What you're describing has been desired by many (including Einstein). However, John Bell more or less proved it impossible[0] in a landmark, sweepingly general result. He would have won a Nobel for it if he had lived long enough.

On the other hand, if you are willing to accept superluminal messages and also unobservable mechanics, there is always the pilot wave interpretation[1]. The fluid analogy is disappointing to see go but pilot wave theory lives on.

[1]https://en.wikipedia.org/wiki/Pilot_wave_theory [0]https://en.wikipedia.org/wiki/Bell%27s_theorem

Edit: fixed order of references.

Thanks for the link to Bell's Theorem (I recalled there being a result like that, but didn't remember the details of it). If the hidden variables really are in a higher dimensional space, then maybe superluminal communication (in our observable dimensions of space) isn't off the table either? But that comes with its own can of worms that would have to be taken care of as well.

If you give me both sides of a superluminal telephone I can use it along with special relativity to set up a time paradox. If I only have one end of the phone, or if I can't have a phone at all (not all apparently superluminal interactions allow signaling) then it's considered an undesirable trait but not paradoxical.

By paradox, do you mean something like reverting order of events in some inertial frames?

The order of events is fair game to reverse so long as they are far enough away from each other that one couldn't have caused the other. The order of pairs of events like that reverse all the time. It's only a time paradox if you can actually do something paradoxical, like killing your grandfather.

> if you can actually do something paradoxical, like killing your grandfather. ... before certain crucial event in his life, you mean, I assume.

How exactly does having a superluminal telephone imply I could change history? Changing history is the paradoxical part - don't assume it can happen.

Here is an article that goes in to the detail[0]. In so many words, you can use the superluminal telephone to transmit information to your own past. In essence, there is a certain amount of freedom in the simultaneity of events that is well-known to exist (having been experimentally verified). You can abuse it to create time paradoxes if and only if you can send messages faster than light - without FTL it is a curiosity that seems strange to some but otherwise doesn't upset anything.

[0] http://www.theculture.org/rich/sharpblue/archives/000089.htm...

Thanks for the link. See also the comments below the essay which give some valid criticisms.

> On the other hand, if you are willing to accept superluminal messages and also unobservable mechanics, there is always the pilot wave interpretation[1]

All quantum interpretations have superluminal characteristics, but that's not the same as superluminal messaging/signaling.

That's true, I should have said "explicitly superluminal mechanics."

FYI your references are swapped.

I hold out some hope that the Holographic Universe principle will prove true and tractable, and in the holographic isomorphism there will still be some profound sense in which two entangled photons still somehow locally share a quantum qubit prior to disentanglement.

Don't be fooled by "local" in there; all non-locality results in 4D spacetime would remain true, because of course they have to. It would be "local" in an isomorphism that will be extraordinarily counterintuitive and probably never really be something anyone can "visualize".

But, if this did pan out, there would be a reasonable sense in which the Copenhagen interpretation would have something physics-al about it (as in, grounded in physics, not necessarily "physical" in the traditional sense), where it wasn't in fact "action at a distance". I for one have no problem with the universe creating probability distributions and then randomly picking a result, as some seem to. (The Universe May Do As It Damned Well Pleases. It's true that a good sense of aesthetics has given us a lot of power up to this point, but "I don't think that's very aesthetic" is not a very strong argument. I'll give it more than 0, but not much.)

At least locally, there are no hidden variables (e.g., in higher dimensional space). You might have a look at Bell's work on hidden-variable theory: https://en.wikipedia.org/wiki/Hidden-variable_theory#Bell%27...

You cannot have (local) hidden variables, Bell showed that. You can have hidden variables only if you forgo locality.