Uncertainty = our ignorance or intrinsic to reality?

[wittgenstein]

TL;DR Summary

Is quantum uncertainty intrinsic to physical reality or a measure of our ignorance?

I realize that it is impossible to know both the speed and position of a particle because of the uncertainty principle. I also know that this is because if you send a photon at the particle to detect its position you alter its momentum. But does that mean that when you measure position it has no momentum? Or when you measure its momentum it has no position? OK maybe that is a stupid question and only intelligent questions are allowed but doesn't that defeat the whose purpose of this site? Please do not delete this question. I really want an answer. I am beginning to think that unless you are an actual physicist this site is useless. I posted a similar question and it was deleted because I was told the question was stupid!

 

[.Scott]

Heisenberg Uncertainty is intrinsic to Physics.
A complete description of a system takes this limit into account. It is not an issue of ignorance - it is a real limit.

 

[hutchphd]

The question is not stupid, but you you need to accept "yes you cannot measure both arbitrarily" as the answer. Insisting that it seems wrong to you is not salient.

 

[wittgenstein]

I have no doubt that no one can measure both simultaneously. My question was, is that because we will never have the ability to measure both simultaneously or because only one predicate ( position or momentum ) can exist at a time. I am not insisting on anything. I am asking for an explanation. I did not say the official explanation was wrong, I was merely asking if the common sense explanation is wrong. I have no problem with knowing that reality transcends our meager intellects.
However, I am a firm believer in Carl Sagan's point that extraordinary statements require extraordinary proof. QM is very extraordinary. I have faith in physicists. But I want to accept QM on more than faith.
"Anyone who is not shocked by quantum theory has not understood it."—Niels Bohr

 

[atyy]

We don't know the answer. In an operational sense, it is intrinsic - but the operational sense is, of course, not about reality.

For certain quantum systems, it can be shown that it is impossible for position and momentum in a certain classical sense to simultaneously exist. However, it may be possible for other hidden variables to provide a classical picture of reality. One proposal for non-relativistic quantum mechanics is Bohmian mechanics.

 

[Demystifier]

Summary:: Is quantum uncertainty intrinsic to physical reality or a measure of our ignorance?

In most interpretations it's intrinsic, but in some (Bohm, Nelson) it's ignorance. Nobody knows which interpretation is right.

 

[PeroK]

However, I am a firm believer in Carl Sagan's point that extraordinary statements require extraordinary proof. QM is very extraordinary. I have faith in physicists. But I want to accept QM on more than faith.

In 2021, the extraordinary claim would be that QM is all a bad dream and we can happily go back to 19th century physics. The onus would be on you to provide the extraordinary evidence for that.

It's pointless to pretend that the body of experimental evidence from atomic and sub-atomic physics from the 20th century somehow does not exist. If you consider QM extraordinary, then there is your extraordinary evidence. The experiments have been done. Physics is not faith; physics is an empirical science. QM, in particular, has a significant body of experimental to support it. More than that, it was the exprimental evidence that drove the theoretical development - no one imagined QM until the experimental evidence pushed them forcibly in that direction.

Do you really believe that Carl Sagan doubted the evidence in support of QM? This is not 1921. QM is not a revolutionary idea that is shaking the world of physics. It has been established mainsteam physics for nearly 100 years. No one takes it on faith. They learn it, repeat the experiments and understand how the theory supports those "extraordinary" experimental outcomes.

Here's a quotation from Ballentine's book about electron diffraction:

This experiment led to the award of a Noble prize to Davisson in 1937. Today, with improved technology, even an undergraduate can easily produce electron diffraction patterns that are vastly
superior to the Nobel prize-winning data of 1927.

The question is: if you are serious about QM, why don't you know that experiments that demonstrate QM phenomena are routinely carried out by undergraduates? This is not hidden away and maintained by high priests of science. This information is readily accessible if you choose to look for it.

 

[WernerQH]

I have no doubt that no one can measure both simultaneously. My question was, is that because we will never have the ability to measure both simultaneously or because only one predicate ( position or momentum ) can exist at a time.

The predicates exist at the same time, but they are only approximate. From the track in a bubble chamber we infer consecutive locations of some charged particle, and from the curvature (because of the applied magnetic field) the momentum of the particle. The predicates refer to some piece of classical fiction ("particle"), but the formalism refuses to provide precise values for them.

