Singulary and Black Hole

Black Holes are a topic that have some standard set of information that every physicist will agree upon; which include the time dilation due to gravity, the existence of event horizon, so-called "spaghettification" etc...; but after a certain point, each physicist will give his/her own interpretation... especially when it comes to what happens at its center.

For example, Leonard Susskind's notion of a black hole comprises of a holographic universe in which (pardon me for my inaccuracy here) everything that happens in this universe has a projection on the event horizon of a black hole. Or in the contrary, we are the projection of whatever is happening in the event horizon of the black hole. Similarly, other physicists say that center of Black Hole consists of a singularity which is a point of infinite density and zero mass; which is obviously impossible for our mortal minds to comprehend at intuitive level; and then there is this firewall event horizon theory... so on and so forth.

Nobody has gone inside a blackhole ever. Even if someone has, it is meaningless to assert such, because any event inside a blackhole cannot be assigned an instance in timeline which we have been experiencing since the beginning of big bang. So any astronaut who went inside a blackhole, never went inside a blackhole technically. This post is touching that area where there is no defined agreement on what happens when something falls inside a blackhole based on assumption that no tidal effects and spaghettification happens. That is to say, entering a black hole is assumed as fairly decent process instead of violent one.

I want to assert my own ideas in this post, without asserting that I am any authority in the subject any more than a curious thinker thereof. So I would like you to have it as a food for thought and maybe comment your response.

Before starting off, I would like to first assert few premises as follows.

1. Our Universe is made up of 3 and 1/2 dimensions: What do I mean by that? I am counting the spatial dimensions (x, y, z) as 3 complete dimensions and the time dimension as a half one. This is because unlike the space where transition from point A to point B in any coordinate is equally valid and easy as transition from point B to point A, we cannot do that in time. If t1 is a point in time coordinate that precedes t2, then there is (at least for now) no known way to go back from t2 to t1.

In other words, 'forward-backward' makes one spatial dimension. 'Right-Left' makes second, and 'up-down' makes the third dimension. Whereas in time, there is transition only in 'future'. There is no backward. So time is a half dimension.

2. The number of dimensions remain conserved under all circumstances: Now this is simple observation. You cannot practically make a cube into a square or a 4D tesseract. A cube is always a cube. We can transform it into sphere or cone or whatever, but whatever we transform it into, it always remains a 3 dimensional object. Similarly, the same rule holds for any 2d object. A square cannot be practically turned into a cube. I don't know if there is any physical law that states otherwise or in accordance, but for the sake of this argument, let's assume that any object existing in n-dimensional space has its dimensions conserved under all circumstances.

3. Universe tends to find a way around the situations where mathematical models show singularities: Let me give you an example. In the simple and humble Newton's laws of gravitation; which is the inverse square law, force of gravitation between two bodies increases with the decrease in the distance between their centers. 

                                                               F=GMmR2

The point of singularity of this equation comes when the distance between the two bodies approaches zero. And we all know this is impossible. This is because each body has some definite amount of size in 3D space which is obviously greater than zero. Given the body is not a black hole or something like that, it has some definite density and so it has to occupy a definite volume which corresponds to a definite radius that its matter occupies. Any other outside body cannot just merge the two centers. Now even if one body digs into another body and goes to its center, for instance, even if we dig down to the center of the earth, we will still not feel infinite gravity, we will feel absolutely ZERO gravity there. This is the clever way nature bypasses any singularity that comes along the mathematical model of the universe.

Let me give you another example. In special relativity, we know that in order for any object to travel at the speed of light, universe demands infinite amount of energy. And we all know it is impossible.

So even if the equation 

                                                                  m=m01−v2c2

turns to singularity when 'v' is replaced with 'c', does not mean that is possible in practical. For things like photons, where v = c in actual, this equation does not simply apply because those objects do not have rest mass at all. This is how nature or the universe conspires to bypass any singularities that may arise in the mathematical model to describe its workings.

Similarly, you cannot approach 0 Kelvin temperature whatsoever. Why? Because that is the point singularities in maths exist. Universe will always and always conspire to either make it impossible to reach that stage, or will cleverly get around it.

Just because our math says infinities, does not mean they actually exist. It simply means, there must be a way around it which universe has engineered cleverly. We can assume the same thing for center of black holes. 

Now let's proceed further. The infinite density and the zero volume that comes up in maths when we take into consideration the center of black hole can be a mere mathematical limitation which we use to describe the situation around a black hole.

Imagine a person crossing an event horizon. Since the escape velocity of black hole after event horizon is greater than speed of light, means even if that person shines a flashlight towards the "outside" of black hole, there is no way that light is going to escape from the black hole.

The flashlight that receded away from him towards the "outside" of black hole will not cross the event horizon boundary. Since gravity is so strong, the photon/s will have to fall back into the center and move in the same direction as the person himself is. It is very much similar to throwing a stone upwards. The stone moves upwards, deaccelerates, comes to a stop and then starts accelerating towards the center of the earth. Photon will experience the same thing. Black Hole's gravity will finally pull the photon back which was trying to escape the event horizon.

