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Shanos

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im doing a 'information search' for physics; its pretty much just a fancy name for an essay.. anyway i opted to do it on 'time as a variable', but iv been struggling with it somewhat, so i figured i might try posting it up here, and see if anyone could help me with it; e.g point out errors, recommendations, better explanations for parts etc, any help would be VERY VERY VERY appreciated, thanks Shane

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Time As A Variable

Time is often defined in terms of change; and the measurable duration it takes for change to occur. At first many observers would assume time is a constant; a second is a second, a minute is a minute, in the classical sense, flowing like a river, independent and unaffected by our activities, however through the discoveries of physicists such as Hendrik A. Lorentz and Albert Einstein, it has been found that time is not a constant, but rather a potentially malleable variable, that is seen to have strong relations with velocity, particularly the speed of light.

Time is something that is alterable, not so much in the sense of ‘time travel’ as seen in movies, but in that the speed that it occurs on a body relative to other observing bodies. To explain the idea of time dilation and proving it as a variable in laymen terms, we first have to examine the ideas in ‘baby steps’, using the most simple of examples to show the effects of relativity in time.

To start off with, imagine two clocks (fig 1.0), both identical, running by a light beam that bounces off a mirror. The light beam leaves the base, hits the mirror and ‘ticks’, then leaves the mirror, returns to the base and ‘tocks’. As long as the clocks remain at rest relative to each other, both clock ‘tick-tock’ at the same rate, with each tick traveling x, and each tock also traveling x. Now one clock, “clock A” is moved at a velocity of v relative to the other clock, “clock B”, in a direction perpendicular to the direction of the mirror (fig 1.1). If a viewer watched one clock each, providing they were relative to their clock, as far as they would see, their clock would continue to ‘tick-tock’ at the same rate as before, with a tick as the light beam hit the mirror, and a tock when it returned. But bring the two clocks back together, there would be a discrepancy between the time passed, with “clock A” appearing to be behind “clock B” as although the difference between the clocks’ base and mirror are the same, the distance the light would have to travel between the base and mirror of “clock A” is further then that of “clock B”, and since the speed of light is constant, from the outside the experiment, it appears the “Clock A” takes longer to ‘tick-tock’ relative to “Clock B”.

This is the basic principle behind the theory that “the closer a body travels to the speed of light, the slower time appears to move on it to an outside observer”. Of course in the example above, Clock A would have to be moving with an enormous velocity for the discrepancy to be noticed; as there have been past experiments in which 2 atomic clocks were used. One clock was taken onto a plane and the other left on the Earth for a period, and once the clocks were brought back together on earth, the discrepancy was found to be in the 1 x 10-15th’s of a second.

A way to measure the discrepancy is the use of the equation to find the “Lorentz Gamma Factor”, which was introduced in 1904 by Dutch physicist, Hendrik A. Lorentz (one year before Einstein proposed his theory of special relativity). Put simply, the Lorentz factor is the time and length change as a function of velocity. For this factor, the equation

‘ c(squared) + (γv)(squared) = γ(squared) '

Is used, with ‘c’ being the speed of light (which for this example we will derive as 1; as it takes 1 second for the clock to travel ‘1 tick’ of the clock, which is the same vertical distance between the mirror and base of both clocks), γ is the Lorentz gamma factor, which is said to be the amount of ticks “Clock B” makes in the time it takes “Clock A” to make one. From this we can then determine that the distance “clock A” moves horizontally from “clock B” is equal to γv, which is the time it moves multiplied by the velocity, v, it moves at. This equation is then derived into

γ = 1 / the square root of 1 - v(squared)

To find the Lorentz Gamma Factor. The gamma factor can then be used in the equation

‘ t = t0γ ’

In which ‘t0’ is the time that appears to pass on the moving clock, ‘t’ is the time that it takes for ‘t0’ to occur as seen by a stationary outside observer, and ‘γ’ is the Lorentz Gamma Factor, defined by the previous equation.