The Speed of Light & Time Dilation

One hundred years after Einstein’s grand publication, his insights remain both pervasive and paradoxical to the modern mind, somehow both elemental and elusive.

For me, three notions from Special Relativity have always stood out:  the fascinating concept of a “universal speed limit”—the Speed of Light—and the curiosities of time dilation and length contraction.

I find simple heuristics useful:  Imagine a “light clock”— a tube of a certain length with a laser on one end and a mirror on the other.  It takes a fixed amount of time for the light to travel to the mirror and back.

Now imagine this clock on a train.  For an observer on the train (Red in the graphic above), the clock “ticks” at the same pace, no matter whether the train is stationary or moving.  But for Blue outside the train, the faster the train travels, the further the light inside the clock must travel.

Yet if the speed of light is a “universal speed limit” (nothing can travel faster than 300 million meters per second), then how can these conditions exist?  How can “one tick” of the light clock cover a longer distance when on a superfast-moving train?

Einstein’s answer of course is time dilation.  From Red’s perspective (or “frame” in physics jargon) only one tick has elapsed, but for Blue, much more time has passed.  Light Speed is fixed, but time is elastic.

The Speed of Light & Time Dilation

For an observer on the train (Red in the graphic above), the clock “ticks” at the same pace, no matter whether the train is stationary or moving.  But for Blue outside the train, the faster the train travels, the further the light inside the clock must travel.

The Speed of Mind & Time Dilation

What if light isn’t the only thing with a speed limit?

What if the human mind has a speed limit?  What if each age cohort of humans has its own mental processing speed—that is, broadly speaking, each of us has a common and limited capability to absorb and digest information?  That is, what if there is a universal mental limit—to borrow from physics, a sort of “Speed of Mind”?

In recent decades, the amount of information and the speed of that data have grown at exponential rates.  Evolving technology, emerging media, accelerating globalization, compounding complexity, rapid cultural change, blossoming intellectual development, and so much more fuel these torrents.  It is commonplace to both marvel at and lament these changes.

But if our minds can only operate up to the Speed of Mind, how do we handle this deluge of information?  If—like the speed of light—our processing speed is the speed limit of thought, then the only way we can process more information at the same Speed of Mind is if time is dilated.

And so, here is my humble proposition of “information relativity”:  in a frame with accelerated information flows, time seems to pass more quickly.  Mind Speed is fixed, but time is elastic.

“Breaking news” at midnight is Facebook-feed at 1am, Twitter-bait at 3am, dissected by pundits by breakfast, and stale by lunch—all through a cacophony of a thousand channels.  Torrential flows compress reportage, analysis, reaction, and commentary:  a cycle that once might have taken a week is collapsed into hours.  Events happen in real time but because of our Speed of Mind, we perceive our hours as days, our days as weeks.

If our Speed of Mind is limited and the information we process increases, the only possible explanation is that more “mind time” has elapsed.  Deluged with information, two Red days of information feels like Blue weeks.

Perhaps, subsequent age cohorts will demonstrate a faster Mind Speed, but for now, data hyper-flows distort time. In finance as in physics, to paraphrase Einstein, time is but a persistent illusion.

The Speed of Mind & Time Dilation

The Speed of Light & Length Contraction

Time dilation’s equally counterintuitive cousin is length contraction.  Special relativity requires that an object traveling at a very high rate of speed contracts in length in the direction of its travel.  Imagine that the light clock above were turned parallel to the ground.  As the train (traveling to the right) approached the speed of light, the right end of the clock would be moving away from the left end of the clock and the clock would never “tick.”  So, from an outside frame (or relative to an outside observer), the clock and the train will be shortened in length.

Similarly, to the observer on the ground, a rocket approaching the speed of light will appear shorter in length.

The Speed of Money & Dislocation Compression

Length contraction reconciles the relative views of two frames, one at rest, the other moving at a very high speed.

An analogous phenomenon, I suggest, occurs in the financial world. Changes in technology, institutions, and most recently extreme monetary policies have dramatically increased the pace and magnitude of financial flows. Capital flows are deeply networked and nearly instantaneous.

In this era of extreme liquidity, markets and money reacts so rapidly that dislocations are compressed.  Consider an exogenous shock (a coup, a pandemic, or similar) that from the perspective (frame) of the non-financial observer generates real uncertainty and risk. The overdevelopment and magnitude of the financial sector tends to compress those disruptions. The pace of capital flows forces markets to (try to) evaluate and internalize risk far faster than those risks can be truly understood.  Dislocations are unnaturally compressed.

Two illustrations.  While SARS had a meaningful impact on financial markets in 2004, Ebola’s impact a decade later was less dramatic and very short-lived—compressed, I would argue by an increasing “speed of money.”  Similarly, Russia’s intervention in Georgia in 2008 rocked financial markets, while those markets seemed to absorb the (more serious) Crimea crisis nearly in stride.

Our economic and social systems (as deeply networked as we are) are more vulnerable to exogenous shocks than ever, and yet somehow our bloated and hyper- (and falsely-) efficient financial markets seem so easily to internalize and smooth these shocks. Like length contraction, dislocation compression is driven a vast difference in velocity between frames of reference:  in our case between the real world and the financial world.

But in finance unlike in physics, the two frames are not hypothetical but real, not detached but linked.  What happens in the real world can, disrupt, destroy, reset, upset, the financial world.  And when that happens, the extreme speed of money will be revealed as folly, not efficiency.

Peter Yu
New York, 2015

The Speed of Light & Length Contraction
The Speed of Money & Dislocation Compression

On the Centenary of the Theory of General Relativity