| Topic: |
Science > Physics |
| User: |
"Jamie Vicary" |
| Date: |
29 Jan 2005 05:12:00 PM |
| Object: |
Generalising physical theories |
Dear all,
Science is about coming up with theories which well describe the
physical world. Sometimes -- as with relativity and quantum theory --
these theories work well in some domains, but poorly or even
incompatibly in others.
Consider the class of all possible theories; a class within which
quantum theory, relativity and any unified theory of nature must exist.
Here, I am using the term "theory" in its most general sense: a
consistent set of rules about objects, the nature of the "rules" or
"objects" being completely unrestricted.
Does it make sense to consider theories in such a general way? I
would suggest that it does, and that meaningful statements about such
generalised theories can be made. For example, it is clearly possible to
create two theories which despite different superficial formulations,
are actually equivalent. Given this, is it possible to count the number
of inequivalent theories of complexity less than some complexity C,
given some objective measure of complexity?
Furthermore, to any possible theory we can assign a particular
interpretation which maps the *abstract* objects in the theory to
directly percievable aspects of the world -- such as {spacetime,
governments, flowering shrubs, etc} -- which our existing theories
{relativity, politics, botany, etc} describe. Again, I am emphasising
here the very general sense in which I am using the word "theory": a
consistent set of rules about objects.
Of course, as physicists, we are chiefly concerned with
interpretations which map abstract objects in our theories -- like
wavefunctions, curvature tensors, quantum operators and so on -- onto
aspects of the physical world like charge, mass and causality. Given a
particular theory -- a particular set of rules about objects -- it might
well be impossible to construct an interpretation on that theory that is
compatible with, for example, general relativity. We would therefore
discard that theory as a possible fundamental description of our universe.
A formalism with which to deal with abstract theories, and their
interpretations as *physical* theories, might allow us to consider the
class of all theories which admit interpretations as BOTH quantum theory
AND general relativity. I suppose superstring theory, for example, might
be a theory in this class. So would another physical theory which we
could trivially construct by gluing classical GR and quantum theory
together and considering them as one.
Having constructed this class of theories -- the class which admit
interpretations compatible with both GR and quantum theory -- an
attractive goal would then be to choose the theory which is least
complex (by some objective definition of complexity), and then state
that this theory -- with some attached interpretation in terms of
physical reality, which can be as complex as we like! -- is the ultimate
theory of reality. This notion of the complexity of the abstract theory
being unrelated, or perhaps inversely related, to the complexity of its
physical interpretation is obviously not new: Einstein's equations are
much, much shorter than any useful explanatory text.
Maybe the idea of considering the class of all possible theories,
and the class of interpretative maps between theories and reality, is a
useful one. At the very least, it seems to me to be the only way of
being sure that there does not exist some excellent, concise, unified
description of nature that we are merely too unimaginative to have
considered!
Criticism welcome.
- Jamie
----------
Jamie Vicary
DAMTP, Cambridge, UK
jamievicary@gmail.com
.
|
|
| User: "Androcles" |
|
| Title: Re: Generalising physical theories |
29 Jan 2005 06:28:23 PM |
|
|
"Jamie Vicary" <jamievicary@gmail.com> wrote in message
news:cth583$1f7$1@gemini.csx.cam.ac.uk...
Dear all,
Science is about coming up with theories which well describe the
physical world.
No way.
Science is about observation first, investigation second ( maybe some
experiments to isolate certain facets of the observation) and THEN
explanation.
Nobody needs a theory of something that doesn't exist. Unfortunately
that is the way things have gone for the last 100 years in physics, so
now people are trying to find the non-existent that will fit their dumb
theories.
My theory is that bright green flying elephants lay eggs. Got any eggs
in your fridge? Ha! That proves my theory! Gimme a Nobel prize, I've
discovered bright green flying elephants.
Sometimes -- as with relativity and quantum theory --
these theories work well in some domains, but poorly or even
incompatibly in others.
Yeah, don't look for eggs in the tool shed. Wrong domain. The best
place to find them is in a wormhole in the fabric of spacetime. Thats
where the elephants lay them, and the grocery store owners pay people
minimum wage to collect them.
It used to be piecework at a penny an egg, but the guv'ment stopped it.
Consider the class of all possible theories; a class within which
quantum theory, relativity and any unified theory of nature must
exist.
Yeah, see, I told you my theory was right. It belongs to the class of
all possible theories.
Here, I am using the term "theory" in its most general sense: a
consistent set of rules about objects, the nature of the "rules" or
"objects" being completely unrestricted.
Well, of course. How else would bright green flying elephants exist if
they weren't hatched from eggs? Entirely a consistent theory, ask me
questions about it, I'll defend it. But don't forget my Nobel prize,
will you? I need the money for further research. I'm going to create
more wormholes, this time in black holes. I'm worried that the
elephants might become extinct. Too many people are eating eggs, we need
to feed mankind, so I'm doing you all a favour by increasing egg
production.
Does it make sense to consider theories in such a general way? I
would suggest that it does, and that meaningful statements about such
generalised theories can be made.
Absolutely! Just don't forget my prize, will you?
For example, it is clearly possible to create two theories which
despite different superficial formulations, are actually equivalent.
Well, yeah... some people have actually suggested Long-horns and Rhode
Island Reds lay eggs, but its a myth, I tell you. Everyone knows Foghorn
Leghorn is a foul male fowl and not an elephant at all. Why, he isn't
even bright green!
Don't forget my prize, will you? After all, I am agreeing with you. I
know I didn't at first, but you seem the sort of person I should agree
with and suck up to, so I do now.
Given this, is it possible to count the number of inequivalent
theories of complexity less than some complexity C, given some
objective measure of complexity?
Would that be in the complex plane, like the time dilation when an
elephant
exceeds the speed of light? You know, sqrt( 1 - (1.414 * c)^2 / c^2)
= i?
Furthermore, to any possible theory we can assign a particular
interpretation which maps the *abstract* objects in the theory to
directly percievable aspects of the world -- such as {spacetime,
governments, flowering shrubs, etc} --
Don't forget bright green flying elephants! (and my prize) and eggs are
of course
directly percievable aspects of the world ...
which our existing theories {relativity, politics, botany, etc}
describe. Again, I am emphasising here the very general sense in which
I am using the word "theory": a consistent set of rules about objects.
