I know otters blow bubbles into their fur to isolate themselves, but this also makes them extra buoyant. For the babies this is quite handy (less drowning etc) but for adults idk if it really helps.
It really depends on the fur texture probably, seals are also coated in fur but streamlined to perfection.
The required temperature depends on the mass of the particles you're considering. You could say photons are always relativistic, so even the photon gas that is the cosmic microwave background is relativistic at 2.7 K. But you're presumably more interested in massive particles.
If you apply the kinetic theory of gases to hydrogen, you'll find that the average kinetic energy will reach relativistic levels (taken to be when it becomes comparable to the rest mass energy) around 10^12^ K. For the free electrons (since we'll be dealing with plasmas at any sort of relativistic temperatures), this temperature is around 10^9^ K due to the smaller mass of the electron. These temperatures are reached at the cores of newly-formed neutron stars (~10^12^ K) [1] and the accretion disks of stellar-mass black holes (~10^9^ K) [2], but not at the cores of typical stars. Regarding time dilation, an individual particle's clock would tick slower from the perspective of an observer in the center-of-mass frame of the relativistic gas, but I don't think this would have any noticeable effect on any of the bulk properties of the gas (except for the decay of any unstable particles). Length contraction would probably affect collision cross-sections, though I haven't done any calculations for this to say anything specific. One important effect would be the fact that the distribution of speeds would follow a Maxwell–Jüttner distribution instead of a Maxwell-Boltzmann distribution, and that collisions between particles could be energetic enough to create particle-antiparticle pairs. This would affect things like the number of particles in the gas, the relationship between temperature and pressure, the specific heat of the gas, etc.
You mention the early history of the Universe in your other comment. You can look through this table on Wikipedia to see the temperature range during each of the epochs of the early Universe, as well as a description of what happened. The temperatures become non-relativistic for electrons at some point during the photon epoch.
To wit, a sufficiently dense concentration of heat, light, or radiation could produce an event horizon similar to that of a black hole, which definitely would count as a noticeable relativistic effect.
Based on one of your comments clarifying what you're wondering, I don't know that this helps you in what you're looking for, but the "OMG particle" came to my mind. It was traveling at such high energy when it hit our atmosphere that...
If the proton originated from a distance of 1.5 billion light years, it would take approximately 1.71 days in the reference frame of the proton to travel that distance.
...
The energy of the particle was some 40 million times that of the highest-energy protons that have been produced in any terrestrial particle accelerator.
...
In the center-of-mass frame of reference (which moved at almost the speed of light in our frame of reference), the products of the collision [with a particle in our atmosphere ] would therefore have had around 2900 TeV of energy, enough to transform the nucleus into many particles, moving apart at almost the speed of light even in this center-of-mass frame of reference. As with other cosmic rays, this generated a cascade of relativistic particles as the particles interacted with other nuclei.
I don't know if that cascade is the same as the Cherenkov radiation it produced, but that radiation is how they detected this particle, and it's interesting a.f.
[It is] emitted when a charged particle (such as an electron) passes through a dielectric medium (such as distilled water) at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium. ... Its cause is similar to the cause of a sonic boom....
I.e., (layman's understanding here) the particle, having a dual particle- and wave-like nature, is propagating through the vacuum of space "close" to the max speed of propagation of causality itself. As it encounters a medium, our atmosphere, it is going faster than causality itself can possibly propagate through that medium. But the energy is still there and isn't going to just vanish, so it has to split out into multiple particles that would, with their fraction of the original energy, then be able to propagate through the medium. Or something amazing like that?
Edit: My layman's understanding of Cherenkov radiation requires a bigger disclaimer, like a strike-through. :)
I have never heard that causality slows down in a medium. I understand the use of "speed of causality" to refer to the speed of light in a vacuum, and while I'm aware that light slows down in air, water, etc I'm not sure it has ever been shown that causality itself slows down. My understanding is that also light slows down just because it's captured and re-emitted by other particles. Though I would be happy to learn something new if my understanding is wrong.
That said, the OMG particle stuff was very interesting, thank you for sharing.
According to GTR, energy density bends spacetime, yes you can have an imaginative sun-sized object moving at c, bending spacetime, bc it is made of photons.
There are places in the universe that are so hot that weird things start to happen. Like the core of Jupiter could be a giant hard hydrogen crystal or in the center of suns where lighter chemicals fuse into heavier ones. Or my favorite, the temperature of the early universe which may have contributed to hyper inflation which would constitute what you refer to as "relativistic effects".
In terms of noticing them we have detected the cosmic microwave background radiation.
There's also a Planck temperature, which is the highest we can currently predict in the Standard Model - that's the temperature at which thermal radiation is at the highest possible energy
First a caveat: An object with mass can’t move at the speed of light, but it could move at speeds arbitrarily close to that.
The most successful model of gravity isGeneral Relativity, which treats gravity as a curvature of 4-dimensional space time. Gravity’s influence travels at the speed of light. There’s a classic thought experiment that sort of answers your question: what would happen if the sun was teleported away? The answer is the earth would continue to orbit around the spot the sun was for 8 minutes, and we would continue to see sunlight for that same amount of time since that’s how long it takes light to travel that distance. Then after 8 minutes the sun would disappear and the first “lack of gravity” would reach us, and things would be bad for earth :(
The fact that gravity travels at the speed of light actually leads to an interesting phenomenon: Gravitational waves If a massive object rapidly accelerates (or decelerates), for example a star sized mass moving quickly and then coming to an abrupt stop, it will emit a ripple in space time called a gravitational wave that will travel outward at the speed of light.
