I was thinking about the unified theory of everything and began to wonder if it was really possible.
My reasoning is this:

We live in - for an anology - an apple universe! This means that everything we apply to understanding our universe involves apples! OK, a bit strange, but this seems the easiest way of explaining it.

So, our mathematic formulas are all geared to working with apples, and we get results that make sense and work with the observations that we see.
But, when we approach things like Black Holes and the very tiny we aren't using apples anymore, but - let us say - oranges.
Therefore the mathematics that we apply don't work because they can't - being callibrated to apples!

Now along comes quantum theory, and I think, is this truly orange mathematics or is it merely apple mathematics with a slightly tangy flavour?
Being which we get things like super string theory because we are still working, in essence, with apple mathematics. Ah, does my standing on super string theory show here? Ha!

Well, I don't think this multiverse theory with millions of universes on the m-brane is feasable, and the main reason for these theories is that we are still using apple mathematics with a slightly tangy flavour, which gives us hybrid results and not the true peel and pith of the orange.

So, back to the main question, a unified theory of everything would involve apples and oranges being smoothly linked together. Is this possible?
Or are we trying to apply apples with a slightly tangy flavour that we say is the truth, but, in reality, is still green with a solid core, with just more apples?

That would hint at unification because both are green with a solid core. They have common denominators to work with. Yet all you could really say about apples and oranges is that they both come from trees! Or, in this case, our universe.

So, what would orange mathematics be? Quantum theory seems to be heading that way, but has it really got there? And when it does, would its structure be so different from our apple mathematics that unification would be impossible?
Or am I barking up the wrong tree?

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I don't believe in mathematics. Albert Einstein

Biologically speaking, if something bites you it's more likely to be female. Desmond Morris.

Quantum analysis is scientific dithering

Professor Frink: My observations n'hey, n'hey, show the universe could be a torus Weh, uh, or toriod it may like the typewriters and bananas and the monkeys with big teeth the biting the screaming Mm-hai!

Homer: mmmmm... doughnuts!

Suppose I'm a particle. Do I come along and say, "How do I feel like behaving at the moment? Shall I do the quantum trick or the relativity trick, exercising choice so as to make my behaviour unpredictable by any conceivable physical law even of a probabilisitic nature?" Or in fact is the way I behave completely described by some physical law(s)?

It seems likely to me that particles behave in accordance with physical laws which completely describe their behaviour, probabilitically as appropriate, in any circumstances. Whether we are capable of discovering/describing them is a separate matter.

Your apples and oranges didn't make much sense to me. Two "different" laws are actually two parts of the same law provided that there is a link between them saying when each applies in a complete and consistent manner.

Absolutely, it is possible so I don't think you're barking up the wrong tree.

But the unified theory should be a fundamental theory to explain all the forces/particles in one symmetrical theory. Many of these have been proposed such as "supersymmetry" and superstrings.

What I am becoming skeptical about is whether or not these theories will ever be VERIFIED by experiments. If they find the Higgs boson at CERN someday, that will pretty much prove the standard model. But they will have to discover a lot more particles to prove these other theories, and I'm not at all sure they ever will.

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"fifty is nifty" , unknown poet

You are merely assuming what you are hoping to argue. If I say that you cannot "be a particle", because there is no such thing, how does your argument still proceed to unification?
But what a mouthful that "probabilistically as appropriate" part is! How does a particle "do something random" when it is "appropriate" to do so? We might be able to unify everything with which we are familiar, like probability concepts, but we will never unify everything there is. Does the thought ever become unified with that which is thinking it?
If we are not capable of unification, then we have no unification. How do we profit scientifically from imagining something exists that we are not capable of demonstrating exists? Like someone using the North star to navigate, we work for unification because that is the proper direction that science is pointed in, not because we think complete unification is attainable.
Except for all the "cracks" that always remain, such as the need to apply boundary conditions to our equations, and the need to be able to design experiments within our technological and intellectual capability.

