/sci/ - Science & Math

>>12262537
ofc

>>10682754
There's no such thing as a global inertial reference frame. This makes arguments that rely on conservation of momentum and conservation of energy easy to get tripped up by.
To explain: let's say you want to argue (A) based on conservation of momentum. To make that kind of argument you first choose "inertial" coordinates on space-time and then argue that the momentum of the block before and after it passes through the portal, in those coordinates, is equal. I think the intuitive thing is to use the coordinates "as shown in the picture"; these coordinates, in particular, are discontinuous at the portal, where as you pass through the plane of the portal there is a sudden rotation, translation, and velocity shift in your coordinates.
Alternatively, someone else might come along and choose coordinates that go smoothly through the portal, but are discontinuous somewhere between the left and right sides of the picture. To be specific, choose coordinates on the left side of the picture such that the orange portal is not moving with respect to us, and on the right side choose coordinates "as shown" (i.e., such that the blue portal is also not moving). There's no reason to believe these coordinates are any "fundamentally" worse than the ones that are discontinuous at the portal, but everyone agrees that in these coordinates the block does something like (B) (since on the left side we're seeing it fly into the orange portal).
How does one distinguish between these two cases? The fundamental difference between these coordinate systems is that in the latter case, the block does not pass through the region of space-time where our inertial coordinates are discontinuous, so classical conservation of momentum should hold. In the former case, there's no reason to expect that conservation of momentum should hold, since we haven't made a choice of coordinate system encompassing everything interesting about the system that looks anything like classical Newtonian physics.