Bermuda Triangle, definitely my
most favorite place in the world around 15 years ago! I was so into all those
stories of lost ships and air fleets and I was pretty sure I knew why that place would be like that. It should have been the time. Of course there are infinite number of timelines and
Bermuda Triangle, because of its electromagnetic properties, is where these
timelines get mixed together. So all those ships and people are right now
somewhere here but in another time. Isn't that obvious? Not only I had a lot of reasoning for my
assumption, I really wanted it to happen to myself as well, to get lost in
time. But it didn't and I got to live the same life as all of yours
(with a little bit of more trouble in it) so after 15 years I can use it as an
introduction in my blog post.
Nowadays I don’t really care
about Bermuda Triangle anymore and my most favorite place in the world is
somewhere in Scotland but time is still one of my main concerns. 15 years and I
never stopped thinking about it. About this feeling that something is wrong. Anytime
that I’m looking at my watch or my cellphone, that’s the first thing that comes
to my mind: ”what’s this that I’m looking for to know?”
Time is the story of a king who
became a slave but never could be a king again so we could make a movie out it!
It used to be the most absolute thing. No one dared put a question mark
anywhere near time. But Einstein showed that not only time is enslaved by all
the massive objects, it’s totally a relative thing. Different observers with
different velocities would feel the time differently. The throne was broken and
a huge question mark kept fallowing time. What is time?
But question mark was not the only
thing following time. there is a little demon that pops out by time
whenever we want to mix it with other physical quantities like space or energy.
A demon labeled as “i”, the square root of -1, which serves as an imaginary
element. For example, in order to write down the space-time coordinates, we
need to have x, y, z and i*c*t. C, the speed of light, gives the time the same
dimension as space in order to make them compatible with each other. But what
about “i”? More generally, what’s an imaginary number? I’ll definitely dedicate
a whole post to these creatures one day but very naively speaking, imaginary numbers
are the numbers that don’t exist but we need them to describe things that
actually do exist. Among all properties of imaginary numbers, I need to
mention one. Only odd powers of imaginary numbers are imaginary. Any even power of an imaginary number is indeed a real number.
You probably read the fourth line
of the above paragraph in less than 30 seconds. I, on the other hand, spent
days and months, just looking at ‘ict’ and thinking about it. In order to have
a space-time, not space and time separately, space and time must be compatible
with each other. As I just mentioned, the speed of time makes their dimensions
compatible. So maybe ‘i’ also has a similar job. It’s making time compatible
with space by making it “real”. What if time itself is imaginary and by
multiplying it by an ‘i’ we’re turning it into a real quantity to be compatible
with the other 3 real quantities that are our 3 spatial dimensions. Something
tells me that we’re going to have a long long fight about what’s real and what’s
not in future and I’m not going to bother now but I want you to know why I’m assuming
time to be imaginary but not space.
A very classical example is displacement, velocity and acceleration. It appears that we have a
pretty good understanding of displacement and we can control it. We can choose
in which direction we want to move and when we move we feel the displacement.
But time doesn't care about us. To us, it's always moving in the same direction
with the same paste and we don’t really understand it. What we see is its
effect on other things like aging or the color change in fall. Though we think
we understand displacement, we don’t feel the constant velocity. If I put you
in a dark box, you can’t ever tell me whether you’re moving with a perfectly
constant velocity or you’re stationary. Again, we understand constant velocity
when we can compare our self with stationary objects or objects possessing
different velocities. We all know that constant velocity is the displacement
over time. If denominator is imaginary, then velocity is imaginary as well. But
if we do the same thing again, this time dividing the velocity by time, both
nominator and denominator are imaginary that will lead to a real quantity,
acceleration. We always feel the acceleration while driving or in a
rollercoaster ride if we can stop screaming.
Now, if you think you’re a little
bit ready to accept that time may be an imaginary parameter, it’s the perfect
time to ask the question of the day: Is time really imaginary?!
I’m not trying to piss you off
but one can easily argue that all I've talked about so far can lead to two
different conclusions. Either time is imaginary or we think that time is
imaginary. Well of course there’s a third case that I’m wrong entirely but I
prefer to ignore that for the sake of ummm, well me. But now let’s take a look
at the other very important aspect of this universe, the quantum world.
Interestingly enough, you’d never
be able to find time in quantum formalism alone. ‘t’ always comes with an ‘i’,
our dear imaginary friend. In the simplest case, the time evolution of any
wavefunction appears to be in the form of exp(it). Also the very significant
difference of the quantum world with our classical world is the time symmetry.
Simply, quantum particles don’t care about time and can freely move forward or
backward in it, something that’s not possible for us poor classical
creatures. Time reversal suggests that time for quantum world is as real as
space and it’s just us who sees time as an imaginary parameter. This indeed may
explain some of the bizarre quantum behaviors such as the time need for quantum
tunneling. Imagine yourself, standing in front of a rigid wall and keep hitting
it with a tennis ball. Of course no matter how many times you repeat this, the
ball will be bounced back to you. But what are the odds for the ball to pass
through the wall without making a hole or any damage on it? The probability of
such a phenomena is so small that if you stop eating, sleeping or going to the
bathroom and keep hitting the wall with a rate of one hit per second, it will
still take you more than the age of universe to see the ball ‘tunnel’ through
the wall. But in a quantum world, a phenomena like this is not only quite
possible, it’s happening all the time. This is what we know as the ‘quantum
tunneling’ effect. But more interestingly than the tunneling itself, is the
time that would take the particle to tunnel through. Theoretically, this time
is absolutely zero for us, as soon as the ball disappears on one side of the
wall, it appears on the other side. This would physically be possible if
quantum particles could have access to a timeline perpendicular to ours so what
a moment appears for us may be a lifetime for them. That’s also another role of
‘i’. keep in mind that on a complex plane, the real and imaginary coordinates are
perpendicular to each other.
This is it for this post but it’s
not it for the time! In the next post I’m going to continue by looking into
some important questions. I’ll try to explain why it should be like this, what
the difference between us and quantum particles is and why we should feel the
time differently. Then we go over the most general question, whether time even
exists or it’s an emergent of a more fundamental thing.
Maybe it’s a good time to say something out of the box. I’m not here to convince you believe anything.
As a matter of fact I don’t really care what you believe in. That’s why you
haven’t seen any reference link or things like that so far. I’m here to give
you some ideas, to challenge you. There’s a huge chance that all or a portion
of what I’m saying is wrong, it’s up to you to figure it out by reading, researching
and more importantly thinking.
To be continued...