Yes, of course. My theory is a consistent set of rules about eggs, and
eggs are definitely objects.
(don't forget my prize... send the money, I'm not interested in fame)
Of course, as physicists, we are chiefly concerned with
interpretations which map abstract objects in our theories --
I'm much more that a physicist, I'm a biologist as well. I've been
studying
BGFEs for years!
like wavefunctions, curvature tensors, quantum operators and so on
Oh, math stuff. Yeah, I guess it's kinda useful if you understand it,
especially when you can go backwards in time so that (x,y,z,t) becomes a
vector because t has an additive inverse such that (-t) + t = 0.
Definition: A vector space, V, over a field F, is a set for which the
following 10 axioms hold. For all v, w, x X V, and all l,m X F
1: v + w X V
2: (v + w) + x = v + (w + x)
3: there exist the element 0 X V such that: v + 0 = 0 + v = v
4: for all v there exists -v such that v + (-v) = 0
http://members.tripod.com/~Paul_Kirby/Linear/linear.html
-- onto
aspects of the physical world like charge, mass and causality. Given a
particular theory -- a particular set of rules about objects -- it
might well be impossible to construct an interpretation on that theory
that is compatible with, for example, general relativity. We would
therefore discard that theory as a possible fundamental description of
our universe.
A formalism with which to deal with abstract theories, and their
interpretations as *physical* theories, might allow us to consider the
class of all theories which admit interpretations as BOTH quantum
theory AND general relativity.
Oh sure... don't forget my prize, will you?
I suppose superstring theory, for example, might be a theory in this
class. So would another physical theory which we could trivially
construct by gluing classical GR and quantum theory together and
considering them as one.
Having constructed this class of theories -- the class which admit
interpretations compatible with both GR and quantum theory --
Yeah yeah.... like I said, I want to create wormholes in black holes for
the elephants to lay eggs in. Don't forget my prize... after all, you
gave one to Hulse and Taylor for finding agreement with GR. I promise
the elephant's eggs will be far more useful.
an
attractive goal would then be to choose the theory which is least
complex (by some objective definition of complexity), and then state
that this theory -- with some attached interpretation in terms of
physical reality, which can be as complex as we like! -- is the
ultimate theory of reality. This notion of the complexity of the
abstract theory being unrelated, or perhaps inversely related, to the
complexity of its physical interpretation is obviously not new:
Einstein's equations are much, much shorter than any useful
explanatory text.
Maybe the idea of considering the class of all possible theories,
and the class of interpretative maps between theories and reality, is
a useful one.
Yeah yeah.... don't forget my prize, though.
At the very least, it seems to me to be the only way of being sure
that there does not exist some excellent, concise, unified description
of nature that we are merely too unimaginative to have considered!
Yes, I totally agree.. just don't forget my prize.
Criticism welcome.
- Jamie
Criticism? I wouldn't dream of it. It is not politically correct to
criticise.
----------
Jamie Vicary
DAMTP, Cambridge, UK
jamievicary@gmail.com
Oh, Cambridge. Not too far away from Kent.
Give my regards to Hawking, would you? His first wife wheeled him away
when I offered to buy him a beer down at Brighton (Sussex U.) In the
early 70's, I think it was.... hmmm.... maybe late 60's. Tell him the
offer is still open.
I never got the chance to straighten him out. I spent so long in the
States I almost said "I never got the chance to straighten his ***** out."
Androcles.
.
|
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|
| User: "Gregory L. Hansen" |
|
| Title: Re: Generalising physical theories |
29 Jan 2005 08:43:46 PM |
|
|
In article <cth583$1f7$1@gemini.csx.cam.ac.uk>,
Jamie Vicary <jamievicary@gmail.com> wrote:
Dear all,
Science is about coming up with theories which well describe the
physical world. Sometimes -- as with relativity and quantum theory --
these theories work well in some domains, but poorly or even
incompatibly in others.
Consider the class of all possible theories; a class within which
quantum theory, relativity and any unified theory of nature must exist.
Here, I am using the term "theory" in its most general sense: a
consistent set of rules about objects, the nature of the "rules" or
"objects" being completely unrestricted.
Does it make sense to consider theories in such a general way?
Isn't that rather like considering music to be any sequence of any
combination of notes? Sure that's (more or less) what music is, but by
making no effort to restrict the domain, absolutely nothing is said about
the subject.
I
would suggest that it does, and that meaningful statements about such
generalised theories can be made. For example, it is clearly possible to
create two theories which despite different superficial formulations,
are actually equivalent.
E.g. special relativity and Lorentz's aether theory, at least as applied
to electromagnetism.
Given this, is it possible to count the number
of inequivalent theories of complexity less than some complexity C,
given some objective measure of complexity?
One researcher (I have the reference at work) claims there exists an
infinite number of aether theories that could be formulated.
In general, I would have to play the ignorance card. There could be any
number of potential theories that just haven't been thought of yet. In
fact, the whole class of modern field theories didn't even exist in the
middle of the 19th century as they were still struggling with the concept
of "stuff" undulating and flowing around. Geometrical theories,
epitomized by the general theory of relativity, are another class that
weren't even conceived of in that time period. But once the first one is
developed, the field opens up in obvious ways; relax the triangle
postulate and see what happens, relax the postulate that the distance
d(x,y) equals d(y,x) and see what happens, etc. And just when you think
you have that figured out, along comes quantum mechanics.
You an enumerate some of the important theories and what distinguishes
them.
