Distant starlight is often presented as a problem for the biblical timescale. Namely, given that galaxies are billions of light years away, it should take billions of years for their light to arrive at earth. And the fact that we see these galaxies shows that their light has indeed traversed this distance. We previously introduced this distant starlight issue and then examined potential solutions and their difficulties. We now move toward a solution to the issue. This solution is surprisingly straightforward, but will require some discussion of the nature of space and time as we now understand them. To that end, we will here investigate the concept of simultaneity and how this concept has developed over time.
Simultaneity
When two events happen at exactly the same time, they are said to be simultaneous. So, the concept of simultaneity concerns how we evaluate the relative timing of two events. This seemingly simple notion turns out to be rather complicated in light of what we now understand about physics. Yet it is crucial to unraveling the distant starlight issue and can influence our understanding of Genesis.
According to Genesis 1:14-19, God made the sun, moon, and stars on day 4 of the creation week. Hence, all stars were made on the same day; they were all made simultaneously (or nearly so – within 24 hours). Likewise, the creation of the stars is simultaneous with the fourth rotation of earth. Therefore, our understanding of the concept of simultaneity will affect our understanding of these verses, either for the better or for the worse.
To illustrate some of the potential complications involving simultaneity, consider the following scenario. Nathaniel’s alarm clock goes off at 8:00 a.m. every weekday. Likewise, Aaron’s alarm clock goes off at 8:00 a.m. every weekday. Are these two events simultaneous? They did happen at the same time, didn’t they? But suppose I add some additional information: Nathaniel lives in New York, whereas Aaron lives in California. Given this new information, we conclude that Nathaniel’s alarm actually activated three hours earlier than Aaron’s alarm because 8:00 a.m. Eastern time is equivalent to 5:00 a.m. Pacific time.
If you have ever made a phone call to someone living in a different time zone, you have probably done a quick mental calculation to make sure you are not calling too early or too late. You might say, “It’s 9:00 a.m. here. So, what time is it there?” It’s a strange question because in one sense, two people must be talking on the phone at the same time in order to have a conversation. Yet, in another sense, they may be talking at two different times. The spherical nature of earth makes it convenient to have two different conventions by which we specify time. We use local time (in which the sun crosses the meridian around noon) for most of our daily activities. We use universal time (defined to be the local time in Greenwich England) when coordinating phone calls or other cooperative efforts that span multiple time zones.
So, let’s consider another scenario. Samantha also lives in New York, only three blocks away from Nathaniel. Her alarm goes off at 8:00 a.m. every weekday, just like Nathaniel’s. So, can we conclude that those two events are simultaneous? They are in the same time zone, after all. Yet, it is improbable that the alarms go off at exactly the same time. Unless they are using atomic clocks, their clocks do not keep perfect time. Over the course of a year one clock might gain a minute or two while the other clock loses a minute or two. Hence, these two clocks are not exactly synchronized – they do not read exactly the same time at the same moment in time. We could verify this by having Nathaniel call Samantha and each would read the time on their clock. This nearly instantaneous communication would confirm whether or not the clocks are synchronized. However, we will find that this method becomes problematic over cosmic distances in which round-trip instantaneous communication is not possible.
Visual Synchrony Convention
A method of deciding or defining whether two events are simultaneous is called a synchrony convention. The most obvious and natural choice for a synchrony convention is called the visual synchrony convention. Under this system, the timing of any event is defined to be the time at which it was observed; things happen at the very instant you see them happening. This is intuitive. If you see a deer run across the road, it wouldn’t even occur to you to think, “I wonder how many millions of years ago that actually happened?” Of course, not. If you see something happening right now, then it is natural to suppose that it is happening right now. Today, we use the visual synchrony convention for just about everything, except celestial events.
When we see a supernova (an exploding star), we are told that even though we are seeing it right now, the event actually happened long ago. This is because we understand that the light has taken time to traverse the enormous distance between there and here. When the event actually happened will depend on its distance from earth and the speed of light. But this is a very modern way of thinking. No one knew what the speed of light was before A.D. 1676, and no one knew the distance to any of the fixed stars before A.D. 1838. So before very modern times, it was not possible to subtract off any light travel time to figure out when the event actually occurred.
