From my Quora time wasting this morning:
String theory predicts a multiverse populated by 10^500 different universes.
Is that true?
Where does the 10^500 come from?
The Rev Dodgson said:
From my Quora time wasting this morning:String theory predicts a multiverse populated by 10^500 different universes.
Is that true?
Where does the 10^500 come from?
I recommend you chase down the author for a citation.
I tried to get ChatGPT to give a meaningful summary of the information contained in this article The String Theory Landscape – Scientific American (https://www.scientificamerican.com/article/the-string-theory-landscape/) but I’m not sure it did that good a job. The article itself is worth reading though.
The following is from ChatGPT:
The estimate of around 10^500 stable vacuum states within the string theory landscape is based on several assumptions and considerations within the framework of string theory and the landscape hypothesis. While the exact number is not calculated directly but rather estimated based on these assumptions, the reasons it’s around 10^500 are as follows:
1) Moduli Configuration Space: String theory posits that the compactified extra dimensions are governed by parameters called moduli. These moduli describe the shape and size of the hidden dimensions. The moduli configuration space is extremely large, with a vast number of possible combinations of moduli values.
2) Random Distribution: It is assumed that the values of these moduli are distributed somewhat randomly within the landscape. This randomness arises due to the complex mathematics of string theory and the geometry of the hidden dimensions. The moduli values are not predetermined but can take on a wide range of values within certain limits.
3) Stability Requirement: For a vacuum state to be considered part of the landscape, it must be stable over cosmological timescales. Stability is a crucial requirement because we want the vacuum state to be able to support the development of a consistent universe. The requirement of stability helps narrow down the set of allowed vacuum states.
4) Anthropic Principle: The anthropic principle is invoked to explain why we observe a vacuum energy close to zero. According to this principle, only universes with vacuum energies within a certain range can support the formation of complex structures like stars and life. Therefore, our universe’s vacuum energy must fall within this range.
5) Combinations of Moduli Values: Given the large moduli configuration space, the randomness in moduli values, and the stability requirement, a vast number of combinations of moduli values can lead to stable vacuum states. This combination of factors leads to the prediction of an enormous number of stable vacuum states.
It’s essential to understand that the specific number, around 10^500, is a rough estimate and not a precise calculation. It arises from the interplay of these assumptions and considerations within the landscape hypothesis. The actual number could vary depending on the exact distribution of moduli values, the stability criteria, and other factors.
The estimate of 10^500 is often used as a way to illustrate the immense diversity of potential vacuum states within the string theory landscape, each of which could correspond to a universe with different physical laws and constants. However, the precise number remains a topic of ongoing research and discussion within the field of theoretical physics, and it may evolve as our understanding of string theory and the landscape hypothesis advances.
esselte said:
I tried to get ChatGPT to give a meaningful summary of the information contained in this article The String Theory Landscape – Scientific American (https://www.scientificamerican.com/article/the-string-theory-landscape/) but I’m not sure it did that good a job. The article itself is worth reading though.The following is from ChatGPT:
The estimate of around 10^500 stable vacuum states within the string theory landscape is based on several assumptions and considerations within the framework of string theory and the landscape hypothesis. While the exact number is not calculated directly but rather estimated based on these assumptions, the reasons it’s around 10^500 are as follows:
1) Moduli Configuration Space: String theory posits that the compactified extra dimensions are governed by parameters called moduli. These moduli describe the shape and size of the hidden dimensions. The moduli configuration space is extremely large, with a vast number of possible combinations of moduli values.
2) Random Distribution: It is assumed that the values of these moduli are distributed somewhat randomly within the landscape. This randomness arises due to the complex mathematics of string theory and the geometry of the hidden dimensions. The moduli values are not predetermined but can take on a wide range of values within certain limits.
3) Stability Requirement: For a vacuum state to be considered part of the landscape, it must be stable over cosmological timescales. Stability is a crucial requirement because we want the vacuum state to be able to support the development of a consistent universe. The requirement of stability helps narrow down the set of allowed vacuum states.
