The radiation part is a really interesting one, pretty much valuable information for realism.

FWIW, I seem to recall from an engineering course 40+ years ago that the leading edge of an airfoil going Mach 3+ (and into hypersonic speeds) will get so warm that it may glow, depending on the material used. (That problem is one of many that the hypersonic aircraft development efforts addresses).

@SevenSidedDie The post you linked to is about non-relativistic speeds, there are some notes about possibilities at relativistic speeds... But I guess everyone dies from air turning to plasma and bursts of gamma rays in the relativistic case.

Actually, if you're moving at the speed of light towards an observer, you're invisible to them. It's not that light doesn't reflect from you or that you don't glow, but THEY can't see you because your punch arrives at the same time as the photons reflected off your fist. You could also take into account the delay in the signal from the eyes reaching the brain, and use that to calculate your necessary speed (lower than c) for arriving after the photons have reached the eye but before the signal has reached the brain, making you "effectively" invisible to your target (at some finite distances)

@Blueriver Yep. I discarded a tangent about red/blue-shifting and what things theoretically might look like when moving greater than c because it’s very theoretical, because it’s not my strong point, because in context the question is about mostly lateral movement relative to a viewer, and because thatwhole section is already a large tangent itself. :)

@ReginaldBlue In the last paragraph. :)

@ReginaldBlue Indeed, it seems like everyone subject to an action by this PC would be eligible to advance to first base according to 6.08(b), which would be quite detrimental to the party if they are playing baseball.

Might want to say "faster than the speed of light in air" to make it clear we're still in the realm of known physics, re: Cherenkov radiation. (The same effect that makes astronauts see a flash when a cosmic ray goes through their eyeball.)

@PeterCordes I’m fuzzy enough on the details, and it’s already quite far out on a tangent, that I thought I’d leave precision as an exercise for the reader.

It's not that complicated. Light moves slower on average through any non-vacuum because of interaction with atoms of the material. e.g. the index of refraction of glass is about 1.3 to 1.5, so e.g. light goes at c / 1.5 through fiber-optic cables. This is how you can get a sonic-boom type effect without ever going faster than c (which is an absolute hard limit).

@PeterCordes It’s more the implications than the mechanics that I’m fuzzy on. But this isn’t physics.se, so I’m touching the physics only as much as it’s needed for the local RPG context and idiom.

I'd still recommend saying "in air" so it's clear to everyone you're not talking about exceeding c. It's 2 words that will avoid giving anyone the wrong idea if they're not totally clear on Cerenkov radiation. I know you don't need to explain the physics, but that would add a lot to the quality / clarity of the summary, IMO. Or just take out the whole thing; does the 5e multiverse even obey special relativity? Is the speed of light finite in 5e?

If monitors display at 60 Hz (or 120 Hz), it's often because that is a good enough frequency for human eyes: so when you're making an action in less than 1/60s, it's practically an invisible action. Think of magicians playing card tricks. Or think about seeing a bullet shot from a gun.

@Cœur That doesn’t lead to invisibility, it leads the brain to switch from processing them as still images to processing them as motion. The brain/eye doesn’t have an upper speed limit on detecting motion because all it needs are sufficient photons, and speed doesn’t change how many photons a moving object reflects to the eye because light is so much faster. As the links in the post explain, to be undetected you need fewer photons and/or much lower contrast with the background.

@PeterCordes Faster than light is on the table because magic. Whether D&D obeys relativity isn’t relevant because that section is about if there’s a real-world speed. At the end I get much less precise and realistic because I’m just pointing out that going to extreme speeds probably doesn’t help. The point isn’t a precise physics presentation, it’s making a point about extremes still not helping… and to throw some interesting links at the non-physicists. The physics aren’t the text’s audience. :)

@Cœur Persistence of vision lets you "see" extremely short pulses of light, much shorter than 1/120th of a second. e.g. a camera flash or strobe light stays on for much less time than that. You're mixing up smooth motion with being able to notice a blur at all.

@SevenSidedDie Ok, that's a fair point that exceeding c is possible because of magic. Hopefully people who don't already know about Cerenkov radiation will think you're talking about magic and not get a wrong idea stuck in their head that faster-than-c is a known thing in our world. That's what I was worried about.

"There is no such speed in reality either." I strongly disagree with that. As I mention in my answer, the question being asked here is better phrased as "How high must a character's movement speed roughly be, to be quicker than the [human] eye?"

The character in OP's video isn't moving at the speed of light. He's moving so quickly that his [super] human opponents cannot observe him doing so. He's not moving at light speed. He's just moving faster than his opponents' eyes and brain can perceive. This is a biology question, not a physics question.

A quick Google search indicates that the limit of the human eye is about 1 millisecond (for not seeing a blur at all). That answers the biological part: if you can complete your entire movement in under a millisecond, you can't be seen. There is also a physics question: How fast is it possible to go without leaving a trail in the air?

I can't answer that question directly, but I can calculate that the speed needed to move 5 feet (one D&D square) in one millisecond is 3400 mph - far more than the speed of sound.