
Fundamental theories of nature aren’t allowed to hide information - dnetesn
http://nautil.us/issue/21/information/is-your-theory-of-everything-pure-enough-rd
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Strilanc
This was a poorly written article, in my opinion. It failed to communicate the
intent of the paper. I _think_ it's trying to say something like...

In quantum information theory there's pure states, like "[Off]", "[On]",
"([Off] + [On])/sqrt(2)", "([Off] - [On])/sqrt(2)", and "3/5 [Off] + 4i/5
[On]". There's also mixed states, which are probability distributions of pure
states, like "35% [On] + 65% [Off]" or "10% [On] + 90% ([Off] +
[On])/sqrt(2)". Pure states behave differently from mixed states (sometimes),
which is why the distinction is worth having. Pure states collapse into mixed
states when measured.

There's a process to convert any mixed state into a pure state, called
purification [1], that works by grafting on a secondary system with the
appropriate entanglements. For example, "10% [On] + 90% ([Off] +
[On])/sqrt(2)" can be purified into "sqrt(1/10) [On and Extra=0] + sqrt(9/20)
[Off and Extra=1] + sqrt(9/20) [On and Extra=1]". This isn't just a
theoretical trick to ignore mixed-ness, it's something you can do in practice.
You can even verify that it works, statistically, because pure states
interfere and correlate in ways that some mixed states can't.

The article appears to be saying that any theory that allows for purification
(however they define it) must secretly be isomorphic to quantum mechanics
(i.e. the state space is tensor products of complex vectors, the operations
are unitary matrices, and measurement outcomes are related to the
eigenvalues/vectors of Hermitian matrices).

1:
[http://en.wikipedia.org/wiki/Purification_of_quantum_state](http://en.wikipedia.org/wiki/Purification_of_quantum_state)

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AnimalMuppet
For every claim in the article, you must remember to prefix it with "If this
asserted principle is true, then..." But as far as I can see, no proof of the
principle is given (that's why it's called a principle, not a theorem).

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Sniffnoy
Here's a link to the referenced paper on arXiv:
[http://arxiv.org/abs/1011.6451](http://arxiv.org/abs/1011.6451)

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ars
> For if every event was predetermined, the outcomes of all experiments should
> be independent of the information possessed by any agent.

I don't see how this follows from what was said before.

I also don't see how he can say that Quantum Mechanics is the _only_ theory
that can be pure.

You don't know that everything is not predetermined, they might be. We don't
know. Quantum randomness might not actually be random.

~~~
lisper
If quantum randomness isn't random then QM is wrong. For quantum randomness to
not be random, that would mean that the outcome of quantum experiments must be
correlated with some other observable somewhere in the universe. QM
specifically denies this, so a demonstration that quantum randomness isn't
random would be a falsification of QM. That would be the biggest breakthrough
in physics in 100 years.

~~~
amelius
But what if an underlying "random number generator" was actually built into
the rules of physics? In other words, that quantum randomness appears to be
random, but is a byproduct of a (probably much more complicated) underlying
scheme that is totally deterministic.

(This random number generator would not be external to the universe, but
implicitly built into the rules of this universe.)

~~~
dTal
[http://en.wikipedia.org/wiki/Hidden_variable_theory](http://en.wikipedia.org/wiki/Hidden_variable_theory)

"Assuming the validity of Bell's theorem, any deterministic hidden-variable
theory which is consistent with quantum mechanics would have to be non-local,
maintaining the existence of instantaneous or faster-than-light relations
(correlations) between physically separated entities."

Basically, you have three choices:

    
    
      1) The universe is genuinely random
      2) The universe is "nonlocal" (i.e. "spooky action at a distance")
      3) Bell's theorem is invalid for some reason.

