I took a video of myself gleefully walking (A) from the front of my recently-acquired 2011 Subaru WRX dream car to the back of it. I also captured a single picture of the front (B) of the car and a picture of the back (C). Conventional philosophy and physics sees the video as time, a flow—sequential steps, cause>effect, even if rolled in reverse—allowed under relativity. Yet, this flow stays within the continuous, linear passage of matter through time, as the video demonstrates.
But modern physics explores entanglement, where two paired particles can influence each other instantaneously, even when separated by trillions of kilometers—violating Einstein’s rule that no information can travel faster than the speed of light (300,000 km/s). This influence is instantaneous. He called it, "spooky action at a distance."
Now, look at the picture of the front of my car (B), then at the back (C). You’ve just "moved" from one to the other instantaneously, bypassing all the clutter, dandelions, dog-poop, and a snazzy side-profile view—like a quantum leap. Nothing could have "stopped" and taken a 'snapshot'—like taking a single frame from the video. It doesn't exist. There is only the front of my new dream car, or the back.
(B)
An electron has an orbit. When a photon hits it, the electron absorbs it and "leaps" to a higher orbit—no visible in-between state. It’s a sudden jump, instantaneous, a quantum leap—something that defies our classical expectation of continuity. And when a photon is emitted (which we see as light) the electron loses energy and falls to a lower orbit, again withoout traversing the space in between.
The photon travels so fast that time (for it, from its' reference point) stops. A photon only "knows" its emission from an electron and its absorption into another, like one in your retina. Its journey is instantaneous. (Before it reaches your eye, it was a wave of probability—but once you detect it, it collapses Schrödinger's wave-function and the wave/particle duality becomes the particle as it is absorbed.) That's a fascinating mind-bender, because you conceivably "create" your own reality by merely "seeing" photons, trillions upon trillions every second, and collapsing their wave-function. It predicts that when you look at something, you make one of the possibilities take the form of a particle. All of the other options split off into multiple universes, better known by its street name, the multiverse.
Human beings perceive motion at approximately 30 frames per second (fps). When watching a video recorded at 30fps (A), it appears to move smoothly and in real-time. This frame rate explains why video tends to seem more "alive" than traditional film, which is typically shot at 24fps. Each frame contains a three-dimensional image, and when these static images are played in sequence, they create the illusion of continuous, natural motion through time—despite being essentially staggered snapshots.
(A fascinating historical fact is that this concept was first employed in a bet to demonstrate that horses gallop with all four hooves off the ground at some point during their stride. Early photographic sequences placed around a spinning drum showed the horse to "appear" to run at full gallop. This was the founding of modern film making, TV cameras, as well as cat video compilations on your "capable of 140fps" iPhones. Additionally, when a video is played backwards, phenomena such as broken glasses seemingly repairing themselves or dogs running in reverse become possible, illustrating how our perception of reality can be manipulated through frame sequencing. Einstein saw this and his Theories of Relativity run backwards and forwards in time. But in certain circumstances, time is an unavoidable arrow.)
The electron doesn't really revolve around a nucleus, it is a "smear" of probabilities. Paul Davies, physicist, said, "Where are we most likely to discover the electron? It's like a crime spree. The greater likelihood of a felony is where the crime is greatest." Einstein fought against this quantum event, for which there is an adequate mathematical reality opposing his relativity, saying, "I cannot believe the moon is not there when I am not looking."
This is why Relativity and Quantum Theory collide. They do not mesh well together. The maths of the universe-at-large are not the maths of the atomic realm. Reconciling these is thought to be found in resolving quantum gravity because the gravity of, say, the earth, must reduce itself to a detectable point. In 2018, Fermilab took important steps toward understanding quantum gravity when gravity waves were first discovered. But the wave-particle duality means that there is a particle, which we have named, as the "graviton," but it has yet to be detected.
CERN in Switzerland has this on its list but we are almost pushing the current Large Hadron Collider (LHC) to its limit. This 27-km donut 200m under the Swiss and French countryside is going to hit its end-game, unable to sharpen the cutting-edge of physics any faster with the machinery at hand. They proposed a new and costly 100-km ring to peer even deeper into the quantum autopsy, as we are now in what is called the end of physics. But if started tomorrow, it would not be running until 2060. Should the graviton be found, it then has an anti-particle, which means, you guessed it, anti-gravity boots, anti-gravity boot by-laws, and Marty McFly's hoverboards (predicted to exist in 2015 as the second Back to the Future film suggested.)
In both black holes and singularities, like the Big Bang, these concepts approach the limits of mathematics because these entities collapse into a dimension-less universe. In such a state, events would occur simultaneously, instantaneously, eternally. Any supposed information would have no distance to cross to communicate. Yeah, it gets bizarre, but there's hope—just kidding, there isn't. Black holes are where mathematics goes to die.
Quantum tunneling is when a particle cannot "get up" a hill. So it "borrows" enough energy to tunnel through—as long as the favor is instantaneously repayed. This energy is mathematically harmonious with quantum foam, which occupies every ounce of space. (That's a misnomer, there is no ounce of space, however when we get to this incredible power of magnification, we use what are called Planck units, where the smallest, shortest, and quickest of measurements are made. These are so incredibly small as to make any meaningful mathematics happen above it. Trillions of Planck units are required to cross an atom.)
I'm not a mathematician, but with the consequences of the conventional video and entangled realities described above, it seems possible to lay a mathematical blueprint using the three versions of my capturing my recently-acquired 2011 Subaru WRX dream car. Somehow there is a numeric value for the video (A) against the pictures of the front (B) and the back (C). Something like: B+C=A^2... That would be elegant enough to fit on a t-shirt but I leave that to the experts. I just don't think that "if" mathematics is the language of the universe, that it would be an ugly equation like: 14.36+0.0326=A^2 for the balance to work itself out. God, when read as the architect of mathematics, would be elegant with His signature.
Although, it’s not like Pi (3.1415926...) or Phi, the Golden Ratio (1.618033...) meet objective beauty standards. The Fibonacci Sequence of adding the last number (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55) might not seem intuitive at first glance, but it is stupendously significant (note that four-leaf clovers are so rare, they're a phenomenon), it's a Mensa-leap to deduce the numeric patterns in shells, hurricanes, and galaxies.
Newton's gravity dissipates with distance at the inverse-square of the distance between bodies. How do you like them maths, he must've thought, in his cave while trying to avoid the Black Plague. It's insanely immaculate. The concepts must agree somewhere, possibly even at the Planck unit of Subarus.
(C)
When the unknown mathematics-legend "Cleo" suddenly appeared on the Mathematics Stack Exchange one night in 2013, she hauntingly answered a complex integral problem with the answer: “I equals 4 pi times the arccotangent of the square root of the golden ratio.” Symbolically, I=4πarccot√ϕ. The square root of phi (√ϕ) stands out to me as a stroke of genius as anyone would, but, almost prescribed and, to my mind, I ask - where was she before solving √ϕ? Was she at √1.6137286702..? I would be inclined to seek harmony in both the 4π and the √ϕ before sitting in a mathematical ditch that stretches out to useless infinities in almost every direction. But it's above my mental pay-grade. Suffice to say the universe frequently speaks to us in numerical poetry. Einstein's E=mc^2 "could" have been E=mc3π√ϕ+12... egads, did Einstein pass this way looking for elegance?
This is a silent nod to a universe where everything is connected, WRXs and Mitsubishi Evos, often in an instant, where the boundaries of the time we experience and the space we dissolve into a single, unified reality—all get played out like a cosmic orchestral symphony, sometimes all the music happens at the same time.
This official, the original, 'Exhibit (A)'