A physical quantity that has a value, eh? What kind of value? You mean, like a numerical value? Wouldn't that make it a mathematical concept?
Yes. That is a mathematical concept. What I'm telling you about is what Einstein said: a field is a state of space.
I'd have no problem talking about the velocity field of the air. This kind of thing is often done in fluid dynamics.
Well I do. Because the wind is not a state of space.
That's what it boils down to.
But that's not what a gravitational field is. It's a region of space where the state of space is described by the stress-energy-momentum tensor, and your measurements of distance and time made using light moving through that space, are described by the metric tensor:
$$G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}$$
To be fair, this is almost a philosophical argument rather than a physics one. We don't ever measure fields directly. We infer things about them from measurements of measurable quantities like force or charge or whatever. The field is a useful mental and mathematical picture that helps us to model the processes behind our actual observations. But it's an abstraction.
A field isn't an abstraction. The space in the room you're in is
"neither homogeneous nor isotropic". Hence light curves downward and your pencil falls down. See
this thread. The gravitational field is there because "the state of space" has been altered by the energy tied up as the matter of the Earth. The effect diminishes with distance such that when you plot it using say light clocks, your plot is curved.
You're right that some of the errors are typos, like the "of/if" error. But that "Not" at the start of the second sentence shouldn't be there at all. Look - the sentence doesn't even make sense with that word. And it doesn't make sense if you replace "Not" by "Nor", either. Take out the "Not" and it's ok. So, it looks like this transcription is not particularly accurate or reliable.
Then look for a better transcript, or maybe a German original.
I'm not dismissing what Einstein said there, by the way (reading it without the "Not", of course). Everything in that quote is solid except for the last sentence, which is more of a statement of Einstein's philosophical position than a statement about any established physics. That's what I'm saying is speculation.
I think you need to think some more about what a field is. Imagine your room is a test chamber, and we empty out the air. A light beam still curves. Why? If you've been following any of the other threads you'll know it isn't because "the spacetime is curved" or because "the space is curved". If you follow the links you can read Einstein saying it's because the space is inhomogeneous, rather like
sonar. This sort of stuff isn't mere philosophy or speculation, it's understanding, it's fundamental physics.
I see no evidence of mathematical competence from you.
I'm no dummy.
You think there's a problem with the Lorentz force equation? Here we go again. Please explain what the problem is. And, importantly, please explain why the equation gives results that match experimental tests, given that it's wrong and all.
It infers point particles when it's quantum field theory rather than quantum point-particle theory, it suggests there's an electric field E and a magnetic field B when
"one should properly speak of the electromagnetic field Fuv rather than E or B separately". It totally ignores the situation where you have two charged particles, each with an electromagnetic field. It ignores the fact that it takes two to tango. All it's saying is that the force is a product of the electric linear force and the magnetic rotational force.
I'll keep a look out. It's only a matter of time until you make another blunder. I don't want to go searching back through old posts. You can take this as an unsupported assertion right now, if you wish.
The mistakes I make are minor, and few and far between. Because I'm not some my-theory guy. I'm not making this stuff up. When I say something, I'm usually backing it up with some rock-solid references, and quotes by the likes of Maxwell and Minkowski and Einstein.
Do you think something in that quote doesn't square with what I've been taught?
Yes. That's the story of my life. What's a field? I take note of Einstein saying it's a state of space, you've been taught it's some scalar/vector/etc value at every point in space. What's an electromagnetic field? I take note of Maxwell and Minkowski and Dirac and say it's twisted/vorticial/spinorial space, you've been taught it's a combination of E and B. It's a fresh eyes thing I guess. I am reminded of Avatar:
Moat: It is hard to fill a cup that is already full.
Jake Sully: My cup is empty. Trust me. Just ask Dr. Augustine. I'm no scientist.
Moat: Then what are you?
Jake Sully: I was a marine. A warrior... of the uh... Jarhead Clan.