I once tried to model this problem by assuming a portal can be defined as the following mathematical relation:

A pair of portals, A and B is defined to be discs $\mathcal{D}_A$ and $\mathcal{D}_B$ such that for every point in $D_A$ there exists a bijective map to a point in $D_B$. More formally

$$\exists f : \forall x \in \mathcal{D}_A \& \forall y \in \mathcal{D}_B, f(x)=y \& f^{-1}(y)=x$$

Now assuming the mapping has circular symmetry. Then it is easy to show that there exists a fixed point c (the centre of the portals) such that

@DavidZ
http://physics.stackexchange.com/questions/27794/is-a-photon-fixed-in-spacetime

When doing some seemly naive minkowski spacetime diagrams (shown in next message), I am wondering whether the perception that the photon is moving is because it is indistinguishable (because a photon's worldline from an event only intersect the time axis of any observer once as shown in the diagram) and thus we cannot tell apart one photon worldine from another emitted from the worldline of the photon source (e.g. a lamp) and interpret that as the same photon being continuously travelling

(~4 hours later) I guess one of my confusion is the following extreme example of a doppler effect:

suppose there's another observer starts -5 ls before the origin of this diagram and there is a massless photon source (that was placed there at the vertex of that triangle of cones in the diagram) heading towards the observer (i.e. the t axis).

For every 1 ls, the source emits a photon.

From the diagram it is clear that 6 ls later at the coordinates (t,x)=(1.0) the observer will see the arrival of the light signals

@ACuriousMind
Now perhaps to me the only mystery is that I am not sure in general how to determine the size of the basis I need to solve some quantum problems

Suppose someone give me a black box. He then shine a light through it. An interference pattern is then projected onto a screen. How can I base on the interference pattern formed determine how many indistinguishable states I need in order to make a complete basis for calculating the probabilities?

(This is really another way to ask the question. How to determine the number of interfering states I need in order to model the problem ex…