Therefore, ancient astronomers defined the time of a celestial event as when that even was observed on earth. This is the visual synchrony convention – the same convention we use when looking in a mirror while shaving or combing our hair. Most ancient scientists believed that the speed of light was infinite, and therefore things do actually happen when we see them happen.[1] But even if anyone suspected that light has a finite speed, no one knew what it was before 1676.[2] Therefore, all people used the visual synchrony convention since no other option was available.
Modern Methods, Measurements, and Misconceptions
This changed in 1676 when the Danish astronomer Ole Rømer used the moons of Jupiter to measure the speed of light.[3] Later, more accurate and precise measurements would show that light travels at the incredible speed of 186,282.397 miles per second.[4] At such a speed, it would take over four years for light to reach our solar system from the nearest star. Light from more distant stars would take even longer. Hence, astronomers began to think of their observations of stars as a window into the past. They might say, “We are not seeing these stars as they are now, but as they were in the past. When you look through a telescope, you are looking back in time.”
This way of thinking constitutes a new and different synchrony convention. Under the visual synchrony convention, events happen when you see them. Under this new modern convention, events happened before you see them. To find out when an event actually happened, you take the time it was observed and subtract its distance divided by the speed of light. Ancient astronomers would not have been able to use this modern convention because they did not know the speed of light nor the distance to the stars.
For those unfamiliar with the physics of Einstein, it will be tempting to think that the older visual synchrony convention is simply wrong. We are inclined to think that the “true” timing of celestial events (when they actually happened) is long before we observed them due to the time it has taken light to travel that distance. Furthermore, in assuming that the visual synchrony convention is wrong, Christians then draw the natural conclusion that the Bible would not use it. Rather, the creation of the stars on day 4 must be according to the modern (allegedly “correct”) synchrony convention, in which case it would take many years for their light to reach earth. This leads to the distant starlight problem.
However, the discoveries of Albert Einstein disprove these assumptions. Einstein demonstrated that both the visual synchrony convention and the modern synchrony convention are equally correct. So, are we seeing the nearest stars as they were years ago, or as they are now? The answer, according to Einstein, is both![5] But how can that be? Einstein realized that the nature of space and time are not what we would intuitively expect. And the speed of light is very special and not like other speeds.
Enter Einstein
In the year 1887, two scientists performed an experiment now named in their honor that involved the speed of light. The Michelson-Morley experiment was designed to measure the change in the relative speed of light as the earth rotated on its axis and orbited the sun. At that time, most scientists assumed all waves required a substance – a medium – in which to travel. The medium of light was thought to be an undetectable luminiferous æther that filled the entire universe, and through which planets traveled. The speed of light was assumed to be constant relative to that medium, and therefore not constant relative to the earth as it traveled through that medium. However, the experiment showed that the speed of light relative to earth was constant regardless of how the earth moved. Similar experiments have shown that the speed of light in vacuum is constant relative to any observer.[6]
The speed of light in vacuum is denoted with a lowercase letter c. All observers always measure the speed of light to be exactly c relative to themselves, regardless of their velocity. This is a strange result, but it’s true. No matter how fast you move, light will always move exactly c faster than you. What is even stranger is that two people will observe the same beam of light moving at c faster than themselves, even if they are moving at different speeds!
Einstein realized the reason for this counterintuitive effect; we had made a false assumption. Our everyday experience suggests that the passage of time and measurements of length are unaffected by motion. When you drive a car, your watch ticks at the same rate it does when you are stationary. But Einstein recognized that this assumption is actually false. Motion does affect the rate at which time passes, and thus the rate at which clocks tick. It also affects lengths – a moving car is slightly shorter in the direction of motion than an otherwise identical stationary car. Einstein discovered the exact mathematical formula to describe these effects of time dilation and length contraction.[7]
Why don’t we notice these effects? The reason is that these effects are far too small to be noticed at speeds that are small compared to the speed of light. For example, in order for a moving clock to be slowed by a mere 1% relative to its stationary counterpart, it would have to move at 14% the speed of light – about 94 million miles per hour. The formula for these effects is given and explained in my book The Physics of Einstein. But we shall not discuss them in any further detail here.
There is a third counterintuitive effect of the constancy of the speed of light in vacuum. This concerns the definition of simultaneous and will be essential to understanding the distant starlight issue. We now turn to this issue.
