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Monday, January 18, 2010

0105: Actus Essendi: Newton, Einstein, Aristotle, and Aquinas

Entry 0105: Newton is to Einstein what Aristotle is to Aquinas

The contribution to the development of modern physics by Newton and Einstein is similar to the contribution of Aristotle and Aquinas to the development of the “philosophy of being.”

Despite the fact that the realm of their intellectual activity is quite different, it is possible to draw a parallelism between the two pairs of thinkers.

Just as Newton’s physics can be said to have been superseded by Einstein’s physics, similarly Aristotle’s “philosophy of being” can be said to have been superseded by Aquinas’ “philosophy of being.”

While it is true that Newton’s physics is contained in Einstein’s physics, one must say, however, that Einstein’s physics is something entirely new.

Similarly, Aristotle’s “philosophy of being” can be said to be contained in Aquinas’ “philosophy of being” but one must say that Aquinas’ “philosophy of being” is something entirely new.

The fact that Newton did not become aware that his mathematical formulations for the phenomenon of motion would not apply to objects moving at or near the speed of light, does not mean that there were no objects moving that fast when Newton made his contribution to physics. (It is well known that Newton’s second law is slightly inaccurate for calculations involving Mercury’s orbit.)

Similarly, the fact that Aristotle did not catch a distinction between “essence” and “actus essendi” in the “things of nature” does not mean that the “things of nature” were not always made that way.

The question then of how did Einstein come up with a new mathematical formulation for the phenomenon of motion -- a more general formulation than that of Newton and a formulation that did not invalidate Newtonian physics, -- is similar to asking how did Aquinas come up with a new set of metaphysical principles, the metaphysical principles of “essence” and “actus essendi,” -- a more foundational distinction than any of the distinctions discovered by Aristotle and a distinction that did not invalidate Aristotelian metaphysics.

Most likely the role played by revealed truth in the emergence of insights in Einstein’s mind was small, to say the least. But in the case of Aquinas, there is no question that revelation played a significant role in his mind to be able to come up with a new and extremely well defined metaphysical distinction, the distinction between “essence” and “actus essendi.”

The “essence” and “actus essendi” distinction applies to all creatures without exception (including purely spiritual creatures) and reaches beyond the created world allowing the human intellect to approach and “define” the essence of God as “pure unparticipated actus essendi.” Aristotle did not come this far.

In Einstein relativity, the ‘equation’ for ‘momentum’ is

[p = (gamma)(m)(v)],

where ‘p’ is ‘momentum,’ ‘m’ is ‘rest mass,’ ‘v’ is velocity, and ‘gamma’ is a ‘factor’ derived by Einstein from mathematical ‘transformations’ and formulated as

[(gamma) = 1/(√(1-(v²/ c²)))],

where ‘c’ is the speed of light. Newton did not come this far.

However, when ‘v’ (velocity) is small, the factor ‘gamma’ in Einstein formulation is approximately equal to ‘1’ and the ‘equation’ for ‘momentum’ becomes

[p = (gamma)(m)(v)] = [p = (m)(v)],

which is precisely the Newtonian equation for ‘momentum’ still valid for motions observable with ordinary instrumentation. Einstein did not invalidate Newton.

Newton’s second law states that

[F = (dp)/(dt)],

where ‘F’ is ‘force,’ ‘p’ is ‘momentum,’ ‘t’ is ‘time,’ and ‘d’ is the sign for ‘first derivative.’

And because, as indicated, ‘m’ -- the ‘rest mass’ -- is a ‘constant’ for ordinary observations where ‘momentum’ is [p = (m)(v)], the equation for ‘force’ in Newton’s second law amounts to

[F = (dp)/(dt)] = [F = (m)(dv)/(dt)].

Now, the ‘term’ [(dv)/(dt)] is simply the mathematical description of ‘accelaration’ which has the formula

[a = (dv)/(dt)],

where ‘a’ stands for ‘accelaration.’ Thus, the final equation for ‘force’ in Newtonian physics is

[F = (m)(dv)/(dt)] = [F = ma].

To conlude, a number of similarities can be established between the contribution of Newton and Einstein to the development of modern physics and the contribution of Aristotle and Aquinas to the development of the “philosophy of being.”

I have directed attention to some of these similarities.

Note on Translation: The expression "actus essendi" is translated into English as "act of being," into Italian as "atto di essere," into French as "acte d'ĂȘtre," into Spanish as "acto de ser," and into German as "Akt des Seins" ("Seinsakt.")