A relatively brief introduction to modern physics

Preface

Fist of all, I honestly did not mean the title as a pun. It happens to be an accurate description of what this post is. Consider this post a precursor to my actual post on string theory. Though I may address it, I don’t intend to discuss the details of string theory here. This post will serve as a brief introduction to post-Newtonian physics. It is important to understand some key ideas before we delve into string theory.


Second, I realize that this is a massive post. I don’t expect many of you to read it in one sitting, if anyone decides to read it at all. If you do decide to read any part of this feel free to ask me any questions if a concept isn’t clear to you. I can’t promise that I can convey it better, but I will try.

Before I start, I must give credit where credit is due. Though there are other sources where I have learned about string theory, special relativity, general relativity, and quantum mechanics most of my understanding on these subjects comes from Roger Penrose’s Road to Reality, Brian Greene’s The Elegant Universe, and Stephen Hawking’s A Brief History of Time.



I want to reiterate that my understanding on these topics is primitive, and there is a (strong) possibility that some of what I post below may contain some inaccuracies. For a better understanding of these topics I strongly recommend reading Greene’s book. For a mathematical foundation on these topics, Penrose’s Road to Reality is excellent. If you aren’t at graduate level math yet, don’t be alarmed. Penrose’s book will walk you through all the mathematics you need to know, although a basic understanding of calculus will be extremely helpful.


Though I have a lot of interest in biology and chemistry, I find physics to be the most fascinating of all sciences. I consider it to be the “purest” form of science. Physicists attempt to model the universe through mathematical equations and manipulate these equations to predict and rationalize new observations.

What is Modern Physics?

There are two major branches of modern physics, one dealing with events on a cosmic scale, and the other dealing with events on subatomic scales. General relativity is the foundation of modern cosmology, and quantum mechanics is the foundation of subatomic physics. Each theory has been heavily tested and has been shown to be unfathomably accurate. The fact that these theories are mutually incompatible has perplexed physicists for the past several decades

The idea that the universe is governed by two sets of laws, one for massive objects, and the other for subatomic objects, is dubious and unsatisfactory. For years, physicists have been working on making these two theories concordant with each other, but with little success. Einstein went as far as rejecting many of the axioms derived from quantum theory, and doubted the validity of the theory altogether. Nevertheless, both theories have withstood the test of time thus far.

The Greeks hypothesized that all matter is made of fundamental, indivisible units. Not too long ago, these parts were thought to be atoms. In the 20th century we discovered that atoms could be further broken down into protons, neutrons, and electrons. Later, we learned that protons and neutrons could be further broken down into quarks. The majority of matter that we encounter is composed of quarks and electrons. Many contemporary physicists believe that quarks and electrons can not be broken down any further. String theory, or superstring theory, claims otherwise. According to string theory all fundamental particles of matter consist of a tiny, vibrating, one-dimensional loop. The properties of fundamental particles are a consequence of the different ways a string can vibrate. Looking at matter as such may reconcile the differences between quantum mechanics and general relativity. Furthermore, string theory may soon be able to put up the claim as being the elusive “theory of everything” as it describes and unifies the fundamental particles and forces of the universe.

Constituents of the Universe

Different combinations of up-quarks and down-quarks make protons and neutrons. Everything you see appears to be made of up-quarks, down-quarks, and electrons. However, there is evidence that the universe consists of more particles. A fourth fundamental particle called a neutrino was discovered in the 50’s. These particles hardly ever interact with other matter, so their presence is difficult to detect. Up-quarks, down-quarks, electrons, and neutrinos make up one family of particles.

Two other families of particles exist, each having analogous particles to the first family. The major difference between the families is that the particles of family 2 are more massive than particles of family 1, and the particles of family 3 are more massive than family 2. Most particles from family 2 and 3 exist ephemerally, and are only seen through high-energy collisions in particle-accelerators. It is possible that such particles have not existed since the big bang except through high energy collisions in labs.

Each particle from each family also has an antiparticle. These antiparticles are identical in mass, but opposite in other respects. When a particle collides with its antiparticle they annihilate each other producing pure energy. This is the reason antimatter is only seen in laboratories. It is possible that other galaxies of the universe are composed entirely of antimatter.