Is quantum uncertainty intrinsic to physical reality or a measure of our ignorance?

I'd say it's a feature of our description of reality. We can't tell if it is "intrinsic" to reality, because we have no access to some true "reality" beyond our description of it.

I have no problem with knowing that reality transcends our meager intellects.

I do have a problem with that. I doubt you can ever "know" something to be "unknowable". But there is always the possibility of finding a new perspective that renders the original question meaningless.

 

[.Scott]

My question was, is that because we will never have the ability to measure both simultaneously or because only one predicate ( position or momentum ) can exist at a time.

First, you're paraphrasing the Heisenberg Uncertainty Principle very imprecisely. A statement of the principle is provided in the wiki article as follows:

Introduced first in 1927 by the German physicist Werner Heisenberg, the uncertainty principle states that the more precisely the position of some particle is determined, the less precisely its momentum can be predicted from initial conditions, and vice versa. The formal inequality relating the standard deviation of position ($σ_x$) and the standard deviation of momentum ($σ_p$) was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928:

where ħ is the reduced Planck constant, h/(2π).

So you can measure both position and momentum simultaneously, but there is a limit on the combined precision of those two measurements - more specifically, the limit is on the product of the precisions of those two measurements.

Second, to get to the meat of your question, the Heisenberg Uncertainly Principle (HUP) appears to be a very real limitation of our universe. As a software engineer, I tend to look at it terms of information. There is less information in "any word" than in "any word that starts with E". And the more specific you get, the more information you are providing. So there is still more information in "the word is Example".

So, as an analogy, let's look at two versions of a word game.
1) From a dictionary of 100,000 words, I will pick one word and allow you to ask questions until you attempt to narrow the choices to less than 300. So, "Yes, it begins with 'E'"; "No, it does not have one or two syllables"; "Yes, there is an 'A' in it"; "Sorry, end of game, I cannot tell you if there is an 'X'".
2) From a dictionary of 100,000 words, I will provide randomly selected answers to your questions for as long as at least 300 words meet the resulting description. So, "Yes, it begins with 'E'"; "No, it does not have one or two syllables"; "Yes, there is an 'A' in it"; "Sorry, end of game, I cannot tell you if there is an 'X'".

To make the statistics for these game versions look the same, for game #2, the random answers will be weighted according to the remaining possible word choices. So, for example, assuming that 8% of the words start with 'E', when your first question is "Does it begin with 'E'", I will respond "Yes" 8% of the time and "No" 92% of the time.

Now we will play the game a thousand times - you ask the questions, I provide the answers. But I will not tell you which version of the game we are playing. And at the end of the 1000 plays, I will ask you which version you think we were playing.

You want to know if there were ever a specific word that you were asking about. And nothing in the game allows you to determine that with certainty.

But you are undeterred - so you renegotiate the rules of the game in order to see how I prefer playing games of this sort.

Instead of asking about a word, you will ask about the angle of a line (its slope) - in the range of 0 to 180 degrees. And your questions will be limited to a selection of these three:
a) Is the angle less than 90?
b) If I add 22 degrees to it, will it be less than 90?
c) If I add 44 degrees to it, will it be less than 90?

Just to be clear, if the angle is 170, adding 44 would make it 34 and therefore less than 90.

Then, in an attempt to force me into picking an angle ahead of time, you require me to send a particle with a spin at this angle to both you and a friend of yours - two separate particles with the same information to two different locations.

In a dry run, both you and your friend always ask the same question and always get the same answer. So it looks as though I am playing fairly - and as expected.

Then you start having fun. Both you and your friend start independently selecting questions randomly and then comparing notes. When, per chance, you both ask the same question, you both get the same answer. And when you ask different questions, sometimes you get the same answer and sometimes you get different answers.

But on closer examination a problem is seen. When the measurements are 44 degrees apart, the spin measurements are different 24% of the time. When the measurements are 22 degrees apart, the spin measurements are different 7% of the time. But how can the difference at 44 degrees be more than twice the difference at 22 degrees? After all, when they are 44 degrees apart, then measurements "a" and "c" (above) were made - and each one could not have been different more than 7% of the time with "b" (the measurement that was not made). So the total could not have been more that 14%!

It would seem that not only am I not pre-selecting a spin value but that I am somehow cheating the game altogether.