Description Geometry Dynamics
of state
---------------------------------------------------------
Newtonian Mechanics | Vector in | Euclidean | Newton's
| phase space | 3 + time | laws
----------------------------------------------------------
Special Relativity | Vector in | Minkowski | Newton's
| phase space | 4 dim | laws
----------------------------------------------------------
General Relativity | Vector in | pseudo- | Newton's
| phase space | Riemannian| laws
----------------------------------------------------------
Quantum Mechanics | Vector in | Euclidean | Newton's
| Hilbert space | 3 + time | laws
----------------------------------------------------------
Relativistic QM | Vector in | Minkowski | Newton's
| Hilbert Space | 4 dim | laws
----------------------------------------------------------
QM of black holes | Vector in | pseudo- | Newton's
| Hilbert Space | Riemannian| laws
----------------------------------------------------------
Go through the list and insert new assumptions. Try quasi-Riemannian
geometry. Extra dimensions have already been tried. Change the reliance
on Newton's laws-- momentum not conserved, F!=dp/dt, etc. The most
profound change was going from a state in phase space to a state in a
Hilbert space. Not only was that not an obvious change to make, it's a
change in a quality that would never have occured to most people could
have been other than what it was. It's a no-brainer now to come up with
the idea of throwing in any weird geometry you can think of, but I don't
know of any way to represent the state other than phase space or Hilbert
space. But there's probably an option 3 waiting out there somewhere, with
an equally profound effect.
--
"Let us learn to dream, gentlemen, then perhaps we shall find the
truth... But let us beware of publishing our dreams before they have been
put to the proof by the waking understanding." -- Friedrich August Kekulé
.
|
|
|
| User: "Jamie Vicary" |
|
| Title: Re: Generalising physical theories |
30 Jan 2005 01:48:27 PM |
|
|
Gregory L. Hansen wrote:
In article <cth583$1f7$1@gemini.csx.cam.ac.uk>,
Jamie Vicary <jamievicary@gmail.com> wrote:
Dear all,
Science is about coming up with theories which well describe the
physical world. Sometimes -- as with relativity and quantum theory --
these theories work well in some domains, but poorly or even
incompatibly in others.
Consider the class of all possible theories; a class within which
quantum theory, relativity and any unified theory of nature must exist.
Here, I am using the term "theory" in its most general sense: a
consistent set of rules about objects, the nature of the "rules" or
"objects" being completely unrestricted.
Does it make sense to consider theories in such a general way?
Isn't that rather like considering music to be any sequence of any
combination of notes? Sure that's (more or less) what music is, but by
making no effort to restrict the domain, absolutely nothing is said about
the subject.
Absolutely! The domain definitely needs to be restricted: we restrict it
by considering only those theories which have the correct structure to
admit interpretations both as GR and QFT. After having done this, we
then take the least complex theory we are left with, and proclaim this
theory to be the theory of reality.
I
would suggest that it does, and that meaningful statements about such
generalised theories can be made. For example, it is clearly possible to
create two theories which despite different superficial formulations,
are actually equivalent. Given this, is it possible to count the number
of inequivalent theories of complexity less than some complexity C,
given some objective measure of complexity?
In general, I would have to play the ignorance card. There could be any
number of potential theories that just haven't been thought of yet. In
fact, the whole class of modern field theories didn't even exist in the
middle of the 19th century as they were still struggling with the concept
of "stuff" undulating and flowing around. Geometrical theories,
epitomized by the general theory of relativity, are another class that
weren't even conceived of in that time period. But once the first one is
developed, the field opens up in obvious ways; relax the triangle
postulate and see what happens, relax the postulate that the distance
d(x,y) equals d(y,x) and see what happens, etc. And just when you think
you have that figured out, along comes quantum mechanics.
You an enumerate some of the important theories and what distinguishes
them.
Description Geometry Dynamics
of state
---------------------------------------------------------
Newtonian Mechanics | Vector in | Euclidean | Newton's
| phase space | 3 + time | laws
----------------------------------------------------------
Special Relativity | Vector in | Minkowski | Newton's
| phase space | 4 dim | laws
----------------------------------------------------------
General Relativity | Vector in | pseudo- | Newton's
| phase space | Riemannian| laws
----------------------------------------------------------
Quantum Mechanics | Vector in | Euclidean | Newton's
| Hilbert space | 3 + time | laws
----------------------------------------------------------
Relativistic QM | Vector in | Minkowski | Newton's
| Hilbert Space | 4 dim | laws
----------------------------------------------------------
QM of black holes | Vector in | pseudo- | Newton's
| Hilbert Space | Riemannian| laws
----------------------------------------------------------
Go through the list and insert new assumptions. Try quasi-Riemannian
geometry. Extra dimensions have already been tried. Change the reliance
on Newton's laws-- momentum not conserved, F!=dp/dt, etc. The most
profound change was going from a state in phase space to a state in a
Hilbert space. Not only was that not an obvious change to make, it's a
change in a quality that would never have occured to most people could
have been other than what it was. It's a no-brainer now to come up with
the idea of throwing in any weird geometry you can think of, but I don't
know of any way to represent the state other than phase space or Hilbert
space. But there's probably an option 3 waiting out there somewhere, with
an equally profound effect.
Exactly!! I completely agree with what you're saying. How can we
find this new, profound approach? It's a treasure hunt of epic
proportions. In the past, we had experiment to guide us --- but we might
now have reached the stage where no new experiments can provide us with
the spark of a new idea that we need to put all of our fundamental
science on a new footing.
So, let's think what features this profound, new approach to
physics might have --- after all, we need a way to know when we've found
it! The only possible defining feature must be that it allows our
existing physical theories, which seem perfect as far as our
experimentalists can tell, to be expressed from the same mathematical
and philosophical foundation.
So, when the fundamental core of the new theory is expressed, you
should be able to describe a single, neat idea --- like the principle of
equivalence, or superposition or whatever --- but this time it would be
an idea that gives rise to *all of physics*, not just some part of it.
(Of course, the WAY in which it gives rise to it would almost certainly
be very complicated, but that's what we expect; our brains have not
evolved to understand physics.) So we would be describing a theory which
*fundamentally* is far simpler than our current confirmed best guess,
which is GR and QFT stuck together, two clearly separate theories
presented side by side as the two halves to our understanding of reality.
For example, maybe superstring theory is the correct fundamental
theory. It would therefore be correct to state the behaviour of these
objects we call superstrings --- the underlying mechanics of the theory
--- and say that this statement encompasses all the physics of the
universe. Now, working out HOW it predicts the things we know to be true
--- i.e., GR and QFT --- is fiendishly difficult (after all, thousands
of people work on string theory worldwide). But if it works, then it works.
What I am spelling out in this thread is the idea that it might be
possible to go about doing fundamental physics in a different way.
Rather than saying "how might the universe work? hmm, maybe there are
these stringy things... let's work out their properties" it might be
possible to say "okay, we've got GR and QFT... what is the simplest
possible fundamental theory that would give rise to these?".