4) Anthropic Principle: The anthropic principle is invoked to explain why we observe a vacuum energy close to zero. According to this principle, only universes with vacuum energies within a certain range can support the formation of complex structures like stars and life. Therefore, our universe’s vacuum energy must fall within this range.
5) Combinations of Moduli Values: Given the large moduli configuration space, the randomness in moduli values, and the stability requirement, a vast number of combinations of moduli values can lead to stable vacuum states. This combination of factors leads to the prediction of an enormous number of stable vacuum states.
It’s essential to understand that the specific number, around 10^500, is a rough estimate and not a precise calculation. It arises from the interplay of these assumptions and considerations within the landscape hypothesis. The actual number could vary depending on the exact distribution of moduli values, the stability criteria, and other factors.
The estimate of 10^500 is often used as a way to illustrate the immense diversity of potential vacuum states within the string theory landscape, each of which could correspond to a universe with different physical laws and constants. However, the precise number remains a topic of ongoing research and discussion within the field of theoretical physics, and it may evolve as our understanding of string theory and the landscape hypothesis advances.
Interesting. :)
More specifically as to your question where does the number 10^500 come from, quoting the Scientific American article I linked above:
“ We cannot be sure how many stable vacua there are—that is, how many points where a ball could rest. But the number could very well be enormous. Some research suggests that there are solutions with up to about 500 handles, but not many more. We can wrap different numbers of flux lines around each handle, but not too many, because they would make the space unstable, like the right part of the curve in the figure. If we suppose that each handle can have from zero to nine flux lines (10 possible values), then there would be 10^500 possible configurations. “
esselte said:
I tried to get ChatGPT to give a meaningful summary of the information contained in this article The String Theory Landscape – Scientific American (https://www.scientificamerican.com/article/the-string-theory-landscape/) but I’m not sure it did that good a job. The article itself is worth reading though.The following is from ChatGPT:
The estimate of around 10^500 stable vacuum states within the string theory landscape is based on several assumptions and considerations within the framework of string theory and the landscape hypothesis. While the exact number is not calculated directly but rather estimated based on these assumptions, the reasons it’s around 10^500 are as follows:
1) Moduli Configuration Space: String theory posits that the compactified extra dimensions are governed by parameters called moduli. These moduli describe the shape and size of the hidden dimensions. The moduli configuration space is extremely large, with a vast number of possible combinations of moduli values.
2) Random Distribution: It is assumed that the values of these moduli are distributed somewhat randomly within the landscape. This randomness arises due to the complex mathematics of string theory and the geometry of the hidden dimensions. The moduli values are not predetermined but can take on a wide range of values within certain limits.
3) Stability Requirement: For a vacuum state to be considered part of the landscape, it must be stable over cosmological timescales. Stability is a crucial requirement because we want the vacuum state to be able to support the development of a consistent universe. The requirement of stability helps narrow down the set of allowed vacuum states.
4) Anthropic Principle: The anthropic principle is invoked to explain why we observe a vacuum energy close to zero. According to this principle, only universes with vacuum energies within a certain range can support the formation of complex structures like stars and life. Therefore, our universe’s vacuum energy must fall within this range.
5) Combinations of Moduli Values: Given the large moduli configuration space, the randomness in moduli values, and the stability requirement, a vast number of combinations of moduli values can lead to stable vacuum states. This combination of factors leads to the prediction of an enormous number of stable vacuum states.
It’s essential to understand that the specific number, around 10^500, is a rough estimate and not a precise calculation. It arises from the interplay of these assumptions and considerations within the landscape hypothesis. The actual number could vary depending on the exact distribution of moduli values, the stability criteria, and other factors.
The estimate of 10^500 is often used as a way to illustrate the immense diversity of potential vacuum states within the string theory landscape, each of which could correspond to a universe with different physical laws and constants. However, the precise number remains a topic of ongoing research and discussion within the field of theoretical physics, and it may evolve as our understanding of string theory and the landscape hypothesis advances.
