The Theory of special relativity
The Theory of special relativity
Prior to albert Einstein’s theory of special relativity there was always an idea about relativity. Through Galilean transformations, which worked perfectly with the newton’s laws of motion, people had formed a vague idea that all motion in this world is relative to something else. There came up the mysterious thing called aether — the medium through which light propagated. The belief in aether had caused a mess of things, in Einstein’s view, by introducing a medium that caused certain laws of physics to work differently depending on how the observer moved relative to the aether. In 1905, Albert Einstein published the theory of special relativity, which explains how to interpret motion between different inertial frames of reference — that is, places that are moving at constant speeds relative to each other.
Einstein explained that when two objects are moving at a constant speed as the relative motion between the two objects, instead of appealing to the aether as an absolute frame of reference that defined what was going on. If you and your friend, say AA, are moving in different spaceships and want to compare your observations, all that matters is how fast you and AA are moving with respect to each other. Special relativity includes only the special case (hence the name) where the motion is uniform. The motion it explains is only if you’re traveling in a straight line at a constant speed. As soon as you accelerate or curve — or do anything that changes the nature of the motion in any way — special relativity ceases to apply. That’s where Einstein’s general theory of relativity comes in, because it can explain the general case of any sort of motion. Einstein’s theory was based on two key principles:
* The principle of relativity: All objects move in a motion relative to one another. No motion except the speed of light is fixed. And the laws of physics don’t change, even for objects moving in inertial (constant speed) frames of reference. * The principle of the speed of light: The speed of light is the same for all observers, regardless of their motion relative to the light source. (Physicists write this speed using the symbol c.)
Explaining theory of relativity and related concepts
Classical Relativity (mechanics theory)
Experiment: (Self thought and practically conducted)
An everyday life situation when you are moving in a straight escalator. Standing on next to an escalator, I measured the speed of my mother, who was standing still on the straight escalator, using a Doppler’s radar. Speed measured by the radar= 3 km/h
Then standing on the same escalator I measured the speed of my mother a few meters from me.
Speed Measured by the radar= 0 km/h
Classical relativity states that all motion in this universe is relative to one another. Nothing is fixed. As measured by the radar the escalator and hence my stationary mother on it was moving at a speed of 3km/h. But when I measured the speed with myself on the escalator, the radar measured 0 km/h. This is because although my mother was still moving with the escalator’s speed her state of motion with respect to mine was stationary.
Maxwell’s theory and the abolishment of aether theory
Maxwell was a scientist who gave various laws with respect to electromagnetic radiation. He, through his equations, proposed that like all other EMRs even the speed of light could be calculated. James Clark Maxwell (1884) devised his famous equation, showing that the four basic equations of electromagnetism (one of which Maxwell invented so his equation would work, but it turned out to be correct), can be combined into a single wave equation. The speed of the wave is determined solely by a term involving known constants that appear in the original formulas. Thus, Maxwell showed that the speed of light was a constant and that its speed could be measured using electromagnetic experiments that were already in place to determine
those constants. Nobody really believed that the speed was actually constant; they assumed that it was constant in some preferred reference frame, called the ether.
But Michelson, together with Morley, attempting to measure the speed of the earth through the ether by measuring the speed of light in many different directions at once, found that the speed was constant in all directions. Nobody knew what to make of that in 1887. Then Lorentz gave his 3 sets of explanations to prove Maxwell’s observations. But all these three explanations were proved wrong by Einstein as he gave the theory of relativity. He believed light to be a constant at all times and abolished the idea of aether. His explanations involved the principles of Spacetime where he unified space and time to create a four-dimensional view of the universe with three dimensions of space and one dimension of time.
Einstein’s theory of special relativity created a fundamental link between space and time. The universe can be viewed as having three space dimensions — up/down, left/right, forward/backward — and one time dimension. This 4-dimensional space is referred to as the space-time continuum. If you move fast enough through space, the observations that you make about space and time differ somewhat from the observations of other people, who are moving at different speeds. According to Einstein, Space and time were a single unit and not absolute but relative. The movement in space affected the movement in time. The faster one moved through space the slower one goes through time. Thought experiment: (self-thought and data input based on other examples to explain concepts): Imagine a car moving at say a 100/s along the east direction and at zero speed toward the north direction.
Then in one second it moves 100m towards east with no progress towards the north. Now say it moves north-east at the same speed. Because its speed is now diverted in two directions, it only moves 50 towards east and 50 m north. Same applies for space and time i.e. the faster you move through space the slower you pass through time. If you move at the speed of light then you make no progress in time and if you move at a speed that is greater than the speed of light, you can go back in time! Therefore, Einstein in order to measure distance between two objects chose to use a single entity called spacetime. Different observers would see different events in space in different ways. Some would see 2 events occurring at the same point in time but far apart in space, whereas other would see the same two events occur in very close to each other in space but far apart in time.
Maxwell, using his 4 equations of electromagnetism proved that the speed of light was a constant. But his idea was rejected and everybody thought the speed of light was relative to a constant frame called aether. Also a concept called ether drift developed whereby light through all other media except aether would undergo a drift called ether drift opposing its speed. This was dependent on the velocity of the object. The more the velocity of the media, the less was supposed to be the speed of light through the media.
