Talk:Uncertainty principle/Archive 1

How is momentum even measurable.
I've always understood it needed to be calculated from two distances at two times to get speed and a measurement of mass, in order to fulfill the equation momentum=mass*speed --Hackwrench
 * You can simply measure the force exerted within a certain time period. See the impulse section of momentum.     &mdash; Cortonin | Talk 18:46, 20 Apr 2005 (UTC)

That's even worse, requiring three position measurements to establish acceleration.
 * Get a friend, put him on roller skates, close your eyes, and throw a softball at him. You can examine the momentum imparted by the softball without concern for where it hit him.  All you need to know is your friend's mass and how fast he was going after the ball hit him.  (Yes, the position must be precise enough to be in your measurement device, but this is pretty huge compared to the scale of the uncertainty principle.)  (And please do not hurt your friends.)     &mdash; Cortonin | Talk 22:08, 21 Apr 2005 (UTC)

C'mon now! If you can measure the mass of your friend and his speed after the ball hits then you can directly apply that process to the baseball. According to your method you would have to send the friend into another friend on roller skates, and measure HIS momentum by sending him into YET ANOTHER friend on roller skates then measure HIS momentum by... you get the picture. I thought you were smarter than that. -Thomas


 * Yes, you can measure the momentum of a baseball as well. The uncertainty principle does not say that either mass or position are unmeasureable.  In fact, both are measureable.  It only says that they cannot both be measured with extremely high precision at the same time, and that if one of momentum or position is measured with extremely high precision, then the other must become uncertain.     &mdash; Cortonin | Talk 03:30, 23 May 2005 (UTC)

Actually, neither are measureable, because "nothing" (as in NO THING) can have a real existence with a defined position or a defined momentum, no matter the uncertanty of the other. This comes from examining the DeBroglie wavelength of your "thing." A "thing" with an absolutely defined momentum would be a pure wave function - a sine wave, to be exact - extending over the entire universe and presumably existing for all time. In essence, depending how you looked at it, it would have either no position or every position. In order to confine this wave function to a particular position, you must add waves of other frequencies and amplitudes - essentially, change the momentum over time. The momentum starts becoming "smeared over time and space." To continue this until the position is absolutely defined you must add frequencies from 0 to infinity, until you have a "wave" with an infinitely small risetime and falltime and 0 duration containing every frequency from 0 to infinity - the definition a pure particle! As an aside, this would also take infinite energy. So a "thing" with an absolutely defined momentum would be a pure wave, and a "thing" with an absolutely defined position would be a pure particle. This is the reason for the wave-particle duality - neither a pure wave nor a pure particle can have any real existence. A side comment is the time problem - up to now in this discussion the "uncertanty principle" has been confined to two dimensions. That is simplistic. there are more dimensions - time is the most obvious. I am hoping that this will be picked up and expanded because I want to get back to Ebay and buy antiques not develop the rather sticky math behind these concepts. Suffice it to say that &#916;&#968;p &#916;&#968;q = (NOT &#8805;) hbar/2 where &#916; is the "smearing factor" not the statistical or empirical distrubution. the > would represent "experimental error" or changes introduced by the measuring process itself. --Thomas

P.S. Yes you can compute the DeBroglie wavelength of your baseball - it is on the order of 1X10-³³ meters - 1X10-¹³ is about the diameter of the nucules. That would allow you to compute the "uncertainty" of its classical "position" and "momentum" when it hits your "friend." It is very small, but even for a baseball, the uncertainty principal applies. --T.


 * The formulation in your above discussion is the reason why I said that either one can be measured with "extremely high precision", rather than "exactly". Is there some point you are trying to make relating to the article?  If so, what is it?     &mdash; Cortonin | Talk 14:54, 25 May 2005 (UTC)

Actually, yes. First of all, after having read hundreds of textbook explanations of HUP this is is one of the few worth reading. Most of course confine HUP to experimental error or changes in the system introduced by the measurement. Neither of these have any application to HUP. Both exist in any classical experiment. Unfortunately, these misconceptions were actually introduced by H. himself - it is my personal opinion that the concept was so far-reaching and astounding that even he could not truly accept his own work.

