If a police officer stops you with a speeding ticket, here is a scientifically valid point that you might try to make: “My speed changed by less than one part in ten thousand relative to the cosmic rest-frame; this is well within the uncertainty in the measured value of my cosmic speed by the best observatories in the world.” Indeed, your change in speed relative to the cosmic microwave background is unmeasurable by all astronomical observatories, as long as we all subscribe to the cosmic perspective.
But in full disclosure, keep in mind that the police officer may have never heard of the cosmic microwave background and was trained to rely on measuring devices that monitor your speed relative to the asphalt in the highway. That relative speed can be measured to a much better precision.
Of course, I can imagine caveats. Passing gravitational waves with a wavelength smaller than your spatial separation from the police officer could make the speed measurement uncertain, but waves of the needed amplitude would only let you off the hook in close proximity to a black hole merger. So far, the LIGO-Virgo-KAGRA detected only weak gravitational waves of a characteristic amplitude that is 22 orders of magnitude smaller than the legal uncertainty in the speed-monitoring devices used by the police.
Given that, if the police officer would show reluctance to engage in a dialogue about the Universe, I would pay the bill. Most people, like this officer, keep their eyes on Earth and focus only on what happens relative to the rock we were born on. Although a cosmologist might argue that this is a narrow-minded perspective, the rule of societal law stands on the side of officers on duty and equips them with a gun to settle violent disputes.
At any event, let me explain the cosmic argument in case it might soothe your soul after getting a speed ticket.
The speed limit on a highway is typically 65 miles per hour, equivalent to 0.03 kilometers per second. This is 15 times slower than the rotation speed of Earth around its axis, a thousand times smaller than the speed of the Earth around the Sun, eight thousand times smaller than the speed of the Sun around the center of the Milky-Way galaxy, and 12,727 times smaller than the speed of the Sun relative to the cosmic rest-frame.
The cosmic rest-frame is represented by the cosmic microwave background, a radiation relic from the hot Big Bang. The Universe started with the same temperature everywhere to within one part in 100,000. This allows us to define the cosmic rest-frame to an exquisite precision because time was ticking at the same rate everywhere to a part in 100,000. Our cosmic motion induces a Doppler effect that is a hundred times larger. Our net speed is a thousand times smaller than the speed of light, creating a Doppler modulation of the background temperature in the direction of our motion at the level of a part in a thousand, two orders of magnitude larger than the primordial variations in the background temperature.
This Doppler effect was measured by the COBE and Planck satellites to an exquisite precision of one part in 3362. The inferred value of the Sun’s velocity relative to the cosmic microwave background is 369.82 kilometers per second, with a measurement error bar of 0.11 kilometers per second. The speed limit on a highway is 3.7 times smaller than the uncertainty in our cosmic motion. As long as you did not reach a speed of 240 miles per hour relative to the asphalt, equivalent to 387 kilometers per hour, you are at no risk of exceeding one standard deviation in the measured cosmic speed. Case closed.
Any motion relative to the cosmic frame is called `peculiar velocity’ and its value for most cosmic observers is of the same magnitude as ours, of order a thousandth of the speed of light. Why is that the case? Why are peculiar velocities typically of order a few hundred kilometers per second?
Peculiar velocities are induced by primordial fluctuations in gravitational potential, which attract matter towards over-dense regions. These fluctuations were likely imprinted by quantum mechanics when the cosmic temperature was nearly a trillion times larger than the highest energy achievable in CERN’s Large Hadron Collider. As already mentioned, the primordial gravitational-potential fluctuations (normalized by the appropriate units of the speed of light squared) were one part in 100,000 on all spatial scales in the Universe, from the small scales of galaxies and up to the cosmic horizon. When matter fell into these gravitational potentials, it enhanced them only mildly. The matter acquired a kinetic energy which is of order half the gravitational potential energy. This implies that the matter acquired a characteristic speed in units of the speed of light which is the square root of a half of 1/100,000, roughly two parts in a thousand. This is why peculiar velocities are usually a few hundred kilometers per second throughout the Universe. Only in rare environments, like the vicinity of black holes, peculiar velocities reach much higher values.
The initial conditions of the Universe explain the motion of Earth relative to the cosmic rest-frame. But admittedly, your motion relative to Earth at more than 65 miles per hour was your own choice. As much as this choice has negligible cosmological significance, most police officers are unfortunately not monitoring the cosmic microwave background.
If you ever move to the Moon, keep in mind that time is ticking faster over there relative to Earth, by an average of 58.7 microseconds per Earth-day. This factoid was remarkably acknowledged by a White House memo from April 2, 2024. At a fixed Earth-normalized speed, it will take you slightly more time to cross a given Earth-normalized distance on the Moon than on Earth. My message to any future lunar residents is to please be patient; leave your base earlier if you do not want to risk a speed-limit violation on the Moon.
For the more ambitious travelers who aspire to venture beyond the Solar system, you will be glad to know that the only speed limit that physics imposes is the speed of light. Gladly, that is ten million times higher than the speed limit on a highway. This does not take into account interstellar police officers. You might wonder whether you will get more sympathy from them. But my advice here encourages caution: do not mess with interstellar law-enforcement officers because their weapons might be far more powerful than you had ever seen.
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. His new book, titled “Interstellar”, was published in August 2023.