Round-Trip Speeds and One-Way Speeds
The Michaelson-Morley experiment attempted to measure potential differences in the speed of light along two different round-trip paths. In other words, light traveling from A to B and back to A was compared with light traveling from A to C and back to A. Line segment AB was identical in length to segment AC, but was in a perpendicular direction. Similarly, other experiments to measure the speed of light generally do so by sending light from A to B and reflecting it back to A. The total time is measured. And the total distance (twice the distance from A to B) is measured. Dividing the distance by the time yields the average speed of light. Many such experiments have been done, and they always give the same answer: c.
But this is a time-averaged speed. In other words, the speed of light may not be constant throughout this round-trip journey. It may be faster than c at times, and slower than c at other times, such that the average is always c. In particular, the speed of light from A to B might not be the same as the speed of light from B to A. Of course, you might ask yourself, “why would it be different from A to B as for B to A? Isn’t it simplest to assume that it is the same speed in both directions?” We know from experiments that the average round-trip speed of light (A to B and back to A) is always exactly c in vacuum relative to any observer. Many people assume that this is also true of the one-way speed: that all observers will measure light to move at speed c from A to B. But as we will see, this assumption leads to some potential difficulties.
Consider the following thought experiment. Leonard attempts to measure the round-trip speed of light in his laboratory by sending light out from A to B, whereupon it is reflected by a mirror at B, sending it back to A. To make the math easy, suppose that A and B are separated by 186,282.397 miles. Leonard would find that light takes a total of two seconds to travel from A to B and back to A. Dividing the total distance (186,282.397 x 2) by the total time (2 seconds) yields the time-averaged round-trip speed of light: c (186,282.397 miles per second).
Suppose Leonard assumes that light from A to B travels at the same speed as light from B to A as measured by Leonard in his laboratory. Therefore, he places a clock at point B and synchronizes it with a clock at A by the following method. A light pulse is sent out from A at exactly noon. When the clock at B receives the light, it sets itself to one second past noon. Leonard believes that these two clocks are now exactly synchronized, since he believes that light takes one second to go from A to B and one second to go from B to A.
This all seems perfectly sensible until we consider another observer. At the moment Leonard performs his experiment, suppose Hannah is traveling in her car at 10% the speed of light.[8] She is also traveling from A to B, and passes point A exactly at noon. At that time, both her onboard clock and Leonard’s clock at A read exactly noon. We know from experiments that Hannah will measure the round-trip speed of light as being exactly c relative to herself. And for the sake of argument, let’s suppose that she also believes that the one-way speed of light is exactly c in any direction relative to herself.
Hannah is of course stationary relative to herself. So, from her point of view, Leonard and his clocks at A and B are moving backward at 10% the speed of light. Therefore, from Hannah’s point of view, the light pulse sent from A at noon will take only 0.9 seconds to travel from A to B. This is because B has moved 10% closer to Hannah in this time, reducing the distance the light has to travel. On the other hand, light will take approximately 1.1 seconds to travel from B back to A, because A is moving backward, increasing the distance light must travel.[9]
From Leonard’s perspective, light takes exactly one second to arrive at B, and therefore arrives at a time of 12:00:01, which matches the reading on clock B. But from Hannah’s perspective, the light takes only 0.9 seconds to reach B, and therefore does so at time 12:00:00.9 which does not match the reading on clock B. Thus, from her perspective, the clocks at A and B are not synchronized. She believes Leonard should have programmed the clock at B to set itself to 12:00:00.9 when the light arrives, since the light took only 0.9 seconds from her perspective to get there.
Do you see the problem? If we assume that the one-way speed of light is the same in all directions for all observers, then we have an apparent contradiction: the clocks at A and B are synchronized and also not synchronized. How do we resolve this dilemma?
Einstein’s resolution was to abandon the idea of objective, universal synchronization and instead make it observer-dependent. In other words, the two clocks are synchronized relative to Leonard, and the two clocks are not synchronized relative to Hannah. (This eliminates the contradiction because the sense is different.) This is called the relativity of simultaneity.
The Relativity of Simultaneity
The relativity of simultaneity follows inexorably from the stipulation that the one-way speed of light is the same in all directions for all observers.[10] The only alternative is to give up that stipulation, and allow the one-way speed of light to be different in different directions for at least some observers. For example, we could all agree by fiat that the one-way speed of light shall be the same in all directions relative to Leonard and only him. Thus, Hannah, could accept that light moving in her forward direction travels at a speed of 0.9c, while light traveling in the backward direction travels at 1.1c relative to her. She would then agree with Leonard that the clocks at A and B are synchronized by his method.