That being said, the article misses the opportunity to give some insight to the tremendous power and reach of HUP. In one simple formula it accounts for almost every facet of Quantum Mechanics. you might say that HUP is a consensation of the entire quantum mechanics. As I said, it explains the wave-particle duality by explaining why neither a wave nor a particle can have any real existence. It explains the nature of quantization. Almost every feature of QM comes back to HUP. I think that having made a better start than maybe, no definately, even H. you should build on that beginning and complete the picture. In particular more attention should be given to the DeBroglie hypothesis which set the groundwork, and the applications to "objects" (I hate to say "particle" because there is no such thing) with both finite and 0 rest mass, and the implications to each. Also, the explanation of why an object with a 0 rest mass must travel at light speed is contained in HUP. Some of these are obliquely alluded to but never developed. I hate to see such a good start not have a similar end. Most of the math is a little sticky but actually simple to understand and some could be included. -- Thomas

h/4&pi; OR h/2&pi;
Are you quite sure it's h/4&pi;? I've always seen the Uncertainty Principle written as &Delta;x &Delta;p &ge; h-bar, which is equal to h/2&pi;. -- Xaonon

I'm not sure, and neither are the experts: I just checked Encyclopedia Britannica, and they give both 2&pi; and 4&pi; in different articles. A case for Making fun of Britannica :-)
 * http://www.aip.org/history/heisenberg/p08a.htm 4&pi;
 * http://thorin.adnc.com/~topquark/quantum/heisenbergmain.html 2&pi;
 * http://zebu.uoregon.edu/~imamura/208/jan27/hup.html 2&pi;
 * http://webs.morningside.edu/slaven/Physics/uncertainty/uncertainty6.html 4&pi;
 * http://theory.uwinnipeg.ca/physics/quant/node7.html 4&pi;

I think we should leave it at 4&pi; -- at least we are on the safe side. --AxelBoldt

I think it's 4&pi;, though it's a while since I did an y QM. Doesn't it come from:
 * (&Delta;A)(&Delta;B) >= (1/2) |[A,B]|

and
 * [x^,p^] = h_bar / i ,

so
 * (&Delta;x^)(&Delta;p^) >= h_bar / 2.

-- DrBob

Ok, I will then happily make fun of Britannica now... --AxelBoldt

Your problem is that there is no mathematicval expression which "defines" the "uncertainty principle." Every "expert" had a different view of what it meant and a different expression - except Heisenberg, who gave none at all until 1928, and then he got it wrong! --Thomas

I think to remember that DrBob is right. The thing is that when you use it to estimate a value, sometimes you say


 * (&Delta;x^)(&Delta;p^) ~ h_bar

that is compatible with the previous--AN


 * There are several mathematical expressions which define the uncertainty principle? It is an inequality minimized by a Gaussian state. CHF 22:48, 11 December 2005 (UTC)

Sadly, the source is a bit old, but in Feynman's lectures, Feynman defines the measurements &Delta;x and &Delta;p to be the width of a gaussian distribution, which may be the source of the confusion. He does, however, state precisely:


 * &Delta;x&Delta;p &ge; h/2&pi;

It was originally published 1963-1965, so I guess it may have changed since then.

BlackGriffen

Ah, that must be it. They never clearly say what they mean with "uncertainty". Feynman takes thh "width", which is probably twice the standard deviation. We take the standard deviation itself, that's why we get half his number. So we are fine, but EB is still screwed :-) --AxelBoldt


 * Not quite Axel. Check the math. If &Delta;x' and &Delta;p' are the standard deviations, equal to half the width, then:


 * (2&Delta;x')(2&Delta;p') &ge; h/2&pi;
 * => &Delta;x'&Delta;p' &ge; h/8&pi;


 * That might be the source of the confusion if the competitors were:


 * &Delta;x&Delta;p &ge; h_bar
 * &Delta;x&Delta;p &ge; h_bar/4


 * I'm not familiar enough with statistical data analysis to say much more, however. Does the width of a gaussian divided by &radic;2 mean anything? --BlackGriffen


 * Yup, &radic;2 times standard deviation is the width of the range where 50% of the values will be. But it only works for a gaussian distribution, and there is no reason to assume that all observables are normally distributed, in fact they're most definitely not, so our use of the standard deviation is much cleaner. --AxelBoldt


 * So, the width over &radic;2 corresponds to the 50% of observations. Doesn't that mean that the formula:


 * &Delta;x&Delta;p &ge; h /2


 * is the incorrect one? the correct ones being:


 * &Delta;x&Delta;p &ge; h
 * &sigma;x&sigma;p &ge; h /4


 * lower case sigma is the standard character for a standard deviation, right?--BlackGriffen


