Kempf Space-time, 2010

[r***@gmail.com]

https://iopscience.iop.org/article/10.1088/1367-2630/12/11/115001/meta

Achim Kempf, "Spacetime could be simultaneously continuous and discrete,
in the same way that information can be" - 2010

Kempf space-time

Kempf writes in natural signal terms continuum mechanics in
the signal continuum mechanics, with field continuity, line continuity,
and signal continuity.

He frames the discrete and continuous in clearly density terms,
here bucket filling in continuous and infinite buckets.

Cantor's theorem is in his way - he works around countable additivity,
keeping of course uncountable non-additivity, where the uncountable
is also the condition that it is relatively uncountable-summability.

(Of the countably additive.)

Neatly!

Then of course it is talking about sampling, the signal analysis,
where the point is that the discrete signal clearly is incomplete,
central.

Sampling under probability, the discrete and continuous
is in the measurement the "signal", as it differs from the
impulse, or the wave (falling wave).

Time terms always speed up to presentation.

(And state.)

Sampling, observation, measurement effects,
these usually work up from measurement effects
(for example pulling up).

Sampling usually first is under effect of measurement effect.

Observation under action and sampling under recognition,
Kempf's space-time as informatic - information is under terms
in Kempf's space-time.

Yeah, information is under terms.

Kempf points to signal processing canon for signal theory -
terms under recognition and action, in a theory.

Indeed, the universe is very information-theoretic.

Filed under real theories.

[r***@gmail.com]

Post by r***@gmail.com
https://iopscience.iop.org/article/10.1088/1367-2630/12/11/115001/meta
Achim Kempf, "Spacetime could be simultaneously continuous and discrete,
in the same way that information can be" - 2010
Kempf space-time
Kempf writes in natural signal terms continuum mechanics in
the signal continuum mechanics, with field continuity, line continuity,
and signal continuity.
He frames the discrete and continuous in clearly density terms,
here bucket filling in continuous and infinite buckets.
Cantor's theorem is in his way - he works around countable additivity,
keeping of course uncountable non-additivity, where the uncountable
is also the condition that it is relatively uncountable-summability.
(Of the countably additive.)
Neatly!
Then of course it is talking about sampling, the signal analysis,
where the point is that the discrete signal clearly is incomplete,
central.
Sampling under probability, the discrete and continuous
is in the measurement the "signal", as it differs from the
impulse, or the wave (falling wave).
Time terms always speed up to presentation.
(And state.)
Sampling, observation, measurement effects,
these usually work up from measurement effects
(for example pulling up).
Sampling usually first is under effect of measurement effect.
Observation under action and sampling under recognition,
Kempf's space-time as informatic - information is under terms
in Kempf's space-time.
Yeah, information is under terms.
Kempf points to signal processing canon for signal theory -
terms under recognition and action, in a theory.
Indeed, the universe is very information-theoretic.
Filed under real theories.

Quotes from Kempf (quotations):

"The formalism establishes, therefore, an equivalence
between discrete and continuous representations of
spacetimes and fields."


"To address this question,
it will be useful to implement the UV cutoff."

"... generically, we may expect (tau) to be invertible,
as we have a map from R^N into R^N and
the determinant of the Jacobian has no _obvious_
reason to vanish."

"We can expand these fields in terms of eigenfunctions, ...".

Thanks, I can read!

"... it is non-trivial to suitably discretize the spectrum of the d'Alembertian."

Here Kempf can expand on the spectrum, for solely potential terms,
then as for out under the d'Alembertian after de Alembert,
d'Alembert is a powerful gradient descent method.

I.e., it is non-trivial, it it super-wave mechanics, yet, over waves,
in a wave model where under sampling we don't know we're
standing under usual wave formulations.

Under sampling....

Restoring measure to sampling is plainly neat then for
"Time, Uncertainty, and Chance" and usual enough
here the stochastic reasoning about the particles in
fields, maintaining the same metric as the field, the lattice.

[p***@gmail.com]

