Limitations of Physics | Seeking Feedback on Ideas

[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[/size]

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[/size]

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[/size]

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.

 

[Pythagorean]

What is so hard to understand about any of this?

Because you're kind of making it up, or at least discussing a particular aspect of position and momentum that is unclear. The position and momentum of a particle aren't jointly exhaustive properties of the particle (and you haven't showed how they are in your responses to me; you've only given more vague implications).

Head and Tails are a textbook dichotomy. The coin can only land on heads or tails (in the probability model; not reality where it can, with some probability, land on it's edge) so they're jointly exhaustive; the coin can't be both heads and tails at the same time, so they're mutually exclusive.

A particle can have a momentum and a velocity at the same time (they're not mutually exclusive properties of the particle) and momentum and velocity aren't the only two properties a particle can have (they're not jointly exhaustive properties of the particle).

So you must be talking about something specific. The HUP isn't dichotomistic: there is some bit of mutually exclusive (if you want to talk about the "crispness" of position and momentum, as you would call it)... but still, you can sacrifice a little from each and have both a momentum and a position that are both equally vague/crisp. It's not fixed to where you must measure one with high accuracy and one with low accuracy. You can compromise... that seems to fail the test for mutual exclusivity.

I can see how HUP might be jointly exhaustive (the HUP, after all, only has two variables in it), but you're still talking about a false dichotomy if only 1/2 conditions are satisfied.

 

[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.

It might to help to know where I am coming from on this. My own background is in mind science, and the evolution of the human mind in particular (four books, reviewed in Nature and American Scientist, columnist for Lancet Neurology, etc).

So I was dealing then with the problem of how to model complex adaptive systems. Which eventually led me to ask about the general principles of systems. I found that the people who talked the most sense about this were concentrated in theoretical biology - hierarchy theorists and other mathematical biologists like Howard Pattee (student of von Neumann), Stan Salthe, Robert Rosen, Robert Ulanowicz.

That led in turn to the next level down of open system or far from equilbrium thermodynamics - dissipative structure theorists, maximum entropy principle, condensed matter physics.

At the same time I - like many in theoretical biology - was struck by how "organic" early greek philosophy was. Enlightenment philosophy was irrelevant as it was largely a confused debate between the Christian church and Newtonian physics. And then there has also been a rediscovery of Peirce over the past 15 years. He has become very important in theoretical biology because semiosis is a logic of complex systems.

So you can see in all this that I have followed a logical path from mind science to the general modelling of systems. But I claim no professional expertise in physics or math. I am just interested in the philosophy of physics and maths because it is necessary to understand exactly what the mainstream presumes (and so how the systems approach differs, or where it connects).

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.

Yeah, you try to talk to some people in a general way and they want to drag you into the small areas of knowledge where they feel they can comfortably have a go at you. You try not to get bogged them down with jargon, and they will use that against you as well.

So for example orthogonal. This has a clear general meaning that is useful. It is simple to see how two axis as right angles are completely excluded by definition from each other's space. It should be a powerful visual image. But Hurkly wants to turn it into a discussion of a particular formalism, Hilbert's space (I am presuming - he never spells things out). In Hilbert's space, it is the rays representing either an infinity of momentum vectors or position vectors that are orthogonal, not the momentum vectors and the position vectors. I get that. And it is not what I was talking about.

Same now with using the terms duality or complementary. You are quite right. I use dichotomy with a very specific technical meaning. But hey, who here has studied hierarchy theory and system science? I'm starting from scratch with most of these guys. And I don't get the impression they are the slightest interested.

Anyway, for me, duality is not dichotomy. A duality is where things are broken apart, no causal connection (like the Christian/Cartesian dualism of mind and matter). A dichotomy is not a breaking but instead a separation. And what gets separated can still mix. Which is where the connection with hierarchy theory and semiotics lies. From the separation of two things you then get arising the third thing of their mixing. This is what makes it a system - separation AND interaction. Differentiation AND integration. There is much more from hierarchy theory such as the claim that the emergence of higher levels acts back to constrain the degrees of freedom of the lower level. Duality is not actually a model of anything. The dichotomy is derived from the specifics of hiearchy theory. Though very much a work in progress.

