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If you want to describe the universe as we know it in its most basic terms, you could say that it consists of a handful of properties. We are all familiar with these properties - so familiar, in fact, that we take them completely for granted. However, under special relativity many of these properties behave in very unexpected ways! Let's review the fundamental properties of the universe so that we are clear about them.
Space is the three dimensional representation of everything we observe and everything that occurs. Space allows objects to have lengths in the left/right, up/down, and forward/backward directions.
Time is a fourth dimension. In normal life, time is a tool we use to measure the procession of events of space. But time is something more. Yes, we use time as a "tool", but time is essential for our physical existence. Space and time when used to describe events can't be clearly separated. Therefore, space and time are woven together in a symbiotic manner. Having one without the other has no meaning in our physical world. To be redundant, without space, time would be useless to us and without time, space would be useless to us. This mutual dependence is known as the Spacetime Continuum. It means that any occurrence in our universe is an event of Space and Time. In Special Relativity, spacetime does not require the notion of a universal time component. The time component for events that are viewed by people in motion with respect to each other will be different. As you will see later, spacetime is the death of the concept of simultaneity.
Matter in the most fundamental definition is anything that takes up space. Any object you can see, touch, or move by applying a force is matter. Most people probably remember from school that matter is made up of millions of billions of tightly packed atoms. Water, for example, is the compound H2O, meaning two hydrogen atoms combined with one oxygen atom forms one molecule of water.
To fully understand matter let's look at the atom. It is now generally accepted that atoms are made up of three particles called neutrons, protons, and electrons. The neutrons and protons are found in the nucleus (center) of the atom and the electrons reside in a shell surrounding the nucleus. Neutrons are heavy particles, but they have no charge - they are neutral. Protons are also heavy particles and they have a positive charge. Electrons are light particles and they are negatively charged. There are many important features that arise from considering the number of these particles in each atom. For example, the number of protons an atom has will determine the atom's place on the periodic table, and it will determine how the atom behaves in the physical universe.
It is first essential to realize that the world Aristotle saw around him in everyday life was very different indeed from that we see today. Every modern child has since birth seen cars and planes moving around, and soon finds out that these things are not alive, like people and animals. In contrast, most of the motion seen in fourth century Greece was people, animals and birds, all very much alive. This motion all had a purpose, the animal was moving to someplace it would rather be, for some reason, so the motion was directed by the animal's will. For Aristotle, this motion was therefore fulfilling the "nature" of the animal, just as its natural growth fulfilled the nature of the animal.
To account for motion of things obviously not alive, such as a stone dropped from the hand, he extended the concept of the "nature" of something to inanimate matter. He suggested that the motion of such inanimate objects could be understood by postulating that elements tend to seek their natural place in the order of things, so earth moves downwards most strongly, water flows downwards too, but not so strongly, since a stone will fall through water. In contrast, air moves up (bubbles in water) and fire goes upwards most strongly of all, since it shoots upward through air. This general theory of how elements move has to be elaborated, of course, when applied to real materials, which are mixtures of elements. He would conclude that wood, say, has both earth and air in it, since it does not sink in water.
Of course, things also sometimes move because they are pushed. A stone's natural tendency, if left alone and unsupported, is to fall, but we can lift it, or even throw it through the air.Aristotle termed such forced motion "violent" motion as opposed to natural motion. The term "violent" here connotes that some external force is applied to the body to cause the motion. (Of course, from the modern point of view, gravity is an external force that causes a stone to fall, but even Galileo did not realize that. Before Newton, the falling of a stone was considered natural motion that did not require any outside help.)
Aristotle was the first to think quantitatively about the speeds involved in these movements. He made two quantitative assertions about how things fall (natural motion):
Notice that these rules have a certain elegance, an appealing quantitative simplicity. And, if you drop a stone and a piece of paper, it's clear that the heavier thing does fall faster, and a stone falling through water is definitely slowed down by the water, so the rules at first appear plausible. The surprising thing is, in view of Aristotle's painstaking observations of so many things, he didn't check out these rules in any serious way. It would not have taken long to find out if half a brick fell at half the speed of a whole brick, for example. Obviously, this was not something he considered important.
From the second assertion above, he concluded that a vacuum cannot exist, because if it did, since it has zero density, all bodies would fall through it at infinite speed which is clearly nonsense.
