Math Mutation 63: Turning Around In Time
I'm sure that if you are the kind of person who listens to this
podcast, you have occasionally speculated about time travel. If Time
is truly another dimension, just like our ordinary three dimensions of
space, then should we be able to change our direction? Are we really
stuck travelling forward at a constant rate, unless we can go fast
enough to benefit from the distortions of relativity? It's fun to
think about what it would look like if we could just decide to make a
U-turn in time, like we can in space.
To make this example concrete, let's suppose I have a doctor's
appointment at noon, and it takes me 10 minutes to walk down the
street to the doctor's office. I look at my watch and notice that
it's noon already. No problem, due to my time-walking ability. I
step outside, spend 5 minutes walking halfway to the doctor's office,
then make a U-turn in time, and walk 5 more minutes, travelling
backwards 5 minutes in time as I continue walking down the street
towards the doctor's office in space. At noon, I am safely at the
office, and start walking forward in time again, entering for my
appointment.
What would this look like to a neighbor couple sitting on their
porch, watching me walk down the street? From my house, they would
see me emerging at noon, and arriving halfway down the street at
12:05. But from the doctor's office, they would see an odd sight.
There would be a backwards-me walking backwards down the street
towards my house, at the same time as the first me is walking
forwards. Think about it: at noon, my backwards-travelling
self arrived at the office; at 12:01, I was one minute away from the
office, travelling backwards in time; at 12:02, I was two minutes
away, and so on. But the most bizarre event happens at precisely
12:05: the backwards-me and forwards-me meet and merge, then suddenly
disappear! At 12:06, I do not exist in the middle of the street,
since at 12:05 I turned around in time. The neighbor couple will
think I have suddenly disintegrated after a collision between my
forward-self and backward-self. Eventually, of course, I will
travel forward again and reach this point in time while in the
doctor's waiting room. In fact, if it's a typical doctor, I will
experience many future epochs of time in that waiting room, but that's
another topic.
This kind of turning-around in time sounds absurd when described
in terms of a person. But, strangely enough, many physicists believe
they have observed precisely this phenomenon in the area of subatomic
particles. A well-known type of interaction occurs when an electron
and a positron collide, releasing a photon. And similarly, it is
possible for a photon to sponataneously break down into an electron
and a positron. But according to a theory first proposed by the
famous physicist Richard Feynman in 1949, we can also just view a
positron as an electron travelling back in time. So when an electron
and a positron collide to generate a photon, what is really happening
is that the electron is hitting a photon and turning around in time,
just like when I turned around in time in the middle of the street.
And the positron it hit is just the same electron, travelling
backwards. Similarly, when a photon spontaneously splits into an
electron and a positron, what's really happening is that a
backwards-electron hit the photon as it travelled backwards in time,
bounced off it, and became an ordinary forward-moving electron.
So, even if I can't change direction in the fourth dimension to
catch up when I'm late for an appointment, such direction-changing on
the subatomic scale is a real phenomemon that has been observed, at
least according to some theories.
And this has been your math mutation for today.
References:
Article
on positrons and antimatter
Another
article on positrons and antimatter