This isn't true because of special relativity. Say you are watching a traveler move at half the speed of light suddenly turn on a flashlight. From your point of view, light moves away from the flashlight at c, and the traveling is moving at half c. So the difference between the speed of the traveler and the speed of light is exactly half c. However, if you are the traveler himself, when you turn on your flashlight, you see light move away from you at c. It's exactly the same as though you were standing still. The reason you have conflicting reports of relative speed is because speed is difference in distance over distance in time. When you approach the speed of light, both distance and time contract so that the speed of causality (light) is always measured with the same value. If you'd like, I could give you some more history/maths in a spoiler tag about how we came to realize that. Einstein didn't invent the concept, he just codified it, Maxwell actually noticed the problem.

Sorry, first principle of relativity is that all observers must observe the same speed of light, regardless of their relative motion with respect to each other. In other words light propagating at rest in the spacecraft reference frame will propagate perfectly normally, regardless of the ship's relative motion to some other reference frame, or equally alternative, another reference frame's motion WRT to the ship. If the ship shines a laser in the direction of travel (toward the bow), or any other direction, and measures the time it takes to make the round trip to to bow and back to the source, it will be exactly the same whether the ship is at rest WRT another reference frame or moving 186,000 miles per second to that reference frame. See the Michaelson-Morley experiment which started all this.

I was thinking about this thread this morning, and though I have already commented, the above-quoted response was to be my new suggestion. What if they aren't just a screen? What if they do something else? Hard Sci-Fi really boxes you in as regards finding a reason for a genuine, old-school CRT to be in your vehicles. Can the look boxy because of another reason?

Just for the sake of accuracy, this experiment was looking for changes in the relative speed of light depending on which direction the Earth was traveling around the sun. They were trying to find the medium which light propagated through (at the time they thought light was a wave.) Spoiler: Discovery of constant electromagnetic speed The constant speed actually came a few decades before that. They'd already known that an excitation in the electric field creates one in the magnetic field. Maxwell showed that the opposite was true too. It was easy from there to determine that an electric excitation creates a magnetic one, which creates an electric one, which creates a magnetic one.... In a wave. It also mathematically describes the speed of this propagation as constant in a vacuum regardless, which violated Newton's laws of relativity.

I believe Michelson-Morley were testing for the aether. c is always constant, regardless of frame of reference, but I think you and Lew and saying the same thing on that point.

They were, aether was the theoretical medium through which light propagated. Like I said, at the time, light was thought to be a classical wave, and waves require a medium. We now know that it's a quantum object, which has some counter-intuitive properties.

You can move relative to a sound wave that you generate, which propagates in a medium. Light does not. The Michelson-Morley experiment was looking for that change in the speed of light (ether drift) caused by the earth's motion, which came up null. The procedure was to measure the speed of light in the direction of earth's rotation (east west), and compare it with the speed of light at right angles to that (north south). They were looking for a phase shift in interference patterns over a twenty four hour period in which the direction of the earth's rotation would go from in the direction of the earth's travel around the sun, to opposite, and back again, while the north south transit should be unchanged. He was a fellow alumnus of mine from the US Naval Academy, though a century removed -we were NOT classmates, he was class of 1873! And there he measured the speed of light in 1877 to a very high degree of accuracy, within .05% of today's accepted value. Michelson Hall, the science building at Annapolis, is named after him. Fundamentally, there is no absolute motion, because you cannot detect your motion because of any physical effects in your reference frame. Not true of acceleration: acceleration is absolute motion, and you can detect your own acceleration without an outside reference. Speed is entirely relative, and you yourself are always at rest.

Right, but didn't establish the constant speed of light, Maxwell had already done that mathematically in 1861 and finished the electromagnetic wave equation in 1865. It was assumed at the time that this constant speed must be relative to a medium, which they called the aether. The Michelson-Morley was run to prove it and baffled scientists at the time because of the negative result. FitzGerald a decade later proposed that the result could be explained by objects contracting at high speeds, then Lorentz independently provided the detailed mathematics in 1892. That lead up to 1905, which was Einstein's breakthrough year. A modified version of the Michelson-Morley experiment was done by Kennedy and Thorndike in 1932 because length contraction alone could predict the results of Michelson-Morley and Einstein predicted that time itself also changed. This lead to a long line of tests for SR that have (almost) always worked as predicted. To be clear, I'm agreeing with you, because of SR, CRTs work at high speeds, just sorting out the history of the physics. Also, don't bring acceleration into this. I hate acceleration. That's general relativity and I hate those equations, they take so long to derive.

