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Mathematics of Eternity Prove The Universe Must Have Had A Beginning -- Part II

Heavyweight cosmologists are battling it out over whether the universe had a beginning. And despite appearances, they may actually agree

  • April 27, 2012

Earlier this week, Audrey Mithani and Alexander Vilenkin at Tufts University in Massachusetts argued that the mathematical properties of eternity prove that the universe must have had a beginning

Today, another heavyweight from the world of cosmology weighs in with an additional argument. Leonard Susskind at Stanford University in California, says that even if the universe had a beginning, it can be thought of as eternal for all practical purposes. 

Susskind is good enough to give a semi-popular version of his argument:

“To make the point simply, imagine Hilbertville, a one-dimensional semi-infinite city, whose border is at x = 0: The population is infinite and uniformly fills the positive axis x > 0: Each citizen has an identical telescope with a finite power. Each wants to know if there is a boundary to the city. It is obvious that only a finite number of citizens can see the boundary at x = 0. For the infinite majority the city might just as well extend to the infinite negative axis. 

Thus, assuming he is typical, a citizen who has not yet studied the situation should bet with great confidence that he cannot detect a boundary. This conclusion is independent of the power of the telescopes as long as it is finite.”

He goes on to discuss various thermodynamic arguments that suggest the universe cannot have existed for ever. The bottom line is that the inevitable increase of entropy over time ensures that a past eternal universe ought to have long since lost any semblance of order. Since we can see order all around us, the universe cannot be eternal in the past.

He finishes with this: “We may conclude that there is a beginning, but in any kind of inflating cosmology the odds strongly (infinitely) favor the beginning to be so far in the past that it is effectively at minus infinity.”

Susskind is a big hitter: a founder of string theory and one of the most influential thinkers in this area. However, it’s hard to agree with his statement that this argument represents the opposing view to Mithani and Vilenkin’s.  

His argument is equivalent to saying that the cosmos must have had a beginning even if it looks eternal in the past, which is rather similar to Mithani and Vilenkin’s view. The distinction that Susskind does make is that his focus is purely on the practical implications of this–although what he means by ‘practical’ isn’t clear.

That the universe did or did not have a beginning is profoundly important from a philosophical point of view, so much so that a definitive answer may well have practical implications for humanity. 

But perhaps the real significance of this debate lies elsewhere. The need to disagree in the face of imminent agreement probably tells us more about the nature of cosmologists than about the cosmos itself.

Ref: arxiv.org/abs/1204.5385: Was There a Beginning?

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