Question about the Heisenberg U.P. & the Observer Effect

[victorhugo]

I studied only half a semester of quantum physics in high school (which i only finished 8 months ago and came first in physics luckily) but i remember Heisenberg's uncertainty principle. All over youtube people were saying things like "this is God's way of keeping us from getting into perfection of perfectly knowing everything", as if it were some universal rule

I never bothered to research much on this but I remember coming to a conclusion that I talked to my physics teacher about and he said that it's right: We observe and measure small particles with other particles (the only way to see something is by interacting it with a photon) so basically, the smaller the wavelength of the photons, then the more energy, but the smaller distance it covers in space. Thus, if a lot of small photons bounce of an object and we analyse the interaction, we can get a good idea of where the object was in space by an accuracy of the size of the photon, BUT since it's a high energy photon, it now exchanged a lot of energy with the particle and changed it's momentum.
so the less energy in the photon, the less it will change the observed particles momentum, but the less accurate position in space we can get, and hence the formula.
is this right of at least a simple version of what is going on?

for the observer effect, i hear everywhere that 'consciousness affects reality' and whatever mystic things people tend to come up with...
is this the same thing, that an electron orbit only exists in a range of probabilities around the atom, and the moment it interacts with a particle a position in space must be decided?

thank you in advance :)

 

[PeterDonis]

is this right of at least a simple version of what is going on?

It's ok as a mechanism for why the uncertainty principle as applied to position and momentum holds for that particular method of measurement. But the principle itself is much more general and fundamental than that. The best simple way I know to state the general principle is: if you have two complementary observables (such as position and momentum), there is no possible state of the system that has exact values for both observables. In other words, the uncertainty principle is a limitation on the possible states of the system, not just on measurement processes.

for the observer effect, i hear everywhere that 'consciousness affects reality' and whatever mystic things people tend to come up with... is this the same thing?

No. The uncertainty principle is part of the basic physics of QM. Claims about "consciousness affects reality" are pop science interpretations that some people make, but have nothing to do with the basic physics of QM.

 

[victorhugo]

It's ok as a mechanism for why the uncertainty principle as applied to position and momentum holds for that particular method of measurement. But the principle itself is much more general and fundamental than that. The best simple way I know to state the general principle is: if you have two complementary observables (such as position and momentum), there is no possible state of the system that has exact values for both observables. In other words, the uncertainty principle is a limitation on the possible states of the system, not just on measurement processes.
No. The uncertainty principle is part of the basic physics of QM. Claims about "consciousness affects reality" are pop science interpretations that some people make, but have nothing to do with the basic physics of QM.

I see

The second question really was " that an electron orbit only exists in a range of probabilities around the atom, and the moment it interacts with a particle a position in space must be decided?" instead of is it consciousness affecting reality... i was almost certain that is pop science ;)
sorry about the communication barrier, English is my second language

 

[vanhees71]

It's ok as a mechanism for why the uncertainty principle as applied to position and momentum holds for that particular method of measurement. But the principle itself is much more general and fundamental than that. The best simple way I know to state the general principle is: if you have two complementary observables (such as position and momentum), there is no possible state of the system that has exact values for both observables. In other words, the uncertainty principle is a limitation on the possible states of the system, not just on measurement processes.

That's also not entirely correct. Even if you have some incompatible observables, i.e., such observables which are represented by self-adjoint operators that do not commute, there may be some common eigen vectors. An example is angular momentum. The components are not compatible since the commutation relations read
$$[\hat{J}_j,\hat{J}_k]=\mathrm{i} \hbar \sum_{l=1}^3 \epsilon_{jkl} \hat{J}_l.$$
However, for $J=0$, i.e., the eigenstate $|J=0,M=0 \rangle$ obeys
$$\hat{J}_1 |J=0,M=0 \rangle=\hat{J}_2 |J=0,M=0 \rangle = \hat{J}_3 |J=0,M=0 \rangle=0,$$
i.e., it is a simultaneous eigenvector for the all three components of the angular-momentum operator.

