# Special and General relativity

## Main Question or Discussion Point

I know this is a stupid question, but my reference gave me too much information on what those two are, causing me a load of confusion. What is the difference between special relativity and general relativity? Can someone maybe try to simplify that? I know most of it already, but I just need a simple one. For future explanation.

Related Special and General Relativity News on Phys.org
SR deals with inertial frames (non accelerating). GR is fundamentally a theory of gravity - both involve time dilation. In SR the difference between clock rates is determined by the relative velocity between the observer and some other frame in uniform motion wrt to the observer. In GR time dilation is related to the difference in gravitational potential - clocks run slower when they are at a lower gravitational potential. The two dilations correspond however - when a clock is centrifuged the clock rate is equal to what one would calculate if they used the tangential velocity - or if they used the GR formula for the increased inertial force.

Chronos
Gold Member
Yogi gave the biggest part of it. Some of the finer points are arguable, but to say SR is GR without gravity is right on the mark.

pervect
Staff Emeritus
Demiwing said:
I know this is a stupid question, but my reference gave me too much information on what those two are, causing me a load of confusion. What is the difference between special relativity and general relativity? Can someone maybe try to simplify that? I know most of it already, but I just need a simple one. For future explanation.
Special relativity considers space-time to be a flat 4 dimensional space (3 space + 1 time).

In this 4-d space-time, there exists a quantity called the Lorentz interval which is the same for all observers.

General relativity considers space-time to be a curved 4-dimensional surface - mathematically it's a manifold. Any manifold can be considered to be locally flat (consider the surface of the earth, for instance - the earth is curved, but it looks flat. (Sharp points of inifinte curvature are not allowed in the mathematics of manifolds. With large but finite curvature, the region of apparent flatness is very small, but as long as the curvature is finite the apparently flat region is there).

The locally flat region of space-time in GR admits the same invariant Lorentz interval as the flat space-time of special relativity. The difference in GR is that space-time is only locally flat, while in SR it's globally flat.

Chronos
Gold Member
Infinite curvature is not just a problem with manifolds.. in GR it results in those pesky things called singularities. Not disagreeing with your point, just attempting to clarify. Your comment on local and globally invariant Lorentz intervals caught my attention. I have this vague feeling there is a deeper issue, but can't put my finger on it right now. That just bugs me to no end. Guess I will be spending some quality time trying to figure that out tomorrow.

jcsd