It was big news about a decade ago when gravitational waves were first detected by LIGO, a series of large interferometers that look for expansion/contraction in spacetime. Their first detection was the collision of 2 black holes; as the black holes spiral around each other and eventually merge, they emit oscillating waves with increasing frequency. They made a cool video showing how the frequency increases by converting it to sound.
Since then LIGO and VIRGO (similar European collaboration) have detected multiple gravitational waves from the collision of black holes and neutron stars. So not only are gravitational waves a neat validation of general relativity, they’re actually being used to do astronomy.
Thank you so much for this excellent write-up! And for providing interesting reading material, too.
It's amazing to me (an uneducated sub-layman) that things like dark matter and dark energy aren't well-understood, but we can nonetheless still do this kind of science and detect black holes colliding through ripples in spacetime 🤯 But then again, it's amazing to me that rivers never run out of water (joking... sort of...).
That LIGO sound clip is for sure going into the intro of a metal song.
Hey now. It's all about perspective. If you think about it in terms of geological history or the history of the universe, the discovery pretty much just happened.
Hah tell me about it. The 2017 neutron star merger happened while I was writing a proposal for an experiment where the physics was sort of related. So of course I completely reframed the proposal around that event, and it got funded! And that was just a few years ago, right?
Man I really need to publish the results of that project…
Using your choice of words it would be "stable/static". Effects of gravity moves at the speed of light. Perhaps a better example would be Earth orbiting the Sun.
The Earth is 8 light minutes away from the Sun. Meaning, the sunlight we see on Earth at this exact second left the Sun about 8 minutes ago. If we wave a magic wand and make the Sun blink out of existence in a fraction of a second, the Earth would continue to orbit the, now non-existent, Sun for the next 8 minutes. After 8 minutes the Earth would stop its circular orbit and head straight out of the solar system at what ever direction it was traveling at the end of the 8 minutes.
That's amazing, thank you! A ghostly remnant of gravity still exerting 8-ish minutes of influence on earth (in the event of the sun's instantaneous disappearance) is something I never heard or thought about before, but it makes sense. It's hard to visualise it though. Like the earth is a marble circling a drain after plug has been pulled and the water is all but gone. Then the minute it is gone, the marble just keeps going in a straight line 👀
That’s amazing, thank you! A ghostly remnant of gravity still exerting 8-ish minutes of influence on earth (in the event of the sun’s instantaneous disappearance) is something I never heard or thought about before, but it makes sense.
Also for us standing on the sun facing side of Earth when the magic wand was waved would still see the sun shining in the sky for 8 minutes because that light had already left the sun before it blinked out of existence. We on Earth would experience the loss of the Sun's gravitational influence on the planet and the light of the sun at the same moment as both light and gravity travel at the speed of light.
I think it's easier if you imagine space/time like a flat plane that dips depending on how much mass the central object (like the sun for example) has. Earth circles around that dip much like your drain plug analogy. If the sun disappears, it still takes time for that dip to rise back up to a flat surface. That's the speed of gravity.
As soon as space/time begins to flatten beneath the earth, its momentum begins to turn into a straight line, rather than an orbit.
Gravity is "emitted" by an object with mass. So to use what might be a better example, if a massive object popped into existence at a particular place, it would start "emitting" gravity waves from that time. Another object one light-minute away would start feeling its gravity about a minute after it appeared.
First, no object could be accelerated to that speed. Relativistic effects make that impossible. However, gravity waves move at the speed of light so there is some delay in gravitational effects. I'm not a physicist, but I'm pretty sure that if your sun-sized object shot through the solar system at 99.9999% the speed of light, and passed between the Earth and the Sun, it would take about 4 minutes for the object's gravity to be felt by either the Earth or the Sun.
Wow, that's an incredible thought. So "ziiiiiiip" there goes the uberobject. 4 minutes later, all of the budgies on earth are knocked off their perches.
Would that uberobject heat up the earth as it passes? Not sure how that would work, but it seems like a good question 🤣
Again, not a physicist, so here's a bunch of words that sum up to "maybe."
With the object moving so fast I'm not sure we'd notice anything much. We would only be in it's gravitational field for a very short time, but it might be long enough to change Earth's orbit, someone with better math skills will need to field that one.
As for heating the Earth, again that's a maybe. Gravity is stronger the closer you are to the center of mass. So the near side of the Earth will feel the pull of the object much more strongly than the further side. That will make the Earth want to stretch towards the object as the near side falls towards the object faster than the far side. It would be very slight, think egg-shaped but not to a noticeable degree, but it could be bad enough.
This is called a tidal effect and would generate some heat if we're in the gravity well of the object for long enough. It would also cause fault lines to pop all over the globe. The object would shoot by very quickly though at 99.9999c so we might be spared the worst of the effects. Again, someone with better math skills could give a more accurate answer.
FYI tidal effects are why the moons of the gas giants aren't frozen ice balls. The constant flexing as they orbit their planet generates tremendous amounts of heat.
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.
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