Jamie
.
|
|
|
| User: "Gregory L. Hansen" |
|
| Title: Re: Generalising physical theories |
30 Jan 2005 03:39:56 PM |
|
|
In article <ctjdmg$r4j$1@gemini.csx.cam.ac.uk>,
Jamie Vicary <jamievicary@gmail.com> wrote:
Gregory L. Hansen wrote:
In article <cth583$1f7$1@gemini.csx.cam.ac.uk>,
Jamie Vicary <jamievicary@gmail.com> wrote:
You an enumerate some of the important theories and what distinguishes
them.
Description Geometry Dynamics
of state
---------------------------------------------------------
Newtonian Mechanics | Vector in | Euclidean | Newton's
| phase space | 3 + time | laws
----------------------------------------------------------
Special Relativity | Vector in | Minkowski | Newton's
| phase space | 4 dim | laws
----------------------------------------------------------
General Relativity | Vector in | pseudo- | Newton's
| phase space | Riemannian| laws
----------------------------------------------------------
Quantum Mechanics | Vector in | Euclidean | Newton's
| Hilbert space | 3 + time | laws
----------------------------------------------------------
Relativistic QM | Vector in | Minkowski | Newton's
| Hilbert Space | 4 dim | laws
----------------------------------------------------------
QM of black holes | Vector in | pseudo- | Newton's
| Hilbert Space | Riemannian| laws
----------------------------------------------------------
Go through the list and insert new assumptions. Try quasi-Riemannian
geometry. Extra dimensions have already been tried. Change the reliance
on Newton's laws-- momentum not conserved, F!=dp/dt, etc. The most
profound change was going from a state in phase space to a state in a
Hilbert space. Not only was that not an obvious change to make, it's a
change in a quality that would never have occured to most people could
have been other than what it was. It's a no-brainer now to come up with
the idea of throwing in any weird geometry you can think of, but I don't
know of any way to represent the state other than phase space or Hilbert
space. But there's probably an option 3 waiting out there somewhere, with
an equally profound effect.
Exactly!! I completely agree with what you're saying. How can we
find this new, profound approach? It's a treasure hunt of epic
proportions. In the past, we had experiment to guide us --- but we might
now have reached the stage where no new experiments can provide us with
the spark of a new idea that we need to put all of our fundamental
science on a new footing.
So, let's think what features this profound, new approach to
physics might have --- after all, we need a way to know when we've found
it! The only possible defining feature must be that it allows our
existing physical theories, which seem perfect as far as our
experimentalists can tell, to be expressed from the same mathematical
and philosophical foundation.
We'll know we've found it when it's shown that it encompasses experimental
details that our current theory chokes on.
Along the line of "If it ain't broke don't fix it", it's not even possible
to claim one theory is correct and another wrong if they make identical
predictions of observable things. It might not even be sensible to say
there's a "correct" theory, as opposed to a human invention that models
physical phenomena arbitrarily well. If you do find the great new theory
that is claimed, in the absence of evidence, to be The Way Things Really
Are, and then data comes in to disprove it, you'll know only that it was
never The Way Things Really Are. And if that data hasn't been found, you
can't rule out the possibility that it will be published tomorrow.
You can make a list of things you'd like to see in a theory. People's
lists vary, but usually include qualities like a small set of universally
applied postulates (not special-casing one experiment or another), a wide
scope with an equally wide range of tests, suggesting new relationships
not thought of before, and certain aesthetic ideals. Some on this
newsgroup don't think a theory is a theory unless it reduces phenomena to
little marbles bumping into each other-- I guess there's no accounting
for taste.
What I am spelling out in this thread is the idea that it might be
possible to go about doing fundamental physics in a different way.
Rather than saying "how might the universe work? hmm, maybe there are
these stringy things... let's work out their properties" it might be
possible to say "okay, we've got GR and QFT... what is the simplest
possible fundamental theory that would give rise to these?".
You're not the first person to ask that. The search for TOEs and GUIs
have been on for almost a century. So far, nobody knows. Sure there's
string theories, but they're still untestable. So if you like them, you
could say they're as good a candidate as anything, at least until data
starts coming in.
I usually let my signature be chosen at random, but I picked this one out.
--
"Experiments are the only means of knowledge at our disposal. The rest is
poetry, imagination." -- Max Planck
.
|
|
|
| User: "Jamie Vicary" |
|
| Title: Re: Generalising physical theories |
30 Jan 2005 04:18:57 PM |
|
|
Gregory L. Hansen wrote:
In article <ctjdmg$r4j$1@gemini.csx.cam.ac.uk>,
Jamie Vicary <jamievicary@gmail.com> wrote:
Gregory L. Hansen wrote:
In article <cth583$1f7$1@gemini.csx.cam.ac.uk>,
Jamie Vicary <jamievicary@gmail.com> wrote:
You an enumerate some of the important theories and what distinguishes
them.
Description Geometry Dynamics
of state
---------------------------------------------------------
Newtonian Mechanics | Vector in | Euclidean | Newton's
| phase space | 3 + time | laws
----------------------------------------------------------
Special Relativity | Vector in | Minkowski | Newton's
| phase space | 4 dim | laws
----------------------------------------------------------
General Relativity | Vector in | pseudo- | Newton's
| phase space | Riemannian| laws
----------------------------------------------------------
Quantum Mechanics | Vector in | Euclidean | Newton's
| Hilbert space | 3 + time | laws
----------------------------------------------------------
Relativistic QM | Vector in | Minkowski | Newton's
| Hilbert Space | 4 dim | laws
----------------------------------------------------------
QM of black holes | Vector in | pseudo- | Newton's
| Hilbert Space | Riemannian| laws
----------------------------------------------------------
Go through the list and insert new assumptions. Try quasi-Riemannian
geometry. Extra dimensions have already been tried. Change the reliance
on Newton's laws-- momentum not conserved, F!=dp/dt, etc. The most
profound change was going from a state in phase space to a state in a
Hilbert space. Not only was that not an obvious change to make, it's a
change in a quality that would never have occured to most people could
have been other than what it was. It's a no-brainer now to come up with
the idea of throwing in any weird geometry you can think of, but I don't
know of any way to represent the state other than phase space or Hilbert
space. But there's probably an option 3 waiting out there somewhere, with
an equally profound effect.