Complementary is also not a term I would normally use - but Bohr did, picking it up from Taoist and Buddhist traditions (which in turn have ancient connections to the organic turn in Greek philosophy - ask Arivero who wrote a couple of nice papers on this; and while you are at it, remember Rovelli has just published a book on Anaximander).

The problem with complementary is that it is a single scale concept. You have a broken symmetry, but as with yin-yang, the two halves are the same size as each other.

The dichotomy, as I am defining it based on hierarchy theory arguments, is instead an asymmetrical breaking of symmetry. The form it takes is always, canonically, local~global. Furthermore, and here I go further than usual, it is a fundamentally dynamical story. It presumes a gradient (as required by far-from-equilbrium modelling) and so always expands.

So it is a technical idea with features that take a lot of explaining unless you are active in current theoretical biology/dissipative structure circles.

Now does this fundamental attempt at modelling "systems" apply to QM and cosmology? To me it seems to. I hear people grappling with the same issues such as "what is emergence", "how do we constrain our landscapes", "doesn't condensed matter physics seem like a good analogy".

And with QM, it just seems to be staring you in the face that mechanicalism no longer works. There is this squirrely two-ness going on that is fundamental.

If people aren't interested in asking why this might be so, and where two-ness - as a symmetry breaking across scale, a local~global two-ness - has popped up in other areas of scientific modelling and metaphysics, then that is their narrow minded choice.

But actually, in this thread I am not interested in defending any basic ideas. I was keen to focus on the quite specific issue of how global (ie: holonomic) contraints can organise landscapes of possibility...until the usual crowd derailed the discussions.

 

[apeiron]

Head and Tails are a textbook dichotomy.

No its not. It is a simple symmetry resulting in two things of the same scale. Which is trivial not deep. There is no reason why you can't have as many faces as you like. A dice has six. There are no natural constraints in this example, just artificial ones - arbitary choices about how many microstates you want your probablistic device to have.

A dichotomy is instead an asymmetry. It is a breaking across scale. And such breakings reduce to a canonical two-ness of local and global, the smallest vs the largest.

So when it comes to coin tossing, it is chance~necessity that is the relevant dichotomy. What you are trying to design is a system that maximises randomness by excluding the forces of determinism. One aspect is being made as large as possible by constraining the other, so making it as small as possible.

And these seem to be mutually exhaustive. The fall of the coin is either described by the chance, or by necessity. Unless of course we toss the coin in a somewhat slow, semi-deliberate fashion. Then we might be in that QM mixed state of being vaguely somewhere in between. We can't rightfully say which category ruled that particular toss.

A particle can have a momentum and a velocity at the same time (they're not mutually exclusive properties of the particle) and momentum and velocity aren't the only two properties a particle can have (they're not jointly exhaustive properties of the particle).

I don't think you can say that a particle has a momentum AND a velocity. If it has a momentum, then velocity is already spoken for. A particle can't have a momentum in one direction yet a velocity in a different one can it? They are not independent or orthogonal properties (whoops, I'm not supposed to say orthogonal). So we are back to position and momentum being the more exhaustive description.

 

[Pythagorean]

I meant momentum and position, I said velocity by accident.

 

[apeiron]

I meant momentum and position, I said velocity by accident.

In that case I already answered that if constraint is a dynamic, active, process, then weak measurements that only weakly constrain will give you weak information about both. But if we want to get crisp and definite - strong measurement - then information about one does exclude the other in the limit, does it not?

Where's the controversy?

In quantum mechanics, the Heisenberg uncertainty principle states by precise inequalities that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known to arbitrarily high precision. That is, the more precisely one property is measured, the less precisely the other can be measured.
...Moreover, his principle is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but it is a statement about the nature of the system itself as described by the equations of quantum mechanics.
...The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength (and therefore an indefinite momentum). Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there can be no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum.

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

 

[DevilsAvocado]

Regarding Heisenberg uncertainty principle, is there really any doubts...

Walter Lewin MIT – The Uncertainty Principle

https://www.youtube.com/watch?v=<object width="640" height="505">
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<param name="allowFullScreen" value="true"></param>
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</object>

 

[Pythagorean]

In that case I already answered that if constraint is a dynamic, active, process, then weak measurements that only weakly constrain will give you weak information about both. But if we want to get crisp and definite - strong measurement - then information about one does exclude the other in the limit, does it not?

