My question was restricted to photons traveling through empty space. Didn't you mean to say "if the wavelength is much SMALLER than occluding objects"? If the medium is very large empty space, doesn't the photon travel in a straight line? Would there be an astronomy experiment that tests...
OK, and a "geodesic" is a shortest-path between two locations. So, what is a shortest-path? Path of null perturbation? I've seen Keplerian orbits described as following geodesic paths. At the foundation of all these path descriptions are coordinate systems necessary to talk about positions...
I'm familiar with lasers and beam divergence. The beam divergence is caused by focussing the beam through a narrow "waist". It's somehow similar to the diffraction you get if you have a coherent low-divergence beam and shine it on a tiny aperture (say 10 lambdas in diameter). You'll get a...
Can anyone explain why a photon seems to travel in a perfectly straight 3D line over unimaginable distances? What exactly defines a straight-line? The concept appeals to Cartesian coordinate space.
Is there any way to quantify the straightness of a photon path? Or, does the path taken by...
The thruster has to be able to deliver torque in order to change the direction the thruster jet is pointing in space. You wouldn't equip a jetpack with a single thruster jet for this very reason. So, let's make it a better jetpack design and allow pairs of torque-producing jets, two sets to...
Willem2 - Here's another thought experiment about flying due North in the northern hemisphere without any wind: At any given latitude, the atmosphere and the aircraft have inertia. Because the Earth is rotating, there is some component of inertia pointing out the right side of the aircraft...
Here is a concrete case to consider: A non-stop, great-circle flight from Denver --> New Delhi. If you plot this route out on a globe, you'll see it takes you right over the North Pole. What bearing do you fly to stay on a straight arc heading toward the North Pole? It's a 12 hour flight...
Algorithmic Geometry approach. This problem is straightforward if you know how to form generalized coordinate rotations (3D matrix rotators). The trick is to coordinate-rotate the entire problem so that the Line L stands perfectly vertical (Z-Axis-Aligned) in rotated space.
Inputs:
Line...
I like this approach for its simplicity and symmetry:
1. Normalize-Cross-Prod the directions of L1 and L2 to obtain the direction of their adjoining lineSeg dL
2. Extrude L1 along direction dL (= plane PL1)
3. Extrude L2 along direction dL (= plane PL2)
4. The endpoints of the shortest LineSeg...