Limitations of Physics | Seeking Feedback on Ideas

[apeiron]

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

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

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

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

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

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

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

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

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

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

 

[apeiron]

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

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

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

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

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

 

[Hurkyl]

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

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

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

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

 

[GeorgCantor]

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

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

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


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

 

[GeorgCantor]

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

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

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

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

 

[Hurkyl]

"Top-down causative agent describer?"


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

 

[apeiron]

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

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

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

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

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

 

[tom.stoer]

then you are talking about meta-mathematics

 

[ConradDJ]

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

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

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

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

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

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

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

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

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

 

[apeiron]

then you are talking about meta-mathematics

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[GeorgCantor]

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

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

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

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

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

True, but how far can this reasoning take us?

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

 

[tom.stoer]

@apeiron: Remarkable post!

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

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

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

 

[GeorgCantor]

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

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


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

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

 

[tom.stoer]

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

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

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

 

[GeorgCantor]

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

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

 

[tom.stoer]

I am not agnostic.

They cannot be both because this would be contradictory; so "neither" is the correct answer. They are quantum objects and "wave" and "particle" do not apply. But in order to understand this one must go through all the reasoning of Bohr et al.

 

[GeorgCantor]

I am not agnostic.

They cannot be both because this would be contradictory; so "neither" is the correct answer.

This would be contradictory only if one assumes a sort of (naive) realism that is refuted by the new physics. Despite the heavy price, assuming a sort of non-separability clears the "contradiction" in its roots.

They are quantum objects and "wave" and "particle" do not apply. But in order to understand this one must go through all the reasoning of Bohr et al.

Even the term 'objects' is misleading and i am certain you are well aware of that.


If we are to return to the reasoning of the fathers of the new physics, here is a relevant quote by Schroedinger on the continuous-discrete dichotomy:


"The world is given to me only once, not one existing and one perceived. Subject and object are only one. The barrier between them cannot be said to have broken down as a result of recent experience in the physical sciences, for this barrier does not exist."


"What is life?", p. 122

 

[tom.stoer]

I agree on what you are saying regarding objects and subjects; I use "quantum object" simply because it's better than "particle" or "wellicle". Perhaps quantum system would be even better.

It is of course only contradictory in terms of naive classical physics. So this context is not suitable for quantum objects, but is is not useless as it is needed to explain why it is not suitable.

Instead of arguing against realism (which is not so easy to describe) I argue against "wave and particle". As this is specified in classical terms it would have to make sense classically - but it can't. Therefore I am arguing that a quantum object IS neither wave nor particle, even so it APPEARS sometimes either as wave or as particle.

This means that I don't want to abandon realism completely, but that I want to limit it in a certain sense. QM cannot tell us what nature IS, but it is rather good in explaining us what nature IS NOT.

 

[Hurkyl]

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

Your metaphysics seems to be 2000 years behind the times.

Discrete is defined by its lack of continuity ... But continuity must also exist, otherwise how could I know it was absent?

Ignoring the substance of this paragraph for the sake of argument -- either you are dressing up in fancy words a trivial fact of classical logic (every predicate has a negation, and is equivalent to the negation of its negation), or this is load of hogwash, depending on what you mean by "exist".

The same has happened in maths with category theory. It has been agreed that the basis of mathematical thinking is the foundational dichotomy - structure~morphism.

Despite your continued use, category theory is one of the worst example you could choose to support your dichotomy thesis, since the original reason for its existence was to study category~functor~natural transformation.

In addition to failing on number, it fails on exclusion too -- mathematicians have been treating functions as objects and objects as functions since long before I was born. Lambda calculus is a particularly nice example of a language in which there is explicitly no distinction between the two ideas.

 

[apeiron]

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

It is amusing that you rail against dichotomies and then jump straight to where they become unavoidable in physics.

When the HUP makes a dichotomy of location~momentum, or energy~time, this is not just some "for the hell of it" metaphysical idea but an experimentally verified fact about reality.

Same with Bohr's complementary principle. Particle~wave. Is that not a dichotomy in the exact way that I have described - alternatives so mutually exclusive that you cannot observe both at the same time in nature?

If you just don't like the word dichotomy, you could talk about reciprocal or complementary.

 

[apeiron]

Your metaphysics seems to be 2000 years behind the times.

Getting desperate are we?