But the problem with this alternative is: why should we agree to Leonard’s stipulation that the one-way speed of light is the same in all directions relative to him? Hannah might insist that the one-way speed of light should be the same in all directions relative to her, and that Leonard should set the clock at B to 12:00:00.9 when the light arrives. If Leonard agrees to this, then he would have to admit that light traveling from A to B travels at a different speed relative to him than light from B to A (because it takes 0.9 seconds to go from A to B, but 1.1 seconds to go from B to A). But there is no objective, physical basis for preferring Hannah’s reference frame to Leonard’s, or Leonard’s to Hannah’s. And so, Einstein’s solution of leaving synchronization observer-dependent seems best.
The relativity of simultaneity means that there is no objective, universal answer to the question “Are clocks at two different locations (A and B) synchronized?” We can only say that they are synchronized relative to some reference frame. To a person in a different location moving at a different velocity, those two clocks will not be synchronized.
One consequence of the relativity of simultaneity is that it eliminates any possibility of objectively measuring (without arbitrary circular reasoning) the one-way speed of light. Leonard simply stipulated that the light must travel at the same speed from A to B as it does from B to A. He didn’t test this. Nor can he test it without first assuming it. In order to measure the speed of light on a one-way trip (say from A to B), you would need to have a clock at A to tell you when the light starts its trip, and a clock at B to tell you when it arrived. Subtracting the start time recorded at A from the recorded arrival time at B gives the time of the journey; dividing the distance by this time yields the one-way speed of light. But this would only work if the clocks at A and B are exactly synchronized.
But Leonard synchronized the clock at B to the clock at A under the assumption that the speed of light is the same in opposite directions relative to himself and not to Hannah. From her reference frame, those two clocks are not synchronized. There is no objective way to synchronize clock B to clock A in such a way that all observers would agree.
It is tempting to think that there is some other way to synchronize the two clocks without first assuming the one-way speed of light. But this is not so. You might say, “just bring both clocks together so that they are at the same place, synchronize them, and then move them to their locations.” But the assumption that they are still synchronized after having been moved is in question because Einstein discovered that motion affects the passage of time. And it does so in a way that depends on the speed of light – the very thing we are attempting to measure.
Furthermore, whether or not clocks are synchronized depends on the observer. And only synchronized clocks can measure a one-way speed. Therefore, there can be no objectively measured universal one-way speed of light since there is no objective universal agreement on the synchronization of two clocks at different locations. The only objective, measurable reality is that the round-trip speed of light in vacuum is always exactly c for all inertial observers. A round-trip average speed can be measured using only one clock, and so there are no unnecessary assumptions about synchronization.[11] The one-way speed is a matter of choice which results in a method of synchronizing clocks that will inherently be observer-dependent.
Leonard’s choice to assume that the one-way speed of light is the same from A to B as for B to A is not a falsifiable hypothesis; it is not something that can be empirically tested without circular reasoning. This is because we must first assume something about the one-way speed of light in order to know if the clock at B is synchronized with the one at A. Thus, the one-way speed of light is a stipulation that allows Leonard to define what he considers to be synchronized clocks. Other observers will disagree with his choice – as is their right since there is no objective way to synchronize two clocks separated by a distance in which all observers would agree.
Einstein discussed this situation in his primer book on Relativity. He considers a thought experiment in which two bolts of lightning strike in two different, but nearby locations: A and B. Is there any way to determine if these two bolts struck at exactly the same time? Suppose we knew in advance approximately when and exactly where they were expected to strike. We could place an observer exactly between these two locations at M, and equip him with two mirrors so that he can observe both A and B at the same time. Assuming that light travels at the same one-way speed from A to M as it does from B to M, then the observer at M will decide that the two lightning strikes are truly simultaneous if he sees their light arrive at the same time. This is how he proposes to define the concept of simultaneous.
Here is Einstein’s discussion on this issue. “I am very pleased with this suggestion, but for all that I cannot regard the matter as quite settled, because I feel constrained to raise the following objection: ‘Your definition would certainly be right, if only I knew that that the light by means of which the observer at M perceives the lightning flashes travels along the length A to M with the same velocity as along the path B to M. But an examination of this supposition would only be possible if we already had at our disposal the means of measuring time. It would thus appear as though we were moving here in a logical circle.’”[12]
In other words, we can only objectively measure the one-way speed of light if we had two clocks at different locations that we knew were synchronized. But we cannot decide if clocks are truly synchronized without knowing the one-way speed of light. Each question requires us to answer the other one first. Hence, both are unanswerable. Einstein’s solution was to recognize that we may choose the one-way speed of light in any one direction, and then this gives us a definition of simultaneity, and a conceptual method to synchronize two clocks separated by a distance.
