### Q: My physics teacher said that it is imposible to go faster than the speed on light, but if you were standing on a train going at the speed of light and you walked from one end of the train to the other, then would'nt you be going faster than the speen of light relative to the ground? and what would happen if you were going at the speed on light or faster? Theoretically - Daimhin

It
may seem like should happen that way. The problem with physics is that
it doesn't always work the way that it seems like it should.

You've
probably learned that the speed of light is a constant (c). But what if
you looked at it from different points of view? For instance, if you're
standing on the Earth, then the speed of light is c. But what if you're
standing on the train that's moving at half the speed of light?
Shouldn't it look like the light is moving at half speed? Well, for all
that it certainly seems like it should, it doesn't. The light moves at
the same speed whether you're standing on the Earth, or on a speeding
train.

But
whoa! How can the light move at the same speed from the Earth's
perspective as from the train's? Because velocity is equal to distance
divided by time, and it seems like everybody should agree on the
distance traveled and the time elapsed. But do they? According to
special relativity (Einstein's work), distance and time don't work the
way that we think they do either, and that get's really important when
you're talking about speeds close to the speed of light.

I
know that this wasn't exactly what you were asking, but I wanted to
emphasize to you how things don't always happen according to the rules
that you're used to. One of the basic rules of space and time is that no
object can travel faster than c. That might seem ridiculous, because if
you can get a train going at 0.9999999999c , you could then walk on it
at 0.0000000002 c relative to the train, and that would add up to
1.0000000001 c. However, velocities don't add that way because time and
space intervals aren't the same as seen from the ground and the train.
Somebody on the train says that your walking at 0.0000000002 c. Somebody
on the ground thinks that your steps are much smaller than you or your
friends on the train think, and that it takes you much longer to take
those steps than you think. So they still end up thinking that you're
traveling at less than c.

You
might think that if you could just keep applying force to something it
would accelerate to greater than c. However, that assumes that F=ma,
which turns out to be false. The effective 'm' in the expression mv for
the momentum (v is velocity) increases for bigger v! When you exert a
force, as v gets near c you end up mainly increasing that 'm', not v.

The
kinetic energy grows more rapidly as v increases than classical physics
would say. As v gets close to c, the energy grows toward infinity. So
to get to the speed of light, it would take an infinite amount of
energy.