Of course there's not a complete set of common eigenvectors for any two incompatible observables.

The correct general statement for the Heisenberg-Robertson uncertainty principle reads:
$$\Delta A \Delta B \geq \frac{1}{2} |\langle [\hat{A},\hat{B}] \rangle|,$$
where the average is with respect to any pure or mixed state.

 

[UsableThought]

That's also not entirely correct

<snip>.

Is the level of mathematical detail in your answer compatible with a "B" level (basic) thread? I ask because I am lurking and wondering, if indeed it is more than B level, then perhaps you might translate into "B" level for the OP's benefit and also the benefit of any "basic" lurkers such as myself? Or if it can't really be simplified, then indicating that this is the case.

 

[dextercioby]

What could be regarded as an "observer effect" is the drastic "observation/measurement collapses the wavefunction" aspect of the Copenhagen/textbook interpretation of the QM formalism. One can search this forum (or simple search through Google) for "quantum Zeno effect".

 

[PeterDonis]

That's also not entirely correct.

You are right, there are some counterexamples, but they're very limited and, as @UsableThought pointed out, this is a "B" level thread.

The second question really was " that an electron orbit only exists in a range of probabilities around the atom, and the moment it interacts with a particle a position in space must be decided?"

Ok. This is not correct as you state it. A correct statement would be that the electron in an atom does not have a definite position unless its position is measured. But not all interactions correspond to a measurement of position. In particular, the electron's interaction with other electrons in the atom, with the nucleus, and with radiation being emitted or absorbed when the electron changes energy levels, do not correspond to any measurement of position. In fact I'm not aware of any experiment where anyone has tried to measure the position of an electron within an atom. The wave functions you see for electrons in atoms, in position space (i.e., diagrams of orbitals), are derived from measurements of other observables and theoretical analysis.

 

[vanhees71]

Is the level of mathematical detail in your answer compatible with a "B" level (basic) thread? I ask because I am lurking and wondering, if indeed it is more than B level, then perhaps you might translate into "B" level for the OP's benefit and also the benefit of any "basic" lurkers such as myself? Or if it can't really be simplified, then indicating that this is the case.

Well, also B-level answers should be correct, shouldn't they?

 

[UsableThought]

Well, also B-level answers should be correct, shouldn't they?

It's not a criticism on my part; just a request to translate the gist of what you said, if you can, into a B-level statement. This might mean leaving out the math but still giving some idea of the nature of your clarification. I imagine this would probably be helpful to the OP as well as to me!

 

[PeterDonis]

just a request to translate the gist of what you said, if you can, into a B-level statement

The gist would be that what I said is not strictly correct, but it's still a good enough approximation for the "B" level.

 

[Physics Footnotes]

The essence of your question, @victorhugo, appears to be this assertion by your physics teacher:

We observe and measure small particles with other particles (the only way to see something is by interacting it with a photon) so basically, the smaller the wavelength of the photons, then the more energy, but the smaller distance it covers in space. Thus, if a lot of small photons bounce of an object and we analyse the interaction, we can get a good idea of where the object was in space by an accuracy of the size of the photon, BUT since it's a high energy photon, it now exchanged a lot of energy with the particle and changed it's momentum.
so the less energy in the photon, the less it will change the observed particles momentum, but the less accurate position in space we can get, and hence the formula.
is this right of at least a simple version of what is going on?

This view is called the Disturbative Interpretation of the Heisenberg Uncertainty Principle (HUP) which, although it is still repeated in most textbooks, has long been rejected by experts in the foundations of physics as the real take home lesson behind the HUP.

To see why, imagine an electron beam prepared in a certain quantum state. Instead of attempting a joint measurement of both Momentum (P) and Position (Q) on each electron, imagine instead taking turns of measuring only P or only Q on each electron. As you collect the data from these measurements you build up two statistical distributions; one for P and one for Q. It turns out (both mathematically and empirically) that the product of the standard deviations of these distributions always satisfies the HUP. Yet, at no stage have we disturbed a measurement of one property by trying to localize its other property.