Though we can verify the existence of all these particles, we don’t know many “whys.” For instance, why 3 families? Why not 4, or 6, or just 1? Why does each particle have a seemingly arbitrary mass? Why not some other number? String theory offers plausible explanations for these questions.

Four Fundamental Forces

There are also four fundamental forces in the universe: the gravitational force, the electromagnetic force, the weak nuclear force, and the strong nuclear force. At the microscopic level, each force has an associated particle: the graviton, the photon, the boson and the gluon, respectively. You can think of each of these particles as the smallest packets of any given force, somewhat like the atom was once considered to be the smallest packet of matter (though we now know that this is not true).

We are most familiar with the gravitational force. It is the force that keeps the planets orbiting the sun, the sun orbiting the center of the galaxy, and the force that holds you and me to the Earth. Gravity is always attractive, and the force of gravity is directly proportional to the mass of the two interacting objects, while inversely proportional to the square of the distance between the two objects. Gravitons are the only particles mentioned above which have not been experimentally verified, however physicists are fairly certain that they do exist.

We are also familiar with the electromagnetic force. You have experienced this force when you get a small shock on a dry day from touching metal, when you power up your computer, or when you witness a lightning storm. The electric charge of an object, when dealing with the electromagnetic force, is analogous to the mass of an object when dealing with the gravitational force. The electromagnetic force can be attractive or repulsive. An object with a net positive charge will repel another object with a net positive charge, and attract an object with a net negative charge.

Strong and weak nuclear forces are less familiar to us because they operate on a subatomic level. Though they are extraordinarily strong forces, their strength rapidly diminishes as the distance between two objects increases. The strong force is responsible for holding the quarks inside a neutron and a proton together, and holding the nucleus of an atom together while the weak force is best known for causing radioactive decay. Particles have intrinsic strong and weak charges that determine how the strong and weak force between two particles will interact.

There are huge discrepancies in the relative strengths of the forces. For instance, the electromagnetic force is tredecillion (10^42) times stronger than the gravitational force. Why? If the relative strengths between the forces were even slightly different, the universe would be a much different place. Why is gravity only attractive? Why does the influence of gravity and the electromagnetic force extend over large distances whereas the influence of the strong and weak nuclear force quickly diminishes over distances. String theory again offers a plausible explanation for these questions. Not only that, it unifies the four forces into one, something that Einstein spent the latter years of his life diligently working on.

Special Relativity

In the 19th century, James Maxwell discovered that all electromagnetic radiation, including visible light, traveled at a certain fixed speed. This speed is the ultimate speed limit of the universe. As far as we know, there is absolutely no way to exceed this speed. [1] One interesting property of light is that it will appear to travel at the same speed regardless of relative velocities between two different observers. This is a bit counter-intuitive. If you are traveling at 40 miles an hour, and a car in the other lane is traveling in the opposite direction at 40 miles an hour it would seem there is approximately an 80 mile per hour difference between your two velocities. Similarly, if you are traveling at 40 miles per hour and the car next to you going in the same direction is also traveling at 40 miles per hour, it would seem like the car adjacent to yours is stationary. However, regardless of how fast you may go, light will always appear to go at the same speed. This concept is the basis of special relativity.

Special relativity claims that observers in relative motion will encounter the phenomena of time dilation and space contraction. In other words, if I am moving with a certain velocity relative to you, the clock on my arm will tick slower than the clock on your arm. Relative motion also has an effect on perceived simultaneity. Also, the length I measure of a vessel in motion from inside will be different than the length a stationary observer calculates.

But what exactly does stationary mean? Is there some uniform medium that permeates the entire universe which we can measure our speed against? At one point, physicists believed in such a medium, termed aether. Today, the definition of stationary has changed a bit. Anyone who remains at a constant velocity can make the claim of being a stationary observer. Velocity is meaningless unless a relative reference point is also given.

Next, lets define what exactly speed is. Speed is the measure of some distance covered in a certain duration. Termed as such, this is an insipid definition. Keep in mind, however, that distance is intrinsically linked with space, and duration is intrinsically linked with time. Revamping our understanding of speed, as the constancy of the speed of electromagnetic radiation forced us to do, consequently required us to revamp our understanding of both space and time.

Time dilation and space contraction occur even when you are simply driving your car. The reason that they are not noticeable is because they occur on an extremely small scale. The closer one gets to the speed of light, the more noticeable the effects of time dilation and space contraction become.