Where's the controversy?

But one doesn't exclude the other. It's like F = ma. For a constant F, m must decrease for a to increase, but neither m nor a are ever excluded, one is just a higher value than the other (or they can be equal values, "medium" values). This is true for HUP, too. Neither is being excluded, especially if you take them to be equal.

A simple proof that this is possible:

that's the equation. There's nothing stopping us from taking:

dx = dp

so that:

h/2 <= dx*dp

-->

h/2 <= dx^2 = dp^2

which one's excluded?

 

[Hurkyl]

apeiron -- assuming for the sake of argument that you have meaningful ideas, you would probably have a much better time conveying them if you used words that mean what you are using them to mean, rather than words that don't mean what you are using them to mean.

 

[apeiron]

which one's excluded?

What is it that you don't understand about the phrase "in the limit".

 

[apeiron]

apeiron -- assuming for the sake of argument that you have meaningful ideas, you would probably have a much better time conveying them if you used words that mean what you are using them to mean, rather than words that don't mean what you are using them to mean.

Wow, thanks for this really intelligent response.

In mathematics, duality has numerous meanings, and although it is “a very pervasive and important concept in (modern) mathematics”[1] and “an important general theme that has manifestations in almost every area of mathematics”,[2] there is no single universally agreed definition that unifies all concepts of duality.

http://en.wikipedia.org/wiki/Duality_(mathematics )

 

[Pythagorean]

What is it that you don't understand about the phrase "in the limit".

Limits are defined, and there's thousands of them. Generally without more details, and in the right context, it means the classical limit of QM, but that would have nothing to do with HUP.

So what specific "limit" are you talking about?

 

[Pythagorean]

Wow, thanks for this really intelligent response.

Personally, I agree with Hurkyl's complaint; but it's about the word "dichotomy" not "duality"

In both philosophy and mathematics, "dichotomy" does have a particular definition (which we have discussed). Duality has all kinds of meanings, but that doesn't make using it any more meaningful... in fact, it makes it less meaningful and gives the user more wiggle room in discussions unless it's clearly defined.

on the coin as textbook dichotomy

No its not. It is a simple symmetry resulting in two things of the same scale. Which is trivial not deep. There is no reason why you can't have as many faces as you like. A dice has six. There are no natural constraints in this example, just artificial ones - arbitary choices about how many microstates you want your probablistic device to have.

Triviality and depth don't exclude things from the definition of dichotomy. The whole point of a trivial example is to illustrate the core mechanics of the definition. Furthermore, if you look at your greek roots, a dichotomy is about only TWO outcomes. If you want three, it's a trichotomy. Any more and it's a polychotomy.

Anyway, let's just ignore that terminology mistake. We're still looking at two independent outcomes (one happens or the other: heads or tails). What we have in HUP is a spectrum from more 'headish' to more 'tailish'. This would make it a false dichotomy.

 

[apeiron]

The whole point of a trivial example is to illustrate the core mechanics of the definition.

And I've already told you why your trivial example failed to illustrate the core mechanics.

Your example lacked scale differentiation. You might have two alternatives, but they were essentially the same thing. They were both microstates - designed to be exactly the same so as to make the coin toss fair. And there was no constraint on the number of microstates possible. You could instead of talked about a routlette wheel with 21 slots. So the two-ness of your probablistic device is just nothing to do with a dichotomy. Your obtuseness here becomes quite staggering.

A dichotomy - as I am actually defining it - involves a symmetry-breaking across scale. The emergence of an asymmetry.

So what we would have in your example is a scale based system we would describe as microstate~macrostate. You can have a system with an infinity of microstates. But the essential causal notion of what constitutes a microstate is singular. As is also obviously that of a macrostate. And 1+1 only makes 2.

I hope you get the difference. It really seems very simple.

As to false dichotomies, you will find that a way to avoid terminological confusion here would be to stick to the term "false dilemmas".

The logical fallacy of false dilemma (also called false dichotomy, the either-or fallacy) involves a situation in which only two alternatives are considered, when in fact there are other options. Closely related are failing to consider a range of options and the tendency to think in extremes, called black-and-white thinking. Strictly speaking, the prefix "di" in "dilemma" means "two". When a list of more than two choices is offered, but there are other choices not mentioned, then the fallacy is called the fallacy of false choice, or the fallacy of exhaustive hypotheses.