Most readers in this forum will recognize that this spin game is based on the Bell inequality - with slight changes to the rules to make the problem more obvious.

But this experiment described by Bell has been performed many times as precisely as possible and the results always follow the "wacky" results I described above.

 

[DrChinese]

I have no doubt that no one can measure both simultaneously. My question was, is that because we will never have the ability to measure both simultaneously or because only one predicate ( position or momentum ) can exist at a time.

Entangled particle pair spins (say photon polarization) have known values when measured at identical angles. You can measure those as simultaneously and precisely as you desire - of course you obtain redundant information when the angle is the same.

If you measure one, and then the other at a different angle, you have new information. Or do you? Clearly, the issues involved in this case have nothing whatsoever to do with our lack of knowledge, or limits to our measurement precision. The uncertainty principle says that regardless of how we attack learning about non-commuting observables, we cannot learn more than it allows.

In your terms, it is "intrinsic". There is some variation between interpretations, but in no interpretation the issue one of measurement precision. It is considered fundamental.

 

[Morbert]

Summary:: Is quantum uncertainty intrinsic to physical reality or a measure of our ignorance?

Quantum theories do not commit you to a position on this question.

 

[PeterDonis]

Moderator's note: Moved thread to the QM interpretations subforum.

 

[PeterDonis]

maybe that is a stupid question and only intelligent questions are allowed but doesn't that defeat the whose purpose of this site? Please do not delete this question. I really want an answer. I am beginning to think that unless you are an actual physicist this site is useless.

All of this ranting is off topic. The fact that you "really want an answer" to a question doesn't mean there is an answer that your current intuition will accept. That means you need to retrain your intuition.

In this specific case, how the intrinsic uncertainty of QM is viewed depends on which interpretation of QM you adopt. That is why this thread has been moved to the interpretations subforum.

I posted a similar question and it was deleted because I was told the question was stupid!

Your previous thread got deleted because the video you referenced had nothing to do with QM, it was about GR.

 

[AndreiB]

I realize that it is impossible to know both the speed and position of a particle because of the uncertainty principle.

This is false. You can prepare a particle with an accurately known momentum and measure the position of that particle with any accuracy. At the time of the position measurement you know both, with in principle unlimited accuracy. The problem is that the position measurement disturbs the particle's momentum so you cannot use the momentum/position pair to predict the particle's future behavior.

I also know that this is because if you send a photon at the particle to detect its position you alter its momentum.

True.

But does that mean that when you measure position it has no momentum? Or when you measure its momentum it has no position?

No, not at all.

What you cannot do is to prepare a state where both momentum and position are known with arbitrary accuracy. The reason for this is that each measurement perturbs the particle. The uncertainty principle quantifies this disturbance. There is nothing mysterious about this.

 

[PeterDonis]

You can prepare a particle with an accurately known momentum and measure the position of that particle with any accuracy.

Yes.

At the time of the position measurement you know both, with in principle unlimited accuracy.

No, you don't, because the position measurement changes the state of the particle--in other words, it decreases the information you have about momentum at the same time as it increases the information you have about position. To know both with in principle unlimited accuracy, there would have to be a possible state of the particle that had very narrow width in both position and momentum, and no such state is possible.

You even know this:

The problem is that the position measurement disturbs the particle's momentum so you cannot use the momentum/position pair to predict the particle's future behavior.

This is equivalent to what I said above: you are simply ignoring the fact that disturbing the particle's momentum invalidates the previous information you had about the momentum, so it is not justified to say that you know both position and momentum with unlimited accuracy.

 

[AndreiB]

No, you don't, because the position measurement changes the state of the particle--in other words, it decreases the information you have about momentum at the same time as it increases the information you have about position. To know both with in principle unlimited accuracy, there would have to be a possible state of the particle that had very narrow width in both position and momentum, and no such state is possible.

In "The Physical Principles of the Quantum Theory", page 20, Heisenberg writes:

"If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated. For these past times, δpδq is smaller than the usual bound."

So, Heisenberg disagrees with you.

 

[AndreiB]

To know both with in principle unlimited accuracy, there would have to be a possible state of the particle that had very narrow width in both position and momentum, and no such state is possible.

Such a state cannot be prepared since at the time you know both the position and momentum, the momentum of the particle was changed.

