Quantum mechanics

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{{main|Uncertainty principle}}{{rquote|right|"''How do the Heisenberg compensators work?''"<br />"''They work just fine, thank you.''"|}}
 
{{main|Uncertainty principle}}{{rquote|right|"''How do the Heisenberg compensators work?''"<br />"''They work just fine, thank you.''"|}}
  
With the wave-like nature of quantum mechanics established, problems began to arise in figuring out the location of particles. Waves do not have a specific location; they're spread out over an area and aren't described the same way as particles. Thus the "uncertainty principle" was established; in short it means you cannot know the location and momentum of a particle to the same degree of accuracy. This isn't a limit in scientific instruments but a fundamental aspect of phyics.
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With the wave-like nature of quantum mechanics established, problems began to arise in figuring out the location of particles. Waves do not have a specific location; they're spread out over an area and aren't described the same way as particles. Thus the "uncertainty principle" was established; in short it means you cannot know the location and momentum of a particle to the same degree of accuracy. This isn't a limit in scientific instruments but a fundamental aspect of physics.  As [[user:humam|one editor]] likes to explain it, even [[god]] can't know the location and velocity of particles at the same time.  It is a physical impossibility.
  
 
This effect arises from the fact that there is a series of states of a particle that have a definite momentum, and a series of states that have a definite position, but those two series of states are not the same.  A state with a definite momentum is a superposition of states with definite position, and vice versa.  The uncertainty principle shows that a particle can be in a state that is a superposition of a small range of momenta and a superposition of a small range of positions simultaneously, but the smallness of one of those ranges cannot be made smaller without making the other range larger.
 
This effect arises from the fact that there is a series of states of a particle that have a definite momentum, and a series of states that have a definite position, but those two series of states are not the same.  A state with a definite momentum is a superposition of states with definite position, and vice versa.  The uncertainty principle shows that a particle can be in a state that is a superposition of a small range of momenta and a superposition of a small range of positions simultaneously, but the smallness of one of those ranges cannot be made smaller without making the other range larger.

Revision as of 06:15, 4 June 2011

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I think I can safely say that nobody understands quantum mechanics.
Richard Feynman, The Character of Physical Law (1965)

Quantum mechanics (QM) is a branch of physics developed to deal with sub-atomic particles and their interactions. Most of the foundations of QM were formulated during the first three decades of the 20th century. Modern quantum physics has advanced considerably, and is used extensively in the study of chemistry and materials, including biological research, and in cosmology and astronomy.

One of the awesome things quantum mechanics explains is why energy is absorbed or emitted by atoms only in discrete amounts, or "quanta". This in turn explains why hot objects (like the sun) shed light in the specific way that they do. Quantum mechanics also explains a host of other phenomena, like superconductivity (used in MRI machines and some high-speed trains), Hawking radiation (theoretically emitted by black holes), the fine structure of the microwave background cosmic radiation (caused by quantum fluctuations on top of flat spacetime), how magnets work, the biochemical properties of proteins, why metals conduct and plastic doesn't, and more.

The most developed quantum theory to date is known as the "standard model", and is considered to be the most accurate physical theory ever created. It has been proved to be valid to a very high precision. However, the standard model does not take gravity into account, and it is believed a more general "Theory of Everything" would be required to incorporate it. Although it isn't clear how, most researchers believe that this theory, too, would be a quantum theory.

Some of the phenomena of quantum mechanics, such as entanglement, were described by Albert Einstein as "spooky" because, at the sub-atomic level, physics as we think we know it breaks down and becomes almost incomprehensible. On the other hand, Eliezer Yudkowsky has said that people describing quantum mechanics as odd or strange are talking bollocks; quantum theory is the real world, and it's our common sense view that we've evolved with that's the illusion.[1][2]

Contents

Core principles

There are a few basic core principles for understanding quantum mechanics and the supposedly spooky oddness that goes on at the level of atoms. It is very important to remember one key thing: quantum mechanics is not classical mechanics. Quantum theory is mostly a mathematical description of how the world works at the atomic level based on very good evidence. Taking any of the interpretations too literally would be a mistake.

