Stress Energy Components: 3 or 4 Densities?

In summary, there is a difference in the way the stress energy tensor is expressed in various sources. While it is usually shown as three densities over a space-like slice, Wikipedia's article on the spin tensor presents it as four-densities. This leads to the question of whether the three density representation is just an approximation. The conversation also highlights the importance of providing sources and not making statements that do not make sense.
  • #1
Ryan Rankin
4
0
I usually come across expressions for the Stress energy tensor showing them as three densities (normally over a space-like slice.
In wikipedia's article on the spin tensor, they clearly (it does not appear to be an error) both write about and express the components of the stress energy tensor as four-densities. Is the three density just an approximation then?
For example:
06db8c0990a297671e457be2a9e4ba13.png

I usually come across this as an integral over three-space.
 
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  • #2
Wikipedia is wrong. In fact the statement itself makes no sense whatsoever. You cannot get momentum at time t if you have integrated t out!

Also, please note that it is customary (and required!) to link to your sources. Others should not have to go through the process of finding something you talk about to verify what you have said.
 
  • #3
https://en.m.wikipedia.org/wiki/Spin_tensor
Apologies.
Thank you for your response, originally I had thought time would necessarily be explicit still as a limit of integration
 

Related to Stress Energy Components: 3 or 4 Densities?

1. What are stress energy components?

Stress energy components refer to the different types of energy and matter that make up the universe. These components include radiation, matter, dark matter, and dark energy.

2. What is the difference between 3 and 4 densities in stress energy components?

The difference between 3 and 4 densities refers to the number of components that are used to describe the universe. In 3 density models, only matter, radiation, and dark energy are included, while in 4 density models, dark matter is also taken into account.

3. How do stress energy components affect the universe?

Stress energy components play a crucial role in shaping the universe and its evolution. They contribute to the expansion of the universe, the formation of structures like galaxies and clusters, and the overall dynamics of the universe.

4. What is the significance of studying stress energy components?

Studying stress energy components helps us better understand the composition and behavior of the universe. It also allows us to make predictions about the future of the universe and its potential fate.

5. Can we observe stress energy components directly?

No, stress energy components cannot be observed directly. They can only be inferred through their effects on the universe, such as the expansion rate and gravitational interactions.

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