# Eternal Inflation Time Will End

• Kevin_Axion
In summary: The probability of selecting a number divisible by 100 is 0.01. The probability of selecting a number divisible by 1000 is 0.001. This is not wrong.
Kevin_Axion
Eternal Inflation "Time Will End"

This paper came out last week and looks very interesting but of course relies on M-Theory: http://arxiv.org/abs/1009.4698

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The argument the authors use is that if time is infinite, all events that are not prohibited are possible. From this observation the authors seem to conclude that if all possible events must occur and must occur an infinite number of times, then the method of assigning probabilities is "undermined." If I understand this argument correctly, it is simply wrong.

The point is easily made with the natural numbers. They are an infinite set. The set of all even numbers is also infinite; so is the set of every 10th number, every 100th number and every $$100^{100}$$ th number. Moreover each of these sets has the same cardinality. Nevertheless it is quite possible to assign the probability of a random number. We can say, for example, that numbers divisible by 100 are only one tenth as likely as those divisible by 10 when sampling from an arbitrarily large or even "infinite" set.

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SW VandeCarr said:
The argument the authors use is that probability theory and science itself is not possible if time is infinite because all events that are not prohibited are possible. From this observation the authors seem to conclude that since all possible events must occur and must occur an infinite number of times, we cannot assign probabilities to events; there is no basis for measurement and science is therefore impossible.

I took a glance at paper, and although it is interesting, that was my first doubt also. How come that probabillity sort of works in our world? Maybe I don't understand something.

Calimero said:
I took a glance at paper, and although it is interesting, that was my first doubt also. How come that probabillity sort of works in our world? Maybe I don't understand something.

Did you follow my argument in the second paragraph of my post? If not, I'll try to explain further. These are generally accepted concepts regarding infinite sets, on which probability theory is based. Note important distributions like the Gaussian are infinite but the integral of the probability distribution function is unity.

EDIT: I edited the first paragraph of my original post since some of the things I said were not explicitly expressed in the paper.

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SW VandeCarr said:
The point is easily made with the natural numbers. They are an infinite set. The set of all even numbers is also infinite; so is the set of every 10th number, every 100th number and every $$100^{100}$$ th number. Moreover each of these sets has the same cardinality. Nevertheless it is quite possible to assign the probability of a random number. We can say, for example, that numbers divisible by 100 are only one tenth as likely as those divisible by 10 when sampling from an arbitrarily large or even "infinite" set.
This is wrong. It is not possible to have a uniform probability distribution over the natural numbers.

chronon said:
This is wrong. It is not possible to have a uniform probability distribution over the natural numbers.

If you read my post, I'm not talking about the probability of selecting a given number. I'm talking about the probabilities of selecting numbers wholly divisible by 10, 100, 1000, etc. as examples. If you take finite random samples of size N from the set of natural numbers, the relative proportions of such numbers in the sample will tend to match the frequency in the set as N grows large. In probability theory this holds even if the set being sampled is infinite provided you can define the set by induction. So the probability of selecting a number divisible by 10 is 0.1.

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## What is eternal inflation?

Eternal inflation is a concept in cosmology that suggests the universe is constantly expanding and will continue to do so forever. This theory states that there are multiple universes, each with their own set of physical laws, and our universe is just one of many.

## How does eternal inflation relate to the concept of time ending?

The theory of eternal inflation suggests that the universe will continue to expand and cool until all matter and energy is spread out evenly and the universe reaches a state of maximum entropy. This state is known as the heat death of the universe, where time and all physical processes will come to an end.

## What evidence supports the theory of eternal inflation?

One of the main pieces of evidence for eternal inflation is the observation of the cosmic microwave background radiation. This radiation is thought to be leftover from the Big Bang and supports the idea of an expanding universe. Additionally, the theory of eternal inflation helps to explain the distribution of galaxies and other large-scale structures in the universe.

## Are there any competing theories to eternal inflation?

There are several competing theories to eternal inflation, including the cyclic model and the ekpyrotic model. These theories suggest that the universe goes through cycles of expansion and contraction, rather than expanding forever. However, there is currently no definitive evidence to support these theories.

## What are the implications of eternal inflation and the end of time?

If the theory of eternal inflation is true and the universe does reach a state of maximum entropy, it would have significant implications for the future of humanity and all life in the universe. However, this scenario is still billions of years away and much is still unknown about the nature of time and the universe.

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