Sunday, July 30, 2006
Time is of the Essence
In my preceding entries, I have been addressing this riff that I propose has formed between science and philosophy. In part, I have implied that science losses some of its insight and thereby much of its utility if it denies to incorporate the “why” into its method of discovery. I however realize, for the most part, when I have been comparing science to philosophy, I have been using examples taken from those of the living world. Now one might ask if the “why”, only has application in relation to the organic realm. Perhaps, the non organic realm or what many may consider the more rudimentary natural world, has no aspect of “why” to be explored. So then at a more fundamental level the “why” question could be simply ignored. It would be agreed by many that the most fundamental of all the sciences is physics. To examine this let’s look at what physics has to show us. Now if you look for a definition of physics today it would be most often taken as the first one supplied, for example in the online resource “The Free Dictionary” and reads:
“The science of matter and energy and of interactions between the two, grouped in traditional fields such as acoustics, optics, mechanics, thermodynamics, and electromagnetism, as well as in modern extensions including atomic and nuclear physics, cryogenics, solid-state physics, particle physics, and plasma physics.”However, I view such definitions as too restrictive for what I consider the most fundamental of the sciences. I prefer the one they describe as the archaic definition, which reads as follows:
“The study of the natural or material world and phenomena; natural philosophy.”The reason I prefer this definition, is it is not as restrictive as the first. For the first almost leads one to understand that we have already identified all the aspects of the natural world there are to explore. My primary reason however, for not proposing the first, is that it also implies that this aspect of “why” is already dispelled. The second definition I find to be more general and takes in not only what we have explored and discovered of the natural world , yet also what we could so explore or discover. It does also not limit the methodology by which it may be accomplished. You might say then I have used Occam’s Razor to make the choice.
So now then, what is it I’m going to hit you with today? I beg that you afford me further license to explain before I come to my point. First I’d like to describe a situation you might find yourself in. You and a fellow, I will call Nerdly, are out for a walk, near, yet not at the sea shore. Now although you like Nerdly, for he is truly a pleasant fellow, he often spouts off to you about the benefits of math and science, which at times you find annoying. As you are walking, suddenly you hear a scream coming from the ocean. Although it is at a some distance, you can see to your dismay, that there is a person flailing in the water, in danger of drowning. So you shout to Nerdly, we must go and try to rescue this poor fellow. To which Nerdly agrees. You then take off on a bee line (a straight course) to the person. However, as you look back, you see Nerdly still standing there, with his calculator in his hand, punching in numbers. You would like to run back and scold him, but you are to concerned for the drowning person to waste the time. Now between youself and the person, there is varying terrain. At first you cross the road that you were walking beside. Then you run across the grass of the park. After this across the sand of the beach and then you must finally be prepared to swim in the ocean to reach the person in distress. On your way, you keep looking over your shoulder, to see what Nerdly is up to. First you see him finally begin and run across the road, as you did and yet not in the same direction as you had. That is in a direction that is straight between you and the drowning person. As you continue to run, you observe that Nerdly has again at times changed course slightly. Now to your great surprise as you are about to finally dive into the water, you see Nerdly already is assisting the person back to shore. You are at this point dumbfounded. For although Nerdly, did not leave as quickly as you had or taken the straight course as you did and you are certain that Nerdly is not more athletic then you. He has, none the less, reached the person first and thus saved them from what could have been a horrible fate.
Now after finally the beach's life guard arrives to take charge of the now fortunate person, you ask Nerdly. How is it that you were able to leave after I did, take what I perceived as ever changing directions and still reach the victim before I was able to? His reply is, that for the most part he only acted as nature might have in the course of his journey. Now this has you more confused and yet curious. So you ask, what exactly does he mean by that? Well, Nerdly says, you took a straight course between yourself and the swimmer without regard for the terrain you were travelling through. For as you should know, one can travel fastest on the road and then less quickly on the grass, then even slower through the sand and slowest of all swimming in the water. Yes you say, that’s true. Nerdly then responds, that he calculated a course that while still headed towards the swimmer, involved the least total time in regards to all the terrain through which he had to travel . One where he would travel further over faster terrain and the least possible distance over terrain that was slower to traverse. The optimum course in this regard is the one he chose. Oh, you say, very cleaver, but how is that like nature? Nerdly then retorts, if for instance you consider a beam of light, it would have done a similar thing when travelling through varying media on its way to a particular destination. Only in this case, light, wouldn’t be spending the time to make the calculations, that I had to before I left. He says for instance, if you are pointing a laser beam at a object that lie at the back of several different layers of transparent media, you will observe it to bend when it strikes the beginning of each new media. Like for instance, if there is a coin sitting beneath a tank that has say two feet of water in it and has also a three foot thick glass bottom. You will first notice if you point the laser beam in the straight direction to the coin it will miss. If you adjust your aim, you will eventually be able to spot the laser on the coin. Then if you were to trace the path it took and do some calculations, you will find it has arrived there in the shortest time possible in relation the speed in can travel within all the related media. In other words, it has taken the shortest course through time and not that of distance. You say but how can light do that.? Nerdly responds, that all science has found, is ways to calculate the path it will take and that it is still somewhat of a open question how exactly this happens. The important thing is, Nerdly says, is we do know it will behave this way.
It is then here where you might ask, what has Nerdly been talking about? Well, what Nerdly was referring to, is a property of nature, known as “least action” or more generally as “action principle”. It’s beginning were with a French mathematician, Pierre de Fermat (1601-1665). Who’s actual way of making a living was that of being of lawyer . Now I know this appears to be ripe for a comment and yet to practice wisdom , I shall refrain from such temptation. Many may be more aware of him for something known as Fermat’s last theorem, to which he claimed in one of his letters he had found a proof , but that it was too large to be included in the margin. This theorem wasn’t actually proven until 1995, by Andrew Wiles. What we are addressing here, is known as Fermat’s Principle, in which he stated that the reason light bends when travelling between varying media is that it is taking the shortest path through time rather then that through distance. This was later refined and expanded through the work of Maupertuis, Euler and Leibniz. It was further refined and incorporated into what is known as Lagrangian mechanics by Joseph Louis Lagrange (1736-1813), which is used as one of the bedrock formalizations of physics to this day. In this formalism, all action in nature is considered to be at its minimal.
Okay, you say once again, what is my point? The point to be made here, is that nature in displaying such behaviour, appears (at least for me) to be revealing yet another aspect of its character. Now we discover as was relayed previously that nature is not only economical in its form, as expressed as what can be loosely (but carefully) described as simplicity. It is also revealed in this that it is economical in its action as well. At this point you may also realize there are obviously “whys” that could be asked of nature in this regard. When presented with this my first “why” is, why would nature consider time over distance. Now I wish I could give you a answer for this, yet I can’t. However, I can offer you one insight it has lent me. As you are probably aware, Albert Einstein developed our now modern theory of gravity called “General Relativity”. As a key element in this theory he expressed time as a dimension, that when taken with the other three spacial dimensions, forms the background in which it should be considered. This background in terms of its shape, in relation to the mass/energy that is contained within, is responsible for what we recognize as gravity. Many may have trouble with this simply because they cannot imagine or admit, that time could possibly be a dimension. What then is a dimension? A dimension, is in the most general sense, a direction or degree of freedom, through which one can travel or merely consider. As is indicated by the above example we have discovered that nature responds to time as one of these degrees of freedom or more simply a direction. In fact, in the example I’ve demonstrated it is the one primary to its action. If looked at this way, it is not only easier to see how time can be a dimension, yet also how surely it must be.