Einstein states, “That light requires the same time to traverse the path A to M as for the path B to M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity.”[13] (emphasis in the original)
So, the one-way speed of light is not a property of nature at all. Rather, it is a humanly-stipulated convention that enables us to define what constitutes synchronized clocks for a given observer. This principle is called the conventionality thesis (or the conventionality of distant simultaneity), and it follows logically and inevitably from the relativity of simultaneity. The conventionality thesis means that we are free to choose the one-way speed of light in a particular direction for a particular observer, and this constitutes a definition of simultaneous for that observer. (Note that the speed in the opposite direction will then be determined by the requirement that the round-trip time-averaged speed of light in vacuum must always be c.)[14] As a definition, it cannot be refuted by any experiment or observation.
As one example, you can stipulate that the one-way speed of light when traveling north is exactly 3c (three times the round-trip speed of light). The speed of light traveling south would then be 0.6c which maintains the round-trip speed of light as c.[15] You can also use a polar or spherical coordinate system in which we consider directions toward or away from the observer. Infinite speeds are also permitted,[16] in which the speed in the opposite direction is 0.5c. This is a particularly interesting and relevant case because the visual synchrony system defines incoming light as instantaneous since celestial events are concurrent with their observation. Therefore, outward moving light must travel at 0.5c in the visual synchrony convention. This is an anisotropic synchrony convention (ASC) because the one-way speed of light is different in different directions.[17] The ASC and the visual synchrony convention are the same thing.
The Astonishing Implication
So, what does all this mean? What is its significance for the distant starlight issue? For one, the conventionality thesis implies that the ancient visual synchrony convention is just as legitimate as the modern Einstein synchrony convention. So, when we look at Alpha Centauri in a telescope, are we seeing it as it is now, or as it was 4.3 years ago? If you have tracked the above discussion, then you know the answer is: both. By the Einstein synchrony convention, we see it as it was 4.3 years ago, and by the visual synchrony convention, we see it as it is right now. People are tempted to ask, “yes but which one is right? When did the light really leave the star?” But such questions are meaningless because they assume the false concepts of absolute time and a universal standard of simultaneity.
Now that we understand that (1) simultaneity is not universal, but observer-dependent, and (2) that there are multiple synchrony conventions by which we define what constitutes simultaneous events (by stipulating the one-way speed of light in a given direction), we must reexamine our assumptions on both issues in regards to the biblical teaching. From Genesis we know that God made the stars and other luminaries on day 4 of the creation week. Thus, the creation of stars and galaxies is simultaneous with the fourth rotation of earth. But we must now ask two questions. First, “simultaneous relative to what reference frame?” And second, “simultaneous by which synchrony convention (visual, Einstein, or some other)?”
Recall that if two events (separated by some distance) are evaluated as simultaneous with respect to one observer (like Leonard), they will not generally be simultaneous relative to another observer (like Hannah). Fortunately, the Bible gives us the reference frame from which all events in Genesis are described: the surface of earth. We know this because the days of creation are earth-rotations described in the Bible as consisting of one evening and one morning. This also implies that creation is being described from one particular spot on the surface of earth (since it experiences the day and night cycle as earth rotates), perhaps the location that would become the Garden of Eden. The exact location doesn’t matter much since light can circumnavigate earth in one seventh of a second. We understand that stars are made on day 4 relative to the earth’s reference frame, and not that of Mars, or Alpha Centauri, or an interstellar asteroid.
We then are left with the one remaining question. “Stars were made simultaneously on day 4 by what synchrony convention?” That the Bible must apply a synchrony convention of some sort is obvious because it describes the timing of celestial events. It describes these events as taking place at the same time (or nearly so) all on day 4. The assumption that the Bible must use the modern Einstein synchrony convention is motivated by the false assumption that this convention is the only correct one. But we have seen that the visual synchrony convention is just as legitimate and compatible with modern physics. The two conventions are equally “true,” merely providing two different definitions of what constitutes synchronized clocks by stipulating different, but equally legitimate, values for the one-way speed of light.
