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CHOWDHURY & BRAHMACHARY: GERMS OF MODERN PHYSICS
Regarding this sutra, Jacobi comments thus:
"Wie die Zeit eine Bedingung fuer die Entstehung etc. eines Dinges ist; denn dars ein Ding jetzt oder spaeter entsteht etc., ist durch die Zeit bedingt."
i.e. time is a condition for the existence of a thing (matter, body).
Whether an object originates now or at another time is conditioned by time or in other words, matter is not independent of time. Thus, it implies that matter is dependent on both time and space for its existence.
5. ākāśasyānantāḥ (Sūtra V, 9, Jacobi, p. 41)
Jacobi interpreted this sūtra as :
Der Raum hat unendlich viele (punkte)
i.e. space contains infinite number of points or space is
continuous.
Explanatory comments:
111
The aforesaid sutras put together reveal that (i) (unlike matter) space, time and force are continuous. (ii) Force is conditioned (defined) by the state of motion or rest of an object. (iii) An object exists in space and time. (iv) Matter is not independent of time. (v) A body continues in rectilinear motion in the 4-dimensional space-time continuum unless a force acts on it to deviate it from its motion.
It is interesting to note that in 1916/17 Einstein3 wrote a popular account of relativity theory. In this, while trying to explain a continuum of space he gave the example of a 2-dimentional space; namely the surface of a marble table. He wrote:
"Ich kann von irgendeinem Punkte desselben aus zu irgendeinem anderen gelangen, indem Ich eine grosse Anzahl von Malen immer zu einem "benachbarten" Punkte uebergebe...ohne Sprunge zu machen... die Oberflaeche sei ein Kontinuum"
i.c. I can move from one point to another point without making any (discontinuous) jump as I go from one point to the "neighbouring" point over a very large number of times..... i.e. the surface is a continuum. This may be compared with Jacobi's interpretation of sūtra No. 2. In this way, we can also conceive of a 3-dimensional space and then of a 4-dimensional space-time continuum.
The famous British litterateur and science-fiction writer H.G. Wells*
3. The collected works of Albert Einstein, Princeton University Press, 1996. 4. H.G. Wells, The Time Machine, New York, U.S.A.
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