Ruled by Relativity

Walking on two legs, time and space seem universal, but take a good look at the universe, and things start to get mushy. Chad Orzel defines time with a circular-sounding title, writing “there isn’t a giant master clock at the center of the universe that everybody sets their watches by.” Although time can only be measured in ticks, two clocks are seldom in agreement. Chad says “Scientists in Colorado have clocks so good they can measure the change in time from moving at walking speed, or from moving one foot higher in elevation.” On Starts With a Bang, Ethan Siegel revisits the speed of light in a vacuum, which nothing apparent can exceed. If you’re a proton instead of a photon, your speed limit is a little bit lower, thanks to interaction with the cosmic background radiation. New upgrades to the Large Hadron Collider will boost the top speed of its protons by 8 m/s, only 3 m/s short of lightspeed.

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Layperson question here:

If time is measured by regular movement or by oscillation or atomic decay, what happens as the universe approaches the maximum entropy state of heat death, where matter has decayed to its most basic state and there is no more measurable movement above the level of Brownian motion?