Re: Why Should We Quantize Geometry?

rof@xxxxxxxxxxxx wrote:

> "Hontas F. Farmer III" <hfarmer@xxxxxxxxxxxxxx> writes:
>
>>We all know that the Planck interval of space-time is the shortest
>>possible measureable interval between two events.
>
> We do? Is there an argument that suggests that we can measure
> intervals of the size of the Planck length but not smaller?

If you want a detailed argument for the Planck length being indivisible see
this site.
http://aklimets.narod.ru/collapse.htm

In summary:

A particle with a wavelength equal to the Planck length will undergo
gravitational collapse into a quantum scale black hole. This follows from
consideration of the following equations. hbar=c=1 E=1/lambda, p=1/lambda,
Rs=2GM, lp=sqrt(G), and mp=(1/squrt(G)). Substitute mp for M in the
formula for Rs.

Rs=2G(1/sqrt(G))=2sqrt(G)=2*lp

For a single quantum particle which carries the Planck Mass would have a De
Broglie wavelength equal to the Planck length which would only be half of
that particles Schwarzschild radius. The particle would become a quantum
black hole. Therefore the Planck wavelength cannot be measured by any
realistic physical method. Such methods depend on the energy of a particle
beam hence the wavelength of a particle beam for measurements that would be
that fine.

[Mod. note: This kind back-of-the-envelope calculation is often used as
motivation for the importance of Planck units at scales where both
quantum and gravitational effects are important. However, it should
be taken with a grain of salt, since none of the formulas used are
known to apply in that regime. So far, there is no theory of quantum
gravity that can substantiate these calculations from basic
principles. -ik]

> There are certainly masses both bigger and smaller than the
> Planck mass. Why is the existence of a natural unit of length
> interpreted as a shortest possible length while the existence
> of a natural unit of mass isn't interpreted in a similar way?

In the theory of quantum space time the Planck mass is seen as the quantum
of mass-energy which will cause a gravitational change. Following the
argument above if a mass that is not n*mp (n={1,2,3,...}) is
gravitationally collapsed we arrive at a black hole which does not have a
Schwarzschild radius that is allowed by the argument above. When a mass
that is not a multiple of the Planck mass is gravitationally collapsed the
excess escapes.

What the theory of quantum space time says is that it takes a mass which is
at least one Planck mass to cause a gravitational field. ( FYI a Planck
massis about as much as a "heavy grain of sand" I don't know who first put
it that way. mp ~ 10^19 GeV) The theory does not say that a Less massive
particles do not feel gravity. They can react to a gravitational field but
they produce none of their own.

> It may be clear that at that scale classical gravity will need some
> quantum corrections, but if one wants to imagine a "fundamental" length,
> is there some reason to choose sqrt(hbar*G/c^3) rather than,
> for example, sqrt(h*G/c^3)?
>
> R.

Choosing hbar instead of h is more of a convention. The fundamental
realities of the theory are unchanged by this as all that occurs is a
change of units.

I hope this brings more clarity than confusion.

--
Let me get this straight we "advanced" from telgraphs to email?-GeorgeCarlin
http://www.geocities.com/hontasfx

.

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