Development of Quantum Theory

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According to theories of 1900 a perfectly insulated black body (or a cavity - like a perfectly insulated oven) would generate an infinite amount of ultraviolet energy - regardless of the heat being applied.  

Max Planck said the mistake is thinking that an infinite number of frequencies is produced and that each frequency has the same energy. He said that each frequency is associated with a single unit (or "quantum") of energy.  The size of the quanta depends on the frequency. The higher the frequency the bigger the quanta. Instead of a radiating a continuous flow of energy for an infinite number of frequencies, a black body will produce a limited number of frequencies and associated quanta. The energy output by the system is proportional to the energy input into the system.

The significance of this theory is that it expresses energy in terms of individual units or things.  At this level, the universe is no longer continuous and smooth. It is lumpy.

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In 1905 Albert Einstein wrote a paper in which he said that light is made up of tiny particles called "photons". According to his theory, the higher the frequency of light, the more energetic the associated photons. This supported Planck's view that bigger quanta correlate to higher frequencies in a black body radiator.  

Einstein proved his theory by referring to the photoelectric effect. Electrons are emitted when light strikes a metal surface. He said that one electron is emitted for each proton and that the speed of the electron depends on the light frequency - higher frequencies being associated with more energetic photons and faster-moving electrons. In contradiction to the theories of the time, Einstein's theory predicted that electrons would be instantly emitted even in weak light. Experiments proved him to be correct.

The significance of Einstein's theory is that it describes light as a particle. This contradicts  - but did not disprove - the first "two slit" experiment performed in 1803 by Thomas Young which showed that light is composed of waves. Both wave-based and particle-based experiments yield positive results. This sets up the wave/particle duality of quantum theory.

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The Rutherford model of the atom pictures a nucleus in the center with electrons orbiting like little planets.

Niels Bohr recast this model in terms of quantum theory. According to Bohr, orbits occur at fixed distances from the nucleus of an atom. Each orbit can only have so many electrons (two in the first, eight in the second, and so on).

As an atom absorbs energy quanta, electrons jump from inner to outer orbits. This is an unstable condition and eventually, the electrons return to the inner orbits. During the process of jumping back, electrons emit photons whose energy corresponds to the input energy quanta. Lower energy quanta produce light at the red end of the scale and higher energy quanta produce light at the ultraviolet end of the scale.

("Jumping"  between orbits doesn't mean that electrons are just moving fast; it means that one orbit looses an electron and the other orbit gains an electron. As quantum effects, electrons just don't move around like the objects we are used to.)

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Louis de Broglie said that matter (such as electrons) has wave properties. In other words, the electrons in Bohr's planetary model of an atom could be described as both particles and waves. Not long after this theory was presented, an experiment with refracted electrons yielded results that could only be explained if electrons are waves.

Matter,  formerly a particle was now a wave as well - and light, formerly a wave was now also a particle.

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Electrons have "state", which can be described in terms of momentum, position and other properties. Pauli said that an atom could not have two electrons with the same state.  This was called the Pauli Exclusion principle. (One state excludes another.) It has particular significance when applied to Schrodinger's wave equations described next.

(When an electron changes from one state to another it is called a "quantum jump".)

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Expanding on de Broglie's theory that matter - such as electrons - can be described as waves, Schrodinger developed equations that describe electrons as standing waves.

(Standing waves are formed by the interaction of travelling waves in a vibrating medium - like air, water, or strings in musical instruments. It happens when a wave traveling out from a source of vibration meets a reflected wave that is traveling back to the source of vibration. Traveling waves appear to stand still when an outwardly moving  wave crest coincides with an opposite, inwardly moving wave crest.)

In familiar media like air, water, or vibrating strings, standing waves are limited to forms in only three dimensions. In an atom, standing waves can take on many different forms in many dimensions - the number of forms and dimensions depending on the number of electrons in an orbit. Combing this notion with Pauli's Exclusion principle lead to the conclusion that each of an atom's orbits could only support so many standing waves - or electrons. The number of standing waves in each orbit corresponded to the number of electrons in Bohr's atomic model (although the electrons were waves not the little spherical objects that Bohr initially envisioned).

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Schrodinger viewed the waves described by his equations as something physically real.  Max Born said that was not necessary - not even possible.  He said that Schrodinger's wave equations describe probable states and not real things. Given an initial state, the equations could predict the probability of other states over time. It was not necessary for anything physical to really be vibrating.  These were waves in mathematical space only.

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Other theorists tried to explain some sort of reality behind their equations. Even Born's probability waves were still "waves".

Heisenberg said that it was inherently impossible (not just difficult) to visualize what happens in sub-atomic processes. He said that all we really know is what we observe at the beginning of an experiment and what we see at the end. This is a "behavioral" view of the world. You can only talk about what you observe. Nothing else is "real".

Two expressions of Heisenberg's views were matrix mechanics and the Uncertainty Principle.

Matrix mechanics (later known as the S Matrix) is a set of tables (i.e., a matrix) which can be used to predict the outcome of experiments given the input conditions.

Heisenberg is most associated in popular culture with the Uncertainty Principle. It says that the more you know about one property of a sub-atomic particle, the less you know about another. For example, the more you know about the position of a particle the less you know about the momentum. As noted above, this uncertainty has got nothing to do with the skill of the observer or the precision of the equipment. It is an inherent feature of the observation process.  It cannot be avoided. It is a true limit to human understanding.

All experiments involving the Uncertainty Principle show it to be true.

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By the end of this period, there were two ways to describe (not explain) sub-atomic operations. One was based on  the wave equations developed by Schrodinger. The other was based on the matrix tables developed by Heisenberg. The results predicted by the two approaches were mathematically equivalent  - although Schrodinger's equation factor in developments over time and Heisenberg's are time neutral.

Together, these two theories became known as quantum mechanics.