Exactly!! I completely agree with what you're saying. How can we
find this new, profound approach? It's a treasure hunt of epic
proportions. In the past, we had experiment to guide us --- but we might
now have reached the stage where no new experiments can provide us with
the spark of a new idea that we need to put all of our fundamental
science on a new footing.
So, let's think what features this profound, new approach to
physics might have --- after all, we need a way to know when we've found
it! The only possible defining feature must be that it allows our
existing physical theories, which seem perfect as far as our
experimentalists can tell, to be expressed from the same mathematical
and philosophical foundation.
We'll know we've found it when it's shown that it encompasses experimental
details that our current theory chokes on.
Of course. We have not yet found such a theory.
Along the line of "If it ain't broke don't fix it", it's not even possible
to claim one theory is correct and another wrong if they make identical
predictions of observable things. It might not even be sensible to say
there's a "correct" theory, as opposed to a human invention that models
physical phenomena arbitrarily well. If you do find the great new theory
that is claimed, in the absence of evidence, to be The Way Things Really
Are, and then data comes in to disprove it, you'll know only that it was
never The Way Things Really Are. And if that data hasn't been found, you
can't rule out the possibility that it will be published tomorrow.
Of course; I agree that it might not be sensible to say that a "correct"
theory can exist. But there must be one that works better than what we
have now, because there are questions we can ask our modern theories
that they cannot answer clearly and unambiguously. It is unacceptable
that A unified theory (not THE unified theory, but A unified theory) --
a theory of which we can ask any question, and get a clear answer in
return -- does not exist.
[snip]
What I am spelling out in this thread is the idea that it might be
possible to go about doing fundamental physics in a different way.
Rather than saying "how might the universe work? hmm, maybe there are
these stringy things... let's work out their properties" it might be
possible to say "okay, we've got GR and QFT... what is the simplest
possible fundamental theory that would give rise to these?".
You're not the first person to ask that. The search for TOEs and GUIs
have been on for almost a century. So far, nobody knows. Sure there's
string theories, but they're still untestable. So if you like them, you
could say they're as good a candidate as anything, at least until data
starts coming in.
I would be surprised if I were the first person to have asked that. I
think other people have asked, but I don't think other people have taken
the approach seriously enough; it would be too difficult and too
unpredictable to base an entire academic career upon, which is what
would be required.
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| User: "Mike" |
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| Title: Re: Generalising physical theories |
30 Jan 2005 03:25:01 PM |
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Jamie Vicary wrote:
[snip]
What I am spelling out in this thread is the idea that it might
be
possible to go about doing fundamental physics in a different way.
Rather than saying "how might the universe work? hmm, maybe there are
these stringy things... let's work out their properties" it might be
possible to say "okay, we've got GR and QFT... what is the simplest
possible fundamental theory that would give rise to these?".
Jamie
You mean give rise both of these at the same time? The answer is none.
That may surprise you but it looks that way. Especially to "cave men"
who look at the "shadows" of reality from a small opening above their
heads (from Plato in Phaedo)
Question: can you derive the compiler code from a random executable
generated by it?
Even worse: there can be no algorithm to decide whether a given
algorithm is free of infinite loops.
Even much worse: If U is an omega-consistent and=AD adequate
arithemtical logic, then U is incomplete.=20
Mike
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| User: "Jamie Vicary" |
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| Title: Re: Generalising physical theories |
30 Jan 2005 04:11:02 PM |
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Mike wrote:
Jamie Vicary wrote:
[snip]
What I am spelling out in this thread is the idea that it might
be
possible to go about doing fundamental physics in a different way.
Rather than saying "how might the universe work? hmm, maybe there are
these stringy things... let's work out their properties" it might be
possible to say "okay, we've got GR and QFT... what is the simplest
possible fundamental theory that would give rise to these?".
Jamie
You mean give rise both of these at the same time? The answer is none.
That may surprise you but it looks that way. Especially to "cave men"
who look at the "shadows" of reality from a small opening above their
heads (from Plato in Phaedo)
I think the answer of "none" is highly, highly pessimistic. I think most
physicists today would be much more optimistic than you; it would hardly
be fair to say that research into unified theories has stagnated in the
slightest.
Question: can you derive the compiler code from a random executable
generated by it?
You cannot completely discern it, no. But if you have a large enough
sample of executables (i.e. experiments) you might be able to tell that
it seems to act in different ways for different types of program (GR and
QFT.) You might have good reasons to believe that, actually, it's really
acting the SAME was all the time (because black holes, for example,
require both sets of ideas to be employed at once) and be upset that you
can't manage to conceive of a single compiler which produces this
apparently diverse functionality from a single set of rules, rules which
don't, at their lowest level of construction, spell out two different
modes of compilation (for GR and QFT respectively.)
The best you can do is say "this is how I think the compiler works ---
it might work differently, but all these different modes of operation
would produce identical results, so of course there's no way I can tell
between them". However, we're not at that stage yet in our understanding
of science. We do not yet have a single theory that can describe all of
the universe; in terms of our metaphor, we don't know how black hole
singularities are compiled! If we could HAVE A LOOK by doing an
experiment, then that would be great, but we can't!
Jamie
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| User: "Androcles" |
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| Title: Re: Generalising physical theories |
01 Feb 2005 02:15:49 PM |
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"Jamie Vicary" <jamievicary@gmail.com> wrote in message
news:ctjm1r$fe3$1@gemini.csx.cam.ac.uk...
Mike wrote:
Jamie Vicary wrote:
[snip]
What I am spelling out in this thread is the idea that it might
be
possible to go about doing fundamental physics in a different way.
Rather than saying "how might the universe work? hmm, maybe there are
these stringy things... let's work out their properties" it might be
possible to say "okay, we've got GR and QFT... what is the simplest
possible fundamental theory that would give rise to these?".
Jamie
You mean give rise both of these at the same time? The answer is
none.
That may surprise you but it looks that way. Especially to "cave men"
who look at the "shadows" of reality from a small opening above their
heads (from Plato in Phaedo)
I think the answer of "none" is highly, highly pessimistic. I think
most physicists today would be much more optimistic than you; it would
hardly be fair to say that research into unified theories has
stagnated in the slightest.
