Fear of Physics

Lawrence M. Krauss

6 annotations • data

First annotation on Jul 18th, 2025.

Chapter 5

Another symmetry of nature goes hand in hand with time-translation invariance. Just as the laws of nature do not depend upon when you measure them, then they should not depend on where you measure them.
The consequence of this symmetry in nature is the existence of a conserved quantity called momentum, which most of you are familiar with as inertia—the fact that things that have started moving tend to continue to move and things that are standing still stay that way.
Momentum conservation says that if a system is at rest and suddenly breaks apart into several pieces—such as when a bomb explodes—all the pieces cannot go flying off in the same direction. This is certainly intuitively clear, but momentum conservation makes it explicit by requiring that if the initial momentum is zero, as it is for a system at rest, it must remain zero as long as no external force is acting on the system. The only way that the momentum can be zero afterward is if, for every piece flying off in one direction, there are pieces flying off in the opposite direction. This is because momentum, unlike energy, is a directional quantity akin to velocity.
The search for symmetry is what drives physics. In fact, all the hidden realities discussed in the last chapter have to do with exposing new symmetries of the universe.
Those that I have described related to energy and momentum conservation are what are called space-time symmetries, for the obvious reason that they have to do with those symmetries of nature associated with space and time, and to distinguish them from those that don't.
This symmetry of nature is possible only if space and time are tied together. Thus, purely spatial translations and purely time translations, which are themselves responsible for momentum and energy conservation, respectively, must be tied together.