1. Just an excuse to keep you updated. The various colors of my web-site.
2. We didn’t make it to the science blog award final round.
Guys we DIDN’T make it into the list of 6 finalists of the 3QD science prize. But there are some excellent blogs out there that did, from which you can learn and enjoy greatly.
Right now I am reading through one, written by Tasneem; which is fabulous as per my own conviction.
It tells you about the action principle.
Which I recently called the principle of choice-less action, the electron just doesn’t have another choice. It has a particular functional form of the action and the calculus of variation doesn’t allow a slew of paths, to be followed by the electron, only a constant, stationary or choice-less path is available.
Its the path which is particular or stationary, in general, not the time which is least, but there are good reason why people often confuse it with a least action or even least time principle. I do have an article where I tried to touch on this matter as I have actually provided an excerpt for, below. But I will get back to this in a later article.
You might also read the following article of mine, on action principle, which might still be a little terse, as it was written years ago, in summer 2012, but highly technical. Yes I will make attempt to make it better readable, but for now I am in a flux **. [You might also wanna read this one. a bit terse perhaps, as well]
First off;
Only some glaring technicalities, in Tasneem’s blog;
1. The light doesn’t want to minimize its time, unlike stated by her, it wants to minimize its path, and NO not for minimizing the time, but for minimizing the action. So its the path which was originally thought to be “shortest time path” that is, geometrical path = straight line.
Then it took centuries to realize “no not geometric path, but optical path”, is what minimizes, the optical path is geometric path adjusted with speed, then came the idea that the physical path would minimize. The physical path is the actual path which is obtained from action itself. Hence action is minimized; this leads to physical path, to be minimized, not time. Time is just the parameter over which the path is traversed.
Note that time is arbitrary, action is not. Its a definite functional form of energy, that is the rate at which energy comes and the spatial function in which energy is distributed makes the particular path which is possible for the particle. Also more and more energy is going to be spent for the same amount of time if the path is more. Hence its the path which is minimized.
The example she gave is quite simple, in which time and path are kind of linear, the speed remains constant hence minimal path corresponds to minimal time. But what one is keeping minimum is the path and the energy. Only when both time and path are minimum the action can be minimum as the speed is constant. Its fine to explain the idea with a simple example. But to say refraction of ray of light follows “minimal time” principle with this simple action is misleading.
The Fermat’s Principle which is whats action principle for light’s motion is based on minimization of optical path (a simple function of speed in any media and the time) and not the time. For more complex situations such as light being considered according to Maxwell’s equations traversing in dielectric media the action is more complicated and not just optical path but a more complicated action is suitable.
If you are not averse to slightly off the topic analogy such as that of psychology which are not quantifiable, there is a physical reason why its not the time, but the energy or action which has to be minimally spent for any trajectory. Love is minimized in a relation, not the time for which love is there. Love is minimized because love is the substance or energy, it can’t be infinite or limitless, not time, time is irrespective of our patience to see that limit. In a simple only situation; time is a reflection of that substance.
Believe it or not action principle in its most basic philosophy, had begun from such ab-initio method of inquiry, which I need a little more research to say exactly by what name its known. But the early philosophers of natural phenomena had realized that nothing can be infinitely stretched, hence there must be contrary forces acting on them. So energy can’t go on increasing, to envisage a path, but has to be cut short somewhere.
Given therefore energy is definitely assigned to a physical system it would mean the energy has to be used judicially or minimally. It therefore in a classical realm as opposed to a new classical or quantum mechanical realm at-least, relates to minimizing the path. The time is just a parameter along which we are calculating. But once the energy finishes, the path has been restricted to a certain length, even though we do not have a minimal time, time can continue to flow.
But for a path which is bigger than the minimal or action-minimal path will spend energy or action less judiciously. The dt multiplied to the E to form the action is not minimal, rather infinitesimal and arbitrary. But the path is what comes from total integration along t = 0 to t = T. Hence path can not be more than the minimum according to the subscription that action be minimal. But there is nothing about time here. In all complex situation one must disregard the tendency to say “least time “principle even though in some really primitive understanding milenia ago thats how the most intellectual human beings thought.
2. I am baffled by one of the things she used in the blog to explain the idea of action. It might be a little inconsistent if what I am thinking is true. When she varied her Kinetic Energy, by changing her velocity eg to v+a and v-a, she is actually also bringing Potential Energy, into the consideration. KE will not change without having a change in PE, right? Because you can’t violate Newton’s first law of inertia, it would continue to move at velocity v, unless there is a force, which she said in the beginning. Force is just potential energy which makes the particle go from velocity of v to v-a and so on. So, that would change the action itself, which she hasn’t included, she went with the assumption that we have only KE, which is why changing velocity v by amount a amounted to not having a minimal action, to be consistent with Newton’s Law which predicts constant velocity under such an inertial situation.
I haven’t read other blogs, but this being immediately appealing to me, because its general physics I just thought about it a little bit.
The material below is more of a personal nature and has nothing to do with the science prize. Its simply a pictorial status update to regular readers here at mdashf.
—– The colors of mdashf —– are what keeps me going … its a bit personal but you might enjoy !
** But good things are happening, Instead of jotting things on my defunct Sony-laptop, I got back my HP all-in-one which I have used previously years ago, a delight for writing and maintaining my website, although the keyboard is a bit hardened, I must do something to get this fixed soon. Also when I said delight I meant the attraction factor, and its a little slow to respond in various situation, so perhaps because its a older generation all-in-one, or may be because its just HP, pun.
Once the gadgets are a delight, it becomes a settling habit to spend more and quality time on this website. I will put a picture of the comp I had uploaded years ago, so you know why I actually love writing here. And, I am actually getting back to regular work, here at my website and my home based-office, after couple years spent for teaching assignments at various places. So, I think I can do justice to my website here, and all the articles that have been waiting to be properly refined for last 4-5 years.
Here are those pictures. But no I did not find a picture at the moment of the white HP all-in-one, but I took one immediately by my smart phone. It does come in handy. So, what we have is the Samsung all-in-one that I used years ago, but not in my possession any more. I just got hold of the pics, how mdashf or Invariance looked years and years ago, say 3-4 yrs ago.
See my desk and office as shown here, I will perhaps add a couple more pics so you get a feel of the mdashf spirit since half a decade. The office space with the Samsung shows our house (and my bed room cum office) from our old house which was built by 2000, so I lived here since 2008 when I returned from USA and Japan. But this house is now our ground floor. We are living in our well spaced and well designed top floor, which you can partly see in some of these pictures. The ground is empty. No its not a coy plan to invite a rentee.
M Dash Foundation: C Cube Learning 