Re: How do you know you're near the spped of light?

Well, basically you don't.  Motion with a constant velocity is only
a relative thing.  If you are moving with constant velocity relative
to some other object, not changing your speed or direction 
(this is called an "inertial reference frame"), then any measurement 
you might make on objects moving with you is exactly the same as if
you were at rest with respect to that object.  In fact, there's no
way to tell if you're moving and the object is at rest or you're
at rest and the object is moving.  It makes no difference to the laws
of physics.  Of course you can always DEFINE yourself as moving, but
somebody else can define you as being at rest, and again there's no
way to prove one of you wrong since motion with constant velocity is
only a matter of definition, and has no physical consequences.

This is always a bit confusing, especially with regards to relativistic
mass, since people tend to think of "mass" as being an intrinsic
property of an object, and unfortunately often don't get the whole
story when being told about the relativity of mass.  Mass is also
a relative quantity: the mass you measure for an object depends on
how it is moving relative to you.  HOWEVER, the mass you measure for
yourself is always the same.  From the above, we see this has to
be the case since all motion is relative, and there's no experiment
you can do to tell if you're moving with constant velocity or not.
Consider two observers, who we'll call Ed and Ted.  They are in
motion relative to each other.  Now, Ed measures Ted's mass to be
increased by an amount which is related to their relative velocities.
However, Ted also measure's Ed's mass to be increased by the same
amount.  But Ed and Ted measure their OWN masses to be the same, no
matter what their relative velocities.

This sounds confusing, but it's really a consequence of the fact that
mass is not what physicists call a "scalar quantity".  Basically,
a scalar quantity is one which does not change no matter how you look
at it.  Consider the following example: you are holding an arrow in
your hand.  No matter what direction you point the arrow, it's length
(which we'll call L) is always the same.  So length is a scalar with
respect to rotation of an object or coordinate system.  However, as
you've probably learned, you can always break the length of something
up into it's horizontal and vertical components, which we'll call
H and V.  Thus, if the arrow is pointing straight up and down, H=0
and V=L, while if it is exactly horizontal, H=L and V=0.  If you
are pointing the arrow somewhere in between, H and V are not zero,
but are related to the total length by Pythagoras' theorem,
L^2 = H^2 + V^2.  So we see that H and V are not individually scalar
quantities, as they change depending on how you point the arrow.  However
they can be combined to make a scalar quantity, the length of the
arrow.  Mathematically speaking, the pair (H,V) is called a "vector",
and while the vector may change under rotation, it's total length
does not.

The case is similar for mass in the theory of special relativity.
Here, mass is no longer a scalar (as it is in Newton's laws), but
one component of an mathematical object we call a "4-vector", in
this case the momentum 4-vector, which consists of four numbers.
These are the momenta in the x, y, and z directions, along with the
mass (or energy, as related via the famous equation E=mc^2).  Now,
as an object is moving relative to you, these four numbers will change
depending on it's motion.  However, you can compute the "length" of
a 4-vector (in a way similar to Pythagoras' theorem, though not quite
the same), and you will find that no matter what velocity the object
is moving with, you always get the same number for this "length".
In fact it turns out that this number is exactly the rest mass of
the object, i.e., the mass that you would measure if the object
were not moving relative to you.  So rest mass is a scalar, but total
mass is not.  This may sound confusing, but really it boils down
to which quantities you choose to measure.  In the arrow example, you
could measure the total length, and find it is the same no matter what
the direction.  But if you measured only H, you would find that it
changed depending on how the arrow pointed.  To get the whole picture,
you need to measure both H and V.

But again, the main point here is that no matter how fast you move
relative to something else, you always measure your mass the same,
because (obviously) you're at rest relative to yourself.

On the other hand, the relativity of mass does have observable effects
for objects moving relative to you.  One of these is that Newton's
second law, F=ma (force = mass times acceleration) is no longer
valid in this form.  Instead, we must use the more general form,
F = dp/dt (force = the time rate of change of momentum; dp/dt is the
derivative of the momentum with respect to time, if you know calculus),
because the mass itself changes depending on the motion.  Thus
the motion you calculate for an object can be quite different if
it is moving close to the speed of light.  One consequence is that
no matter how hard you push, you can never accelerate an object
beyond the speed of light.  Consider a rocket with a constant thrust.
At low speeds, the acceleration of the rocket will appear constant
(though this is only approximate).  However, as the rocket approaches
the speed of light, the acceleration will get smaller and smaller,
approaching zero, but never reaching it.