Is the small world uncertain, or is that just our perception?

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In summary: Now, many people believe that this is a clear demonstration that quantum mechanics must be incomplete - that there must be some other, unknown, level of reality behind the quantum level. But that's a different discussion.In summary, quantum mechanics is a theory that describes the behavior of particles that are very small. Properties like position and speed are uncertain, but are certain in some cases. There is a possibility that there are "hidden variables" that cannot be explained by quantum mechanics, but we don't know enough about them to say for sure.
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bt101
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When it comes to the properties of a small particle (position, speed, etc) are those properties "certain" in reality and just "uncertain" to us (the observer). Or are they truly uncertain in reality? I never really hear experts be clear about that. In fact they leave the impression that there is this mysterious weird quantum world where particles live in a cloud, which I interpret as them saying that it is a reality that the particles properties are truly not certain.

I'd like to submit that they are truly certain in reality, but only uncertain to us because of our limited observing abilities and all the maths that were derived from those limited observing abilities.

Let me give an example.
Let's say a race of aliens landed on Earth and they were giants and blind etc. Because of their limited observing abilities and tools, they could not observe anything smaller than a car. They suspect that a car has tires on it but cannot observe them. We humans know that the positions of the tires are certain because we can observe them. When the giant aliens do all of their experiments and maths based on those experiments, would they not conclude (as we do with small particles) that the positions of the tires are uncertain and tires only exist in this statistical cloud around the car (when in reality that is not the case).

Isn't it the same with us humans and small particles? Ok, what I'm saying is we are a bunch of clumsy oafs who just don't have the tools to measure something small, and concluding a reality that really isn't true ;-)

Of course we keep using our limited observing abilities and maths derived from then to experimentally prove our theories (of course they are going to match because they are all based on the same limited observing abilities).
 
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  • #2
bt101 said:
When it comes to the properties of a small particle (position, speed, etc) are those properties "certain" in reality and just "uncertain" to us (the observer).
There are some properties that are, I think, certain (e.g. mass of an electron), but as a general thing they really are uncertain until measured. The Heisenberg Uncertainty Principle does not describe a measurement problem, it describes the fundamental uncertainty of quantum properties.

I'd like to submit that they are truly certain in reality, but only uncertain to us because of our limited observing abilities and all the maths that were derived from those limited observing abilities.
Then you are proposing a personal theory that (1) is demonstrably wrong and (2) against the rules of this forum.

This can be confusing stuff, but as you study more you'll quickly realize your fundamental misunderstanding.

On this forum, it's a very bad idea to make categorical statements about things you have not studied. Questions are fine, including questions about why your misunderstandings seem to be wrong, but saying that you have your very own theory of stuff you don't understand is a terrible idea.
 
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  • #3
bt101 said:
I'd like to submit that they are truly certain in reality, but only uncertain to us because of our limited observing abilities and all the maths that were derived from those limited observing abilities.
That is called “counter factual definiteness”. It is inconsistent* with the math of QM, and has been experimentally disproven.

*Technically it is the combination of counterfactual definiteness and locality that is inconsistent with QM.
 
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  • #4
bt101 said:
I'd like to submit that they are truly certain in reality, but only uncertain to us because of our limited observing abilities and all the maths that were derived from those limited observing abilities.

The possibility of "hidden variables" has been discussed many times. What we know is that in many cases, these hidden variables cannot obey the equations of classical physics, and they must also violate some notion of causality or locality in classical special relativity (see "Bell's theorem"). While coherent proposals for the equations governing the hidden variables exist for some areas of quantum physics (see "Bohmian mechanics"), we lack proposals for other important areas of quantum physics.
 
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  • #5
bt101 said:
When it comes to the properties of a small particle (position, speed, etc) are those properties "certain" in reality and just "uncertain" to us (the observer). Or are they truly uncertain in reality?
The next few paragraphs are just an expansion of what @Dale said above.

As far as quantum mechanics is concerned, there's no way of getting rid of the uncertainty - it's a consequence of the fundamental mathematical structure of the theory. However, that doesn't mean that the uncertainty must be real, it just means that that there might be more going on than quantum mechanics can explain.