(1) No I'm not. Particles have been observed. To assert otherwise is either to argue for a nontestable theory of existence such as "reality doesn't exist, it's all a dream", or else is vexatious.
(2) So you don't like what I say because it's a mouthful. What kind of an argument is that? Quantum theory is described probabilistically, so I am saying nothing unusual or novel here. I didn't really need to say it, given that our existing theories are probabilistic, but I was predicting a common but fallacious objection before someone made it. (I have discovered the need to do that here).
(3) Pythagoras' theorem was there even before people discovered it. If we haven't yet discovered Pythagoras and I say that in principle geometry must exist, then I am saying "it exists because it is there to be found". You say "ah but if we don't find it then it doesn't exist for us", well, I don't think that is the kind of non-existence OP is interested in. Obviously it is unknowable whether we will ever find something, even if we can prove it is there to be found. Rather like the well-ordering of the reals that is predicted by an existence argument based upon the Axiom of Choice, but which no one thinks can ever be exhibited.
(4) I said "complete and consistent", ie no cracks. Electro-weak-strong unification which sticks 3 laws together without cracks. If there are actually cracks in reality, then there are situations when the particle doesn't "know" what to do. Which I think is nonsense, and that is the only real point I am making here.

Edit: In (3) the Axiom of Choice suggestion is not a good analogy on second thoughts. A better one is the Navier-Stokes equations, which we have found but can't solve. So we have a theory but can't use it. But the theory is still there.

Neither one, actually. Particles are models. What makes that obvious enough is that if you ask ten theoretical physicists in different subfields what a particle is, you will likely get 10 very different answers. This is what I mean when I say that you are assuming your argument when you assume a meaning for "particle", as if your own images around that word are the same thing as the reality. Your concept unifies your familiarities, someone else's unifies theirs. This is why I say that we can never unify everything that is real, because we will never have access to total familiarity.
That wasn't the argument part. The meaning of "mouthful" is that there is a lot behind the words that is being glossed over. What is being glossed over was the argument part.
My point is that one of the great efforts at unification that occurs is the effort to unify what appears to be a random outcome with underlying causal factors. If you are willing to leave that step out, as most quantum mechanics is formulated to do, then you have not unified everything and cannot use it in an argument that everything is unifiable. Personally, I have no problem with leaving the probabilistic aspects ununified, but then I'm arguing that complete unification is as impossible as walking north to Polaris.
Our "existing theories" are ununified! Ergo, citing aspects of current theories is not an argument for unifications that have not yet been achieved.
But how do you know what is there to be found until you find it? Again you are simply imposing your philosophy on your argument, and then extracting as conclusions what you put in as assumptions. You define "what exists is what is there to be found", then argue from that definition of existence that everything that exists is there for us to find. It's circular reasoning. Science normally differentiates what exists from our best descriptions of it, and for good reason, especially if one is wondering what is unifiable.
Actually, I say neither that we what don't find doesn't exist, nor that everything that exists is there for us to find. Either claim would beg the issue at hand, which is what we can find and unify out of what exists. I am using words that leave the question open, you are using words that simply assume your conclusions and then use them to reach those conclusions.
Axiomatic systems are the perfect example of finding the ramifications of your own assumptions. The effort to understand reality is not like that, because reality is not subject to our choice of axioms, but rather the other way around. Mathematicians are not used to that state of affairs!There are always cracks, which have to do with connecting the axiomatic structures to reality. This is the part of physics that a lot of people don't seem to recognize. The way it works is, we form an axiomatic structure of some kind to be able to draw on its consistency and provability. This is generally called "idealization", and there is no axiomatic structure for choosing idealizations, that's the art of physics (that often gets overlooked even though it is always the first step.) We then confront that axiomatic system with observations to see how useful that consistency and provability are in practice. That process involves all kinds of "cracks", because it has the "fingerprints of the practitioner" all over it. The first, and most important, fingerprint is the choice of the axioms in the first place. The meaning of "particle" is a perfect example of this-- different practitioners with different goals will adopt different axioms around the meaning of a particle, from classical descriptions, to the way the term is used in elementary quantum mechanics, to how it is used in field theory, string theory, or even abstract mathematical formulations. All different, involving different idealizations, different accuracy, and requiring different information to analyze.

