MU-3: If the Maths Allows It...
It’s
one thing to trust the maths wherever it leads or whatever it implies; but soon
scientists had to abandon any understanding of what was being described…even as
the “the unreasonable effectiveness of mathematics” continued to march on. This
was especially true in the field of quantum mechanics because it left “an uncomfortable
blank space where their picture of reality was supposed to be”, as James Gleick
put it in his biography of Feynman, Genius.
Or as Gleick puts it in another part of his book:
“They could write numbers and
symbols on their pads, but their mental picture of the substance beneath the
symbols had been reduced to a fuzzy unknown.”
Of
course, not all physicists were happy with this state of affairs. But the
majority just accepted it as the new normal. One of quantum mechanics’
founders, Heisenberg, suggested that we just accept it and move on by saying:
“The equation knows best.”
The
other famous statement on this perspective of quantum mechanics was:
“Shut up and calculate!”
Remember
those equations from school that had a negative and a positive solution and we
ignored the negative solution based on context? Dirac didn’t do that. Rather,
he “resisted the temptation to dismiss the negative solution as a quirk of
algebra”, writes Gleick, and declared that the solution corresponded to a
particle that had never been observed. He was proven right! Dirac was one of
the early ones to trust the maths.
If
some of these things sound very esoteric and make you wonder, “Does any of this
make any difference to anything in real life?”, consider this: the GPS on your smartphone
wouldn’t work if the fact that time flows at different rates for different
objects weren’t built into its calculations. That slowing of time, by the way,
was something that the maths of relativity had predicted long before the
phenomenon was ever observed.
Soon
weirdness was the new normal, at least for physicists. Or as Gleick puts it:
“In the era of Einstein and
Bohr, what was one more paradox?”
So
prevalent was this feeling that Feynman said that it was the mark of a good
physicist to never say, “Oh, whaddyamean, how could that be?”
Anything
was possible…as long as the maths allowed it.
To be continued…
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