GR and piezoelectricity?

Ken S. Tucker · science forum Guru Joined: 30 Apr 2005 Posts: 1230

I have a question about piezoelectricity in GR...

In conserving energy in GR, it's accepted Div T =0 , i.e.
T^uv;v=0.

That is also an exchange between the mechanical
energy density I'll denote M^uv and the EM energy
density I'll denote E^uv such that,

M^uv;v + E^uv;v = 0,
and
M^uv;v = - E^uv;v

I think that's standard text book stuff,
and a good demonstration of that is used
in piezo-electrically based electronic weigh
scales, where a mass (pressure) deforms
a piezoelectric-crystal which in turn produces
a voltage, and then that voltage is measured
and displayed.

1) What is the maximum accuracy of the
measurement of the voltage output?

1a) Is it infinite or does the Heisenberg Uncertain
Principle (HUP) apply and thus quantizing the
measurement?

I'll assume (1a) is true and assume HUP applies,
but then I get into trouble with the continuous
transfer given by,

M^uv;v = - E^uv;v (2)

which is not quantized.
2) Should it be quantized?

I would reword (2) to ask, if the generation of
electricity by mechanical action, (hydroelectric
power) is quantized, to which I would think yes.
The reasoning for the quantization of power is
because voltage causing a current flowing through
a resistor produces heat, and that heat in turn
appears as infared radiation, and thus photons.

So I'll try modifying Eq.(2) to a quantized form,

M^uv - Delta M^uv = E^uv + Delta E^uv , (2a)

where the deduction of Mechanical M^uv
denoted -Delta M^uv generates Electricity
by +Delta E^uv, with the "Delta's" being a
quanta exchange, in place of a continuous
exchange of energy density in (2).

What I imagine is Eq.(2) describes a power
transfer, but because power is quantized,
Eq.(2a) is suggested in place of (2).

Using Eq.(2a) every covariant derivative in the
4 terms therein now vanish, because there is no
*continuous* transfer of energy, from the stand
point of the application of the Quantum Theory.

IMO, an outstanding issue that needs resolution
is whether Lorentz force vanishes as AE suggests
in GR1916 Eq.(65a), denoted therein by
kappa_sigma = 0.
If the affirmative is presumed, then the predicted
(from Eq.(2a) above)

E^uv,v=0 == kappa_sigma=0,

is also true, thereby uniting GR with QT, at least
removing some outstanding issues that seem to
separate these seemingly distinct theories.
Regards
Ken S. Tucker

Igor Khavkine · science forum Guru Joined: 01 May 2005 Posts: 607

Ken S. Tucker wrote:

[... M and E are, respectively, the mechanical
and EM stress energy tensors ...]

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