It's an interesting question, but a bit vague. Even at room temperature, relatively needs to be considered for the motion of electrons.
You're probably thinking about bigger stuff though. The short answer is that temperature is unbounded so yes, there is a temp at which it is significant for the motion of all particles. I think inside of stars this can happen, but my knowledge jn that area is pretty limited.
Veritassium has a recent video about some of this that you may find interesting if you haven't already seen it.
Temperature is a measure of kinetic energy at the molecular/atomic level. That said, the gasses falling into a black hole would likely reach such hypothetical temperatures as they near the event horizon.
Certainly! You can see discrete emission lines from the ionized air molecules, which only occurs because of quantum physics. I realize that’s not what you’re asking though.
I did a quick calculation and for a plasma torch (~27000 Kelvin) and assuming air molecules, the average velocity of the plasma ions would only be like 6000 m/s. That’s 0.001% the speed of light, so you aren’t going to see any relativistic effects.
Gravity at the event horizon is inversely related to the mass of the black hole. So for a supermassive black hole, gravity at the event horizon can be weak. But you still can't escape because it's too large.
Imagine light trying to escape the Earth's gravity. Its path is slightly deviated by the Earth, then it gets far enough away that the Earth has little further effect.
Now suppose at that distance, it still experienced the same gravity. So the trajectory of light is deviated a little more. It keeps moving farther away but gravity barely changes, even at huge distances. Eventually all those little deviations add up and it's going back where it came from. Light can't escape. It's a black hole.
I see what you mean... I think. Let's see if I can be more specific:
Considering that time slows down for particles moving near lightspeed, I was trying to visualize the universe immediately after the Big Bang, if it being so hot - or energetic, I think I mean to say - made time slow down in the entire, still tiny universe. And what effect this may have possibly had in the outcome we observe today.
Surely time had also only just sprung into being so shortly after the big bang? If "everything" was moving near C, there was no "other" time to be relative to?
Yeah... what are the dynamics of such an extreme moment? How does a moment like that unfold from the perspective of a particle that was there?
Does time "start slow" before reaching the "stable rhythm" we experience today?
The fact that I felt compelled to use quotes twice in the previous sentence betrays the fact that I don't even know how to ask what I'm trying to ask.
I think these are all excellent questions, but to my limited knowledge they haven't been answered yet. I think these are all active areas of research in cosmology.
They are fun to wonder about though. If you have a deep interest maybe check out your library or bookstore. Once in a while scientists in these fields will write a book about their work in these areas.
I suspect you may be misunderstanding time dilation. From the perspective of a particle, time always passes by at 1 second per second. If you yourself were to travel at relativistic speeds (relative to, say, Earth) your perspective of time wouldn't change at all. However, observers on Earth would see your "clock" to tick slower. That is, anything you do would progress more slowly from their perspective. In the very early Universe, a given particle would see most other particles moving at relativistic speeds, and so would see their "clocks" tick slower. These sorts of relativistic effects would influence interactions between particles during collisions, decay rates, etc, but are all things we know how to take into account in our models of the early Universe.
The way I understand it, (which is virtually not at all really!) there is no overall universal time or background clock like a force field of time or "stable rhythm" that everything experiences. But every observer experiences its own time, relative to whatever point of reference is used.
This is where my meager brain fully melts down.....
If everything is moving through spacetime, the faster through space, relative to C, the slower you travel through time, the slower through space, the faster through time.
So if every particle is moving away from each other equally at C, from each ones perspective it's own time is slowed to 0, so now everything is eternally rushing away from everything else with no time passing.
Now my reasoning and vocabulary fail completely tbh,
Veritassium ignores a bunch of stuff in that video and hand-waves it away.
I only hear about his videos from other, better channels that correct his mistakes. He's dead to me ever since that "faster than light" electricity video where he didn't once use the word induction and made it sound super mystical. Fuck that guy with a thousand meters of wire.
Here's the video I saw on it. Anyone watching the Veritassium video should watch this after:
Or better yet, find a different video on the relativistic movement of electrons and electron holes in wires, and how it causes magnetism. I don't have one handy.
It's a really bad sign when half of his videos need corrections by other channels. Sure, you could say they're just riding on his popularity, but the fact that he needs corrections is the problem.
The video you linked summarizes the intent and benefit of Veritasium videos at about the 2:25 mark, stating that they are for a general audience. I agree that Veritasium isn't perfect, and doesn't provide complete depth, but they do a good job of creating interest in topics. So they accomplish their goal.
Additionally, the video you linked is wrong about the principles it discusses. The drift and diffusion velocity (group velocity) of electrons and holes is small compared to the speed of light. The relativistic effects discussed are caused by the phase velocity, which will be closer to the speed of light in the medium for even small currents.
Edit: originally, I incorrectly worded the last sentence which implied that the electrons and holes had a phase velocity equal to the speed of light. I hope the statement is more clear now, but I'm happy to provide additional clarification if necessary.