Question: can you derive the compiler code from a random executable
generated by it?
You cannot completely discern it, no. But if you have a large enough
sample of executables (i.e. experiments) you might be able to tell
that it seems to act in different ways for different types of program
(GR and QFT.) You might have good reasons to believe that, actually,
it's really acting the SAME was all the time (because black holes, for
example, require both sets of ideas to be employed at once) and be
upset that you can't manage to conceive of a single compiler which
produces this apparently diverse functionality from a single set of
rules, rules which don't, at their lowest level of construction, spell
out two different modes of compilation (for GR and QFT respectively.)
What black holes? I've never seen one.
Mike is talking about a compiler.
We might get a black hole out of one if we feed Shakespeare's Macbeth
into it.
GIGO, chum.
Read Hamlet's soliloquy:
To be, or not to be: that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them? To die: to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to, 'tis a consummation
Devoutly to be wish'd. To die, to sleep;
To sleep: perchance to dream: ay, there's the rub;
That's what are doing. Dreaming of black holes.
The best you can do is say "this is how I think the compiler works ---
it might work differently, but all these different modes of operation
would produce identical results, so of course there's no way I can
tell between them".
Only if you've found black hole. So far you haven't, but by golly, if
you ever do, you'll be all set, wont you? Waht will you do if a bright
green flying elephant's egg turns up instead? Got a theory ready for
that as well?
However, we're not at that stage yet in our understanding of science.
You are not at the stage for understanding logic either.
The second sign of insanity is a big black hole in the palm of your
hand.
The first sign is looking for it.
We do not yet have a single theory that can describe all of the
universe; in terms of our metaphor, we don't know how black hole
singularities are compiled! If we could HAVE A LOOK by doing an
experiment, then that would be great, but we can't!
We've had a single theory for eons. God made it. Before that, lots of
gods made bits of it. Thor made thunder and lightning. Mars made war.
Now you want a new theory, but it has to be based on your old religion,
just as the joyous feasts to celibrate the rebirth of the Sun follows
after the shortest day is now called Christmas.
Oh joy, the Messiah Einstein is at the right hand of god, steering the
universe along its course.
Care for a black hole, anyone? Save the strawberry ones for me, would
you?
Androcles.
Jamie
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| User: "Mike" |
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| Title: Re: Generalising physical theories |
31 Jan 2005 10:37:55 AM |
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Jamie Vicary wrote:
[snip]
I think the answer of "none" is highly, highly pessimistic. I think
most
physicists today would be much more optimistic than you; it would
hardly
be fair to say that research into unified theories has stagnated in
the
slightest.
[snip]
Your emotive approach to science is of no interest to me. The problems
are well known. Try to pinpoint the position of an electron and there
momentum goes out of certainty. Or, try to make a complete theory and
suddenly it becomes inconsistent and vice versa.
Before you plunge yourself into the type of hard questions you cannot
answer, try to answer a simple one:
There is only one barber in a small village who naturally shaves all
men who do not shave themselves.
Does this barber shave himself? that is the question.
If he does, then he does not
If he does not, then he does
Mike
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| User: "Uncle Al" |
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| Title: Re: Generalising physical theories |
29 Jan 2005 07:20:45 PM |
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Jamie Vicary wrote:
Dear all,
Science is about coming up with theories which well describe the
physical world. Sometimes -- as with relativity and quantum theory --
these theories work well in some domains, but poorly or even
incompatibly in others.
Boundary conditions. Initial assumptions. Postulates.
Consider the class of all possible theories; a class within which
quantum theory, relativity and any unified theory of nature must exist.
Here, I am using the term "theory" in its most general sense: a
consistent set of rules about objects, the nature of the "rules" or
"objects" being completely unrestricted.
Planck's constant (h, enforces uncertainty in measurement; h-bar is
the fundamental unit of action), Newton's constant (Big G, scales
gravitation), and lightspeed (c, enforces information transfer delay)
define physics:
? h=h G=G c=infinity
mechanics,
electrostatics: h=zero G=zero c=infinity
classical physics: h=zero G=G c=infinity
quantum mechanics: h=h G=zero c=infinity
special relativity: h=zero G=zero c=c
general relativity: h=zero G=G c=c
quantum field theory: h=h G=zero c=c
Theory of Everything: h=h G=G c=c
Does it make sense to consider theories in such a general way? I
would suggest that it does, and that meaningful statements about such
generalised theories can be made. For example, it is clearly possible to
create two theories which despite different superficial formulations,
are actually equivalent. Given this, is it possible to count the number
of inequivalent theories of complexity less than some complexity C,
given some objective measure of complexity?
M-theory. About 10^300 legitimate possiblities.
Furthermore, to any possible theory we can assign a particular
interpretation which maps the *abstract* objects in the theory to
directly percievable aspects of the world -- such as {spacetime,
governments, flowering shrubs, etc} -- which our existing theories
{relativity, politics, botany, etc} describe. Again, I am emphasising
here the very general sense in which I am using the word "theory": a
consistent set of rules about objects.
Of course, as physicists, we are chiefly concerned with
interpretations which map abstract objects in our theories -- like
wavefunctions, curvature tensors, quantum operators and so on -- onto
aspects of the physical world like charge, mass and causality. Given a
particular theory -- a particular set of rules about objects -- it might
well be impossible to construct an interpretation on that theory that is
compatible with, for example, general relativity. We would therefore
discard that theory as a possible fundamental description of our universe.
A formalism with which to deal with abstract theories, and their
interpretations as *physical* theories, might allow us to consider the
class of all theories which admit interpretations as BOTH quantum theory
AND general relativity. I suppose superstring theory, for example, might
be a theory in this class. So would another physical theory which we
could trivially construct by gluing classical GR and quantum theory
together and considering them as one.
10^300 legitmate formulations of M-theory. Counting is hard. 10^30
possibilities would be a nightmare.
Having constructed this class of theories -- the class which admit
interpretations compatible with both GR and quantum theory -- an
attractive goal would then be to choose the theory which is least
complex (by some objective definition of complexity), and then state
that this theory -- with some attached interpretation in terms of
physical reality, which can be as complex as we like! -- is the ultimate
theory of reality. This notion of the complexity of the abstract theory
being unrelated, or perhaps inversely related, to the complexity of its
physical interpretation is obviously not new: Einstein's equations are
much, much shorter than any useful explanatory text.