In order to show why time dilates lets devise a special kind of clock. This clock consists of two parallel mirrors facing each other. In the middle of these two mirrors we will put a photon, the smallest quanta of light. This photon will bounce off of the two mirrors indefinitely. We will define the time that the photon takes to traverse the vertical distance between the two mirrors as a billionth of a second. Once we start the clock up, the photon keeps bouncing back and forth. It is a simple contraption, yet a very accurate clock. Now, what happens if instead of watching the photon bounce between the two mirrors while the clock is stationary compared to us, we set it in motion? Once the clock is set in motion, we will notice that the photons take longer to traverse the distance in between the two mirrors. The reason for this is that the photon must not only traverse the vertical distance between the two mirrors, it must now also traverse the horizontal distance that the mirrors have traveled in the time it takes the photon to traverse the vertical distance between the two mirrors. A stationary observer will notice the photon traveling at an angle. Keep in mind that the photon is traveling at the same speed whether it is stationary compared to an observer or whether it is moving compared to an observer. Since the photon has to travel further when in motion relative to us at its original speed, it will take longer for it to cycle between the mirrors. Note that the faster the clock is moving compared to an observer the further the photon will have to travel, therefore the more time will dilate. Also, note that since the clock has a constant speed it has the right to make the claim that it is stationary. Since the photon is moving with the same speed as the mirrors, from the clock’s perspective the photon will bounce back and forth between the mirrors in the same time that it did when it was stationary compared to us. Essentially this shows that an observer moving with the same speed as the clock will notice a different cyclical rate than an observer moving at some other speed.

As I mentioned before, relative motion also affects perceived simultaneity. To demonstrate this lets set up a different scenario. Let’s have two people sitting at opposite ends of a train facing each other equidistant from a central light source. Once the light reaches each person, he must immediately stand up and begin doing jumping jacks. To an observer on the train, it will look like each individual begins doing jumping jacks simultaneously as expected; however to an observer outside the train it would seem that the person at the back of the train began doing jumping jacks before the person near the front of the train. Both observers on the train and observers outside the train would be correct in their assertion. The reason for this is because to an outside observer the individual at the back of the train is moving towards the light wave while the individual at the front of the train is receding away from the light wave; therefore the light wave has to travel a shorter distance to the individual at the back of the train. Since light moves at the same speed in all directions, it will arrive at the back of the train first since it has to travel a shorter distance to get their, and therefore the individual at the back of the train will seem to have started his jumping jacks before the individual at the front of the train. This example shows how relative motion affects perceived simultaneity of events.


Based on our understanding of relative motion’s effect on time, we can easily see the effects it has on space as well. For instance, let’s say there are two people, Sov, and KA, Sov in a car and KA outside. When the car’s front bumper passes a certain marker both people start a stopwatch, and when the cars rear bumper passes the same marker both people stop their stopwatch. Both people calculate the length of the car by multiplying the speed of the car by the time elapsed in between the front and rear bumpers passing the marker. Since from Sov’s perspective he is stationary, he knows that KA’s watch is running slower than his own, therefore he knows that KA will have calculated the car’s length as shorter than what Sov would have calculated it to be. Essentially, relative motion causes space to contract. As a car moves faster and faster, the distance between its front bumper and rear bumper lessens.


It is an important fact about our universe that space and time are intertwined. It is not correct to think of them as two separate ideas, but rather as one single idea – spacetime. Time is simply the fourth dimension. In fact, it may help to describe the effect of motion on spacetime.


Again, we’ll use a car analogy. If a car is traveling supposed to travel 100 miles west, and it’s traveling at 100 miles per hour towards the west, it is safe to assume that the car will reach its destination in one hour. However, if some of that speed were deflected to a southward direction so the car was moving southwest, it would take the car longer to travel 100 miles west. And if it were moving completely in a southern direction, it would never complete its journey towards the west. Similarly, all matter is constantly traveling through spacetime. In fact, all matter travels through spacetime at the speed of light. Our motion is simply far more directed in the time dimension than in the three spatial directions most of the time. Note, the faster we move in the three spatial directions the slower we move in the time dimension. Also, note that since photons move at light-speed through the three spatial dimensions, they do not move through the time dimension at all. That means a photon that has been around since the big bang has not aged at all.

