MadSci Network: Physics |
Only if you were a massless particle could you travel at the speed of light. Very near the speed of light things would certainly look different but it would not be dark. Part of a discussion of light speed and relativity is posted below from the MADScience archives... 884117781.Ph The two fundamental postulates of the Special Theory of Relativity are +All motion is relative +The velocity of light is always constant with respect to an observer The consequences of second postulate can be seen in the following example : If a star emitting light and the earth are approaching each other at 1*10^8 m/sec, it does not mean that an observer on the earth will see light travelling at (3+1)*10^8 m/sec (the speed of light being 3*10^8 m/sec). Rather, the speed of light will still be 3*10^8 m/sec as seen by an observer on the earth. Similarly, even if they are moving away from each other, the observer on earth will not see the speed of light as any less than 3*10^8 m/sec, rather he will observe it as 3*10^8 m/sec. Now, proceeding from these postulates, a physical situation into which these may be incorporated is taken. An experiment may be conducted where an observer (A) describes an object (B) moving at a constant velocity relative to him. The behaviour of light waves will influence the description, since it is the reflection of the light waves from the object to the observer which enables him to see and to describe the object. Let A and B move at a relative velocity of VAB. Lorentz postulated certain transformations to describe the physical attributes of A and B moving with velocities relative to each other. A few of the Lorentz transformations are looked at below to help in answering the question of the maximum velocity that objects can attain. (The derivation of the Lorentz transformations has not been gone into, you can ask for a more detailed explanation including the derivation if you would like) Let us first consider the length of B as described by A. The Lorentz transformation equations predict that the length observed L' and the actual length L will be related as follows. L'=L*(1- VAB^2/c^2)^(1/2) where c is the velocity of light. [ Eqn. 1 ] We can see that this reduces to L'=L at low values of VAB, the same as what is predicted by conventional Newtonian Physics. Further, when the velocity of B with respect to be A is to be determined, the Lorentz postulates state that VAB is not given by VA + VB as the Newtonian mechanics would predict. Rather, it is given by VAB = (VA + VB)/ (1+ VA*VB/c^2) [Eqn. 2] We can see that [Eqn. 2] reduces to VAB = VA + VB at low values of VA and VB, thereby obeying Newtonian mechanics. We can also see that the maximum velocity that may be reached is VAB = c. This is due to the fact that (VA + VB) is reduced by the scaling factor of (1+ VA*VB/c^2) which is always greater than 1. Hence, even if = VA = c and VB = 80% of c, you can see that VAB will not equal 180% of c, but rather 1.8*c/(1+.8) = c. You can play around with different values of VA and VB and see what value of VAB you get. Further, we can see from [Eqn. 1] that as VAB approaches c, L' approaches 0. VAB cannot exceed c, or the sign under the square root will become negative. Hence, we see that the velocity of light c is the maximum velocity beyond which nothing can go.
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