You are simply ignoring the fact that disturbing the particle's momentum invalidates the previous information you had about the momentum, so it is not justified to say that you know both position and momentum with unlimited accuracy

OK, let's consider a different experiment. You have an electron gun and a fluorescent screen placed at some arbitrary distance. You start the gun for a very short time and write down that time. You also register the time of detection. Now you can calculate both position and momentum with arbitrary accuracy (you can increase the accuracy by increasing the distance between the gun and the screen) for the entire route between the gun and the screen. Sure, after detection, the electron chances its state so you cannot use this past knowledge to make further predictions.

 

[Demystifier]

In "The Physical Principles of the Quantum Theory", page 20, Heisenberg writes:

"If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated. For these past times, δpδq is smaller than the usual bound."

So, Heisenberg disagrees with you.

No, Heisenberg talks about $\delta q$ and $\delta p$ evaluated at different times, while @PeterDonis talks about uncertainties at the same time.

 

[AndreiB]

No, Heisenberg talks about $\delta q$ and $\delta p$ evaluated at different times, while @PeterDonis talks about uncertainties at the same time.

No, he does not. He continues:

"Then for these past times $\delta q$ and $\delta p$ is smaller than the usual limiting value, but this knowledge of the past is of a purely speculative character, since it can never (because of the unknown change in momentum caused by the position measurement) be used as an initial condition..."

Exactly what I said.

 

[Demystifier]

He continues:

Heisenberg or PeterDonis?

 

[AndreiB]

Heisenberg or PeterDonis?

Heisenberg. You can check the preview on Google Books to see the entire context. He also speaks about "the usual bound". What bound could be referring to if not the uncertainty relations?

 

[Motore]

Heisenberg. You can check the preview on Google Books to see the entire context. He also speaks about "the usual bound". What bound could be referring to if not the uncertainty relations?

And that uncertainty relation cannot be arbitrarily small when measuring both position and momentum at the same time, which you are proposing (knowing both position and momentum with unlimited precision at the same time would lead to uncertainty relation of zero).

 

[PeroK]

OK, let's consider a different experiment. You have an electron gun and a fluorescent screen placed at some arbitrary distance. You start the gun for a very short time and write down that time. You also register the time of detection. Now you can calculate both position and momentum with arbitrary accuracy (you can increase the accuracy by increasing the distance between the gun and the screen) for the entire route between the gun and the screen. Sure, after detection, the electron chances its state so you cannot use this past knowledge to make further predictions.

The Uncertainty Principle is a statistical law, where the uncertainty $\sigma$ is the standard deviation of measurements (plural) taken on an ensemble of identically prepared systems.

In this case, the uncertainty in momentum is not the accuracy with which the momentum is measured, but the spread of different momentum measurements that you get over a set of experiments. This spread of measurements is the intrinsic uncertainty in the momentum of the particles prepared by the electron gun.

Any actual experiment to measure the momentum of electrons produced by this gun would introduce an added experimental error, but that experimental error is not what the UP is talking about - it's talking about the underlying variation in momentum where the experiment is repeated.

The other point is that there must be uncertainty in the time that the electron is emitted. To say that the gun fires the electron at a precise time is not possible. Trying to assume that you know that an electron starts a classical trajectory from point A at time $t = 0$ is already not possible when you consider the uncertainty in the subatomic processes would that emit an electron.

In order to see the UP in this experiment, you would have to add, for example, an initial measurement to get the position of the electron at some initial time. Then you would have two measurements that vary over the repeated experiments:

Some initial position measurement at $t_0$: note that this measurement is then essentially part of the electron preparation.

Some final position measurement at $t_1$.

From these two you can infer the electron's momentum in every run of the experiment. What the UP says is that the more precisely you establish the initial position of the electron, the wider the spread of measured momentum. In each experiment, you may assume an almost perfect accuracy of measurement. The UP does not prohibit that.

 

[PeroK]

Heisenberg. You can check the preview on Google Books to see the entire context. He also speaks about "the usual bound". What bound could be referring to if not the uncertainty relations?

Are you claiming that Heisenberg himself is arguing against his own uncertainty principle?!

My interpretation of what he's saying is that speculative measurements (based on an assumed position and momentum at some time where they were not actually measured) count for nothing. This, I assume, is laying the foundations for his (Heisenberg's) idea that such speculative measurements are not part of the theory of QM.