Using this when Michelson, together with Morley, attempted to measure the speed of the earth through the ether by measuring the speed of light in many different directions at once, they found that the speed was constant in all directions and equal to the constant calculated by Maxwell. Now a question arose: how was this possible? The explanation to this was given by Einstein who abolished aether and said that the speed of light was a constant and through his theory of relativity demonstrated that how this was possible.
To understand the fact that speed of light is a constant, we need to change our perspectives on distance and time from them being a relative quantity from a fixed quantity. This introduces to us two new concepts of time dilation and length contraction. Both time dilation and length contraction are immediate consequences of the Lorentz transformation
Thought experiment: (taken from YouTube video on relativity)
Consider this thought experiment. You and AA are in 2 different spaceships in space. Both of you are measuring trying to measure the speed of light. Your spaceship is stationary while your friend’s spaceship is moving at a constant speed, say 0.5c. To calculate time (which can be calculated by using any device that measures a certain event periodically) both of you are using 2 plates reflecting light against each other. (Look at the diagram below)
Now in the (1) clock is the clock in the stationary clock i.e. the one on the stationary spaceship whereas the (2) clock is on the moving spaceship. Both clocks are identical. It is known that the speed of light is the same at all times. Therefore here in the stationary clock light moves up and down in a perpendicular distance the shortest distance. If the clock moves by 5 min every time the light touches the bottom plate then the clock would run at a certain speed and change appropriately. Now in case of the moving clock the light beam is travelling diagonally as the plates are constantly moving along with the spaceship in which they are present. Therefore the light takes a longer time to hit the bottom plate (as the speed of light is constant and light has to travel a longer path). Therefore the (2) clock runs slower than the (1) clock despite them being exactly identical. This phenomenon is known as time dilation, where the time on a ship moving very quickly appears to pass slower than on Earth.
The theory of special relativity revolutionized not just our understanding of time but our understanding of space too. I have already described the phenomenon of time dilation, whereby pairs of clocks in uniform relative motion each tick more slowly with respect to the other. A closely related effect is the phenomenon of length contraction (sometimes known as “Lorentz contraction”, “FitzGerald contraction” or even “Lorentz-FitzGerald contraction” after the physicists who predicted it on the basis of a crude forerunner of special relativity). Thought Experiment: (Taken from You tube Video But self-data input) Now in the spaceships example I have been using it can be said that if the two spaceships when at the same point i.e. when one is directly below the other and they release a beam of light and measure the speed of light after 12 seconds on the clock on the stationary ship which would be around 9 seconds on the clock aboard the moving ship if we calculate it using Lorentz’s transformations. Since the stationary ship is at rest in the space dimension therefore the rulers or any distance measuring instrument used would show that light travelled 12 light-second (the distance light travels in one second).
The actual speed of light is 1light-second per second. Since the total time measured was 12 seconds. Therefore the speed would that would be calculated is 12 light second per second which is nothing but one light second per second. Since the second spaceship was moving at a speed half the speed of light it should calculate the distance of the light beam from the ship after 12 seconds on the clock aboard the stationary ship to be 6 light-second. But the actual distance measured by the rulers or any other measuring instrument onboard the moving ship will be 9 light-second. This is because of a phenomenon called length contraction.
When an object moves at a very high speed i.e. a speed which is equal to or greater than 30% of c, then this length contraction can be seen up to some extent. Since the second spaceship was moving at 0.5*c, therefore the ship and all rulers or the measuring instruments used shrunk and the light beam was measured to be a distance of 9 light-second in 9 seconds, which is nothing but 1light-second per second.
As strange as it seems, this example (and many others) demonstrates that in Einstein’s theory of relativity, space and time are intimately linked together. If you apply Lorentz transformation equations, they work out so that the speed of light is perfectly consistent for both observers, i.e. one in motion at a constant speed and other stationary or at rest. This strange behavior of space and time is only evident when you’re traveling close to the speed of light, so no one had ever observed it before. Experiments carried out since Einstein’s discovery have confirmed that it’s true — time and space are perceived differently, in precisely the way Einstein described, for objects moving near the speed of light.
The Consequence of Theory of Relativity: Unifying mass and energy (E=mc2) The most famous work of Einstein’s life also dates from 1905, when he applied the ideas of his relativity paper to come up with the equation E=mc2 that represents the relationship between mass (m) and energy (E). Einstein found that as an object approached the speed of light, c, the mass of the object increased. The object goes faster, but it also gets heavier. If it were actually able to move at c, the object’s mass and energy would both be infinite.
A heavier object is harder to speed up, so it’s impossible to ever actually get the particle up to a speed of c. for example consider a proton accelerating towards the speed of light. As is moves closer to the speed of light its mass increases thus acting as a hindrance to the movement of the object. Until Einstein, the concepts of mass and energy were viewed as completely separate. He proved that the principles of conservation of mass and conservation of energy are part of the same larger, unified principle, and conservation of mass-energy. Matter can be turned into energy and energy can be turned into matter because a fundamental connection exists between the two types of substance. Thus if an object moves at a speed of light then it would have an infinite mass, negligible length and would make no progress in time.
University/College: University of California
Type of paper: Thesis/Dissertation Chapter
Date: 18 December 2016
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