Thankyou esselte and Chatbot
The Rev Dodgson said:
esselte said:
I tried to get ChatGPT to give a meaningful summary of the information contained in this article The String Theory Landscape – Scientific American (https://www.scientificamerican.com/article/the-string-theory-landscape/) but I’m not sure it did that good a job. The article itself is worth reading though.The following is from ChatGPT:
The estimate of around 10^500 stable vacuum states within the string theory landscape is based on several assumptions and considerations within the framework of string theory and the landscape hypothesis. While the exact number is not calculated directly but rather estimated based on these assumptions, the reasons it’s around 10^500 are as follows:
1) Moduli Configuration Space: String theory posits that the compactified extra dimensions are governed by parameters called moduli. These moduli describe the shape and size of the hidden dimensions. The moduli configuration space is extremely large, with a vast number of possible combinations of moduli values.
2) Random Distribution: It is assumed that the values of these moduli are distributed somewhat randomly within the landscape. This randomness arises due to the complex mathematics of string theory and the geometry of the hidden dimensions. The moduli values are not predetermined but can take on a wide range of values within certain limits.
3) Stability Requirement: For a vacuum state to be considered part of the landscape, it must be stable over cosmological timescales. Stability is a crucial requirement because we want the vacuum state to be able to support the development of a consistent universe. The requirement of stability helps narrow down the set of allowed vacuum states.
4) Anthropic Principle: The anthropic principle is invoked to explain why we observe a vacuum energy close to zero. According to this principle, only universes with vacuum energies within a certain range can support the formation of complex structures like stars and life. Therefore, our universe’s vacuum energy must fall within this range.
5) Combinations of Moduli Values: Given the large moduli configuration space, the randomness in moduli values, and the stability requirement, a vast number of combinations of moduli values can lead to stable vacuum states. This combination of factors leads to the prediction of an enormous number of stable vacuum states.
It’s essential to understand that the specific number, around 10^500, is a rough estimate and not a precise calculation. It arises from the interplay of these assumptions and considerations within the landscape hypothesis. The actual number could vary depending on the exact distribution of moduli values, the stability criteria, and other factors.
The estimate of 10^500 is often used as a way to illustrate the immense diversity of potential vacuum states within the string theory landscape, each of which could correspond to a universe with different physical laws and constants. However, the precise number remains a topic of ongoing research and discussion within the field of theoretical physics, and it may evolve as our understanding of string theory and the landscape hypothesis advances.
Thankyou esselte and Chatbot
Smart idea to thank bots, machines, etc if they take over they might remember it
Cymek said:
The Rev Dodgson said:
esselte said:
I tried to get ChatGPT to give a meaningful summary of the information contained in this article The String Theory Landscape – Scientific American (https://www.scientificamerican.com/article/the-string-theory-landscape/) but I’m not sure it did that good a job. The article itself is worth reading though.The following is from ChatGPT:
The estimate of around 10^500 stable vacuum states within the string theory landscape is based on several assumptions and considerations within the framework of string theory and the landscape hypothesis. While the exact number is not calculated directly but rather estimated based on these assumptions, the reasons it’s around 10^500 are as follows:
1) Moduli Configuration Space: String theory posits that the compactified extra dimensions are governed by parameters called moduli. These moduli describe the shape and size of the hidden dimensions. The moduli configuration space is extremely large, with a vast number of possible combinations of moduli values.
2) Random Distribution: It is assumed that the values of these moduli are distributed somewhat randomly within the landscape. This randomness arises due to the complex mathematics of string theory and the geometry of the hidden dimensions. The moduli values are not predetermined but can take on a wide range of values within certain limits.
3) Stability Requirement: For a vacuum state to be considered part of the landscape, it must be stable over cosmological timescales. Stability is a crucial requirement because we want the vacuum state to be able to support the development of a consistent universe. The requirement of stability helps narrow down the set of allowed vacuum states.
