Document 5
Rømer Gave No Velocity.
Huygens Did Arithmetic.
The Number Was Wrong.
Introduction
Documents One through Four of this series established the condition of Rømer’s record, the geometric account of what changed in his observation, the hard measurement boundary that no instrument has ever crossed,and Cassini’s specific empirical objection that the propagation interpretation has never resolved. This document examines what happened immediately after Rømer made his announcement, the arithmetic that produced the first numerical value for the speed of light. It examines who performed that arithmetic, what inputs they used, what the result was and how far it was from the figure that has been accepted ever since.
What Rømer Actually Claimed
Ole Rømer’s 1676 publication in the Journal des Sçavans is six paragraphs long.
It presents his qualitative interpretation of the timing variation he observed, that light takes a finite time to travel across the solar system and it gives one specific figure: that light takes approximately 22 minutes to cross the full diameter of Earth’s orbit around the Sun.
That is the entirety of what Rømer claimed numerically.
Rømer did not give a velocity. He did not calculate a speed. He did not state how many kilometers or miles light travels per second. He stated a transit time across a known geometric distance. The velocity that is attributed to Rømer, the figure that appears in every textbook as the first measurement of the speed of light, was not calculated by Rømer. It was calculated by Christiaan Huygens, working from Rømer’s stated transit time and his own estimate of the diameter of Earth’s orbit.
Rømer never actually gave a value for the velocity of light, which is ironic considering he is famous for being the first to measure that speed.
– Optics and Photonics News
Huygens’ Arithmetic
The Inputs
Christiaan Huygens was among the first to read and support Rømer’s 1676 paper. He was the leading mathematical physicist in Europe at the time, the inventor of the pendulum clock and the author of a major treatise on light. When he received Rømer’s result, approximately 22 minutes for light to cross the diameter of Earth’s orbit, he performed a straightforward calculation to derive a velocity.
The calculation requires two inputs.
The first is the transit time: Rømer’s figure of approximately 22 minutes, or 1,320 seconds.
The second is the diameter of Earth’s orbit: twice the mean distance between Earth and the Sun, a quantity known as the astronomical unit. The velocity is simply the diameter divided by the transit time.
The diameter of Earth’s orbit was not well established in the 1670s. The astronomical unit, the mean Earth-Sun distance, had been estimated by Cassini and Jean Richer from observations of Mars in 1672, just four years before Rømer’s announcement. Cassini’s estimate placed the astronomical unit at approximately 87 million miles, approximately 140 million kilometers. The accepted modern value is approximately 149.6 million kilometers. Cassini’s estimate was approximately 7 percent too small.
Huygens used Cassini’s estimate of the astronomical unit to perform his calculation. The diameter of Earth’s orbit in his calculation was therefore approximately 280 million kilometers, compared to the correct value of approximately 299 million kilometers. His input for the orbital diameter was wrong by approximately 7 percent before he began.
Huygens’ Arithmetic
The Result
Huygens divided his estimate of Earth’s orbital diameter, approximately 280 million kilometers, by Rømer’s stated transit time of 22 minutes, 1,320 seconds. The result was approximately 212,000 kilometers per second. This is the figure published in Huygens’ Traité de la Lumière in 1690, the first numerical value for the speed of light to appear in a published scientific work.
The accepted modern value for the speed of light is 299,792 kilometers per second. Huygens’ result of approximately 212,000 kilometers per second is approximately 29 percent below the accepted modern value.
The discrepancy has two sources: Rømer’s transit time estimate of 22 minutes was too long, the correct value derived from modern orbital parameters is approximately 16.7 minutes, and Huygens’ estimate of Earth’s orbital diameter was approximately 7 percent too small.
Both errors pushed the result in the same direction: too low.
This is the arithmetic chain that produced the first numerical speed of light. Rømer observed timing shifts in Io’s eclipses. He interpreted them as evidence of finite light travel time. He estimated that light takes 22 minutes to cross Earth’s orbital diameter. Huygens divided a wrong orbital diameter by that wrong transit time and got a velocity approximately 29 percent below the correct value. That velocity was then cited as the first measurement of the speed of light. The measurement that was never directly made was assigned a numerical value derived from two wrong inputs.
Rømer estimated that light required twenty-two minutes to cross the diameter of the Earth’s orbit. The correct value is 16.7 minutes. The difference was due to errors in Rømer’s estimate and to an imprecise knowledge of the Earth’s orbital diameter.
