What is Quantum Mechanics?

This is a review of chapter four in A Brief History of Time: The Uncertainty Principle. By the way, if you haven’t read chapters 1-3, you should read them in order first.

Newton’s success with gravity and other theories let the Frenchman, Marquis de Laplace around the early 19^th century to argue that the universe was made in a way such that if we knew the position and velocity of every object at one time then we could predict the future. It is understandable in the case of predicting a planet’s rotation, but predicting human behavior, that’s hard to believe. In early 20^th century, two British scientists, Sir James Jeans and Lord Rayleigh said that a hot body must radiate infinite amount of energy. To avoid this ridiculous result, German scientist Max Planck suggested in 1900 that waves were emitted in packets called quanta and making each quanta required a certain amount of energy that is higher than the frequency of the wave making the energy emitted being finite. This suggestion lead to a bigger discovery. In case you forgot, light is a wave. This suggestion about quantum made a German scientist, Werner Heisenberg to say that the longer the wavelength of an object, the easier it is to tell it’s velocity and harder to tell the position and vice-versa with a high wavelength. Because of this, Laplace’s argument might be true, but will never be used since it impossible to tell and objects’ position and velocity at the same time. This became known as the Uncertainty Principle. If you multiply the uncertainty in the position of a particle times the uncertainty of the velocity of the particle multiplied by the mass of the particle your product will always be less than a certain amount known as the Plank’s constant.

Because of the Uncertainty Principle, a new theory called Quantum Mechanics, led by Werner Heisenberg, Erwin Schrödinger, and Paul Dirac, sprang up in the 1920’s. This theory stated that objects did not have specific positions and velocity but rather a quantum state, in which they had a combination of both. In general, Quantum Mechanics didn’t predict a single observation rather the probability of that observation. This received a lot of criticism, especially from Einstein but most scientists agreed with it. Quantum Mechanics tells that things can’t be particles or waves, but it is the observation that is a particle or wave. A result of this idea is that when two wave crests and two wave troughs occur at the same time, the wave is reinforced and in phase. If the crests happen at the same time as a trough then both waves cancel each other out and the wave is out of phase.

A good example of this is the two slit experiment. This experiment is shown in the picture above. Say you have a partition with two narrow slits. There is a light source shining at it. Behind the slit is a screen. On the slit, the light creates a pattern of light and dark fringes. How is that possible? When the light passes through the slit the distance of the screen for each photon traveling through the partition is different. Because of that when the light reaches the screen, some of the light will be in phase, and some will be out of phase. The light out of phase will cancel each other out making the dark pattern and the light in phase will reinforce each other and create the light fringe. This results in the pattern of light and dark fringes. Now the remarkable thing about this experiment is that if you replace the source of light by a source of particles which have a definite speed, like an electron, you’ll get the same light and dark fringe pattern. If the partition had one slit, you would have a uniformly amount of electrons on the screen. This whole experiment is proves that waves can interfere with each other.

Before Quantum Mechanics is that the electrons should lose energy and spiral into the nucleus. That means all matter should collapse into a very high density. That can’t be true because it has not happened to all matter! A partial solution was discovered by Danish scientist Niels Bohr in 1913. He said that electrons could only orbit from certain distances form the nucleus. The problem with this is that it was seemed very reasonless. This was fixed in Quantum Mechanics because it said that the electron would travel like a wave.

Quantum Mechanics has helped in technology, creating circuits, building computers and televisions, chemistry, and even biology. General Relativity and Quantum Mechanics have not fully been combined, but will have to work together with other forces of nature to create a single unified theory of the universe.

Chapter Three: The Expanding Universe from A Brief History of Time

The third chapter in A Brief History of Time is called The Expanding Universe. This chapter first begins to talk about "fixed stars" and how they really aren't fixed. It's just that they move so slowly, they appear fixed. The book continues by talking about how small Earth is in comparison with our solar system, our galaxy, and even our Local Group. The book talks about how people know so much about stars. Scientists look at a star's luminosity and color to learn about it. If a star is brighter, it is closer, darker means farther. The scientist also use color to determine which elements a star is made of. Light is a type of wave. The largest waveleghnths to the shortest in order are: radio waves, about a meter, microwaves, o.1 meters, infared, 0.00001 meters, visible light, 0.000001 to 0.0000001 meters, ultraviolet, o.ooooooo1 meters, x-rays, 0.0000000001 meters, and gamma rays, 0.000000000000001 meters. The longer the wavelength, the more "redder" it is, the more shorter, the more " bluer" it is. If a stationary object is giving a certain wavelength, you will recieve the same wavelength. If an object is moving away, the length will be longer, if it is moving to you, it will be shorter. This is called the doppler effect and it is explained in the picture above. Edward Hubble, who was currently using wavelenghths to measure the movement of the stars, discovered that almost all stars were on the red side of the spectrum. In 1929, he published a paper saying that the entire universe must be expanding.

