I Why is an improbable early universe unacceptable?

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The discussion centers on the improbability of the early universe and the challenges of understanding its origins through quantum fluctuations. Participants argue that while the universe's ordered state seems highly improbable, it is not surprising in hindsight since it has already occurred. The Boltzmann brain problem is mentioned as a philosophical issue rather than a true paradox, highlighting the self-selecting nature of observers in the universe. The multiverse theory is critiqued for pushing the problem of improbability into an unobservable realm, complicating the understanding of cosmic evolution. Overall, the conversation emphasizes the confusion surrounding probability assessments in cosmology and the subjective nature of our universe's perceived uniqueness.
  • #31
houlahound said:
Please define what a measure problem is.

A measure problem is either when different measures applied to the same space in a theory produce different predictions or there is no way to define a measure on a space at all.

Measures in set theory and topology are ways to assign numbers to subsets. They generalise lengths, areas and volumes.

https://en.wikipedia.org/wiki/Measure_(mathematics)

Measures also apply to probability spaces so come into topics like entropy and quantum theory.

Measure problems are endemic in cosmological theories and many different regularisation procedures have been created to overcome them but none are generally accepted. In eternal inflation theories the problem is how to apply probability measures to infinite sets of causally disconnected universes. In canonical quantum gravity the Wheeler-deWitt equation is regularisation dependent.

https://en.wikipedia.org/wiki/Measure_problem_(cosmology)

houlahound said:
Please define what a measure problem is.
 
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