## Does the Quantum Sum Rule Hold at the Big Bang?

**Authors:** A.W. Beckwith

In Dice 2010 Sumati Surya brought up a weaker Quantum sum rule as a biproduct of a quantum invariant measure space. Our question is, does it make sense to have disjoint sets to give us quantum conditions for a measure at the origin of the big bang? We argue that the answer is no, which has implications as to quantum measures and causal set structure. What is called equation (1) in the text requires a length, and interval, none of which holds at a point in space-time.singularity. Planck’s length, if it exists, is a natural way to get about the ‘bad effects’ of a cosmic singularity at the beginning of space-time evolution, but if a new development is to believed, namely by Stoica in the article, about removing the cosmic singularity as a break down point in relativity, there is nothing which forbids space-time from collapsing to a point. If that happens, the cautions as to no disjoint intervals at a point, raise the questions as to the appropriateness of Surya’s quantum measure with full force. However, if we have to have Planck’s length, then the existence of quantum vector measures cannot be challenged and equation (1) holds. The existence of well defined equation (1) rests upon if a minimum Planck’s length is essential in the cosntruction of cosmology.

**Comments:** 9 pages, re do of paper to accomodate great work by Stoica about removing GR singularity problem in cosmology

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### Submission history

[v1] 2012-06-17 02:58:59

[v2] 2012-06-17 12:55:20

[v3] 2012-06-19 02:07:04

[v4] 2012-06-19 08:20:20

[v5] 2012-06-19 11:05:31

[v6] 2012-06-19 16:21:05

[v7] 2012-06-21 20:32:23

[v8] 2012-06-23 14:09:14

[v9] 2012-07-24 23:05:11

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