two verson of uncertainty principle

[gib65]

Ok, this is going to be a very complex question, so bare with me...

 

I've been delving pretty deep into quantum physics lately, and I'm particularly interested in the Heisenberg Uncertainty Principle. After researching it a bit, I'm starting to get the impression that there's an "early" version of it and a "later" version, and I want to know if I'm onto something here.

 

The early version seems not to break from classical mechanics too much, although there is some "fuzziness" to it, and the later one seems to be in the thick of quantum indeterminism in a more matured and established overview of what quantum mechanics comes down to us as today.

 

The early version comes straight out of Heisenbergs mouth:

 

At the instant of time when the position is determined' date=' that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position. At the instant at which the position of the electron is known, its momentum therefore can be known only up to magnitudes which correspond to that discontinuous change; thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely (Heisenberg, 1927, p. 174-5).

[/quote']

 

The source for this is the Stanford Encyclopedia of Philosophy, and the article goes on to say:

 

This is the first formulation of the uncertainty principle. In its present form it is an epistemological principle' date=' since it limits what we can [i']know[/i] about the electron.

 

In order to grasp what Heisenberg means by a change in momentum, one need only imagine particles bumping into each other in the classical sense - changing each other's speeds and directions.

 

I might also add that our good friend and resident physics expert swansont enlightened me about the reason why position is hard to measure if one knows the momentum:

 

You can tell where the particle was' date=' but the photon imparts momentum to the particle, so it will have moved. You can't know the energy (and thus momentm) of the detected photon perfectly, either. And to better know the position you have to use smaller wavelengths, imparting more momentum; longer wavelengths will diffract rather than reflect.

[/quote']

 

source: http://www.scienceforums.net/forum/showthread.php?t=28206

 

Longer wavelengths will diffract rather than reflect, so it becomes increasingly difficult to read a particle's position the longer the wavelength.

 

All well and good. However, this, at least in my mind, still falls in the camp of classical mechanics. It's very much on the periphery, but still within the boundaries, I'd say. What Heisenberg seems to be going on about, in this early phase of the principle, is what kinds of implications fall out of the quantization of energy into particles called "photons" - coupled with de Broglie's hypothesis that the reverse is also true: that material particles can be described as waves much like energy. There is an unquestionable transition here - from rigid bodies to fuzzy waves - but based solely on this alone, there is no reason - none that I'm aware of at least - to say that this "fuzziness" of a particle's position crosses over to momentum. As Heisenberg's quote above describes it, changes in momentum can still be thought of as particles bumping each other - very much the lingo of classical mechanics. Furthermore, as swansont said, the uncertainty we have to tolerate when we measure a particle's position using a long wavelength photon is because of diffraction - not because the particle's position is inherently undetermined. In short, the early version of Heisenberg's uncertainty principle seems to be articulated more in terms of shortcomings in our approaches to measurement rather than inherent uncertainty in the things being measured.

 

But I've heard so many times that the uncertainty is indeed inherent. In fact, I've been to this website, and it not only vouches for the "inherently uncertain" view, but it explains exactly how it works. If I'm not interpreting it wrong, it says that in order for a particle to precisely establish a specific position for itself, it must "superimpose" various wavelength of itself together. That is, it's wavelength must be a superposition of a range of values. The wavelength also so happens to correspond to momentum (shorter wavelength = greater momentum, if I'm not mistaken). So a superposition of wavelength is equivalent to a superposition of momentum. The flip side of that coin is, of course, that to reduce the variety of wavelengths to one value (or as near to one value as one can get), thereby establishing a precise value for momentum, you have to accept that the form the particle takes will be a wave that spans the whole of space (or as close to the whole as one can get), thereby making its position indeterminate. Now, this strikes me as inherently uncertain - it's like that regardless of the approach we take to measurement, even one of abstaining from all measurement whatsoever. Yet this is a far cry from the way Heisenberg articulated the uncertainty principle in the 1920s. I don't know - he may have had this more "inherent" understanding all along, but going by how he articulated it, it doesn't seem like it. In my very humble opinion, it seems like HUP went through two phases. The first expressed as Heisenberg put it in the quote above (and the accompanying link expands upon), and the second expressed as the other website I provided a link to above.

 

Is it indeed fair to say that there were, as a historical development of the theory of quantum mechanics, two phases that the Heisenberg Uncertainty Principle went through?

[someguy]

I'm not totally sure but i think that i read somewhere in wikipedia that heisenberg originally thought like you say that it was a limitation of our ability to observe. but i think another physicist was looking at it with him and they figured the issue was an inherent property of particles.

 

I posted this once in another thread. it's a way that would make the uncertainty principle have more classical sense. i haven't been able to verify it mathematically yet, but i haven't found a reason why this way of thinking is wrong yet either. i think it may explain why the uncertainty principle must be, and also wave particle duality.

 

the faster an object moves, the closer it is to being in more than one place at once. should an object be able to move infinitely fast it would indeed be in multiple places at once, probably why going to the speed of light is so difficult since the object is gaining mass and length as it goes faster. it is in a way existing in more places than one. if you do that with a particle you might get a wave.

 

so that would mean that a point moving very quickly would need to become a rod type thing.

 

if you do that with a particle and someone asks you to know both the position and momentum of a particle you are kind of stuck with a difficult problem.

 

this is because either you locate the particle as a point and therefore have lost the rod part of it and thus the speed portion. or you can keep the rod part of the particle, know the momentum yet its exact position is hazy.

 

if this would hold any value it would need to be true that the greater particles move the the greater the uncertainty principle holds, meaning the more uncertain of position you would be if you knew momentum exactly and vice versa.

