The key to special relativity, as suggested by its name, is reference frames. The picture below shows an observer standing in the back of a pick-up truck. The pick-up truck is moving with a velocity v in reference to a second observer who is stationary on the ground. The first observer throws a ball straight up into the air and then catches it. To this first observer it appears as if the ball goes up and down without changing its horizontal coordinate. However, as the truck moves by the second observer, she observes the the path of the ball forming a parabola when the ball is thrown into the air. What Einstein purposed, in short, is that neither observation of the ball is the "true" observation. Because there is no reference frame with more accuracy or consistency that any other reference frame we can begin to grasp Einsteins two postulates that form his basis for special relativity.
1. The laws of physics must be the same in all inertial reference frames.
2. The speed of light in a vacuum(300,000,000 meters per second)has the same value regardless of the velocity of the observer or the velocity of the source emitting the light.
The second postulate is really implied by the first*
When you are moving in a truck at velocity v and you throw a ball, at velocity v', in the same direction as the velocity of the truck, it makes sense that the total speed of the ball with respect to a stationary observer would be v + v'. In classical mechanics, any projectile fired from a non-stationary object, adds to the velocity of that non-stationary object. So since light travels at a velocity c it would appear that when emitted from a moving reference frame with speed v, the total speed of that light with respect to a stationary reference frame would be v+c. Light, however, is a fundamental property of the laws of physics. According to Einstein's two postulates the speed of light must be the same in each reference frame. Regardless of if the observer is moving at a velocity close to that of light, say 0.95c, the observer should still measure the speed of light at 300,000,000 m/s. Regardless of if he thinks he is moving or stationary.
This seems quite counter-intuitive. To understand this concept we must first think about how velocity is measured. Meters per second is an amount of space(meters) covered in some period of time(seconds). In order to keep the speed of light the same when changing inertial reference frames we need to subtlety edit this definition. This brings us to the topic of time dilation. Einsteins theories remove some of the separation we intuitively place on space and time. We need to alter our perceptions of space and time in order to conceptualize the effects of special relativity. Every time we change inertial reference frames(move) we affect not only space but time also. Our perception of time changes as our velocity changes. This is not illusion. It is a principle of time itself. The reason why light appears to move at the same velocity with respect to an observer regardless of if that observer is also moving is because as that observer moves, their perception of time changes. Time is slower in a moving reference frame than in a stationary one. However, to the observer, time always appears to "pass" the observer, in each reference frame, at the same speed. In other words, though less time occurs in a moving reference frame in comparison to a stationary reference frame, no observer in any reference frame thinks they're in fast or slow motion. It is interesting to explain the effects of such a proposition. The equation for this time dilation is
This gives us the amount of time passed in a moving reference frame in comparison to the amount of time passed in a stationary one. For example, if 0.5 seconds passes in stationary time(t) then the amount of time passed in a reference frame with a velocity of 200,000,000 meters per second is 0.5(sqrt(1-((2*10^8)/(3*10^8)))) or about 0.29 seconds. If apparent time is shorter and therefore occurring slower, it follows that apparent distance must be shorter. Another way of explaining this is that to keep the consistency over reference frames, as the value of seconds decreases, meters must also decrease. In order to maintain the same apparent velocity the ratio m/s must remain constant. This is called length contraction. It is described by the equation
 |
| Where L = stationary length and L' = contracted length |
I'll give one last example on this post regarding the effects of time dilation. This involves an experiment involving a set of twins. Both twins are 20 years old. One of the twins happens to be an astronaut and sets out on a journey to a planet 20 light years away. His ship is capable of reaching a speed of 0.95c. When he arrives at the planet he immediately turns around and comes back to Earth at the same speed. To the twin that stayed stationary 42 years have passed. He is now 62 years old. According to the equation for time dilation, when the traveling twin returns he would only be 33 years old. To him, a mere 13 years would have passed. This is an famous example of time dilation used in the twin paradox. (http://en.wikipedia.org/wiki/Twin_paradox).
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