Recent content by jcsd

Oops in fact I've made a mistake and the puzzle isn't quite as interesting. the answer is just as close to c as possible.

I like the lateral thinking but not the answer I was thinking of!

Hello I have not posted here for a while, but just wanted to post this puzzle I devised. Was posted on Reddit, but no takers. I think the solution is interesting. The Puzzle You are flying around in space and you see your friend Steve chilling in an inertial frame in his own spaceship and you...

I think the usual definition is in terms of the standard coordinates, my point though is that the standard definition still represents a non-arbitrary invariant.

It's invariant in the sense that the maximum amount of proper time along a past-directed timelike curve at any given event is the age of the Universe at that event. This definition of the age of the Universe doesn't require you to define coordinates.

The Alcubierre drive requires negative energy regardless of whether the global velocity of the warp bubble is below c.

If V is a finite-dimensional real vector space than any linear function from V to R is a one-form. An example of a one-form would be v*(w) = <v,w> and an example of a (higher rank) tensor would be the metric tensor g(v,w) = <v,w>. The definition as you state it is not quite sufficient t...

For a vector space V over K the one-forms are the set of all linear functionals p:V->K. The space of all the one-forms P is called the (algebraic) dual vector space of V We can define vectors in V as linear functionals v:P->K using v(p) = p(v), for real finite-dimensional vector spaces. A...

The problem is that the singularities aren't actually points in spacetime and you want to be able to define a black hole generically

I completely missed the analogy with matrix rank. I suppose the metric must always be rank 4 for this meaning of rank as it has a non-zero determinant. I also would guess that the rank of a tensor field could change from point to point, for example in any tensor field that was zero at some...

Rank = n+m. The tensors of a tensor field will always be of the same type. For example you wouldn't have field that was vector-valued at some points and scalar-valued at others.

I would actually bring up an interesting point: there is actually a massive element of unpredictability in the framework of general relativity. For any given set of initial conditions (though in some cases even the concept of initial conditions can become tricky), there are actually an infinite...

Sure on a manifold where some geodesics are closed(?) and some are not this can't be true

There's good reasons within the limits of big bang theory to say that the Universe had a beginning. The reason is , if you make certain assumptions (that most people would find to be reasonable, e.g. no negative energy density), when you trace the history of any object in the Universe back in...

Gravity in general relativity is modeled as the curvature of spacetime. Sufficiently faraway from the black hole's event horizon where the physics are close enough to be being Newtonian and when we can talk about the force due to gravity in terms of the local acceleration required to keep an...