Ignoring the substance of this paragraph for the sake of argument -- either you are dressing up in fancy words a trivial fact of classical logic (every predicate has a negation, and is equivalent to the negation of its negation), or this is load of hogwash, depending on what you mean by "exist".

The law of the excluded middle does require that the middle be excluded. There is a process that has to come before the fact. But again this is "ancient metaphysics".

Despite your continued use, category theory is one of the worst example you could choose to support your dichotomy thesis, since the original reason for its existence was to study category~functor~natural transformation.

So you are saying that structure and morphism are not dual? Really?

 

[Hurkyl]

When the HUP makes a dichotomy of location~momentum, or energy~time, this is not just some "for the hell of it" metaphysical idea but an experimentally verified fact about reality.

The HUP doesn't make a dichotomy of anything; it merely makes a precise, quantitative statement about quantum states.

One could try and reinterpret that statement as a dichotomy, but point it becomes far more useful to learn from what it actually says rather than trying to shoehorn it into one's a priori vague^* philosophical notions.
* see below

Note that the HUP isn't even a statement about measurement or observation -- quantum states inherently have some amount of localization in both position and momentum, and the HUP is merely a constraint on just how localized they can be.

There is a useful duality between position and momentum -- the Fourier transform swaps the two (up to a sign) -- but that doesn't have any resemblance to a dichotomy.

Same with Bohr's complementary principle. Particle~wave. Is that not a dichotomy in the exact way that I have described - alternatives so mutually exclusive that you cannot observe both at the same time in nature?

How so? I suppose you can define "observed a particle" and "observed a wave" so that they are exclusive things and so any measurement can only yield one or the other -- but one of the main reasons QM was invented is because this was an instance where nature demonstrably did not organize itself neatly into our notions of how it should behave.

If you just don't like the word dichotomy, you could talk about reciprocal or complementary.

Don't all three of those words mean very different things?

The law of the excluded middle does require that the middle be excluded. There is a process that has to come before the fact. But again this is "ancient metaphysics".

"A process that has to come before the fact?" I can't extract any meaning from that.

We use a logic with the law of the excluded middle because we find it useful, not because the ancient Greeks decreed that we should.

So you are saying that structure and morphism are not dual? Really?

I can't think of any meaningful dualities or dichotomies between them.

Getting desperate are we?

 

[GeorgCantor]

It is amusing that you rail against dichotomies and then jump straight to where they become unavoidable in physics.

You miss the point. There ARE dichotomies of course, but they belong to the naively classical domain.

When the HUP makes a dichotomy of location~momentum, or energy~time, this is not just some "for the hell of it" metaphysical idea but an experimentally verified fact about reality.

These are not dichotomies that represent how reality is(and that's what my point was about) but how reality behaves in certain modes of inquiries.

Not to nipick, but you can know both position and momentum of a particle but with bad accuracy. That's not really a case of dichotomy(i.e. "division into two mutually exclusive, opposed, or contradictory groups" - www.dictionary.com, 2nd def.)

Same with Bohr's complementary principle. Particle~wave. Is that not a dichotomy in the exact way that I have described - alternatives so mutually exclusive that you cannot observe both at the same time in nature?

A particle is discrete by definition, a wave(field) is continuos. The false dichotomy lies in the fact that, in reality, superposed particles that undergo 'collapse' display both continuos and discrete behavior at the same time, but in THEIR nature, they are NEITHER. Reality is represented in the continuous-discrete dichotomy in our, admittedly naive, classical mode of reasoning, but in its deep nature, it's neither. The dichotomy is false.

 

[GeorgCantor]

The HUP doesn't make a dichotomy of anything; it merely makes a precise, quantitative statement about quantum states.

One could try and reinterpret that statement as a dichotomy, but point it becomes far more useful to learn from what it actually says rather than trying to shoehorn it into one's a priori vague^* philosophical notions.
see below

Yep. Bad example of a dichotomy.

 

[apeiron]

Not to nipick, but you can know both position and momentum of a particle but with bad accuracy. That's not really a case of dichotomy(i.e. "division into two mutually exclusive, opposed, or contradictory groups" - www.dictionary.com, 2nd def.)

If your accuracy is bad, then you don't really know. Your knowledge is vague and the reality you describe is still relatively indeterminate.