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

The simple standard definition of a dichotomy is indeed "a set of two mutually exclusive, jointly exhaustive alternatives".

A system of mutual constraint that produces two choices in the limit as I said from the start.

The extra bit which would be new to most people is that to maximise a dichotomy, the separation has to happen across scale. This statement comes directly from hierarchy theory. It is a further modern development of a very old idea.

But, going back into greek metaphysics, it can be seen how the most fundamental and enduring dichotomies were the ones that indeed maximised asymmetry - a difference in scale. They took the canonical form of local~global (the dichotomy that IS hierarchy theory).

But you don't really want to know any of this...

 

[Pythagorean]

I'm fine with heirarchy theory and even duality in heirarchy theory (which is basically what you've described). It's the bastardization of the word dichotomy that is misleading, especially since it already has a formal (and useful!) meaning in philosophy.

 

[apeiron]

I'm fine with heirarchy theory and even duality in heirarchy theory (which is basically what you've described).

Citation please. Whose hierarchy theory are you talking about? I'm not familiar with any that are not dependent on scale.

 

[GeorgCantor]

Apeiron, your dichotomies surely work up to a point(it's amazing you keep missing this subtle point). They are not a fundamental constituent of the world and this is beyond doubt.

The discrete-continuous naive chatter dissolves at the Planck scale. The macro world of objects and appearances(and dichotomies!) is the last phenomenon that should be considered a framework for fundamental conclusions about reality.

If the scientifically presumed symmetry and reductionism are the right approach to truths about the reality we find ourselves in, the focus should be placed where those dichotomies cease to exist and blend into a sea of endless possibilities. This is currently one of the few limitations of physics that is certainly a serious roadblock towards further inquiry into why things happen the way they do.

Your bad example with the HUP is flawed in more ways than one, you forget that you exist in a relative reality. The momentum that YOU think you can know with precision is actually different in different referrential frames. So your "precision" is just a reflection of your position relative to the movement of other objects in space and an electron has multiple momentums and positions at the same time, depending on where and how you measure. There exist infinite "dichotomies" between position-momentum and neither of them is fundamentally right(the momentum you know with precision is WRONG and inaccurate in another FOR). There are no and there can be no fundamental dichotomies in this "world" of 4 relative, fundamental forces and their manifestations.

 

[apeiron]

Apeiron, your dichotomies surely work up to a point(it's amazing you keep missing this subtle point). They are not a fundamental constituent of the world and this is beyond doubt.

What is a "fundamental constituent"? Please define. Is a constituent an entity, a structure, a process?

In the meantime, remember that I am talking about the modelling of reality. And the three important "constituents" of this model are:

1) Vagueness - a model of how things begin.
2) Dichotomies - a model of how things develop.
3) Hierarchies - a model of how things end.

This is a modern re-working of Peirce's synechism.

 

[GeorgCantor]

What is a "fundamental constituent"? Please define.

That's difficult, but i'd put my bets on "my experience", "quantum vacuum" and "planck scale".

Is a constituent an entity, a structure, a process?

Possibly all of these plus awareness. At the same time, none of these. The deeper we delve, the harder it becomes to recognize discrete, distinct objects and structures in the blur.

In the meantime, remember that I am talking about the modelling of reality. And the three important "constituents" of this model are:

1) Vagueness - a model of how things begin.
2) Dichotomies - a model of how things develop.
3) Hierarchies - a model of how things end.

Agreed. That's very much inline with all i can think of. Dichotomies are models that belong to certain scales, where size and dimensions become meaningful constructs.

 

[Hurkyl]

That's difficult, but i'd put my bets on "my experience", "quantum vacuum" and "planck scale".

Is that a definition of the word "fundamental constituent", as you mean it?

1) Vagueness - a model of how things begin.
2) Dichotomies - a model of how things develop.
3) Hierarchies - a model of how things end.

Is that a definition of those three words, as you mean them?

 

[apeiron]

Is that a definition of those three words, as you mean them?

Definition? I was describing how systems models divide into three general components. Hopefully this makes it clear that dichotomies are only a third of the story. Even if they are central in representing the mechanism of change, of self-organising development.

