"we mathematicians should write our own expositions of basic physics"
Peter
at the end of a review of Barut's 'Electrodynamics' (1964) I have found the
following sentences which I would like to make known to our group.
"The greatest obstacles to a mathematician grasping the problems
that are on the frontiers of physics is his lack of conditioning in the
fundamentals and his own overspecialized training and research.
Ideally, we mathematicians should write our own expositions of basic
physics, so as not to cut our profession off from its historical roots;
until then, we can only applaud efforts such as this one that bridge
the gap, and hope that more such striking expositions will be written."
ROBERT HERMANN
Bull. Am. Math. Soc. 70 (1964) 5, 658-660,
http://projecteuclid.org/euclid.bams/1183526246
Hoping you enjoy it,
Peter
Oh No
>"The greatest obstacles to a mathematician grasping the problems that
>are on the frontiers of physics is his lack of conditioning in the
>fundamentals and his own overspecialized training and research.
>Ideally, we mathematicians should write our own expositions of basic
>physics, so as not to cut our profession off from its historical roots;
>until then, we can only applaud efforts such as this one that bridge
>the gap, and hope that more such striking expositions will be written."
>
>ROBERT HERMANN
>Bull. Am. Math. Soc. 70 (1964) 5, 658-660,
>http://projecteuclid.org/euclid.bams/1183526246
I would say more than that. Not just ideally, but that it is essential
to take such an approach. Typical approaches to physics lose sight of
mathematical structure and consider physics as established facts. But on
the frontiers, facts and speculations become blurred. The issues on the
frontiers are interpretation of quantum theory and unification. The
essential requirement of a resolution to these issues is consistency,
both internal consistency and consistency with observation. Mathematics
can be seen as the study of consistency. Only by applying a
mathematical, axiomatic, approach can one address issues of consistency.
Only by constructing such an approach oneself from first principles, by
doing the logical steps oneself, does one really understand the logical
structures required by physics. The lack of such approaches in modern
physics is to me part and parcel of the stagnation of advance in physics
over the last 50 or so years..
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
Hendrik van Hees
>
> at the end of a review of Barut's 'Electrodynamics' (1964) I have
> found the following sentences which I would like to make known to our
> group.
That's a nice booklet, but one has to read it with care. There are lots
of mistakes in the mathematics even a humble physicist can find!
--
Hendrik van Hees Institut für Theoretische Physik
Phone: +49 641 99-33342 Justus-Liebig-Universität Gießen
Fax: +49 641 99-33309 D-35392 Gießen
http://theory.gsi.de/~vanhees/faq/
Oh No
>Charles Francis wrote:
>>Thus spake Peter:
>physics. To insist on an axiomatic basis for physics puts a major
>constraint on understanding nature.
The only constraint is that nature must be consistent. Do you dispute
it?
>It is, what I like to call, a
>religious fundamentalist's approach to science. You don't need a
>laboratory if you have axioms.
At the frontiers of physics, we do not have axioms. That is, we need to
determine what the axioms are.
>It would be nice to think that axioms can be found that nature is
>obliged to follow to construct all natural laws, but nature always seems
>to be throwing spanners into the gearbox. The Greeks had an excellent
>set of axioms that explained everything, because they forced it to fit
>everything.
They only had axioms for Euclidean geometry. Certainly that did not
explain everything.
>Physics has only progressed because of the laboratory.
While I don't dispute the value of the laboratory, or indeed the need
for it, the big advances have been conceptual and mathematical, as when
Newton wrote down his laws, Maxwell his equations, or when Einstein
developed relativity (in particular the general theory).
>Mathematics is an extremely useful tool to explain what is observed, but
>the major chore a physicist has regarding mathematics is trying to
>understand what the mathematics mean. Answering these kinds of questions
>occupies most of the space in this ng, as one would expect.
Indeed, it should. However, I do not see physicists, in the main, trying
to understand what the mathematics means. I see them doing experiments
and calculations and trying to match results, and I see them denying
that there is more to physics than that.
