Uncertainty = our ignorance or intrinsic to reality?

[PeroK]

Holding on to the past at all costs is not what I have proposed.

Only that it's nonsensical to do otherwise, which amounts to the same thing.

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.

From a logical point of view that gives an unncessary and inexplicable preference for the previous idea. I.e. if we have idea A and idea B, then we hold to idea A because it came first historically? If you were given the same two ideas, but were told that idea B originated before idea A, would you automatically prefer idea B because it came first?

I would tend to judge ideas A and B on their respective merits - not on which idea was thought of first.

 

[A. Neumaier]

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

the Heisenberg Uncertainly Principle (HUP) appears to be a very real limitation of our universe.

Yes. It is mathematically the same as Nyquist's theorem that imposes very real limitations on the simultaneous determination of frequency and amplitude of a classical signal at a fixed time. Nothing strange here!

 

[PeroK]

Well, I hoped that your intuition is enough, but if you want calculations, here they are:

electron speed: 10^6 m/s
gun opening size: 1µm

The velocity uncertainty calculated using this calculator:

https://www.omnicalculator.com/physics/heisenberg-uncertainty

is ~60 m/s.

Distance is 10^10 Km, so deltaX is 10^13m.
Time measurement error is 1ms. Total travel time would be 10^7 +-10^(-3) s.

The velocity is in the interval 999999.9999 - 1000000.0001 m/s. The uncertainty is about 0.0002 m/s.

0.002 is smaller than 60. Satisfied?

The UP says that you will measure significantly different momentum across several experiments. It has nothing to do with how accurately you can measure the momentum on any particular run - that's what this whole debate is about.

What QM says is that as you reduce the shutter time, you get a greater variance in momentum measurements. If you make the shutter time really small (so you've effectively highly localised the electron initially), you should expect a wide range of momentum results.

This, again, is very similar to single-slit diffraction: once the slit becomes sufficiently narrow, the elecron beam spreads out after the slit - with widely varying electron y-momenta.

The acid test is, of course, to run an experiment:

Your claim would be that as you reduce the shutter time, you get no change in the distribution of momenta from the gun.

QM would claim that the UP must be obeyed.

We cannot resolve this by discusson or calculation: we would have to do the experiment to see who's right.

PS you could also look at this from the time-energy UP: the shorter the shutter time the more variance there is in the energy (hence momentum) of the electron.

 

[PeroK]

I don't disagree with this and this is not what I was arguing against. I said that UP does not preclude one to know both position and momentum of a particle, at the same time, in the past. The experiment I proposed proves this to be possible.

In other words, if we do two ultra-accurate measurements of a particle's position at very accurately measured times, then we can infer an ultra-accurate value for its (average) momentum during the intervening time interval?

The UP has nothing to say about that. There's no argument there, as far as I'm concerned.

 

[vanhees71]

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.

Well, the problem with classical physics first is that it is impossible to describe obvious facts with it, among them the stability of the matter around us and last but not least ourselves. Another very obvious fact is the discreteness of the spectral lines of atoms and molecules and many more phenomena, which look at the first glance pretty classical, but they cannot be explained in any consistent way using only classical physics. Last but not least there are experimental setups which cannot even be planned without using QT, among them technology like lasers or transistors and ICs or the creation of true photon Fock states and the quantum-optical phenomena being demostrated quantitatively with highest precisions ever reached.

On the other hand it's also pretty well understood why the classical description of macroscopic matter works very well and what the precise realm of its validity is. If there is a drawback of QT it's that we don't know in which direction the precise realm of its validity is violated. I think the lack of any evidence for a violation of the fundamental rules of QT is the main obstacle to find possible extensions or even completely new theoretical concepts to make the description of the gravitational interaction (today described by GR, i.e., a classical field theory) consistent with quantum theory.

 

[vanhees71]

The UP says that you will measure significantly different momentum across several experiments. It has nothing to do with how accurately you can measure the momentum on any particular run - that's what this whole debate is about.

It is very important to be precise in interpreting the Heisenberg-Robertson UP, which is very simple to derive. You can do it in QM 1 in the first few lectures.

This UP is not about the ability or disability to precisely measure observables but about the impossibility to prepare a system in a state where two incompatible observables take a determined value (to be precise there are exceptions: e.g., if you prepare a system in a total angular-momentum state with $J=0$, then all components of the angular momentum take the determined value 0, but that's another story).

In principle, you can always measure any observable as precisely as you like, independent of the state the measured system is prepared in. Often, of course, when measuring one observable (e.g., the position of a single electron), you cannot measure another incompatible observable precisely at the same time (in our examiple the momentum of the electron). On the other hand quantum states and preparations determine only statistical properties about the outcome of measurements, and if you can repeatedly prepare (in our example) and electron precisely in the same state, you can first make a very precise measurement of the position on an ensemble of indpendently such prepared electrons (the precision of your apparatus can be much better than the expected uncertainty of position of the electron) and then make a very precise measurement of the electron's momentum on another ensemble of independently such prepared electrons (the precision of your apparatus can be much better than the expected uncertainty of the electron's momentum). In fact, if you want to test the UP, you have to measure both position and momentum in this sense with much higher precision/resolution than the expected values of the uncertainties of these quantities.

 

[fresh_42]

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!

Here is a quotation of Heisenberg about the concept:

"Uncertainty" is NOT "I don't know." It is "I can't know." "I am uncertain" does not mean "I could be certain." ~ Werner Heisenberg

 

[vanhees71]

Again, from which paper by Heisenberg is this from? One has to read statements about the interpretation of quantum theory always in context.

In my understanding of QT it's not only that "I can't know" (both position and momentum) about a particle but that a particle cannot even have accurate position and momentum, because in any state the particle can be in the Heisenberg-Robertson uncertainty relations $\Delta x_k \Delta p_k \geq \hbar/2$ are valid, i.e., the more accurately I prepare the particle's momentum the less accurate it's position is prepared and vice versa.

 

[PeterDonis]

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[PeterDonis]

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