MU-2: Unreasonable Effectiveness
In
my last
blog, I talked about maths becoming the language of physics and how a few
mathematical predictions from the equations of relativity, though totally
counter-intuitive, seemingly outrageous and not matching any observed
phenomenon till date yet proved out to be correct.
The
other major theory of physics, quantum mechanics, was not only mathematical
(like all theories since Newton) but was also unimaginably accurate. For
example, in 2006, the theoretical and experimentally measured values for the
magnetic moment of an electron (it doesn’t matter if you don’t know what that
means) matched to a precision of eight
parts in a trillion! This unbelievable accuracy of theory led Freeman Dyson
to comment:
“I’m amazed at how precisely
Nature dances to the tune we scribbled.”
Besides,
the sub-microscopic reality that quantum mechanics describes is so tiny, so
unlike anything we’ve seen or experienced (and hence not evolved to imagine
either) that it’s hard, if not impossible, to come up with any physical
analogies to describe it. That didn’t deter physicists: if they couldn’t
imagine it, they’d at least describe it (via equations).
The
maths of the electroweak theory predicted
the existence of three particles that had never been observed before. These
particles were discovered later in accelerator experiments. So not only was
maths predicting hitherto unobserved phenomenon of nature; it was even
predicting unobserved particles of nature!
But
wait, there’s more. There were even branches of maths invented for other
purposes (and even no practical purpose at all) that later turned out to
describe some aspect of the universe. For example, the branch called knots
theory eventually helped describe how the famous DNA molecule makes copies of
itself! Another branch called matrix mechanics proved, decades (if not
centuries) later, to be one way to describe quantum mechanics (though it wasn’t
easy to use).
To
summarize, maths was predicting phenomenon and particles that nobody had
observed and proving to be right time and again. Branches of maths were found
to describe nature’s behavior decades later.
No
wonder then that the physicist, Eugene Wigner, coined the phrase “the
unreasonable effectiveness of mathematics” when it came to describing the
universe.
To be continued…
Mathematics is a real 'monster' among sciences! :-) It domain is so vast that it can terrify, not just the children who are struggling with it, but even those who are more years to their advantage and are fairly good at maths. Naturally maths seems to have no problem in accommodating any need of the physicist.
ReplyDeleteThese days when I go to the supermarket to buy ordinary things, which were easily picked up once upon a time when supermarkets were unknown, the same procedure bewilders me. There are many choices: do you want super or luxury or ordinary? Do you want with X in it or Y in it or just classic (that is, without X or Y)? Do you want the crunchy one or smooth one or something which is smooth when you start eating and turns crunchy when you are about to finish! :-) etc. etc. etc. Worse, I stand defenseless before my wife's lament on my return from the shop, "I asked for that and you are bringing this!" [By the way, long long back, I cleverly managed to arrive at the same situation when choices were minimal; but that is a different story!]
Mathematics is outclassing all supermarkets put together, I would say. It has unlimited options to meet every need of the physicist. In the maths supermarket, all that the physics person has to do it to tell the shop attendant what he needs to describe. Out out shelf number 2,045,789 and 360,178 the shop assistant produces the equations the physics person requires. If fine tuning required, shelf numbers 466,890 and 39,5437,711 would certainly help etc. :-)
Maybe the days of scientists like Faraday and Rutherford are gone. Those scientists looked at emerging physical realities without surrendering to maths. Even Einstein preferred a secondary role for maths in physics. But soon started feeling uneasy that the days of his preference were numbered. It may all be good anyway! Within a few decades, at best a century, we may stop understanding most all physics and keep reeling off equations after equations. Elaborations of these equations may sound more like fairy tales than physical realities in future. Perhaps that is going to be the entertaining part of physics that awaits future generations! :-)
Skeptical? Here is my proof:
x ^ 2 = alpha ^ (3 / beta) * d/dx (f)
where f is the Laplace Function of the harmonic resonance of x in six dimensions.
Good luck!