The cracks I refer to are not in reality, they are in our understanding about reality. We cannot discuss the unification of the former directly, as unification exists in the latter and extends by implication to the former. Hence our discussion is not about reality, it is about the axiomatic systems we invent to describe reality. The distinction is usually ignorable, but only at our peril in discussions that try to get to the heart of what science can achieve.We have no disagreement that the theory is there.

I was asserting that IF I have good reason to believe that it MUST exist, then it exists even though I haven't exhibited (ie found) it.

You seem to accept that with Navier Stokes. You seem happy to accept that there is a solution that describes the behaviour of (eg) a mountain stream, even though no one can exhibit that solution. A mountain stream run again with the same boundary conditions would behave the same way, obeying the Navier Stokes law. The Navier Stokes equations provides an existence argument for the solution, even though we can't exhibit such a solution.

I will go a step further. I would argue that we knew that a theory of fluid dynamics must exist even if we hadn't actually discovered the Navier Stokes equations yet, and did not know if we ever would. Because if we run fluid systems again, they respond to the same causes in the way. To assert otherwise is to give the objects in physics some indeterminism that smacks of religion (the god of gaps as Dawkins calls it).

That is in effect my position. To summarise it, if effect follows reliably from cause (which includes effects described probabilistically, which most people are happy with accepting would constitute a valid scientific theory, even if you aren't) then there must exist in principle a description of how the effect depends upon the causes. I never sought to say we would actually find it, in fact I explicitly said we might not.

What is a good reason to believe something must exist? And what is the "it" in your last statement, other than "that which exists"? Unless you can offer a different meaning for that word, you are saying that "that which exists does so even if I haven't found it". I can't disagree with that, but it certainly doesn't tell us anything about the prospects for unification.
When we say something "obeys" an equation, we are using imprecise colorful language that we can normally get away with, but not when we are trying to look deeply into what science is. Mountain streams don't "obey" anything, that is a personalization-- they just are. It is we who decide what they "obey", when we decide how we will treat them and what we will consider to be "suitably law abiding" behavior. And when the behavior does not obey our laws, we don't throw the system in jail, we just change our sense of what the laws are. Fingerprints all over the "crime scene".

Again that is simply confusing the axiomatic system we invented to describe the behavior for the behavior itself.
Of course theories of fluid dynamics exist, that became true as soon as our brains developed enough to count as able to make theories.
But there are many such descriptions, and we have found plenty already. The issue is not if there are ways of describing reality, the issue is how completely unified can they be. Reality does what it does, all we do is assemble familiarities and try to unify them into what we can call an explanation. To think we are doing something different is to lose track of the process and mistake reality for our own language about reality. Our goal is certainly to seek unification whereever we can find it, but the absence of complete unification is a natural consequence of using language to describe something that is not language.

Ken, you have now explicitly agreed with the totality of the limited point I am trying to make, even if apparently you didn't like some of the way I couched it. Evidently what you are trying to say is something different.

It is interesting that you would claim that I agree with everything you said, because to me this statement is the core of your position, and I have advanced an argument to point out the flaws in this position. Particles don't behave in accordance with laws, we create an axiomatic system that creates both the concept of particles and the concept of laws, so we are of course capable of discovering/describing them, we created the concepts. When we are done creating the concepts, we evaluate their usefulness in understanding reality, and iterate the process, but if we lose track along the way of the difference between our mental constructions and reality, we are led to make unsupportable claims like "everything is unifiable". To me that position seems completely counter to the one you were advancing, so I guess we'll have to agree to disagree on whether or not we agree!

KenG. I agree. pete

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A third rate theory forbids
A second rate theory explains after the fact
A first rate theory predicts...A. Lomonosov

I thought, when I stated precisely the same view, but using the example of fluid dynamics (ie a theory we already have, but pretending we didn't have it yet) rather than particle physics, that you had overtly assented to exactly my point. Although I did notice (but chose to ignore) you added some stuff afterwards which seemed to contradict yourself.

