Fractional spacetime, dimension equation

In summary, the conversation discusses the possibility of using fractional derivatives in General Relativity and the existence of a local group symmetry ##SO(3-\epsilon,1+\epsilon)##. However, there is concern over the sensibility of using fractional dimensions for Lie groups such as SO(p,n). More clarification and explanation is needed to fully understand and discuss this concept.
  • #1
jk22
729
24
Suppose we use fractional derivatives (https://en.m.wikipedia.org/wiki/Fractional_calculus) in GR, hence we have a local group symmetry ##SO(3-\epsilon,1+\epsilon)## does any reference exist about an equation for ##\epsilon## ?, since it could depend on coordinates too.
 
Physics news on Phys.org
  • #2
Woah there Tex! Fractional derivatives is one thing (a purely algebraic concept). Fractional dimensions is another (ah la fractal geometry). But I don't think you can sensibly talks about fractional dimension parameters for Lie groups such as SO(p,n). If you wish to then you need to go into the lengthy coherent exposition of exactly what you mean but that, including explaining whether you're still even talking about a group much less a Lie group.
 
  • Like
Likes WWGD

1. What is fractional spacetime?

Fractional spacetime is a theoretical concept that suggests that the dimensions of spacetime may not be whole numbers, but instead may be fractional or non-integer values. This idea has been explored in various theories, such as loop quantum gravity and string theory.

2. How does fractional spacetime differ from traditional spacetime?

Traditional spacetime is described by four dimensions: three dimensions of space (length, width, and height) and one dimension of time. However, fractional spacetime proposes that these dimensions may not be whole numbers, leading to a more complex understanding of the structure of the universe.

3. What is the dimension equation in fractional spacetime?

The dimension equation in fractional spacetime is a mathematical expression that describes the number of dimensions in the universe. It is often represented as D = DS + DT, where D is the total number of dimensions, DS is the number of spatial dimensions, and DT is the number of temporal dimensions.

4. How is fractional spacetime related to quantum mechanics?

Fractional spacetime is closely related to quantum mechanics, as it is often explored in theories that attempt to reconcile the principles of quantum mechanics with those of general relativity. It is believed that understanding the fractional nature of spacetime may help to bridge the gap between these two fundamental theories of physics.

5. Is there any evidence for fractional spacetime?

Currently, there is no direct evidence for the existence of fractional spacetime. However, some theories and mathematical models have been proposed that incorporate fractional dimensions, and these have been used to make predictions that have been tested in experiments. Further research and experimentation are needed to fully explore the concept of fractional spacetime.

Similar threads

  • Beyond the Standard Models
Replies
0
Views
1K
  • Beyond the Standard Models
Replies
2
Views
2K
  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
3
Replies
93
Views
4K
Replies
24
Views
974
Replies
9
Views
1K
  • Special and General Relativity
Replies
16
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
840
  • Special and General Relativity
Replies
23
Views
3K
  • Special and General Relativity
Replies
8
Views
901
Back
Top