I think it is much more expensive to accept Visa payments than to accept Bitcoin payments.

Knowing the weather of tomorrow already is a great advantage. Especially if that weather might include a hurricane.

You don't need any mathematical calculations to see that the two statements

• The laws of physics don't depend on the inertial reference frame
• There's an upper limit to the possible velocities

imply that this upper limit must be the same in every reference frame, and thus anything going at that speed does so in every reference frame. That's elementary logic.

Photons can send states, you can send binary ascii this way. therefore send classical information foreward, very easy to do and then use that classical information to send backwards through the limited communication medium.

Sorry, but it doesn't work that way. You have to send the classical information from the sender to the receiver (because it's at the sender where it is generated). That classical information also isn't "extra", by itself it is just as random as the measurement results on the quantum system. Only if you combine both, you get transmission of information.

There are several proposals (and calculations) about entangling (microscopic, but still large compared to typical quantum systems) cantilevers, but I'm currently not aware of an experiment which already did this (and didn't find any with a quick Google Scholar search).

But the encryption key is completely random.

And with C60 molecules.

Also, ions have been entangled.

If you look at the paper closely, you'll see that it derives that under the given assumptions you get either SR (Lorentz transformation) or Newtonian space and time (Galilei transformations). The fact that he terms Galilei symmetry as degenerate Lorentz symmetry (which is mathematically true) doesn't change the fact that this argument doesn't decide between the two options. It only excludes that there's a third option.

Oops, I just notice I mixed up the terminology: It's of course not a Bell measurement (although a Bell measurement is involved in the teleportation/"entanglement swapping" step), but the measurement of a Bell inequality violation.

Can we use this trick to create closed time loops?

No.

B sends message to A using ordinary speed-of-light (or even speed-of-sound) communications.

OK, no problem in this step. ;-)

A sends the message back in time to B, via entangled photons, since B can measure his photon before A's photon ever existed.

No. You cannot send a message just using entangled photons. You always have to send classical information along in order to communicate. So to use entanglement for sending information into the past, you'll first have to solve the problem of sending classical information into the past.

Think of the entangled photons as being an encryption key. It doesn't help you if you get the encryption key, as long as you don't also get the encrypted message.

No, it's not a measurement error. It's exactly what you'd expect from such a setup, without assuming entanglement over time. However, if they had described this experiment as what it actually is, a standard Bell measurement where one of the photons was quantum-teleported before measuring it, but after having measured the other photon, I'm sure it would not have generated much interest.

Actually de Broglie-Bohms unobservable particle trajectories are the exact equivalent to the epicycles: Additional complications, introduced to save certain assumptions on the world (epicycles: only circular motion, with the earth in the center; Bohm trajectories: movement of well-localized particles in space).

Also, de Broglie-Bohm is incompatible with special relativity.

Lorentz transformations only cover special relativity. In general relativity, you can indeed have the distance between two points grow faster than light. Of course not if the points are at the same place.

Actually, there's a very simple interpretation of this experiment which doesn't need entanglement over time at all:

First, you create a normal entangled pair (no over-time entanglement involved).

Then, you measure one of the photons, breaking entanglement. The other particle now has the corresponding state. If we were to measure it immediately, we'd find the correlations with the first photon we use to detect entanglement that was present before the first measurement.

But we don't immediately measure it, but we use a second pair of entangled photons to quantum-teleport it. Note that there's no entanglement swapping going on here, because there's no longer entanglement in the first photon. It's just normal quantum teleportation (well, actually entanglement swapping is also just quantum teleportation of an entangled particle). Of course the teleported photon has the same state as the non-teleported.

Now the teleported photon is measured. Of course we find the correlations with the first-measured photon. That doesn't mean this photon was ever entangled with the original one.

That code isn't bug-free. It's just insufficiently tested.