Uncertainty Principle for Space–Time Algebra-Valued Functions

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Youssef El Haoui
Keyword(s):  
Uncertainty Principle ◽  
Space Time

SPACE–TIME ENERGY–MOMENTUM, THE OBSERVER AND UNCERTAINTY IN GENERAL RELATIVITY

2010 ◽  
Vol 19 (14) ◽  
pp. 2353-2359 ◽  
Author(s):  
F. I. COOPERSTOCK ◽  
M. J. DUPRE
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Uncertainty Principle ◽  
Ricci Tensor ◽  
Space Time ◽  
Energy Integral ◽  
New Approach ◽  
Extended Space ◽  
Energy And Momentum

In this essay, we introduce a new approach to energy–momentum in general relativity. Space–time, as opposed to space, is recognized as the necessary arena for its examination, leading us to define new extended space–time energy and momentum constructs. From local and global considerations, we conclude that the Ricci tensor is the required element for a localized expression of energy–momentum to include the gravitational field. We present and rationalize a fully invariant extended expression for space–time energy, guided by Tolman's well-known energy integral for an arbitrary bounded stationary system. This raises fundamental issues which we discuss. The role of the observer emerges naturally and we are led to an extension of the uncertainty principle to general relativity, of particular relevance to ultra-strong gravity.

scholarly journals Effect of GUP on the Kepler problem and a variable minimal length

2014 ◽  
Vol 92 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Fatemeh Ahmadi ◽  
Jafar Khodagholizadeh
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Kepler Problem ◽  
Rotational Symmetry ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Minimal Length ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Perihelion Shift

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg uncertainty principle near the Plank scale, known as the generalized uncertainty principle (GUP). Here we study the effects of GUP, which preserves the rotational symmetry of the space–time, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild – de Sitter space–time with the resultant value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the space–time. Now, if the cosmological constant varies with time, we have a variable minimal length in the space–time. Finally, we investigate the effects of GUP on the stability of circular orbits.

Heisenberg, Bohr, Robertson, and the Uncertainty Principle

2020 ◽  
pp. 133-156
Author(s):  
Jim Baggott
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Laboratory Experiments ◽  
Space Time ◽  
Spectral Lines ◽  
Planck’S Constant ◽  
Classical Space ◽  
Planck's Constant

From the outset, Heisenberg had resolved to eliminate classical space-time pictures involving particles and waves from the quantum mechanics of the atom. He had wanted to focus instead on the properties actually observed and recorded in laboratory experiments, such as the positions and intensities of spectral lines. Alone in Copenhagen in February 1927, he now pondered on the significance and meaning of such experimental observables. Feeling the need to introduce at least some form of ‘visualizability’, he asked himself some fundamental questions, such as: What do we actually mean when we talk about the position of an electron? He went on to discover the uncertainty principle: the product of the ‘uncertainties’ in certain pairs of variables—called complementary variables—such as position and momentum cannot be smaller than Planck’s constant h (now h / 4π‎).

scholarly journals THERMODYNAMICS OF NONCOMMUTATIVE DE SITTER SPACE–TIME

2009 ◽  
Vol 18 (01) ◽  
pp. 159-171 ◽  
Author(s):  
B. VAKILI ◽  
N. KHOSRAVI ◽  
H. R. SEPANGI
Keyword(s):  
Uncertainty Principle ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Heisenberg Algebra ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Quantization Rule ◽  
Thermodynamical Properties ◽  
Noncommutative Parameter

We study the effects of noncommutativity of space–time geometry on the thermodynamical properties of the de Sitter horizon. We show that noncommutativity results in modifications in temperature, entropy and vacuum energy and that these modifications are of order of the Planck scale, suggesting that the size of the noncommutative parameter should be close to that of the Planck. In an alternative way to deal with noncommutativity, we obtain a quantization rule for the entropy. Since noncommutativity in space–time geometry modifies the Heisenberg algebra and introduces the general uncertainty principle, we also investigate the above problem in this framework.

scholarly journals SPACE–TIME UNCERTAINTY PRINCIPLE FROM BREAKDOWN OF TOPOLOGICAL SYMMETRY

1998 ◽  
Vol 13 (03) ◽  
pp. 203-209 ◽  
Author(s):  
ICHIRO ODA
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Space Time ◽  
Topological Quantum Field Theory ◽  
Time Interval ◽  
Quantum Field ◽  
Higher Symmetry ◽  
Time Uncertainty ◽  
Topological Quantum ◽  
Large N

Starting from topological quantum field theory, we derive space–time uncertainty relation with respect to the time interval and the spatial length proposed by Yoneya through breakdown of topological symmetry in the large-N matrix model. This work suggests that the topological symmetry might be an underlying higher symmetry behind the space–time uncertainty principle of string theory.

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