Confusion Related to Planck Mass

[klen]

Hi all,
According to quantum mechanics, the graviton is the measure of the smallest amount of curvature possible in space-time. I read that the mass which would be required to create this curvature is Planck Mass which is close to the value 10^-5g.
But the elementary particles, like electrons, are much lighter than Planck mass, wouldn't they create gravitational fields less than the graviton level?
In other words, since the basic curvature is produced by mass close to 10^-5g, how do we account for the gravitational field of elementary particles like electrons which should produce gravitatonal field less than the graviton level?

 

[Buzz Bloom]

the smallest amount of curvature possible in space-time

Hi Klen:

I found a somewhat different interpretation of the Planck Mass on Wikipedia:

https://en.wikipedia.org/wiki/Planck_mass
The Planck mass is nature’s maximum allowed mass for point-masses (quanta) – in other words, a mass capable of holding a single elementary charge. If two quanta of the Planck mass or greater met, they could spontaneously form a black hole whose Schwarzschild radius equals their Compton wavelength.[citation needed] Once such a hole formed, other particles would fall in, and the black hole would experience runaway, explosive growth (assuming it did not evaporate via Hawking radiation). Nature’s stable point-mass particles, such as electrons and quarks, are many, many orders of magnitude lighter than the Planck mass and cannot form black holes in this manner. On the other hand, extended objects (as opposed to point-masses) can have any mass.

Unlike all other Planck base units and most Planck derived units, the Planck mass has a scale more or less conceivable to humans. It is traditionally said to be about the mass of a flea, but more accurately it is about the mass of a flea egg.​

So the criteria about smallest curvature seems to be related to having sufficient curvature to form a black hole rather than being the smallest possible curvature.

Regards,
Buzz

 

[Vanadium 50]

I'm afraid that neither premise is correct. That means that the conclusion does not follow.

 

[klen]

I'm afraid that neither premise is correct.

Hi Vanadium,
Actually I was reading about the Penrose interpretation of Quantum Mechanics, where he assumes that the state vector reduction occurs only if the difference between the alternatives is equal or greater than a graviton level. He then says that matter having mass near the Planck Mass would be able to produce such an energy difference.
Does this mean that electrons or other elementary particles produce curvature which is smaller than this graviton level, and hence stay at two places at once. I found it contradicting because according to his book 'Emperor's New Mind' graviton is the smallest unit of curvature which would be allowed according to Quantum Mechanics. How could it be 'smallest' if electrons are producing fields weaker than a graviton level?
I do not have clear understanding of graviton, could you please elucidate above contradiction.

 

[Vanadium 50]

Doubling down on incorrect statements is not helpful.

 

[klen]

Doubling down on incorrect statements is not helpful.

Could you at least tell me what are you finding vague in the question so that I can rephrase it.

 

[Vanadium 50]

I'm not finding anything vague. I'm saying that the premise you are starting from is wrong.

 

[klen]

I'm saying that the premise you are starting from is wrong.

What premise are you talking about