**Quantum Physics** or **Quantum Mechanics** is a well proven theory of Physics. Despite this, it still is very hard to model a picture graphically. Quantum physics is the most surreal form of Science. This is because at its roots, it states that it is impossible to know everything about a situation: the best we can do is give a probability. It is not that we can't find out--experiments have proven that it is actually impossible to know, because any attempt to make a measurement will change something else. To quote Richard Feynman: "I think I can safely say that nobody understands quantum mechanics."

Ideas, in increasing order of weirdness:

## Contents

## Wave-particle duality

This is a very weird feature of quantum mechanics that has been verified numerous times. It is counterintuitive and difficult to picture. According to QM, *everything* has wave-particle duality, but most macroscopic entities are either particlelike or wavelike, with the opposite aspect being too small to observe without specially designed experiments. Are microscopic entities particles or waves? They are probably something different that we don't understand with some particle properties and some wave properties.

### Double slit experiment

Imagine a wall, penetrated by two holes, in front of a screen. Tennis balls, fired through these holes, will travel normally, making two stripes on the far screen. Electrons, however, are small enough to act like waves in this situation. Each electron will pass though *both holes*, interfering with itself. The end result gives a pattern that looks the same as that of light, proving that particle-wave duality does exist.

### Quantum Tunneling

Another implication of the wavelike nature of matter means that it is possible for matter to go through a barrier. In macroscopic life, walls are solid. However, at a quantum level, it is possible for a particle to travel through a barrier that it otherwise could not cross. This probability decreases as the barrier height and thickness increases, which means that it very rarely is observable. However in certain cases (such as super-small transistors), this effect can be a problem, because it means that electrons can "leak" out of "closed" containers.

Quantum tunneling also explains some radioactive decays like alpha decay and spontaneous fission. If one tries to reverse the decay in time, the resulting nuclei will stop before meeting each other. But because of their wavelike properties, they can go the rest of the way by quantum tunneling. Reverting to the original time direction, they thus do the first part of their outward journey by quantum tunneling. Calculating decay rates using quantum tunneling gives reasonable agreement, including for very long-lived nuclides like uranium-238.

## Uncertainty Principle

Strictly speaking, there are are many uncertainty principles, one for every pair of quantities which cannot be simultaneously measured. However, the best-known one is that of position and momentum. This is because of wave-particle duality:

- momentum = h/wavelength = h*wavenumber = hbar*(angular wavenumber)
- h = Planck's constant
- hbar = reduced Planck's constant = h/(2*pi)
- wavenumber = 1/wavelength
- angular wavenumber = 2*pi*wavenumber

If one tries the measure a wave's position and wavenumber at the same time, one finds that one cannot. One needs a spread of position L to measure the wavenumber K, and that spread of position means that one's measurement of the wave's position is uncertain over a distance L. Actually measuring K involves counting wave cycles over L, and that number is K*L. Since that will be imprecise to within 1 cycle, the uncertainty of K is about 1/L. Thus,

- (uncertainty of position L) * (uncertainty of wavenumber K) ~ 1

Getting back to momentum, we find

- (uncertainty of position) * (uncertainty of momentum) ~ h

A more precise calculation finds (1/2)*hbar. Some similar ones are

- (uncertainty of time) * (uncertainty of energy) ~ h
- (uncertainty of angle) * (uncertainty of angular momentum) ~ h
- (uncertainty of AM 1) * (uncertainty of AM 2) ~ h * (AM 3)

where AM is the angular momentum, and 1,2,3 are components of it.

The uncertainty principle explains why quantum-mechanical ground states have more energy than their classical-mechanical counterparts. In the classical limit, a ground state for a particle moving in a potential will be at a minimum of that potential. However, from the uncertainty principle, zero position uncertainty = infinite momentum uncertainty = infinite kinetic energy, meaning that the particle must be spread out away from the minimum point. The quantum-mechanical ground state is the spread of position where the particle's average potential-energy increase its approximately is kinetic energy.

This explain why atoms are stable, which was a big physical paradox when Ernest Rutherford discovered in 1911 that the positively-charged parts of atoms are much smaller than the atoms themselves. Why don't the electrons spiral in? From quantum mechanics, they don't, because if they tried, they would gain too much kinetic energy from being confined in too small a space.

## Quantization

The concept that Quantum Mechanics is named after. This merely states that there are aspects of reality which are "quantized"--they can only have specific values. Most macroscopic quantities are continuous, and can have any value. However, things like "number of people in the room" are discrete. Unexpectedly, a number of quantum values are quantized like this. This means that, for example, the energy of an electron in an atom has a set of allowed values. This gives rise to effects like electron shells (why chemistry works) and transition lines (why spectrometry works).

## Bose-Einstein vs. Fermi-Dirac Statistics

Another quantum-mechanical oddity is the spin-statistics theorem. Particles have built-in angular-momentum and spin, which is quantized in multiples of 1/2 when measured in quantum-mechanical units. Their statistics is closely related to their spin value, with integer spins producing "Bose-Einstein" statistics and half-odd spins producing "Fermi-Dirac" statistics.

