How Math Explains the World.pdf

(Marcin) #1

observation in the physical universe, and when does it take place? A
widely held view in the physics community is that an observation consists
of an interaction with the universe. Our intuitive notion of reality—that
things have definite states and attributes—collides with the world pre-
sented by quantum mechanics, in which things have a probabilistic mix-
ture of states and attributes, and only interaction with the universe can
create an actuality from what was initially just a possibility.


Schrödinger’s Cat


Erwin Schrödinger came up with a tremendously provocative way to visu-
alize the weirdness inherent in quantum behavior. He imagined a box
containing a cat, a vial of poison gas, and a radioactive atom, which has a
probability of 50 percent that it will decay within an hour. If it does, it trig-
gers a mechanism releasing the poison gas, killing the cat (it seems likely
that Schrödinger did not actually own a cat—although he may have
owned one that was more trouble than it was worth). An hour goes by. In
what state is the cat?^4
The conventional answer to the question is that the cat is either dead or
alive, and we’ll know when we open the box. Quantum mechanics an-
swers this question by saying it’s half dead and half alive (or that it’s
neither)—and the answer will be determined when the box is opened,
and observation collapses the wave function.
Counterintuitive though the half-dead, half-alive cat may be, that’s the
interpretation that quantum mechanics gives—and how can we refute it?
Without an observation (which need not consist of actually looking at the
cat, but simply obtaining information about the state of the radioactive
atom whose decay determines the outcome), how can we know? Could
your reclusive neighbor, whom you hardly ever see, be in a half-dead,
half-alive state, which is only determined when he interacts in some way
with the world? Just recently, a man was found in a mummified condition
in front of a TV set—he had been dead (and the TV set on) for thirteen
months before anyone decided to check up on him.
As a computational method, quantum mechanics is probably the most
accurate in physics—confirmed to more decimal places than there are dig-
its (including pennies) in the national debt. Some physicists feel that this is
all physics can do—give computational rules that enable us to build com-
puters and magnetic resonance imagers. A much larger number of physi-
cists feel that this is telling us something deep and important about
reality—but the physics community has not yet come to a consensus about
what reality is, and if they can’t, it’s going to be difficult for the rest of us.


All Things Great and Small 53 
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