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Author:

Hontas Farmer

License:

Creative Commons CC BY 4.0
^{(?)}

Abstract:

To get the correct answer one must ask the correct question. In the field of Quantum Gravity the question has been how do we quantize General Relativity or derive a quantum theory which becomes General Relativity at low energies. Observing that Quantum Field Theory was the result of making Quantum Mechanics into a relativistic theory, I asked myself why not make QFT obey the principles of GR? I answered this question with a model I call Relativization. In a series of three papers I presented an answer to this alternative question which gives finite results for everything from black holes to particle physics.

Presented at the April meeting of the American Physical Society

Tags:

` ````
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\begin{document}
\title{Quantum Gravity: Have We Been Asking The Right Question? }
\author{Hontas F Farmer}
\institute{Malcolm X College, City Colleges of Chicago, Chicago, Illinois, USA}
\institute{Richard J Daley College, City Colleges of Chicago, Chicago, Illinois,
USA}
\institute{College of DuPage, Glenn Ellyn, Illinois, USA}
\institute{\url{http://www.ccc.edu/colleges/daley/Staff/Pages/Hontas-Farmer.aspx}}
\institute{hfarmer@ccc.edu}
\date{April 11th 2015}
\titlegraphic{\includegraphics[height=0.2\paperheight]{Logos}}
\makebeamertitle
\lyxframeend{}\lyxframe{Abstract}
To get the correct answer one must ask the correct question. In the
field of Quantum Gravity the question has been how do we quantize
General Relativity or derive a quantum theory which becomes General
Relativity at low energies. Observing that Quantum Field Theory was
the result of making Quantum Mechanics into a relativistic theory,
I asked myself why not make QFT obey the principles of GR? I answered
this question with a model I call Relativization. In a series of three
papers I presented an answer to this alternative question which gives
finite results for everything from black holes to particle physics
\cite{10.15200/winn.140751.17561,1:e141487.76774,winnowerunpub}.
However, others may answer this question more elegantly than I have.
Have we by studying Quantum Gravity for 50 + years been asking the
wrong question, and thus experiencing difficulty, all this time?
\lyxframeend{}
\lyxframeend{}\lyxframe{Inspiration}
\begin{itemize}
\item For over 50 years physicists have sought a quantum field theory of
gravity which would reduce to General Relativity at low energies.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Inspiration}
\begin{itemize}
\item For over 50 years physicists have sought a quantum field theory of
gravity which would reduce to General Relativity at low energies.
\item There have been many attempts to do this such as String/M-Theory,
Loop Quantum Gravity, and others. All of which met with some success.
Each has hit various roadblocks.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Inspiration}
\begin{itemize}
\item For over 50 years physicists have sought a quantum field theory of
gravity which would reduce to General Relativity at low energies.
\item There have been many attempts to do this such as String/M-Theory,
Loop Quantum Gravity, and others. All of which met with some success.
Each has hit various roadblocks.
\item So I decided to look at this as if I was a Martian, almost as if I
had never heard of Quantum Gravity.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Another Point of View}
\begin{itemize}
\item One way physical theories develop is by the recognition that one model
is somehow more fundamental than the other.
\item One can look at this as a sort of theoretical family tree.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Another Point of View }
\begin{figure}
\includegraphics[height=0.5\paperheight]{Untitled1}
\caption{A theoretical family tree. The theory on the left is taken as more
fundamental than the theory on the right. The one on the left is sort
of the father theory and the one on the right is the mother theory.
The ``family'' the theory belongs to being determined by the father
theory. }
\end{figure}
\lyxframeend{}
\lyxframeend{}\lyxframe{Another Point of View}
\begin{itemize}
\item One way physical theories develop is by the recognition that one model
is somehow more fundamental than the other.
\item The underlying assumption of all theories of Quantum Gravity has been
that quantum is somehow more fundamental than relativity. That General
Relativity needs to be quantized in some way.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Another Point of View}
\begin{itemize}
\item One way physical theories develop is by the recognition that one model
is somehow more fundamental than the other.
