Living on Two Levels: Special Relativity and the Buddhist Doctrine of Two Truths

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The Train and the Tunnel

One of the postulates of Special Relativity is the following: the laws of physics are the same in all non-accelerating frames of reference. If I’m driving a train at a constant velocity of 30km/h towards a tunnel — the laws of physics are the same from both the perspective of the train at rest, and the tunnel at rest. From the perspective of the train— it’s perfectly valid to say that the tunnel is moving towards it at a speed of 30km/h, while the train remains stationary. Similarly, taking the tunnel’s perspective, we can say the train is what’s moving. These are both valid viewpoints, and almost trivial things to consider.

The situation because non-trivial once we consider relativistic speeds — velocities that approach the speed of light (3,000,000,000 m/s).

Suppose the following:

The tunnel is fit exactly for the train — both ends can be inside at the same time

The tunnel has metal doors that open and close on either end

There is an observer on a hilltop nearby

Relativistic speeds are now involved — and we have 3 perspectives to consider. The hilltop observer, the train’s perspective and the tunnel’s perspective. For the hilltop observer, the train simply passes through the tunnel, and is totally hidden from view for a brief moment (as the tunnel is sized to fit it). However — from the train’s perspective, the tunnel is racing towards it at close to the speed of light. The tunnel experiences a length contraction and shrinks. This means that as the train passes through — from its perspective, the front end is outside of the tunnel before the back end has even entered (since the tunnel is now smaller). Even stranger still, let us consider the tunnels perspective. It sees the train racing towards it at close to the speed of light, so the train now experience a length contraction and becomes smaller. Now the train is smaller than the tunnel and fits snuggly inside with room to spare. We now have three seemingly contradictory reports of the same event:

The train and tunnel are the same size (hilltop observer’s perspective)

The tunnel is smaller than the train (train’s perspective)

The train is smaller than the tunnel (tunnel’s perspective)

This is all fair, but what actually happens? Suppose, from the hilltop observer’s perspective, the moment the train is completely inside the tunnel both metal doors slam shut, simultaneously, for an instant. If either end of the train is actually sticking out, then it will get chopped off. Surely this will rectify our apparent paradox.

Instead of solving this issues, we are forced to reconsider our notion of simultaneity. The hilltop observer indeed sees the train enter the tunnel — both doors slam shut, and the train emerges unscathed. From the train’s perspective the following scenario plays out. The front end of the train reaches the end of the tunnel and the front metal door slams and opens and the train keeps moving. As the back end of the train enters the tunnel, just as it passes by the entrance the back door slams and opens. An analogous situation occurs from the tunnel’s perspective, in which the doors again do not slam simultaneously.

We are once again left with an apparent paradox — 3 different events seem to occur from 3 different frames of reference. However, this paradox is illusory, existing only in the mind. It persists due to our notion of an absolute reference frame. A point of view to which everything else is related to. The astonishing discovery of Einstein is that this simply does not exist. There is no absolute perspective — everything is relative. All of these scenarios actually play out in their respective reference frames. We even have coherent mathematics to transform one scenario into the other (Lorentz Transformations). The confusion only arises when we mistakenly believe that the world is centered around us, and that our reference frame is privileged.

Conventional Reality and Ultimate Reality

We are surrounded by conventional objects: chairs, cups, phones, notepads and so on. It would be foolish to deny their phenomenal existence — I can clearly discern between my phone and the coffee mug adjacent to it. This is the truth of conventional reality — the phenomenal world exists and appears to us.

The truth of ultimate reality is as follows: conventional objects are empty of intrinsic self being. They contain no essence, and deep down, we have no substantial ground from which to individuate them. What is the irreducible essence of this chair I sit upon. Is it the parts? The form? The colour? The abstract gestalt? The chair is all of it — yet these properties are themselves not attached to some amorphous essence. The chair is the nexus of a complex web of causes and conditions. Try applying this same deconstructive reasoning to your sense of self. Is it intrinsically existing — or simply the conjunction of parts? Many forms of Buddhist meditation focus on this form of self-enquiry.

However, we now have a dichotomy — another apparent paradox. On one level, we refer to objects as substantial concrete entities. Yet upon analysis, they are empty of the essence our language imbues them with. My phone and coffee mug are both empty of an essence — a fundamental differentiating element. On one level we have form, and the other emptiness. A paradox only emerges when we take one reference frame as absolute. If we think of Ultimate Reality as underlying Conventional Reality — we have missed the point. As in our example from Special Relativity, all frames are equally valid. The Mahaprajnaparamita Sutra explains this concept succinctly and beautifully.

Form is Emptiness and Emptiness is Form

Going beyond is nothing other than returning to where you always where.

Written by

Insatiably curious student of life | Writing about Physics, Philosophy, & Dharma | Newsletter @ apsis.substack.com | Personal Site @ sashamanu.com

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