# Is uncertaninty principle unbeatable?

1. Aug 17, 2004

### eljose79

let suppose we have two observables A and B so its conmutator [A,B]=f(p,q)
then let,s define a new observable C so [A,BC]=0 so we could measure A and BC with C a function of (q,p)the statement above is equivalent to (A,BC)=0 with () the Poisson Bracket then let,s put A=q and B=p then we must have [x,pC]=0 so we now can meassure x and pc with c is a function g(q,p) then c=g(q,p) inverting we have g^-1(c,q)=p so we can meassure p.

2. Aug 17, 2004

### zefram_c

It's as unbeatable as quantum mechanics. Try actually implementing it: it won't work. Presumably you can get [x, pC] = 0, but most likely you will not be able to carry out the inversion.

3. Aug 17, 2004

### eljose79

why not? just try numerical analisis....

4. Aug 17, 2004

### zefram_c

I mean the inversion will be mathematically impossible. As a silly example, set C=0 always. This gives [x,Cp]=0 but there's no way you can use the measured Cp to recover p.

Edit: In addition, you can show x does not commute with C either if C is not zero and [x, Cp]=0

Last edited: Aug 17, 2004
5. Aug 17, 2004

### eljose79

Then we could try using two observables A(q,p) and B(q,p) and input c so [A,BC]=0 with tha we could know the values of A(q,p) and B(q,p)C(q,p)=D(q,p) now we have
A(q,p)=f(q,p) or f^-1(A,p)=q and if D(q,p)=g(q,p) inverting g^-1(D,q)=p and obtan p and q from this equations.

6. Aug 17, 2004

### zefram_c

In other words, you're discarding B and C completely, and you're only measuring A and D=BC. You run into the same inversion problems. Try coming up with something explicit and see how it breaks down for yourself.

7. Aug 19, 2004

### eljose79

But if you can meassure the postion x if we meassure to close position,let,s call x(t+h) and x(t) taking the diference we get x(t+h)-x(t)=hv(t) and velocity v(t) is related to momentum.

8. Aug 19, 2004

### zefram_c

You're working with a very classical picture of momentum. Granted, you can perform both position measurements, but that doesn't tell you anything about the momentum after the second measurement. Knowing the average momentum over a given time interval after the fact does not contradict UP. The whole point is that the momentum was changed by each measurement of the position. If you hadn't made your first measurement of position at t, the outcome of the measurement at t+h would have been different.

9. Aug 19, 2004

### Tau_Muon_PlanetEater

Uncertainty Principle is incorrect.

It relies on EM radiation as its probe. It is merely the best we can do with current technology.

10. Aug 19, 2004

### Tom Mattson

Staff Emeritus
This is wrong. The uncertainty principle is a derivable consequence of QM, and it does not represent a technological limit of experimental resolution.

11. Aug 20, 2004

### humanino

12. Aug 20, 2004

### eljose79

Then how can explain the EPR paradox? you have that [x2-x1,p1+p2]=0 so you can meassure x2-x1 and p1+p2 (hte diference betwwen the two particles and the momentum of center of mass) then another observer could meassure [x2,p1] with these we could obtain x1 and p2 for each time.

Another question is,let,s suppose we meassure two momentum in t and t+h with h a very small quantity of time (let,s suppose we can construct a quartz clock that can meassure intervals of 10^-20 seconds then we would have
[p(t+h)-p(t)]h=m[x(t+2h)-2x(t+h)+x(t) taking h infinitesimal (for example Planck time lp/c,wich is suppose to be the smallest interval of time we can meassure,then the differential equations become difference equation that can be solved to obtian x(t) for each tmthe proble is that we don,t have the technology to meassure so small intervals of time.

another question [x,pC(q,p)]=0 does not imply c=0 but C(q,p)=p^-1f(x) being f(x) an arbitrary function of the postion x,then we can meassure x and c and from this we could tak ethe inversion to obtain p as p=f(x)C^-1(q,p) or p=xc.