Maybe the idea of considering the class of all possible theories,
and the class of interpretative maps between theories and reality, is a
useful one. At the very least, it seems to me to be the only way of
being sure that there does not exist some excellent, concise, unified
description of nature that we are merely too unimaginative to have
considered!
Criticism welcome.
OK in principle but not reducible to practice. It is like saying we
could create literature by strumming random letters across a page.
Call it a dot matrix printer 65-character line with 55 lines/page.
We'll drop the q's and add a space,
[(65)(55)]^(26) = 2.43x10^92 different pages
Even a single line impossibly hurts,
(65)^(26) = 1.37x10^47 different lines
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
.
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| User: "Jamie Vicary" |
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| Title: Re: Generalising physical theories |
30 Jan 2005 01:27:40 PM |
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OK in principle but not reducible to practice. It is like saying we
could create literature by strumming random letters across a page.
Call it a dot matrix printer 65-character line with 55 lines/page.
We'll drop the q's and add a space,
[(65)(55)]^(26) = 2.43x10^92 different pages
Even a single line impossibly hurts,
(65)^(26) = 1.37x10^47 different lines.
Sure! That's an awful lot of possibilities. A huge great number of
theories could be generated. But I'm certainly not suggesting some kind
of manual search through every possible theory! I'm talking about some
mathematical way --- some kind of extension of category theory, perhaps
--- that you could use to isolate those possible theories which are
mutually inequivalent, and which admit interpretations confirming our
two well-established theories, GR and QFT.
Some of these theories will be complicated, but some would be simpler,
letting the mathematical structure of GR and QFT emerge from the same
type of fundamental interaction between abstract objects. It's the
nature of those fundamental interactions that we're interested in, after
all.
Jamie
.
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| User: "Uncle Al" |
|
| Title: Re: Generalising physical theories |
30 Jan 2005 03:01:49 PM |
|
|
Jamie Vicary wrote:
OK in principle but not reducible to practice. It is like saying we
could create literature by strumming random letters across a page.
Call it a dot matrix printer 65-character line with 55 lines/page.
We'll drop the q's and add a space,
[(65)(55)]^(26) = 2.43x10^92 different pages
Even a single line impossibly hurts,
(65)^(26) = 1.37x10^47 different lines.
Sure! That's an awful lot of possibilities. A huge great number of
theories could be generated. But I'm certainly not suggesting some kind
of manual search through every possible theory! I'm talking about some
mathematical way --- some kind of extension of category theory, perhaps
--- that you could use to isolate those possible theories which are
mutually inequivalent, and which admit interpretations confirming our
two well-established theories, GR and QFT.
Some of these theories will be complicated, but some would be simpler,
letting the mathematical structure of GR and QFT emerge from the same
type of fundamental interaction between abstract objects. It's the
nature of those fundamental interactions that we're interested in, after
all.
The small, countable infinity is the number of integers. The number
of numbers (points on a line) is an infinitely bigger infinity and not
countable at all. The number of functions through a point is
infiniitely bigger than the number of points on a line. The number of
theories will be inconveniently large to consider content in any way.
Any viable interesting theory beyond GR and QM will
1) Be predictive.
2) Explicitly accept c=c, G=G, and h=h all simultaneously. Its
real world-applicable subsections will selectively have c=infinity,
G=0, and h=0 as limiting cases.
That very nicely limits the number of "good" new theories to zero.
Initiate with simplicity. Postulate c=c (speed limit of information
propgation), G=G (gravitation scaling), h=h (limits to measurement
certainty) and go on from there.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
.
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| User: "Androcles" |
|
| Title: Re: Generalising physical theories |
30 Jan 2005 07:26:46 PM |
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"Uncle Al" <UncleAl0@hate.spam.net> wrote in message
news:41FD4B3D.B247F2FC@hate.spam.net...
Jamie Vicary wrote:
OK in principle but not reducible to practice. It is like saying
we
could create literature by strumming random letters across a page.
Call it a dot matrix printer 65-character line with 55 lines/page.
We'll drop the q's and add a space,
[(65)(55)]^(26) = 2.43x10^92 different pages
Even a single line impossibly hurts,
(65)^(26) = 1.37x10^47 different lines.
Sure! That's an awful lot of possibilities. A huge great number of
theories could be generated. But I'm certainly not suggesting some
kind
of manual search through every possible theory! I'm talking about
some
mathematical way --- some kind of extension of category theory,
perhaps
--- that you could use to isolate those possible theories which are
mutually inequivalent, and which admit interpretations confirming our
two well-established theories, GR and QFT.
Some of these theories will be complicated, but some would be
simpler,
letting the mathematical structure of GR and QFT emerge from the same
type of fundamental interaction between abstract objects. It's the
nature of those fundamental interactions that we're interested in,
after
all.
The small, countable infinity is the number of integers.
Let's count them.
0
-1, 1..... that's 2
-2, 2..... that's 4
-3, 3 ... that's 6
-4, 4.... that's 8
Hmmm.... looks like the small, countable infinity is twice infinity.
You are spewing psychotic fucking idiot with no wang, Schwartz.
Androcles.
.
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| User: "tj Frazir" |
|
| Title: Re: Generalising physical theories |
01 Feb 2005 06:43:24 PM |
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The standard modle is mass V.
evryting falls twards the center of the atom and the faster it moves
the more space it takes up.
the wavical universe
the fixed amount of energy from the big bang taking up more space.
Gravity is a push to less energy as a low energy rate forms around
mass.
Up is a gain in mass across the atom.
All the atoms mass falls twards its center.
1/2 the atom has more mass falling in one direction than the other.
The atom pushes its sef down the energy slope. The gain in mass is F.
F is pushing the atoms wieght.
evry gain of mass is proportional to the mass of evry atom.
F--MA
.
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| User: "Jamie Vicary" |
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| Title: Re: Generalising physical theories |
30 Jan 2005 04:03:54 PM |
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Uncle Al wrote:
Jamie Vicary wrote:
OK in principle but not reducible to practice. It is like saying we
could create literature by strumming random letters across a page.
