The Heisenberg Uncertainty Principle.

[Gordon Freynman]

Quantum mechanics is perhaps the strangest theory ever devised in all of science, yet it is by far the most accurate scientific theory ever developed with some of it's predictions tested accurate up to 9 decimal places. Quantum mechanics has shown that our typical notion of stable and predictable world using Newton's force laws does not apply on atomic scales and has left a profound impact on the way we view the world. Here I'm going to introduce one of it's most fundamental concepts and some of the consequences that arise from this concept. As the title suggests that concept is the famous Heisenberg Uncertainty Principle (referred to as HUP from now on).

The HUP states that you cannot simultaneously know the position and the momentum (velocity) of a particle with high precision. The more precisely you know the position of a particle, the more uncertain you become of it's momentum. Extensions to the HUP can be made, in that you cannot know the amount of spin on a particle over more than one axis which I'm going to ignore here, and that you cannot know accurately the amount of energy in a state that exists for shorter and shorter times which I will cover later. For now we will only be concerned with position and momentum. Position-momentum uncertainty is described mathematically by the following inequality,



where ΔX and ΔP are measurements of certainty of position and momentum respectively and ħ is the reduced Planck constant.

So how does the HUP apply to the real world? You might be inclined to think that this uncertainty is merely a consequence of experimental observation of particles, that when you measure the position of a particle you inherently disturb it's velocity and hence it becomes indeterminable, and that particles always have a definite position and velocity. While this is partly true, several decades of countless experiments have proven this interpretation to be incomplete. It turns out that the HUP is not only a statement about our limitations in measurement, it is also a statement about nature itself at the most fundamental level. Particles truly do not ever have a definite position or velocity, until they are observed or interact with the environment.

So how do we come to grips with this unintuitive concept? How does a particle end up having an indefinite position and/or velocity? Well, it turns out that particles are not always particles, in fact most of the time they are waves and can be described by a so-called wavefunction. Every fundamental particle exhibits wave/particle duality, which you can get a basic introduction to here, http://www.twcenter.net/forums/showthread.php?t=89042

But what does it mean to say a particle can be described by a wavefunction, and how does it go from a wave to a particle? There are several different answers to these questions, called interpretations of Quantum Mechanics, but no one knows which is right. The most popular one is the Copenhagen Interpretation, which describes a particle's wavefunction as being a measure of the probability of that particle having a certain position or velocity, and when the particle interacts with the environment the wavefunction momentarily collapses to a precise value. The second most popular (probably the most mind boggling) is the Many Worlds Interpretation, which states that there are an infinite number of parallel universes in a quantum superposition, in which all possible quantum events are realized, and when a particle interacts with the environment it under goes quantum decoherence rather than a wavefunction collapse.


Energy-time Uncertainty

An extension to the HUP is the energy-time uncertainty principle, as described by the following inequality:



Where ΔE and Δt are the measures of uncertainty in energy and time respectively, and h is again the reduced Planck constant. The key thing to note here is that time is not an operator in this equation, rather it is a parameter. What this basically means is that it is not a measurement of when an event occurs, instead it is a measure of the time it takes for an event to occur, or the time in which a certain state exists.

Now that you have a basic idea of the HUP, let's examine some of the consequences of it.

The Electron Cloud

Some of you may be aware of the illustrative images depecting atoms with little electron balls circling a nucleus of protons and neutrons, which is called the Bohr model of the atom. However as some of you may also know this is a very inaccurate depiction. Electrons do not really orbit the nucleus of an atom in a sense that they spin around it in circles, rather they hang around in what is called the electron cloud which surrounds the nucleus. Inside the electron cloud electrons are zipping around and jumping chaotically all over the place. You may wonder why, if the electrons and protons attract each other, electrons don't just fall into the nucleus. Well, the HUP again provides an answer. The radius of the nucleus of an atom is around a 100,000 times smaller (depending on the element) than the radius of the atom itself, so the nucleus is a much more confined space when compared to the size of the atom. Hence if an electron were buzzing around inside the nucleus it would have a more definite position, and hence a more indefinite amount of momentum. Eventually the fluctuations in the momentum would fling it back out of the nucleus.


Quantum Fluctuations

Quantum fluctuations are temporary changes in the energy of a field at a certain point in space, and are a result of the energy-time uncertainty principle. On shorter and shorter timescales, the energy embodied by a field becomes more and more uncertain. One consequence of this is that the conservation of energy can potentially be violated for very short periods of time, although whether or not it does get violated is difficult to be certain at this point.

