Quantum Physics | What is Quantum Theory? – Video & Lesson Transcript …

Origin of Quantum Theory

In the 1900s, the field of Physics seemed, for the briefest time, to be at a halt. We were, however, at the brink of the discovery of one of the most revolutionary theories proposed to date: quantum physics. This theory was developed by a German physicist named Max Planck: he proposed that the energy of electromagnetic waves, unlike previously thought, was not a continuum, but rather, that there was a minimal, unbreakable, quantifiable unit of energy, that we call quanta. Plank's theory was shortly thereafter extended by Einstein, who found that the quantization of radiation provided an explanation for the photoelectric effect.

A lot of experiments, including the double-slit experiment by the famous mathematician Thomas Young, and Einstein's aforementioned photoelectric effect, provided extensive proof that waves and particles were not two different physical objects, but rather, that at a small enough scale, particles exhibit wave-like behavior, and electromagnetic waves (that is, light) behave as if they were tiny massless particles made of units of energy: the famous quanta. Wener Heisenberg would further build on this idea of particle-wave duality and postulate in 1927 one of the main axioms of quantum mechanics: the uncertainty principle. This theorem tells us that, for subatomic particles, we cannot exactly measure simultaneously their position and their velocity, giving a fundamental limit to measurements, a property that is based on the wave-like nature of particles.

Finally, it was Paul Dirac and Erwin Schrodinger who formulated the mathematical framework that tied together atomic theory with quantum mechanics. They developed the Schrodinger equation, which allows us to compute the wavefunction of a quantum system, and the more general, relativistic version, called the Dirac equation. Their work ultimately led to both of them winning a Nobel prize in Physics in 1933.

The fundamental postulates of quantum theory are:

In simpler terms, a wavefunction is a probabilistic description of a system. Many times it is said that a quantum system can be in a superposition of different states, and indeed, the wavefunction represents all of the possible states on which you can find a quantum particle (for example, all of the different possible positions) and their associated probability.

$$i hbar frac{partial}{partial t}Psi(t,x) = left( - frac{hbar ^2} {2m} frac{partial^2}{partial x^2 } + V(t,x) right) Psi(t,x) $$

This equation appears difficult at first sight, but it can be broken down into pieces in the following way: the left-hand side of the equation indicates the time evolution. {eq}hbar {/eq} is the plank constant, which gives us a sense of the energy scale of the system we are working with. On the right-hand side, we find two different terms, the first one involving the velocity of the particle, and thus corresponding to the kinetic energy, and the second one, {eq}V(t,x) {/eq}, corresponding to the potential energy.

When we measure a particle, the wavefunction is said to "collapse" - that is, the particle will not be in a superposition of states with associated probabilities anymore, but in a definite single state, corresponding to the measured quantity.

These principles have many consequences and have been used to derive many important theorems, but two of them are the most notable: Heisenberg's uncertainty principle and the existence of entanglement.

As mentioned before, Heisenberg's uncertainty principle states that one cannot know with perfect accuracy both the position and the velocity of a quantum particle. Plainly said, there is a fundamental limit on the information one can extract out of a quantum system, and this is because when we measure a particle and the wavefunction collapses, there is a loss of information happening during that collapse. Another way to understand this principle is to think about it in practice: Let's say that we have an electron and that we wish to measure its location. For that, we would need to look at the electron, either by shining a laser at it or by taking a photograph. Both processes are invasive and disrupt the state of the electron, causing a change in its internal energy, since we would be bombarding it with a ray of light. This change of energy, which is needed to determine the position, will affect the velocity of the electron. Therefore, we cannot know with exactitude the speed of the electron anymore. the same happens if we try to measure the velocity: in that case, it will be the position of the electron the one we would not be able to determine exactly.

Entanglement is a different phenomenon that occurs when two quantum particles interact. Sometimes, two interacting quantum particles can stay connected - in quantum terms this means that instead of there being two different wavefunctions, one representing each particle, there is a bigger, single wavefunction representing both of them at the same time. The result is that both of these particles stay connected, and can influence each other even if they are thousands of miles apart. The coolest (and most spooky!) thing is that, because we know that measurements affect the state of a quantum system, that means that if you separate two entangled particles and then you measure the state of one of them, the state of the other one will immediately be affected as well, no matter how far it is located.

Let's try to clarify all of these ideas with a famous example: Schrodinger's Cat.

This is a thought experiment that is aimed at illustrating the concept of superposition. Let's say we have a hypothetical cat, and that we put it inside of a box with poison, and then we close the box. We will also assume that the cat has a 50/50 chance of eating the poison. Therefore, until we open the box, we do not know with certainty if the cat will be dead or alive - there is a 50/50 chance of him being either. At that stage, if we imagine that the cat is a quantum particle, we can write the cat's wavefunction, for example, to be something like this:

$$Psi = 0.5 |text{dead}> + 0.5 |text{alive}> $$

This means that the cat is in a state which is a superposition of dead and alive: it is dead with a 50% chance, and alive with a 50% chance. Let's say that we now open the box, and find that the kitty is alive. The measurement, or the act of opening the box, has made the wavefunction collapse, and now we find the cat in a state of 100% aliveness.

Another spooky and plain amazing phenomenon that quantum particles can exhibit is that of quantum tunneling.

In the classical world, when you throw a ball against a wall, you know exactly what will happen. The wall acts as a barrier that is impenetrable, and the ball will certainly bounce back. However, this is no longer true for quantum particles. Given that quantum particles can be in a superposition of position states, they sometimes exhibit really spooky characteristics. When you throw a quantum particle against a barrier, there might be a small probability of finding the particle on the other side of the barrier. This means that, if you repeat the experiment again and again measuring the position of the particle right after hitting the barrier, while most of the times you will find that the quantum particle bounced back, a small portion of the times you will find the particle on the other side of the barrier: this is called quantum tunneling.

Today we learned that Quantum Theory is the branch of physics that studies atomic and subatomic particles, and their associated phenomena. It was developed in the early 1900s by Max Plank, and the theory was extended by many physicists including Einstein, Heisenberg, Dirac, and Schrodinger.

Quantum particles are described by a wavefunction, and when we observe them (that is when we measure them) we can alter their state. Quantum particles can be found in a superposition of states, but we do not know which one until we measure them: this is best exemplified by the hypothetical Schrodinger's cat, a thought experiment consisting of putting a cat on a box with poison, which results in the cat being in a superposition of dead and alive, with the observer not knowing until they open the box.

Some important principles of Quantum theory include the Heisenberg uncertainty principle, which indicates that we cannot know with perfect accuracy both the position and the velocity of a quantum particle, and the existence of entanglement, a long-range interaction effect that interacting quantum particles can have on one another.

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Quantum Physics | What is Quantum Theory? - Video & Lesson Transcript ...