| 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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