The fourth level of the Max Tegmark multi-universe
Almost 10 years ago I read an article by Max Tegmark , a brilliant physicist and philosopher, and found in it answers to many questions that had tormented me all my life. The article is amazing, two months I went under the impression of her. Unfortunately, this is a longrid, also in English. So I decided not to even translate it - the translation would still be too long for Habr, but at least to present the basic idea in the order it seems logical to me, and removing unnecessary details (Max forgive me!)
What it is? It is unlikely that this formula tells you something. And if I write it like this:
Then you immediately recognize Newton's law in it. Of course, both formulas are equivalent, we just got used to the fact that force is denoted by F, mass m, moreover, we mean that it happens in three-dimensional space, that the bodies have coordinates, and so on. That is, the theory has two components: formulas and bla-bla around them. Max calls the second component verbal baggage .
Consider the tree of existing theories:
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At the bottom is a sociology, where there are almost no formulas, but many words. Gradually moving upward, we meet with increasingly complex mathematics. But words are getting worse and worse: try to figure out what time is from a scientist who is engaged in fundamental physics. It is obvious to you that time is a sequence of events and it flows forward . The more you know and the deeper you go, the less it becomes obvious. The description of what time is, more and more, collapses to the fact that time is the letter t , which participates in such and such equations.
So, Max notices that:
As one moves toward an increasingly fundamental level, mathematics becomes more and more complex, and baggage begins to degenerate more and more. In the limit, assumes Max, TOE (Theory of Everything) has no baggage . So, TOE consists only of formulas .
This is the first ingredient. Remember it.
How is that even possible? Physics is trying to find equations for our world, based on observations and experimental data. Max proposes to consider “Physics on the contrary” - “ Physics from Scratch ” - you set the equations, what kind of world do you get?
We can set the laws of the world ... well, for example, the game "life". Can we do without a verbal description? How, for example, to say that the space of cells is two-dimensional? Through the equations, by indicating the power law, how quickly the number of cells grows no further than N. Another example, the string theory equations converge only if the dimension of space is 10, 11, or 26. Perhaps, first, to formulate physics axiomatically seems complicated, but mathematicians have done well in creating axiomatic theories (and worlds). Take, for example, Peano's axioms . These are pure formulas, it does not explain what a “number” is, what “add” or “multiply” is.
What do we have? We have (will) a TOE describing ALL of the things.
Just a second ... And what does “describing” mean? Here, for example, mechanics describes the movement of bodies. But we know that all this is possible thanks to a bunch of simplifications: bodies are not material points, there is air resistance, friction, and so on. There are formulas that describe reality, but we know that the real world is different from the ideal one described by formulas.
But in the case of TOE it is not: any, absolutely any physical aspect of reality is described by formulas - or it is not TOE. What is the difference between theory and reality in this case, if they are absolutely equivalent?
Max claims that in the case of the TOE, mathematics does not describe reality, and mathematics is reality . If you suddenly disagree, the reverse would mean that there are equations with their solutions, there is exactly the same world, which completely obeys the specified formulas, but is also real . In this case, the words “ also real ” are purely verbal baggage , which we have refused above, such a modern anima sola of physics. Thus, we have to admit that at the fundamental level, physics and mathematics are one and the same.
Max was not the first with similar ideas. Hawking himself posed the question: “ And what exactly does the flame breathe into these equations, creating the universe? " "
If we said that our universe is special because it exists , we would again be thrown a step back to the concept of “anima sola”. No, nothing blows flame into our formulas. It would be strange if all the axiomatic systems of mathematics would be divided into two unequal classes: systems for which there are universes and systems that are not lucky. This contradicts the whole hypothesis of the mathematical universe.
All this can be explained only in this way: if there is no anima sola, then all axiomatic systems are equal and the universe corresponds to each axiomatic system. Yes, most likely, most systems are trivial, and, perhaps, most axiomatics do not give an opportunity to develop (that is, appear in solutions) to complex, non-trivial systems and, especially, life.
“Physics on the contrary” is still waiting for its future researchers. I would give dearly to find out whether our universe is the simplest of those where intelligent life is possible or not.
Interestingly, after the first step (TOE has no baggage), the second step (mathematics and physics are the same) and the third step (each axiomatics creates the universe) was forced. That's how far we got.
Why does the universe even exist?
Answer: because it can exist.
When did these structures arise and why did they arise?
Mathematical structures do not exist in time and space. They just exist.
Are we emulating?
Not. The existence of mathematical structures does not require any machine that “calculates” them. The number 19 is simple regardless of whether or not there is a computer that all the time trying to divide it in a loop, checking for simplicity
How can we postulate something that we fundamentally cannot verify? Max expects this criticism. In fact, this is not the first time we do this. We have long been accustomed to the multiverse concept.
At level 1, we are talking about areas of the Universe that are so quickly moving away from us due to expansion, that they will never again be in causal communication with us. However, not a single cosmologist will turn his tongue to say that there is nothing there, because we cannot go there.
At level 2, we speak of other “bubbles” in the theory of eternal inflation, where, possibly, with the same laws of physics, other initial conditions and other physical constants
Level 3 is formed by the alternative multiverse universes interpreted by Everett . This will be a separate article.
