# A crank's idea about Uncertainty Principle

1. Nov 5, 2007

### neelakash

Uncertainty principle is a quite revolutionary concept and go hand in hand with the so-called probabilistic picture of the quantum particle.

What is worrying me for last a few days if there has been any attempt---theoretically or, experimentally to check the position and momentum uncertainty of a quantum state by two different experimenters employed for each uncertainty at the same time.

I absolutely agree that uncertainty principle holds when one tries to measure the position and momentum of a (generalized) state.But,what if one experiment is done to "see" its position and another to see its "momentum"?These two experiments need to be completely independent of each other and yet it needs to consider the same quantum state.They might correlate their data from time instants recorded...

The conservation of information occurs obviously.The experiment who "see" the momentum would lose the information regarding momentum.The other experiment would recover this "lost momentum" while surrendering the information regarding position to the first experiment.

The correlated data may be interpreted as the response of the (generalized) state over time.

What follows is that if this can be done,it will make a revolutionary change in the present idea.A new mechanics will be needed.

Please note that my intention is not to claim that (x,p) pair can be measured accurately and...But somehow it looks to me "we are forced" to take the wave picture of the (generalized) states as we cannot see them really for the difference in our dimension.I am interested in the more real picture,if possible.For example,does an electron "see" another as we "see" them?

When we "see" we make a relation between a microscopic(possibly,picoscopic or femtoscopic) state and macroscopic observer through a macroscopic apparatus.But suppose an elementary particle interacting with another.Somehow,they come to know about each other.In that case,it is believed that certain virtual particles mediate their interaction.

In this case,the striking difference is that the state to be observed,the instrument of "observation" and the "observer" are all so-called microscopic.
So,should we not expect an altogether different "observation"?

There are suggestions from my classmates that the two simultaneous experiments are going to kill whatever observable to the observers...But that does not convince me...Rather what I believe that such an experiment(if possible) will reveal a (generalized) state (with its response to the parameters of the experiments)...

One of my friends have gave a very good blow to me.She says since QM theories give very good result in experiments it cannot be wrong...I also do not say it is wrong...but the thing is that if we can make our understanding a bit better...

Truly speaking,measurement process in QM cast a strange awe on us.We observe what we intend to observe.If you try to "focus light" on an electron,you will "see" it as a particle...But does that mean electron is necessarily a particle?The picture in QM is not like that.

I am thinking of designing such an experiment though I do not know a great deal about it...If you think I should continue please tell me.And can anyone give me some link to Uncertainty Principle Experiments?How delta x and delta p are measured in reality (not by Fourier Transform property or,gamma ray microscope---they are all in books).

Regards,
neelakash.

2. Nov 5, 2007

### martix

Now I probably didn't get all of this you are writing. But from what I did manage to get the first phenomena is called quantum entanglement and is the hope for all the future quantum super computers, teleportation and stuff like that. Like when we have a system of some physically observable properties and we know say that position and momentums are in correlation. Then we measure position on one particle and momentum on the other and that way you get the whole picture.
As for the other thing you are suggesting - its intriguing. Lets wait for some geek to come along. I mean how can they interact properly if they can't read all the data needed for it. And if microscopic interacting particles can, macroscopically why can't we?

3. Nov 5, 2007

### f95toli

What you are describing is called state tomography and can be used to e.g. "measure" the Wigner function. However, there is still no way to measure both p and x (or whatver conjugate variables you are interested in) at the same time.

Two experiments are -by definition- not independent if they are both trying to measure the same system at the same time; it is still a single measurement. The uncertaintly principle always holds no matter how you try to extract the information.
In tomography the system is measured many times which makes it possible to -quite litteraly- build up a picture of the state of the system, but that of course also assumes that the system can be re-initialized to the same sate over and over again.

If you want more information just google "State tomography" or "quantum tomography".

4. Nov 5, 2007

### ueit

Of course there is a way. By detecting a particle far away from a point source you can measure both momentum and position with any accuracy you like. HUP is not about what you can measure, it is about what you can predict.

5. Nov 5, 2007

### neelakash

f95toli seems to have a better understanding of my question.

But your observables are different even if the eigenfunction is the same.

6. Nov 5, 2007

### Bork

As soon as one observer measures the x position of the particle (or technically, restricts the wavefunction so most of it is contained in a small interval), that sets the value for the other person's measurement, so the measurements can never be independent, even if in your lab frame they're done simultaneously.

7. Nov 5, 2007

### f95toli

No, it is also about what you can measure (and there is no real difference between between predicting and measuring, in the latter case you are simply trying to indirectly infer properties of a system via some macrosopic variable).
This is well known in optics. E.g. light in a coherent state has, by definition, the minimum uncertainty in amplitude and phase set by the uncertainty principle.
More generally, the so called standard quantum limit (SQL) refers to the refers to the minimum level of quantum noise in a system. In optics (and some other systems) it is possible to go beyond SQL using squeezed light to reduce the uncertainty in one quadrature; but you always "pay" for this by an increased uncertainty in the other quadrature which means that UC still holds.

8. Nov 6, 2007

### ueit

There is a clear difference between being able to "measure" if a bomb explodes when dropped and predicting if a bomb would explode in case it is dropped.