For violent motion, Aristotle stated that the speed of the moving object was in direct proportion to the applied force.
This means first that if you stop pushing, the object stops moving. This certainly sounds like a reasonable rule for, say, pushing a box of books across a carpet, or a Grecian ox dragging a plough through a field. (This intuitively appealing picture, however, fails to take account of the large frictional force between the box and the carpet. If you put the box on a sled and pushed it across ice, it wouldn't stop when you stop pushing. Galileo realized the importance of friction in these situations.)
Mass has two definitions that are equally important. One is a general definition that most high school students are taught and the other is a more technical definition that is used in physics.
Generally, mass is defined as the measure of how much matter an object or body contains - the total number of sub-atomic particles (electrons, protons and neutrons) in the object. If you multiply your mass by the earth's gravitational force, you get your weight. So if your body weight is fluctuating, by eating or exercising, it is actually your mass that is changing. It is important to understand that mass is independent of your position in space. Your body's mass on the moon is the same as its mass on the earth. The earth's gravitational force, on the other hand, decreases as you move farther away from the earth. Therefore, you can lose weight by changing your elevation, but your mass remains the same. You can also lose weight by living on the moon, but again your mass is the same.
In physics, mass is defined as the amount of force required to cause a body to accelerate. Mass is very closely related to energy in physics. Mass is dependent on the body's motion relative to the motion of an observer. If the body in motion measured its mass, it is always the same. However, if an observer that is not in motion with the body measures the body's mass, the observer would see an increase in mass when the object speeds up. This is called relativistic mass. It should be noted that physics has actually stopped using this concept of mass and now deals mostly in terms of energy. At this stage, this definition of mass may be a little cloudy, but it is important to know the concept. It should become clearer in the special relativity discussion. The important thing to understand here is that there is a relationship between mass and energy.
Energy is the measure of a system's ability to perform "work". It exists in many forms…potential, kinetic, etc. The law of conservation of energy tells us that energy can neither be created nor destroyed; it can only be converted from one form to another. These separate forms of energy are not conserved, but the total amount of energy is conserved. If you drop a baseball from your roof, the ball has kinetic energy the moment it starts to move. Just before you dropped the ball, it had only potential energy. As the ball moves, the potential energy is converted into kinetic energy. Likewise, when the ball hits the ground, some of its energy is converted to heat (sometimes called heat energy or heat kinetic energy). If you go through each phase of this scenario and totaled up the energy for the system, you will find that the amount of energy for the system is the same at all times.
Light is a form of energy, and exists in two conceptual frameworks: light exhibits properties that have characteristics of discrete particles (eg. energy is carried away in "chunks") and characteristics of waves (eg. diffraction). This split is known as duality. It is important to understand that this is not an "either/or" situation. Duality means that the characteristics of both waves and particles are present at the same time. The same beam of light will behave as a particle and/or as a wave depending on the experiment. Furthermore, the particle framework (chunks) can have interactions which can be described in terms of wave characteristics and the wave framework can have interactions that can be described in terms of particle characteristics. The particle form is known as a photon, and the waveform is known as electromagnetic radiation. First the photon…
A photon is the light we see when an atom emits energy. In the model of an atom, electrons orbit a nucleus made of protons and neutrons. There are separate electron levels for the electrons orbiting the nucleus. Picture a basketball with several sizes of hula-hoops around it. The basketball would be the nucleus and the hula-hoops would be the possible electron levels. These surrounding levels can be referred to as orbitals. Each of these orbitals can only accept a discrete amount of energy. If an atom absorbs some energy, an electron in an orbital close to the nucleus (a lower energy level) will jump to an orbital that is farther away from the nucleus (a higher energy level). The atom is now said to be excited. This excitement generally will not last very long, and the electron will fall back into the lower shell. A packet of energy, called a photon or quanta, will be released. This emitted energy is equal to the difference between the high and low energy levels, and may be seen as light depending on its wave frequency, discussed below.
