Thread: It's a small world, after all.

The point of Zeno's paradox is that it is a logical aporia; it's about the artificiality of thought and not intended to be taken seriously altho, perhaps, it often has been...

Well said!

Originally Posted by Sebastiani

The general consensus is probably that the Uncertainty Principle is correct (at least most sources I've read seem to present it as a fact). But I think the matter is certainly debatable. Statistics is indeed a useful tool for analysing systems, but does it really model reality? I think not. It "works" because it simplifies an infinitely complex problem, and as long as we understand it as such then there is no harm done. But what Heisenberg and others have done is to essentially assert that these probablistic terms of the equation are *in fact* undeniable aspects of nature. This is a terrible mistake! Any observation is going to record a measurement that falls within a certain minima/maxima simply because it is impossible to integrate the infinite number of factors that influence the system.

Going back to the artificiality of thought, and the fact that mathematics is a language, you would be asserting that math and thought are not artificial hence could grasp absolutely the physical nature of the universe if it were not "impossible to integrate the infinite number of factors that influence the system", ie, that all such factors, despite their infinite number, could be understood individually with our existing methods, if only we had the resources to do so, and then everything would be known. Maybe, but perhaps not with the current models, hence Heisenberg.

My understanding of the Heisenberg principle, and the way I always remember it being presented in school (inc. University), is that it reflects the paradoxes of a wave/particle model and is not intended to indicate a shortcoming in our ability to measure, but rather an intrinsic limitation of the way in which we measure/what the "focus" of our measurements are, ie, that "uncertain" elements CANNOT be reduced out because they are indicative of the artificiality of the system (again "aporia" is a nice word here).

He and Nils Bohr, I believe, had arguments along these lines, vis whether their models could literally represent the form of the atom (Heisenberg asserting they did not do that, but are only pragmatically/statistically valid). AFAICT, today Heisenberg's attitude is more widely accepted, and this is partially why modern physics is in search of a paradigm switch or grand unifying theory.

Well the Uncertainty Principle has a mathematical formulation, Sebastiani. That's why I was so surprised with your... ermm... assertiveness

This isn't just some philosophical formulation. At the infinitely small level where the Uncertain Principle should be applied, it surely has been shown as being a rather correct principle. It even helped explaining some inconsistencies in classical physics.

On the other hand, the Uncertainty Principle does not stop you from collecting statistical information or formulate from deduction. It merely stipulates that the more accurate is your measurement of a certain property, the less accurate it will be the measurement of another. You can easily extrapolate from this that it is still possible to obtain fairly reasonable estimates.

Going back to the artificiality of thought, and the fact that mathematics is a language, you would be asserting that math and thought are not artificial hence could grasp absolutely the physical nature of the universe if it were not "impossible to integrate the infinite number of factors that influence the system", ie, that all such factors, despite their infinite number, could be understood individually with our existing methods, if only we had the resources to do so, and then everything would be known. Maybe, but perhaps not with the current models, hence Heisenberg.

That is a very common interpretation of the Uncertainty Principle, but that was not actually Heisenburg's import.

In the sharp formulation of the law of causality-- "if we know the present exactly, we can calculate the future"-it is not the conclusion that is wrong but the premise.
--Heisenberg, in uncertainty principle paper, 1927

He is not simply saying that we, as imperfect observers, cannot know the exact initial state of the system and thus the outcome, but that the initial state itself is governed by probablility! Read his paper yourself and draw your own conclusions, but that is what I got from it.

Originally Posted by Mario F.

Well the Uncertainty Principle has a mathematical formulation, Sebastiani. That's why I was so surprised with your... ermm... assertiveness

This isn't just some philosophical formulation. At the infinitely small level where the Uncertain Principle should be applied, it surely has been shown as being a rather correct principle. It even helped explaining some inconsistencies in classical physics.

On the other hand, the Uncertainty Principle does not stop you from collecting statistical information or formulate from deduction. It merely stipulates that the more accurate is your measurement of a certain property, the less accurate it will be the measurement of another. You can easily extrapolate from this that it is still possible to obtain fairly reasonable estimates.

On the contrary, I think that it is highly philosophical, and I would argue that this was partially Heisenberg's intention. Had he only stated that we cannot measure a system perfectly, due to our inherent limitations, I would have wholeheartedly agreed with him, but that is not the issue here.

But Heisenberg did not focus on the mathematics of quantum mechanics, he was primarily concerned with establishing that the uncertainty is actually a property of the world — that it is in fact physically impossible to measure the position and momentum of a particle to a precision better than that allowed by quantum mechanics*. To do this, he used physical arguments based on the existence of quanta, but not the full quantum mechanical formalism.

*The implication here is that quantum mechanics is based on probability, and thus reality itself must be.

Originally Posted by Sebastiani

On the contrary, I think that it is highly philosophical, and I would argue that this was partially Heisenberg's intention.

