The Andromeda Paradox is not a good argument for the Block Universe

This morning, I opened YouTube to check on my recently posted video and saw this video from Sabine Hossenfelder on the Andromeda Paradox. In turn, she was responding to a somewhat garbled discussion of the paradox from Neil DeGrasse Tyson’s StarTalk show.

The Andromeda Paradox comes from Roger Penrose’s 1989 book The Emperor’s New Mind and describes a situation where two people traveling at walking pace relative to one another can have vastly different planes of simultaneity when you stretch those planes out to the Andromeda Galaxy, 2 million light years away.

This Paradox is a concrete example of the Rietdijk–Putnam argument for the so-called Block Universe, the idea that the past and the future must exist at all times, and the present being the only time that exists, a belief known as “Presentism”, is an illusion.

The argument goes that if two people’s idea of simultaneous events can differ so much, even at slow velocities, then surely those distant events must co-exist in a higher four-dimensional reality. We cannot have one event exist and the other not, based on some arbitrary definition of the present.

This argument is poor for a couple of different reasons. First, it assumes that the time at which distant events that are not causally linked to a local event have meaning. But more importantly, on curved surfaces, it is perfectly natural for tangent planes not to line up with each other. That doesn’t automatically imply the curved surface is a higher-dimensional object. This is a fallacy that comes from the difficulty we have envisioning curved surfaces that are not embedded within a higher-dimensional flat space.

First, let me explain what a plane of simultaneity is. In Einstein’s relativity theory, whether two events occur at the same time depends on either your state of motion or the gravitational field.

For example, suppose you are on a spaceship and you are about to fight a duel with an alien, a mercenary bounty hunter bent on killing you. You both have your laser guns. You are expected to pace off and fire at the same time, according to the space duelist code.

You stand back to back and walk away from one another. When you each reach your appointed positions, you turn. A signal light in the center is designed to tell you and your opponent when to fire. You see the light, fire, and the alien misses you, but you score a hit!

Suddenly, a passing spaceship radios the ship’s captain. They saw the whole thing from their ship, and they know that you shot first, in violation of the code. The captain of your ship assures them that all the rules were followed. The fight was fair.

Given there is a dispute, however, the captain reviews a recording that the other ship made of your encounter, and, indeed, it seems as if you shot first! Yet, the recording your captain made of the event shows you firing at the same time. How can that be?