\item The underlying assumption of all theories of Quantum Gravity has been
that quantum is somehow more fundamental than relativity. That General
Relativity needs to be quantized in some way.
\item This is due to the wild success of Quantum Field Theory which is the
result of making Quantum theory obey Special Relativity.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Another Point of View}
\begin{figure}
\includegraphics[height=0.5\paperheight]{Untitled2}
\caption{A theoretical family tree where big daddy QFT sort of ``gives his
name'' to the child theory Quantum Gravity. Put this way we have
been trying to create a certain kind of child theory. }
\end{figure}
\lyxframeend{}
\lyxframeend{}\lyxframe{Another Point of View}
\begin{itemize}
\item One way physical theories develop is by the recognition that one model
is somehow more fundamental than the other.
\item The underlying assumption of all theories of Quantum Gravity has been
that quantum is somehow more fundamental than relativity. That General
Relativity needs to be quantized in some way.
\item This is due to the wild success of Quantum Field Theory which is the
result of making Quantum theory obey Special Relativity.
\item Maybe that assumption is what is holding us back? Maybe we have been
trying to force nature in a direction it cannot go on this case.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{The Question}
\begin{itemize}
\item Given the difficulty of traditional quantization why not try asking
a different question towards the same ends?
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{The Question}
\begin{itemize}
\item Given the difficulty of traditional quantization why not try asking
a different question towards the same ends?
\item An alternative question would be ``How can we make QFT comply with
the principles of General Relativity?''
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{A Definition}
\begin{definition}%{}
Relativization the act or result of making relative or regarding as
relative rather than absolute \cite{Websters}.
In the context of physical theories Relativization means the act or
result of making a theory obey the principles of Special or General
Relativity.
\end{definition}%{}
\lyxframeend{}
\lyxframeend{}\lyxframe{The Question}
\begin{itemize}
\item Given the difficulty of traditional quantization why not try asking
a different question towards the same ends?
\item An alternative question would be ``How can we make QFT comply with
the principles of General Relativity?''
\item Put another way, ``How can we relativize QFT?''
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{GR + QFT from Another Point of View.}
\begin{figure}
\includegraphics[height=0.5\paperheight]{Untitled3}
\caption{Instead of a quantization of General Relativity I propose \emph{relativization
}\cite{Websters} of Quantum Field Theory. Instead big black hole
filled General Relativity is the father and little dainty QFT is the
mother. The resulting child theory is then more fundamentally a relativistic
theory, not a quantum theory. }
\end{figure}
\lyxframeend{}
\lyxframeend{}\lyxframe{An Early Relativization Answer}
\begin{itemize}
\item I asked myself this question and in a series of papers (\cite{10.15200/winn.140751.17561,1:e141487.76774,winnowerunpub})
and found answers stemming from this question.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{An Early Relativization Answer}
\begin{itemize}
\item I asked myself this question and in a series of papers (\cite{10.15200/winn.140751.17561,1:e141487.76774,winnowerunpub})
and found answers stemming from this question.
\item The question was stated in terms of the relationships between Hilbert
spaces and Riemannian manifolds.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{An Early Relativization Answer}
\begin{itemize}
\item I asked myself this question and in a series of papers (\cite{10.15200/winn.140751.17561,1:e141487.76774,winnowerunpub})
and found answers stemming from this question.
\item The question was stated in terms of the relationships between Hilbert
spaces and Riemannian manifolds.
\item The basic axioms and principles that would describe a relativized
QFT were set down.
\end{itemize}
\lyxframeend{}\lyxframe{An Early Relativization Answer}
\begin{itemize}
\item I asked myself this question and in a series of papers (\cite{10.15200/winn.140751.17561,1:e141487.76774,winnowerunpub})
and found answers stemming from this question.
\item The question was stated in terms of the relationships between Hilbert
spaces and Riemannian manifolds.
\item The basic axioms and principles that would describe a relativized
QFT were set down.
