Cosmology Lecture 2 Mr. Kiledjian

Transcription

1 Cosmology Lecture 2 Mr. Kiledjian Lecture 2: Quantum Mechanics & Its Different Views and Interpretations a) The story of quantum mechanics begins in the 19 th century as the physicists of that day were grappling with the issue of what was to be eventually termed the hydrogen disaster problem. According to classical physics, a charged particle should radiate energy as it is traveling. When this theory was applied to the electron s orbit (this was their attempt at trying to come up with a model for the atom), it predicted that the electron should lose energy as it orbited the nucleus and eventually crash into the nucleus. So, according to classical physics, it was hard to explain the existence of stable electron orbits. Another problem was termed the blackbody radiation. (Greene s book explains this very well in chapter 4). Max Planck was struggling to explain these problems in the 1890 s and eventually he was led to believe that Energy comes in packets or bundles. Particles are only allowed to have certain Energy levels (later this was going to be termed electron orbitals). Also, particles can only emit certain packets of energy (later this was going to be termed photons by Einstein). This energy is proportional to the frequency of the wave given off and the proportionality constant was term This is now one of the fundamental constants of nature and will reappear over and over in our future discussions. In 1905 as Einstein was dealing with another problem called the Photoelectric Effect, he used the notion of bundles of energy that Planck had come up with. The essence of this effect was that light shining on a metal plate was emitting electrons from that plate, depending on the Frequency of the light. Also, the electrons were emitted instantaneously as soon as the light was shined upon them. According to classical physics, it should have taken some time to emit electrons. This proved that light comes in bundles and each bundle immediately imparts its energy to an electron. He got the for this theory in 1919.

2 Another development in the history of quantum mechanics was the experiment performed by Compton in the 1920 s which scattered light off electrons. This experiment also proved that light has momentum which is also dependent on its frequency. Building on the previous developments,. He made the assumption that not only is the energy of electrons quantized, but their Angular Momentum also. From this assumption, he worked out the math and was able to explain the existence of these spectral lines. Every time the electron jumped from a higher orbit to a lower orbit, it emitted a photon of a certain frequency. i.e. all things are quantized instead of being smooth and free-flowing. Another effect of quantum mechanics was pointing to a duality in nature waves have a particle nature and particles have a wave nature. Louis de Broglie was the next to come in the scene and in 1926 for his PhD thesis; he proposed that particles also are waves. Using this, he was able to calculate the same electron orbits as Bohr did, by claiming that a certain amount of whole number of wavelengths of these waves have to fit within the orbit of the electron This was eventually to lead to the Wave Particle duality concept. b) As soon as the ground work for quantum mechanics was laid, scientists tried to explain it by different means and formulas. Heisenberg explained quantum mechanics in terms of an Uncertainty in Nature. In other words, the very act of observing a particle, since it involves having to shine light on it with a certain frequency, disturbs the position, momentum, and energy of the particle for a split second. {Later, this was to become the basis upon which the existence of virtual particles was predicted. A particle can quickly pop in and out of existence in a vacuum by borrowing energy from the vacuum and giving it back right away!!!!!!} Heisenberg s law actually reads the uncertainty in the position times the uncertainty in the momentum > Planck s constant divided by 4 pi. Don t worry about the formula, but the interesting thing is that Planck s constant reappeared again. (Another way you can explain this uncertainty is that a Particle is actually a localized wave; therefore, one would not expect to be able to pinpoint its exact location or its velocity --> momentum is just

3 velocity times mass!!!) John Wheeler was eventually to call this quantum mechanical uncertainty and frenzy the Quantum Foam!!!!! Schrödinger also gave a mathematical interpretation to quantum mechanics by describing an object by a Wave Function. The wave function of a particle in a box is localized to that box, but the equation does predict that there is a slight possibility that the wave function does leak out!!! He expressed this wave function theory in an equation now called the Schrödinger wave equation. Schrödinger came up with a thought experiment called the Schrödinger s Cat to explain the bizarre nature of this wave function. His answer is both. The cat is in some combined state given by the total wave function of the cat. As soon as you open the box, the wave function collapses to either the state of aliveness or deadness. Wow, this is esoteric!!! Max Born came along the road and used this wave function theory and gave it a meaning of Probabilities. The square of the wave function of a particle gave the Probability of finding the particle in a certain region. When this was applied to the hydrogen atom, it predicted the same electron orbits as Bohr s equation, but it added another element. The electrons didn t just go around in circular orbits around the nucleus; instead, they existed somewhere in an electron shell ---> 1s, 2s, 2p, 3s, 3d, etc. Soon after these developments, in the 1930 s, another interesting aspect of quantum mechanics was explored. According to relativity, gravity was the effect of the curvature of space-time caused by a mass., quantum mechanics was to view gravity, and for that matter all the other forces, as an interchange of a particle. This was going to spawn the future science of Particle Physics, which we will get into in a later lecture. One object feels the force from another object and vice versa by them interchanging some kind of carrier particle among them. c) Alongside the development of quantum mechanics along the lines of physics, came its development along the lines of philosophy/metaphysics. Quantum mechanics was redefining reality, nature, and the universe. Just like relativity was to have its effect on philosophy and culture by advocating social relativity, quantum mechanics was to

