Mathematics of The Multi Dimensional Universe

In summary, the conversation discusses the mathematics behind multiple dimensions and whether or not mathematics allows for the existence of more than four dimensions. It is noted that in theoretical mathematics, any finite or infinite number of dimensions can exist and be at right angles to each other. The question of multiple dimensions is considered a physics question and there are examples in physics, such as the decomposition of a signal into its frequencies, that use infinite dimensional space. It is also mentioned that multidimensional space is common in mathematics and can be used to describe physical theories. Ultimately, the addition of new information to a tuple can increase the dimension, but a meaningful metric may not always exist.
  • #1
What are the mathematics behind multiple dimensions? Does mathematics allow for the existence of more than four dimensions? What allows the ability to possesses more that four dimensions, if there is already proof? I looked around, but I didn't find much by way of the answer I was looking for.
 
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  • #2
Yes, mathematics allows as many dimensions as you desire. Even an infinite amount.
 
  • #3
Suppose you agree that you can add time to the known physical (x,y,z) dimensions to get (x,y,z,t). What stops you from adding more: (x,y,z,t,a,b,c,d,...)? You might object to the idea that they can all be at right angles to each other, but that is just because you are trying to imagine it within a 3 (or 4) dimensional space. That leads to the question of whether so many dimensions can all be at right angles to each other. The answer is yes. In theoretical mathematics, angles can be defined using "inner products" and then there are examples where there can be any finite or even infinite number of dimensions, all at right angles to each other (see https://en.wikipedia.org/wiki/Orthonormal_basis )
 
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  • #4
The question of multiple dimensions that you are posing is a physics question. As others have noted there is nothing in mathematics that restricts you to any number of dimensions.
 
  • #5
mathman said:
The question of multiple dimensions that you are posing is a physics question. As others have noted there is nothing in mathematics that restricts you to any number of dimensions.
But even within physics, the decomposition of a signal into its frequencies is a good example of using an infinite dimensional space.
 
  • #6
Cool, thanks FactChecker! That's the simplistic answer I was looking for :D
 
  • #7
Multidimensional space are very common in mathematics. Part of models describe also physical theories, as example the Hilbert spaces that are infinite dimensional for the quantum mechanics or Calabi Yau manifolds in string theory ...
 
  • #8
In fact, any time a new bit of information is added to a tuple and that information was not already determined by the prior information in the tuple, the dimension has been increased. If I was keeping track of an object, I might include its position at a time, it's weight, its dimensions, etc. (x_position, y_position, z_position, time, mass, height, width, length). This is a 8-dimensional state-space. So you can certainly make high dimensional state-spaces with ease. Things get more complicated if you want a metric for that space. There might not be a meaningful metric.
 

1. What is the "Mathematics of The Multi Dimensional Universe"?

The "Mathematics of The Multi Dimensional Universe" is a theoretical framework used to describe and understand the universe beyond the three dimensions of space and one dimension of time that we experience in everyday life. It involves using mathematics to explore and explain higher dimensions, such as the fourth dimension and beyond.

2. How many dimensions are there in the universe according to this theory?

In this theory, the universe is believed to have multiple dimensions, potentially infinite. However, the exact number of dimensions is still a subject of debate and research in the scientific community.

3. How does mathematics play a role in understanding higher dimensions?

Mathematics is a powerful tool for understanding and describing the physical world, including higher dimensions. It provides a language and framework for visualizing and modeling complex concepts and phenomena that cannot be directly observed. Through mathematical equations and models, scientists can make predictions and test theories about the multi dimensional universe.

4. Are there any real-world applications of this theory?

While the multi dimensional universe theory is still largely theoretical, it has potential applications in fields such as quantum mechanics, string theory, and cosmology. It could also have practical implications for technologies such as teleportation and time travel, although these are currently only speculative.

5. How can we prove the existence of higher dimensions?

Proving the existence of higher dimensions is a challenging task, as these dimensions cannot be directly observed. Scientists use indirect evidence and mathematical models to support the existence of higher dimensions and their impact on the observable universe. Further research and experimentation in areas such as quantum mechanics and cosmology may provide more evidence for the existence of these dimensions.

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