G "has nothing to do with Avogadro's number"??
Can you derive a value for either independently, to support your claim?
Use any equation which involves G but no N_a, which is pretty much all of them, because if you know all the other quantities in the equation, you can find G. There's no bound on the masses or energies when you're using things like the Einstein Field Equations other than staying above the Planck length, in terms of energy, which is easy because its all we're capable of. As DH's link and many more will explain, we've done many high precision measurements of G. Yes, in general we use large quantities of matter to do that but that's because G is small so you need a lot of matter to get an effect. We don't need to know how many moles of substance are in the Earth to know its mass. And once we know its mass we can get G by simply weighing objects.
G requires us to know masses, not quantities.
Guess what: I know there's "nothing wrong with using G" in any frame; except for all the problems with calculating the energy in spacetime.
Apparently the constants we use yield a value which is "embarrasing" (although hardly anyone, unlike me, whines about it).
Last I heard, the gap was about 120 zeros wide.
That is nothing to do with our choice of units, it is to do with the fundamental difference between quantum field theory and general relativity. Quantum field theory doesn't count the energy of space-time proper, because it doesn't treat gravity as a quantum field properly, general relativity does treat gravity properly over large distances. So when you try to model something like the cosmological constant, the intrinsic energy of space-time usiing a non-quantum gravity field theory you get a wrong answer. A very wrong answer.
It's not because we're using G, but because when you naively try to quantise general relativity you find graviton self interactions spiral out of control and basically give everything, even the empty universe, a hinking huge mass. The fact this mass is pretty much the Planck mass is simply a rephrasing of "The energy level of quantum gravity is the Planck mass", just as when you break electroweak symmetry the W and Z bosons are around 90GeV, that's the electroweak scale.
Nothing to do wiith units, everytning to do with the fundamental non-renormalisability of gravity in 3+1 dimensions. Which I'm sure is beyond your comprehension. No matter how many sigma Lie algebra lecture notes you're looked at.
As the string theorists say, you can use coupling interactions instead; nonetheless there is no way to scale these to G or gravity's constant.
Hang on, let me check something....
....
Yeah, I
am doing a PhD in supersymmetric gravity models, which includes Planck scale physics. For a moment I thought I wasn't because what you say doesn't square up with what I do.
Tell me, do you know about running couplings? Effective couplings? The relationship between the Planck scale and dimensions? Or with compact dimensions? I doubt it, so stop trying to make claims about an area you don't work in and clearly don't understand.
IF h is "the smallest" anything; it gauges anything small (maybe anything big too). Since h is apparently the smallest - energy, length, mass etc. Unless mass is "h-less"; but this does not appear to be the case, all mass quanta have spin we are told, therefore "h gauges mass" - we might not know how it does, but we know that it does. Unless there are 'spinless' quanta with mass. Maybe so, who knows?
Who said h was the smallest anything? Firstly, its not a length, energy or mass. Secondly, jsut because light comes in integer multiples of it doesn't mean nothing else can be smaller. Thirdly, you misuse the term 'gauge' in a way which makes you think you're almost deliberately trying to use it because you know its a physics buzzword but you've no idea its meaning and fourthly, who says all mass quanta have spin? What kind of spin? Where did you learn this?
I don't get it, you know you don't know any quantum field theoory or relativity and you know there's people here who do, yet you try to BS anyway, either by trying to tell us our work, which you don't know or understand or by simply making stuff up. Why? Don't you realise your lies don't stand up to even the slightest bit of scrutiny?
