A Larger Estimate of the Entropy of the Universe

Egan, Chas A.; Lineweaver, Charles H.

doi:10.1088/0004-637x/710/2/1825

Cited by 182 publications

(212 citation statements)

References 36 publications

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“…Some estimates [28][29][30][31] place S g /k B at around 10 104 . While a somewhat lower value of our entropy would clearly be desirable, the fact is that the upper bound set by the holographic principle is respected by all of our results.…”

Section: Discussionmentioning

confidence: 99%

“…The bound (28) has been determined by a purely classical argument; although the uncertainty principle will shift the minimum energy (28) by a positive amount, this correction can be discarded for our purposes, as it will be negligible compared to (28) itself.…”

Section: Nonperturbativementioning

confidence: 99%

“…We set l = 0 in Equation (23) and use E = E 0 from (28) to arrive at the eigenvalue equation for the vacuum state:…”

Section: Approximate Eigenfunctions For the Vacuum Statementioning

confidence: 99%

“…The effect of having x 0 < 1 reduces this value somewhat, and the holographic bound is no longer saturated. However, the reduction thus attained is negligible, far from the necessary ∼10 −19 that would be required to bring the entropy from the holographic bound ∼10 123 down to its estimated value ∼10 104 [28][29][30][31]. One readily verifies that Equations (45) and (47) continue to hold if one replaces the hyperbolic sine with a hyperbolic cosine in the wavefunction (42).…”

Section: Approximate Eigenfunctions For the Vacuum Statementioning

confidence: 99%

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Boltzmann Entropy of a Newtonian Universe

Cabrera

Córdoba

Isidro

2017

Entropy

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A dynamical estimate is given for the Boltzmann entropy of the Universe, under the simplifying assumptions provided by Newtonian cosmology. We first model the cosmological fluid as the probability fluid of a quantum-mechanical system. Next, following current ideas about the emergence of spacetime, we regard gravitational equipotentials as isoentropic surfaces. Therefore, gravitational entropy is proportional to the vacuum expectation value of the gravitational potential in a certain quantum state describing the matter contents of the Universe. The entropy of the matter sector can also be computed. While providing values of the entropy that turn out to be somewhat higher than existing estimates, our results are in perfect compliance with the upper bound set by the holographic principle.Keywords: newtonian cosmology; emergent quantum theory The Approach via Emergent Quantum TheoryIn this article, we will argue in favour of emergent quantum mechanics as providing an appropriate framework to estimate thermodynamical quantities of the Universe, such as the entropy.The notion that quantum mechanics is an emergent theory has been discussed at length in the literature [1][2][3][4][5][6][7]. Combined with the idea that spacetime is also is an emergent phenomenon [8][9][10][11][12], this paves the way for a computation of some thermodynamical properties of spacetime in quantum-mechanical terms. We would like to remark that a quantum-mechanical approach to the expansion of the Universe was called for long ago in Reference [13], where it was suggested to regard the expansion of the Universe as a scattering problem in quantum mechanics.The expansion of the Universe is a long-standing experimental observation [14] that has in recent years been refined thanks to very precise measurements [15,16]. In the Newtonian approximation, this receding behaviour of the galaxies can be easily modelled by a phenomenological potential-namely, an isotropic harmonic potential carrying a negative sign:As the angular frequency, we take the current value of Hubble's constant H 0 . Thus, U Hubble has the dimensions of energy per unit mass, or velocity squared.In the emergent approach to spacetime presented in Reference [12], gravity qualifies as an entropic force. If gravitational forces are entropy gradients, gravitational equipotential surfaces can be identified with isoentropic surfaces. Recalling the arguments of Reference [12], a classical point particle approaching a holographic screen causes the entropy of the latter to increase by one quantum k B . Here we will analyse a quantum-mechanical model in which the forces driving the galaxies away from each other can be modelled by the Hubble potential (1). We will replace the classical particle of Reference [12] with a collection of quantum particles (the matter contents of the Universe) described

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Section: Discussionmentioning

confidence: 99%

Section: Nonperturbativementioning

confidence: 99%

“…We set l = 0 in Equation (23) and use E = E 0 from (28) to arrive at the eigenvalue equation for the vacuum state:…”

Section: Approximate Eigenfunctions For the Vacuum Statementioning

confidence: 99%

Section: Approximate Eigenfunctions For the Vacuum Statementioning

confidence: 99%

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Boltzmann Entropy of a Newtonian Universe

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Córdoba

Isidro

2017

Entropy

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“…4 , we need to know S ( t ) and S max . In Egan and Lineweaver ( 2010 ) , we reviewed previous estimates of S ( t ). Based on the latest observations of the mass function of supermassive black holes, we found S ( t ) to be at least 30 times larger than previous estimates.…”

Section: The Entropic Paradox: a Low Initial Entropy Seems To Con Fl mentioning

confidence: 99%