics" and "metamathematics".

By "mathematics" I will mean the (finite, or potentially infinite) set of truths derivable from logic and associated philosophies. "Mathematics" is what we write down, talk about, and use to solve problems.

By "metamathematics", I will mean the (actually infinite - see below) set of truths or principles upon which reality is based. "Metamathematics" includes those hidden processes and relationships which govern the nature of things, according to your (and others') belief in the MUH.

Therefore the problem boils down to whether or not there is really a "metamathematics" at all - you are convinced there is, and I am led to believe there is not.

In the ZFC set theory axioms, a set is not allowed to belong to itself. If the set of metamathematical truths were finite, then it would be possible (in theory) to list them all. However, such a list would contain a statement of all metamathematical truths, which would be semantically equivalent to metamathematics. So metamathematics would have to "contain itself", as it were, if there were only finitely many truths in it. Therefore, we can conclude that there are infinitely many metamathematical truths, given that the ZFC axioms, and the resolution to Russel's Paradox, are correct.

Another interesting note is that, if there is a metamathematics, I don't think our mathematics would have anything to do with it. Here's my reasoning: I'm not sure how any system can simultaneously encode its information along with a means for expressing that information, if the means for expressing it must also be included in the information. Let me try to come up with a concrete example.

Say you want to write a very simple, single program that saves a copy of itself to disk. Assume there is no OS to do it for you; the only thing you can do is write immediate data to the disk.

It's simple enough to copy the rest of the program, with the saving procedure excluded, and write that to disk. If your total program took 100 lines and the saving procedure took 20 lines, you would write 80 lines to disk and be done.

However, you want to write a program that's also capable of copying itself; one which can not only provide a representation of itself, but which can do so in such a way that the representation can also represent itself, and so on ad infinitum.

I think that with a little thought you'll agree that it's not possible to do this unless you have a third party come in and act on the whole program without the program's intervention.

So what does this all have to do with us? Well, if metamathematics really existed, it would have to encode in itself a way in which to represent it, that is, mathematics. Remember, mathematics (if it has anything to do with metamathematics) *is* the way to encode metamathematics. Anyway, I think you'll also agree it's reasonable to say that we have ways of encoding mathematics (notations, conventions, etc.) Ergo, metamathematics must be capable of representing not only a non-empty subset of itself, but also the rules for encoding this non-empty subset of rules.

And herein lies the rub: even if you assume metamathematics, there must be a higher level of abstraction - a manager - if our mathematics is to have anything to do with metamathematics. And if metamathematics is completely unrelated to mathematics, then why think of it like mathematics at all?

I have skim read your very interesting post (about metamathematics etc) but will re-read it more closely when I have more time (there is a lot to read).
I think one of your points is whether algorithmic objects that use complex mathematical structures can self-design to model to a self-consistent universe, and then implement it. Its a very interesting question.
I can posit a few possible ontologies in that direction (but of course, I do not have a definitive answer), the easiest being that we, ourselves, are 'products' of a such a universe and can already construct a (very bad) model of a universe in a computer which will (or could) be improved using quantum computers and more advanced information processing methods in the future, until it resembles more and more our present Universe (I personally would make the universe a little smaller and set c to be slightly less).
The resulting system (if we were clever enough) would exist in information (which, in this view, the universe is also in information). I don't view our 'intelligence' as not belonging to the universe, more in the direction of it being another natural object of the universe and related to logic and mathematics.

 

[weichi]

particles made in von Neumann-like machines does make sense (to me at least). It explains a lot of quantum bizarreness easily.

Easily? Can you elaborate? Or post a link to a paper which explains this?

 

[alxm]

However, you want to write a program that's also capable of copying itself; one which can not only provide a representation of itself, but which can do so in such a way that the representation can also represent itself, and so on ad infinitum.

I think that with a little thought you'll agree that it's not possible to do this unless you have a third party come in and act on the whole program without the program's intervention.

It's quite possible. It's called a http://en.wikipedia.org/wiki/Quine_(computing).

 

[AUMathTutor]

"It's quite possible. It's called a quine. "
Yikes. I guess you're right. Interesting information, thanks for that. Hmm...

I guess a computer program was a bad example. Still, I'm pretty sure that ZFC sets can't contain themselves. One of the fun things about computers is, I guess, they can... well, now that I think about this, it's obvious.

Still, I hope my point stands, even if the example was bad.

 

[Dmitry67]

Still, I'm pretty sure that ZFC sets can't contain themselves.

Correct, this is called an Axiom of Regularity:
http://en.wikipedia.org/wiki/Axiom_of_regularity

Note that there are version of set theory without this axiom.

 

[camboy]

Also, camboy:
I'm not sure I follow your logic. So if Feynman says that nobody knows the machinery of QM, but Bohm says he knows, how do you know Bohm is right? Your argument seems to rest on the fact that it's not fair to say Bohm is wrong since he can't be proven wrong, but then you go on to say that he's right. I don't think it's fair to draw this conclusion either... in fact, science is such that we'll never know if any of it is right, or just works by some strange coincidence.

The logic is not complicated. Feynman actually says 'nobody knows any machinery', not 'nobody knows the machinery'. The substitution of one little word for another makes a profound difference.

Saying nobody knows any machinery (and this conclusion is backed up by the rest of Feynman's arguments in The Character of Physical Law etc.) implies Feynman thinks that nobody nowhere ever has been able to come up with a plausible 'mechanism' which implies the observed results (usually referring to the double slit experiment). It does not imply anything about whether such a model is actually `what really happens'.

Simply saying that there exists both a particle and a wave (which is what pilot-wave theory does - no extra mathematics, just now we have probability of a particle being at x rather than being found there in a suitable measurement) implies an obvious mechanism for the two-slit experiment. Is this correct? Who knows...?... but it it is clear that someone does know some machinery.

According to Towler's Lecture 7 referred to earlier, Feynman not only knew Bohm well (they used to go chasing girls on Copacabana beach together) but he thought highly of Bohm's work - so it is puzzling to me why he would make such a statement. I don't know the source of Towler's information.

 

[AUMathTutor]

I think you have a misunderstanding of the semantics of "know" in Feynman's sentence.

There is a difference between "knows" and "thinks of", or "imagines", or "believes". Know means (1) you think it, (2) you believe it, and (3) it's true. So does Bohm "know" a machinery? Let's check.

(1) Clearly, Bohm thought about the theory.
(2) Clearly, Bohm believes it.
(3) Who knows whether it's true or not? Maybe it is, maybe it isn't.

To be fair, you never really "know" anything in science, so Feynman really was misleading with his statement. In a less specific sense of the word "knows", then I guess you're right. But for what Feynman said, I think you'd have to be reading between the lines to misinterpret his statement to read "Nobody thinks they know any machinery".