Call it a dot matrix printer 65-character line with 55 lines/page.
We'll drop the q's and add a space,
[(65)(55)]^(26) = 2.43x10^92 different pages
Even a single line impossibly hurts,
(65)^(26) = 1.37x10^47 different lines.
Sure! That's an awful lot of possibilities. A huge great number of
theories could be generated. But I'm certainly not suggesting some kind
of manual search through every possible theory! I'm talking about some
mathematical way --- some kind of extension of category theory, perhaps
--- that you could use to isolate those possible theories which are
mutually inequivalent, and which admit interpretations confirming our
two well-established theories, GR and QFT.
Some of these theories will be complicated, but some would be simpler,
letting the mathematical structure of GR and QFT emerge from the same
type of fundamental interaction between abstract objects. It's the
nature of those fundamental interactions that we're interested in, after
all.
The small, countable infinity is the number of integers. The number
of numbers (points on a line) is an infinitely bigger infinity and not
countable at all. The number of functions through a point is
infiniitely bigger than the number of points on a line. The number of
theories will be inconveniently large to consider content in any way.
Any viable interesting theory beyond GR and QM will
1) Be predictive.
2) Explicitly accept c=c, G=G, and h=h all simultaneously. Its
real world-applicable subsections will selectively have c=infinity,
G=0, and h=0 as limiting cases.
That very nicely limits the number of "good" new theories to zero.
Initiate with simplicity. Postulate c=c (speed limit of information
propgation), G=G (gravitation scaling), h=h (limits to measurement
certainty) and go on from there.
That is a very, very big statement, to say that that limits the number
of "good" new theories to zero. Certainly, it limits the number of
viable theories to a vanishingly small subset of the total. To say that
it truly limits the number to *zero*, though, is saying no unified
description of nature can exist. I hope many people would agree with me
when I say your pessimism is not generally accepted.
Of course we need a theory which involves, somehow, our three important
constants of nature; maybe, if we're unlucky, it needs other things like
coupling constants as well. Saying "Postulate c=c, G=G and h=h and go on
from there" is all very well --- but the question is, going on from
there is rather difficult, and has essentially been the driving force
behind a large section of physics for half a century! What I am
proposing is a methodology that would give direction to how to "go on
from there".
Jamie
.
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| User: "Uncle Al" |
|
| Title: Re: Generalising physical theories |
30 Jan 2005 06:12:25 PM |
|
|
Jamie Vicary wrote:
Uncle Al wrote:
Jamie Vicary wrote:
OK in principle but not reducible to practice. It is like saying we
could create literature by strumming random letters across a page.
Call it a dot matrix printer 65-character line with 55 lines/page.
We'll drop the q's and add a space,
[(65)(55)]^(26) = 2.43x10^92 different pages
Even a single line impossibly hurts,
(65)^(26) = 1.37x10^47 different lines.
Sure! That's an awful lot of possibilities. A huge great number of
theories could be generated. But I'm certainly not suggesting some kind
of manual search through every possible theory! I'm talking about some
mathematical way --- some kind of extension of category theory, perhaps
--- that you could use to isolate those possible theories which are
mutually inequivalent, and which admit interpretations confirming our
two well-established theories, GR and QFT.
Some of these theories will be complicated, but some would be simpler,
letting the mathematical structure of GR and QFT emerge from the same
type of fundamental interaction between abstract objects. It's the
nature of those fundamental interactions that we're interested in, after
all.
The small, countable infinity is the number of integers. The number
of numbers (points on a line) is an infinitely bigger infinity and not
countable at all. The number of functions through a point is
infiniitely bigger than the number of points on a line. The number of
theories will be inconveniently large to consider content in any way.
Any viable interesting theory beyond GR and QM will
1) Be predictive.
2) Explicitly accept c=c, G=G, and h=h all simultaneously. Its
real world-applicable subsections will selectively have c=infinity,
G=0, and h=0 as limiting cases.
That very nicely limits the number of "good" new theories to zero.
Initiate with simplicity. Postulate c=c (speed limit of information
propgation), G=G (gravitation scaling), h=h (limits to measurement
certainty) and go on from there.
That is a very, very big statement, to say that that limits the number
of "good" new theories to zero.
That's the fact, Jack. NO extant predictive theory allows
simultaneous c=c, G=G, and h=h. Nobody has the slightest
hallucination of an inkling of an idea how to pull it off. M-theory
is 100% non-predictive. Lattice quantum gravitation cannot reproduce
relativity.
Certainly, it limits the number of
viable theories to a vanishingly small subset of the total. To say that
it truly limits the number to *zero*, though, is saying no unified
description of nature can exist. I hope many people would agree with me
when I say your pessimism is not generally accepted.
Fine. Quote a counterexample. There are none.
Of course we need a theory which involves, somehow, our three important
constants of nature; maybe, if we're unlucky, it needs other things like
coupling constants as well. Saying "Postulate c=c, G=G and h=h and go on
from there" is all very well --- but the question is, going on from
there is rather difficult, and has essentially been the driving force
behind a large section of physics for half a century! What I am
proposing is a methodology that would give direction to how to "go on
from there".
If it is a proper complete theory it does not need 22 empirical inputs
like the Standard Model to set masses. The Standard Model is 100%
massless. As the universe is visibly massed, this was a problem. The
Higgs mechanism is an ad hoc patch. A proper complete theory is ab
initio.
GR and QM are awesome in their respective venues - not a single
experimental or observational exception to prediction from quarks to
the whole universe. For all that, they blatantly contradict where
they overlap. We have no idea at all what overall theory GR and QM
are special cases of.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
.
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| User: "robert j. kolker" |
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| Title: Re: Generalising physical theories |
30 Jan 2005 07:15:00 PM |
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Uncle Al wrote:
If it is a proper complete theory it does not need 22 empirical inputs
like the Standard Model to set masses. The Standard Model is 100%
massless. As the universe is visibly massed, this was a problem. The
Higgs mechanism is an ad hoc patch. A proper complete theory is ab
initio.
This would imply one could deduce all of reality a priori. This is the
kind of nonsense Plato taught. I simply do not believe it. I would have
to see it done first.
Bob Kolker
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