The Photoelectric Effect

In the late nineteenth century, James Clerk Maxwell formulated a theory of electromagnetism that described a wide range of electrical phenomena, and in particular described light as an electromagnetic wave. Despite the success of this theory, the early twentieth century found it unable to describe certain aspects of the photoelectric effect.

When exposed to light, certain materials release electrons. Studying this effect, researchers found that for a fixed frequency of light, the rate of electron emission is directly proportional to the intensity of the indecent incident light, but if the frequency of the light was below a certain threshold, no electrons would be emitted no matter how intense the light was. It was no longer a matter of how much power was being imparted to the photoelectric material -- a very high-power, but low frequency source was incapable of liberating electrons, while a source with significantly lower power output at a higher frequency would liberate electrons.

This effect was explained by describing the light as a stream of particles, called "photons". Each photon has a small amount of energy which is proportional to its frequency. More intense light has more photons, but each photon has the same energy. The electrons in the photoelectric material only interact with one photon at a time, so if a single photon doesn't have enough energy to liberate an electron, no electron will be liberated no matter how many photons per second are interacting with the material.

Needless to say, this description of light as a series of particles, albeit ones with a "frequency" associated with them, conflicted with Maxwell's description.

Quantisation of energy

Prior to quantum theory, energy was thought of as necessarily analogue; taking any value it liked and acting as a smooth transition. In the macroscopic world, this observation remains fairly true. Like a hosepipe that can deliver whatever amount of water you like by turning the tap in small amounts.

For bound systems at the quantum level, such as electrons bound to atoms, energy can take on certain discrete values. This is analogous to a car that can only travel at 10, 20, 30 or 40 (and so on) miles per hour, rather than a smooth and seemless increase of speed. If you don't give it enough energy to make the transition between 20 mph and 30 mph, it'll stay at 20 mph. This forms the basis of spectroscopy - and without this quantisation of energy, such analytical tools would be impossible.

To muddy the waters even further, particles need not be in a single energy state at all, but might be in what is called a "superposition of states". Using the previous car as an example, this is analogous to that car travelling at 20, 30, and 50 mph all at once. A particle in this state cannot even really be said to have an energy, although it can be said to have an average energy depending on how much of it is in each state. Some scientists suspect that superposition states will vanish when quantum, theory is further refined.

This superposition of states is fundamental to the idea of "wavefunction collapse" in the Copenhagen interpretation[3], which states that an observation of energy forces a particle that was in a superposition state into one of the states it is composed of with various probabilities depending on the specifics of the superpostion. So a measurement of the quantum car in a superposition of 20, 30, and 50mph will show the speed as 20, 30, or 50mph, and after the measurement the car will be in the single energy state corresponding to whichever speed you measured.

Particle-wave duality

Classical mechanics treats particles and waves as different things. A particle is a point, a speck with mass and an exact location. A wave is a little more abstract but it has wavelength - it's spread out, with frequency and speed. In quantum mechanics there is no distinction. Particles can be waves and waves can be particles - although really they're something else entirely with the properties of both. We've evolved in a macroscopic world where we can see a distinction, but there isn't in the quantum world.

The evidence for this comes from two experiments. Classically, light was treated as a wave - there was no quanta or a concept of individual particles, just waves of energy. This explained Isaac Newton's optics pretty well. However, work done on something called the photoelectric effect, which Albert Einstein won the Nobel Prize for, smashed this interpretation. Einstein noted that the details photoelectric effect - where a metal gave off electrons when exposed to light of discrete kinetic energy - could only be explained if light was a particle. If light consisted as particles then it would explain why the effect was instant (waves would take time to absorb as light waves are hundreds of times larger than atoms), that energy given off was proportional to the frequency and there was a cut-off point where the effect didn't happen below a certain frequency. Each photon carried a discrete amount of energy, proportional to its frequency, and delivered it to the metal. Needless to say, starting to describe light as a particle seriously caused issues with optics and the concept of frequency; waves can have a frequency, but particles cannot.

