No matter what basis they measure in, the receiver will observe results consistent with the ion being in whatever state it was already in before the senders even did anything. This is a result of the linearity of quantum mechanics. If the overall wavefunction is a sum of two nearly-orthogonal vectors, then the evolved wavefunction is the sum of each vector evolved separately, and the terms in this sum will also be nearly-orthogonal. In equations:
If wasn't there, then would still evolve to and see the exact same outcomes. To get communication, there would have to be significant amplitudes for the universe's state to spontaneously shift from being in one world to the other. (i.e. even if world 1 is initially the only world, it still has some amplitude to end up in world 2). This is not realistic for the physics of macroscopic objects. We don't see, either theoretically or experimentally, large amplitudes for a dead cat to turn into a live one, etc, even if the initial decision to kill the cat or not was made by measuring polarization of a single photon.
EDIT: Also, it is a well known fact in QM that "one does not simply measure whether a system is an eigenstate or a superposition". If you measure a spin of up for an electron, you do not know whether it was actually spinning up, or it was spinning left and you happened to measure the "up" component of the left spin.
But if you're just concerned about energy conservation, such a complicated fix is not needed anyways: There are many systems that have multiple quantum states with identical energy, momentum, angular momentum, etc, yet are still orthogonal (i.e. perfectly distinguishable by measurement).
So the real reason it doesn't work is linearity, not energy-conservation or anything like that.
No, I'm pretty sure publishing sightings of law enforcement is legal in the US. Some traffic radio stations report on where police are using radar guns for example, and this is fully legal. Indeed, considering that mapping ICE sightings could be of academic/intellectual interest (and that it is actually perfectly reasonable for law-abiding US citizens to want to limit their time spent in close proximity to ICE agents) this is far more centrally "helping people get away with doing illegal things" (speeding) than robertzk's project.
I didn't learn anything from this. It looks like there are things to learn here, but you seem to have deliberately chosen a writing style that does not permit it.
That is pretty annoying.
I think its spread through rationalist-land originated at this post by Alice Maz: https://alicemaz.substack.com/p/you-can-just-do-stuff
Though by following the trail of links from Haiku's comment one can find people saying similar things farther in the past.
Overall a nice insightful post, but recorded music is like upwards of a century old, so I don't think the timing works out. I was in a dancing club at one point and we used recorded music and I think that requiring us to use live music would have prevented the club from existing.
Yeah, there's definitely a few relevant things here:
- Representation theory is relevant (in particular representations of cyclic groups, which is basically the circle arithmetic you're talking about). Representation theory gives you matrices that use complex numbers, even for discrete finite groups. So number theory isn't the only place where complex numbers poke their nose into discrete business.
- There's apparently a whole theory of Dirichlet series and Dirichlet convolution which is analogous to Fourier series and Fourier convolution. Complex numbers are the nicest way to do Fourier series, so it makes sense that they're also the nicest way to do Dirichlet stuff.
- I guess just in general complex numbers are the best field and a lot of the math of number theory is turning things into vector spaces and linear operators and doing linear algebra on them. And if you're picking a field for your vector space, what better choice than ?
- A Dirichlet series is a function of a variable , and complex functions can have complex analysis done on them, and complex analysis is uniquely nice, so why not make a complex variable?
The post author seems to already know a lot of math, so I guess they're looking for a deeper kind of answer.
1Oh, cool, that's great.
I was referring to the older style of sailboat design, like this one, where the sails are all controlled by a bunch of ropes. Single rotating airfoil sounds a lot simpler. One advantage of an airfoil over a kite is that it would allow the ship to gain some propulsion, even when travelling at an angle upwind, right?
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Obstacles to this idea:
- Hydrodynamic drag on many smaller hulls is larger than on one big one.
- Ports cost money. It seems hard to make a port which unloads individual 1-container vessels faster than a conventional port can pull containers off a large vessel using cranes. As for just making more numerous & smaller ports, it probably ends up being much more expensive.
- It's an existing technology for large ships to fly kites to save fuel when the weather is favourable and the wind is blowing in the right direction. I think most ships still don't do this, so I'm not sure if it's currently economical, but it at least demonstrates that making a ton of tiny sailboats is not the only way to take advantage of the wind. Sailboats have a lot of moving parts, and maintenance on so many of them would be a nightmare.
- Even though containers have taken over a lot of things, not all loads are containers even today, so we still need large ships for fuels and bulk cargo.
I'd be eager to hear about anything similar to this which is already discussed somewhere, if you know of anything.
I wrote a post in 2023 about somewhat similar ideas: https://www.lesswrong.com/posts/uDXRxF9tGqGX5bGT4/logical-share-splitting The market mechanism there is based on the formula P(A)+P(B)=P(A∧B)+P(A∨B) from probability theory.
In that post, shares aren't expected to have continuous-valued payoffs, but merely continuous-valued prices representing binary payoffs with some chance of happening. So that's a relevant difference that means the interpretation of is not quite the same (in particular, it doesn't involve a max function, since there are no continuous values to take a max of), though there's still a sense in which it's as good as having your choice between and .
You mean linearity equation?
If the ion is isolated, that means you take a tensor product of its state with the state of the environment. If u,v are orthogonal, then a⊗u and a⊗v are still orthogonal.
Why does your "repeated measurement" method not also work to use entangled qubits to send signals faster than light? (Since measuring one qubit also collapses the state of the other.)
Or, maybe just tell me the density matrix for the ion that you expect the reciever to see if the sender sends a 0, and also the density matrix for if they send a 1?