In writing Astronomical Returns, I find theoretical physics to be the most challenging space-related topic to generate ideas for. Lucky for me, a fascinating theory fell right into my lap several months ago, and only now have I had the time to lay it out for you all!

In case you were wondering, sadly I'm not the banker in question who came up with this theory of "quantum time." It's the brainchild of one of the vice presidents in my investment banking group, but unlike me and my measly bachelors in finance, he has both an undergraduate and master's degree in theoretical physics! We also both happen to be avid space fans, and one night he excitedly came by my desk with several pages of markups. For the uninitiated, in investment banking lingo, "markups" are paper sketches of slides that senior bankers draw out for us junior bankers to create in PowerPoint. And as you can imagine, getting a markup late at night is a sure sign the night's about to get much longer (oof!). But these markups weren't PowerPoint slides, they contained the outline of my VP's groundbreaking theory, one which promised to eliminate Einstein's Theory of Relativity and revolutionize the field of quantum mechanics!

The top half of the first page of the actual markup from my VP's theory of quantum time Deciphering handwriting is part of the job of a banking analyst - keep reading and you'll find my cleaned up version below

Before I summarize his theory, here's some background: the two pillars of modern physics are relativity and quantum mechanics, both of which are impeccably accurate in their respective fields (click here to learn more). Relativity describes gravity and the immense expanse of space-time as continuous and uninterrupted, while quantum mechanics describes the realm of the infinitesimally small as discrete wave-particles. The problem, in fact one of the greatest unsolved questions in science, is that the two theories are mutually exclusive; they cannot be mathematically reconciled. Today's physicists have long sought a "quantized" model of gravity and time, just has how physicists a century ago defined the photon as a quantized particle of light.

The Standard Model defines all known particles in the Universe. Maybe one day, we'll add the "graviton" and the "chronon" to the diagram

My VP's rationale for his theory was this: Special Relativity states that in order for the speed of light to remain constant in all inertial frames (an empirically proven fact), time must be relative depending on the observer (see this video for a visualization, particularly starting at 1:37). But Einstein never provided any physical explanation for why time dilates; it's just a mathematical consequence of setting time as the "plug" in the equation. So perhaps we need a new framework that can provide a better answer.

I'd say I personally can only comprehend about 40% of his theory, but part of the fun of writing this article was trying to follow his train of thought and decipher his formulas. For some of his conjectures, although I couldn't fully put my finger on it, I felt like I had a fuzzy sense of where he was trying to go. And beyond that, it's nice to see how varied people's interests can be and the interdisciplinary pursuits they dedicate themselves to - just as there are investment bankers who write space blogs and develop theories of quantum time, I'm sure there are also aeronautical engineers who read the Wall Street Journal every morning and know the ins and outs of mergers & acquisitions far better than I do! It makes for a more exciting future, and a more fun world

Qualitative Summary 

<MAKE SURE YOU SCROLL BELOW AS WELL, THE DIAGRAMS IN THE DETAILED EXPLANATION ARE VERY HELPFUL>

There is no such thing as time. There is an infinite scalar field that has infinite energy and 0 vector potential. At the moment of the Big Bang there was a perturbation which propagated a wave of that field. Think of the scalar field as a string and the wave as time particles - our world is observed within that perturbation as nothing more than time particles traveling at the speed of light

Time particles occur at a rate of Planck's length / c. The theory assumes Planck's length (the minimum possible length quantum physics allows in the Universe) is not actually a constant, but in fact varies with a moving observer. These time particles set the "strobe light" of infinite state measurements defining what we perceive as the past and the future, whereby uncertain time particles collapse into a measured state that is 100% certain, forming the past. This is consistent with existing thermodynamic theories relating time as an increase in entropy: the past is ordered (100% certain because it's been measured by a time particle), while the future is disordered because it's a range of probabilities.

What we perceive as energy is really an absence of time particles in a given region, and due to Einstein's mass-energy equivalence, by extension we can consider mass as a displacement of time quanta

The challenge with Special Relativity is that it's just a mathematical consequence of the speed of light being a universal constant - it doesn't actually explain why time dilates as velocity increases. Under this model, Special Relativity can be explained as a Doppler shift between the moving observer "catching up" to the wave of time particles. Because the observer interacts with less time particles, he experiences less time

Meanwhile, General Relativity states that as an observer approaches a gravitational field, time slows down while mass and energy increase, up to the point where mass and energy are infinite and time literally stops inside a black hole. In this theory, we have defined mass-energy as the absence of time quanta, so the continuously increasing gaps between time quanta explain both time dilation and the increase in mass-energy as gravity increases, and General Relativity falls away

Detailed Explanation and Supporting Mathematical Appendices