In 1935 Einstein and two collaborators published a paper (google for "EPR paper") making pretty much this argument: that one particular corner case seemed to imply the existence of definite values where QM said there had to be uncertainty, so more was going on than QM could explain. Subsequently David Bohm proposed a clearer version of the EPR argument based on the properties of entangled particle pairs (google for "singlet state"). Neither Bohm's nor the EPR arguments went anywhere because there was no way of testing them - it's hard to get anyone excited about the difference between "It is either X or Y, we don't know which but we'll find out if we measure it" and "if we measure it, we'll find that it's either X or Y".

Then in 1965 John Bell discovered that there are subtle statistical differences between the "no definite value until we measure" model of quantum mechanics and the "definite value but we don't know what it is" model (Google for "Bell's Theorem"). These differences can be experimentally tested, and over the next half-century many experimental teams have done these experiments with ever greater refinement. The results of these experiments (Google for "loophole-free Bell test") leave absolutely no room for doubt: QM is correct, the uncertainty is real, there are not definite values that we just can't measure.
I never really hear experts be clear about that. In fact they leave the impression that there is this mysterious weird quantum world where particles live in a cloud, which I interpret as them saying that it is a reality that the particles properties are truly not certain.
Some caution is in order here. The history that I described above is known to everyone who is up to date with the developments of the past fifty years. If (as your post suggests) any of this is new to you... you have not been learning your QM from reliable sources.
 
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  • #6
bt101 said:
I'd like to submit that they are truly certain in reality, but only uncertain to us because of our limited observing abilities and all the maths that were derived from those limited observing abilities.
The theoretical framework we have, quantum mechanics, really does involve things being "actually uncertain" in various ways. It can't even represent a situation where a particle simultaneously has an exact position and an exact momentum, owing to how these complementary properties are represented in wavefunctions. (The coordinates for momentum are the Fourier transform of the coordinates for position, and localizing a waveform in one set of coordinates, making that property "more certain", will cause the waveform to spread in the Fourier-transformed set of coordinates, so that the complementary property is "less certain".)

Furthermore, there are well-known difficulties to reproducing the (successful) predictions of quantum mechanics, in a deeper theory where there are no "actual uncertainties". The Bohm theory mentioned by @atyy in comment #4 is the most elegant, but runs into trouble with "spin 1/2". John Bell defined a more generally applicable approach in "Beables for Quantum Field Theory", but it conflicts with the spirit of relativity (in that it requires an objective universal time).

The bottom line is that we don't know what kind of theory will be required to get rid of "actual uncertainty". It may require a picture of reality very far from "things in space". Meanwhile, for a century, progress in particle physics has occurred only within the quantum framework. So it seems it's not so easy to improve on it.
 
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  • #7
Another possibility, which I tend to believe in more than on philosophical speculations, is that nature is simply inherently probabilistic. There's not a single observation contradicting quantum theory, including socalled Bell experiments always agreeing with the predictions of QT rather than speculations of deterministic hidden-variable theories. As long as there is no clear empirical contradiction to QT I don't see any rational argument against it, including its probabilistic form.
 
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  • #8
The real answer is we do not really know. But that is nothing new, strictly speaking science is more about 'doubt' than 'such and such' is true - and make no mistake about it. The mathematics of QM is actually what is called a generalised probability model:
https://arxiv.org/abs/1402.6562

Thanks
Bill
 
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  • #9
I’m reading “Remarks on the Mind-Body Question” by Eugene Wigner. In a footnote he Quotes Heisenberg. This is 60-year old text; I don’t know how these ideas are viewed today. Here’s the footnote:

W. Heisenberg expressed this most poignantly [Daedalus, 87, 99 (1958)]: “The laws of nature which we formulate mathematically in quantum theory deal no longer with the particles themselves, but with our knowledge of the elementary particles.” And later: “The conception of objective reality … evaporated into the … mathematics that represent no longer the behavior of elementary particles but rather our knowledge of this behavior.”
 
  • #10
Well, yes, Heisenberg and partially also Wigner had some strange thoughts about the interpretation of quantum theory... Too much philosophy for my taste SCNR.:oldbiggrin:
 
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  • #11
gmax137 said:
I’m reading “Remarks on the Mind-Body Question” by Eugene Wigner. In a footnote he Quotes Heisenberg. This is 60-year old text; I don’t know how these ideas are viewed today. Here’s the footnote:
...