The Planck scale describes a yo-yo limit of certainty. As we approach certainty of location, we exclude certainty about momentum, and vice versa.

 

[apeiron]

The HUP doesn't make a dichotomy of anything; it merely makes a precise, quantitative statement about quantum states.

One could try and reinterpret that statement as a dichotomy, but point it becomes far more useful to learn from what it actually says rather than trying to shoehorn it into one's a priori vague^* philosophical notions.
* see below

Note that the HUP isn't even a statement about measurement or observation -- quantum states inherently have some amount of localization in both position and momentum, and the HUP is merely a constraint on just how localized they can be.

There is a useful duality between position and momentum -- the Fourier transform swaps the two (up to a sign) -- but that doesn't have any resemblance to a dichotomy.

Despite your every attempt to wiggle around the issue, there is still the basic fact of position~momentum as mutually excluding measurements.

You and Georg are confusing yourselves by attempts to maintain a classical picture of reality where things just exist. I am talking about the detail of a process metaphysics where reality is formed by self-organising constraints.

This is kinda what metaphysics is, ancient or modern. If you don't want to be part of that discussion, it's fine by me.

 

[Hurkyl]

If your accuracy is bad, then you don't really know.

The fact that most quantum states have inherently inaccurate position doesn't prevent us from doing precise, accurate position measurements on them. It's just that if we repeat the experiment with identical states, we will see a wide distribution of positions.

(How do we know the measurement is accurate? We can check it by feeding in a known well-localized position states)

The fact that most quantum states have inherently inaccurate momentum doesn't prevent us from doing precise, accurate momentum measurements on them. It's just that if we repeat the experiment with identical states, we will see a wide distribution of momentums.

(How do we know the measurement is accurate? We can check it by feeding in a known well-localized momentum states)

The HUP says there do not exist states that are both well-localized in both momentum and position. That doesn't stop us from precisely and accurately measuring both. It's just that if we repeat the experiment with identical states, we will see a wide distribution of results.

I am talking about the detail of a process metaphysics where reality is formed by self-organising constraints.

I thought pure reason was discredited centuries ago?

 

[apeiron]

The fact that most quantum states have inherently inaccurate position doesn't prevent us from doing precise, accurate position measurements on them. It's just that if we repeat the experiment with identical states, we will see a wide distribution of positions.

(How do we know the measurement is accurate? We can check it by feeding in a known well-localized position states)

The fact that most quantum states have inherently inaccurate momentum doesn't prevent us from doing precise, accurate momentum measurements on them. It's just that if we repeat the experiment with identical states, we will see a wide distribution of momentums.

(How do we know the measurement is accurate? We can check it by feeding in a known well-localized momentum states)

The HUP says there do not exist states that are both well-localized in both momentum and position. That doesn't stop us from precisely and accurately measuring both. It's just that if we repeat the experiment with identical states, we will see a wide distribution of results.

Err, you are still dealing with a basic duality. The observations you can make divide neatly into two mutually exclusive categories - that is the meaning of orthogonal.

This is actually very important for a constraints based approach to modelling reality. For some reason, constraining a quantum potential so as to reduce its local degrees of freedom is dichotomous. Successfully reducing the degrees of freedom in one direction (say location), increases the degrees of freeom in the other (momentum).

If you are concerned with maintaining a mechanical, classical, view of reality, you will go to any lengths to avoid confronting these kinds of issues face on. I understand that.

I thought pure reason was discredited centuries ago?

And your point is?

 

[Hurkyl]

The observations you can make divide neatly into two mutually exclusive categories

A position measurement is not a momentum measurement. But that's not what you had been saying -- you had been saying a position measurement precludes you from also making a momentum measurement.

(And you forgot about all the other kinds of measurements that aren't functions of position or functions of momentum)

that is the meaning of orthogonal.

No, orthogonal means having inner product (or similar) equal to zero. In common parlance, refers to aspects that are independent of one another.

Classically, position and momentum are orthogonal in the latter sense. They most certainly are not orthogonal in quantum mechanics.

 

[apeiron]

A position measurement is not a momentum measurement. But that's not what you had been saying -- you had been saying a position measurement precludes you from also making a momentum measurement.

(And you forgot about all the other kinds of measurements that aren't functions of position or functions of momentum)

No, I've been saying one excludes the other. Complete information completely excludes information about the other...and partial information partially excludes information about the other.

