Why massive particles may travel faster than light.

There is a lot of hue and cry these days at an experiment that has detected a neutrino travelling faster than light. Many physicists are skeptical and are asking for extraordinary evidence as they feel this is an extraordinary result. Many are calling for more accurate measurements of time, distance and masses involved. I believe this may not be an extraordinary circumstance as in my humble interpretation of special relativity it only prohibits massive bodies from traversing the light speed barrier and do not say anything about particles born travelling at speeds greater than the speed of light.  My interpretation is as follows:

Special relativity holds that when massive bodies travel at speed , their length in the direction of motion contarcts by a factor of  (sq root of (1 - v squared / c squared)) . Similarly their mass increases by the same factor, and finally their clock slows down by the same factor.

The above three effects can be readily understood if we consider a 2 – dimensional world (for the sake of this discussion) and add time as a third dimension to this world. We need to make just one conjecture to explain the above three effects in this 2+1 space time continuum. The conjecture is that as a body travels in space with a velocity v, it tilts up in the time dimension. The angle of inclination depends upon the velocity. I will illustrate this conjecture with a diagram:

Figure 1 A cross section of 2+1 space time

Let us suppose that a rocket R₁R₂ is travelling at velocity v toward right. According to the conjecture only its ‘shadow’ R₁R₃ is visible to the inhabitants of the 2D space.  Obviously length L of the rocket visible to the inhabitants is smaller than its rest length L_o. Now special relativity tells us that L = L_o(sq root of (1 - v squared / c squared)).

From Eq.2 when v = 0, K = 0 and when v = c, K = L_o. That is when the rocket is at rest, there is no tilt and hence no length contraction. As the speed of the rocket increase the tilt increases, therefore the length visible to 2D people shrinks. Now, when the rocket is tilted, another effect comes into being. As the Force applied to the rocket to accelerate it in the right direction (in space) is actually being applied at an angle to the space dimension it produces less acceleration in x direction as compared to the expected value (From F = ma law). 

From Eq.2 force available for acceleration in space dimension is reduced by a factor (sq root of (1 - v squared / c squared)), the 2D people interpret it by saying the mass of the rocket has increased by the same factor. Now as v approaches c, the inclination angle gets steeper and steeper and the force component available in space becomes smaller and smaller. Eventually at v = c the rocket is completely vertical and travelling only in the time dimension, and to space people it seems that no matter how much force they apply to the rocket it wont budge an inch, and they therefore conclude that its mass has become infinite and its length has become zero. 

Finally we can explain the time dilation by considering the following fact. If a boat is traveling at a speed v, which is the same as the speed of the water in the river, but in the opposite direction, to an observer standing on the bank of the river the boat looks still.

Figure 2 standing boat

Now when the rocket is vertical it is moving in the time dimension with the speed at which time seems to be moving to the inhabitant of 2D space but in the opposite direction, consequently giving the impression to the observers that the rocket time is stationary.

However, if a body travels at a speed faster than the speed of “time river”, its length may become  negative and its time will start flowing in the reverse direction, and in presence of these two effects its mass will become meaningless. (in other words, instead of offering resistance to the force, the rocket will start attracting the force, whatever that might mean)  (Assuming that the angle will keep on increasing).

On the other hand, the angle of 90 degree may be some kind of a limit, after which the movement of the body would remain vertical, but only increase in speed. In this case, a massive body born travelling at a speed greater than the speed of light will remain undetectable to 2D space people. However, if, in rare cases, they are somehow able to detect the birth and demise of such particles, they may indirectly conclude that it must have traveled at speeds faster than that of light.

Levels of reality

These are actually levels of order within matter. At the fundamental level we have fundamental particles. These particles have their own properties, tendencies and laws of behavior. Using these laws and tendencies they form structures like nucleus and atoms and their movements are also determined by non-deterministic laws expressed in probabilities. At this level we have physics that describes the reality. When these atoms combine to form molecules they also acquire new behavior and these new rules can not be derived from the rules used to describe the atoms and sub atomic particles. Since molecules have structures that have their own reality, which determines how they combine and react, they require their own rules and laws - applicable to these structures. Since these structures do not exist at atomic level, molecular laws can not be applied to atoms. Thus chemistry is the science that describes this second level of reality, so as to speak. 

God

This is just a brief note. I realize that writing a brief note on God would beg the question why or what for, but anyway, maybe in the future i will expand.

So the gist of most of the arguments that claim that science has demolished God's delusion is that all the reasons or attribute people have attributed to God, can now be fully explained by science, with absolutely no need to invent a God to explain those things. Well, let me point out the limitations of this argument. Number one, their thrust is against people who claim in the existence of God and not on God itself. Secondly they rely on the concept of proof and logic. Third their proof is faulty.

So, am I saying that I can prove that God exists? No. Let me explain. First, I do not disagree with those who find flaws with arguments that seek to attribute causes of various natural phenomenon to God. I believe all natural phenomenon have natural causes or explanations, that is it is always or should be always possible to say X is or X happens because Y is or Y happens or something like that. In other words, most of the world works in a "clockwork" fashion, albeit without the connotations of determinism. The universe is a non-deterministic clock work - the future has a definite link with the past, provided you do not think of definite as one to one. In this respect it is right to say that science can or will be explain everything eventually. My question is " is explanation sufficient" in other words, are how questions the only legitimate ones. Maybe not. Maybe why questions are also equally important.

Secondly, it is quite evident by now that logic has its limits, maybe even severe limits, when it comes to accessing truth or achieving truth. There will always be truths that lie beyond logic. Logic is a framework that guarantees correct results within the framework. However, the size, scope and complexity of this framework is finite and limited.

Thirdly, how by showing the non necessity of an entity in a certain process establish non existence of that entity?

to be continued...

Kant

Do I dare write about Kant? So far I haven't. But now I feel,if I don't write I'll never be able to "wrap my head around him". Funny phrase - gives me a headache already. Anyway, when I read that Kant wanted to reconcile or reproach the gap or divide between rationalism and empiricism, but he couldn't quite succeed - I ask why? Is this not sort of obvious. Lets take an analogy - a modern day computer (unfortunately not yet invented in Kant's time). Lets equip this modern day computer with a lot of sensors so that it could accumulate a lot of sensory data. The sensors are capable of sensing and storing this data we assume. Also provide this computer with a state of the art processing core. Now turn this computer on. It starts collecting lots of empirical data - images, video, sounds, temperature, texture, scents, and perhaps even pain and happiness. If this computer is to ever start talking it needs to have some pre- installed instructions of how to respond  and 'make sense of'' this rapidly accumulating data. So there needs to be some before hand warnings of what to expect and some pre existing receptacles for this incoming data. How else can this data be ever useful? However, it is also obvious that not all empirical data can even in principle be fed before hand into this computer as most of this data gets generated in real time as a result of interactions of all moving things. This is what I feel Kant wanted to say. To see if I am wrong I have to read him again. So lets do it.

Theory of society