Assuming you understand the basics, then let's look a little deeper.
Pythagoras into Einstein in Two Easy Steps
where do we start? Well let us start with one of the greatest triumphs of the
human mind, the great theorem of Pythagoras, a true pillar of all mathematics
and physics. The theorem, which is applicable to right angled triangles in flat
Cartesian (Newtonian) space takes the form of:
c2 = a2 + b2
where a, b and c are the lengths of the sides of the triangle.
Next we will jump straight to Einstein's theory of Relativity which states that neither time, length, or indeed mass remain constant
additive quantities when approaching the speed of light c. Our simple ideas of
time and space come from the fact the we are so used
to living in a three dimensional universe. Einstein showed that this was simply
not true and in fact all the "foundational" three laws of Newton have to be
fudged by the Lorentz factor
Lf = (1 - v2/c2) -1/2
Elementary Guide to Relativity
are, however, certain quantities that do remain constant. These constants are
related to four-dimensional quantities known as metric tensors. From this
Einstein proved that space and time are two aspects of the same thing and that
matter and energy are also two aspects of the same thing. From the second of
these concepts we get the most famous equation in physics
E = mc2
Now since time and space are aspects of space-time and we wish to travel through
time and not build atom bombs we will leave E=mc^2 for the moment. To illustrate
this, look at the extension of Pythagorean theorem for the distance, d, between
two points in space:
d2 = x2 + y2 + z2
where x, y and z are the lengths, or more correctly the difference in the
co-ordinates, in each of the three spatial directions. This distance remains
constant for fixed displacements of the origin.
In Einstein's relativity the same equation is modified to remain constant with
respect to displacement (and rotation), but not with respect to motion.
For a moving object, at least one of the lengths from which the distance, d, is calculated is contracted relative to a stationary
observer. The equation now becomes:
d2 = x2 + y2 + z2 (1-v2/c2)1/2
and this implies that the distances all shrink as one moves faster, so does this
mean there are no constant distances left in the universe? The answer is that
there are because of Einstein's revolutionary concept of space-time where time
is distance and distance is time! So now
s2 = x2 + y2 + z2 - ct2
and this new distance s (remember s stands for Space-time) does indeed remain
constant for all who are in relative motion. This distance is said to be a
Lorentz transformation invariant and has the same value for all inertial
observers. Since the equation mixes time and space up we have to always think in
terms of this new concept: space-time! This means that time isn't constant and
that by simply increasing the velocity (to close to the speed of light for it to
have an affect) significant time dilation effects can be seen. It will be a very
long time indeed before we have the capability to build a time machine and
travel the universe.
Where are the Time Travellers?
We now know that the theoretical evidence for
time travel is considerable. There is, however, one question we have avoided
until now. If time travel is possible, where are the time travellers? There
are a number of possibilities. The most obvious and pessimistic of these is
that life on Earth may simply not survive long enough for the technology to
evolve. Nuclear wars, giant asteroids smashing into our planet, quantum
instabilities developing within the Sun etc. could all stop mankind (or any
other race) in its tracks.
Yet the absence of time travellers need not indicate anything
nearly so sinister. It is possible that they have been here, and are here
right now, but have been discreet about their presence in order to ensure
that they return to something closely approximating the future universe of
their departure. A further possibility is simply that none has arrived in
this particular universe! Many conspiracy theories are based on the
possibilities of time travelling aliens having the ability to control all
world events on Earth while managing to remain completely hidden from our
view. The CIA may be stranger than you think.
to summarise, we have seen some simple ways of travelling vast distances and
have noted some of their drawbacks. We have also looked at some of the more
exciting possibilities, but some more real break-throughs are required. New mathematical methods need to be developed and new physical
models of the universe must be conceived. Not a job for the faint hearted!
Fortune it is said favours the brave. Nowhere will that be more true than in the race to understand the
ultimate laws of physics. The race that achieves that first will go straight
to the top of the premiership of civilisations. Lets make sure it's going to be us!