4 have its effect on our definition of reality, existence, and even psychology. There is a wonderful article on this in Scientific American February 2001 edition called, 100 Years of Quantum Mysteries. For the sake of brevity, I will mention each one shortly and leave it to your imagination to decide which one is correct or if all of them are correct. Personally, I believe all of them are correct to a certain degree. One of the first was the According to this view, reality consists of 2 kinds of reality, Actual and Potential. Potential states of existence can initiate actual observed states such as quantum tunneling and virtual particle production. Potentialities can travel faster than the speed of light causing instantaneous correlations; this was to be coined non-locality or action-at-adistance. David Bohm s take on it is called. All entities and potentialities are really hidden actualities but our technique for looking and measuring them are too crude. According to this theory, signals don t travel faster than light; they don t need to. As soon as you observe an object, its hidden variable becomes an actuality. {In other words, not only is our knowledge of a particle s position and momentum uncertain, but its actual position & momentum are also uncertain.} ---> 2 protons are shot from a common source in opposite directions. He conjectured that their spins should be instantaneously correlated (up and down). Einstein saw this as a paradox and violation of Special Relativity (actually, Einstein never really liked the probabilistic nature of quantum mechanics; he has a famous quote, God doesn t play dice.) Einstein wrote a paper with Podolsky and Rosen called the refuting Bohm s theorem. According to Bell, if Bohm s thought experiment is true, then it would reveal a new aspect of nature previously unknown. In other words, Bohm s theory would seem to indicate that there is whole side of reality hidden from our view. Aspect and Bell performed an experiment similar to Bohm s thought experiment in the 1970 s and proved that it was correct. The protons did have opposite spins. They new of each other s state because they were from the same source, but otherwise there is no objective reality that is for certain. It is hidden in the particle. According to all we can say about systems is that they give rise to certain measured quantities once we do experiments on them. Thus, it divides reality into a quantum realm and a classical realm and is NOT concerned between their interplay. The observer makes actualities when they observe the system or object. Physical theories describe all we can know about reality, NOT reality itself. Therefore, this theory gives up Reality as an

5 objective entity. The observer takes the central role in the universe and is not concerned about asking, what s real and not real. Do you see how this borders on philosophy??? Richard Feynman A particle in going from point A to point B, covers all possible paths simultaneously. However, each path does not have the same probability. When applied to the universe, this would seem to indicate that the universe has evolved along infinite paths, one of which is the one we observe. That s why this view easily leads to According to this view, there are multiple universes all existing at the same time. This gets rid of the need for the collapse of a wave function once someone observes an object. What happens instead is that the observer and the rest of the universe enter the different superpositions of reality, i.e. they fall into one of the infinite number of universes existing simultaneously. According to Everett, all parallel perceptions of reality are on an equal footing. Finally comes In 1970, Dieter Zeh of Heidelberg showed that the Schrödinger equation gave rise to a type of censorship which is known as decoherence. This theory seeks to explain why the many superpositions or possibilities are not all visible at once and secondly why certain classical states of existence are chosen. It does not eliminate the need for many worlds or a Copenhagen interpretation. It states that coherent superpositions of the many worlds persist only as long as they remain secret. The environment, the object, and the observer are in a triangular relationship. In other words, our very existence, and the fact that we observe reality, force it to be a single entity. If we didn t exist, there would be infinite versions of the universe all coexisting with a different probability attached to each one. Well, so much for quantum mechanics. Coupled with relativity, it was the basis of the emerging science of Particle Physics, String Theory, and Cosmology. It will take many generations to fully realize and understand its impact.