Crossing the ultimate speed barrier!

Last year scientists at the particle accelerator declared that in the experiment that they carried out in the atom smasher, they found that neutrinos travelled 60 nanoseconds faster than the speed of light – the theoretical speed limit that cannot be surpassed as per Einstein’s special theory of relativity and also as per Maxwell’s equations. The experiment which is hailed as perhaps the most important experiments in modern times is being carried out again to rule out possibility of any missing piece. The results of the original experiment were scrutinized extensively for around 6 months, before the result was announced to the public. Even thought there is some hesitance in accepting the result, as it shatters the very basic assumption which the special relativity is based on, scientific community has not out rightly rejected it either. Over the period of time scientists have understood that in science no law, no theory is final. And this has been proven again and again. This is the reason why today they might be willing to scrutinize the experiment and its result closely, rather that ruling it out as theoretical impossibility.

Interesting thing is that, this news made me think about a question – what would happen if some object indeed travelled faster than light. In the past I had thought about it, but could not go much further as I ended up believing that it might not be worth thinking , as it had already been already established experimentally and theoretically that crossing the speed limit is impossible. This news has brought the question back into my attention. So I started thinking about it. In the first few attempts I could not make any headway. But one day when I was not doing anything and sitting idle, I thought it would be good time to think about this. And it is this time my though experiment led to an interesting result. This blog is about my thought experiment and an interesting result that follows from it.

[Disclaimer: I am not sure in a universe where speed of light is the ultimate speed limit for any motion as suggested by the works of great physicist like Maxwell, Einstein and many others, does it even make sense to talk about speeds greater than speed of light. I don’t know if it is like talking about motion of a spaceship when spaceship is the only object in a universe. You can’t say if spaceship is moving or at rest if it is the only object in the universe. Talk about speed of such spaceship makes no sense. I don’t know if my imagination here falls in same category. But then I say, that in classical world of physics when the new counter-instinctive theories of physics like – relativity, quantum mechanics, string theory were not known someone could have thought about my thought experiment the way though about it. Without bearing the burden of keeping in mind that speed of light cannot be surpassed. So it is with this classical approach in mind I am attempting to write about this interesting thought of mine. I am not responsible if I have missed something and if the conclusions drawn here are wrong ;)]

In order to correctly carry out the thought experiment we need to understand few things. We need to understand the action of seeing more closely. So what happens when we look at an object ? What do we see ? Well, we see the object! But if you think little you will realize, what we see is not the object but object’s image as it existed some time back. How much back in time ? Well by the same amount of time as required by light to travel the distance between the object and your eyes. In a sense we are looking in the past – the object’s past and we see how it looked then. This is the reason they say when you look at distant stars, galaxies you are not looking at them but in their past, you are looking at cosmic history. So the point is when we look at an object, we look at its image as it existed then. When we look at an object for a while, we look at the series of images of the object as it existed in that entire duration of time. What is true for an stationary object is also applicable to a moving object. Let’s say a Red ball is approaching you. What you see is series of images of the Red ball as it existed at different points in a path from its original position to you. When the speed of the ball is less than the speed of light, the image of the ball at rest will reach your eyes before the image of ball midway in the path. At each point in its travel, the ball is emitting image .But as speed of the ball is less (in fact much less) than that of light, the images of ball reach your eyes in the correct temporal order. Which means the image of object when it was at rest will reach your eyes before the image of the object midway in the path because the object was at rest before it came midway in the path. So all good when speed of object is less than speed of light. What happens when speed of the objects exceeds speed of light ? How will see this approaching red ball at such a speed ? Well, this is the interesting part of this blog post.

Imagine speed of the object is twice the speed of light. Now consider that the object has actually reached a point midway between you and objects original position. Assume that the object reached the midway at time t1. Meanwhile this is what has happened. A ray carrying object’s image left heading towards yours eyes when the object was at initial position at say time t0. Let’s call this ray r0. At the same instant the object itself left its initial position heading towards you with twice the speed of the ray of light. Therefore when object is at halfway in the path, the ray carrying objects initial position- r0 has travelled only a quarter of the total distance. In other words r0 is lagging behind the actual object. Now at time t1, the object emits another ray of light with the image of the ball at midway. This is ray – r1. Now since the both r0 and r1 are light waves they will travel at constant and same speed. But since r1 has got a head start and less distance to travel (only half of the total distance) than r0(which has to still travel 3/4th of total distance) , r1 will reach you before r0. So we will see ball at the midway before we see it at initial position. This will be true not just for r1 but for all the rays emitted by object on its way towards us. Hence the ray emitted by the ball when it is very close to us, will have got the longest head start and would have least distance to travel. Let’s call it r10. So the first image of ball we will see will be r10. This will be followed by images of r9, r8…r1, r0. In other words we will see the object moving away from us, while it is actually approaching us! Bingo! We will see the ball having reached us before it left its initial position. The only time we see object in its real position, is when it has reached us.

What happens next ? Well object continues to move with twice the speed of light and goes past us. And while going away from us, it will again leave trail of images behind it – the images of object moving away from us. These images will however be in the correct temporal order. The object’s image at far away distance will reach us later than the one where it just went past us.
After combining above part we have following interesting conclusion in summary. After the point of impact (the moment when the object has reached us) we suddenly see an object front of us. It is as if the objects magically materialized in front of us. Then as the actual objects moves past us, we see two simultaneous images of the object in two opposite directions (one in which object approached us and the other in which it left us). In fact we will see series of such images. So effectively we will see the same object moving toward us and going away from us at the same time! If the initial position was at an infinite (or very very very far) distance from us and the ball goes past us to an infinite distance, then perhaps we won’t be able to know the direction in which it came and the direction in which it went. All we will have is a ball which magically appeared in front of us and went in two opposite directions past us! Interesting though experiment… right ?