Given this, it seems obvious that the Bible would use the more ancient visual synchrony convention. This convention was the only one possible for ancient observers and is still understandable today. Conversely, the Einstein synchrony convention is of modern origin. And its implementation requires knowledge of the distance to stars and the round-trip speed of light, both of which were unknown to the ancient world. If God used the Einstein synchrony convention to describe the celestial events in Genesis, then His Word could not have been understood properly until the twentieth century. The perspicuity of Scripture therefore implies a synchrony convention that is understandable throughout history – and that is the visual synchrony convention.
Under that convention, there is no distant starlight problem because the creation of the stars is concurrent with the arrival of their first light on earth. No time is required to traverse the distance, and we see the universe as it is now. The perception of starlight problem arose from the assumption that the visual synchrony convention is wrong, and the Einstein synchrony convention is correct. But such an assumption is not compatible with modern physics.
Nonetheless, the notion that the one-way speed of light can be stipulated and cannot be objectively measured without circular assumptions is deeply counterintuitive, especially to those who have had little exposure to the physics of Einstein. Therefore, people sometimes raise objections to the conventionality thesis. There are some observations and experiments that seem at first glance to measure the one-way speed of light without first assuming it. Although there is a rich history of discussion on this issue in the technical literature, most people are not familiar with this literature and may not even have access to it. So, these issues deserve discussion. More to come.
[1] This assumption works quite well as an approximation for just about all of our everyday activities on earth. Light could go around the earth seven times in one second. So, it is nearly instantaneous for most earthly practical purposes.
[2] In the early 1600s, Galileo suspected that the speed of light might be finite. He unsuccessfully attempted to measure it using lantern signals separated by a distance. He rightly concluded that the speed of light was too fast to be accurately measured by such a method.
[3] At first glance, Rømer’s observations would seem to be a measurement of the one-way speed of light (the average speed of light from A to B). Yet, in reality, Rømer’s observations actually measured a round-trip speed of light (the average speed of light from A to B and back to A). This is because he made two false assumptions that essentially cancel each other, resulting in a correct value for the round-trip speed of light. This is covered in the book “The Physics of Einstein.”
[4] A physicist would naturally ask, “186,282.397 miles per second relative to what?” Isaac Newton had demonstrated that all motion is relative and that the laws of physics do not prefer any particular velocity frame to any other. Yet, the amazing answer to this question is “relative to any observer.” This surprising result demonstrated that space and time were not the objective and invariant foundation that nearly everyone had assumed, and it paved the way for the physics of Einstein.
[5] Note that this does not violate the law of non-contradiction because the sense is different. Two events can be simultaneous by the visual synchrony convention, and also non-simultaneous according to the modern synchrony convention. Einstein demonstrated that nature does not prefer one convention over the other; they are equally legitimate.
[6] Specifically, this refers to inertial observers – those that move with uniform (non-accelerating, non-rotating) motion. It also works as an approximation for observers whose deviation from uniform motion is small (such as earth).
[7] To see how Einstein was able to deduce these effects, see the book “The Physics of Einstein.”
[8] This choice of speed allows us to ignore the effects of time dilation and length contraction since they will be less than 1% for velocities less than 14% the speed of light.
[9] Astute students of math will realize that the value is slightly larger than 1.1 seconds, but we have rounded to the nearest 10% since time dilation and length contraction would need to be included for effects nearing 1% precision.
[10] This is also true of other choices in which the one-way speed of light is relative to the observer, even if that speed varies with direction.
[11] A single clock is necessarily synchronized to itself. It must read the same time that it reads.
[12] Einstein, A. Relativity: The Special and General Theory, p. 22-23.
[13] Ibid, p. 23
[14] If the chosen one-way speed of light in one direction is s, then the speed of light in the opposite direction will be c/(2 – c/s) where c is the round-trip speed of light in vacuum.
[15] This is computed from the formula in the previous footnote.
[16] For those uncomfortable with infinite values, we can select a value that is arbitrarily high, such as 10100 meters per second. At such a speed, any trip will be nearly instantaneous.
[17] Actually, any synchrony convention except the Einstein synchrony convention has an anisotropic one-way speed of light. But I reserve the term ASC to refer to the one in which incoming light is defined to have infinite (or arbitrarily high) speed.