So your point is? Or perhaps you don't have one...

 

[Pythagorean]

Citation please. Whose hierarchy theory are you talking about? I'm not familiar with any that are not dependent on scale.

Specifically, Timothy Allen, but your must have misunderstood something I said. I made no claim about it not being dependent on scale. I'm talking about the misuse of the word dichotomy. What you're talking about seems to be "duality in heirarchy". There's no need to altar the meaning of another word (i.e. dichotomy).

Allen's essay is actually the first hit on google for "heirarchy theory" Scroll down to "dualities in heirarchy". The word dichotomy isn't needed and it just confuses the issue.

 

[apeiron]

Specifically, Timothy Allen, but your must have misunderstood something I said. I made no claim about it not being dependent on scale. I'm talking about the misuse of the word dichotomy. What you're talking about seems to be "duality in heirarchy". There's no need to altar the meaning of another word (i.e. dichotomy).

Allen's essay is actually the first hit on google for "heirarchy theory" Scroll down to "dualities in heirarchy". The word dichotomy isn't needed and it just confuses the issue.

Hah, you bluffer. You googled hierarchy theory (perhaps you even spelt it correctly) and that was the first time you had ever heard of Allen.

If this is not the case, then I'm sure you can tell me where you first came across Allen's work and how you feel it differs from other hierarchy theory approaches - why you would choose it "specifically", rather than say Stan Salthe or Howard Pattee.

But anyway, you want to turn this into some kind of debate over which words I'm allowed to use based on your attempts to position yourself as an "expert" in the field of hierarchy theory. Well, my distinctions between these various terms - dual, complementary, dichotomy - actually arose from many years of discussion with actual hierarchy theory experts like Salthe and Pattee. So if they didn't mind, perhaps you could afford to be a little more relaxed as well.

So scroll down to duality and read on...

"The dualism in hierarchies appears to come from a set of complementarities that line up with: observer-observed, process-structure, rate-dependent versus rate-independent, and part-whole."

Part~whole, or local~global, is in fact the key one here (or speaking as someone au fait with hierarchy theory, are you suggesting something else is more central?).

Also worth noting - simply in the vain hope that we might get this thread back on track - is what Allen then says about the dichotomy of construction~constraint. The complementary actions of local and global scale.

Constraints come from above, while the limits as to what is possible come from below. The concept of hierarchy becomes confused unless one makes the distinction between limits from below and limits from above. The distinction between mechanisms below and purposes above turn on the issue of constraint versus possibility.

This is what it is all about. (Though Allen does not express the idea too clearly.)

Global scale acts downwards with constraint to restrict local degrees of freedom. But in turn, those freely expressed degrees must act bottom up to construct the global constraints. The parts have to (re)construct the whole that is forming them as parts in the first place. This is the logic of hierarchical self-organisation - a dynamic process view of systems. And the necessary causal connection between what is separated (the local from the global) is why we would call it also complementary.

Applied to QM, this model would suggest that the universe arises as a system of measurement (of global, holonomic, constraint) because it is able to restrict (decohere) what would otherwise be an infinity of degrees of freedom (indeterminacy, vagueness). And the decohered grain of material events in turn is exactly that which is sufficient to (re)build the universe as the decohering global device.

But why am I explaining the basics of hierarchy theory to you when you are already an expert and are probably penning a wiki page as we speak?

 

[Pythagorean]

Wow, that whole post was basically a personal attack.

I never claimed authority on hierarchy theory, I never said I didn't google it. I just said I don't have a problem with it (having read another source besides you). Yes, it was a google hit, but being the first hit wasn't as important as it being from a scientist. I also google scholar'd it and skimmed other authors to make sure it was consistent subject matter (and it was).

Coincidentally, the research I do falls within the domains of hierarchy theory, so a lot of the technicalities aren't difficult to grasp for me.

Anyway, the whole point is that you're wasting your time trying prove that hierarchy theory is legit or tell me about it or what the mechanics are. My problem was with you making up your own definitions, and I'm quite over it by now.

 

[apeiron]

Anyway, the whole point is that you're wasting your time trying prove that hierarchy theory is legit or tell me about it or what the mechanics are. My problem was with you making up your own definitions, and I'm quite over it by now.