\item Numerical calculations which show that the resulting simplest relativized
standard model can reproduce Hawking radiation in a way which agrees
with observations so far were done. (i.e. The black holes can form
nicely and don't blow themselves apart. Although there are some small
differences or corrections from my model.)
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Quantum Gravity by relativization of Quantum Field Theory}
\begin{itemize}
\item In ``Quantum Gravity by relativization of Quantum Field Theory.''
\cite{10.15200/winn.140751.17561} I first posed the question and
addressed the fundamental mathematical structure of relativized quantum
field theory. The paper drew on approaches such as geometric algebra
and QFT in curved space time.
\item A closer look at what it means to have Hilbert space in the same model
as one with a curved Riemannian background and established a formalism
for discussing Hilbert spaces ``on top of'' locally flat space-time
``on top of'' globally curved space time.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization}
In ``Fundamentals of Relativization''\cite{1:e141487.76774} I proposed
the following collection of principles as axioms.
\begin{description}
\item [{\noun{Relativization}}] \noun{Principle:} \emph{All physical theories
must obey the Einstein Equivalence Principle}. ``That for an infinitely
small four-dimensional region, the relativity theory is valid in the
special sense when the axes are suitably chosen.'' \cite{einstein1916}
In other words physical theories must be formulated in a way that
is locally Lorentz covariant and globally diffeomorphism covariant.
Stated with equations.
\end{description}
\[
x^{\mu}=e_{a}^{\mu}x^{a}
\]
$x^{a}$ is a vector in the locally flat space near a point.
$e_{a}^{\mu}$ is a vielbien connecting local flat space to the globally
curved manifold.
$x^{\mu}$ is a vector in the curved space time manifold.
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization}
\begin{description}
\item [{\noun{Spectrum}}] \noun{condition:} All possible states of a QFT
will be in the Fock-Hilbert space $\mathcal{H}$. An operator on $\mathcal{H}$
must map states to other states in $\mathcal{H}$.
\item [{\noun{Normalization}}] \noun{condition:} The inner product on $\mathcal{H}$
must be in a set isomorphic to the division algebras $\mathbb{R}$,$\mathbb{C}$,$\mathbb{H}$,
$\mathbb{O}$. \cite{2012FoPh...42..819B} For example an inner product
on $\mathcal{H}$ of the form $\left\langle \psi\right|\left.\psi\right\rangle =j^{a}$
with $j^{a}\in\mathcal{M}$ and $\forall$ $\left|\psi\right\rangle \in\mathcal{H}.$
\item [{\noun{Locality}}] \noun{Principle of QFT }: QFT interactions occur
in the locally flat space at the point of interaction. The propagation
of particles between interactions is governed by Relativity.
\item [{\noun{Specification}}] \noun{condition}: Relativized QFT's are
defined by the above and the tensor product of their state space with
Minkowski space. For a theory T, $T=\left\{ \mathcal{H},\mathcal{H\otimes\mathcal{M}},A\left(\mathcal{H\otimes\mathcal{M}}\right)\right\} $
(Inspired by a similar statement in \cite{2014arXiv1401.2026H}.)
\end{description}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization}
\begin{itemize}
\item Following those axioms I was able to work through numerous mathematical
steps detailed in \cite{1:e141487.76774} to a modification of the
standard model to include a relativized gravity in which local QFT
interactions influence the curvature of space time and vice versa.
\item \textrm{
\begin{multline*}
L=\sqrt{-g}\left(-\frac{1}{4}F^{ab}F_{ab}+i\bar{\psi}\gamma^{a}D_{a}\psi+\psi_{i}g_{ij}\psi_{i}\phi+h.c.\right.\\
\left.+\left|D_{a}\phi\right|^{2}-V(\phi)+R-\bar{\phi}\gamma^{a}R_{ab}\phi\gamma^{b}\right)
\end{multline*}
}
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization}
\begin{itemize}
\item Following those axioms I was able to work through numerous mathematical
steps detailed in \cite{1:e141487.76774} to a modification of the
standard model to include a relativized gravity in which local QFT
interactions influence the curvature of space time and vice versa.
