And Moses said: “Thus saith the Lord: About midnight will I go out into the midst of Egypt; and all the first-born in the land of Egypt shall die, from the first-born of Pharaoh that sitteth upon his throne, even unto the first-born of the maid-servant that is behind the mill; and all the first-born of cattle. (Ex. 11:4-6)
In the original verse, in Hebrew, Moses uses an unusual expression “k’hatzot halayalah.” The normal way of saying would be, “hatzot halailah” – at the midnight. (in Heb. laila means “night,” and hatzot means “the middle,” i.e., the middle of the night, or midnight.) However, the verse says, “k’hatzot halayalah.” Every commentator struggles with the addition of “k” before “hatzot.” Grammatically, the prefix “k” in Heb. is called kaf hadimiyan and signifies a likeness or an approximation. It is usually translated as “like,” “as,” “about,” or “approximately.” The verse, therefore, means, “about the midnight,” or “approximately at the midnight.”
The commentators are puzzled by this translation. Couldn’t Moses predict the precise moment in time when the plague of the firstborns would be visited upon Egypt? The classical commentaries are well known and printed in most traditional editions of the Chumash. This past Shabbat, as I was listening to the reading of the Torah, when this verse was read, my mind took me down the memory lane to my childhood.
I was thirteen-years-old and very interested in science. By that time, I have already decided to become a physicist and was gobbling up popular books on physics one after another.
In one book about quantum mechanics, I read about the Plank time. Plank time is an unthinkably small interval in time on the order of 10-44 s ((This scientific notation simply means that there are 44 zeros before the first significant digit in this number). It is thought to be the shortest possible interval of time, beyond which time became meaningless. Similarly, there is Plank length thought to be the smallest length possible. In other words, space and time are not continuous, but granular.
This made me think. I knew from studying calculus that the definition of a derivative relies on an assumption that there is an infinitesimally small quantity over which we differentiate. Thus, differentiating over time (for example, to obtain a velocity or an acceleration) assumes that there is an infinitesimally short time interval; and differentiating over space coordinates assumes that there is an infinitesimally small distance. If Plank time and Plank length are the smallest units of time and space respectively, there could not be an infinitesimally small unit of either space or time. Calculus presumes the continuity of space and time, which apparently was not the case. This seemed to me problematic for physics, because everything in physics is expressed in derivatives and integrals. I was convinced that to develop a quantum field theory, we mustn’t use traditional derivative and integrals that rely on continuous space and time and infinitesimal small quantities that don’t exist. So, not knowing any better, I set out to develop a new form of calculus where derivatives and integrals did not rely on the existence of infinitesimally small quantities.
Once my “theory” was developed, I traveled to Moscow to present my work at the Seminar for Theoretical Physics at the Moscow State University. To my disappointment, I was told that what I have developed was a well-known technique called Finite Differences. Nobody, however, attempted to apply it to quantizing spacetime.
My childhood experience with the Plank time suddenly came to mind during the Torah reading this past Shabbat. Moses was telling Pharaoh that the plague of the firstborns would visit upon Egypt approximately at the midnight. Approximately, because time is not infinitely divisible – the Plank time set the limit on the smallest time interval. As I explained in the earlier post “It’s the time, stupid!” Moses was the master of time. Did he know, that because of the Plank time, it was impossible to pinpoint the midnight with absolute precision?