General Relativity

The development of special relativity gave rise to another problem in physics. According to Isaac Newton, and the accepted theory at the time, gravity was a force that was felt instantaneously. This means that the presence of mass sent the information of its presence across universal distances at a speed faster than light. According to special relativity, this was simply not allowed.

Newton’s theory of gravity fell short on one other point as well. Though it defined the effects of gravity superbly, it did not actually describe what gravity was. In his book, he left his readers to figure that out.

Again, Albert Einstein stepped in to solve this problem. He realized that an object in the presence of a gravitational force is no different than an object experiencing accelerated motion. In other words, if you were trapped in a box you would have no way of knowing whether you were on earth, or accelerating through a vacuum at 9.8 m/s2. This realization eventually lead him to the conclusion that matter warps the fabric of spacetime. I will explain what this means a bit later, however for now it is important to know that Einstein’s conclusion solved the problem of the instantaneous gravitational effect, and also described exactly what gravity is. Let’s try and examine some of the logic Einstein used to come to his conclusion based on what we know about special relativity.

For the following set up, it is important to know that any object in circular motion is constantly accelerating. Though its angular speed may be the same, its linear velocity is constantly changing due to a change in the direction of its motion. If you have ever been inside a twister ride, it may be easier for you to follow this example. For those that haven’t, the twister ride basically has many people inside it. Once the ride starts, it picks up angular speed. The people inside feel an outward push, and are eventually pinned to the wall. If the ride were suspended in a vacuum, this would basically act as gravity. The wall could be considered the floor.

To see the curving of space we must examine the circumference and radius of the ride while in motion. From above, we know that the length of an object in motion will contract in the direction of its motion. Therefore, the circumference will contract while the ride is on. However, since the radius of the ride does not move in the direction of the motion, it does not contract. How is it possible for one radius to produce a circle with two different circumferences? Well, in Euclidean geometry, it’s not. However, if we assume that space curves during acceleration, and assume that it is not flat during the ride as Euclidean geometry would have us believe, then this is possible. For instance, a circle with radius r on a sheet of paper will not have the same circumference as a circle with radius r drawn on a sphere.

We know that an object in the presence of a massive body and a body in accelerated motion are practically the same thing. Knowing this, Einstein postulated that mass, which causes gravity, warps space around it. Imagine stretching a bed sheet out by its four corners. Now, imagine placing a bowling ball in the center. Just as the bowling ball warps the fabric of the bed sheet around it, a massive body warps the fabric of the cosmos around it. From this example, we can see that many of the conclusions derived from general relativity match Newton’s observations. The further out you get from a massive body, the less space is warped. Also, the more massive a body, the more space is warped. This agrees with Newton’s findings. Einstein’s theory takes Newton’s theory one step further. It defines exactly what gravity is: the bending of spacetime. Also, Einstein’s theory conforms to the rules of special relativity. Gravity’s effect is no longer instantaneous.

How exactly does a satellite stay in orbit? Imagine the same setup as before except this time add a ping pong ball. Assuming that the bed sheet is frictionless, if you give the ball a sufficient speed inside the depression created by the bowling ball, the ping pong ball will continue to endlessly orbit the bowling ball. If the ball had no initial velocity, it would fall into the bowling ball just as expected.

There are a couple of pitfalls to this example, however. In the case of the bowling ball, it is due to the force of gravity that the bed sheet is bent. This is not the case when considering the effects of mass on space. The mass itself warps the space around it. It does not require the presence of an outside force for assistance. Secondly, when considering the ping pong ball, it is again the force of gravity which is keeping the ping pong ball in orbit rather than having it fly away on a tangent. This is not the case for a satellite orbiting a star or a planet. Rather, the satellite takes the path of least resistance. Warped space causes these paths to be curved. Keeping these facts in mind, the bowling ball analogy is perfectly acceptable to help visualize the concept of the curving of space.

The above example gives a concept of the warping of space. I can’t think of an acceptable analogy that will convey the warping of time. However, know that acceleration, and gravity, do cause time to warp. The greater the magnitude of one’s acceleration, the slower time passes. In other words, time moves slower in Houston than in Denver, albeit the difference being far too small to measure. However, in the presence of a sufficiently massive body the warping of time could be easily observed. Near the event horizon [2] of a black hole, time could conceivably be 10,000 times slower than here on Earth.