I am actually writing a paper/small book on the subject. And acceleration is included because it is motion with respect to your previous trajectory, becomes incredibly easy to analyze, and drops out the mass rise and energy equations as a trivial exercise in trig. key points 1. Everything travels at the speed of light. 2. Matter travels in a single direction, which becomes for that body the direction of time. 3. Light travels in all four directions (x/y/z/ct) 4. Relative motion is the a difference in direction, sin (theta) = v/c, cos (theta) =sqrt (1--sin^2)= sqrt(1-v^2/c^2), not speed; relative motion projects a component of the temporal velocity of one onto the spatial axes of the other. 5. The reason that you cannot exceed the speed of light is that the maximum you can project onto another plane is all your temporal velocity (velocity angle of 90 deg) 6. Constant linear acceleration in xy plane is circular motion in the x-y-ct volume, and the inertial force felt is centrifugal about a radius rho =c^2/a. The observed trajectory of a body undergoing constant acceleration in its own reference frame is hyperbolic in the frame of an non-accelerating body, becoming asymptotic to c. Since it is measured as undergoing less and less acceleration, eventually zero as speed increases toward c, the unaccelerated observer will determine the mass to be increasing as m/sqrt(etc)

Wait, are you writing a book on special or general relativity? Sounds like you have a pretty good understanding of special relativity, more than I would have expected, which is why I used simplified arguments that aren't entirely true. As long as your acceleration is constant (meaning no change in direction, acceleration, or gravity) SR works as you described without requiring curved space (space is flat in SR.) An as long as you've already done the differential it won't require calc. You might be interested to know that there is an easier way to think about spacetime than envisioning a 4 space. Since your 3 spacial dimensions are completely interchangeable and the time dimension is always at 90 degrees to all of them, space can be compactified. It gives you a nice 3space on one axis and time on the other, and the speed of light is now 45 degrees instead of 90, anything moving slower than it moves less than that. It's called a Penrose diagram and it's quite useful in SR and really illustrates the concept that the faster you move through space, the slower you have to move through time.

Mine is based on the Brehme diagram. Accidentally, since I developed this independently, not knowing his work. I am an engineer, not a physicist. And in fact I was in touch with Dr. Brehme up to several years ago. One of the problems with all other graphical solutions is that they all assume that the measurement and the event that generated it have to be collocated... mine does not, and as a result, everyone retains the same units of measure and the same orthogonality, they are just rotated through the velocity angle. As a result, I can depict simultaneously as many reference frames observing events as I have colors to keep their axes separate. One of the more interesting is this: Sally departs earth at 0.5c. Sam departs at some greater speed, at right angles to Sally. This actually becomes an exercise in spherical trig, not dissimilar to the navigation triangle. If Sam departs at a speed close to c, he will see, on his x-y plane, what I call the velocity triangle between Sally and the Earth, Earth at the negative of his speed ~c in the x direction, and Sally also ~c but 30 degrees (sin 30 =0.5) inclined WRT earth. I use the radar equation to determine measurements of x and ct to locate an event, such that x=c(tr-tt)/2, where tt is time of transmission and tr time of reception, and the reflection occurred (ct=(tr+tt)/2. It turns out everything I measure is exactly classical and I can't get any other result, and special relativity only comes into play when I somehow receive a measurement that originated in the other reference frame. For example, at tt=1 after Sally left earth, Sam interrogates Sally with a radar pulse, gets the reply at tr=3, and determines that she was at x=2 at t=1, and therefore going at 0.5c. The problem come if he, for example, sent her a radio message asking her what time is it? She would reply, reading her clock, and say "it is 1.732 since I left." If he were to look at her spacecraft with a powerful telescope that could see her wall clock through the cabin window at t=3, he would also see that it did indeed read 1.732 units, so she must be at 0.866 units of distance. The measurement he obtained was in his reference frame, the proper time is the absolute ground truth, and all observers will agree on the proper time t'=sqrt(ct^2-x^2), but will have widely differing ideas on the value of x and ct in their reference frames. In the Sam and Sally case, t=sqrt(2^2-1^2)=1.732, which is the actual time she received his message. The x=1 and ct=2 measurement is real but not the same.... I don't force them to overlap and it simplifies everything But we had better put a hold on this before the lit majors go into connniption fits!

BTW, if they are traveling at 0.5 c and someone takes a Polaroid photo (retro), how long do they have to flap it to speed up the drying?

I think it was a Regulator pendulum clock, like they used to have in railway stations. But a very big face so it can be seen from half a light year away

Now the more I think about the alternate history route, the more I like it. It fits in with a lot of aspects I wanted to throw in the story that I thought wouldn't work out with the setting I originally thought of. I wrote up a brief timeline of "What if the space race didn't end with Apollo missions?" thinking it'd be silly. But I think It works. I even read up on NASA's loss of public interest after Apollo and Werner von Braun's proposed Mars project was rejected by President Nixon in favor of the Space Shuttle. I think I can do something with this without even changing the makeup of most of my story.