this post was submitted on 02 Feb 2024
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They wouldn't go faster than terminal velocity if you keep air in the chamber, and even if you remove it, they won't go faster than c. They'll still go pretty fast, though.
I don't think the drag force due to air would work the same in a system with such a high concentration of rocks. It's not like one object falling through undisturbed fluid, which then has to get out of the way, in this case the air would gradually start to move along with the rocks.
This might be better modelled as turbulent flow of a mixed solid/air suspension. But there's no 'edges' to the flow due to the looped dimension, so the viscous forces are pretty uniform... There would still be a terminal velocity, but much much higher than a rock falling through an atmosphere
Also I imagine the rocks would quickly grind themselves to very fine dust, once they pick up a bit of kinetic energy, so then it would behave more like a fluid with uniform density... Could it even end up as laminar flow?
i don't think they would grind themselves to dust, as they're all moving in the same direction therefore their reaktive Velocity compared to each other would be (near) 0, not giving them much energy
It's a really interesting question, I would love it if someone who understands this kind of physics properly would chime in!
By my understanding of Reynolds number etc, the faster they go, the more turbulent the flow, so the rocks would be constantly hitting against each other sideways, and surely grind to dust in the constantly accelerating scenario.
But maybe the infinite (looped) nature of this 'dimension' means that this logic doesn't apply. What would even be the 'characteristic length'? Are we thinking about established flow at the centre of an infinitely wide pipe? Am I wrong to think of constantly accelerating rocks with air in between as a type of fluid flow?
No I think you're right about the fluid dynamics aspect, as we do have an indefinitely long pipe, but in the prompt the walls do still exist, so they'll probably do create some friction. The question is, would the rocks build up some sort of boundary layer of slower flowing particles near the wall, and how much do the boundary layer and "main" center flow mix?
Thinking about it, it isn't even an indefinitely long pipe really, as there are no "new" sections of wall coming up, instead it's constantly passing the same section of wall, and same section of boundary layer...
If someone knows how to simulate this in a physics engine or virtual air tunnel I'd be really interested in that!
I guess I was imagining it with the walls torn out as well, but you're right the op (of this comment chain) said top and bottom broken. If the walls are somehow firmly fixed forever no matter how much force they experience, and are not subject to thermal degradation, then we have a square pipe with 3m sides and infinite length. If the walls break down then it's also infinite diameter.
In terms of modelling it there's a FOSS option openfoam.org but I don't know how to use it and don't have time to mess about with it right now.
Any energy lost to air friction would be transferred into the air. In a closed looped system with constant acceleration a single falling brick would eventually stir the air up into a light-speed wind.
Keeping the air was a mistake but I don't see why it wouldn't be able to go faster than c.
According to special relativity, the energy of an object with rest mass m and speed v is given by γmc2, where γ is the Lorentz factor defined above^1. [...] The γ factor approaches infinity as v approaches c, and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass[...] This is experimentally established in many tests of relativistic energy and momentum.
More generally, it is impossible for signals or energy to travel faster than c. One argument for this follows from the counter-intuitive implication of special relativity known as the relativity of simultaneity. If the spatial distance between two events A and B is greater than the time interval between them multiplied by c then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous. As a result, if something were travelling faster than c relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated. In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded, and would lead to paradoxes such as the tachyonic antitelephone.
More info here
1 γ = (1 − v2/c2)−1/2
What about quantum entanglement sending a signal faster than light?
(I’m just some schmo who watched an extra credit history series on quantum computing, so there’s every chance in the world that I don’t have it right. )
While the entanglement "signal" is near instantaneous, for various reasons no meaningful information can be deciphered faster than C.
Assuming our quantum theory, while not complete, is not wrong. We will not be able to engineer our way around this limit. A lot of funky shit becomes possible if you can break causality even with "just" information.
I thought the reason quantum theory is so controversial is because it does break causality. Like, currently we can’t decipher it, but is that supposed to be a permanent state- that quantum information is indecipherable until it would no longer transmit information faster than light?
You can transmit something, but it has a noise added to it. To decode it, you need to send the readings to the other end, via normal means. Basically, the receiver can tell, in hindsight, that a message was sent, but only once its other half has been received via normal means. The best you can do is get a timestamp of when the message was sent, as well as a message channel that is impossible to intercept.