We are forced to accept the existence of level 4 , corresponding to other mathematical universes, which we are only to study (theoretically).
Formulas and Luggage
What it is? It is unlikely that this formula tells you something. And if I write it like this:
Then you immediately recognize Newton's law in it. Of course, both formulas are equivalent, we just got used to the fact that force is denoted by F, mass m, moreover, we mean that it happens in three-dimensional space, that the bodies have coordinates, and so on. That is, the theory has two components: formulas and bla-bla around them. Max calls the second component verbal baggage .
Consider the tree of existing theories:
')
At the bottom is a sociology, where there are almost no formulas, but many words. Gradually moving upward, we meet with increasingly complex mathematics. But words are getting worse and worse: try to figure out what time is from a scientist who is engaged in fundamental physics. It is obvious to you that time is a sequence of events and it flows forward . The more you know and the deeper you go, the less it becomes obvious. The description of what time is, more and more, collapses to the fact that time is the letter t , which participates in such and such equations.
So, Max notices that:
As one moves toward an increasingly fundamental level, mathematics becomes more and more complex, and baggage begins to degenerate more and more. In the limit, assumes Max, TOE (Theory of Everything) has no baggage . So, TOE consists only of formulas .
This is the first ingredient. Remember it.
Physics “On the contrary”
How is that even possible? Physics is trying to find equations for our world, based on observations and experimental data. Max proposes to consider “Physics on the contrary” - “ Physics from Scratch ” - you set the equations, what kind of world do you get?
We can set the laws of the world ... well, for example, the game "life". Can we do without a verbal description? How, for example, to say that the space of cells is two-dimensional? Through the equations, by indicating the power law, how quickly the number of cells grows no further than N. Another example, the string theory equations converge only if the dimension of space is 10, 11, or 26. Perhaps, first, to formulate physics axiomatically seems complicated, but mathematicians have done well in creating axiomatic theories (and worlds). Take, for example, Peano's axioms . These are pure formulas, it does not explain what a “number” is, what “add” or “multiply” is.
Description vs Equivalence.
What do we have? We have (will) a TOE describing ALL of the things.
Just a second ... And what does “describing” mean? Here, for example, mechanics describes the movement of bodies. But we know that all this is possible thanks to a bunch of simplifications: bodies are not material points, there is air resistance, friction, and so on. There are formulas that describe reality, but we know that the real world is different from the ideal one described by formulas.
But in the case of TOE it is not: any, absolutely any physical aspect of reality is described by formulas - or it is not TOE. What is the difference between theory and reality in this case, if they are absolutely equivalent?
Max claims that in the case of the TOE, mathematics does not describe reality, and mathematics is reality . If you suddenly disagree, the reverse would mean that there are equations with their solutions, there is exactly the same world, which completely obeys the specified formulas, but is also real . In this case, the words “ also real ” are purely verbal baggage , which we have refused above, such a modern anima sola of physics. Thus, we have to admit that at the fundamental level, physics and mathematics are one and the same.
Formulas and Flames
Max was not the first with similar ideas. Hawking himself posed the question: “ And what exactly does the flame breathe into these equations, creating the universe? " "
If we said that our universe is special because it exists , we would again be thrown a step back to the concept of “anima sola”. No, nothing blows flame into our formulas. It would be strange if all the axiomatic systems of mathematics would be divided into two unequal classes: systems for which there are universes and systems that are not lucky. This contradicts the whole hypothesis of the mathematical universe.
All this can be explained only in this way: if there is no anima sola, then all axiomatic systems are equal and the universe corresponds to each axiomatic system. Yes, most likely, most systems are trivial, and, perhaps, most axiomatics do not give an opportunity to develop (that is, appear in solutions) to complex, non-trivial systems and, especially, life.
“Physics on the contrary” is still waiting for its future researchers. I would give dearly to find out whether our universe is the simplest of those where intelligent life is possible or not.
Answers to some questions
Interestingly, after the first step (TOE has no baggage), the second step (mathematics and physics are the same) and the third step (each axiomatics creates the universe) was forced. That's how far we got.
Why does the universe even exist?
Answer: because it can exist.
When did these structures arise and why did they arise?
Mathematical structures do not exist in time and space. They just exist.
Are we emulating?
Not. The existence of mathematical structures does not require any machine that “calculates” them. The number 19 is simple regardless of whether or not there is a computer that all the time trying to divide it in a loop, checking for simplicity
And is this generally, like - science or fantasy?
How can we postulate something that we fundamentally cannot verify? Max expects this criticism. In fact, this is not the first time we do this. We have long been accustomed to the multiverse concept.
At level 1, we are talking about areas of the Universe that are so quickly moving away from us due to expansion, that they will never again be in causal communication with us. However, not a single cosmologist will turn his tongue to say that there is nothing there, because we cannot go there.
At level 2, we speak of other “bubbles” in the theory of eternal inflation, where, possibly, with the same laws of physics, other initial conditions and other physical constants
Level 3 is formed by the alternative multiverse universes interpreted by Everett . This will be a separate article.
We are forced to accept the existence of level 4 , corresponding to other mathematical universes, which we are only to study (theoretically).
Source: https://habr.com/ru/post/443894/
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