Sunday, October 23, 2005

Why Singularities Don't Need a Cause

Causality, the idea that everything has a prior cause, serves an important function in physics. It makes predictions possible. If future conditions do not depend on past conditions, then the universe would be unpredictable. You can think of the laws of physics as being rules that constrain the future to depend on the past.

In physics, there's also the concept of locality. Let's say that events do depend on the past, but that signals from the past can travel faster than light. In that case, there would be frames of reference in which the future appears to affect the past. Naturally, this won't do because, again, we would be unable to make any predictions. Instead, each event is dependent on prior events in its "reverse light-cone."

Your reverse light-cone contains all the things in the past that might affect your current state. This cone is big. It is roughly 300,000 kilometers in radius for each second you go back into the past. Your current state is affected by the light and gravity of Apollo hardware sitting on the Moon's Sea of Tranquility as it was a bit more than a second ago (the Moon is roughly 400,000Km away). Anyway, physics requires that events be consistently related to prior events that are in their reverse light-cone.

What would happen if there were one, single, initial event in history? Causality would be meaningless for the initial event as there would be no prior events for the initial event to depend on. In the case of the Big Bang, the reverse light-cone gets squashed so that it contains no prior events. Therefore, science can be completely consistent without the need for something to cause the first event.

I think it's interesting to consider conservation laws for initial events, too. Conservation laws, like the conservation of energy and momentum, are due to symmetries. Noether's Theorem tells us that when a physical system has a symmetry, there is a corresponding conserved charge. In the case of energy and momentum, the symmetry is that of translation through space and time. Because the laws of physics don't change between yesterday and tomorrow, or between my house and yours, then energy and momentum are conserved over that time, too.

Yet, if there is one single event at the beginning of all space and time, there is no symmetry of translation in space and time. We cannot compare the laws of physics one second before the Big Bang to those one second after the Big Bang because there was no universe to compare against beforehand. Therefore, we should not expect energy or momentum to be conserved by the first event of the Big Bang.

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