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Yes. I should have said c=speed of electromagnetic waves *and* massless particles.

Momentum is defined as p = mv, where "m" is mass and "v" velocity, and Einstein's famous E=mc² also applies to photons. It is, therefore, meaningless to speak of a particle having a momentum but not mass. In fact it is just as we used to say (jokingly) "all vector, no force."

The gravitational force (or "pit" in timespace jargon) that is required to detectably affect the photon mass is much greater than anything we can create on earth. The force is much greater than even our sun's gravitational pull.

This is why the discovery of the gravitational lens (predicated by Einstein) proves that photons are subject to gravity and therefore must have mass, otherwise the GR formula E=mc² does not apply to photons.

So if all this sounds a little bit like "lawyering" it's because it is! Which is why we can say there are is always some doubt, and no absolutes, and no one understands it and there are always convenient "loopholes" or "angles" from which these issues can be handled, sometimes leading to completely different conclusions, yet all of them true!

Let me give you an example in optics. Optical designs can be "optimized" by a series of reiterations on a "subatomic" level, so to say, as minute changes in element specifications. This is where entry-level integral calculus comes in handy, because that's what integration is—minute adjustments where even complex exponential entities can be treated as linear regressions over very short intervals.

A perfect example of this is your eprception of these letters as being curves (such as letters c, s, q, p, etc.) when in fact they are shapes ahcieved by miniscule dots (and the distance between each two dots is simply a straight line) which under a micorscope would lose their smoothness and continuous appearance. In your eyes they are "integrated" into smooth and continuous complex curves.

and the same image reduced 10 times (size=10)

This is no different than looking at your perception of taste on an electron microscope level showing how a molecule of orange juice gets attached to a molecule of your taste buds. Of course, this misses the "bug picture" of what orange juice tastes line on a macroscopic level, i,.e. how we "experience" it, but is not necessarily wrong.

And just as a single brick does not define a house, neither does quatum mechanics describe the world. Just as the photograph of the earth from space does not reflect what it's like to be on earth, neither does the Einstein's theory of relativity describe how we experience gravity (i.e. as spacetime "pits").

In terms of human experience, which is our reality, no science can capture or adequately describe it, and neither can words. But at the same time, we must never fall for the error of believing that what we experience is how things really are, although many do.

For each aspect of reality we must use the most adequate tool ("measuring stick"), and always be aware that it is only one aspect of what is really out there.

"Actually, photons do have mass, although some "purists" insist they only have a momentum, But we know they have mass because photons are affected by gravitational pull (see "light bending," as well as black holes). Momentum is defined as p = mv, where "m" is mass and "v" velocity, and Einstein's famous E=mc2 also applies to photons. It is, therefore, meaningless to speak of a particle having a momentum but not mass.

That's not the definition of momentum and photons are massless, so the equation, "E=m_oc²" does not apply to photons. m_o represents the rest mass of a particle and photons have none, since they travel at the speed of lightand never rest. If they had a rest mass, their mass would be infinite at their normal propagation velocity.

Momentum is defined by the equation E²=p²c²+m_o²c². Since the rest mass of the photon is 0, the momentum of the photon is, p=E/c.

for the photon:
E=hν then p = hν/c = h/λ, where λ is the wavelength.

Note that only the presence of energy generates a gravitational field and only energy is affected by the field. Mass is energy, but the field and the effect of the field depend on the value of the energy only.

" The gravitational force (or "pit" in timespace jargon) that is required to detectably affect the photon mass is much greater than anything we can create on earth. The force is much greater than even our sun's gravitational pull. This is why the discovery of the gravitational lens (predicated by Einstein) proves that photons are subject to gravity and therefore must have mass, otherwise the GR formula E=mc2 does not apply to photons.

"E-m_oc²" is not a GR formula, it's part of special relativity(SR) and was published in 1905. GR is the theory that space itself is warped by the energy contained in it. Space itself(gravity) is a result of the existance of energy and has an energy value equal in magnitude, but opposite in sign. One article of evidence to back up the theory was the observation f starlight bending during a solar eclipse in 1917.

"How does Einstein's theory account, for example, for the read shift?"

Space expands, because of the negative pressure of the vacuum. That expansion results in a loss of photon energy to the gravitational field, which is space. The longer a photon flies in interstellar space, the longer it's wavelength becomes and the energy "loss" appears in the gravitational field.

" So if all this sounds a little bit like "lawyering" it's because it is! Which is why we can say there are is always some doubt, and no absolutes, and no one understands it and there are always convenient "loopholes" or "angles" from which these issues can be handled, sometimes leading to completely different conclusions, yet all of them true!

Rubbish.

" A perfect example of this is your eprception of these letters as being curves (such as letters c, s, q, p, etc.) when in fact they are shapes ahcieved by miniscule dots (and the distance between each two dots is simply a straight line) which under a micorscope would lose their smoothness and continuous appearance. In your eyes they are "integrated" into smooth and continuous complex curves.

Rubbish.

"and just as a single brick does not define a house, neither does quatum mechanics describe the world."

Quantum mechanics does describe the world, regardless of your analogy.

"ust as the photograph of the earth from space does not reflect what it's like to be on earth, neither does the Einstein's theory of relativity describe how we experience gravity (i.e. as spacetime "pits")."

GR does describe gravity and how one would experience it. ...In spite of your analogy.

"For each aspect of reality we must use the most adequate tool ("measuring stick"), and always be aware that it is only one aspect of what is really out there."

BS detectors are nice.