Answer 1:
The problem with describing the object as
moving at the speed of light towards the light is
that given relativity, there's no welldefined
rest frame for the beam of light. Its a bit hard
to describe without invoking math, but basically
everyone looking will say that the beam is
traveling at the speed of light, but there are
lots of possible answers to what speed the object
is moving. However, using some math, there are
some quantities that everyone can calculate to
agree on, such as the "proper time" or "proper
length" of that object, which tell us about the
rest frame of that object. If they tried to
calculate it for the light beam, they would get
ridiculous answers like infinity. And thus the
rest frame of the beam of light is badly defined.
Simply reversing a statement does not cause
any time dilation or length contraction effects.
These effects only exist when you say with respect
to what other frame you're making the
measurements. Different observers in different
frames observe different values for time dilation
and length contraction. So when doing relativity,
you must always define what frame you're doing the
calculations in to get physical measurements.
For instance, in your next question you ask
about traveling half the speed of light. Note
that this must be defined with respect to the
earth. If there were another object also moving
at half the speed of light away from the earth in
the same direction, the two objects would measure
no time dilation with respect to each other, but
both would measure it for the earth. Given the
principle of relativity, the effect of such a time
dilation would be 2/Sqrt (3) times the rest frame
time. So people on earth see the people on the
rocket move that much slower. However, people on
the rocket observe people on the earth moving that
much slower as well, by relativity. The only time
you can find out who aged more is if you turn one
around. Otherwise earth sees the rocket as being
time dilated slower, and the rocket sees the earth
getting time dilated slower in the same way. If
the rocket turns around, then there's an
acceleration (not just a frame change) that causes
the discrepancy in age (people on the rocket age
slower). However, if instead we accelerated the
earth towards the rocket to catch back up to it,
then it's the people on the earth that will age
slower than the people on the rocket!
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