Rules:
*You can teleport into and out of it at will
*It has a couple of plug sockets and can connect to internet from the region you teleported in from
*You can take objects and people with you
*As already stated, it is (3m)^3 (3m*3m*3m). The walls are plain plaster with a light in the middle of the ceiling. The pocket dimension is topologically toroidal, so if there weren’t walls and a ceiling/floor (which you can actually destroy) you would loop if you went more than 3m in any direction. Gravity, then, is artificial and can be altered to anywhere from 0 to 2g from a dial on the wall.
Edit: additional specifications
*You can only teleport out to where you teleported in from.
*Time proceeds at the same rate inside the pocket dimension
*There is an eject button for those inside to get out if something happens to you
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
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.
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. )
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.