Difference Between Special & General Relativity

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SUMMARY

The discussion clarifies the fundamental differences between Special Relativity (SR) and General Relativity (GR). SR, characterized by the constant speed of light and the equation E=mc², applies to scenarios where gravity is negligible, resulting in flat spacetime. In contrast, GR addresses the influence of gravity on spacetime, which is curved. The mathematical complexity of GR necessitates advanced skills such as multi-variable calculus and tensor calculus, while SR can be understood with high school algebra.

PREREQUISITES
  • Understanding of Special Relativity concepts, including E=mc²
  • Basic knowledge of spacetime and its properties
  • Familiarity with high school algebra for SR
  • Advanced mathematics, including multi-variable calculus and tensor calculus for GR
NEXT STEPS
  • Study the derivation of Lorentz transformations in Special Relativity
  • Explore the mathematical foundations of General Relativity, focusing on differential geometry
  • Research the twin paradox and its implications in Special Relativity
  • Learn about non-linear partial differential equations relevant to General Relativity
USEFUL FOR

Students of physics, mathematicians, and anyone interested in understanding the complexities of relativity theories, particularly those pursuing advanced studies in theoretical physics or applied mathematics.

Jaami M.
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Nugatory said:
This idea is one of the essential concepts behind Special Relativity, so if you're comfortable with it you're well-positioned to start learning SR.
So what is the difference between the two? Special Realitivity and General Relativity.
 
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Here goes (had to try it) ;)

Special: speed of light, E=mc2
General: gravity
 
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m4r35n357 said:
Here goes ;)

Special: speed of light, E=mc2
General: gravity
Thank you
 
Jaami M. said:
what is the difference between the two? Special Realitivity and General Relativity.

SR only deals with situations in which gravity is not present or can be neglected; in such situations, spacetime is flat, or can be approximated as being flat.

GR deals with situations in which gravity is present and cannot be neglected, and spacetime is curved.
 
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PeterDonis said:
SR only deals with situations in which gravity is not present or can be neglected; in such situations, spacetime is flat, or can be approximated as being flat.

GR deals with situations in which gravity is present and cannot be neglected, and spacetime is curved.

And, if OP is wondering about why the names are what they are...

The case in which gravity is not present or can be neglected is a special case (curvature is zero) of the more general theory that works for all values (zero or non-zero) of the curvature.
 
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Although not directly related to the question, OP may also be interested in the relative difficulty of the math behind the two theories.

High school algebra can get you to a decent understanding of SR: derivation of Lorentz transforms from Einstein's postulates; calculation of spacetime intervals and proper time along the worldlines of objects moving at constant relative velocities; able to explain the elementary "paradoxes" such as pole-barn, bug-rivet; the various approaches to the twin paradox.

GR requires multi-variable calculus, differential geometry, tensor calculus, solving some of the most challenging non-linear partial differential equations you'll ever encounter. There's close to a decade of high school and college math between SR and GR.
 
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