inside Ninja's Brain

In the earlier post, there was a mention of paradoxes. For those who are quite unaware of paradoxes let me give explain what is means. It may be defined as a sentence or a group of sentence which leads to a contradiction or situation which defies logic. Lets see it in the form of an example, ie. If I say the following statement “When i dropped the phone it went up and down at the same time”. Now this statement is not logical as, the phone cannot go up and down at the same time since it would do only one of the movements in a given time frame. The biggest reason why time travel is a confusing concept for everyone is due to the many paradoxes it presents. Lets see how we can look at those.

The Clock Symmetry Paradox

    Now
In special relativity, clocks slow down by a factor of 1/sqrt(1-v²), sometimes called the “time dilation factor” or “gamma”, Where v is the relative velocity of the subject as per the observer. But according to the principle of relativity as used in special relativity, any uniformly moving observer will see the same effects if they consider themselves to be at rest. Therefore, if two observers are moving, each relative to the other, then each will “see” the other observer’s clock “running slow”. Now relative velocity implies that they need not be necessarily moving in the same direction! But isn’t this a paradox? After all, how can it be that both A’s clock is ticking slower than B’s clock and B’s is ticking slower than A’s?

    No, it’s not a paradox, not if you can explain it. The resolution is because of the fact that the relationship of one space-time coordinate system to another in special relativity is mathematically a kind of rotation. It is the same effect one would get if one had two x-y coordinate systems, and there was an angle between the two x axes. Consider this diagram, of two x-y coordinate systems, one with coordinate axes rendered in blue, the other with coordinate axes rendered in red.

Now, let’s build a brick wall along each of these two x axes. The analogy here is, each brick in the wall is analogous to a clock tick along the timeline of a moving observer in special relativity(a clock tick can be a second, a minute or any form of periodic event which is constant). Consider a person using the red coordinate system to compare x-length of red and blue bricks.

We can see that somebody using the red coordinate system will think the x-extent of the blue bricks is less than the x-extent of the red bricks, and at the very same time, looking at the very same bricks, somebody using the blue coordinate system will think the x-extent of the red bricks is less than the x-extent of the blue bricks. ( Look at the comparison lines drawn. Basic Cartesian coordinate system rules say that measurement in any axis should be taken in alignment with the coordinates, which is exactly how we are doing the calculation in the given diagram).

Grand-father Paradox

    Now this is more of an interesting and a real life imaginable kind of a paradox. Now consider this scenario. You go back in time around 100 years, then find out where you grandfather lives and then you do something which prevents him from meeting your grandmother which results in him marrying someone else other than your granny. This would imply that your father/mother did not exist and thus implies that You do not exist. If that is the case, then how can you meddle with this whole scene in the first case? This simple paradox is known by various name including the billiard ball paradox, the grandmother paradox etc etc.

    To understand the paradox further and to see an possible resolution for the same check the picture below.

In the first pic, the same paradox is shown as a billiard ball version. The worm-hole shown is nothing but a form of a time travel which we could discuss later. Now, if a ball was fired into the entry of an time machine, and it exits the machine in such a way that it knocks the original ball (remember that the ball is travelling back in time), thus preventing it from entering the time machine in the first place. This is similar to the grandfather paradox. The resolution to this can be seen from a more simple perspective in the second diagram but is quite difficult to accept. The claim of resolution being that nature will permit the ball to exit only in such manner that the it does not hit the incoming ball at all.

    Before we jump into conclusion, this can be shown mathematically using probability theory. Consider the probability that the exiting ball will hit the entering version of it as X. Now using simple probability law, we could say that X=1-Y, where Y is the probability of the ball not hitting and 1 is the maximum probability. Calculation of Y based on conditional probability itself would be very tough and would approximately near Infinity (chance of ball getting stuck + chance of ball exploding+ etc etc). This would imply that the probability of the ball hitting it is almost 0, which is next to impossible. What scientists claim is that nature would shift probability in such a way that, no matter what the ball will not hit itself.

PERSONAL VIEW: I don’t or can’t accept the scientist view, coz of one reason mainly. A slight modification of this scenario would render me a super-human provided the scientist views are correct. Consider this scene, where I come back in time but NOT alone, I time-travel with my son. Once in the past, I could do anything to try and get myself killed but I just would not die, since If I die then how can my son who is with me exist? So nature should technically prevent me from dying at all costs, implying that I am a super human with the only weakness being my son. So I don’t think this probability play is a resolution to the grandfather paradox.

    Another resolution which is provided by the scientists is an adherence to the multiverse theory. According to this theory, there exists not one universe, but an infinite number of parallel universe which will contains every possibility of events. For example, there could be a universe in which I do not write this blog, or one in which I might even die writing this blog. So when I travel back in time, I do not travel back in time to this universe, but I travel back to a universe where things would be as it fits. So if I go and kill my grandfather, it will NOT affect my universe but another universe where already my grandfather was dead and there did not exist me, in the first place. In my original universe, I would just be missing from my present!!! This is a more acceptable version of the theory but a bit too hokum as the number of combinations of the universes would be too much to even imagine…

PERSONAL VIEW: I kind of somewhat like the above theory, but then the implications are huge. I would rather stick to a modified version of the same, which is a kind of a triggered multiverse theory. In this, a secondary universe is created only when a time travel is initiated, implied that the Time travel triggers a mirroring of the existent universe to a parallel one, between whom the time travel machine is the bridge. Any change which is made there, only affects the other universe and not the original one. So if I were to travel and kill my grandfather, then there would be a parallel universe in which I don’t exist but if i return back to the exact time of me travelling, then I will return to my own universe where, I will be existing since, I did not kill anyone in my past. Effectively speaking, I just would not be able to change everyone’s present, but would just be given a choice of living in the past, I chose to create. I can be visualized from the diagram shown below.

    In the above diagram, the red line indicates the original universe in which you live. If you use a time machine to travel back into the past, you create a parallel universe represented by the blue line. Now the green line represents the path you took to reach here, if you take any other part than this one, you end up creating yet another universe. So if you have to return to your universe, the only way is the green route. Now if you kill you grandfather or if you get killed at this point, the Blue universe just would not have you. Everything else would work out perfectly well. Now moreover, if you return back after killing your grandfather (through the green route), you will reach back the red universe where you as well as your grandfather had existed. But if you choose to live in the blue universe, then you will have a normal existence with probably a double version of you, in case you don’t mess with your creation. This hypothesis would very clearly give a clear resolution to the grandfather paradox. We might be living in the red universe, or maybe in a parallel universe created by someone due to his time travel. We just don’t know. Moreover, that would also explain why no one has gone into the past and changed anything, coz even if someone did, it would not make any difference to us. This simple solutions is the reason why I came up with this triggered multiverse theory. (the analogy to this would be us creating a copy of crucial data provided we intend to mess with it. The copy never affects the original no matter what we do with it!)….

Now that the paradoxes are done, How we intend to do it will come soon. Till then think whether a modified version of matrix is really how the world is existing now…

-Ninja-