The Impossibility of Infinitely Elapsed Planck Times

Observation indicates that a flat universe with an incomplete past (1) begins, (2) endlessly expands, and (3) forever develops a finite age. Nothing ever binds the continuous aging of a flat universe while the universe endlessly develops a finite age. Despite an infinite number of Planck time coordinates independent of phenomena, an infinite number of Planck times will never elapse in a single lineage. Likewise, an infinite number of Planck times have never elapsed in a single lineage. Time and the universe could not have been past eternal.

Imagining time travel to any past event in a world with an eternal past also helps to explain the impossibility of infinitely elapsed time. For example, if a time traveler in a world with an eternal past could survive a two-minute journey in a wormhole to any past event, then the time traveler could never possibly travel an infinite number of Planck times but only possibly travel to time coordinates with real values. The apparent unlimited time travel ability would never cover an infinite number of Planck times.

The observations of limits for the elapse of time in time travel and the aging of a flat universe exclude the possibility of all cosmology models with a past infinite number of Planck times. For example, Mithani and Vilenkin [1] recently refuted three categories of models with an eternal past: (1) past eternal inflation, (2) cyclic evolution, and (3) emergence from eternal static seed. Apart from reasons supported by Mithani and Vilenkin, those models also fail on the grounds that infinitely elapsed time is impossible.

Susskind [2] responded to Mithani and Vilenkin by arguing that the universe is past eternal. He supported his argument by using an analogy of a semi-infinite one-dimensional landscape with an incomplete past and an infinite population size of people. However, Susskind's semi-infinite landscape falsely analogizes a universe/multiverse with an incomplete past except for a multiverse with at least one node that simultaneously branches into an infinite number of branches, which Susskind does not model. Apart from the respective exception, an indefinitely branching multiverse with an incomplete past will never have a landscape with a semi-infinite size. Susskind's assumption of a semi-infinite landscape is invalid.

In sum, any scientific model of cosmology must have an incomplete past: that is, a beginning. And all apparent merits in cosmology models that include an infinite elapse of time are futile unless the merits are transferable to models with an incomplete past.

References
1. A. Mithani and A. Vilenkin, "Did the universe have a beginning?," arXiv:1204.4658 [hep-th]
2. Leonard Susskind, "Was there a beginning?," arXiv:1204.5385 [hep-th].


Copyright © 2012 James Edward Goetz

An Infinite Elapse of Time is Impossible and Unscientific

This article evaluates the concept of an infinite lapse/passage of time and concludes that an infinite lapse of time is impossible, which was proposed in the sixth century AD by John Philoponus. Likewise, models of cosmology that require infinitely lapsed time such as models of a genuinely cyclic universe or a multiverse with past eternal vacuum energy are impossible and unscientific.

Modern day observation of a flat universe indicates that a flat universe endlessly ages and always has a finite age. For example, a flat universe has a potential infinite age and a continuously increasing finite age. Nothing ever stops the aging of the universe while the universe endlessly has a finite age. Despite a potential infinite age, an actual infinite age never occurs.

The observed impossibility of an infinite lapse of time indicates the impossibility of infinitely lapsed time. Likewise, all scientific hypotheses of cosmology should exclude the possibility of infinitely lapsed time. For example, the technical definition of a "cyclic universe" implies an infinite number of past cycles. This indicates that the concept of a cyclic universe is unscientific, regardless of widely published papers in scientific journals about cyclic models. Other concepts widely published in scientific journals that require an unscientific infinitely lapsed time include "eternal inflation" with no beginning.

Some scholars skirt around the impossibility of infinitely lapsed time and propose the philosophical concept of eternalism, which holds that future phenomena already exist. For example, the universe is uncaused with absolutely no distinction between the past, present, and future while all appearance of lapsed time and sequential events are an illusion. This concept of radical simultaneousness for all supposedly past, present, and future events disputes the impossibility of an apparent infinite lapse of time but at the expense of rejecting the concept of lapsed time. Also, rejecting the concept of lapsed time disputes every theory involving cause and effect, which includes the concept of scientific theory. In this case, perhaps nobody can disprove eternalism while the appearance of lapsed time is merely an illusion, but such philosophical theories are incompatible with the concept of science.

My argument about the impossibility of infinitely lapsed time sometimes prompts debate about Zeno's fifth century BC paradoxes of infinity. Zeno pointed out problems with the concept of infinity while attempting to support the nonexistence of motion and change, which is still in vogue today with the philosophical eternalism mentioned above. For example, Zeno said that all apparently finite lengths such as a cubit are infinitely divisible and likewise nothing has actually traveled the length of a cubit. But this amusing paradox never explains observations of objects that travel a cubit.

In sum, this brief paper proposes that the science of cosmology excludes impossible concepts such as infinitely lapsed time and limits itself to inference based on scientific observation.



Updated with minor corrections on 5/5/2012

Copyright © 2012 James Edward Goetz