Post by r***@gmail.com

Post by r***@gmail.com
https://iopscience.iop.org/article/10.1088/1367-2630/12/11/115001/meta
Achim Kempf, "Spacetime could be simultaneously continuous and discrete,
in the same way that information can be" - 2010
Kempf space-time
Kempf writes in natural signal terms continuum mechanics in
the signal continuum mechanics, with field continuity, line continuity,
and signal continuity.
He frames the discrete and continuous in clearly density terms,
here bucket filling in continuous and infinite buckets.
Cantor's theorem is in his way - he works around countable additivity,
keeping of course uncountable non-additivity, where the uncountable
is also the condition that it is relatively uncountable-summability.
(Of the countably additive.)
Neatly!
Then of course it is talking about sampling, the signal analysis,
where the point is that the discrete signal clearly is incomplete,
central.
Sampling under probability, the discrete and continuous
is in the measurement the "signal", as it differs from the
impulse, or the wave (falling wave).
Time terms always speed up to presentation.
(And state.)
Sampling, observation, measurement effects,
these usually work up from measurement effects
(for example pulling up).
Sampling usually first is under effect of measurement effect.
Observation under action and sampling under recognition,
Kempf's space-time as informatic - information is under terms
in Kempf's space-time.
Yeah, information is under terms.
Kempf points to signal processing canon for signal theory -
terms under recognition and action, in a theory.
Indeed, the universe is very information-theoretic.
Filed under real theories.

"The formalism establishes, therefore, an equivalence
between discrete and continuous representations of
spacetimes and fields."
"To address this question,
it will be useful to implement the UV cutoff."
"... generically, we may expect (tau) to be invertible,
as we have a map from R^N into R^N and
the determinant of the Jacobian has no _obvious_
reason to vanish."
"We can expand these fields in terms of eigenfunctions, ...".
Thanks, I can read!
"... it is non-trivial to suitably discretize the spectrum of the d'Alembertian."
Here Kempf can expand on the spectrum, for solely potential terms,
then as for out under the d'Alembertian after de Alembert,
d'Alembert is a powerful gradient descent method.
I.e., it is non-trivial, it it super-wave mechanics, yet, over waves,
in a wave model where under sampling we don't know we're
standing under usual wave formulations.
Under sampling....
Restoring measure to sampling is plainly neat then for
"Time, Uncertainty, and Chance" and usual enough
here the stochastic reasoning about the particles in
fields, maintaining the same metric as the field, the lattice.

====================
a nice salad of words

apace is nothing and can do nothing
physics is not mathematics
ie
first of all we have to understand it physically
if you dont understand it physically and rightly
no mathematical bla bla will help you !!
dont expect from space anything it is not
or can t do
=====================================================
MASS IS THE CREATOR OF ALL FORCES INCLUDING GRAVITY
======================================================
if not understanding it
no mathematical bla bla will help you in advancing further

====

TIA
Y.P
==================

[r***@gmail.com]

Post by r***@gmail.com

Post by r***@gmail.com
https://iopscience.iop.org/article/10.1088/1367-2630/12/11/115001/meta
Achim Kempf, "Spacetime could be simultaneously continuous and discrete,
in the same way that information can be" - 2010
Kempf space-time
Kempf writes in natural signal terms continuum mechanics in
the signal continuum mechanics, with field continuity, line continuity,
and signal continuity.
He frames the discrete and continuous in clearly density terms,
here bucket filling in continuous and infinite buckets.
Cantor's theorem is in his way - he works around countable additivity,
keeping of course uncountable non-additivity, where the uncountable
is also the condition that it is relatively uncountable-summability.
(Of the countably additive.)
Neatly!
Then of course it is talking about sampling, the signal analysis,
where the point is that the discrete signal clearly is incomplete,
central.
Sampling under probability, the discrete and continuous
is in the measurement the "signal", as it differs from the
impulse, or the wave (falling wave).
Time terms always speed up to presentation.
(And state.)
Sampling, observation, measurement effects,
these usually work up from measurement effects
(for example pulling up).
Sampling usually first is under effect of measurement effect.
Observation under action and sampling under recognition,
Kempf's space-time as informatic - information is under terms
in Kempf's space-time.
Yeah, information is under terms.
Kempf points to signal processing canon for signal theory -
terms under recognition and action, in a theory.
Indeed, the universe is very information-theoretic.
Filed under real theories.

"The formalism establishes, therefore, an equivalence
between discrete and continuous representations of
spacetimes and fields."
"To address this question,
it will be useful to implement the UV cutoff."
"... generically, we may expect (tau) to be invertible,
as we have a map from R^N into R^N and
the determinant of the Jacobian has no _obvious_
reason to vanish."
"We can expand these fields in terms of eigenfunctions, ...".
Thanks, I can read!
"... it is non-trivial to suitably discretize the spectrum of the d'Alembertian."
Here Kempf can expand on the spectrum, for solely potential terms,
then as for out under the d'Alembertian after de Alembert,
d'Alembert is a powerful gradient descent method.
I.e., it is non-trivial, it it super-wave mechanics, yet, over waves,
in a wave model where under sampling we don't know we're
standing under usual wave formulations.
Under sampling....
Restoring measure to sampling is plainly neat then for
"Time, Uncertainty, and Chance" and usual enough
here the stochastic reasoning about the particles in
fields, maintaining the same metric as the field, the lattice.