"Objective reality" has a special meaning in this context. It may be contrasted with "subjective reality" which is the same thing as "observer dependent" reality. When a measurement is made, the observer - by how she chooses to make the measurement - is shaping reality.

That occurs because the choice of measurement basis casts the quantum system into a state where the non-commuting observables are uncertain (i.e. are now in a superposition of states). A different choice of measurement basis would have resulted in a different quantum state.

To go back to your original example: commuting observables can be known to unlimited precision. Only non-commuting observables - such as position and momentum - display the Heisenberg limit. Experiments with entangled particles show that the Heisenberg limit is present there too. On the other hand, there is no experimental evidence supporting the existence of simultaneously well-defined values for non-commuting observables.
 
  • #12
But there is nothing subjective in quantum theory only because it's probabilistic. We are drifting again towards interpretation (not to say esoterics). Maybe some moderator can move the thread to the interpretation section.

Concerning the uncertainty relation: All observables can be known to arbitrary precision by measurement, indepdendent of the state of the quantum system. The precision is limited by the measurement device not by fundamental laws of nature. What the usual texbook uncertainty relation tells you rather is that a quantum system in general does not allow for states where two incompatible observables have determined values (or arbitrarily precisely determined values in the case of a value in the continuous spectrum) at once.

For position and momentum components in the same direction, e.g., you can determine either the position component ##x## or the momentum component ##p_x## very precisely but not both simultaneously, because
$$\Delta x \Delta p_x \geq \frac{1}{2} |\left \langle \mathrm{i} [\hat{x},\hat{p}_x] \right \rangle|^2 = \frac{\hbar}{2}.$$
Nevertheless you can meausure position or momentum at any precision you like, no matter which state the particle is prepared in.

That's an objective fact about nature. There's nothing subjective in it. As far as we know today, the indeterministic/probabilistic meaning of the state a system can be in, is objective, i.e., it has nothing to do with incomplete knowledge about "hidden variables". At least today nobody has ever come up with such hidden variables at all let alone with a deterministic theory describing all well-established empirical facts perfectly described by QT.
 
  • #13
vanhees71 said:
But there is nothing subjective in quantum theory ... That's an objective fact about nature. There's nothing subjective in it.

This is a position that is not shared by most physicists. Said a different way: your use of the word "objective" is not appropriate in the context of this thread, and specifically not in response to my post #11. I'm not referring to the HUP itself, which of course is fine as you have it. But clearly, the reality we experience is observer dependent (contextual) and therefore subjective. And that is a direct consequence of the HUP, and exactly what Einstein (in EPR) objected to in 1935. Which position (EPR) was later proven incorrect by experiment.

Most believe that the observer's choice of measurement basis shapes the quantum state and therefore reality. Virtually all interpretations are contextual (even MWI and Bohmian) so I don't think there is any benefit to getting into a discussion of interpretations.

I think the following words from Wigner are just fine and are consistent with views today: "The conception of objective reality … evaporated..."
 
  • #14
This thread is closed. Please make sure to keep interpretations discussions inside the appropriate sub-forum.
 
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Related to Is the small world uncertain, or is that just our perception?

1. Is the concept of a small world scientifically proven?

Yes, the concept of a small world is a well-researched and scientifically proven phenomenon. It has been studied in various fields such as sociology, psychology, and mathematics.

2. How does the small world phenomenon relate to the uncertainty principle?

The small world phenomenon does not directly relate to the uncertainty principle in physics. However, both concepts suggest that there is a level of unpredictability and interconnectedness in the world.

3. What evidence supports the idea of a small world?

There is a significant amount of evidence that supports the idea of a small world. For example, the famous "six degrees of separation" theory suggests that any two people in the world can be connected through a chain of no more than six acquaintances.

4. Is the perception of a small world influenced by social media and technology?

Yes, the rise of social media and technology has made the world feel smaller and more interconnected. This can influence our perception of the world as a smaller and more uncertain place.

5. Can the small world phenomenon be applied to other systems besides human social networks?

Yes, the small world phenomenon has been observed in various systems such as animal social networks, transportation networks, and even the internet. This suggests that the concept of a small world is not limited to human interactions.

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