From: Ronald Wong (ronwong@inreach.com)
Date: Wed May 16 2001 - 00:33:54 PDT
Message-Id: <l03102803b727cf40c2ea@[209.209.20.30]> Date: Wed, 16 May 2001 00:33:54 -0700 From: Ronald Wong <ronwong@inreach.com> Subject: re: relativity
Jhumki Basu said:
>A few student questions that I cannot answer:
>
>1) If objects cannot travel at the speed of light (time, length problems are
>created), why can light travel at the speed of light?
First, you must make clear to your students that the "speed of light"
referred to here is it's speed in a vacuum (299 792 458 m/s).
The reason light travels at that speed in a vacuum is because that is what
it does. It wouldn't be light if it didn't. In fact that is the only speed
it can have in a vacuum. That speed is a property of all electromagnetic
waves in a vacuum (of which light is just one form).
When light travels through matter it interacts with it and, as a result,
travels at speeds less than 299 792 458 m/s. It is important to note that
in such materials, it IS possible for objects to travel at speeds greater
than light - in that material. When these objects travel through the
material at these speeds they radiate energy (called Cerenkov radiation).
The angle at which this radiation can be detected relative to the path of
the moving particle is directly related to the particle's speed. This is
one of the ways of finding the speed of sub-atomic particles in high-energy
interactions.
>2) As the velocity of an object approaches the speed of light, I think the
>object's mass increases. Is there a formula that shows this relationship? Or
>can you tell me the ratio between change in velocity and change in mass?
The observed mass = the rest mass divided by the square root of (1 minus the
square of the relative speed divided by the
square of the speed of light)
or: observed mass = rest mass / sqrt(1- v^2/c^2)
The rest mass is the mass measured by someone in the frame of reference of
the rest mass (i.e. the person is moving along with the mass and thus the
mass is at rest relative to that person)
The observed mass is the mass someone moving with a velocity, v, relative
to the mass would observe.
ron
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