Universal wave function, 12

The uncertainty principle states the limit of reductionism. Science is based on reductionism, which assumes we can investigate part of the universe. So the uncertainty principle, in effect, states the limit of science.

— Me@2011.11.29

2012.02.05 Sunday (c) All rights reserved by ACHK

The last decade in theoretical physics has simply settled this question – whether someone likes it or not – and the answer is “No”. The spacetime geometry cannot be fundamental at the Planck scale. It is subject to transitions, dualities, and holography, among other phenomena that prove that it must be flexible and it cannot arise from a graph because a graph is too local. In neither of the existing descriptions we can find a discrete spacetime and it seems rather unlikely that there exists a description where it is discrete.

— Quantum Graphity

— Lubos Motl

2012.02.01 Wednesday ACHK

The answer to all questions is No. In fact, even the right reaction to the first sentence – that the Planck scale is a “discrete measure” – is No.

The Planck length is a particular value of distance which is as important as 2π times the distance or any other multiple. The fact that we can speak about the Planck scale doesn’t mean that the distance becomes discrete in any way. We may also talk about the radius of the Earth which doesn’t mean that all distances have to be its multiples.

In quantum gravity, geometry with the usual rules doesn’t work if the (proper) distances are thought of as being shorter than the Planck scale. But this invalidity of classical geometry doesn’t mean that anything about the geometry has to become discrete (although it’s a favorite meme promoted by popular books). There are lots of other effects that make the sharp, point-based geometry we know invalid – and indeed, we know that in the real world, the geometry collapses near the Planck scale because of other reasons than discreteness.

— Is reality discrete at the quantum level?

— Lubos Motl

2012.01.31 Tuesday ACHK

Universal wave function, 11

Bohm’s pilot wave can be regarded as a global hidden variable.

But like any global hidden variable, it is not totally observable to a local observer.

— Me@2011.11.22

2012.01.26 Thursday (c) All rights reserved by ACHK

Uncertainty principle, 4
 
 
The uncertainty principle is due to the phenomenon of wave function collapse. No collapse, no uncertainty.

The universal wave function does not collapse.

However, since the “final result” is a superposition of eigenstates, we can re-define the uncertainty in terms of the eigenvalues and their probability weightings.

— Me@2011.11.22

— Me@2012.01.15
 
 
The last sentence tries to answer

Is the uncertainty principle still meaningful if there are never wave function collapses?

or

What is the meaning of “uncertainty” if the universal wave function just evolves unitarily and deterministically?

— Me@2018-01-21 10:03:35 PM
 
 
 
2012.01.15 Sunday (c) All rights reserved by ACHK

Dear Deepak, because the geometry simply cannot work in the same way for sub-Planckian ultrashort distances – the usual notions of geometry break down, the quantum fluctuations of proper lengths are of order 100%, the topology of spacetime is spontaneously changing over there (quantum foam), etc. The spacetime with gravity can’t be the same or self-similar at/beneath the Planck scale. Even wrong theories of quantum gravity such as loop quantum gravity clearly imply this – in the LQG case, the proper areas can’t be nonzero but much smaller than the Planck area (quantization). Think about it. – Lubos Motl Mar 24 ’11 at 5:36

2012.01.10 Tuesday ACHK

Universal wave function, 7

De Broglie–Bohm’s pilot-wave can be regarded as the universal wave function, representing the entanglement structure of the whole universe.

— Me@2011.11.22

2012.01.08 Sunday (c) All rights reserved by ACHK