Monica loves Quantum stuff as much as the next gal...here she tries to simplify it for the masses.
Quantum physics was born with XXth century thanks to the Max Planck's workson the black body radiation. According to the classical theory the energytransfers inside a black body were supposed to be continuous. This theorypredicted that the radiation intensity of a black body for a given wavelengthwas proportional to the fourth power of the wavelength (Raleigh and Jeansmodel). The resulting black body radiation spectrum did not agree with theexperiment. In addition according to this model the amount of energy radiatedby a black body would be infinite, which is obviously not physically correct.
Planck found out the correct analytical expression which depicts the blackbody spectrum at a given temperature. To achieve that it had to assume thatthe energy transfers were no longer continuous but discrete i.e. multiplesof very small quantities of energy. Planck hoped that this very small quantitiesmight have been equated to zero, thus conforming to the classical continuousview. However, it didn't work. This small quantity couldn't be nullified: he had to admit that it was a finite quantity. It was called the Planck'sconstant and represented by the letter h.
According to the Planck's model the energy transfers look discrete, discontinuousi.e. multiple of the Planck's constant (h times the radiation frequency)while the classical description of the electromagnetic field involved continuousenergy exchanges. Planck called these small and lowest amounts of energyquanta (plural of the latin word quantum whichmeans quantity). The Planck's discovery states that any energy transfer betweentwo bodies is the sum of elementary but finite transfers of quanta. Thisbrand new idea in physics contained the seeds of an extraordinary revolution: the quantum physics.
Planck was unable to interpret correctly his sound discovery so far it wasfrom the classical view of the laws of nature. The effective step towardsa good interpretation of quanta was made by Albert Einstein in 1906. Backin 1905, Albert Einstein was looking into the photoelectric effect problem.A metal surface exposed to light radiation emits electrons. Actually, theelectron emission depends on the light frequency : above a given thresholdthe emission starts. This phenomenon couldn't be well interpreted using theclassical theories. According to the Einstein's interpretation of thephotoelectric effect, the light quanta are absorbed by the metal atoms upto the trigger frequency threshold. Above it the quanta energy make theperipheral electrons no longer bound to the atom and it is then emitted.Einstein viewed quanta as finite energy "bags".
In 1906, extending his view, Einstein interpreted the quanta as lightgrains - i.e. particles of light. He called themphotons.
In 1923, a new effect was observed by Compton confirmed the existence ofthe Einstein's photons. Compton bombarded a metal surface with X-ray whichis no more than high energy light. The electrons were expelled as if lightquanta behaved such as microscopic balls punching out the electrons in themetal.
The Einstein's assumption that light is composed of particles was veryoutstanding since the Maxwell's theory of electromagnetism established 50years ago that light is made of waves. The Maxwell's theory was very successfuland rested on experimental evidence such as diffraction and interferencephenomenon. Einstein couldn't eliminate the Maxwell's theory so sound wereits foundations. So he proposed that photons might be an hybrid physicalentities, a mix of waves and particles.
If light is both wave and particle what about matter particles such as electrons? Louis de Broglie made the audacious assumption that matter could be a mixof wave and particle too. He formulated his idea in the wavemechanics. De Broglie's theory was only based on intuition, notexperiment. However, this striking new vision of matter was confirmed a fewyears later in 1925 by Clinton Davisson. He succeeded in making electronsdiffract in a crystal so displaying the wave behavior of electrons. So, onone hand electrons, protons and neutrons (i.e. matter) and on the other handphotons (i.e. light) have the same quantum nature : they are both wave andparticle ! As same as photon energy, the electron energy is directly linkedto its wave frequency E = hv where E stands for the energy, h is thePlanck's constant and v is the electron wave frequency.
Translation :
Inspired by the wave mechanics, Erwin Schrödinger tried to find outthe quanta wave equation. He started his work from the classical Hamilton-Jacobiequation and obtained a brand new wave equation describing the behavior ofquanta.
This equation is known as the Schrödinger's equation. The solutionsof this equation are the quanta waves and are commonly referred to as the"wave functions".
So matter particles and light are both quanta. Quanta behave sometimes aswaves (e.g. in the Davisson's or in light interference experiments) and sometimesas particles (e.g. in Compton scattering). Niels Bohr postulated that waveand particle behaviors are complementary descriptions of the same quantumobject. This principle was called the "complementarityprinciple". In other words, quantum objects are both a wave and aparticle !
Consider an electron. We can easily understand what a particle behavior meansfor an electron, but what is the physical significance of the electron wavefunction ?
For a photon, the wave function is just an electromagnetic wave as describedby the Maxwell electromagnetic waves equation. Electromagnetic waves aremere evidence of electromagnetic field oscillations. So the photons wavefunction has an intelligible physical meaning. The situation is radicallydifferent for the electron : electrons are not electromagnetic waves norany oscillation of known physical field ! So, what are they ?
Consider the famous light interference experiment such as the one illustratedbelow. The original light beam is separated into two coherent beams thatinterfere. One can observe on a screen perpendicul ar to the light beamsinterference figures made of succession of bright and dark strips : in brightstrips the light intensity is maximal while in dark strips it is minimal.
Translation :
Now give up the old good image of waves and let us consider photons, i.e.light quanta. We can easily state that the dark strips are dark because nophoton reach this area and in opposite bright strips are bright because lotsof photons reach them.
Photons cannot be individually identified. Consequently the distributionof them on the screen can be calculated with a statistical point of view.In this way, bright strips are locations where photons are more likely tobe while dark strips the probability of finding a photon is very low.
So the light intensity on the screen expresses the probability of findinga photon. The brighter the light is the higher the probability of findinga photon is. Now the light intensity is proportional to the square of thewave amplitude, therefore the probability of finding a photon is proportionalto the square of the wave amplitude as well. This result is fundamental :the probability of finding a photon is proportional to the square of thewave amplitude. We can rephrase this conclusion by saying : the light waveamplitude at a given location measure the probability of finding photonsat this location.
This conclusion can be extended to any quantum object and we get the followinginterpretation for any quantum wave :
The wave amplitude of a quantum object at a given location measures theprobability of finding the quantum object at this location.
Why does a quantum object behave sometimes as a wave and sometimes as a particle? What does determine the way it behaves ? As we saw above, the energy ofa quantum object is proportional to its wave frequency : E = hv. Themore energetic the quantum object, the higher the frequency. On the otherhand several experiments suggest that the higher the energy of a quantumis, the more likely particle-like its behavior is. Actually, if the wavelengthis bigger than the dimensions of the objects involved in the experiment thenthe behavior is rather wave-like. Otherwise, the behavior is more likelyparticle-like. Therefore, high energy phenomenons tend to display particle-likebehaviors.
Translation :
Basically, a measurement process consists of information - i.e. energy -transfer between the observed bodies and the observer through the experimentalapparatus. To that respect any measurement process interferes with the experimentitself. In classical mechanics the perturbations of the measurement processare supposed to be as weak as expected. Therefore physicists can theoreticallymeasure simultaneously any quantity with the precision they want.
In the context of quantum physics the quantities one tries to measure areso weak that perturbations may make the experiment outcome totally wrong.However, according to classical physics, it is theoretically possible toreduce the perturbations as far as we want. That means that the energy transferwhich occurs during the measurement process can be as weak as we want.Unfortunately, Max Planck's discovery - the quantization of energy transfers- is incompatible with the classical postulate since energy transfers arefinite or in other words cannot be as weak as one wants !
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