Kind | Statistics | Spin | Rotate 360d | Occ Number | Interchange | Example |
---|---|---|---|---|---|---|

Boson | Bose-Einstein | 0, 1, 2, 3, ... | R(360d) = + 1 | 0, 1, 2, 3, ... | X(x2,x1) = + X(x1,x2) | Photon |

Fermion | Fermi-Dirac | 1/2, 3/2, 5/2, ... | R(360d) = - 1 | 0, 1 | X(x2,x1) = - X(x1,x2) | Electron |

Occ Number = occupation number, how many quanta can be in a quantum state.

The Pauli exclusion principal states that two Fermions cannot occupy the same state. Bosons, on the other hand, have no such restriction. This means that while it is possible to fill up a box with electrons, there is no limit to how many photons one could put in the box (until it melts or whatever, but this is physics so we are allowed to use indestructible boxes).

Bose-Einstein and Fermi-Dirac statistics can make dramatic differences in properties. Some very cold materials have "Bose-Einstein condensates", with particles collecting in the lowest state, like superfluid liquid helium. On the other side, electrons pile up in atoms to make atomic structure. When they fill one orbital, they start filling up the next orbital.

Macroscopic objects? For macroscopic particlelike objects, Bose-Einstein vs. Fermi-Dirac statistics make no observable difference, since their wavefunctions are too small to measurably overlap. Macroscopic wavelike objects are all bosons, however. This includes gravity and electromagnetism, and also "collective excitations" or "quasiparticles" like sound. Also superfluids and superconducting states.

## Entanglement

Yet another odd feature is entanglement of particle states. This is a result of many sorts of particle states being mixed states that cannot be cleanly decomposed into individual particle states. This is a common consequence of combining the angular momentum of two particles, for instance; the combined states typically have mixtures of the projected angular momenta of the individual particles.

A much-studied case of entanglement occurs for photons. An electron in an atom may jump down in energy by emitting a pair of photons in opposite directions, especially if it is jumping from 0 to 0 angular momentum. The photons' polarizations are entangled because the photons are in a mixed state:

- Linear: X = 1/sqrt(2)*(X1(dir1)*X2(dir1) + X1(dir2)*X2(dir2))
- Circular: X = 1/sqrt(2)*(X1(left)*X2(left) + X1(right)*X2(right))

Both are equivalent descriptions of that state.

Alain Aspect: Shedding new light on light and atoms - CNRS Web site - CNRS

Alain Aspect did some experiments on the entanglement question, and he showed that emitted photon pairs could stay in mixed states over the size of his lab equipment. Each photon's polarization by itself was completely random, but the two photons together had correlated polarizations. Furthermore, their correlation was in agreement with the large-mixed-state hypothesis and not with alternatives, like "local hidden variables".

## Many Worlds Theory and Quantum Suicide

Many worlds is an interpretation of quantum mechanics that a Scientist called Hugh Everett started. It is becoming increasingly popular among scientists, especially among cosmologists. By no means all scientists agree with many worlds. The theory states that having only one of each possible quantum-mechanical option (remember, random things happen a LOT) be the one that happens does not make sense. Instead, EVERY possible thing happens, and the universe splits into one copy for each result. Thus, everything, regardless of plausibility, happens somewhere and new worlds split off continuously to contain every different way any event can pan out. The problem with this idea is that there is no way to test the theory, which lends problems to its credibility.

It's not hard to see why so many people find these ideas disturbing. For if they are correct, they have profound implications for our understanding of the nature of the Soul, because the Soul (if there is such a thing) must branch along with the worlds that contain it. It would appear that the writings on which many contemporary religions are based make no mention of such an idea.

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## Quotes

"'Cogitus, ergo, sum,' I think, therefore, I am." [Renee Descartes] "The first step to understanding everything is to admit that you know nothing." Albert Einstein "I yam what I yam [this makes sense in context.]" [Ralph Waldo Emerson, *The Invisible Man*

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### Videos

## Conclusion

The quantum physics theory is a very hard theory to wrap your head around, but if correctly used, it provides a framework which can explain some very weird phenomena. It is very rarely necessary to use, but some (mostly nanotech) applications require the accurate descriptions it can provide.

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## External links

- A Lazy Layman's guide to Quantum Physics
- ThinkQuest, What is Quantum Physics?
- Stanford University Quantum Mechanics
- The Many-Worlds Interpretation of Quantum Mechanics

### Videos

- Quantum Mechanics for Dummies - Electrons Are Weird Video
- Amazing Facts of Quantum Physics Video
- The 11 Dimensions of Reality This video may help you understand quantum theory or confuse you further.

Further Reading:

## Footnotes

- ↑ The Many-Worlds Interpretation of Quantum Mechanics
- ↑ Do parallel universes really exist?
- ↑ This article needs an examination by someone who understands more about these theories.