The Latent Meaning of Forcing in Quantum Mechanics

We analyze random forcing in QM from the dual perspective of the measure and category correspondence. The dual Cohen forcing allows interpreting the real numbers in a model

M

and its Cohen extension

M[G]

as absolute subtrees of the binary tree (Cantor space). The trees are spanning non-trivial Casson handles of smooth exotic 4-manifolds, like

\mathbb{R}^4

. We formulate the consequences for the cosmological model with random forcing where dual smooth non-standard and non-flat Riemannian geometries have to appear.

References(17)

Figures(0)

[1]

Remarks on Mathematical Foundations of Quantum Mechanics

- Acta Phys.Polon.B 46 (2015) 7, 1309
•
DOI:
- 10.5506/APhysPolB.46.1309

[2]

R.A. Van Wesep

- Annals Phys. 321 (2006) 2453

[3]

Two Applications of Logic to Mathematics, Kano Memorial Lecture 3, Math. Soc. Jpn., Princeton, USA

G. Takeuti

[4]

Set Theory: On the Structure of the Real Line, A.K Peters, Wellesley, Massachusets, USA

T. Bartoszyński
,
H. Judah

[5]

An Introduction to 4-Manifolds and Kirby Calculus, American Mathematical Society, Rhode Island

R.E. Gompf
,
A.I. Stipsicz

[6]

C.H Exotic Smoothness and Physics, World Scientific, Singapore

T. Asselmeyer-Maluga

[7]

Inflation and Topological Phase Transition Driven by Exotic Smoothness

Torsten Asselmeyer-Maluga
(
- DLR, Berlin
)
,
Jerzy Król
(
- Silesia U.
)

- Adv.High Energy Phys. 2014 (2014) 867460
•
DOI:
- 10.1155/2014/867460

[8]

The Structure of the Real Line in Quantum Mechanics and Cosmology

- Acta Phys.Polon.B 46 (2015) 11, 2375
•
DOI:
- 10.5506/APhysPolB.46.2375

[9]

Model and Set-Theoretic Aspects of Exotic Smoothness Structures on R4, in: At the Frontier of Spacetime, T Asselmeyer-Maluga ed

J. Król

[10]

Set theoretical forcing in quantum mechanics and AdS / CFT correspondence

Jerzy Krol
(
- Silesia U.
)

- Int.J.Theor.Phys. 42 (2003) 921-935
•
e-Print:
- quant-ph/0303089
•
DOI:
- 10.1023/A:1025410204119

[11]

Background independence in quantum gravity and forcing constructions

J. Krol
(
- Silesia U.
)

- Found.Phys. 34 (2004) 361-403
•
DOI:
- 10.1023/B:FOOP.0000019620.04821.a2

[12]

Measure and Category, 2nd ed NY

J.C. Oxtoby

[13]

Discovering Modern Set Theory. II. Set-Theoretic Tools for Every Mathematician, AMS, Providence

W. Just
,
M. Weese

[14]

Absoluteness, Truth, and Quotients, in: Proceedings of the IMS, Workshop on Infinity and Truth, C.T. Chong et al. (eds.) pp. 1-24

I. Farah

[15]

& Team Freedman, Bing Topology and Casson Handles, Santa Barbara/Bonn Lectures

M.H. Freedman

[16]

T. Kato

- Contemp.Math. 347 (2004) 113

[17]

Ž. Bižaca

- Proc.Am.Math.Soc. 123 (1995) 1297