# I need all the information about theHeisenberg's uncertainty principle

1. May 29, 2013

### lee.spi

I really can't understand the uncertainty principle,and now there are some experiment that violate the uncertianty principle, I need deepen understanding of quantum uncertainty,who can give me all the information about the uncertainty principle,such as new ideas,related study or books,thanks

Last edited by a moderator: May 29, 2013
2. May 29, 2013

### Staff: Mentor

Can you cite the experiment you are refering to?

Regarding information about the HUP any of the textbooks listed as Quantum here should have a good treatment:
https://www.physicsforums.com/forumdisplay.php?f=224 [Broken]

Without some more detail I am afraid that is all that can be done to help you. The question is too broad for an internet forum.

Last edited by a moderator: May 6, 2017
3. May 29, 2013

### Simon Bridge

Please provide a reference to the experiment that violates the uncertainty principle.

Which art of the uncertainty principle do you have trouble with?

4. May 29, 2013

### Charles Wilson

Post removed by author.
Nevermind.

CW

Last edited: May 30, 2013
5. May 29, 2013

### Ravi Mohan

I think this is totally wrong. It is more like
(Spread in position)(Spread in momentum) >= h-bar (mathematically spread is standard deviation here)

Also I can find the true position (a peak or dirac delta in position distribution) or the true momentum of the particle. But uncertainity principle says that I cant have both of them simultaneously.

So it goes like

1) There is a system and I measure its position. I get it as x = 3 (true value). But at this point I am uncertain of its momentum.
2) To know the momentum I measure the momentum and I get p = 5 (true value) but now the position is no longer x = 3. Momentum measurement has disturbed the system and thus the system is no longer in x = 3 state. Now I am uncertain of its position.
3) Now I again measure the position. But there is a probablity that I dont get x = 3. I might get x = 192. And now again I am uncertain of its momentum. I cant say its momentm is p = 5. Position measurement has disturbed the system is no longer in p = 5 state.

A piece of advice: Dont start with infinite dimensional hilbert spaces. The uncertainity principle, there, will surely confuse you. Start with two dimensional hilbert space (spin for instance). See how non-commuting operators introduce uncertainity. Then advance to cauchy-schwarz inequality. See how, in general, you can arrive at uncertainity formula. Then apply this concept to infinite dimensional hilbert spaces.

You can start off with J.J. Sakurai first chapter (provided you know the postulates of quantum mechanics and linear algebra). He has show uncertainity principle using stern-gerlach apparatus.

Last edited: May 29, 2013
6. May 30, 2013

### phinds

I repeat Simon's request

Please provide a reference to the experiment that violates the uncertainty principle.

7. May 30, 2013

### lee.spi

there is one of the experiment that violate uncertainty principle:arXiv:1201.1833

8. May 30, 2013

### lee.spi

there is one of the experiment that violate uncertainty principle:arXiv:1201.1833

9. May 30, 2013

### lee.spi

there is one of the experiment that violate uncertainty principle:arXiv:1201.1833,i have not trouble with any art of the uncertainty principle

10. May 30, 2013

### Fightfish

I browsed through the paper, and don't see how it violates the uncertainty principle.
All they seemed to be doing to experimentally demonstrating a general uncertainty for the noise (error) and disturbance on the system.
So, this showed that Heisenberg's original idea involving disturbance in his thought experiment was incorrect. It does not however, violate the uncertainty principle as we know it now (formulated in terms of standard deviations).

11. May 30, 2013

### vanhees71

The uncertainty relation cannot be violated as long as quantum theory is not disproven. However, the interpretation still given in many textbooks after some 70 years of the correction of Heisenberg's very first interpretation by Bohr, is not correct.

The Heisenberg-Robertson uncertainty relation reads
$$\Delta A \Delta B \geq |\langle [\hat{A},\hat{B}] \rangle|.$$
Here $A$ and $B$ are the observables under consideration and $\hat{A}$ and $\hat{B}$ are the self-adjoint operators representing these observables in the quantum-theoretical formalism. The expectation value has to be taken with respect to the (pure or mixed) state the quantum system is prepared in.

Thus the only correct interpretation is that for any possible preparation of the state, there is this limit of the product of the standard deviations of the observables given by this inequality, and that's it.

The very first interpretation by Heisenberg was wrong! He thought the uncertainty relation tells us that we are not able to jointly measure two incompatible observables with arbitrary precision. This is plain wrong and was corrected by Bohr shortly afterwards. For some reason this wrong interpretation stuck however even in textbooks.

There are other relations, dealing with the disturbance of the outcome of measurements of observable $B$ through a previous measurement of observable $B$. These relations are different from the Heisenberg-Robertson uncertainty relation given above, and this was demonstrated experimentally in the cited paper arXiv:1201.1833.

Some time ago, I tried to discuss this issue in this forum, using another example from the literature, which I think is easier to understand than the example given in the quoted paper, because it deals with the spin of neutrons in a Stern-Gerlach-experiment like setup. Nobody has taken up the topic, but here's my posting. Maybe it is helpful to get a better idea about the fundamental difference between the Heisenberg-Robertson uncertainty relation and the noise-disturbance relations:

12. May 30, 2013

### lee.spi

thanks for your explain in detail and advice

13. May 30, 2013

### lee.spi

as i know,this is not just a thought experiment, his experiment have been achieved

14. May 30, 2013

### lee.spi

thanks for your explain in detail,and i think this will be helpful to me to get a better understand the uncertainty principle