Einstein, the searcher : $b his work explained from dialogues with EinsteinMoszkowski, Alexander
Philosophy
Einstein, the searcher : $b his work explained from dialogues with Einstein
Moszkowski, Alexander
Einstein, Albert, 1879-1955; Relativity (Physics)
M.: I should like to touch on other limiting cases, in particular two
that I find it impossible to interpret. Lotze mentions them in his
Logic. The first concerns the infinitely long lever whose fulcrum, or
turning-point, is at the confines of the universe. According to the Laws
of Levers, a mass of magnitude zero will suffice to keep in equilibrium
at the end of the other lever-arm any weight, no matter whether it is a
million times heavier than the earth. Our imaginations cannot even
picture this. Yet I cannot feel satisfied with the mere explanation that
it is an exceptional case, an extension of a general law to a case in
which it is no longer applicable. The second example is still more
perplexing because it does not require a journey into other worlds, but
leads us into inconceivable consequences even if we remain on the earth.
Lotze considers this second limiting case easier; to me it seems more
difficult. It is this: The force that a wedge exerts is inversely
proportional to its thickness. If it is infinitely thin, this formula
gives an infinitely great result, whereas, actually, the force exerted
is nil. This very thin wedge, transformed finally into a geometrical
plane, should be able to split in twain any wooden or even steel block.
And now, consider a special arrangement of this wedge in which it is
resting with its extremely sharp edge vertically downwards, whereas at
the top it broadens to a little ledge which supports a weight. We then
get the incredible result that this wedge, which can be imagined
concretely, should be able to cut through the whole earth with its
extremely fine edge, if placed on some base. Where is the fallacy in
this case?
EINSTEIN: The mechanical facts have not been taken sufficiently into
consideration.--He illustrated his further remarks by drawing a few
strokes with his pen, and proved from his diagram that a wedge of this
sort would be able to perform what I assumed, only if the base on which
it is placed is composed of separate laminae. Otherwise the assumption
that the force is infinitely great would be erroneous.
* * * * * * * *
After this digression to a limiting case on the earth we returned to
more general problems, and the question of the finitude or infinitude of
the universe. Shortly before, Einstein had given an address to the
Berlin Academy on this point, involving difficult calculations, and I
hoped to hear from him an easy explanation at least in general terms.
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Elsewhere in the archive
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account