Would time
freeze if you can travel at the speed of light?
Stes de Necker
I read with interest Einstein's Theory of Relativity and
his proposition about the speed of light being the speed limit for anything
with mass.
So, if I were to travel in a spacecraft at the speed of light, would
I freeze and stop moving? Would the universe around me freeze and stop moving?
Who would the time stop for?
Even if it would, does that mean that time will only stop
for me as individual, because only if I could returned to the place where I
started, will I be able to realize that I have had a different experience of
time. Without returning to compare my time/ageing
with the origin of my travel, it would not be possible for me to have experienced
any slow motion or such observable discrepancies.
So, if I went out into space for 1 light year and then
returned, all at the speed of light, and you stayed on earth, what would be the
relative difference between us? Does it mean that you will be a year older and I
will still be the same age?
Or to put the question in a different way, if I went into
space and return to earth, all at the speed of light, and you stayed on earth,
but earth also now travels at the speed of light, will we still be the same age
when I return from space?
This question has a long and honorable history. As a young
student, Einstein tried to imagine what an electromagnetic wave would look like
from the point of view of a motorcyclist riding alongside it. But we now know,
thanks to Einstein himself that it really doesn't make sense to talk about such
observers.
The most straightforward argument is based on the positivist
idea that concepts only mean something if you can define how to measure them
operationally. If we accept this philosophical stance, then we need to be able
to physically realize this frame in terms of an observer and measuring devices.
But
we can't.
It would take an infinite amount of energy to accelerate Einstein
and his motorcycle to the speed of light.
Since arguments from positivism can often kill off perfectly
interesting and reasonable concepts, we might ask whether there are other
reasons not to allow such frames. There are.
According to the scientists qualified in the field of
physics, the most basic geometrical ideas is intersection. In relativity, we
expect that even if different observers disagree about many things, they agree
about intersections of world-lines.
Either the particles collided or they didn't. The arrow
either hit the bull's-eye or it didn't. So although general relativity is far
more permissive than Newtonian mechanics about changes of coordinates, there is
a restriction that they should be smooth, one-to-one functions.
If there was something like a Lorentz transformation for
v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible
with the structure of relativity. An easy way to see that it can't be
one-to-one is that the length contraction would reduce a finite distance to a
point.
What if a system of interacting,
mass-less particles was conscious, and could make observations?
The argument given in the preceding
paragraph proves that this isn't possible, but let's be more explicit.
There are two possibilities. The
velocity V of the system's center of mass either moves at c, or it doesn't. If
V=c, then all the particles are moving along parallel lines, and therefore they
aren't interacting, can't perform computations, and can't be conscious.
This is also consistent with the
fact that the proper time s of a particle moving at c
is constant, ds=0.
If V is less than c, then the
observer's frame of reference isn't moving at c. Either way, we don't get an
observer moving at c.
The reason some people will say that time freezes at the
speed of light is that it's possible to take two points on any path going
through space-time at less than the speed of light and calculate the amount of
time that a particle would experience as it travels between those points along
that path. The calculation is as follows:
Δτ2=Δt2−1c2(Δx2+Δy2+Δz2)
Where Δτ is the amount of time experienced by the travelling
particle, and the other Δ's are the differences in space and time
coordinates between the two points as measured by an external observer.
If you take this same calculation and blindly apply it to a
path which is at the speed of light, you get Δτ=0.
If somehow, you were able to travel at the speed of
light, it would seem that 'your time' would not have progressed in comparison
to your reference time once you returned to 'normal' speeds. This can be modelled
by the Lorentz time dilation equation: T=T01−(v2/c2)
When travelling at the speed of light (v=c), left under the
radical you would have 0. This answer would be undefined or infinity if you
will. The reference time (T0) divided by infinity would be 0; therefore, you
could infer that time is 'frozen' to an object travelling at the speed of
light.
Velocity is relative, so it doesn't matter if you're
"travelling" at some speed relative to something, or something is
travelling at some velocity relative to you - the effects are the same.
Right now you have objects in the universe travelling at a
wide range of velocities relative to you. If you decided to change your speed
to close to the speed of light compared to what it is now, you will find that
there is still the same range of velocities of objects relative to you. That's
because objects that were travelling close to c in the direction of your
increase will have slowed down, and objects that were travelling in the
opposite direction will have increased their velocity.
However, you will also find that as objects increase their
speed relative to you, the sequence of events there slow down, and that
includes the running of their clocks from your view point, which approaches
zero as their speed approaches the speed of light.
I'm a total novice but as I understand it, "your"
space and time share a finite amount of energy at any given moment called
Space-Time.
So the finite amount energy available at any given moment
can be consumed "either" by motion through space or the time of some
clock.
But the more you use that energy for one aspect of Space-Time
i.e. motion or ‘clock time’, the less there is for the other. Almost the way
your computer seems to run slower the more programs you run at once, i.e. a
finite amount of processing power is available at any given moment to be
distributed among applications.
The upper limit of motion being the speed of light.
So the closer you travel to the speed of light the more
energy for a given moment is assigned/consumed by motion, leaving less and less
energy for time to tick (relative to someone else). Therefore (relatively
speaking) the slower time goes.
So the faster you go, the slower time "appears" to
go relative to a slower observer because most of your space-time energy is
being consumed by motion, whereas more of theirs is being used for time to
tick.
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