I quite agree that you have been wasting my time here. You have demonstrated that you have no real knowledge on which to base any opinion about my choice of definition. To pretend otherwise was dishonest.

 

[Pythagorean]

Read my language, I used words like "seems like" and even mentioned the googe hit. How do you confuse this for authority?

Anyway, like I said, it's all very similar to the research I do (complex systems, bifurcations, chaos, spatiotemporal dynamics, etc.), It just has a name now is all.

Here's something I came across pertaining directly to our discussion though, albeit in another case besides HUP:

A single-level, scale-insensitivec oncept of patches has
led to the misleading dichotomy between "fine-grained"
and "coarse-grained" organisms( MacArthura nd Levins
1964, Pianka 1983). These terms have been used to
imply that organisms may either respond to the patch
structure( coarse-grained) or perceive the environment
as homogeneous( fine-grained).A given mosaicm ay be
used in a coarse-grainedm annerb y one organism( e.g.
a barnacle settling on an intertidal rock) and a finegrained
fashion by another (e.g. a shorebird foraging
over a large area of rocky intertidal). The distinction is
useful in calling attention to such species differences in
responses to environmental patchiness, but it fails to
consider the effects of scale or levels in patch hierarchies.
Thus, an organism that does not respond to
patchiness at one scale (fine-grained) may be sensitive
to patch differences( coarse-grained)a t other scales of
heterogeneity (Morris 1987). The shorebird that ignores
small-scale patchiness within a rocky intertidal may differentiate
strongly between a patch of rocky intertidal
habitat and patches of sandy beach or exposed dunes at
a broader scale. Whether or not an organism is fine- or
coarse-grainedi s scale dependent, yet these terms are
usually applied in a scale-insensitive manner.

from JSTOR: Oikos, Vol. 59, Nov. 2

Multiple Scales of Patchiness and Patch Structure: A Hierarchical Framework for the Study of Heterogeneity.

 

[GeorgCantor]

That's difficult, but i'd put my bets on "my experience", "quantum vacuum" and "planck scale".

Is that a definition of the word "fundamental constituent", as you mean it?

Examples of what i consider to be the building blocks(and possibly source) of reality.


What are the unchanging, non-relative, non-contextual building blocks of the universe in your opinion?(suppose for a moment there do exist such fundamental blocks that explain the existence of relative space, matter and time)


The common opinion among physicists would probably center around the idea of supersymmetry that if you keep drilling down to find out what the smallest things are made of, you would eventually find just one thing that everything is made of, guided by some sort of universal rules of physics. It feels right, but doesn't explain the emergence of 3D space and especially the passage of time, the origin of the universal rules of physics, personal experience and free-will. At the deepest levels of inquiry, it becomes hard to make a distinction between the organizing universal rules and what one may choose to call 'the Mind of God'.

 

[apeiron]

Anyway, like I said, it's all very similar to the research I do (complex systems, bifurcations, chaos, spatiotemporal dynamics, etc.), It just has a name now is all.

That is an impressive range of areas that you do research in. Out of interest, how many papers have you published so far?

Here's something I came across pertaining directly to our discussion though, albeit in another case besides HUP.

Now how does this actually pertain to our discussion? I am baffled so please spell out what you mean.

I hope you didn't just get excited by the juxtaposition of the words "misleading" and "dichotomy" because of course you will have understood that the misleading bit (according to the authors) lies in applying the dichotomy of coarse~fine (ie: discrete~continuous) to the animals when really it should be applied to the environment the animal perceives.

So the passage is straightforward enough and indeed demonstrates the use of the term "dichotomy" in precisely the same "division by scale asymmetry" sense that I have been using it.

But I can't believe your intent here was to support my position!

 

[Pythagorean]

That is an impressive range of areas that you do research in. Out of interest, how many papers have you published so far?

Actually, it's not a wide range by any means. It's all one paper: when you look for chaos in complex systems, your largest contributing tools are spatiotemporal and bifuraction analysis. One of the more important tests is the Lyapunov exponent (which can actually be framed as a scaling problem).

You can learn all of this in one book:
Nonlinear Dynamics and Chaos
Steven Strogatz

As for papers published, I've contributed to two (maybe three soon) papers, but that doesn't really matter. Being able to understand the journal papers that are already written is more important. You have to actually climb up giants to stand on their shoulders.

