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

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 eff ectively 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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Mathematics of Eternity Prove The Universe Must Have Had A Beginning

Cosmologists use the mathematical properties of eternity to show that although universe may last forever, it must have had a beginning

The Big Bang has become part of popular culture since the phrase was coined by the maverick physicist Fred Hoyle in the 1940s. That's hardly surprising for an event that represents the ultimate birth of everything.

However, Hoyle much preferred a different model of the cosmos: a steady state universe with no beginning or end, that stretches infinitely into the past and the future. That idea never really took off.

In recent years, however, cosmologists have begun to study a number of new ideas that have similar properties. Curiously, these ideas are not necessarily at odds with the notion of a Big Bang.

For instance, one idea is that the universe is cyclical with big bangs followed by big crunches followed by big bangs in an infinite cycle. 

Another is the notion of eternal inflation in which different parts of the universe expand and contract at different rates. These regions can be thought of as different universes in a giant multiverse. 

So although we seem to live in an inflating cosmos,  other universes may be very different. And while our universe may look as if it has a beginning, the multiverse need not have a beginning.

Then there is the idea of an emergent universe which exists as a kind of seed for eternity and then suddenly expands. 

So these modern cosmologies suggest that the observational evidence of an expanding universe is consistent with a cosmos with no beginning or end. That may be set to change.

Today, Audrey Mithani and Alexander Vilenkin at Tufts University in Massachusetts say that these models are mathematically incompatible with an eternal past. Indeed, their analysis suggests that these three models of the universe must have had a beginning too.

Their argument focuses on the mathematical properties of eternity--a universe with no beginning and no end. Such a universe must contain trajectories that stretch infinitely into the past. 

However, Mithani and Vilenkin point to a proof dating from 2003 that these kind of past trajectories cannot be infinite if they are part of a universe that expands in a specific way. 

They go on to show that cyclical universes and universes of eternal inflation both expand in this way. So they cannot be eternal in the past and must therefore have had a beginning. "Although inflation may be eternal in the future, it cannot be extended indefinitely to the past," they say.

They treat the emergent model of the universe differently, showing that although it may seem stable from a classical point of view, it is unstable from a quantum mechanical point of view. "A simple emergent universe model...cannot escape quantum collapse," they say.

The conclusion is inescapable. "None of these scenarios can actually be past-eternal," say Mithani and Vilenkin. 

Since the observational evidence is that our universe is expanding, then it must also have been born in the past. A profound conclusion (albeit the same one that lead to the idea of the big bang in the first place).  

Ref: arxiv.org/abs/1204.4658: Did The Universe Have A Beginning?

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