# What's wrong with Heisenberg's microscope?

1. Jun 28, 2008

### kahoomann

One way in which Heisenberg originally argued for the uncertainty principle is by using an imaginary microscope as a measuring device [2] he imagines an experimenter trying to measure the position and momentum of an electron by shooting a photon at it.

If the photon has a short wavelength, and therefore a large momentum, the position can be measured accurately. But the photon will be scattered in a random direction, transferring a large and uncertain amount of momentum to the electron. If the photon has a long wavelength and low momentum, the collision will not disturb the electron's momentum very much, but the scattering will reveal its position only vaguely.

If a large aperture is used for the microscope, the electron's location can be well resolved (see Rayleigh criterion); but by the principle of conservation of momentum, the transverse momentum of the incoming photon and hence the new momentum of the electron will be poorly resolved. If a small aperture is used, the accuracy of the two resolutions is the other way around.

The trade-offs imply that no matter what photon wavelength and aperture size are used, the product of the uncertainty in measured position and measured momentum is greater than or equal to a lower bound, which is up to a small numerical factor equal to Planck's constant.[4] Heisenberg did not care to formulate the uncertainty principle as an exact bound, and preferred to use it as a heuristic quantitative statement, correct up to small numerical factors.

Can we really use this disturbance theory to explain the Heisenberg uncertainty principle?
Does the Heisenberg uncertainty principle has anything to do with disturbance theory?
For example, if we measure the temperature of hot water, its temperature would change due to the measurement itself

Last edited: Jun 28, 2008
2. Jun 28, 2008

### Ciokko

as far as i know, heisenberg first explained the uncertainty principle with the disturbance theory, but then he changed his mind and now the current interpretation is that some couples of variables can't be defined with arbitrary precision at the same time: the uncertainty principle is a sort of property of the matter.

heisenberg's microscope is one way in wich the principle applies to reality (reality often uses these tricks in order to save quantum physics), but i don't think that it expresses the core, the real nature, of the principle.

anyway, wait for more experienced users

3. Jun 28, 2008

### cesiumfrog

Think of an ordinary classical wave: it cannot simultaneously have a well defined position (like a solitary pulse) and well defined wavelength (like infinite plane waves), regardless of how tricky your measurement may be.

4. Jul 16, 2008

### exponent137

I think that the correct answer is: "position and momentum (in Heisenberg microscope) are local hidden variables, but test of Bell formula showed that local hidden variables do not exist."

Can someone correct me?

5. Jul 17, 2008

### muppet

Position and momenta aren't hidden variables, and Bell's inequality didn't show that hidden variables do not exist. Sorry
Bell's inequality showed that any theory which would yield identical predicitions to QM could not satisfy the requirements of determinism (if a system is known to be in some state at a particular time, it is known what state it will be in at some later time) and locality (events at a point A cannot be influenced by events that happened t seconds previously at point B x metres away from A, unless x < ct where c is the speed of light).[Technically that strict inequality should be a less than or equals sign.]

6. Jul 17, 2008

### Maaneli

Hey Muppet. The guy you are respond to was actually correct. Position and momentum are not "hidden variables" in the sense that they are not what we see in experiments. If anything, the wavefunction is a hidden variable. Bell made this point many times in his papers on QM. Also, the guy you are responding to said Bell's theorem shows that local hidden variables can't be compatible with QM, not just hidden variables. Also, it is an error to state Bell's inequality as suggesting an incompatibility between the assumptions of determinism and locality. Yes, locality is one of the problematic assumptions, but determinisim isn't at all. A stochastic local hidden variable theory does not violate the Bell inequality either. The second problematic assumption that Bell made was causality (the statement that the initial conditions of the particles are physically independent of the future measurement settings). Please have a look at the following papers.

Locality and Causality in Hidden Variables Models of Quantum Theory
Authors: Stefan Teufel, Karin Berndl, Detlef Dürr, Sheldon Goldstein, Nino Zanghì
http://arxiv.org/abs/quant-ph/9609005

Bell Locality and the Nonlocal Character of Nature
Authors: Travis Norsen
http://arxiv.org/abs/quant-ph/0601205

J.S. Bell's Concept of Local Causality
Authors: Travis Norsen
http://arxiv.org/abs/0707.0401

7. Jul 17, 2008

### Maaneli

My bad, I misread your words. You also said position and momentum aren't hidden variables, which generally speaking is correct. But, in terms of Bell's theorem, they are actually characterized as such.

8. Jul 19, 2008

### muppet

Maaneli... I'll weigh in with my 2 cents on Bohmian mechanics on another thread. But as a general observation, when someone who is very obviously new to this stuff asks a 'textbook' question, I think the general consensus on this forum would be that we give them a textbook answer before advancing views that are held by a minority of physicists.

Anyway, with regards to the OP: The key point is Ciokko's. The central idea of Heisenberg's uncertainty principle is that prior to an act of measurement, variables such as position and momentum are not defined to within greater precision than that specified by the HUP. Heisenberg considered that all physics could do was predict the outcome of experiments, because what a philosopher would call the ontology of subatomic particles- their 'real existence', independent of human perception, was inherently indeterminate. His derivation/proof of the uncertainty principle was completely independent of his microscope 'gedanken' (thought) experiment. The point of that was to investigate whether or not it was possible to experimentally measure a particle to be in a state that was more precisely defined than was allowed by the uncertainty principle, which would be a fairly lethal blow to the theory. As it turns out, it isn't (at least at the time of the first measurement of a particular system), which made Heisenberg a happy man.

9. Jul 19, 2008

### Maaneli

Muppet, where did I mention deBB theory on this thread? I was simply correcting you on the statement of Bell's theorem. That's all. Unless you are referring to another thread?

10. Jul 19, 2008

### muppet

Explicitly you didn't, but your references to hidden variables theories were provided without any qualifying remarks to someone who wasn't already aware of the present picture of interpretations of QM.

11. Jul 19, 2008

### Maaneli

No, muppet, you misunderstood. Bell's theorem inherently involves discussion of hidden variables. Any accurate explanation of Bell's theorem must necessarily mention hidden variables. That has nothing a priori to do with deBB theory. Please read Bell's original papers if this isn't clear to you.

12. Jul 19, 2008

### muppet

I didn't misunderstand... I just didn't read beyond the titles of your references. Having done so I apologise.