You can get an even less disturbative measurement model by making these measurements only on entangled twins of the electrons in the beam, and yet still Quantum Theory and experiment show that the HUP holds firm in the undisturbed beam.

In fact, you can do even better than this. You can show mathematically (although I'm going to skip the nuances), without making any measurements at all, that it is impossible even in principle to assign a joint P-Q distribution of values to the electrons in the beam in such a way that their marginal distributions (i.e. the projected distributions of P and Q by themselves) agree with those predicted by Quantum Theory and confirmed many times over by laboratory experiments.

Although there are always physicists investigating subtle loopholes in these arguments, the overwhelming majority accept the view expressed above by @PeterDonis: the uncertainty principle is a limitation on the possible states of the system, not just on measurement processes. That is, states in which both P and Q are both arbitrarily localized simply do not exist in the first place, regardless of whether or not a big clumsy human comes poking around.

Note 1: One should also heed @vanhees71 more advanced warning that the HUP is a mathematical theorem, rather than a general principle, which has to be derived carefully on a case by case basis. For some pairs of observables a HUP-like relationship can fail on some states, or fail to be defined at all on others.

Note 2: To the extent that 'consciousness' is a physical process, it is no more special than 'digestion' as far as Quantum Theory is concerned. To the extent that consciousness is (or might be) a metaphysical process, Quantum Theory is silent on the matter; that is, Quantum Theory neither corroborates nor requires such a metaphysical appendage.

 

[victorhugo]

The essence of your question, @victorhugo, appears to be this assertion by your physics teacher:

This view is called the Disturbative Interpretation of the Heisenberg Uncertainty Principle (HUP) which, although it is still repeated in most textbooks, has long been rejected by experts in the foundations of physics as the real take home lesson behind the HUP.

To see why, imagine an electron beam prepared in a certain quantum state. Instead of attempting a joint measurement of both Momentum (P) and Position (Q) on each electron, imagine instead taking turns of measuring only P or only Q on each electron. As you collect the data from these measurements you build up two statistical distributions; one for P and one for Q. It turns out (both mathematically and empirically) that the product of the standard deviations of these distributions always satisfies the HUP. Yet, at no stage have we disturbed a measurement of one property by trying to localize its other property.

You can get an even less disturbative measurement model by making these measurements only on entangled twins of the electrons in the beam, and yet still Quantum Theory and experiment show that the HUP holds firm in the undisturbed beam.

In fact, you can do even better than this. You can show mathematically (although I'm going to skip the nuances), without making any measurements at all, that it is impossible even in principle to assign a joint P-Q distribution of values to the electrons in the beam in such a way that their marginal distributions (i.e. the projected distributions of P and Q by themselves) agree with those predicted by Quantum Theory and confirmed many times over by laboratory experiments.

Although there are always physicists investigating subtle loopholes in these arguments, the overwhelming majority accept the view expressed above by @PeterDonis: the uncertainty principle is a limitation on the possible states of the system, not just on measurement processes. That is, states in which both P and Q are both arbitrarily localized simply do not exist in the first place, regardless of whether or not a big clumsy human comes poking around.

Note 1: One should also heed @vanhees71 more advanced warning that the HUP is a mathematical theorem, rather than a general principle, which has to be derived carefully on a case by case basis. For some pairs of observables a HUP-like relationship can fail on some states, or fail to be defined at all on others.

Note 2: To the extent that 'consciousness' is a physical process, it is no more special than 'digestion' as far as Quantum Theory is concerned. To the extent that consciousness is (or might be) a metaphysical process, Quantum Theory is silent on the matter; that is, Quantum Theory neither corroborates nor requires such a metaphysical appendage.

Thank you, that was a great explanation.
So regardless of the way P and Q can be measured, it always holds, as you said, "That is, states in which both P and Q are both arbitrarily localized simply do not exist in the first place, regardless of whether or not a big clumsy human comes poking around."And so no matter where and how eg an electron is, the equation holds true regardless of whatever way you decide to measure p and q in that system?