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Does anyone have any questions on Special Relativity?

... or can tell me where to find some? Just some simple questions on using the time dilation, length contraction and mass formula

I need a bit of practise but I can't find anything on the internet (just FAQs) and theres only a few questions in the book i'm using.

It's for the AQA turning points in physics a2 module but I'd rather not use the questions from the past exam papers just yet.

Thanks! :smile:
an interesting 1 to try is the twin paradox

1 twin stays on earth for 10 years whilst other sets of on journey at .995c

if u do special relativistic calculations on this u find the first one ages 10 years whilst other is like 0.6 days off having aged just 1 year!!!
Reply 2
Avatar for john!!
john!!
1
Why not just do the past exam papers, and then do them again later with different coefficients? what kind of questions?
Nickf
Does anyone have any questions on Special Relativity?)
Plenty, they just all involve general relativity too :p:
Reply 4
Avatar for Mehh
Mehh
8
AlphaNumeric
Plenty, they just all involve general relativity too :p:

How does one make the geometric extensions to space time? Cartessian coordinates, spherical polar and cyinderical polar all up until now are the coordinate spaces I have learnt. However they all work on the principle of having orthogonal vectors to define each direction, hence each position is unique (bar the singularity at the origin, and the z axis). However in Riemannian space, we lose the concept of parallel lines, which I assume leads to a simliar break down of the concept of orthogality.
How is space time defined in a unique way.
Is it defined as a maping onto a Euclidian geometric space and then redefine straight lines as something else, specifically geodesics?
latentcorpse
an interesting 1 to try is the twin paradox

1 twin stays on earth for 10 years whilst other sets of on journey at .995c

if u do special relativistic calculations on this u find the first one ages 10 years whilst other is like 0.6 days off having aged just 1 year!!!


... but thats not the paradox, that's just what happens in special relativity. The paradox is that to each twin, the other's watch appears to be going more slowly, to for each twin, the other ages more slowly: but they cant BOTH be younger than the other one!

it turns out special relativity can't handle the situation of the twin paradox as initially both twins are in the same frame of reference and then one twin (which twin doesnt matter - it depends on whose frame YOU are in...) has to ACCELERATE out of this frame into another frame. Special Relativity cant handle this, general relativity can. It turns out as latentcorpse said: the twin who stays on Earth ages faster so is older (because the 'proper time' is the time in the Earth twin's frame... or something...)
Mehh
How does one make the geometric extensions to space time? Cartessian coordinates, spherical polar and cyinderical polar all up until now are the coordinate spaces I have learnt. However they all work on the principle of having orthogonal vectors to define each direction, hence each position is unique (bar the singularity at the origin, and the z axis). However in Riemannian space, we lose the concept of parallel lines, which I assume leads to a simliar break down of the concept of orthogality.
How is space time defined in a unique way.
Is it defined as a maping onto a Euclidian geometric space and then redefine straight lines as something else, specifically geodesics?
You define a metric, which tells you how to measure length at any given point in space time (bar a few singularity points).

For instance, the metric which describes the Schwarzchild black hole solutions is

ds2 = -(1-[2m/r])dt2 + (1-[2m/r])-1dr2 + r2(dθ2+sin2θ dφ2)

From this you get a Lagrangian

L = -(1-[2m/r])(t')2 + (1-[2m/r])-1(r')2 + r2((θ')2+sin2θ (φ')2)

where t' = dt/d(tau), tau being 'proper time'.

From that point on it's down to using things like the Euler-Lagrange equations to get equations in t', r' etc and using a few other results from calculus of variation (ie, since L is independant of tau, L is constant).

Once you're given ds2, you can write down the metric gab, for instance grr would be the coefficent of dr2 in ds2, while gφt would be the efficent of dφdt (the Schwarzchild metric is static, so doesn't have such a term but the Kerr metric for spinning black holes does).

Once you've got gab you can start working out things like curvature, using a bunch of formulas.

The initial derivation and construction of GR is very rigorious, and much more subtle than my first GR course made out (which was really only a crash course in GR), but if you aren't bothered about that and just happy to use the results, it's not too bad (at least when you start :p: ).
Reply 7
Avatar for Nickf
Nickf
OP
My topic got confusing.

I ended up just doing some of the exam questions I had.

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