You read the part where I mention the principle has a mathematical formulation? And that this formulation has been applied to both quantum mechanics and classic physics in a rather successful manner?

If that's philosophy...

EDIT: On second thought, I do understand that are a few detractors that feel uncomfortable around the lack of determinism. They may even question the whole Quantum Mechanics field. Probably the most notorious of them having been Einstein. Are you sure you aren't perhaps focusing your literature on that side?

Originally Posted by Sebastiani

He is not simply saying that we, as imperfect observers, cannot know the exact initial state of the system and thus the outcome, but that the initial state itself is governed by probablility!

Hey now -- I didn't say anything about the "imperfect observer" or the "influence of the observer" because that seems trivial. The significance of the observer is relevant in some senses but not all, I don't have much of an opinion about it and that wasn't my point. That "it is not the conclusion that is wrong but the premise" is I think in keeping with "perhaps not with the current models". The idea that something is "governed by probability" might be a nice way of saying to scientists that sometimes, when a child asks "Why?" over and over again, infinitely regressing, the question might start to seem suspicous (ie. the answer is "why not?").

@Mario: it's easy to retreat into a corner and say "this is hard science, not philosophy" (esp. if you are not really a scientist!). Witness Heisenberg and Bohr did not do that, which is why they argued about the philosophical premises behind (or implied by) their "formal theories".

Originally Posted by Mario F.

You read the part where I mention the principle has a mathematical formulation? And that this formulation has been applied to both quantum mechanics and classic physics in a rather successful manner?

If that's philosophy...

No, no. As I said earlier, probablistic functions (including Heisenberg's) are useful and *necessary* if we are to obtain measurements that agree with the calculations. But that doesn't mean we should assume that these statistical methods model reality, per se, which was Heisenberg's assertion. Whether he is correct or not on a philosophical level is beside the point. It is impossible to prove the validity of either determinism or randomness, naturally, so the question really has no place in physics anyway.

Oh, I see your point now!
My sincere apologies.

... Well, that does bring the debate into philosophical grounds. But that's because you decide to discuss it on that assumption. You are essentially questioning the principle based on a generic idea that it's not possible to... ok, I'm starting to struggle with words here... ascertain reality simply from the methods that seem to explain it.

Face it, what really bothers you about the uncertainty principle is the exact same thing that bothered Einstein. You are too attached to classical physics and are having an hard time accepting such concepts as uncertainty, randomness, duality or entanglement as perhaps being more accurate models at atomic level

Determinism is understandably more comfortable. However, while I do not possess the knowledge to truly support the quantum fields of science against your arguments, I'm not shocked by its formulations. Especially when they have been successful at explaining certain systems.

Unless... well, there could be a tension with Religion. But I'm sure this is not where you are coming from.

Are you sure you aren't perhaps focusing your literature on that side?

I am a very open-minded person, generally. If you were to state a belief that life on Earth was the result of an astroid containing DNA, I would consider your arguments seriously and objectively, no matter how much it contradicts my current views. I don't rule things out simply because I've already accepted some explanation.

Probability has always bothered me because people tend to over-emphasize it's importance. Statistics are just generalizations. They have very limited meaning, and should only be considered useful gauges of "what to expect", and not "how things are", which is a very important distinction.

Originally Posted by Sebastiani

Probability has always bothered me because people tend to over-emphasize it's importance. Statistics are just generalizations. They have very limited meaning, and should only be considered useful gauges of "what to expect", and not "how things are", which is a very important distinction.

Statistics and probability do provide boundaries for "how things are not".

In a naive sense, you could then say "Well, the electron really is in a particular place, within the bounds of probability, even if we do not know exactly where, and the bounds of this probability are sufficient to permit us to move on and do X Y and Z". Maybe that is almost religious -- "God must exist, even if we cannot be sure where".

Another perspective would be that the electron is not really in a particular place; it is a phenomenon accurately described in terms of probability. That is problematic, philosophically speaking, since scientists must still conceptualize things within the certain bounds of credulity, such as Occam's razor.

But on an atomic level, I think it is impossible to avoid some set of "unscientific" (or pseudo-scientific) assumptions. In keeping with Occum's razor, the first set (the Bohr model) is that the electron is a little orbiting ball object, because to a world used to classical physics, that is the "least assuming" kind of assumption. Which Einstein also wanted something like this, and did explicitly connect it to his belief in God and that because of God, chance does not have a place in evolution of physical laws since the big bang (now here is a great new philosophical adaptation: God is the prima causa of the big bang!). In other words, 1) there was only one way everything could end up, and 2) there is only one way things can be. AFAICT, you can assume this is true, or you can assume it is not true, but either way, philosophically speaking, you are philosophizing. No matter how much you want to trust "only to hard facts", you will still be left with the need to make certain philosophical assumptions of this sort*.

*mine are here