 * In stats, they use sigma, but it seems that physisists use &Delta;x both for standard deviation and for the 50% range, and call both "uncertainty". If we used &Delta;x for the 50% range and &sigma;x for the standard deviation, then the correct formulas would be


 * &Delta;x&Delta;p &ge; h
 * &sigma;x&sigma;p &ge; h /2


 * But the first of those is really pointless since it makes the unjustified assumption that the variables are normally distributed. --AxelBoldt

If there are two differing definitions of &Delta;x and &Delta;p we should note this, and that the uncertainity principle takes different forms depending on what definition is chosen. -- SJK --- h-bar is h/2pi. Standard deviation of uncertainty principle is 1/2(h-bar). In other words either written as h-bar/2 or 1/2 x h/2pi = h/4pi.--Voyajer 03:06, 22 December 2005 (UTC)

I removed the reference to the energy--time uncertainty principle
, since it is not really correct. While energy surely is an operator in quantum mechanics, time is not, it's a parameter. One derives uncertainty inequalities from commutators of operators (i.e. if the commutator between two operators is not zero then there is an uncertainty relationship between the standard deviations). Since time is not an operator, it commutes with everything. I would suggest that the primary author of this article read the relvent sections of L. Ballentine's _Quantum_Mechanics_A_Modern_Development_ for a very clear discussion of the HUP.

While I'm ranting, I would suggest dropping the stuff at the end about Einstein. First off, he never denied the empirical validity of the HUP, and second even if he did his opinion on the the structure of QM is best left to another page. - It's actually messier than that. In standard non-relativistic QM, position is an operator and time isn't. If you extend this to relativistic QM, things get very messy, since there isn't even a quantity that stands up and says that "I'm the position operator".


 * Granted, I was thinking of the non-relativistic theory. Perhaps a paragraph about the relativisitic theory is in order? --matthew

--- I'll need to read Ballentine to see what he says, but this seems wrong. The variable t does not commute with the Hamiltonian operator, and mathematically, a wave function of finite time does not have a defined energy and the mathematical relationship between energy and time appears to be the same as momentum and position. -- Chenyu

The more I think about it, the more I think that Ballentine is wrong if he is asserting that there is no energy-time uncertainty relationship


 * That's not what I (or Ballentine) said. I merely recommended Ballentine's book as a very clear discussion of the HUP. --Matthew Nobes

or that time commutes with energy.


 * Huh? Time commutes with *EVERYTHING* in non-relativistic QM.  It's a parameter, there is no time operator. --Matthew

I've found these links on the web

http://www.aip.org/history/heisenberg/p08a.htm http://press.web.cern.ch/pdg/cpep/unc_vir.html

Granted, these are popular pages, but one presumes that AIP and CERN had someone proofread the pages. There is also the discussion in

http://math.ucr.edu/home/baez/uncertainty.html

which I think we should fold into the article -- Chenyu


 * Umm the link to Dr. Baez's page renforces what I said. Notice the derved relationship is between the total energy and the time derivative of some operator.  That's why I deleted the energy--time reference, because this type of UP requires more careful thought --Matthew

-- I don't think that time does commute with energy in NR QM. To calculate the time expectation value of wave function phi, you use the expression . To calculate the energy function you use an operation which has a time derivative in it. t and d/dt do not commute. It's formally exactly the same relationship as x and d/dx. Yes you can make a distinction between t the parameter and t the operator, but you can do exactly the same thing between x the operator and x the parameter.


 * Okay, I think you realize the error below, but just in case let me reiterate, there is no time operator in non relativistic QM. Such a thing *does*not*exist* in the theory.  Dr. Baez's webpage, which you cite, gives a plausible way of constructing something that might look like a time operator, but it won't be time itself.  And things get worse in the relativistic theory, since there is not good position operator either. Your expression above shows this as well, say you set


 *  = .


 * Now t is not a operator, so this is


 *  = t  = t (=1).


 * This is *not* the same thing as x= since there is no particular reason to assume that |phi> is a position eigenstate. -- Matthew

I really don't see any reason why t should be treated differently in NR QM than position. -- Chenyu


 * Becuase time is not an operator. X and P~d/dx are operators. -- Matthew

--

Never mind - I think I just saw it.

On second thought I don't see it --- Chenyu

--

AARRGRRHHHHH!!!!! My mind is frying.....

