How do you square the following notions?
a) dark matter does not interact with measurable matter
b) proof of dark matter's existence derived by the measurable, relative, interaction of mass and energy
a) dark matter does not interact with measurable matter
b) proof of dark matter's existence derived by the measurable, relative, interaction of mass and energy
Regular matter interacts via the four forces: strong interaction, weak interaction, electromagnetism and gravity.
Strong interaction: binds fundamental particles together to make atoms. In every day terms, it’s what makes mass, mass.
Weak interaction and electromagnetism: causes radioactive decay and EM radiation (photons). In every day terms, it’s how we get light, radio, cell phones, etc. Also nuclear power.
Gravity: attraction of mass across great distances. It’s how we stick to the earth and why the earth circles the sun.
There are particles that don’t act through forces but are affected by them:
Photons don’t have mass so don’t cause gravity but are affected by it.
Neutrinos don’t have an electromagnetism effect so they can’t be seen at all only measured in very rare weak interactions.
Dark matter: No strong interaction so not a part of atoms. No EM interaction so we can’t see it blocking light. No weak interaction that we have observed. However they do cause gravity, so we can see that. All of the proofs of existence are via gravity and relate only to mass — we can’t observe any other properties.
However, good news: several possible dark matter particles have been proposed, all of which interact very very slightly non-gravitationally as well. Practically all such proposals start with a particle physicist trying to repair some problems in the standard model of particle physics. When such proposed particles are decent candidates for cold dark matter, astrophysicists and physical cosmologists take note.
One family of candidates are the WIMPs, which feel the weak force, and so can produce a recoil reaction in atomic nuclei, and we can spot such recoils produced by neutrinos sourced by the sun or nuclear reactors. Galactic dark matter doesn't have a "bright spot" like the sun or the Super Kamiokande reactor, so distinguishing recoils from Brownian motion is tricky, since a WIMP may enter a recoil-detector from any direction. The density of WIMPs (if they exist) is much lower than the neutrinos streaming out of SK reactor or the sun, so there will be fewer recoils in the first place. WIMPs are generally found in various attempts to explain chirality in the standard model.
Another family of particle-physics-problem-solving dark matter candidates are the axions which feel both the strong and weak forces, and axions can be smashed up into photons (or formed from photons) in a very strong magnetic field.
There are several much less popular hypothesized particles that can be detected in principle because they feel one of the non-gravitational fundamental forces. This does not mean it is easy to detect them, though: whatever the microscopic makeup of dark matter, it is very sparse inside the solar system, and galactic dark matter reaches Earth with relatively low momentum, so even when it does interact with ordinary matter on Earth, it won't produce a large reaction.
> orbiting with crazy speeds around our planet
Galactic dark matter particles must move with the rotation of the galaxy, and for the most part so does our whole solar system, so the speeds will be slow, and in particular not at all relativistic. Also, because dark matter forms a dust where the individual bits of dust have extremely low mass, they will not be drawn into orbit around the Earth. The dark matter particles' orbits around the centre of the galaxy will be very slightly perturbed by the Earth, though.
They do have momentum though, and their momentum flux is encoded in the stress-energy tensor, which up to constant factors forms the right-hand-side (the "source" or "matter" side) of the Einstein Field Equations of General Relativity.
So photons are a source of curvature, and thus to say that they "don't cause gravity" is wrong.
This has been known since the late 1920s, and was made very clear in some correspondence between Einstein and Bohr on the topic of "Einstein's box" (box of light).
See e.g. the following subsection (and the figure it refers to) https://en.wikipedia.org/wiki/Bohr–Einstein_debates#Einstein...
A more extreme case is https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)
In flat spacetime, we can alternatively start by considering the special-relativistic dispersion equation, E^2 = (mc^2)^2 + (pc)^2, m being intrinsic mass and p being momentum. Usually you see this as E = mc^2, taking square roots and considering the centre of momentum to be fixed. When you let a beam of light (or even a photon) travel across a set of coordinates, rather than keeping it fixed at some coordinate (e.g. the origin), p is nonzero, even though m is always zero. Since (pc)^2 is positive, so is E^2, so even though light is massless, it has (frame-dependent) energy. Indeed, being more formal, one says that light has momentum-energy. A further relationship E = hf, h being Planck's constant and f being the frequency of the beam of light (or just a photon), also underlines this: E = hf = pc^2, so the momentum of light relates to it's frequency, or alternatively it's wavelength (as f = c / lambda, where lambda is the wavelength). Light's frequency is observer-dependent because of relativistic doppler effects or equivalently light's wavelength is observer-dependent because of relativistic length contraction. (And this should not be surprising as even in high school physics you will have learned that kinetic energy is a frame-dependent dependent quantity. Relativistic kinetic energy is E.)
When we add gentle curvature and use suitable coordinates, E is simply promoted into the time_time component of the stress-energy tensor. (Gory details if you look up "comma-goes-to-semicolon rule", which you can find discussed here https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll... or in most decent textbooks on General Relativity. Carroll prefers to call it the energy-momentum tensor instead of the stress-energy tensor; they're the same thing.)
Since any nonzero component of the stress-energy tensor serves as a source of curvature, then light must generate curvature.
You were half-right though: photons do indeed respond to curvature.