How Everything Works
How Everything Works How Everything Works

Question 1071

Why does a body at rest remain at rest and a body in motion remain in motion, in the absence of unbalanced force? — AW, Karachi, Pakistan
That observation, known as Newton's first law of motion, is one of the fundamental characteristics of the universe. I could answer simply that that's the way the universe works. But a more specific answer is that the universe exhibits translational symmetry—meaning that the laws of physics are the same from your current vantage point as they would be if you shifted a meter to your left. Shifting your vantage point along some linear path—a process called translation—doesn't affect the laws of physics. The laws of physics are said to be symmetric with respect to translations and, because translations of any size are possible, this symmetry is considered to be continuous in character (as opposed to mirror reflection, which is a discrete symmetry). Whenever the laws of physics exhibit a continuous symmetry of this sort, there is a related conserved quantity. The conserved quantity that accompanies translational symmetry is known as momentum. An isolated object's momentum can't change because momentum is a conserved quantity—it can't be created or destroyed. Since momentum is related to motion, an isolated object that's at rest and has no momentum must remain at rest with no momentum. And an isolated object that's moving and has a certain momentum must remain in motion with that same momentum.

Incidentally, the laws of physics also exhibit rotational symmetry—meaning that turning your head doesn't change the laws of physics—and this symmetry leads to the existence of a conserved quantity known as angular momentum. The laws of physics also don't change with the passage of time, a temporal symmetry that leads to the existence of a conserved quantity known as energy.


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