Anyway, I don't have any objection to the article as it stands. I misunderstood the original comment to say that there wasn't an Energy-Time relationship rather than to say that its derviation is tricky. Maybe we need another article just for the energy-time relationship. --- Chenyu

-- I suppose `one copy of THE system ... and another, identical one' is meant to refer to two real life systems with the same specs. But the formulation sounds much like ensembles of systems from conventional statistics, i.e. just thought experiments. I feel the statement would be stronger if the fact that the systems are real is stated more explicitely. That is, if I'm correct about that. RitaBijlsma

If you mean


 * Disturbance plays no part since the principle even applies if position is measured in one copy of the system and momentum is measured in another, identical one.

then I agree that the statement needs to be clarified. Check out the no cloning theorem. -- CYD

Recently, an addition was made to the article claiming that "Conciousness interpretation" of QM have been proven wrong. I seem to remember an experiment where the two slits of a double slit experiment are equipped with detectors. If the detectors record which slit an electron took, and somebody looks at the results, then no interference pattern occurs. But if the detectors record the information, and subsequently the information is destroyed before anyone has a chance to see it, then the interference pattern does occur. How are these results being interpreted nowadays? --AxelBoldt


 * As far as I know, what you described should not happen: in both circumstances there should be an interference pattern. Can you provide a link? We need an article quantum decoherence. I will get around to writing that one of these days, if no one else does it. -- CYD


 * Huh? This whole thing confuses me.  Here's what you might be thinking of, if you put dectectors at the slits, and they function at 100% then there will be no interference.  It doesn't matter wether somebody reads the output of the detectors or not.  If the dectectors worked then the interference is destroyed.  There is an interesting effect if the detectors are not 100% efficient.  Then the interference pattern get's ``washed out''.  There is a brief attempt at an explanation on my home page see


 * http://www.sfu.ca/~manobes/posts/twoslit.html


 * for some details. Also I think what is needed is one long complete article on quantum mechanics, not a great mass of micro articles on various features.  Actually even better would be two long articles, on for laymen and one more advanced. --Matthew Nobes


 * I think the current approach is fine. We already have what you suggest, in the articles quantum mechanics and mathematical formulation of quantum mechanics. These lay down the framework of the theory. However, it is necessary to have "micro articles" such as this, simply because the secondary requirements and implications of quantum mechanics are so numerous. The uncertainty principle is not a postulate of the theory.


 * That's true, it's a theorem about operators. This is my point though, for a layman's type article the HUP requires a couple of sentences, there is no need for a micro article. From a mathmatical standpoint it is an easy to prove theorem, again a couple of lines in a long article.  However, since I don't have the time to write any long articles right now I'll quit critiquing the approach others take, and stick to physics issues. -- Matthew


 * In my understanding, position and momentum don't have to be noncommuting observables; the fact that they are is a result of our choice of Hamiltonian and state space, which is motivated by experimental results (phenomenology).


 * That's not how I'd put it. Momentum is the generator of translations, as such it will not commute with position.  This is true even in classical mechanics where x and p~d/dx have a non-zero Poisson bracket. -- M.


 * The Pauli exclusion principle is another example of a principle often associated with, but not strictly required by, quantum mechanics. --CYD


 * That's not really true. The PEP is a theorem in the relativistic formulation.  You cannot construct a consistent theory of fermions without it (at least in three space + one time dimension) look up the ``Spin-Statistics theorem''.  *Historically* it was a phenomenological principle, but from a logical perspective it is contained in the theory. -- M.


 * I put in the various statements about the consciousness interpretations

of QM. As far as I am aware of, few if any physicists have ever believed that consciousness has a special role in wave function collapse. The problem is that many popularizations of QM have made it seem that there is a connection, and the fact that a lot of people seem to be influenced by that is why I keep emphasizing the point that you can demonstrate that it isn't. I'm not aware of the experiment that you referred to.


 * I searched around and couldn't find it either anymore. The closest I found was an experiment involving polarization and a double slit, which might be interpreted as "the interference pattern reappears if the polarization information is destroyed by another polarization filter", but that hardly qualifies as an introduction of conciousness into QM. --AxelBoldt


 * In the sound wave example, it is possible to calculate the exact frequency of a sound wave at a given time. The mathematics for this calculation are exact, notwithstanding the measurement error introduced by the uncertainty principle.

