quantum theory basics, hyperphysics momentum

quantum theory basics

Quantum theory is modern physics which describes the behavior of sub-atomic particles. It was established by two great scientists , namely Albert Einstein and Max Planck. Max Planck showed that energy of a process is quantized. Any periodic process can carry energy that is integer multiple of hv [ its frequency times Planck’s constant h]. Einstein later showed that light is composed of energy packets called photon. Planck’s theory was applied by Bohr inside atom and a successful atomic model was created. Any electron in its quantum orbit can emit or absorb light of certain frequency and jump from it. Later Schrodinger was very frustrated by this weird quantum jumping of electron.

Schrodinger cat

Luis De Broglie hypothesized that sub-atomic particles act like wave. He also showed exact relationship between matter wave and particle’s momentum which is mass times velocity. Every elementary particle like electron is a wave and every wave is a particle of some sort. In classical mechanics this effect is negligible due to short wavelength associated with the massive objects. In quantum world a tiny particle shows more waviness.

The last revolution was the Schrodinger’s wave equation which describes the wave function of particle in terms of probability. Schrodinger’s equation successfully explains Hydrogen and other simple atoms and shows how bizarre an atom looks. An electron does not exist in a definite place but it has only some probability to be in some place at a time. Electrons tend to exist at some place. This was the consequence of Heisenberg’s uncertainty principle. What we call electron is really a collection of radiations which try to be localized at some point in space.

Earlier Heisenberg stated his uncertainty principle which shocked everyone. In quantum world nothing has definite position and momenta. If we measure position more precisely the momentum becomes more uncertain and vice versa. We can not know both of them simultaneously with arbitrary precision. The nature has set a limit to our knowledge about it.

Secret of creation :

The beginning of our universe was a quantum event. General theory of relativity fails at this event when universe was very tiny and dense. Whenever small object is concerned quantum mechanics is necessary to describe its behavior. Spacetime is smooth and continuous on large scale. All the stars , galaxies and planets exist in a continuous spacetime manifold. What if spacetime may not be smooth in quantum level? It might have holes and gaps like the pretzels and doughnuts. The secret of the universe can only be traced in quantum level where everything is governed by chance and discontinuity. We do not know , in advance , when an electron will jump from one orbit to another. We only know if they do they will emit a photon of specific wavelength to go into another orbit. Nature, so it seems, is full of revolutionary occurrences , whose cause is never known. All we can predict is the probability of an outcome : like the chance of getting a six by throwing a six headed dice.

It is hard to reconcile quantum mechanics into the framework of general theory of relativity. There arise many mathematical problems while doing that. Quantum mechanics and general relativity become very antagonistic to each other. They do not shake hands at all. Quantum mechanics certainly holds the key to unlocking secrets of the universe. Three fundamental forces can be explained by the principles of quantum mechanics. Quantum mechanics has changed the view of our world completely when it comes to how these fundamental forces work. Electromagnetic force is the exchange of photons between two charge particles. Similarly strong nuclear and weak nuclear forces are carried by other sub-atomic particles like gluons and boson. Electromagnetic force is long range while strong and weak nuclear forces are short range where strong magnetic has the special property that when the distance in the nucleus increase the intensity of the force also increase. This has to do with another weird phenomena that quantum theory describes. This phenomena is quantum fluctuation.

Heisenberg’s uncertainty principle and quantum theory basics

Vacuum is not truly empty. It is full of activities dues to random generation of particle -antiparticle pairs all the time. This is also a consequence of Heisenberg’s uncertainty principle. The energy of vacuum can not be zero because in context of quantum mechanics zero is a precise number. Electron and positron pair can come into existence out of nothing. So vacuum is not truly passive . It is always seething with virtual particles and energy.

The greatest mystery is probably quantum entanglement which states that information can travel faster than light, which is also known as the spooky action at a distance. Einstein was deeply worried by this fact and unfortunately he could never come up with any valid counter argument to refute this. An electron when entangled can communicate instantly with its entangled pair over a larger distance; probably at the other side of the universe. Secret of creation or secrets of the universe deeply lies at the heart of quantum mechanics. I like to rephrase Nikola Tesla : If you want to find the secret of the universe think in terms of vibration , energy and frequency. In quantum mechanics all particles are vibrations or oscillations in their corresponding quantum field. Oscillation in the quantum field creates energy and that energy, in turns, create particles according to Einstein’s famous energy mass equivalence formula (E=mc^2). Einstein was a strong opponent of quantum theory throughout his whole life.

what is science?