 

[Demystifier]

Heisenberg writes:

"If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated.

How exactly that can be calculated according to Heisenberg? Does he mean classical equation of motion for particle trajectory?

 

[PeroK]

How exactly that can be calculated according to Heisenberg? Does he mean classical equation of motion for particle trajectory?

It takes a special talent to read Heisenberg and find a vindication of classical trajectories over intrinsic quantum uncertainty!

 

[PeroK]

If this understanding is correct then the UP does not limit the knowledge of position and momentum for a single determination, right?

That's right - although you have to define "knowledge" in this case. With position and momentum there is still the element of inference: two position measurements over a time interval and an inferred momentum for the particle at the first time. What is happening is this:

The state of the electron at time $t_0$ is $\Psi(x, t_0)$, where we assume $\Psi$ is a Gaussian with very a small variance in $x$ ($\sigma_x$).

We measure the particle at time $t_1$ and infer a momentum for the particle in that experiment. In principle we can measure this with unlimited accuracy.

If we repeat the experiment we get a variance in our momentum measurements $\sigma_p$. Then the UP says that $\sigma_x \sigma_p \ge \frac{\hbar}{2}$.

Note: we did not measure the momentum of the particle at time $t_0$; we did not disturb that state. There was no simultaneous measurement of $x$ and $p$.

This is not a problem. The velocity is calculated as X1-X0/T1-T0, where X0 is the position of the electron gun's opening, X1 is the position of the spot on the screen, T0 is the emission time and T1 is the detection time. By increasing the distance between the gun and the screen i can make both X1-X0 and T1-T0 arbitrarily large, so any error associated with emission/detection time (which is fixed) becomes arbitrarily small

You still must measure the emission time. In QM the emission event cannot be assumed to be $(x, t)$ without measurement of $x$ at time $t$.

 

[PeroK]

We measure the particle at time $t_1$ and infer a momentum for the particle in that experiment. In principle we can measure this with unlimited accuracy.

If we repeat the experiment we get a variance in our momentum measurements $\sigma_p$. Then the UP says that $\sigma_x \sigma_p \ge \frac{\hbar}{2}$.

Note: we did not measure the momentum of the particle at time $t_0$; we did not disturb that state. There was no simultaneous measurement of $x$ and $p$.

PS this is essentially no different from electron diffraction (single slit). The slit is taken to be a measurement of the lateral position of the electron. That's a measurement of $y$ at some time. The dot on the screen at a lateral distance from the slit gives an inferred measurement of the lateral momentum of the electron (on that run of the experiment). In principle, we "know" that the electron went through a narrow slit and had a certain y-momentum in that particular run of the experiment.

What the UP says (and what is shown in a single-slit diffraction) is that the narrower the slit, the wider the range of impact points on the screen. I.e. the more tightly we limit the y-position, the greater the variance in y-momentum. But, there is nothing in the narrowness of the slit that affects the accuracy with which we may measure a dot on the screen. And hence nothing that limits the accuracy of our measurement of the y-momentum. The width of the slit and the accuracy of subsequent measurements on the screen are unrelated.

 

[Demystifier]

It takes a special talent to read Heisenberg and find a vindication of classical trajectories over intrinsic quantum uncertainty!

So how did you interpret his words that position before measurement can be computed?

 

[vanhees71]

Do we have the precise paper by Heisenberg, where he makes such a strange and enigmatic statement? He usually is very enigmatic, but as one of the hardcore Copenhagians it's hard to believe that he really made such a statement. He's even more Copenhagian than Bohr himself!

 

[PeroK]

Do we have the precise paper by Heisenberg, where he makes such a strange and enigmatic statement? I usually is very enigmatic, but as one of the hardcore Copenhagians it's hard to believe that he really made such a statement. He's even more Copenhagian than Bohr himself!

It's probably just taken out of context. And that the statement itself was not the conclusion - which no doubt followed.

 

[Sunil]

In 2021, the extraordinary claim would be that QM is all a bad dream and we can happily go back to 19th century physics. The onus would be on you to provide the extraordinary evidence for that.

I disagree. To give up successful classical scientific principles just because some interpretations of QT reject them remains nonsensical as long as there are interpretations which are compatible with those principles.

All the "extraordinary evidence" which would be necessary would be an interpretation compatible with the classical 19th century physics. And to reject them, we would need extraordinary evidence.