Given a sound signal, you cannot talk about the exact frequencies contained in the signal at a specified point in time. In order to do Fourier analysis, you always need to look at the function over a whole interval; a single point is not enough. And if you make the interval smaller, the uncertainty in the frequencies increases proportionally. It's very much analogous to the uncertainty principle, and in fact, the same theorem underlies both effects. --AxelBoldt


 * That's not true. It is not the same theorem.  Standard QM uncertaintaty relations are derived from a theorem about operators on a hilbert space.  These are not things that occur in classical wave mechanics.  This idea about frequency and intervals is what underscores the time-energy relations, which is precisly why I cautioned against talking about them in the same language as standard QM relations. -- Matthew


 * There is a theorem relating the "uncertainty" in a function and the uncertainty in its Fourier transform. In standard wave mechanics, the Fourier transform is a Hilbert space automorphism which translates between the position observable x and the momentum observable -i d/dx. So the Fourier theorem can actually be used to prove the space-momentum uncertainty relation. --AxelBoldt

-

I'd like to put this sentence back in the main article. It's a clear layman-accessible explanation of what the uncertainty principle is all about.

accessability of the article
I this article would be more useful if it worked harder to explain the concept to non-physicists. Not necessarily dumb it down, but help the reader along more. ike9898 14:39, Aug 6, 2004 (UTC)

I agree with the above statement, I like to think Im fairly clever, but the article was hard work.

source of the uncertainty principle.
Can someone clear this up for me. Someone has said that the "uncertainty principle" is a result of mathematics and NOT a result of the physical world/physics. And that if the physical world did not exist there would still be the uncertainty principle in mathematics.

The article did not clear this up one way or the other.


 * I guess both are true. In the physical world/physics (to use yor term) the position and momentum observables can be modelled by self adjoint operatprs P, Q which satisfy a commutation relation


 * $$ [P, Q] = r I $$


 * for some r. That's a fact of physics. The rest is mathematics. Now in the historical development of quantum mechanics, the sequence of events is more complicated. CSTAR 00:26, 18 Nov 2004 (UTC)

I suggest a seperate page, for a math perspective on the uncertainty principle, both to be more accessable to (some) mathemations, and for clearing up some issues. The uncertainty principle is central in Harmonic analysis, Signal processing, Wavelets and Information theory (all very close of course).


 * The uncertainty principle is measureable, and thus it's real. That's the important point.  It is commonly observed in things like quantum tunneling.  When we say the uncertainty principle "comes from" a particular equation or mathematical formulation, that doesn't mean this is the reason for it, it just means this is how the correct result is derived.  It comes from reality, ultimately, it's just that in a descriptive sense, the uncertainty principle is not a postulate itself, but a result of other postulates.  Cortonin 02:05, 18 Nov 2004 (UTC)

I'm sorry but I'm talking about something like this: Is the uncertainty principle a fact of mathematics rather than quantum physics.

The Heisenberg Inequality of quantum mechanics (position times momentum is greater than a fixed, non-zero lower bound) has analogs in several other fields. Radar engineers speak of the time-bandwidth product (time duration of a radar pulse times its half-height bandwidth in the frequency spectrum), which is bounded away from zero for all radar systems. The Nyquist bound of a communication system governs how much information can be transmitted in a given time interval.

This looks like the best place to add this.

I never really understood the Heisenberg Inequality until I ran across it in information theory. It turns out that what Heisenberg actually proved is a simple mathematical result, that if you take any signal, its localization in time times the localization of its Fourier transform has an absolute minimum that you cannot go below. (That minimum is achieved by a bell-curve.) This purely mathematical result about Fourier transforms says something about physics when two physical properties (eg position and momentum, or energy and time) are related to each other by a Fourier transform.

I cannot honestly claim that I really understand the HeisenbergUncertaintyPrinciple now that I have learned how the it limits what wavelet transforms of sampled data can do. But at least I know that I am misunderstanding something different than I thought I was misunderstanding before. :-)


 * Of course, Cortonin is right. The uncertainty principle for QM is an experimentally verifiable fact and historically the experimental verification (probably) preceded derivations of it from first principles. (However, history of science is always tricky, so seemingly obvious assertions about precedence of discoveries are often wrong.) Nevertheless, in this article, the uncertainty principle has a somewhat different status from the purely QM expression of it since it has manifestations in other areas of physics and mathematics.CSTAR 04:13, 18 Nov 2004 (UTC)


 * In summary, the stated uncertainty relation applies to position and momentum whenever you're dealing with the position and momentum involving a wave packet. The gaussian is the minimization of the product of the uncertainty of these two things, and thus, you get the relation stated in the article.  I believe Jackson's E&M has a discussion on uncertainty of x and k of electromagnetic waves from a classical perspective, since this also applies. Cortonin 05:05, 18 Nov 2004 (UTC)


