Friday, March 19, 2010


From Wiki's entry on Leibniz:

Leibniz contributed a fair amount to the statics and dynamics emerging about him, often disagreeing with Descartes and Newton. He devised a new theory of motion (dynamics) based on kinetic energy and potential energy, which posited space as relative, whereas Newton felt strongly space was absolute. An important example of Leibniz's mature physical thinking is his Specimen Dynamicum of 1695.[30]

Until the discovery of subatomic particles and the quantum mechanics governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. For instance, he anticipated Albert Einstein by arguing, against Newton, that space, time and motion are relative, not absolute. Leibniz's rule is an important, if often overlooked, step in many proofs in diverse fields of physics. The principle of sufficient reason has been invoked in recent cosmology, and his identity of indiscernibles in quantum mechanics, a field some even credit him with having anticipated in some sense. Those who advocate digital philosophy, a recent direction in cosmology, claim Leibniz as a precursor.

From  the Encyclopedia Britannica:

Contrary to Descartes, Leibniz held that it would not be contradictory to posit that this world is a well-related dream. If visible movement depends on the imaginary element found in the concept of extension, it can no longer be defined by simple local movement; it must be the result of a force. In criticizing the Cartesian formulation of the laws of motion, known as mechanics, Leibniz became, in 1676, the founder of a new formulation, known as dynamics, which substituted kinetic energy for the conservation of movement.


Phil Warnell said...

Hi Steven,

Actually I’ve become aware of Leibniz central role in the development of the dynamical approach to physics resultant of my reading of a Book by Prof. Harvey Brown called ‘Physical Relativity’. In this book Brown makes the argument for the dynamical approach, with pointing out that although SR departs from the notion of absolute time, it still clings to the concept of absolute space, with General Relativity an attempt to resolve this. However according to Brown Einstein was not entirely successful in this in the denial of the existence of a preferred (fixed) reference frame, which the insistence for is the central premise of his book. However he does point out Einstein’s thoughts in all this when he says in page 140 the following:

”It was a source of satisfaction for Einstein in developing the theory of General Relativity ( he was able to eradicate what he saw as an embarrassing defect of SR; violation of the action-reaction principle. Leibniz held that a defining attribute of substance as their both being acted and acted upon. It would appear Einstein shared this view (He wrote in 1924 that each physical object ‘influences and in general is influenced in turn by others. It is contrary to the mode of scientific thinking, he wrote in 1922, ‘to conceive of a thing ....which acts itself, but which cannot be acted upon’.). But according to Einstein the space-time continuum, in both Newtonian Mechanics and special relativity, is such a thing. In these theories space-time upholds only half of the bargain; it acts upon physical bodies and or fields, but is in no way influenced by them.”

So I find it curious for someone like you, that expounds on the importance of mathematical insight in physics to be so concerned with the metaphysical underpinnings as much as you are. Not that I find this in contradiction, yet rather impressed you recognize that it be important. I myself have spent much time on this problem, to find that the difficulty to be more related to how most all think resolution must be entirely one way or the other and have my own thoughts on all of this. I’m hoping some day these thoughts might be proved justified as in finding that someone else strikes upon them, who is actually a physicist of note, with the insight coupled with an ability to thus able to extend them to full explanation, part which of course would incorporate a rigorous mathematical treatment and description. In the meantime I’m more then content to read, study and gather my thoughts and look forward to perhaps discovering how they might work in better completion.



Steven Colyer said...

Thanks Phil. When I started back on my boyhood love of Math/Physics approx 1 year ago, I swore to myself I would allow absolutely zero "Philosophy" at the time.

I was young in the field and therefore ignorant of course as those two things have a way of going together, and thanks to you and Plato I learned not to confuse "Philosophy": with "Pop Philosophy", which i abhor and continue to abhor.

What you taught me was to rather, focus on the 3 men, Socrates, Plato and Aristotle, on which our entire culture is built, and stray not a whit (or at least as little as possible), and I have you to thank for that.

I also appreciate the whole "Descartes v. Leibniz" debate thanks to your blog, and how under-appreciated Leibniz is in the pantheon of the greats. My mind in more open now because I am more knowledgeable.

Phil Warnell said...

Hi Steven,

No need to thank me, as I find our exchanges beneficial.That is as like me I imagine you find such discussion not to be welcomed in regular company, even if it be at one’s own dinner table. That’s to say its seldom you will find others that have any non trivial conception of either math,science or philosophy and even less that find it enjoyable to have them discussed.

As for you saying in the past you were too young to have such considerations, I would render the fault more to the primary (pre college) education system to which we were exposed. In support I would say it be difficult to point to any truly great mathematician or physicist, who was not as inspired by what else they had read and learned being outside of his chosen vocation and this I would suggest it be a reason equal to the difficulty of the current problems, as to why it seems at least for now we are stuck. So I will just leave you with two quotes of Einstein, with one drawing notice this contention yet also the consequences when it’s not recognized as to be realized.

“Somebody who only reads newspapers and at best books of contemporary authors looks to me like an extremely near-sighted person who scorns eyeglasses. He is completely dependent on the prejudices and fashions of his times, since he never gets to see or hear anything else. And what a person thinks on his own without being stimulated by the thoughts and experiences of other people is even in the best case rather paltry and monotonous. There are only a few enlightened people with a lucid mind and style and with good taste within a century. What has been preserved of their work belongs among the most precious possessions of mankind. We owe it to a few writers of antiquity (Plato, Aristotle, etc.) that the people in the Middle Ages could slowly extricate themselves from the superstitions and ignorance that had darkened life for more than half a millennium. Nothing is more needed to overcome the modernist's snobbishness.”

“It has been often said, and certainly not without justification, that the man of science is a poor philosopher. Why, then, should it not be the right thing for the physicist to let the philosopher to the philosophizing? Such might indeed be the right thing at a time when the physicist believes he has at his disposal a rigid system of fundamental concepts and fundamental laws which are also well established that waves of doubt cannot reach them; but, it cannot be right at a time when the very foundations of physics itself become problematic as they are now. At a time like the present, when experience forces us to seek a newer and more solid foundation, the physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations; for, he himself knows best, and feels more surely where the shoe pinches. In looking for a new foundation he must make clear in his own mind just how far such concepts which he uses are justified, and are necessities.”