Fritz London's "Superfluids, Volume 1", I have found
at this store, Poynting vector and really an excellent
treatment of the potential, in the superfluid and
superconductivity model, that the wave model has.

Kempf's signal model, for example usually waves,
has a novel modern mathematical placement,
the Shannon and Nyquist and signal continuity -
and real value- here for example in transport
over that in for example waves, or, rational terms.

[r***@gmail.com]

Post by r***@gmail.com

Post by r***@gmail.com

Post by r***@gmail.com
https://iopscience.iop.org/article/10.1088/1367-2630/12/11/115001/meta
Achim Kempf, "Spacetime could be simultaneously continuous and discrete,
in the same way that information can be" - 2010
Kempf space-time
Kempf writes in natural signal terms continuum mechanics in
the signal continuum mechanics, with field continuity, line continuity,
and signal continuity.
He frames the discrete and continuous in clearly density terms,
here bucket filling in continuous and infinite buckets.
Cantor's theorem is in his way - he works around countable additivity,
keeping of course uncountable non-additivity, where the uncountable
is also the condition that it is relatively uncountable-summability.
(Of the countably additive.)
Neatly!
Then of course it is talking about sampling, the signal analysis,
where the point is that the discrete signal clearly is incomplete,
central.
Sampling under probability, the discrete and continuous
is in the measurement the "signal", as it differs from the
impulse, or the wave (falling wave).
Time terms always speed up to presentation.
(And state.)
Sampling, observation, measurement effects,
these usually work up from measurement effects
(for example pulling up).
Sampling usually first is under effect of measurement effect.
Observation under action and sampling under recognition,
Kempf's space-time as informatic - information is under terms
in Kempf's space-time.
Yeah, information is under terms.
Kempf points to signal processing canon for signal theory -
terms under recognition and action, in a theory.
Indeed, the universe is very information-theoretic.
Filed under real theories.

"The formalism establishes, therefore, an equivalence
between discrete and continuous representations of
spacetimes and fields."
"To address this question,
it will be useful to implement the UV cutoff."
"... generically, we may expect (tau) to be invertible,
as we have a map from R^N into R^N and
the determinant of the Jacobian has no _obvious_
reason to vanish."
"We can expand these fields in terms of eigenfunctions, ...".
Thanks, I can read!
"... it is non-trivial to suitably discretize the spectrum of the d'Alembertian."
Here Kempf can expand on the spectrum, for solely potential terms,
then as for out under the d'Alembertian after de Alembert,
d'Alembert is a powerful gradient descent method.
I.e., it is non-trivial, it it super-wave mechanics, yet, over waves,
in a wave model where under sampling we don't know we're
standing under usual wave formulations.
Under sampling....
Restoring measure to sampling is plainly neat then for
"Time, Uncertainty, and Chance" and usual enough
here the stochastic reasoning about the particles in
fields, maintaining the same metric as the field, the lattice.

Fritz London's "Superfluids, Volume 1", I have found
at this store, Poynting vector and really an excellent
treatment of the potential, in the superfluid and
superconductivity model, that the wave model has.
Kempf's signal model, for example usually waves,
has a novel modern mathematical placement,
the Shannon and Nyquist and signal continuity -
and real value- here for example in transport
over that in for example waves, or, rational terms.

"... or, rational terms."

Borel, A., Linear Algebraic Groups
Smirnov, B.M., Introduction to Plasma Physics
Born, M., Problems of Atomic Dynamics

This Wagoner and Goldsmith "Cosmic Horizons",
the cosmic bellows, is under stellar dust.

i, -1, e?

"Rational Terms"

Looking at Saunders' "The Geometry of Jet Bundles",
it interests me explaining the relevance of its contents
the modern geometrical space-time theories, including
for example classical mechanics and relativity and all.

This is quantum mechanics is explaining things
in terms of discrete (excluded) particles as a model
of a continuous wave, of which the particle is a part.

Pauli exclusion is a usual feature of atomic and quantum
theories, here for example the nuclear for example as
with big bang or black hole models of the atomic nucleus,
it's also expanded upon in those theories as particle interactions
(which are waves).

This is the particle in the classical and the potential in waves.


https://en.wikipedia.org/wiki/Villarceau_circles

"The torus plays a central role in the Hopf fibration
of the 3-sphere, S^3, over the ordinary sphere, S^2,
which has circles, S^1, as fibers. "

"For any point [on the torus] there exist 4 [Villarceau] circles
on the torus containing the point."

