19 March 2006

The First Postulate of the Special Theory of Relativity

The first postulate of the theory of special relativity is not too hard to swallow: The laws of physics hold true for all frames of reference. This is the simplest of all relativistic concepts to grasp. The physical laws help us understand how and why our environment reacts the way it does. They also allow us to predict events and their outcomes. Consider a yardstick and a cement block. If you measure the length on the block, you will get the same result regardless of whether you are standing on the ground or riding a bus. Next, measure the time it takes a pendulum to make 10 full swings from a starting height of 12 inches above its resting point. Again, you will get the same results whether you are standing on the ground or riding a bus. Note that we are assuming that the bus is not accelerating, but traveling along at a constant velocity on a smooth road. Now if we take the same examples as above, but this time measure the block and time the pendulum swings as they ride past us on the bus, we will get different results than our previous results. The difference in the results of our experiments occurs because the laws of physics remain the same for all frames of reference. The discussion of the Second Postulate will explain this in more detail. It is important to note that just because the laws of physics are constant, it does not mean that we will get the same experimental results in differing frames. That depends on the nature of the experiment. For example, if we crash two cars into each other, we will find that the energy was conserved for the collision regardless of whether we were in one of the cars or standing on the sidewalk. Conservation of energy is a physical law and therefore, must be the same in all reference frames.

Why all this...

My initial purpose was to explain dark energy and and dark matter. To understand that, and the behaviour of it, one must first have a clear understanding of SR and GR.

Frames of Reference: Uderstand this, and you could explain relativity to your grandmother

Einstein's special theory of relativity is based on the idea of reference frames. A reference frame is simply "where a person (or other observer) happens to be standing". You, at this moment, are probably sitting at your computer. That is your current reference frame. You feel like you are stationary, even though you know the earth is revolving on its axis and orbiting around the sun. Here is an important fact about reference frames: There is no such thing as an absolute frame of reference in our universe. By saying absolute, what is actually meant is that there is no place in the universe that is completely stationary. This statement says that since everything is moving, all motion is relative. Think about it - the earth itself is moving, so even though you are standing still, you are in motion. You are moving through both space and time at all times. Because there is no place or object in the universe that is stationary, there is no single place or object on which to base all other motion. Therefore, if John runs toward Hunter, it could be correctly viewed two ways. From Hunter's perspective, John is moving towards Hunter. From John's perspective, Hunter is moving towards John. Both John and Hunter have the right to observe the action from their respective frames of reference. All motion is relative to your frame of reference. Another example: If you throw a ball, the ball has the right to view itself as being at rest relative to you. The ball can view you as moving away from it, even though you view the ball as moving away from you. Keep in mind that even though you are not moving with respect to the earth's surface, you are moving with the earth.

16 March 2006

First about the Lorentz Transformations....

The Lorentz Transformations are mathematical equations that allow us to transform from one coordinate system to another. Why would we want to do this? Because special relativity deals with frames of reference. When you analyze properties from one frame to another, it is necessary to first transform from one coordinate system to another. Thus, we can utilize the Lorentz Transforms to convert length and time from one frame of reference to another. For example, if you are flying in an airplane and I am standing still on the ground, you could apply the transformations to transform my frame of reference into your frame of reference and I could do the same for you in my frame of reference. The previous statements imply that lengths and times are not the same for objects that are in motion with respect to each other. As unbelievable as this may seem, it is a result of SR. Einstein utilized the transformations because they provide a method of translating the properties from one frame of reference to another when the speed of light is held constant in both.

11 March 2006

All Roads lead to Relativity!

Now! Now! I am trying to figure out why on earth I started this blog. The next posting is about explaining Special Relativity. And that is giving me a bit of a buzz! All this started with me taking a ride on dark matter. Having said that, I seem to have hit on something that might explain why Dark Matter behaves the way it does. It is something to do with gravity and latency. Sounds a bit outragous!!! Very soon you can read about it. The next one is on Relativity. When, I do not know. Considering the fact that time is relative, today can be tomorrow or 10 years from now. Not forgetting that it could be 10 years ago!!! Cheers!

Universal Basics...

It might be a good idea to first understand the fundemental properties of the Universe. As we know it today, the universe consists of a few standard properties. Most of us maybe familiar with it, that we take it for granted. Still, under different conditions they all behave very differently. Which is common place in space. Space 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 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 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. Motion Anything that is in the act of changing its location in space is said to be in motion. As you will see later, consideration of "motion" allows for or causes some very interesting concepts. Mass 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 pull of earth's gravity, 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 pull, 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 (see the section on the unification of mass and 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 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 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. 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 shiny 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 e light wave enters a prism, 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. Next we should take a look at Relativity. Note: Most of the above contents have been taken from 'How things work'. It does not make sense trying to re write the basic all over!!