The Big Bang

A revelation from the mathematics of general relativity revealed that the universe can not be static. The universe either had to be expanding or shrinking. The idea of a non-static universe was too much for even Einstein to handle. He added a cosmological constant to his equations just to ensure that the universe stayed static. 12 years after Einstein’s mathematical formulation of general relativity, Edwin Hubble experimentally showed that the universe was expanding. Einstein went back and removed his cosmological constant from his equations and called it the biggest blunder of his life.

Since space is expanding, what would happen if time were to run in reverse? We would find that space was constantly condensing. As the universe compresses, it becomes hotter. If we run the clock back approximately 15 billion years, it would seem as though all the energy and matter in the universe, everything making up the cosmos, is condensed into a singularity. From this singularity, a rapid expansion of spacetime erupted. Originally the temperature of the universe was extremely hot. However, it is inaccurate to think of the big bang as an explosion. An explosion happens at a certain time and place. The big bang was a rapid expansion of everything.

I do not intend to cover the evolution of the universe in this post, nor do I intend to defend this theory from its (mostly non-scientific) critics. It is important to understand that this theory is not some crazy old kook’s inane rambling. It is supported by a plethora of theoretical and experimental evidence. Most likely, this theory will not be replaced. New evidence may cause scientists to revise the theory of genesis, however most physicists believe that additional evidence will support, or help develop our understanding of the big bang, not overthrow it.

Still to come:

Wave-Particle dual nature of light
Wave-particle dual nature of matter
Heisenberg's uncertainty principle
QM vs GR

Looks good from what I got through, first four posts, I'll have to come back and get the rest when I'm sober and feel like learning.

Looking good, I love Physics.

The Wave-Particle Dual Nature of Light

In the 17th century there was much debate about the nature of light. Newton advocated a particle nature of light, while others argued that light was a wave. Early in the 19th century, a scientist named Thomas Young carried out an experiment which is now known as the double-slit experiment. At that time Young’s conclusions nullified Newton’s theory on the nature of light.

It is worth describing Young’s double-slit experiment here, as it will provide a startling insight into the nature of matter in the next section. His experiment was simple, and is easily reproducible. Essentially, it consisted of three flat pieces of cardboard, a powerful flashlight, and a wall to shine the flashlight towards. Each piece of cardboard had slits in them. The first piece had a slit towards its left side, the second piece had a slit towards its right side, and the final piece had two slits, one on the left side and one on the right side. When the piece of cardboard with the slit on the left side was placed between the beam of light and the wall, the wall had a single “streak” of light towards the left as expected. Similarly, when the cardboard piece with the slit on the right was placed between the wall and the beam of light, a streak of light towards the right was observed. If light truly has a particulate nature then when the third piece of cardboard is placed between the beam of light and the wall then we should see two streaks of light. Instead, what is observed is an interference pattern, a wave phenomenon.

Any amount of cash you have can be represented by an integer number of pennies. This is the fundamental American currency denomination. In 1900, Max Planck postulated that there is a fundamental energy denomination for light. Light can carry energy only in integer multiples of this fundamental energy denomination. Planck also postulated that the energy carried by light is proportional to its frequency.

The phenomenon that gave us insight into the particulate nature of light is known as the photoelectric effect. By the beginning of the 20th century the phenomenon had been well established, however there was no universal concurrence in the physics community as to what the consequences of the observations were. Once again, Einstein stepped in to enlighten the physics community. He would eventually be awarded the Nobel Prize for his explanation of the photoelectric effect.

In first year chemistry, you learn that metals have loose valence electrons. This is why they are such good conductors for electricity. This is also the basis of the photoelectric effect. When light strikes a metal, it dislodges some of the valence electrons. This in itself is not too puzzling. What baffled physicists was the fact that no matter what the intensity of the light was, the dislodged electrons moved with the same speed. Intensity of light only affected the number of electrons that were dislodged.
However, if the frequency (color) of the light was changed, the speed that the electrons were ejected at changed. What was more bewildering was the fact that below a certain frequency, no electrons were ejected at all despite the blinding intensity of the light.