[r***@gmail.com]

Post by r***@gmail.com

Post by r***@gmail.com

Post by r***@gmail.com

Post by r***@gmail.com
https://iopscience.iop.org/article/10.1088/1367-2630/12/11/115001/meta
Achim Kempf, "Spacetime could be simultaneously continuous and discrete,
in the same way that information can be" - 2010
Kempf space-time
Kempf writes in natural signal terms continuum mechanics in
the signal continuum mechanics, with field continuity, line continuity,
and signal continuity.
He frames the discrete and continuous in clearly density terms,
here bucket filling in continuous and infinite buckets.
Cantor's theorem is in his way - he works around countable additivity,
keeping of course uncountable non-additivity, where the uncountable
is also the condition that it is relatively uncountable-summability.
(Of the countably additive.)
Neatly!
Then of course it is talking about sampling, the signal analysis,
where the point is that the discrete signal clearly is incomplete,
central.
Sampling under probability, the discrete and continuous
is in the measurement the "signal", as it differs from the
impulse, or the wave (falling wave).
Time terms always speed up to presentation.
(And state.)
Sampling, observation, measurement effects,
these usually work up from measurement effects
(for example pulling up).
Sampling usually first is under effect of measurement effect.
Observation under action and sampling under recognition,
Kempf's space-time as informatic - information is under terms
in Kempf's space-time.
Yeah, information is under terms.
Kempf points to signal processing canon for signal theory -
terms under recognition and action, in a theory.
Indeed, the universe is very information-theoretic.
Filed under real theories.

"The formalism establishes, therefore, an equivalence
between discrete and continuous representations of
spacetimes and fields."
"To address this question,
it will be useful to implement the UV cutoff."
"... generically, we may expect (tau) to be invertible,
as we have a map from R^N into R^N and
the determinant of the Jacobian has no _obvious_
reason to vanish."
"We can expand these fields in terms of eigenfunctions, ...".
Thanks, I can read!
"... it is non-trivial to suitably discretize the spectrum of the d'Alembertian."
Here Kempf can expand on the spectrum, for solely potential terms,
then as for out under the d'Alembertian after de Alembert,
d'Alembert is a powerful gradient descent method.
I.e., it is non-trivial, it it super-wave mechanics, yet, over waves,
in a wave model where under sampling we don't know we're
standing under usual wave formulations.
Under sampling....
Restoring measure to sampling is plainly neat then for
"Time, Uncertainty, and Chance" and usual enough
here the stochastic reasoning about the particles in
fields, maintaining the same metric as the field, the lattice.

Fritz London's "Superfluids, Volume 1", I have found
at this store, Poynting vector and really an excellent
treatment of the potential, in the superfluid and
superconductivity model, that the wave model has.
Kempf's signal model, for example usually waves,
has a novel modern mathematical placement,
the Shannon and Nyquist and signal continuity -
and real value- here for example in transport
over that in for example waves, or, rational terms.

"... or, rational terms."
Borel, A., Linear Algebraic Groups
Smirnov, B.M., Introduction to Plasma Physics
Born, M., Problems of Atomic Dynamics
This Wagoner and Goldsmith "Cosmic Horizons",
the cosmic bellows, is under stellar dust.
i, -1, e?
"Rational Terms"
Looking at Saunders' "The Geometry of Jet Bundles",
it interests me explaining the relevance of its contents
the modern geometrical space-time theories, including
for example classical mechanics and relativity and all.
This is quantum mechanics is explaining things
in terms of discrete (excluded) particles as a model
of a continuous wave, of which the particle is a part.
Pauli exclusion is a usual feature of atomic and quantum
theories, here for example the nuclear for example as
with big bang or black hole models of the atomic nucleus,
it's also expanded upon in those theories as particle interactions
(which are waves).
This is the particle in the classical and the potential in waves.
https://en.wikipedia.org/wiki/Villarceau_circles
"The torus plays a central role in the Hopf fibration
of the 3-sphere, S^3, over the ordinary sphere, S^2,
which has circles, S^1, as fibers. "
"For any point [on the torus] there exist 4 [Villarceau] circles
on the torus containing the point."

"Electroweak Interactions: An Introduction..."?

"Exotic Atoms '79"?

"... Fundamental Interactions and Structure of Matter".

https://link.springer.com/chapter/10.1007%2F978-1-4615-9206-8_5

https://www.nap.edu/read/6288/chapter/8

"Reversal of time is the only discrete transformation
of space-time that has not been demonstrated
to be broken."

"A deeper understanding of time-reversal invariance
may hold the key to understanding the origin of the universe."

"At present, a half-dozen direct searches for neutrino mass
from the decay of tritium, have found no evidence for finite
neutrino mass. However, the high-precision data are not completely
understood, and all the experiments indicate a systematic deviation
from the normal theory of beta decay."