– American Museum of Natural History
The Best-Fit Procedure Behind
the 22-Minute Figure
Document One of this series established that Rømer’s 22-minute figure was not derived by summing a continuous sequence of individually measured timing shifts. It was produced by a best-fit procedure applied to approximately thirty observations from 1671 to 1673. Rømer fitted those observations to find the value that produced the smallest overall discrepancy with the predicted eclipse times. The value that fitted best was eleven minutes for light to cross the radius of Earth’s orbit, doubled to 22 minutes for the full diameter.
A best-fit procedure within an assumed interpretive framework is not the same as a derivation from independent data. The propagation interpretation was assumed. The data was fitted within that assumption to find the value that best reproduced the observed pattern. The 22-minute figure is the output of that fitting procedure, the value that makes the propagation interpretation fit the observations most closely. It is not an independently derived measurement that confirms the propagation interpretation. The interpretation is assumed. The data is fitted to it.
The peer-reviewed literature acknowledges this directly. A 1998 analysis in the American Journal of Physics stated that Rømer’s case was built on four observations, one of which clearly failed, one of which was successful, and two of which were quite questionable. The timekeeping available to Rømer, Picard, and Cassini was, at best, not quite up to the task of measuring the necessary times with sufficient accuracy. The best-fit procedure applied to data of acknowledged limited accuracy produced a figure that was 32 percent too large. Huygens divided that figure by an orbital diameter that was 7 percent too small and produced a velocity that was 29 percent too low.
The Chain from Observation
to Accepted Constant
It is worth stating the full chain precisely so that each link can be examined on its own terms.
Link One: Rømer observed timing shifts in Io’s emergences from Jupiter’s shadow correlated with Earth’s orbital position. That observation is documented and not in dispute. The timing shifts exist in the record.
Link Two: Rømer interpreted those timing shifts as evidence of finite light travel time rather than as a product of his changing observational platform geometry. That interpretation is an assignment made to the data. It is not contained in the data. Document Two of this series showed that the geometric platform account is equally consistent with the observed timing shifts.
Link Three: Rømer fitted approximately thirty observations to find the transit time value that best reproduced the observed pattern within the propagation interpretation. The best-fit value was 22 minutes. That figure is a product of the fitting procedure applied to data of limited accuracy, not a direct measurement. Document One established this.
Link Four: Huygens divided Rømer’s 22-minute figure by Cassini’s estimate of Earth’s orbital diameter, an estimate that was approximately 7 percent too small and produced a velocity of approximately 212,000 kilometers per second. This arithmetic has two wrong inputs. The result is approximately 29 percent below the accepted modern value.
Link Five: The velocity produced by Huygens’ arithmetic was reported as the first measurement of the speed of light. Every subsequent measurement refined the numerical value. None of them revisited whether the original interpretation in Link Two, the assignment of propagation as the mechanism, was established by direct observation or assumed as an interpretive framework and fitted to data.
The speed of light as a physical constant rests on this chain. Each link in the chain is a documented historical fact. The chain as a whole has been treated as an established measurement. What this series has shown, document by document, is that the chain contains an interpretation at Link Two that was never directly verified, a fitting procedure at Link Three that acknowledges its own data limitations and an arithmetic result at Link Four that was wrong by 29 percent. The numerical value has been refined since Huygens. The interpretation at Link Two has not been revisited.
What This Document Establishes
Rømer gave no velocity. He stated a transit time estimated by a best-fit procedure applied to approximately thirty observations of limited acknowledged accuracy. Christiaan Huygens performed the arithmetic that produced the first numerical speed of light, using Rømer’s 22-minute figure and Cassini’s estimate of Earth’s orbital diameter. Both inputs were wrong. The result was approximately 29 percent below the accepted modern value. The chain from Rømer’s observation to the accepted speed of light as a physical constant contains an unverified interpretive assumption at its foundation, a best-fit procedure applied to data of limited accuracy and an arithmetic result derived from two wrong inputs.
Document Six, the closing document of this series, examines the one observation that resolves every question this series has raised: what light and darkness actually are outside the atmospheric boundary where every one of these measurements was made.
Produced by The Lilborn Equation Team:
Michael Lilborn-Williams
Daniel Thomas Rouse
Thomas Jackson Barnard
Audrey Williams