4) Anthropic Principle: The anthropic principle is invoked to explain why we observe a vacuum energy close to zero. According to this principle, only universes with vacuum energies within a certain range can support the formation of complex structures like stars and life. Therefore, our universe’s vacuum energy must fall within this range.
5) Combinations of Moduli Values: Given the large moduli configuration space, the randomness in moduli values, and the stability requirement, a vast number of combinations of moduli values can lead to stable vacuum states. This combination of factors leads to the prediction of an enormous number of stable vacuum states.
It’s essential to understand that the specific number, around 10^500, is a rough estimate and not a precise calculation. It arises from the interplay of these assumptions and considerations within the landscape hypothesis. The actual number could vary depending on the exact distribution of moduli values, the stability criteria, and other factors.
The estimate of 10^500 is often used as a way to illustrate the immense diversity of potential vacuum states within the string theory landscape, each of which could correspond to a universe with different physical laws and constants. However, the precise number remains a topic of ongoing research and discussion within the field of theoretical physics, and it may evolve as our understanding of string theory and the landscape hypothesis advances.
Thankyou esselte and Chatbot
Smart idea to thank bots, machines, etc if they take over they might remember it
Gotta hedge your bets.
The Rev Dodgson said:
From my Quora time wasting this morning:String theory predicts a multiverse populated by 10^500 different universes.
Is that true?
Where does the 10^500 come from?
I’ve heard that.
In a nutshell,
The 10^500 comes from topology in 11 dimensions (or 10 dimensions).
The extra dimensions have been folded back on themselves in order to effectively vanish in 4-dimensional space time. But there are multiple ways in which these can be folded back on themselves.
Consider 2-D space, it can be folded back on itself in (at least) two ways, as a sphere or as a torus. The two are topologically different.
In 3-D space there are more ways to fold the space back on itself. I could demonstrate with a diagram but don’t feel inclined to.
For string theory, the ways that space is folded back on itself is called the Calabi-Yau manifold. https://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold
The different topological foldings give different physical properties to the universe, and nobody has yet found one of these 10^500 universes that has properties similar to our own universe.
Is that good enough?
mollwollfumble said:
The Rev Dodgson said:
From my Quora time wasting this morning:String theory predicts a multiverse populated by 10^500 different universes.
Is that true?
Where does the 10^500 come from?
I’ve heard that.
In a nutshell,
The 10^500 comes from topology in 11 dimensions (or 10 dimensions).The extra dimensions have been folded back on themselves in order to effectively vanish in 4-dimensional space time. But there are multiple ways in which these can be folded back on themselves.
Consider 2-D space, it can be folded back on itself in (at least) two ways, as a sphere or as a torus. The two are topologically different.
In 3-D space there are more ways to fold the space back on itself. I could demonstrate with a diagram but don’t feel inclined to.For string theory, the ways that space is folded back on itself is called the Calabi-Yau manifold. https://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold
The different topological foldings give different physical properties to the universe, and nobody has yet found one of these 10^500 universes that has properties similar to our own universe.
Is that good enough?
There’s a slight chance that i may be able to count that 10^500
Let’s have a go. Start with 1-D
There is one way that one dimension can fold back on itself, forming a circle.
Let’s denote that as ‘1’.
In 2-D opposite faces of a square can join back together with or without a 180 degree twist. Call ‘1’ without a 180 degree twist and ‘2’ with a 180 degree twist. A square has two sets of opposite faces, so there are THREE ways two dimensions can fold back on itself.
11 = torus
12 = sphere
22 = Klein bottle
In 3-D opposite faces can join back together without a twist ‘1’, with a 180 degree twist ‘2’ or with a 90 degree twist ‘3’. So possibilities are:
111, 112, 113, 122, 123, 133, 222, 223, 233, 333, ten different ways in all.
Permutations and combinations. That’s not going to be enough to give us 10^500 different universes from string theory, but you can see how the number of possible universes increases as the number of folded up dimensions increases.