Things that do not depend on the choice of Cauchy surface

In summary, "things that do not depend on the choice of Cauchy surface" are properties or quantities in physics that remain constant regardless of the specific Cauchy surface chosen. Identifying these things is important because it allows for a more general understanding of physical systems and their behavior. Examples include energy, momentum, and electric charge. We can determine if something does not depend on the choice of Cauchy surface by analyzing the governing equations and laws. While these things may remain constant, they can still change over time due to interactions and transformations within the system.
  • #1
naima
Gold Member
938
54
A Cauchy surface is a 3d spacelike slice of spacetime.
Could you read the definition (17) p18
the author says that "one can proove that ##\sigma## does not depend on the choice of the Cauchy surface because the functions obey the law of motion."
Could you elaborate?
Thanks

Could anyone add "h" in the title (choice)?
 
Physics news on Phys.org
  • #2
Sorry
I found the proof several lines below!
 

FAQ: Things that do not depend on the choice of Cauchy surface

What are "things that do not depend on the choice of Cauchy surface"?

"Things that do not depend on the choice of Cauchy surface" are properties or quantities in physics that remain constant regardless of the specific Cauchy surface (a hypersurface used to define the initial conditions of a physical system) chosen in a particular problem or scenario.

Why is it important to identify things that do not depend on the choice of Cauchy surface?

Identifying things that do not depend on the choice of Cauchy surface is important because it allows us to understand and analyze physical systems without being limited by the specific choice of initial conditions. It also helps us to make more general and universal predictions about the behavior of physical systems.

What are some examples of things that do not depend on the choice of Cauchy surface?

Examples of things that do not depend on the choice of Cauchy surface include energy, momentum, and electric charge. These physical quantities remain constant regardless of the specific Cauchy surface chosen, allowing us to make predictions and calculations about their behavior in various scenarios.

How do we determine if something does not depend on the choice of Cauchy surface?

We can determine if something does not depend on the choice of Cauchy surface by analyzing the equations and laws that govern the behavior of the physical system. If a property or quantity remains constant regardless of the specific Cauchy surface chosen, then it can be considered as something that does not depend on the choice of Cauchy surface.

Can things that do not depend on the choice of Cauchy surface change over time?

Yes, things that do not depend on the choice of Cauchy surface can change over time. For example, the total energy of a closed physical system may remain constant regardless of the choice of Cauchy surface, but the distribution of energy within the system can change over time due to interactions and transformations.

Similar threads

A Can a Null Surface Satisfy the Requirements for a Cauchy Surface?
Replies
13
Views
2K
A Is delayed choice remote entanglement of photons derived from TDSE?
2
Replies
58
Views
3K
I Show Maxwell's Eqns. on a Cauchy Surface (Wald Ch. 10 Pr.2)
Replies
1
Views
1K
B Further Understanding Simultaneity Conventions
2
Replies
51
Views
3K
BRS: euclidean surfaces a la Cartan
Replies
3
Views
1K
A Interior volume of a black hole
Replies
23
Views
3K
Measuring Height of Meniscus in Capillary Action
Replies
1
Views
3K
Surface roughness in 2D sinusoidal corrugation
Replies
1
Views
3K
Computing Curvature: 2D Plane & Axi-Symmetric Surfaces
Replies
1
Views
2K
Classical I need some self-contained introductory books on Fluid Mechanics
Replies
19
Views
4K

Hot Threads

Recent Insights

Back
Top