Feel lost in time? Is it just a feeling?!

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...