\item \textrm{
\begin{multline*}
L=\sqrt{-g}\left(-\frac{1}{4}F^{ab}F_{ab}+i\bar{\psi}\gamma^{a}D_{a}\psi+\psi_{i}g_{ij}\psi_{i}\phi+h.c.\right.\\
\left.+\left|D_{a}\phi\right|^{2}-V(\phi)+R-\bar{\phi}\gamma^{a}R_{ab}\phi\gamma^{b}\right)
\end{multline*}
}
\item $R_{ab}$ is an operator which tells how QFT interactions effect the
curvature of space time.
\item $\widehat{R_{ab}}=\left(d\langle\phi|\phi\rangle(\gamma^{0})^{2}\wedge\gamma_{b}\right.\left.+\langle\phi|\phi\rangle(\gamma^{0})^{2}\wedge\gamma_{c}\wedge\langle\phi|\phi\rangle(\gamma^{0})^{2}\wedge\gamma_{b}\right)\langle\phi|.$
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization}
\begin{itemize}
\item Following those axioms I was able to work through numerous mathematical
steps detailed in \cite{1:e141487.76774} to a modification of the
standard model to include a relativized gravity in which local QFT
interactions influence the curvature of space time and vice versa.
\item \textrm{
\begin{multline*}
L=\sqrt{-g}\left(-\frac{1}{4}F^{ab}F_{ab}+i\bar{\psi}\gamma^{a}D_{a}\psi+\psi_{i}g_{ij}\psi_{i}\phi+h.c.\right.\\
\left.+\left|D_{a}\phi\right|^{2}-V(\phi)+R-\bar{\phi}\gamma^{a}R_{ab}\phi\gamma^{b}\right)
\end{multline*}
}
\item Then derived the locally correct gravitational modification to a QFT
interaction $R_{0}\propto\Lambda$ .
\item
\[
\overline{\left|M_{GG}\right|}=\frac{1}{2}\left(\bar{\phi}\gamma^{a}R_{ab}\phi+\bar{\phi}\gamma^{a}R_{ab}\phi\right)\gamma_{a}\gamma^{b}\approx R_{0}\,\, Cosh(\hbar p)
\]
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization II with Computational Analyses}
\begin{itemize}
\item In \textrm{``}Fundamentals of Relativization II with Computational
Analyses\textrm{'' \cite{winnowerunpub},} using Mathematica I modeled
black holes with the following equation in which \textrm{$x=\gamma^{a}x_{a}$.
(L here designates am arbitrary length scale.)}
\item
\[
-\frac{L}{hc}\frac{\hbar^{2}\psi''(x)}{2M}+\frac{\hbar^{2}R_{0}}{2M}\frac{L}{hc}Cosh(x)\psi(x)-\text{En}\frac{L}{hc}\psi(x)=0
\]
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization II with Computational Analyses}
\begin{itemize}
\item Which with the proper boundary conditions even and odd energy eigenstates
and eigenvalues were found in terms of Mathieu functions.
\item $\psi_{a}(x)=\frac{e^{i\left(n+\frac{1}{2}\right)}\text{MathieuC}\left[a_{n+\frac{1}{2}}\left(-2L^{2}R_{0}\right),-2L^{2}R_{0},\frac{ix}{2L}\right]}{\text{MathieuC}\left[a_{n+\frac{1}{2}}\left(-2L^{2}R_{0}\right),-2L^{2}R_{0},\frac{i}{2}\right]}$
; $\ensuremath{\text{En}=-\frac{\hbar^{2}a_{n+\frac{1}{2}}\left(-2L^{2}R_{0}\right)}{8L^{2}M}}$
\item $\psi_{b}(x)=\frac{e^{i\left(n+\frac{1}{2}\right)}\text{MathieuS}\left[b_{n+\frac{1}{2}}\left(-2L^{2}R_{0}\right),-2L^{2}R_{0},\frac{ix}{2L}\right]}{\text{MathieuS}\left[b_{n+\frac{1}{2}}\left(-2L^{2}R_{0}\right),-2L^{2}R_{0},\frac{i}{2}\right]}$
; $\text{En}=-\frac{\hbar^{2}b_{n+\frac{1}{2}}\left(-2L^{2}R_{0}\right)}{8L^{2}M}$
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization II with Computational Analyses}
\begin{itemize}
\item In the latest paper\textrm{\cite{winnowerunpub},} an expression for
a black hole's luminosity was derived. (The ``E'' in the denominator
stands for an elliptic integral.)