And what other kinds of measurements do you want to talk about? And how would that alter things for the most fundamental kind of measurement we seem interested in?

Energy~time is also treated as a dichotomous or complementary pairing, but there are reasons why it is not as "pure" a case as position~momentum.

No, orthogonal means having inner product (or similar) equal to zero. In common parlance, refers to aspects that are independent of one another.

Classically, position and momentum are orthogonal in the latter sense. They most certainly are not orthogonal in quantum mechanics.

Yes, and what was I saying? Classical mechanics presumes position and momentum to be orthogonal, independent, measurements. There is no need for a further constraint to make this so. This is just the way reality is. It is a fact that simply exists. Why would we even see them related by some particular relation? You would just have position as a physical fact, momentum as another physical fact...and why stop at two? Why not a whole succession of further unrelated physical facts.

But QM showed instead that these two aspects of reality are in fact related in a very definite fashion (the HUP, the Planck scale, etc). And they are a duality. They are orthogonal. And furthermore, they are asymmetric (opposed in scale).

So QM introduces the necessity of a relationship. Position and momentum are all mixed up as a state of indeterminancy. And then further constraints have to be imposed to decohere this mixed state. (Or vague state would be more metaphysically accurate).

Classical mechanics claims position and momentum are unrelated, actually independent. QM shows they are deeply related and orthogonally organised. Constraints are needed to turn possibilities into certainties. But in a "conservation of indeterminancy" type closed system principle, increased certainty in one direction of measurement decrease certainty in its complementary direction.

 

[Pythagorean]

apeiron, how are position and momentum dichotomistic? Specifically, how are they:

a) jointly exhaustive
b) mutually exclusive

I can see how you might carefully select language to make b work, but a) doesn't make any sense to me.

 

[Hurkyl]

I can't think of any meaningful dualities or dichotomies between them.

I should add that for those who advocate categories as mathematical foundation, the main^* philosophical point actually has little to do with category theory itself -- it's that set theory unduly emphasizes the identity of mathematical objects over the interactions between mathematical objects. Category theory just happens to be a rather effective tool for describing such things.

*: Some may have other points. This is the one I'm mainly familiar with.

 

[Pythagorean]

I should add that for those who advocate categories as mathematical foundation, the main^* philosophical point actually has little to do with category theory itself -- it's that set theory unduly emphasizes the identity of mathematical objects over the interactions between mathematical objects. Category theory just happens to be a rather effective tool for describing such things.

*: Some may have other points. This is the one I'm mainly familiar with.

http://en.wikipedia.org/wiki/Abstract_nonsense

 

[apeiron]

apeiron, how are position and momentum dichotomistic? Specifically, how are they:

a) jointly exhaustive
b) mutually exclusive

I can see how you might carefully select language to make b work, but a) doesn't make any sense to me.

Metaphysics arrived at a variety of dichotomies that appeared exhaustive. That is, you had two terms, each of which was defined as having nothing of the other, but which also together then covered all possibilities.

So for instance, stasis~flux. You had a separation into that which was defined by its lack of change, and its antithesis which was defined by its lack of fixity. It was agreed - because no one could come up with anything to contradict it - that these two terms defined the landscape of what was possible.

Now modern physics uses a number of dichotomies that are rooted in stasis~flux, such as space~time (the set of locations, the space of possible transformations), and position~momentum (again what is fixed vs what moves).

What is so hard to understand about any of this?

 

[tom.stoer]

@apeiron:

For some time I had the feeling that I understand what you are saying in into which direction this discussion will go. I saw no problem in referring to pre-socratic philosophy as most intersting problems in metaphysics have already been spelled out then and have been discussed but solved since.

In the meantime I have ot say that the discussion has somehow went astray. One insists on "dichotomies" and "dualities" which are just words and which are used to explain wave-particle-xxx whereas wave-particle-xxx is used as an example for the above mentioned words.
Orthogonal has a very precise mathematical meaning (not so for duality) but is is used for position and momentum; just to remind you: orthogonal means nothing else but qp=. I am sure it's definately NOT what you want to say.
Then you use wave-particle- and position-momentum-"duality"; but these two "dualities" are something very different. Bohr called the first one "complementary" and never mixed it up with position-momentum-xxx afaik.

I still read this thread but I do no longer know how I should respond.