After this, however, came the double-slit experiment. This experiment fired electrons through two slits. Under classical mechanics, the electron was a particle. The last thing you would expect from a particle being fired through two slits would be an interferrence pattern but this is what was observed. The electrons were exhibiting interference; a properties of waves. The extra "spooky" part was that when the electrons were reduced to the point where only one would flow through the slits at a time the pattern was still seen; not only did the wave of the electron intefere with other electrons, it interfered with itself.

From these observations, particle-wave duality was born. At the quantum level, there is no clear distinction between waves and particles. Various interpretations have been put forward to explain this in a way that "makes sense" - however, all suffer from the fact they are trying to interpret quantum mechanics as classical mechanics.

Uncertainty

See the main article on this topic: Uncertainty principle
"How do the Heisenberg compensators work?"
"They work just fine, thank you."

With the wave-like nature of quantum mechanics established, problems began to arise in figuring out the location of particles. Waves do not have a specific location; they're spread out over an area and aren't described the same way as particles. Thus the "uncertainty principle" was established; in short it means you cannot know the location and momentum of a particle to the same degree of accuracy. This isn't a limit in scientific instruments but a fundamental aspect of physics. As one editor likes to explain it, even god can't know the location and velocity of particles at the same time. It is a physical impossibility.

This effect arises from the fact that there is a series of states of a particle that have a definite momentum, and a series of states that have a definite position, but those two series of states are not the same. A state with a definite momentum is a superposition of states with definite position, and vice versa. The uncertainty principle shows that a particle can be in a state that is a superposition of a small range of momenta and a superposition of a small range of positions simultaneously, but the smallness of one of those ranges cannot be made smaller without making the other range larger.

Interpretations

There are many interpretations of quantum mechanics, which attempt to come up with an intuitive framework to explain the equations - essentially, trying to get them to "make sense" because, frankly, they really don't. Common ones include the Copenhagen and Many Worlds interpretations. Interpretations usually try to translate quantum physics into classical physics terms so our piddly ape brains can grasp it all. (Some claim not to do this and then do it anyway.)

The Copenhagen interpretation, favoured by quantum mechanical pioneer Neils Bohr, envisages that the wavelike behaviour of particles "collapses" upon observation. It proposes that superpositions of states should be taken extremely literally and that a wavefunction is nothing more than an abstract concept that just reflects our uncertainty and lack of knowledge prior to an observation. It's illustrated best by thought experiments such as Schrödinger's cat, whereby a cat is thought to be both dead and alive at the same time until observed (although Schrödinger did initially propose the experiment to show the absurdity of extrapolating the Copenhagen interpretation to macroscopic objects, people still take it literally). Objections to the Copenhagen interpretation evoke its non-deterministic nature. The many worlds interpretation, invented in 1957 and popularised from the 1970s on, states that the apparent randomness and statistical nature of quantum mechanics is caused, literally, by the universe splitting into different sections each time an observation is made. This interpretation rejects the wavefunction "collapse" of the Copenhagen interpretation and seems to be favoured by physicists who enjoy science fiction. There are many other interpretations[4] and a minor industry of physicists coming up with them.

The problem with interpretations of quantum mechanics is that it's the same mathematical theory, and these interpretations are experimentally indistinguishable. This leads to attempts to discriminate between them on subjective piddly ape brain criteria such as intuitive beauty, invocation of Occam's razor, thought experiments (rather than the physical kind) and so forth. This means that even an intellectually honest interpreter ends up writing pseudo-philosophy which is not scientifically rigorous, objective or testable. If you work on the interpretations right, you can get QM to say whatever on earth you first thought of before starting. While interesting, the interpretations are the bane of a philosophy of science known as instrumentalism, which states that theories be judged entirely on predictive qualities, not their ability to make sense to our particular brains.

See also

Footnotes

  1. http://lesswrong.com/lw/hs/think_like_reality/
  2. On the other hand, he then comes up with his own idiosyncratic interpretation, declares this reality and uses it to support his personal philosophies on LessWrong.
  3. Other interpretations of quantum mechanical observation that don't involve wavefunction collapse, such as the many-worlds hypothesis, are postulated, but the wavefunction collapse interpretation is one of the oldest and easiest to describe.
  4. http://en.wikipedia.org/wiki/Category:Interpretations_of_quantum_mechanics
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