Virtual Pair Particles

Ah, the infamous virtual particles. Virtual particles are themselves a result of quantum fluctuations and in turn a result of the energy-time uncertainty principle, however the position-momentum uncertainty also applies heavily to VPs. Excitations in fields from quantum fluctuations produce particle-antiparticle pairs, which briefly come into existence and annihilate one another. In case you weren't already aware, when a particle and it's anti-particle come in contact, they annihilate into pure gamma radiation, or in this case one of the particles has negative energy so they annihilate back into nothing. Since virtual particles exist for only brief moments in very localized areas, there is a very large amount of uncertainty in their energy and momentum, which may cause some very weird things to happen on small enough scales, such as...

The Quantum Foam

On smaller and smaller scales, larger and larger values for energy and momentum for virtual particles can arise as allowed by the uncertainty principle. From Einstein's General Relativity, we have little doubt that the presence of matter causes space to warp and bend. Virtual particles with sufficiently high energies can therefore cause significant distortions in the fabric of space. On scales of the order of the Planck length (~1.6 x 10^-35 meters) the uncertainty in energy allowed in virtual particles becomes so large that it is possible that space becomes something akin to a bubbling foam bath, hence the name quantum foam. Some speculate that on these scales tiny wormholes to other points in space or whole other universes even could be created. However, without a quantum theory of gravity (more commonly named a theory of everything) we cannot truly know what happens to space on these extreme scales.



That's all I really feel writing about now. I'm sure there are at least a few things in that wall of text that need further elaborating so feel free point out anything that needs clarification.

[Yoda Twin]

Very cool stuff, we've just been studying this in my physics class for my final year, definately my favourite part of the course

[Maximus Macro]

the double slit experiment is a very good example of this.
if we shoot matter true 1 slit it forms a light line patern on the screen behind it.if we ad a second slit we would expect 2 line patern in the place on the wall behind these 2 slits.now look at waves they move true the one slit and hit the wall with the most intencity where the light line formed when they moved true as a particle instead of a wave.

but when we add the second slit somethign different happens.when the top of one wavefunction hits the bottom of an other they cancel eachother out.so now there is an interfierance patern.(a prison bar patern).
places where the high end of the function meat form the light patern as before.but places where the low part of the function meet theres nothing(the dark shadow between bars).
so when trow matter true 2 slits we expect 2 bands of matter behind the slits.but with waves we get and interfierance patern of many bands(prison bars patern).

when you shoot multiple particles(electrons) true this slits an interferance patern emmerges(they interact and bounce of each other.but when 1 particle go true the double slits without being observed , it behaves in the very same interferance patern as multiple would.

the single electron leaves as a particle.and becomes a wave of potentials true both slids and interfiers with itself.to hit tha wall as a particle.mathematical it means this one particle goes true both slids and neither,or true one or the other.all of this potentials are in super position with each other.

but when physicist decided to observe the process something amazing happened.they put a measuring device at one slit to see wich one it went true and let it fly.when they observed, the particle did not behave like a wave like it did previous but went true like a particle once again.it produced a patern of 2 bands not an interfierance patern of many.the very act of observing ment it only went true one not both.

the conclusion the observer collapsed the wavefunction of the particle simply by observing.

[numerosdecimus]

At the present in order for the theory of everything to be theoretically plausible, Supersymetry should be also verifiable, as well as the very basis of M theory which is it's multidimentional approach to subatominal particle physics and at the level of quantum foam. If not, under a worse case scenario these entire concepts have to revised and something else must envisioned.

As for the concept of quantum foam, there's a possibility it may present itself as an opportunity to make at least for some part quantum mechanics as a predictable phenomenon(however I'm not advocating the principle of Determinism), such as for instance the duality of an electron as it can be in two places at the same time. If the fundamental factors are determinted through the study of quantum foam them the positioning of an electron for instance might became a predictable and experimentaly possible science, at the very least under a significant probability.

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Every fundamental particle exhibits wave/particle duality

One excellent example of this would be a fission/fusion reaction, the principle of wave/particle duality is known as the telltale sign if any of these phenomenons is occuring, through the meaurement of neutron radiation, however, some reasurences have to be made so that the scientist isn't confusing background neutron radiation as neutron radiation from the experiment.