Quantum Leaps, WRXs, and the Elegance of Discontinuity
I recently captured three views of my newly-acquired 2011 Subaru WRX dream car.
- (A) A video of myself gleefully walking from the front to the back.
- (B) A still photograph of the front.
- (C) A still photograph of the rear.
Conventional philosophy and physics read the video as time: sequential steps, cause → effect, reversible under relativity. This “flow” stays within the continuous, linear passage of matter through time.
But modern physics reveals stranger things. Consider entanglement: two paired particles can influence each other instantaneously, even when separated by trillions of kilometers. Einstein dismissed it as “spooky action at a distance,” because it violates his rule that nothing travels faster than light.
Now return to the WRX. Look at (B), the front. Then look at (C), the back. You’ve just leapt from one state to another, bypassing all the intermediate clutter — dandelions, dog-poop, snazzy side profile. The leap is discontinuous, like a quantum event.
(B)
Frames, Perception, and Illusion
Human beings perceive motion at roughly 30 frames per second. A video at 30fps (A) feels alive because discrete frames create the illusion of continuous motion. This is why early photographic sequences — such as Muybridge’s bet that horses leave the ground mid-stride — birthed modern cinema.
Reversing the frames produces reverse-causal illusions: glasses un-breaking, dogs running backwards. Einstein saw that relativity allows time’s arrow to run both ways under certain conditions. But quantum mechanics resists smooth continuity.
Electrons are not little planets orbiting nuclei. They are probability distributions — smears. Paul Davies once said: “Where are we most likely to find the electron? Where the crime is greatest.” Einstein resisted this view, quipping (apocryphally), “I cannot believe the moon is not there when I am not looking.” Relativity and quantum theory collide: the smooth mathematics of the large do not mesh with the probabilistic mathematics of the small.
Quantum Gravity and the Edge of Physics
Reconciling these worlds may require quantum gravity. Gravity must ultimately reduce to a particle — the graviton — though it has never been detected. Fermilab’s 2018 detection of gravitational waves was a milestone, but CERN’s LHC may already be nearing its limits. Its 27-km ring is straining at the end-game. A proposed 100-km collider might not run until 2060.
If a graviton is found, so must its antiparticle. Then comes speculation: anti-gravity boots, anti-gravity by-laws, Marty McFly hoverboards.
Yet at black holes and singularities — the Big Bang — mathematics collapses. Spacetime folds into dimensionless points. Events become simultaneous, instantaneous, eternal. Information has no distance to cross. Black holes are where mathematics goes to die.
Quantum Tunneling and Planck Units
Particles sometimes cheat. A particle unable to climb a barrier may “tunnel” through it, borrowing energy so long as it instantly repays the debt. This is supported by the quantum foam — the seething field of Planck-scale fluctuations. At these scales, the units of space and time are unimaginably small, so tiny that “ordinary” mathematics begins to fail.
Toward an Elegant Equation
Here is the intuition:
- Video (A) = continuity, relativity, the arrow of time.
- Still (B, C) = discontinuity, quantum jumps, entanglement.
There must be a simple relationship between them, something more elegant than an ugly balance of decimals. Perhaps:
B+C ≈ A2B + C \; \approx \; A^2B+C≈A2
A T-shirt equation, a signature of elegance. If mathematics is the language of God, it will not be clumsy. It will be compact, poetic.
Elegance in Numbers
Pi (π ≈ 3.14159) and Phi (ϕ ≈ 1.61803) are not “pretty” by human standards, but they govern elegance. The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, …) generates shells, hurricanes, galaxies. Deviate slightly, and the patterns collapse.
Newton’s law of gravitation dissipates at the inverse square of distance. Simple, immaculate. Perhaps relativity and quantum mechanics will agree at the Planck scale — even for WRXs.
In 2013, an anonymous mathematician “Cleo” solved an integral on Math Stack Exchange with the haunting formula:
I=4π \arccotφI = 4 \pi \, \arccot \sqrt{\varphi}I=4π\arccotφ
A blend of π and √ϕ that reads more like poetry than calculation. Did Einstein once glimpse such a symmetry? Did he turn away, searching for elegance?
This is a silent nod to a universe where everything is connected — WRXs and Mitsubishis, photons and gravitons — often instantaneously. A universe where time and space dissolve into a unified field, played like a cosmic symphony. And sometimes, perhaps, all the music happens at once.
(C)
This official, the original, 'Exhibit (A)'