A crank's idea about Uncertainty Principle

[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.

 

[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. Let's 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?

 

[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".

 

[ueit]

However, there is still no way to measure both p and x (or whatver conjugate variables you are interested in) at the same time.

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.

 

[neelakash]

f95toli seems to have a better understanding of my question.

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.

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

 

[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.

 

[f95toli]

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.

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.

 

[ueit]

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).

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.

 

[Galileo]

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.

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?

 

[ueit]

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?

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.

 

[Galileo]

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.

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?

 

[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.

 

[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

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

 

[ueit]

But not only are those two measurements (not a single one where you determine both Sx and Sy)

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.

you also didn't actually measure the x-component the second time.

That's not necessary because of angular momentum conservation.

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.

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

You mean to say the particle really HAD a position and momentum (or a spin in the x and y directions)

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.

but how would you reconcile that with the violation of Bell inequalities?

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.

 

[ueit]

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

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

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?

 

[OOO]

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?

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 ?

 

[f95toli]

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

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.

 

[Galileo]

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.

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?

 

[ueit]

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 ?

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

 

[ueit]

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.

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.

 

[OOO]

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

Yes, of course. But the de Broglie relation does have to hold, no matter if it's a definition or not. I can't see that the momentum you get with your two subsequent position measurements are in any way related to the wavelength.

 

[RandallB]

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?

NO

That is no different that the testing you do at your first test. You are allowed to “know” where your particle was started (point A). When you wish to determine both location and momentum with a test at B. QM calls for and experiments have demonstrated the uncertainty relationship between “x” & “p” at test B even though one of the two is well known at start A.
Adding a new test at C changes nothing.
You can know “x” at both B & C but “p” at C will depend on exact knowledge of two earlier “p” vectors. The unknown momentum vector absorbed by the particle at test B from the test system, along with the uncertain “p” in the particle at B will define exactly how the particle curves through or bounces off the measuring device in area B.
Without knowing both these “p” vectors with precision you cannot define the exact path to the observed “x” location measured at test C, you can only make assumptions. Therefore your calculation of “p” at C will suffer the same uncertainty as already defined by QM.

So NO your procedure does not give well defined momentum and position for a particle at the same time.

 

[ueit]

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.

On the contrary, I think it is the only universe that makes sense (at least to me). It doesn't contradict well established physics (like non-local theories do), doesn't "solve" the problem by unfalsifiable philosophy (MWI + anthropic principle) and it doesn't claim that the problem does not exist (non-realism).

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.

No, this is not what I'm saying. It is the spin of the entangled particles that is causaly related to the detectors' orientation. I maintain that the emission of the entangled particles could be influenced by the surrounding fields produced by the detectors (and any matter around). A detector with a different position produces a different EM and gravitational field. The source can "adjust" the spin of the particles to this field. Assuming a deterministic universe the source can also extrapolate the future detector orientation from the past information, explaining in a local realistic way the delayed choice experiments.

 

[RandallB]

The predetermined description by Galileo of what you are saying is much better than your own.

Assuming a deterministic universe the source can also extrapolate the future detector orientation from the past information, explaining in a local realistic way the delayed choice experiments.

Your changing your use of “local” to “local realistic” doesn’t make it so, and there is nothing to support such phrasing. As said before deterministic BM may design a unrealistic version of local. But if you wish to claim it can “extrapolate the future detector orientation from the past information” you need to at least provide a hypothetical mechanism that “past information” is retained or memorized to be useful. It needs to predetermine how a pair of photons are created and how later settings at two space-like separated detectors are made from the past history in a way that coordinates the observations. Only the unrealistic assumption that some Weird Magic 'action at a distance' can make the complex calculations and manipulation of detectors and photons to effect the statistical correlations of many photon pairs, without reveling a predictable link between a single pair.

If you had a realistic description of how that could happen, (even if it could not be tested experimentally) you should add it to your posts in: https://www.physicsforums.com/showthread.php?t=181904"

A deterministic BM is not the same as the determinate variable considered by Einstein, EPR, or Bell. Determinism and determinate variables are not the same thing and there is no way Determinism can be considered local realistic.

 

[ueit]

Yes, of course. But the de Broglie relation does have to hold, no matter if it's a definition or not. I can't see that the momentum you get with your two subsequent position measurements are in any way related to the wavelength.

How do you propose to measure the velocity of a particle if not by measuring its position at two times? And why do you claim that such a measurement is not a valid one?