This means, there will be a time when the photon will come to stop. At that instant, when the photon has come to stop (after which it will accelerate towards the center of black hole), things start becoming inconsistent.

1. Photon cannot slow down or speed up; let alone stop. The speed of light is constant whatsoever. Theory of Relativity crashes if that happened.

2. Speed of light is constant for all observers. We know this already.

Now to circumvent this problem, there is only one thinkable way. That is, that the observer who was shining his flashlight towards the "outside" of blackhole while falling in, cannot simply do that. To place it more elegantly, we can say that the direction in which he can potentially travel to come out of the event horizon is simply not available to the person who fell in. The only direction he is now moving is towards the "inside", or we can say he will only fall towards the center of black hole. There is no possibility that any event wherever in space, and whenever in time can occur that occupies a direction that leads towards the event horizon boundary from inside of the black hole.

Consider this. If no event is possible in the direction of 'outside' the black hole, means the direction itself is not available at all. At this point, I would like to introduce some humble notations.

Allow me to write the three space dimensions and one time dimensions like this...

(x1,y1,z1,t12)
The number 1 in the subscript represents the degree to which that coordinate system is available in the given coordinate system. As discussed earlier, (x, y, z) are spatial coordinates and allow any event to occupy both positive and negative magnitudes respectively without any difference; and so each coordinate will be counted as one complete coordinate. Whereas time 't' is half and allows an event to occupy only positive magnitude of it. No event can occupy any scope in the negative 't' side. This is why it is counted as a half dimension only.

In the scenario above in which an observer was falling in a black hole, we saw that the direction which pointed towards the event horizon from inside is simply not available as it will lead to inconsistencies.

Let us calibrate our coordinate system so that the person is entering the event horizon in a positive 'x' direction. Before he hits the boundary (he doesn't actually hits anything physical though), we have consistent coordinates 

(x1,y1,z1,t12)

Now after he crosses the event horizon, we see that negative x is not available to him. If you are thinking that he can simply turn his head around to see the universe going away from him as he falls into the abyss, he can't. That direction is unavailable to him. We can therefore say that the -x is missing from the whole coordinate system and therefore we can rewrite our coordinate systems as:

(x12,y1,z1,t12)
And here comes the problem. Adding it all up, we find that anything going inside a blackhole turns out to be a complete 3 dimensional entity. Earlier, we discussed that what we assume to be 3 dimensional is not actually 3 dimensional, but 3.5 dimensional. However, while falling towards the center of black hole, half of 'x', one complete 'y', one complete 'z', and half of 't' actually sum up to 3. Not 3.5.

We have to keep the total dimensions conserved. And for that we cannot bring back the negative x as it will inherently violate the definition of black hole. Bringing back the negative x will imply that the events which lead to the outside of black hole are possible. And hence, there is no black hole. This will not work. 

So the only possible way we can keep everything consistent is by adding a negative 't' to our whole coordinate systems and rewriting it as follows:

(x12,y1,z1,t1) 
You see, in this coordinate system, we have our 3.5 dimensions conserved. And the dimension which we saw as "time" is now a spatial dimensions beyond event horizon. The existence of negative 't' implies that a person can freely move from what we call the 'past' and 'future'. Our time, becomes the observer's space.

Does that mean he can see our past and our entire future? Well, no. This is because if there are two observers, one outside the event horizon and other inside, the "time" of outside  observer is another spatial direction for inside observer. In order for the inside observer to see outside one's past and future, he needs to coincide other three coordinates as well. Because the whole life time of outside observer happened in an (x, y, z, t) system totally different from the (x, y, z, t) system the inside observer is now at. As an example, the point (1, 3, 6, 2) is not coinciding with (1, 9, 4, 7) Just because the first coordinate is same does not mean the whole point do. Similarly in spacetime coordinate system, 

x12=t12
does not imply the two observers will be able to see each others' past and future 

And the half 'x' dimension that the observer inside is now experiencing is actually what he calls his timeline. Which leads us to think that crossing an event horizon (ignoring the violent scenarios) actually does nothing more than transforming the 3.5 dimensional coordinate system. And thus, falling towards the center of a black hole is nothing but travelling towards the future.

So maybe, we who are ageing and living our lives in our limited time are actually falling towards center of a black hole so gigantic that it encompasses whole universe. Our "past" is direction from where we can escape this black hole... and which is why time travel in past is not possible.

And this may answer what was "before" the Big Bang. Nothing. All it might be another universe that had a black hole which sucked us inside it. We are just drifting towards the center of that black hole which we perceive as time progressions.

Well we can go on and on with the fantasies... but most importantly, I think this is how universe has engineered itself to bypass all the singularities and infinite densities and other crazy mathematical scenarios which come across general relativity. Universe simply switches the count of the set of 3.5 dimensions among the total 4 that potentially is what the universe (on macro scale) is made of.


What do you think?