\end{itemize}
\includegraphics[height=0.35\paperheight]{UnderConsideration3}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization II with Computational Analyses}
Using the following approximation, and the effective black body temperature
to luminosity relationship, I computed the temperature due to Hawking
type radiation from a set of typical astronomical masses. Specifically
a one kilogram black hole, an 8 M$_{\odot}$ black hole and Sagittarius
A{*}.
\[
L_{BH}\approx\frac{1}{16}\left|\frac{\hbar^{2}\left(a_{n+\frac{1}{2}}\left(-8G^{2}M^{2}R_{0}\right)+b_{n+\frac{1}{2}}\left(-8G^{2}M^{2}R_{0}\right)\right)}{G^{4}M^{5}t_{p}}\right|
\]
The temperatures would be for the one kilogram, eight solar mass,
and super massive Sagittarius A{*} black holes would be.
\noindent
\[
\ensuremath{T_{\text{BH}}=\frac{\sqrt[4]{L_{\text{BH}}}}{2\sqrt[4]{\pi}\sqrt{G}\sqrt{M}\sqrt[4]{\sigma}}}
\]
\noindent
\[
\ensuremath{\text{\{5.5\ensuremath{\times}10\ensuremath{^{10}}},\text{1.4\ensuremath{\times}\ensuremath{10\ensuremath{{}^{-44}}}},\text{5.9\ensuremath{\times}10\ensuremath{^{-54}}}\}}K
\]
\lyxframeend{}\lyxframe{Fundamentals of Relativization II with Computational Analyses}
\begin{figure}
\includegraphics[height=0.5\paperheight]{fig3}
\caption{A plot of temperature vs mass comparing my model to the Beckenstein-Hawking
model. The predictions of my model derived by very different means
are very close to the accepted semiclassical model.\textrm{ }\label{fig1}
\textrm{\cite{winnowerunpub}}}
\end{figure}
\lyxframeend{}
\lyxframeend{}\lyxframe{Fundamentals of Relativization II with Computational Analyses}
\begin{figure}
\includegraphics[height=0.5\paperheight]{fig4}
\caption{At larger mass scales my model predicts much colder black holes, and
a possibly observable ripple in their temperature-mass relationship.
\label{fig:fig2-1} \cite{winnowerunpub}}
\end{figure}
\lyxframeend{}
\lyxframeend{}\lyxframe{Is Relativization the Right Question?}
\begin{itemize}
\item Could be.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Is Relativization the Right Question?}
\begin{itemize}
\item Could be.
\item With few resources and little time I was able to come up with a reasonable
model to answer this question.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Is Relativization the Right Question?}
\begin{itemize}
\item Could be.
\item With few resources and little time I was able to come up with a reasonable
model to answer this question.
\item Imagine what might happen after 50 years of studying this approach
with the proper support and a number of much more talented researchers.
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Is Relativization the Right Question?}
\begin{itemize}
\item Could be.
\item With few resources and little time I was able to come up with a reasonable
model to answer this question.
\item Imagine what might happen after 50 years of studying this approach
with the proper support and a number of much more talented researchers.
\item The right question should lead to an answer in a way which is simple
or at least tractable. This question seems more tractable based on
the fact I was able to start to answer it (and I'm not that smart).
\end{itemize}
\lyxframeend{}
\lyxframeend{}\lyxframe{Thank you for your time.}
\includegraphics[width=0.75\paperwidth]{Thankyouinwriting}
\lyxframeend{}
%\begin{frame}[allowframebreaks]References
\bibliographystyle{plainnat}
\bibliography{QGright_2}
%\end{frame}
\end{document}
```

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