I don't think we need to agree to disagree ... yet. You have now made yourself sufficiently clear (at last) I think I can see why you seemed to agree with me but persist in saying you don't.

You say that "particles don't behave in accordance with laws...". I would like to propose that I might from time to time quote you on that, for example as follows: "Ken has said elsewhere 'particles don't behave in accordance with laws...' (precise quotation). Just so you know where he is coming from in general."

But it is a quote out of context. When I say "particles do behave in accordance with laws" I think I am actually using my words with different meanings from when you apparently say the opposite. I think I am actually saying the thing you do believe. And you are saying something that I think is a fairly pointless philosphical quibble, though please go ahead and enjoy yourself making it. When I read what you say about axioms etc, I actually make similar points myself in another thread about is mathematics true. But I don't feel the need to worry about it, as you clearly do. Whether particles "exist" or not, or whether my "particle" is actually a model in an axiomatic system or not, who cares, in my view. I'm a "just do the sums and don't worry about what it really is" man.

In science the only thing that objectively exist are measurements. Theories explain measurements (Popper). So when I say "particles do behave in accordance with laws" what I am actually saying is that "measurements we make can be explained in accordance with laws, and given measured initial conditions, measured later conditions will reliably behave the same way each time, so that in principle laws exist even if we haven't found them yet". As to what the thing is that actually is being measured, well sages, priests and philosophers can argue about that, to no useful purpose in my view. Measurements is all we will ever really have, and I do believe that the measurements will show reliable and repeated behaviour. To deny that is to deny the possibility of reliable scientific laws in a Popperian sense. I don't think you are going that far.

If your point is that our theories don't directly affect reality, we can agree on the truth of that, but not its relevance to the OP. The issue is, can our theories completely unify everything that happens.
I thought I was perfectly clear in this thread, for example (added bolds):

and

If you want to quote me out of context, you will be engaging in logical fallacy.
I think you are forgetting the entire purpose of the debate: to establish whether or not we should expect reality to be completely unifiable. News flash: that is a philosophical topic! If you didn't want to address "philosophical quibble", why did you assert an arbitrary position in the first place?
Same question as above. But I'm glad we agree on the difference between what is "true" and what "stems from the axioms", an important distinction I have also made on other threads. But this thread is about whether or not we can make an axiomatic system that is complete in its application to reality-- something we cannot do in regard to the real numbers. You are therefore arguing that reality is less rich than the real numbers, whereas I argue that at best we can hope that its projection onto objective measurement is less rich than the reals, but I don't see why we should expect that projection to maintain a complete axiomatic structure in the first place.

Obviously the answer as to whether or not we should care about that distinction depends on the context of interest. When the context is "is a unified theory of everything possible", I can hardly see why that would not be an important issue.
A perfectly valid view-- but why did it lead you to post on this thread? If that was really your position, the answer to the OP is "who knows-- I just calculate".
Then we agree on the meaning of "objective existence".
So then what you are actually saying is that "everything is unifiable because it behaves consistently, whether or not it is possible for us to find unifiable laws". You are simply assuming that "unifiable" may be equated with "behaves consistently", whereas I see those as completely different issues.

Why would I deny it? That is essentially the point I've been making. Yet I claim it leads to "we should not expect everything to be unifiable", and you claim the same thing leads to "we should expect everything to be unifiable, even if we can't do it". Personally, I think that if we can't do something, then that's the definition of "not possible" for us, which I think is what the OP was asking.

Ken, You have now characterised my views quite accurately, including what I think of "unifiable". I thought that was relevant to what OP was asking, but then what he wrote wasn't very clear.

So it was all a semantic mess-up between us. I'm pleased about that. I misunderstood you so badly until your last post that I was starting think you were taking a counter-scientific position, as you probably noticed. Pleased I was wrong about that.

As I said, OP's thread was not the clearest. He hasn't been back to clarify, and I don't blame him. Given we each had difficulty understanding the other, lord help poor OP.