The problem comes when QM meets relativity. With instant communication, you can send information into its own past. E.g. A and B are 2 planets. C is a ship, passing planet B at relativistic speeds. Planet A sends a message to B, over the FTL link. B then sends it to C, over a normal link. C, finally sends it back to A over FTL. Due to the 'tilt' of C's light cone, the "now" of A-C is behind the "now" of A-B. This allows for paradoxical situations. The maths of Relativity implies that you can't form a closed time loop like this. Such behaviours tend to imply some deeper rule, even if we haven't found its cause yet.
Quantum mechanics has a lot of strangeness. It also seems to play fast, but not loose with causality. E.g. objects can move backwards in time, but still obey causality. Others can be smeared over time space, but still collapse to a causality obeying state. Etc
I so wish we could experiment with this to see where it actually breaks down
That's one of the things we are looking for with particle accelerators, like CERN.
Quantum Mechanics is ridiculously accurate, within its domain. However, it doesn't predict, or allow for General Relativity.
GM is ridiculously accurate, within its domain, but doesn't allow for quantum mechanics.
Therefore we know both must be wrong (or at least incomplete).
Unfortunately the overlap is when gravitational forces become significant on quantum scales. There's 4 ways to study this.
We can pack a ridiculous amount of energy into a tiny space, in a controlled manner. This is the best method. We also can't do it.
We can pack a ridiculous amount of energy into a tiny space, in an uncontrolled, brute force manner. We can then hope to get lucky, or do it enough to beat the odds. This is what particle accelerators like CERN do. We can't control what hits when accurately, but we can do enough collisions that 1 in a trillion is useful, then sift through the data looking for it.
We can use tricks to 'stretch' the quantum realm. This method is limited, but interesting. Gravity wave detectors effectively do this. They can use a laser to create an effect quantum object measured in meters or more.
We can look for places where quantum gravity is dominant, and see what happens. This is what things like the web space telescope are good for. We can look closely at black holes, and neutron stars, and see what they do to space time. Unfortunately, we are also stuck with whatever the universe happens to have done.
In short, the problem is being chipped at. It's painfully slow, and buried in ever more complex maths, but it's being done. I would love to see this "solved" in my lifetime. It's unlikely, but could happen.
Quantum theory is only "controversial" to the general public, mainly because we haven't found a way to explain in simple terms things like superposition, entanglement, quantum tunneling. Quantum theory is spectacularly successful, though incomplete.
Even the "simple" stuff like the uncertainty principle takes a detailed understanding to properly grasp why there are pairs of properties that are inherently linked, and that information about one dictates how much you can know about the other. e.g. position/momentum and energy/time.
Well there’s my problem- that stuff does seem easy, so I’m probably skipping the work to understand it somewhere.
I might be wrong, but iirc quantum theory just straight up doesn't give a shit about causality. Where everything else requires the cause to be observable before effect (something travelling faster than light would result in effect being potentially observed before cause), quantum theory says, "why does the universe give a fuck whether or not we can see it? If it happened, it happened, regardless of whether or not we observed cause before or after effect."
Basically as far as we can tell there there is no information traveling at FTL speed so it just works? All information that is traveling is just as fast as c or slower.
"Certain phenomena in quantum mechanics, such as quantum entanglement, might give the superficial impression of allowing communication of information faster than light. According to the no-communication theorem these phenomena do not allow true communication; they only let two observers in different locations see the same system simultaneously, without any way of controlling what either sees." link
"In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer." link
Thank you for this, by the way. I was thinking of the two entangled electrons as communicating with each other, rather than people communicating with each other through the entangled electrons, which I think makes a difference, because it doesn’t rely on interpretation, but obviously we can’t measure how or if electrons “communicate.” Is it correct that one of the limitations is in interpretation or am I reading this wrong?
Well, yes. We don't know if the measurement we take is the result of a wave form collapse (we caused it) or the result of someone else having measured it, which would giving us the oposite value that they measured. We can't tell if someone "sent" information or if it was the random result and we have no way to chose what value we (or the other end) gets when we collapse it.
This isn't easy to explain over text so I'd recommend watching this video, specifically chapter "How to exploit?" as the visuals make it easier to understand.
Here is an alternative Piped link(s):
this video
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I'm open-source; check me out at GitHub.
Hmmmmmmmm, now, how much energy does the box have to generate that constant 2g of acceleration? In this hypothetical the box appears to have an infinite amount of energy to generate that force though...
Yes it seems to have infinite energy but the throughput is limited to 2g of acceleration, unless you give it infinite time as well it will not reach c, though it would approach it.
Doing some calculation the final speed of 33kg, falling in 2g, for 70 years, without friction is "only" 99.77% the speed of light.
Edit: Forgot to convert the 0.9977c to percent.
Velocity changes how time works. The faster you go, the slower it happens.