13. Aug 20, 2004

### DrChinese

Of course, if you accept the HUP then there is no paradox.

Einstein, Podolsky and Rosen asked this same question 69 years ago. An experiment was run (Aspect et al) and the limits of the HUP were seen, just as predicted by QM. Clearly, tests on spin components of entangled particles doesn't yield any "extra" information. Why would you think that a test of position and momentum would yield any different results?

In other words, there is plenty of evidence to counter the argument that the HUP is a result of technological limitations. And you are familiar enough with QM to be aware how its limits are calculated. And you are aware of the arguments that have already been considered historically. And I presume you are aware of the results of that experiment.

After all, your hypothetical test of position and momentum on entangled particles - to try and outsmart the uncertainty relations - falls victim to this major problem. You tacitly make 2 assumptions: locality and reality. Locality=the results of an experiment at one place do not affects the results at another. Reality=momentum and position have well-defined values when not being observed. Tests of EPR show that at least one of these assumptions are false.

Last edited: Aug 20, 2004
14. Aug 20, 2004

### eljose79

To Dr. Chinese:= then Do you think the HuP is only a result of teh limits of our technology?..how could you prove it.
Another question when a particle is not observed? does have a momentum and position?,wehat would happen if the EPr where made with 2 particles separated a distance for example 1 light-year,then the information would not reach from one particle to other in less than a year,then how it is possible that the results of an experiment affect to the other?.

15. Aug 20, 2004

### ZapperZ

Staff Emeritus
You should reread what he said, which was...

He is saying that the argument that says HUP is the result of technological limitations is not valid since there are plenty (and I mean PLENTY) of evidence to counter that.

I think it is imperative that before you start making statement if HUP can be violated, etc, that you first learn the fundamentals of QM. Having read this thread, it appears as if you think HUP appears out of nowhere and simply and ad hoc addition to QM. Nothing could be further than that. HUP is a logical CONSEQUENCE of the formulation of QM. It appears because x and p, for example, are fourier pairs of each other. So you simply cannot look at the tail end of an animal and think you know what the whole animal looks like.

Zz.

16. Aug 20, 2004

### DrChinese

1. Thanks, ZapperZ. I thought I was clear... you made it more so.

2. ElJose79: This test has ALREADY been performed (a kilometer instead of a light year) and the results are exactly the OPPOSITE of what you suppose. Locality IS violated - the results of one observation clearly affect the observed results at the other location (if you assume reality - that there are clearly defined values for the observables independent of observation). I am sorry if that violates your view of common sense, but that's the facts.

It would be helpful to this discussion to know whether you accept the results of already run experiments or you deny them.

17. Aug 20, 2004

### zefram_c

No dice. One can easily show that x and C don't commute from the following relation:
[x, pC] = [x,p]C + p[x,C] = ihC + p[x,C]
So if one assumes [x, pC]=0, either C=0 or [x,C] don't commute.

18. Aug 20, 2004

Staff Emeritus
What Aspect says at your link is that the Innsbruck experiement is evidence for "quantum inseparibility", not FTL communication. What is the difference from what you say? Quantum mechanics does not assume reality in your sense, "that there are clearly defined values for the observables independent of observation"; that is precisely the issue! The original EPR paper, and Bell's inequality, were efforts to save reality within quantum mechanics. But the Aspect and subsequent experiments showed that you have to choose between relativity and realism. and quantum mechanics is set up to prefer relativity.

19. Aug 20, 2004

### eljose79

-To Dr. Chinese:=Uum that,s right but a kilometer is not far enoguh,light takes 3,3x10^-10 seconds to run the kilometer ( i am not denying the experiment but saying perhaps is not accurate enough), so perhaps the information of a particle can jump to other and this spoils the meassure.
with respect to "reality" (particle has an assigned position and momentum when is not observed) i don,t know what to say,how could we know it if we can not meassure,i prefer Bohmian mechanics is more elegant than usual one it,s a pity is not accepted.

