The Measure Problem and the Youngness Paradox

• Salamon
In summary, Max Tegmark's book "The Mathematical Universe" addresses the Measure Problem in physics, which is a problem of counting probabilities with infinities. The problem arises in eternal inflation, where the universe is infinite and there is no unique way to assign probabilities. The youngness paradox occurs when using one particular way of counting infinities, but it can be avoided by considering a model of the universe that is explicitly finite. Some theorists have recently done so, as seen in the video "Multiverse: Switching to the Finite."
Salamon
I have read Max Tegmark's book "The Mathematical Universe" and he describes this thing called The Measure Problem as the biggest problems in physics. I am having difficulty understanding the problem so I will try to sum up my understanding of what he said.

As a result of inflation, the volume of space doubles every 10-38 seconds.
So there should be 21038 more big bangs occurring each second than in the previous second. Therefore, it is 21038 more times likely that we would find ourselves in a universe that is one second younger than the current universe we live in.

So in essence, is the measure problem that we never should have existed to begin with because it is always infinitely more probable that we would originate in a universe in the future?

Can't you just get around this problem by applying the anthropic principle and saying that if our universe was different than it is then we wouldn't be here?

I just don't see how this is a physics problem.

The measure problem is a different issue. It's a problem of counting probabilities with infinities. For example, if you have eternal inflation, that universe is infinite in extent into the future. This presents a problem with regard to computing probabilities because there is no unique way to assign probabilities. You simply cannot count up the relative number of outcomes X compared to outcomes Y, because both X and Y are infinite and their ratio depends upon how you do the counting.

The youngness paradox occurs because of one particular way of adding up those infinities. But it's very easy to take a different definition that doesn't have that problem.

Perhaps the best way to avoid this problem is to consider a model of the universe that is explicitly finite, and recently a few theorists have done precisely that. For example:
http://worldsciencefestival.com/videos/multiverse_switching_to_the_finite

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1. What is the Measure Problem?

The Measure Problem is a paradox in the field of cosmology that arises when trying to measure the age of the universe. It refers to the fact that there are multiple ways to define and measure the age of the universe, and these methods often yield conflicting results.

2. What is the Youngness Paradox?

The Youngness Paradox is a related paradox that arises when considering the question of why the universe appears to be so young, despite being measured to be billions of years old. This paradox highlights the discrepancy between the measured age of the universe and the apparent age of the objects within it.

3. How does the Measure Problem and the Youngness Paradox relate to each other?

The Measure Problem and the Youngness Paradox are closely related, as they both deal with the concept of the age of the universe. The Measure Problem deals with the difficulty in measuring the age of the universe, while the Youngness Paradox focuses on the discrepancy between the measured age and the apparent age of the universe.

4. What are some proposed solutions to the Measure Problem and the Youngness Paradox?

There are several proposed solutions to these paradoxes, including the concept of cosmic inflation, which suggests that the universe underwent a period of rapid expansion in its early stages. Other solutions include the idea of a cyclical universe or the possibility of multiple universes.

5. How do these paradoxes impact our understanding of the universe?

The Measure Problem and the Youngness Paradox highlight the limitations of our current understanding of the universe and the need for further research and exploration. These paradoxes challenge our current theories and push scientists to come up with new explanations and solutions to better understand the age and origins of the universe.

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