If the universe was expanding, shouldn't it eventually collapse? General Relativity Theory supported that the universe must be in motion. Einstien, who liked a static universe, introduced an " antigravity force" that keeps the universe in balance. The only person willing to take Hubble seriously was Alexander Friedmann. Friedmann made two assumptions about the universe: It looks approximatly identical in whichever direction you look and that this would be true wherever you were. In 1965, two American physisist, Arno Penzias and Robert Wilson, were working with a sensitive microwave detector. The detector detected an almost equal amount of microwave energy outside the atmosphere. They had accidently proved the first of Friedmann's assumptions! As for the second assumption, there has been nothing to prove or disprove it. Friedmann, seeing that the galaxies are moving apart theorized that they must have been at the same place, long ago. This led to the first Friedmann model of the universe, saying that the world began with the Big Bang and will begin to expand, and eventually contract into the Big Crunch. They're actually two other models, one stating the universe will expand forever and the other saying the universe expansion force will eventually become smaller and smaller but never quite reach zero. No one knows which model represents our universe.

A lot of people didn't like the big bang theory but it was became generally accepted. In 1965, Roger Penrose, a British mathematician said that General Relativity Theory predicted the Big Bang. He said that a star's gravity might pull all the mass into zero volume. This space-time bending phenomena is called a black hole. In the next few years Stephen Hawking used this theory, reversed it and removed technicality with complex mathematics. In 1970, Penrose and Hawking wrote a paper that proved the Big Bang. This paper used general relativity as proof, but in turn saying that general relativity is a partial theory. This therory will have to combine with the quantum theory of gravity.

Chapter Two: Space and Time

10.02.10

The second chapter of A Brief History of Time is called Space and Time. In this chapter Hawkings talks about the fact that, in zero air resistance, any 2 objects will fall at the same time. Say you have one lead ball. And then you have another lead ball that is twice as heavy. Gravity will pull on it twice as hard on it as it will on the other ball. Then how do they both land at the same time? I'm getting to that. If you have 2 cars, one 50cc and another 100cc and the 100cc one is exactly twice as big as the 50cc, they will both go at equal speeds. Same with the balls. The fact that the second ball is twice as big as the other one cancels out the fact that is being tugged by gravity twice as much as the other one giving both balls an equal acceleration.

The chapter explains how this is relevant to Newton's First Law and gravity. If the sun is twice as big, the force is twice as big. The book then explains that measuring space is not absolute. Huh, how is that possible? Say there are 2 ping-pong matches. One takes place on the sidewalk, and one takes place on a bus. Say, according to the people on the bus, the ball on this match is going at 4 miles per hour. According to the the people on the sidewalk, the ball is going 44 miles per hour. Neither of them are wrong. The ball could have moved 9 feet for the people on the bus and 39 feet for the people on the sidewalk. Therefore, space is not absolute. But time is, right?

Wrong! In 1676, a Danish astronomer Ole Christensen Roemer noticed that their seemed to be a delay in the timing of Jupiter's moon. He argued that this was because light seemed to have actually taken time to reach Earth. Until then, everyone thought light had an infinite speed. In 1865 a British physicist James Clerk Maxwell made a theory of electricity and magnetism which predicted that light should have a fixed speed. But absolute space and speed were gotten rid of because of Newton, as mentioned above. It was then suggested that a substance called "Ether" that was everywhere, even in "empty space." Light would travel through the ether like sound waves through air, and the speed should be relative to the ether. Earths was orbiting through the ether so the speed of light in the direction of our revolution should be higher than if measured in the right angle of the revolution.

In 1887, the Americans Albert Michelson and Edward Motley timed light in the direction of the revolution and of right angles and found out that the times were the same! A bunch of ether supporters tried to say why they turned up with these results, but in 1905, Einstein created the death blow to ether. He said that ether completely unnecessary if we abandon the idea of absolute time. He said that the speed of light is fixed, regardless of the viewer. This idea lead to the famous e=mc². It means that energy is mass accelerated to the speed of light. It also means that the closer you get to the speed of light, the more mass the object gains and the more energy you need to feed in. Say when you reach 10% the speed of light the objects mass will increase by 0.5 but when you reach 90% the mass will double, including all the mass accumulated till 89%. When the object reaches the speed of light, it will have infinite mass so you will need an infinite amount of energy which is impossible. Therefore all regular objects are limited and cannot go the speed of light.

Then the book talks about the four dimensions and how you can graph the relations between them: length, width, height, and time. You can use time-space graphs and light cones. Einstein explained that gravity is a result of the fact that space-time is not flat. It can be bent if an object's mass is big in enough! It can even bend light. For an example, if a distant star's light is shining close enough the sun, Earth will see the star in a different place than it really is. This was proved during a solar eclipse in 1919 by a British team. Since light is a wave that gets weaker and weaker the farther away from it's source, Einstein predicted that time appears to be slower the closer you are to the ground. This was proven in 1967 when a tower was built with a clock on the bottom and a clock at the top. The upper one slowly became ahead of the smaller one. If time and space are not absolute, this brought up questions like, did the universe have a beginning, or will it have an end.