Special and General relativity

[Demiwing]

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.

 

[yogi]

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]

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]

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]

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]

Basically spe cial relativyt says the laws of physics are the same in certain frames of refrence known as inertial or Lorentz frames (or in other words it says not only does there exist a frame of refrence where the laws of physics as stated hold, but any observer traveling with constant velocity in this frame also defines a frame for which the laws of physics are the same). Genreal relativity in the other hand says that the laws of physics are the same in all reference frames. This is why they are called the special and general theories; general relativity deals with relativity between all sets of refrence frames, whereas special relativity deals with relativity between a special set of reference frames, special relativity therefore is just a special case of genreal relativity.

By far the easiest way to tackle relativity is in terms of the geometry of spacetime, in special relativity we only deal with flat spacetime (a flat space is one where Euclid's parallel postulate applies, though it's not necesssarily Euclidean, Minkowski spacetime is an example of a flat non-Euclidean space), but the genreality of the general theory means that we must consider a much wider classe of spacetimes than we would if we just limited ourself to flat spacetime (as pervect says these can be thought of as locally flat, i.e we can say there is a flat spacetime tangent to every point).

In special relativity gravity is a problem as it stops us from defineing a global Lorentz frame, which means we cannot treat gravity in special rleativty. Gravity does allow us to define a local Lorentz frame however (i.e. it allows special rleativty to be correct in in a local area, but as we saw earlier gemral relativity is a theory which allows special relativity to hold locally), so armed with the equivalence principle as well as just the principle of general relativty, we can treat gravity in GR.