 * We can let Niels Bohr answer the question as to the source of the uncertainty principle: "There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature."  In other words, there may be no quantum leaping, there may be a definite position of a particle, but the only way we mere humans can describe mathematically in a useful way what we see in the real world is to use Quantum Mechanics.  Theories are simple models of complex systems. The universe is too complex to describe without simple models.  See new "history" section where Heisenberg was abandoning the too complicated description of a 3-D orbital in favor of a 1-D anharmonic oscillator model. Because QM is useful and continues to provide sound mathematics when tested, it is a mainstream theory of the universe (at least at the quantum level).  With the evolution of the human brain, and the evolution of technology, in a hundred years or more (or maybe even less), QM may likely collapse and be replaced by a more useful theory that more accurately describes the natural world in the same way that Einstein replaced Newton.  Is QM from nature?  Yes, as far as we can tell by experiments.  Is QM from mathematics?  Absolutely.  It was the only way humans could think of to describe nature as we could see it.  Niels Bohr's comment was saying that he himself believed that the natural world was probably different than the explanation given by QM.--Voyajer 15:34, 22 December 2005 (UTC)

Examples of observables which satisfy the commutation relations
Your addition in the corresponding subsection to the article requires a little more explanation. ALso for the angular momentum operators Jx you wrote the commutation relations not the uncertainty relations. Could you add this or should I? CSTAR 04:13, 18 Nov 2004 (UTC)

I agree that it could use a little more explanation than it has, and a bit more content than it has. I just think that it would be useful to have a list of common uncertainty pairings condensed into one spot. I'm not entirely sure what the best way to do this is, so go ahead and edit. Perhaps it could have both the commutation relations and the uncertainty relations for each pair. Cortonin 05:10, 18 Nov 2004 (UTC)

Common observables which obey the uncertainty principle
One other remark regarding this section, specifically, on the time-energy uncertainty relation. One has to be more careful about the meaning of a time operator. See for instance the discussion by John Baez .CSTAR 02:19, 19 Nov 2004 (UTC)

Total angular momentum
The link points to classical angular momentum. There doesn't seem to be any page on quantum angular momentum.CSTAR 21:52, 24 Nov 2004 (UTC)

Anonymous comment
An anonymous user (who probably didn't understand what a talk page is for) added this text to the page after "...transmit information to each other to ensure that the correlations in behavior between particles occur." I'm moving it here, because it's, well, talk. (I don't know enough about quantum mechanics and am not awake enough right now to do anything about what he's commenting on.)

"(This directly contradicts Copenhagen Interpretation page which states: 'The completeness of quantum mechanics (thesis 1) has been attacked by the Einstein-Podolsky-Rosen thought experiment which was intended to show that there have to be hidden variables in order to avoid non-local, instantaneous 'effects at a distance'. Deterministic hidden variables avoid the problem of spooky action at a distance.)"

-&#8472;yrop (talk) 06:13, Jan 14, 2005 (UTC)


 * The anonymous user makes a good point, but it's the Copenhagen article which was unclear. I corrected it.     &mdash; Cortonin | Talk 09:08, 14 Jan 2005 (UTC)

More Humor
Vimes: Does this mean I'm going to die? Death: POSSIBLY. Vimes: You turn up when people are *possibly* going to die? Death: OH YES. IT'S QUITE THE NEW THING. IT'S BECAUSE OF THE UNCERTAINTY PRINCIPLE. Vimes: What's that? Death: I'M NOT SURE.

Alternative
Here is an alternative

hdot / lP = pP

hdot = h / 4.pi lP = Planck length pP = Planck momentum

An object with a length of lP and an angular momentum of hdot, has a momentum of pP. This makes me ask the question, "What uncertainty?"