Einstein postulated that light was quantized in little packets called photons. This simple assumption explained all the observations of the photoelectric effect. Instead of the light-wave being dispersed evenly throughout the entire metal, implying that the intensity (total energy) of light should directly affect the energy of an ejected electron, a single photon only carried a fixed amount of energy, and this is why an electron’s speed was invariable with intensity since only a single photon will strike an electron. It also explained why electrons weren’t ejected below a certain frequency. The energy carried by the photon was simply not enough to dislodge the electron at these low frequencies. With increasing intensity, more photons were fired at the metal; therefore more photons struck and dislodged more electrons. Hence, the particulate nature of light was revealed.

This is some of the last stuff we talked about in my last physics class. And that each point of a wave can be a source. Like with light any point on the wave can be a point light source. Electrons act like both particles and waves too methinks.

Electrons act like both particles and waves too methinks.

That's where the real weirdness starts. That will be my next post...either tonight or tomorrow. Depends on how bored I am.

Wave-Particle Dual Nature of Matter

Things get increasingly peculiar from here on out. Relativity forced us to reexamine our basic assumptions of time and space, but quantum mechanics is absolutely absurd. It would appear at the quantum level the universe acts in a way so obscure and contradictory to the familiar that even physicists have trouble making sense of it.

In 1923, Prince Lous de Broglie reasoned, roughly speaking, that Einstein, through special relativity, equated matter with energy, Planck related energy with waves, therefore matter may have wave-like properties as well. De Broglie’s theory was soon verified experimentally by the double-slit experiment. Rather than using a wall, however, a phosphorescent screen was used to track the end-locations of electrons. Even if a string of single electrons were fired they somehow found a way to interfere with each other, creating the interference pattern akin to waves. This was a remarkable discovery. Physicists were forced to conclude that matter exhibited wave-like properties in conjunction with particle properties more commonly associated with matter.

There is another interesting phenomenon associated with this experiment. What if you wanted to ‘look’ and see which slit an electron went through? One way to do this would be to shine light on the electron to see it – that is bounce photons off of it. The problem with this approach is that by doing this, you have modified the experiment. On macroscopic scales the energy carried by a photon is negligible, but when dealing with something as miniscule as an electron the energy carried by a photon could severely alter the trajectory of the electron. When this is done to the double-slit experiment, the resulting pattern on the phosphorescent screen is no longer an interference pattern, but it is a pattern we would expect if electrons only had particle properties. It’s as if the electrons know they are being watched and respond accordingly!

The logical question that follows from these realizations is how do these conclusions coincide with real world experiences. When de Broglie mathematically determined the wavelength of matter waves, he found that they are proportional to Planck’s constant. Since the constant is so small, the wavelength of matter waves are also consequently small.

The next question I suspect most people would have is what exactly is matter a wave of. The answer proposed by Max Born in 1926 is perhaps the most shocking conclusion of modern science. Born suggested that the electron wave is actually a probability wave of where the electron will be found. In other words, at the fundamental level, the universe intrinsically has a seed of randomness. This has interesting consequences on the philosophy of determinism, which I intend to discuss in the next section.

This means that if an experiment involving a fundamental particle of the universe such as an electron were repeated multiple times in an identical manner the results would vary with each experiment. Erwin Schrodinger defined an equation for the probability wave. Though quantum experiments can’t be reproduced identically, the probability wave created by iterated experiments can be mathematically modeled, tested and reproduced. The probability wave has been tested and reproduced with high-fidelity making Born and Schrodinger’s counterintuitive suggestions a valid scientific theory and a seemingly accurate description of the quantum world.

Following WWII, Feynman took quantum theory in a new direction. Richard Feynman’s perspective did not change the mathematics behind quantum mechanics but he provided a new way to analyze the probabilistic nature of matter. Feynman theorized that electrons did not travel through only one slit in the double-slit experiment, but through both slits simultaneously. Not only that, the electron traversed every possible trajectory it could take. It went smoothly through the left slit. It went zig-zagged through the right slit. It took a trip to the Andromeda galaxy and came back. Feynman assigned a number to each of these paths. When he averaged them out he found the exact same result as the probability wave of Born and Schrodinger. This drastic change of perspective alleviated the quantum world from the compulsory probability wave but proposed something perhaps more bizarre.

Once again, it is important to answer why these effects are not noticed on a macroscopic scale. Feynman showed for all particles larger than atoms his method of assigning numbers to paths allows all paths except one to cancel each other out, What we’re left with is the path that us macroscopic sentients are familiar with.