For many purposes, light can be considered to be a wave, like an ocean wave. The primary differences are that there is no medium (the ether was a ruse!) and the "wave" is a periodic electromagnetic disturbance. This being the case, we can define the wavelength lambda, which is just the distance between wave crests, and the frequency, nu, which is the number of waves that pass a certain point in space per unit time. The period T is simply the inverse of the frequency -- it is the time it takes for one wavelength to go past a point. The wavelength and frequency are related by the speed of light:
This frequency is the frequency referred to above -- simply think of light as a period train of pulses, each separated by the period T of the light wave. Note that this relationship ought to be valid in all frames, since the speed of light is invariant. However, there is nothing that requires that the wavelength and frequency be invariant, but their product must be.
The wave form of light is actually a form of energy that is created by an oscillating charge. This charge consists of an oscillating electric field and an oscillating magnetic field, hence the name electromagnetic radiation. We should note that the two fields are oscillating perpendicular to each other. Light is only one form of electromagnetic radiation. All forms are classified on the electromagnetic spectrum by the number of complete oscillations per second that the electric and magnetic fields undergo, called frequency. The frequency range for visible light is only a small portion of the spectrum with violet and red being the highest and lowest frequencies respectively. Since violet light has a higher frequency than red, we say that it has more energy. If you go all the way out on the electromagnetic spectrum, you will see that gamma rays are the most energetic. This should come as no surprise since it is commonly known that gamma rays have enough energy to penetrate many materials. These rays are very dangerous because of the damage they can do to you biologically . The amount of energy is dependent on the frequency of the radiation. Visible electromagnetic radiation is what we commonly refer to as light, which can also be broken down into separate frequencies with corresponding energy levels for each color.
As light travels its path, through space, it often encounters matter in one form or another. We should all be familiar with reflection since we see bright reflections when a light hits a smooth shinny surface like a mirror. This is an example of light interacting with matter in a certain way. When light travels from one medium to another, the light bends. This is called refraction. If the medium, in the path of the light, bends the light or blocks certain frequencies of it, we can see separate colors. A rainbow, for example, occurs when the sun's light becomes separated by moisture in the air. The moisture bends the light, thus separating the frequencies and allowing us to see the unique colors of the light spectrum. Prisms also provide this effect. When light hits a prism at certain angles, the light will refract (bend), causing it to be separated into its individual frequencies. This effect occurs because of the shape of the prism and the angle of the light.
If you look closely at what happens as the light wave enters the prism in the second diagram, you will notice that it bends down. This bending occurs because the light travels faster through the air than it does through the prism. When the lower portion of the wave enters the prism, it slows down. Since the upper portion of the wave (still in the air) is traveling faster than the lower portion, the wave bends. Similarly, as the wave exits the prism, the upper portion exits first and begins travelling faster than the lower portion that is still in the prism. This speed differential causes the wave to bend once again. Think of a skateboard rider going down the driveway. If the rider turns and goes into the grass, his body will lunge forward and actually fly off of the board if he is traveling fast enough originally. This is analogous to light bending as it goes through different mediums. The skateboard and the rider are moving at the same speed until the wheels hit the grass. Now suddenly, the skateboard is traveling slower than the rider is, so the rider begins to bend forward (the rider is trying to continue traveling at the same speed he was before the wheels hit the grass).
Now that we have a little understanding of the composition of light, we can begin to resolve the oft under explained concept of "the speed of light". Since light itself is just a form of electromagnetic radiation, the speed of light is just an easy way of talking about the speed of electromagnetic radiation in general. If you think about it, the speed of light is the "speed of information". We can not acknowledge that an event has occurred until the information about that event reaches us. The information is contained in the electromagnetic radiation from the event via a radio signal, a flash of light etc. Any event is just an occurrence of space and time, and any information that can be transmitted about an event is emitted outward as radiation of some sort. The information (electromagnetic radiation) from the event travels at 186,000 miles/second in a vacuum. If you picture a long train that begins to move forward from a stopped position, you do not expect the very last car to begin moving instantaneously. There is an amount of time that passes before the last car begins to get pulled. Thus, there is an expected delay for last car to "receive" the information that the first car is moving and pulling. This delay is analogous to the transfer of information in special relativity, but SR only imposes an upper limit on the speed of the information; the speed of light. You can make the train example as detailed as you like, but regardless, you will always find that there can be no reaction without a time delay of at least the speed of light between the action and reaction. In the special relativity section we will further discuss the importance of this speed.
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