Theory of relativity throws a little light on the secrets of creation. It has some philosophical consequences and some applications can be found in causal theory of perception and analysis of mind. Mind and matter are not very different from relativistic point of view. What we call mind is certain group of events connected with specific relation. These are all the events that have space-like interval between them so any other observer can judge any of two to be simultaneous. What we call matter is also a group of time-like events. What happens when we look into another people’s eye are the events connected with one light rays. These events has light-like or zero interval. Quantum theory might be more fundamental than theory of relativity but relativity is able to describe four fundamental forces. Special theory of relativity describes three forces whereas general relativity describes one force.

Quantum theory basics :

The most important basics of quantum theory may be coherence and de-coherence. In an isolated quantum system there is quantum coherence. That is , the states remain uniform and in phase. Schrodinger’s equation describes a quantum system as an smeared out probability of finding a particle like electron in space. These probability wave evolves through time. Schrodinger’s equation also states that particle can exist at different places at the same time , which is known as quantum superposition. That is what we better know as the Schrodinger’s cat. Schrodinger cat is alive and dead at the same time unless we look at it. That means, there is coherence in the system unless we observe any such quantum system. After the system is observed, the system collapsed to one of the states of the system. This can be explained as the particular state of the Schrodinger cat , which can either be dead or alive after box is opened. Decoherence is the act of observation which collapses the system. Due to decoherence the quantum system no longer remains coherent and this happens through the interaction with the environment.

Common sense and quantum theory:

There is no place for common sense in quantum theory. Our common sense always seems to be violated by quantum mechanics principles. Suppose there are several glasses and plates on a table and you through a ball on the table. The common sense tells that the ball can only hit one glass or plate at one time . But if you throw an electron then it can hit all the glasses and plates at the same time. Again suppose you have a box with a book inside it. If you open the box you would think that the book must be found only inside the box. But according to the principles of quantum mechanics the book can be found anywhere is the entire universe. This kind of weirdness is inherent in quantum mechanical world and countless experiments have proven quantum theory with precision. Einstein could not prove it wrong by his thought experiments. He was always refuted with counter arguments. One of the thought experiments was devised to refute Heisenberg’s uncertainty principle.

Heisenberg’s uncertainty principle

Einstein thought a hypothetical box containing a photon source, which weight can be measured with a spring balance system as shown. The box is under the influence of earth’s gravitational field. When the photon escapes at a particular time the box can be weighted and the energy of the photon can be measured simultaneously with time. But Neil’s Bohr showed that there will be an uncertainty of time due to the principle of general theory of relativity that Einstein discovered. The box must change its position vertically and clock at two positions of the box above the earth will tick differently. Hence there will be an uncertainty of time , which corresponds to the red-shift of the photon’s wave length. This implies the Heisenberg’s uncertainty principle of the pair energy and time ; (dE)(dt) => h/2 . Einstein was again defeated by Bohr and accidentally his own theory has disproved him in this case.

Quantum entanglement and spooky action:

This is the phenomena which deeply worried Einstein. Einstein considered quantum mechanics as incomplete theory. Quantum entanglement led to EPR paradox. Entanglement is a phenomena where information can travel faster than light. This faster than light traveling is called “spooky action at a distance”. But according to the principles of special relativity nothing travels faster than light. Suppose we have two particles like electrons or photons.

quantum entanglement

They are produced in a way that their momenta are known . Now the two particles are separated from each other at a far distance. As the momentum is always conserved , we can find momentum of one particle by measuring momentum of the other particle. This will make the state of one particle say spin dependent on the spin of the other particle. We will, thus, be able to teleport quantum information at a far distance instantaneously faster than light. This is the EPR paradox which seems to violate locality. Locality is a principle which says that we can only measure or compare local quantities. There must have causal relationship between events that are measured. This is thus the same thing as saying that nothing can travel faster than light. Quantum hidden variable theory had been devised to challenge that nothing spooky whatsoever happens in quantum world. This was developed by John Bell and an inequality called Bell’s inequality . But experiment at quantum level seems to violate Bell’s inequality. Once again Einstein was shocked by the weirdness of the quantum world. He could not prove his claim. For the rest of his life he struggled with quantum theory and its consequences.

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