This is not an article that purports to establish any link between what I have to say about Black-holes and what I have to say about Action Principle.
First off, there are always a connection between action principle and anything else in Physics. Everything in principle can be derived from the action principle. The action principle is the general principle of all sorts of mechanics in Physics and has the weird power of superiority over everything else, at-least in principle.
So if you want to claim something is inconsistent in Physics, take a piece of chalk and chalk out how it is that the action principle is inconsistent with anything that you want to discard. The action principle has the key to proving how consistent or inconsistent Physics is.
And I am not stating the action principle much, either. I just wish to mention two ideas that have no explicit connection to be brought out by this article. Hence they are to be read without any purported conjunctions of one with the other.
The black-holes are expensive hotels of gravity. What are hotels. Hotels sell you space and time. You take a well designed space for a stipulated amount of time for a stipulated amount of money. You can’t have space and time in a hotel if you don’t have enough ability to make the payment.
The black holes do the same thing. They are intense gravitational regions. A gravity is a particular negative energy configuration of space and time. That is, you can acquire space and time in such a region only if your energy is negative and that too in a very stipulated way. Any other ways are not allowed.
Anything that occupies space and time in such regions of space and time are to be negative in their energy. Which is to say the region of space and time charges you energy, much the way the hotels charge you cash or credit. The source that creates such regions of space and time also has to pay energy.
In other words its own energy becomes so negative it can’t escape the space and time or the region, without making energy payments at first. The Black Holes, the owners of space and time of intense gravitational regions, can’t themselves escape such a region, without first paying huge sums of energy.
The fact that they are the entrepreneurs of such intense negative energies doesn’t see them through any energy exits. Nobody is willing to bail them out either. They just ran out of favor because they got themselves into the most expensive energy malls. Nobody else has enough energy to bail out these Bill Gates of gravitational energy. Black Holes are such a big fire that there is no water to douse out their flame.
What happens when you or me go into these swanky energy malls? Before we can come out of these energy hotels, they have charged our accounts by billions of Joules, that we simply do not posses. We were there to inquire if we can rent some space and before we realized we were already charged in terms of energy. So we are trapped. We are still paying the Black-holes energy. And we are crushed in the process because that’s the only way the black-holes thought we could generate some energy for its energy hungry teeth.
The very fact that you showed up in the hotels of black-hole simply means you incur charges on yourself. That’s how expensive they are in terms of energy.
I already mentioned that these are the most authoritative forms of Physics Equations. The equations of motion that tell us everything we need to know about a physical system are simply special forms of these action principle. So, yes, the Newton’s laws are simply special forms of action principle. The Fermat’s principle that dictates the light to travel straight lest its energy will be unnecessarily spent, is just a special form of action principle.
Whats action principle. Before that we need to ask ourselves whats action? Action is merely the product of energy and time. In an elemental sense.
Therefore if I got 5$ for a week’s time what it tells is I have 5 dollar-week amount of action. It doesn’t mean I must spend that 5 $ in only 1 week. I can spend it in an instant much to the botheration of my mother-in-law. I can spend it over the weeks in little denominations of nickels and dimes. I can spend it in a years time, some of these months will see no expenditure and some will see … well a dollar and two.
But when I add up I must not see more than 5 dollar-week. Remember that the time has to be broken into smallest units so that I know I spent some action/dollar in that small unit of time or not. Which is why I said they are elemental. If I say, I spend a dollar in a months time, I get 1 dollar-month = 4 dollar-week, that’s inconsistent. So increasing time does not increase the action, increasing the energy does increase the action. Time is the container but energy is the substance.
So action is much like the ability to do something and the ability is not just energy but also the parameter time, over or along which we do everything.
And action principle says “we spend action in such a way that we would not have any other choice of spending that action”. Its called stationary action. Because there were no other values of action expenditure, that was possible.
You are moving on a highway because its stationary. If its a little edgy you can’t move. Its not stationary anymore. It gives a little accommodation and a big hole. You don’t like that, but you can’t do anything about it. Same with light, its choice-less about its action, instead of saying choice-less out loud, Physicists say constant or stationary. Light travels a path of stationary action, everything does. When you fall into the Governmental crater on the highway, its because you were choice-less. Physicists are funny; they say “he took the path of stationary action”. [that is choice-less action]
Accidents alone are not lack of choice, moving along is also a lack of choice. Accidents are as legitimate as moving along. That’s because the highways existing in space is your imagination, but the highways existing in time is not. Time is happening independent of our imagination. So when we met accidents they were as choice-less as when we were moving. We didn’t create the time in which the highways exist constantly so that we can move, the times existed independent of our wish, we were just lucky to catch on to reach home.
If you want to blast your Governments this is your chance, when they say they create 100 kms of highways, tell them its not enough, they must mention the time for which they remain highways, lest action can’t be defined.
So light is not doing anything funny, when its moving on straight lines. Its simply a constant line rather than a straight line. In other words the same amount of action (energy * time) would be spent by light, if it tries to move a little off. It doesn’t therefore make a difference and the light finds its highway. But in moving a little off if it meets a big difference in action (action = energy * time, again) then it would take the path; where it can save its action.
Which is why light curves in intense gravity and this is why it curves inside lenses. The energy and time factors are now so that yet another path in the immediate vicinity is available to light that offers it a lower price, of ‘action’. It takes that. It continues to bargain along its motion and saves itself dollars and weeks. It glides along to a ‘better’ inexpensive action path. On an average (that is, over larger amount of time or space) we see that light has deviated from its straight or constant path, a lot. But that’s still another constant.
Everything in nature saves action, because action is difficult to achieve.