Radiation pressure comes from the transfer of momentum from a photon to a massive particle. It isn't really the total Energy (E = hc/l) of the photon that provides the push, it's the momentum = h/l. Because of the way hc = constant in Setterfield terms, the energy and momentum of a photon are now bizarrely decoupled. A green photon in early days has no momentum compared to now, h being so much tinier than now. There is no c in the formula to counterbalance.
So there's less momentum to do the pushing. What has changed about the about the mass to be pushed?
The mass of a massive particle goes down with c squared back through time. There are two things we're going to do with the mass. One is accelerate it. That is, we're going to change its current momentum. The other is we're going to lift it some distance against the resistance of gravity until its new momentum is lost and it starts to fall back again.
Mass in the formula f = ma is a resistance to acceleration. It takes more force (torque) to get a fully-loaded 18-wheeler off the drag strip starting line than it does a motorcycle. Because of the low mass of early-universe particles, they're a snap to get moving.
You can isolate this property from what we call "gravitational mass." Out in the depths of space, everything is weightless but it still has mass. You smack into something, it resists acceleration according to its mass.
If you swat a fly (never mind how it got out there), it is accelerated rapidly away from you while you are microscopically accelerated in the opposite direction. You don't notice much acceleration because of your mass compared to the fly.
So, anyway, in the early c days, if a photon smacks into a smallish particle of matter, it sends it flying 11 million times better than in the same situation now. The photons have lost momentum inversely with c, but the massive particle has lost resistance to acceleration inversely with c squared.
That's right. The changes don't even cancel (a c-squared change the wrong way and a c change to mitigate). The problem is worse by another factor of c. That's what I was figuring earlier.
But I forgot something. The solar particles in question are in a strong gravitational field. Gravity is cancelling the mass difference. All of it. That's right. Gm = constant. We did that to keep orbits the same.
Now the photons have less swat to lift the gas particles, but the gas won't fly up much except for the fact there are 11 million times more photons banging into it. But against THAT, 11 million times more particles than now have the property of opacity in the first place so there's more to lift.
So now we got rid of the c-squared factor. We have 11 million more photons, each with almost the same energy as now, but tiny momentum compared to now.
One thing this means is the opacity doesn't red-shift the light very much when it eats the momentum. There isn't much to eat.
That in turn means that the "opacity" you get by adding a crazy number of "opaque" particles almost isn't opacity at all. The "opaque" particle absorbs the photon, re-emits a photon of almost the same wavelength as before and its own momentum is barely changed. Yes, there's a scattering effect but they're all still going to find their way out. This isn't doing its job.
That alone means there's still a problem and this isn't working, but let's never mind that just for now.
If we ignore the problems already noted with the low-momentum escape clause, you are perhaps in the clear if I'm keeping score accurately. The star doesn't have to swell too awfully much, maybe. Everything has nominally canceled.
I thought at first that we had lost the equivalence principle between inertial and gravitational mass here. That among other things is why a feather and a cannonball fall at the same speed on Earth in a vacuum's chamber. But that's probably hyperbole.
What has happened is that radiation pressure doesn't work the same in low-gravity environments across quantum jumps. If you go that way, that has to be an easily falsifiable prediction.
I suspect that we see radiation pressure events in astronomical objects, some of them under low gravity. Nebulae and so forth. Old supernova remnant puffs in the neighborhood of stars, maybe in the Magellanic Clouds, for instance. Perhaps different things farther out.
Thus, we could see the rules changing for low gravity radiation pressure if the rules did change. I suspect we would have noticed by now.
This mess just ain't workin' for me.
It makes things very different on Earth, too. Nothing really gets a lot of energy from absorbing a photon. Yes, there are a lot--11 million times--more photons to absorb, but you can't cancel one number with another one in this case.
Things look different than now. Everything then is pretty much one color, the "color" of a mirror. Every particle on Earth or in the sky that absorbs a photon re-emits almost exactly the same thing. Chlorophyll doesn't work. No photochemical reaction works the same as now. Plants starve. Eyes are blind, even though there are photons of the proper wavelength subspectrum to go around after all. The optical properties of everything on Earth are really screwed up.
You can't go there. But you already did.
This one I think an error. Opacity is not obtained by adding opaque particles, but by dissipating more photons by scattering and absorption (so opacity can be caused by lower density). You have described scattering correctly, but particles also absorb photons into their own kinetic energy without re-emitting them. Scattering changes photon trajectories including sending them back inward to cancel other photons; absorption converts them entirely into kinetic energy. Opacity is defined as the coefficient by which scattering and absorption reduce the photon output.
I think you're assuming that all photons "find their way out" as photons. No, they can turn into heat energy which is then convected outward and dissipated into local space; convection is an alternative mechanism to radiation. They can contribute to an increased internal equilibrial radiation pressure. And so on. The excess energy need not remain in the form of light.
The narrative by which you conclude the cancellations is correct in the broad outlines, but I believe the final cancellation is not "a strong gravitational field" but the massive particle's increased velocity, which increases its "resistance to acceleration" by the same degree as your cancellation.
I think this also answers your concerns about whether past radiation pressure process could be observed as different: they wouldn't be any different. If you think there would be an observable major change in radiation pressure please explain that a little better, thanks.