It's pointless to pretend that the body of experimental evidence from atomic and sub-atomic physics from the 20th century somehow does not exist. If you consider QM extraordinary, then there is your extraordinary evidence. The experiments have been done. Physics is not faith; physics is an empirical science. QM, in particular, has a significant body of experimental to support it. More than that, it was the exprimental evidence that drove the theoretical development - no one imagined QM until the experimental evidence pushed them forcibly in that direction.

Fine. But as long as there is an interpretation of QM which does not have to reject the principles of classical physics, all the evidence for QM is not evidence against those principles of classical physics. And in this case your extraordinary evidence for quantum mysticism is empty.

And historical accidents do not have scientific value. At least, they should not have. So it does not matter if some interpretation which is in agreement with classical principles was not the first most popular one, or that it has been proposed only recently. And it does not even matter too if it is completely ignored by the scientific community - once it exists, it counts.

For quantum theory, the interpretation most compatible with classical principles is entropic dynamics proposed by Caticha:

Caticha, A. (2011). Entropic Dynamics, Time and Quantum Theory, J. Phys. A 44 , 225303, arxiv:1005.2357

It contains trajectories of the configuration $q(t)\in Q$. Those trajectories are also part of de Broglie Bohm theory (Bohmian mechanics) which is older and more widely known, and Nelson's stochastics. So, to believe that trajectories exist is compatible with quantum theory. In dBB theory, those trajectories are even smooth and deterministic. That means, that there exists a velocity too is unproblematic too, and compatible with QM too. $p = m v$ is a classical formula, which does not hold in these interpretations. Instead, $p, H$ and so on are not properties of the system taken alone, but depend on the measurement device too, and there are, in particular, no continuous trajectories $p(t), E(t)$.

In Caticha's entropic dynamics, the wave function simply describes the incomplete knowledge about this trajectory. Such an epistemic interpretation of the wave function is therefore possible too.

 

[PeroK]

I disagree. To give up successful classical scientific principles just because some interpretations of QT reject them remains nonsensical as long as there are interpretations which are compatible with those principles.

You could say that about anything. You could refuse to accept any new ideas unless and until all the alternatives have been disproven. Yours is an ultraconservative position, where old ideas are retained until there is not the slightest possibility that that may be valid. That would effectively prevent progress in any practical matters.

Why are old ideas automatically better than new ideas? And why is rejecting old ideas fundamentally nonsensical? It's no more nonsensical that holding on to the past at all costs.

 

[Sunil]

You could say that about anything. You could refuse to accept any new ideas unless and until all the alternatives have been disproven. Yours is an ultraconservative position, where old ideas are retained until there is not the slightest possibility that that may be valid. That would effectively prevent progress in any practical matters.

No. Whenever there is no classical explanation for something, revolutionary ideas are welcome, and can be useful. I have no objection neither against the relativistic nor the quantum revolutions.
But after a scientific revolution there should be also time for a counterrevolution, when people look at which of the revolutionary steps are really necessary.

Why are old ideas automatically better than new ideas? And why is rejecting old ideas fundamentally nonsensical? It's no more nonsensical that holding on to the past at all costs.

Old ideas are better than simply rejecting old ideas. Rejecting old ideas, as well as new ideas, is not fundamentally nonsensical but requires extraordinary evidence. Not evidence which can be, without problems, made compatible with the rejected old ideas.

Formally, you can care about the predictive power. Rejecting ideas without necessity decreases predictive power and therefore should be rejected.

Holding on to the past at all costs is not what I have proposed. Those who prefer to reject the past has to present the costs, or better the gains they expect from their new ideas.

 

[phinds]

I realize that it is impossible to know both the speed and position of a particle because of the uncertainty principle.

I'm not even sure that's true but it's beside the point of the HUP. As @PeroK pointed out:

The Uncertainty Principle is a statistical law, where the uncertainty is the standard deviation of measurements (plural) taken on an ensemble of identically prepared systems.

What makes QM different than classical is that in classical, if you know EVERYTHING about how a test is prepared and you can make it the same every time, then you will always get the same result ever time, whereas what the HUP tells us about the real world is that if you know EVERYTHING about how a test is prepared and you can make it the same ever time, you will NOT get the same results every time. You will get similar results within the limit stated by Heisenberg