Indeterminacy in computation
Can someone explain to me what indeterminacy in computation has to do with the uncertainty principle? It seems to be related to something much larger than quantum scale. Hence, not completely relevant. Koffieyahoo 5 July 2005 06:50 (UTC)


 * I agree that putting a reference to the actor model here looks more like spam, although note that the person that contributed that graf is (or at least uses the name of) a notable academic. See my comment to him on his talk page. There is arguably a relation between computational non-determinism and various sources of non-determinism in physics, but as you say "It seems to be related to something much larger than quantum scale" .--CSTAR 5 July 2005 14:33 (UTC)


 * Okay, so I thought a little about this and I agree this the first sentence of this part of the article in the sense that: yes, computer components are becoming smaller and, hence, quantum effects will started to get noticed (no dispute here). On the other hand, as far as I can see, the remainder of this part of the article has to do with concurrency, not with indeterminism and this is something that happens on all physical levels, not just a the quantum level. Koffieyahoo 5 July 2005 18:49 (UTC)


 * Moreover, what would an arbiter be in quantum mechanics? Koffieyahoo 6 July 2005 12:34 (UTC)


 * Your basic point is correct: Asynchronicity and the need for a hardware "arbiter" arise for many reasons (including heat effects, possibly decoherence) not directly related to the "uncertainty principle". I would not have put the actor link in this article.--CSTAR 6 July 2005 14:01 (UTC)


 * Arbiters do in fact introduce indeterminacy into computation. If the inputs to an arbiter arrive at almost the same time then the response of the arbiter is in fact indeterminate--the same kind of indeterminacy as in quantum theory.--CarlHewitt 2005 July 6 15:20 (UTC)

Reply
Hello:

Regarding your reply to my comments, I have a few comments of my own. For reference I have numbered some of your comments. I believe the context of each is clear, but please tell me if you believe otherwise:


 * 1) Arbiters do in fact introduce indeterminacy into computation
 * 2) the response of the arbiter is in fact indeterminate--
 * 3) the same kind of indeterminacy as in quantum theory.

I think we are in agreement about 1) and 2). However, I think 3) is wrong. To begin with, indeterminacy in quantum mechanics means several distinct things.


 * Decoherence, brought about by measurement. This transforms a pure state into a density matrix and can be regarded as introduceing "indeterminacy"
 * The uncertainty principle which is meaningful at the level of pure states, that is without ever having brought up density matrices; in fact historically I believe this is the case.
 * Complementarity

Now I have no objection to your placing a comment about indeterminacy in this article. However, the way it currently is stated it is inappropriate for (at least) three reasons.


 * a) There are other physical sources of indeterminacy (for example heat generation may cause hardware clocks to drift); You should mention at the very least that "quantum indetermincay" is just one source.
 * b) As you are well aware, there are many other theories of asynchronous processes, besides the actor model. Why not mention these?
 * c) Quite frankly, this currently reads like self promotion, which in most instances (if not all) is against Wikipedia policy.

Thank you.

--CSTAR 6 July 2005 16:37 (UTC)

Thanks for your comments. An arbiter leaving its metastable state can be viewed as a kind of decoherence. Arbiters do not in fact require clocks. I put in a reference to Process calculi. How could the paragraph be reworded to read less like self promotion?--CarlHewitt 2005 July 6 19:13 (UTC)


 * Quantum mechanical phenonena are all "related" in some form but as I mentioned, decoherence and uncertainty principles are two distinct things. Decoherence is mathematically accounted for by master equations (such as the Lindblad equation) or Hilbert space amplifications (such as the many-worlds interpretation). This article is about uncertainty principles, not about decoherence. I suggest you move the subsection in question to the decoherence article, with an explanation of the statement An arbiter leaving its metastable state can be viewed as a kind of decoherence. That would make it more useful, I believe. Thanks.--CSTAR 6 July 2005 19:30 (UTC)


 * I moved the section on "Indeterminacy in computation" to Quantum indeterminacy which in turn references Quantum decoherence.--CarlHewitt 2005 July 6 22:51 (UTC)


 * Thanks. I think that makes a lot more sense. --CSTAR 6 July 2005 22:57 (UTC)

External link
The following reference seems to be appropriate for this article:
 * D. A. Arbatsky, The certainty principle.

What??
''Other (equally misleading) analogies with macroscopic effects have been suggested to explain the uncertainty principle: One such involves pinpointing a watermelon seed with one's finger. The effect is well known - one cannot predict how fast or where the seed will disappear. This random outcome is based entirely on randomness that can be explained in purely classical terms.'' What does this para actually mean?? Anyone care to explain so I can rewrite it?--Light current 23:23, 3 October 2005 (UTC)


 * It doesn't mean anything that I know of. Somebody kept reinserting it, so rather than continue with a revert war, I just put it in a paragraph on misconceptions. You can delete the whole paragraph as far as I'm concerned. --CSTAR 00:43, 4 October 2005 (UTC)

Done!--Light current 02:17, 4 October 2005 (UTC)