-to Zefram:=sorry it was my fault but with you argument you are agreeing me that you can have a C non zero so [x,pC]=0 so we could meassure x and pC and from this obtain the momentum.

20. Aug 20, 2004

### DrChinese

The Innsbruck team took the time to traverse the separation distance into account (do you want the link?). There was plenty of accuracy, to be sure, since that was the entire point of the experiment. As to whether the "information" "jumps" to the other one... well that is the issue, isn't it? It does! However, no one realizes that until much later when the results are tallied so there is no useful FTL communication going on.

Bohmian mechanics is explicitly nonlocal. If it is more elegant to you, have at it! There is still no getting around the HUP in it though.

21. Aug 20, 2004

### Chronos

For reasons not clear [to me anyhow], there seems to be this persistent, 'urban legend' that HUP is an empircal derivation [limits of technology, etc.]. This, of course, is patently false. HUP is a mathematical derivation. No experiments were necessary, no data was required, just a pencil, paper and a little mathematical genius. One oft used explanation is that a function and its Fourier transform cannot both be compactly supported. This, however, is not very enlightening if you don't already know your function from a Fourier transform. Try here for a more complete explanation:
http://en.wikipedia.org/wiki/Uncertainty_principle

22. Aug 20, 2004

Staff Emeritus
The information did not "jump the gap." The constraint was already imposed when the entangled state was created that if one particle goes this way the other goes that way, and vice versa. Before measurement the entangled state has both particles are in superpositions of this and that, with the constraint in posse. When either particle is measured the state collapses with both particles satisfying the constraint; one goes to this and the other to that. The fact that the state is spacelike extended is what one means by quantum inseparibility. It does not violate relativity because an unmeasured state is not physical. The quantum concept of superposition removes the realist idea that the far particle was switched around somehow.

Last edited: Aug 20, 2004
23. Aug 21, 2004

### DrChinese

That description is fine. Clearly, the ultimate issue is that something gives. In your description, you are clearly saying that there were not 2 particles each with well defined quantum states prior to the observation. That would violate one of Bell's 2 key assumptions.

But if you are a realist, you might believe there were such values. There is nothing about the experiment that rules this out, but you would be saying that effects propagate FTL. That would violate the other of Bell's 2 key assumptions.

Of course, one of these assumptions IS wrong. That is what the experiment says. I am not arguing one of these positions over the other. Clearly, there are plenty of folks who come down on one side or the other. And the debate over the semantics of this continues. Articles even debate what Bell himself thought on the matter. But the mathematics of it is pretty clear.

24. Aug 22, 2004

### zefram_c

Before I try to figure out how this breaks down (as it has to, if QM is to stand), I will need more information, more specifically on what you mean by 'pC'. Is C another operator, and you measure it, then you measure p? That doesn't work, since measuring C or p invalidates the measurement of x. Is pC a single observable? (Can you show that it is in fact a physical observable, ie it is something that actually corresponds to something we can measure?) Then we should denote that as D (a new observable) and go from there. Also we should try to study a different system, since measuring x collapses the wave function to a highly localized function. That doesn't keep its shape for long under time evolution, and once we allow that, the mathematics becomes harder. We should go to a cleaner system to study - how does the (classical) spin-1/2 system sound?

25. Aug 25, 2004

### cronxeh

I've noticed some of you using words 'spin' and 'momentum/velocity' in same sentence with HUP, as well as locality thrown in there.

I dont know how you guys learned your QM, or how your professors learned it or how the book writers learned it. I guess its a common legacy of misconception.

But, HUP relates to measurement problem (where EM is used). Spin relates to a completely different measurement problem (Stern-Gerlach) where magnetic field is used. And issue of locality/non-locality is spanned from superposition of states.

Now I dont see how all things being equal QM prevents you from having both information of momentum and position at the same time. I dont see any theory or experimental proof that its impossible. There is HUP that states you cant measure both. But that is like saying you cant expect the driver of a car to be nice to you after you throw a baseball at his windshield, traveling 60 mph.