Now how does this actually pertain to our discussion? I am baffled so please spell out what you mean.

I hope you didn't just get excited by the juxtaposition of the words "misleading" and "dichotomy" because of course you will have understood that the misleading bit (according to the authors) lies in applying the dichotomy of coarse~fine (ie: discrete~continuous) to the animals when really it should be applied to the environment the animal perceives.

So the passage is straightforward enough and indeed demonstrates the use of the term "dichotomy" in precisely the same "division by scale asymmetry" sense that I have been using it.

But I can't believe your intent here was to support my position!

Actually, the whole point is that there is no dichotomy. That the properties are not mutually exclusive (like momentum and position).

We'll look at it closer:

mutually exclusive (either or statement)

These terms have been used to
imply that organisms may either respond to the patch
structure( coarse-grained) or perceive the environment
as homogeneous( fine-grained).

(emphasis added)

and to elaborate, he says:

The distinction is
useful in calling attention to such species differences in
responses to environmental patchiness, but it fails to
consider the effects of scale or levels in patch hierarchies.
Thus, an organism that does not respond to
patchiness at one scale (fine-grained) may be sensitive
to patch differences( coarse-grained)a t other scales of
heterogeneity (Morris 1987).

In other words, the linear thinking fails to account for every possible observation of the system. The mutually exclusive case is a special case (an exception, not a rule) and it's misleading to carry it as such. The scale variance can (not must) affect the grain sensitivity, further complicating the system (obviously, if it's one or the other, it simplifies the system).

 

[GeorgCantor]

Regarding Heisenberg uncertainty principle, is there really any doubts...

Walter Lewin MIT – The Uncertainty Principle

https://www.youtube.com/watch?v=<object width="640" height="505">
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That's remarkable. This is actually the 'border' between the classical and quantum domain, in action. He states the opening is 1/100th of an inch wide, or 0.25 mm when the HUP becomes noticeable(and quantum effects kick in). Pretty damn impressive! It's always great to learn something new.

 

[apeiron]

As for papers published, I've contributed to two (maybe three soon) papers, but that doesn't really matter.

What does contributed mean? You are a co-author?

Actually, the whole point is that there is no dichotomy. That the properties are not mutually exclusive (like momentum and position).

I feeling further confused. So you are saying now momentum and position are mutually exclusive? You seemed to say something different in post 71 - "A particle can have a momentum and a velocity [sic] at the same time (they're not mutually exclusive properties of the particle)".

And you also want to say that coarse and fine are not mutually exclusive terms? That coarse is not defined by its lack of fineness, fineness by its lack of coarseness?

In other words, the linear thinking fails to account for every possible observation of the system. The mutually exclusive case is a special case (an exception, not a rule) and it's misleading to carry it as such. The scale variance can (not must) affect the grain sensitivity, further complicating the system (obviously, if it's one or the other, it simplifies the system).

Your attempt at explanation is far less clear than the passage you quote. In fact it makes no sense.

Quite clearly, the dichotomy of patchy and homogenous is anchored in "must" fashion to the scale of the observer. And this in fact is a statement straight out of hierarchy theory - particularly Stan Salthe's book on scalar hierarchies, Evolving Hierarchical Systems.

The shoreline will look patchy - inhomogenous - to the bird on its scale of perceptual interest. So it will distinguish between the rocks and the beach. But patchiness at a fine grain, such as between different coloured grains of its sand under its feet, will blur into a continuous indifference. Equally, patchiness at a scale much greater than its perceptual interest, such as perhaps the patchiness of tectonic plates, will also disappear from sight, but for precisely the opposite reason. The bird will not be able to see to the boundaries of the patch it happens to exist in.

So yes this is hierarchy theory. Yes this is also a story of upper and lower bounds of scale, it is also about an asymmetric dichotomy, following my definition. There are two bounding constraints (or event horizons) on perception - when the grain of perceptual interest becomes either too fine, or too coarse. And note, just two constraints, not three, four or some other arbitrary number.

So you say your research experience in chaos and nonlinear systems gives you an ability to understand technical papers in hierarchy theory. Well, I await evidence of that claim.