EPR paradox, 2

Two assumptions drove the desire to find a local realist theory:

1. Objects have a definite state that determines the values of all other measurable properties, such as position and momentum.

2. Effects of local actions, such as measurements, cannot travel faster than the speed of light (in consequence of special relativity). Thus if observers are sufficiently far apart, a measurement made by one can have no effect on a measurement made by the other.
   
— Wikipedia on Bell’s theorem

It is no longer possible to adhere to both the principle of locality (that distant objects cannot affect local objects), and counterfactual definiteness, a form of ontological realism implicit in classical physics. Some interpretations of quantum mechanics hold that a system lacks an actualized property until it is measured, which implies that quantum systems exhibit a non-local behaviour. Bell’s theorem proved that every quantum theory must either violate local realism or counterfactual definiteness.

— Wikipedia on Naive realism

1. The principle of locality:

There are two possible meanings of “locality” here.

1.1 The principle is correct in a sense that no causal influence can be faster than light.

1.2 The principle is incorrect in a sense that distant particles can be entangled. Correlation without causation can be instantaneous.

Assume that a pair of particles are entangled. Measuring one particle will collapse the wave function, which governs both particles, instantaneously.

2. Counterfactual definiteness:

2.1 It is correct in a sense that an object has a definite quantum state.

2.2 It is incorrect in a sense that, most often than not, the definite quantum state is not corresponding to a definite classical state (aka eigenstate). Instead, that quantum state is a superposition of different eigenstates. 

— Me@2012-04-07 11:36:01 AM

2012.04.07 Saturday (c) All rights reserved by ACHK

Moreover, there is this statement that “distances smaller than Planck length don’t exist” that confuses many people. They heard it and misunderstood it, thinking it applies to coordinate differences. It can only apply to Lorentz-invariant “proper” distances, otherwise relativity is broken.

– Lubos Motl Jan 23 ’11 at 8:19

2012.04.06 Friday ACHK

In block spacetime, there is no motion, except for labeling convenience.

— Me@2011.10.25

2012.04.03 Tuesday (c) All rights reserved by ACHK

The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state.

The state of one system can be entangled with the state of another system. For instance, one can use the Controlled NOT gate and the Walsh-Hadamard gate to entangle two qubits. This is not cloning. No well-defined state can be attributed to a subsystem of an entangled state. Cloning is a process whose end result is a separable state with identical factors.

Consequences

    The no-cloning theorem prevents us from using classical error correction techniques on quantum states. For example, we cannot create backup copies of a state in the middle of a quantum computation, and use them to correct subsequent errors. Error correction is vital for practical quantum computing, and for some time this was thought to be a fatal limitation. In 1995, Shor and Steane revived the prospects of quantum computing by independently devising the first quantum error correcting codes, which circumvent the no-cloning theorem.

    The no cloning theorem prevents us from viewing the holographic principle for black holes as meaning we have two copies of information lying at the event horizon and the black hole interior simultaneously. This leads us to more radical interpretations like black hole complementarity.

— Wikipedia on No-cloning theorem

2012.04.01 Sunday ACHK