 

a particle would never be a full rod from point of departure to arrival since it cannot move at speed infinity. it could only be a small moving rod. but light can move at speed infinity, c, and can be a full rod from point of departure to point of arrival. is it possible that this could explain wave particle duality?

[iNow]

On a much deeper level, uncertainty describes the probabilities. If you did not have uncertainty as a fundamental part of the measured system, then one could predict the outcome of each eventuality with 100% accuracy.

 

 

Uncertainty and unitarity are coupled. I think...

[swansont]

The position and momentum probability distributions are Fourier transforms of each other (as are energy and time). The uncertainty principle falls straight out of that.

[gib65]

The position and momentum probability distributions are Fourier transforms of each other (as are energy and time). The uncertainty principle falls straight out of that.

 

I would think so, but what does the math mean (apart from the antagonism between position and momentum)? What I'm asking is, in conveying what the math means, did Heisenberg offer an "early" interpretation, and then a "later" intepretation (either by Heisenberg again, or someone else)?

[iNow]

You might check these pages:

 

http://www.aip.org/history/heisenberg/p08.htm'>http://www.aip.org/history/heisenberg/p08.htm

http://www.aip.org/history/heisenberg/voice1.htm'>http://www.aip.org/history/heisenberg/voice1.htm

 

 

...from this site:

 

http://www.aip.org/history/heisenberg/

 

 

I believe that the existence of the classical "path" can be pregnantly formulated as follows: The "path" comes into existence only when we observe it.

--Heisenberg, in uncertainty principle paper, 1927

 

 

 

[pioneer]

One theory I have about the uncertainty principle has to do with the speed of an electron. It travels about 1/14 the speed of light more or less. So when we look at an atom, the nucleus is on our reference and the electron is in slight relativistic reference. When we try to measure an electron, we assume one reference, so it is not exactly where it should be.

 

For example, say a relativistic train passed by, it would look distance contracted to us. If we assume it is in our reference and did not take into consideration special relativity, it was alway be too narrow to explain how it can cause an affect, before we see its leading edge visually appears to get there. Back during the time of Heisenburg, they did not yet know the speed of an electron. He was a good scientist and would not have attempted to speculate. He stuck with the observation and let that speak for itself.

[swansont]

There is no such thing at the speed of the electron. The HUP applies to the conjugate variables energy and time, too, and particles other than the electron.

[vincent]

The position and momentum probability distributions are Fourier transforms of each other (as are energy and time). The uncertainty principle falls straight out of that.

 

Right. It is a direct result of the basic principles of quantum mechanics that the narrower the probability distribution of one obervable is, the broader that of it’s conjugate will be.

 

However the time-energy inequality is not on the same footing as the position-momentum uncertainty principle since there is no Hermitian operator corresponding to time. Yes, time is a dynamical quantity in that it varies with time, but in a trivial self-referential way and is really just a parameter on which other quantities depend. The actual meaning of ΔE and Δt in the time-energy inequality are respectively the spread in the energy distribution and the amount of time it takes for the wavefunction to changed appreciably.

 

 

On a much deeper level, uncertainty describes the probabilities…

 

…therefore contradicting the tenets of quantum mechanics. Fine. But I would apply the term “on a much deeper level” instead to the relation between the uncertainty principle and the principle of complementarity.

 

When due to the basic principles of quantum mechanics the use of one classical concept excludes the use of another, they are said to be complementary. The principle of complementarity says that the experimental arrangements that measure complementary properties are mutually exclusive and are both needed to demonstrate all of the physics of quantum mechanical systems.

 

For example, consider wave-particle duality as applied to an electron which is the first form in which one usually encounters the concept of complementarity. Wave-particle duality is often erroneously described as meaning that the electron is simultaneously wave and particle. But this is impossible since particle and wavelike characteristics are strictly incompatible. What saves us is the uncertainty principle which says that there are no experiments one can perform in which the position of the electron, this being the particle aspect, and the momentum of the electron, this being the wave aspect, can be simultaneously measured to arbitrarly high precision.

 

Thus the deeper meaning of the uncertainty principle is that it is the condition that ensures the logical consistency of quantum mechanics.

 

Uncertainty and unitarity are coupled. I think...

 

A unitary quantum theory is one in which probability is conserved. Though they're pathological, one can imagine nonunitary theories in which the uncertainty principle formally still holds.

 

I personally think there must still be a better explanation than that which has been offered, as this is a bit like saying the bible exists because religion would not have any central tenets without it. There is something inherent in the universe that makes the outcome of events non-absolute. The principle of uncertainty is a description of this.

 

All I can do is explain the role of the uncertainty principle in quantum mechanics. Do you believe that the uncertainty principle has a deeper role in quantum mechanics? Do you believe quantum mechanics to be incomplete?

[iNow]

All I can do is explain the role of the uncertainty principle in quantum mechanics. Do you believe that the uncertainty principle has a deeper role in quantum mechanics? Do you believe quantum mechanics to be incomplete?

 

Vincent, first let me thank you for your willingness to share your knowledge on this topic. I've barely even stratched the proverbial surface of QM, and what I have scratched has been self-taught from various reading. That said,...

 

My point was to suggest that there is much more to the Uncertainty Principle than this idea of bumping a photon with another particle used during the measurement. I see the UP as an inherent part of reality, and at the heart of QM. My knowledge after that is really rather limited, and what I typed above in Post #3 was more waxing philisophical after a nice glass of scotch than anything mind-blowingly significant or challenging.

 

To your question, I do believe that QM is incomplete, but that makes my curiosity, interest, and respect of it as a field no less valid.

 

 

Thanks again, and I look forward to exploring the concept further with learned individuals such as yourself.