As I said before, you can measure simultaneously both momentum and position of the same particle with any accuracy you want by simply detecting the particle at an arbitrary large distance from the source. The uncertainty in momentum can be lowered by increasing the distance of travel and/or by letting the source emit for a shorter time and the uncertainty in position depends only on the detector resolution. Of course, once you measure the particle in this way you cannot say much about its future, and this is what HUP is about.

9. Nov 6, 2007

### Galileo

I`m curious. Would you say, then, that it's also possible to simultaneously measure the x- and y-component of an electron's spin? OR do you consider that a fundamentally different case?

10. Nov 7, 2007

### ueit

You can, by measuring first along x axis and then along y. That gives you the spin components the particle had between the two measurements.

11. Nov 8, 2007

### Galileo

But not only are those two measurements (not a single one where you determine both Sx and Sy), you also didn't actually measure the x-component the second time.

Saying that you can measure, or know, the values of both observables (either Sx or Sy, or position and momentum or any pair of noncommuting observables) is a violation of Bohr's principle of complementarity. You mean to say the particle really HAD a position and momentum (or a spin in the x and y directions), but how would you reconcile that with the violation of Bell inequalities?

12. Nov 8, 2007

### dextercioby

Actually, the way the whole mathematical formalism is built, it doesn't follow from the uncertainty relations for x and p_{x} that both p_{x} and x cannot be measured simultaneously with arbitrary precision.

13. Nov 8, 2007

### OOO

The mainstream understanding of quantum mechanical measurement is that after you measure position with arbitrary precision, the particle is in a position eigenstate after the measurement. But if it's in a position eigenstate then the probability for measuring momentum is equal for all possible momenta (i.e. momentum is infinitely uncertain). It all boils down to the formula

$$2\pi \delta(x) = \int e^{ikx} dk$$

14. Nov 8, 2007

### ueit

I didn't claim to determine both variables in a single measurement. What I claim is that it is possible to measure their value at a given time. Two measurements are required and the result only applies for the time between them.

That's not necessary because of angular momentum conservation.

I am not a believer in the philosophical implications of Copenhagen interpretation.

Yes. To be more precise I think that the particle always has well-defined properties, described by some hidden variables. It is possible for example that what we call x-spin or y-spin is not a property of the particle but a result of the interaction between the particle and the instrument.

If every particle has well defined properties and the time evolution is deterministic, it follows that the universe as a whole is superdeterministic. Bell's theorem does not apply to such an universe because one of its premises (statistical independence between the entangled particles' spin at the source and detector orientation) is rejected.

15. Nov 8, 2007

### ueit

OK. But if you measure the position again with arbitrary precision you determine the momentum the particle had between the two position measurements with arbitrary precision, right?

16. Nov 8, 2007

### OOO

I guess no. This is not what QM calls a momentum. Momentum is rather associated with the wavenumber through $p=\hbar k$. So how do you determine $k=2\pi/\lambda$ from two position measurements ?

17. Nov 8, 2007

### f95toli

This has nothing to do with philosophy. The UP is already a real "technical problem" in metrology since it might prevent us from doing measurments we would like to do in the future (such as detection of gravitational waves, look e.b. at the LIGO website and you will find quite a few papers on squeezing).
In so-called "quantum enhanced" metrology effects like squeezing, entanglement etc is used to improve the measurement precision. Of course we can never "beat" the UP, but we can go beyond the standard quantum limit (SQL basically means that the uncertainties are "divided" equally between the two variables) . There are also a number of other "quantum tricks" that can be used to enhance our measurement capabilities, such as quantum non-demolition measurements etc.
So far most of these methods have only been used in quantum optics, but they are now being gradually introduced in experiments on e.g. solid state systems as well.

I should perhaps point out that the SQL was reached in optics many years ago, and squeezing is often demonstrated by simply showing that the noise in one quadrature of the system is lower than the SQL.

18. Nov 8, 2007

### Galileo

Well, that's one way to look at it. But I hope you agree that a superdeterministic local and real universe is pretty bizarre given the violation of Bell's inequalities. It means that the choice of detector orientations at both sites are correlated, no matter by what means they are chosen, it was simply predetermined from the beginning of time that every time we perform a Bell test, the detectors are chosen as to violate the Bell inequality. But we don't see such highly correlated results between two objects for any classical system, why would this be any different under your assumptions?

19. Nov 9, 2007

### ueit

That is the de Broglie equation, relating the particle's momentum to its wavelength. It's not the definition of momentum.

20. Nov 9, 2007

### ueit

I fully agree with what you are saying. HUP limits our ability to make predictions about the particle's behavior. However, HUP doesn't stop us to measure the complementary variables to any accuracy in the time interval between measurements. I cannot measure both momentum and position of a particle without interacting with it and therefore change its future in a more or less unpredictable way. But I can prepare a particle with an accurately known momentum and then measure its position by detecting it on a screen. This doesn't remove the technological limitations of HUP because after the second measurement the particle's momentum changes.

I was speaking about philosophical implications because, in my understanding, Copenhagen interpretation claims that a particle cannot HAVE well defined momentum and position at the same time because position and momentum correspond to different measurement setups. I reject this interpretation as it is not required by HUP or any experiment to date.