 * Thanks. --CSTAR 02:18, 4 October 2005 (UTC)


 * Re: your edit summary for your edits to the article: you don't need to "get anybody's approval" to make a change. On the other hand, I (or anybody else) can legitimately revert if the change is not regarded as an improvement. Generally, changes are improvements so long as the technical accuracy is not sacrificed -- people generally want to improve readability. At other times, dealing with individuals that insist on inserting some text (such as the one that inserted the watermelon business which you thankfully deleted) is just too much trouble. All your changes so far have been reasonable and I am certainly happy to see the article improve.--CSTAR 02:48, 4 October 2005 (UTC)

Just being polite (especialy since physics is not my forte) and I seem to have upset a few people lately!!--Light current 02:52, 4 October 2005 (UTC)

Dimensions in uncertainty relations
Does anyone know whether the dimensions of any relation have to be the same on both sides of the inequality? I would think they do-- but I dont know.--Light current 06:00, 4 October 2005 (UTC)


 * Yes, they have to be. Note that the uncertainty relation is an identity for Gaussian states.--CSTAR 14:30, 4 October 2005 (UTC)

OK Thanks. That helps me understand it a bit more.--Light current 22:34, 4 October 2005 (UTC)

position/momentum bias?
It seems to me that the Robertson-Schrödinger relation is the root of the whole thing and the theorem section would be better placed at the top of the article instead of being buried towards the end.

While there is an attempt to point out the generality of the uncertainty principle in the start, the focus on position/momentum in the first few sections tends to obscure this. I guess this is related to the "source of the uncertainty principle" above.

Near-Complete Relativisitic Uncertainty Principle
This is drawn from research into GUT. Reference to be added when made available to public.


 * If it's not public, it doesn't belong here. When it becomes public and you can cite sources, then by all means put it in. --CSTAR 05:06, 16 October 2005 (UTC)

Vandalism?
24.226.10.99 changed \Delta x \Delta p \ge \frac{\hbar}{4} to \Delta x \Delta p \ge \frac{\hbar}{2}. However, due to this user's behaviour on many other pages, I am reverting this change. My apologies if it was legit. -- user:zanimum


 * There were two successive changes made by that user. The last change, that is the one you mentioned, reverted back to the correct form, from the previous incorrect form.--CSTAR 22:49, 17 October 2005 (UTC)

"Topics in Quantum theory" box
The "Topics in Quantum theory" navigation box is awfully far down in the article. I'm considering moving it up to the top, where such boxes usually go, but I wanted to check if anyone had already tried that and found it not to work well... Jamie 00:03, 16 November 2005 (UTC)


 * How about just getting rid of it entirely? linas 01:06, 16 November 2005 (UTC)
 * Thing is, navboxes are really useful. I just wish this one weren't so big.  If I don't have any better ideas if a couple of days I'll try moving it to the top and see how it looks. Jamie 07:17, 16 November 2005 (UTC)


 * Yes, except that this navbox is filled with utter crud. I mean, have you actually looked at it? The things that are important in QM, and the topics that are related, have little/no resemblance to what's in that navbox. I am contemplating starting a vote-for-deletion for the thing, given how badly broken it is.linas 16:08, 16 November 2005 (UTC)


 * I doubt this "navbox" is of any help to anybody.--CSTAR 16:28, 16 November 2005 (UTC)


 * Wow, that is huge! I would just take each section title and use that (or a slight modification of it) for ONE link, rather than a whole section.  WhiteC 21:28, 16 November 2005 (UTC)


 * OK. Looks like people want it gone...  so I've removed it.  If someone would like to put back as smaler version, I'm sure it would be better.

dE dt >= h/2 debate
This entire debate is completely pointless. Yes x,p are observables in NRQM. Yes t is not an observable, but an externally provided parameter in NRQM. But this is not an article about observables and external parameters and how NRQM is ultimately dumb. These are problems carried over from NRCM not being covariant. The fact is that the wave nature of QM and Fourier analysis provide the exact same inequality relationship for x,p and for t,E. And both are useful. Particle physicists use dtdE>hbar/2 all the time to rationlize things, and they use it in the exact same manner as dxdp. The full relativistic uncertainty principle for x,p derives from the commutator $$[x_\mu,p_\nu] = i \hbar \eta_{\mu,\nu}$$. It is a property of the manifold's tangent bundle and fundamental QM principles that transcend the assumptions of NRQM. CHF 23:09, 11 December 2005 (UTC)