Anyway, I can give you another way of finding out momentum and position with any accuracy required. Prepare a particle of known momentum (by any means you like) and detect the particle at a screen.

 

[ueit]

NO

That is no different that the testing you do at your first test. You are allowed to “know” where your particle was started (point A). When you wish to determine both location and momentum with a test at B. QM calls for and experiments have demonstrated the uncertainty relationship between “x” & “p” at test B even though one of the two is well known at start A.
Adding a new test at C changes nothing.
You can know “x” at both B & C but “p” at C will depend on exact knowledge of two earlier “p” vectors. The unknown momentum vector absorbed by the particle at test B from the test system, along with the uncertain “p” in the particle at B will define exactly how the particle curves through or bounces off the measuring device in area B.
Without knowing both these “p” vectors with precision you cannot define the exact path to the observed “x” location measured at test C, you can only make assumptions. Therefore your calculation of “p” at C will suffer the same uncertainty as already defined by QM.

So NO your procedure does not give well defined momentum and position for a particle at the same time.

I didn't say anything about a third measurement. I perform two position measurements at A and B, the momentum being calculated from them afterwards. This momentum is the one the particle had only between A and B when no interaction could change its value. It is not the momentum the particle had before A or after B.

 

[ueit]

The predetermined description by Galileo of what you are saying is much better than your own.

It may be better but it's not what I have in mind.

Your changing your use of “local” to “local realistic” doesn’t make it so, and there is nothing to support such phrasing. As said before deterministic BM may design a unrealistic version of local. But if you wish to claim it can “extrapolate the future detector orientation from the past information” you need to at least provide a hypothetical mechanism that “past information” is retained or memorized to be useful.

You shift the burden of proof here. I only need to point out that such a mechanism could exist in order to keep the hypothesis of local-realism alive.

Nevertheless, you can look at how the non-local force in Newtonian gravity was replaced by a local mechanism in GR. The past information is retained in the space curvature. The massive object reacts to this curvature.

We can imagine that the position/momenta of every quark/electron in the detector is transferred at the speed of light via some type of EM curvature. The source reacts to this curvature by creating a pair of particles with suitable spin.

 

[RandallB]

I didn't say anything about a third measurement. I perform two position measurements at A and B, the momentum being calculated from them afterwards. This momentum is the one the particle had only between A and B when no interaction could change its value. It is not the momentum the particle had before A or after B.

Not asking you to make a third measurement. I expect you to define the assumptions you make in order to define the exact ‘p’ from only knowing the location information at A & B. You cannot do it without knowing the complete and exact path A -> B. You cannot know that without knowing both unmeasured vectors ‘p’ for the particle before the testing at A, and for one added to the particle from the test at A. Just as you cannot arbitrarily assume a 100% inelastic interaction from the test to assume a perfect straight line from A to B. The point is you only have two measurements, no matter how precise the other three pieces needed are uncertainties. And if you did a fair job of considering those uncertainties, you will see they same level of uncertainty, already defined in defined in the QM interpretation. Even Bohm admitted BM was a non-local interpretation of QM. And BM redefined with “histories” only exchanges the non-local uncertainty with an unexplained unrealistic retention of histories.

You shift the burden of proof here. I only need to point out that such a mechanism could exist in order to keep the hypothesis of local-realism alive.

Nevertheless, you can look at how the non-local force in Newtonian gravity was replaced by a local mechanism in GR. The past information is retained in the space curvature. The massive object reacts to this curvature.

No I don’t; The fact that a mechanism exists is know because it happens. The question is how does one rationally describe and understand a mechanism to explain it all. QM successfully does this in a theory it clearly identifies as Non-Local. You only declare that a mechanism must exist, which is already known is true, and create one in BM that you simply insist is “local & realistic” without providing a realist description of just how local-realism is maintained and demonstrated. And the “burden of proof” for that lies squarely on BM and you, nowhere else. If you want to act like a scientist you cannot duck the obligation. Otherwise, you are just talking a philosophy and IMO sophist at that.

As to General Relativity I’m a Local Realist and I don’t accept GR as local either until the issue of a dependent vs. independent background for it is acceptably settled as well. If you don’t know about that you need to do some research. Use Smolin, Perimeter Institute, background independence


As for the OP.

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.

neelakash
The statistical “correlated data” you a describing here is just the kind of thing that helped define QM. It is OK to re-plow old ground (it can be a learn experience) but QM is the “new mechanics” that accounted for those kind of measurements. Nothing new in that.