>And I don't agree that there has been a "stagnation" in the advancement
>of physics. Physics is evolving just has its always evolved. The
>gathering of new data and the attempt to making it fit a theory.
Actually, it is theories which must be constructed to fit data :-)
>There
>have been lots of dead-ends, but there have also been successes. That
>has always been true and will always be true. That's the nature of
>science.
I do not recall hearing of much successes in the dark ages :-).
I cannot think of important advances in the laboratory since Gell-Mann's
discovery of the eightfold way and quarks. It is true, there have been
enormous advances in observational cosmology, and, as I believe, we are
set to make even greater advances with the next generation of
telescopes. But those advances have not lead to a deeper understanding
of Cosmology than has been derived from general relativity. On the
contrary, we have a state of confusion which has been described as a
"crisis in Cosmology", because of the mass of contradictions in the
observations. Nor is it likely that studying the data will resolve the
contradictions, or that theory will come from data. Imv we need a
consistent theory of quantum gravity before cosmological data can be
properly interpreted and understood. A consistent theory of quantum
gravity can only be found mathematically, by seeking out a consistent
axiom set.
I do not, btw, mean to suggest that axioms can be chosen without
reference to physics. Rather they must be found by studying physics,
much as Einstein found axioms for relativity.
>Time for a confession: In my earlier years I had a strong interest in
>mathematics and had very mathematical approach in my understanding of
>physics. Then I was standing next to my thesis advisor who was engaged
>in a discussion with another physicist. The other physicist made a
>remark that "physics was mostly solving equations". My advisor said "not
>quite, it was trying to figure out what the equations mean". The insight
>of that remark impressed me greatly. My attitude changed from primarily
>trying to understand the mathematics in mathematical way to trying to
>understand it in a physical way. Although I was aware prior of the two
>approaches, my sophistication in understating needed this "epiphany". I
>finally appreciated the physical approach that so many really good
>physicists used.
>
For myself, I see understanding what mathematics says about a given
subject as an intrinsic part of mathematics - the distinction between
applied maths and pure if you like, but still mathematics. I object to
the idea that maths is only calculation of results, and only the results
are meaningful physics, a view commonly expressed by quantum field
theorists. To understand the mathematics, we must understand and
interpret the axioms.
Shubee
> Charles Francis wrote:
>
> >I would say more than that. Not just ideally, but that it is essential
> >to take such an approach. Typical approaches to physics lose sight of
> >mathematical structure and consider physics as established facts. But on
> >the frontiers, facts and speculations become blurred. The issues on the
> >frontiers are interpretation of quantum theory and unification. The
> >essential requirement of a resolution to these issues is consistency,
> >both internal consistency and consistency with observation. Mathematics
> >can be seen as the study of consistency. Only by applying a
> >mathematical, axiomatic, approach can one address issues of consistency.
> >Only by constructing such an approach oneself from first principles, by
> >doing the logical steps oneself, does one really understand the logical
> >structures required by physics. The lack of such approaches in modern
> >physics is to me part and parcel of the stagnation of advance in physics
> >over the last 50 or so years..
>
> >Regards
>
> physics. To insist on an axiomatic basis for physics puts a major
> constraint on understanding nature.
"A great physical theory is not mature until it has been put in a
precise mathematical form, and it is often only in such a mature form
that it admits clear answers to conceptual problems." A. S. Wightman,
Hilbert's sixth problem: mathematical treatment of the axioms of
physics, in: Proc. Sympos. Pure Math., Vol. 28, AMS, 1976, pp.
147-220.
Don't you believe that coming up with "clear answers to conceptual
problems" is being productive?
> It is, what I like to call, a religious fundamentalist's approach
> to science. You don't need a laboratory if you have axioms.
The observation of nature is an excellent starting point to begin
Hilbert's program for the axiomatization of all of physics. And the
laboratory will continue to be the best place to search for new
axioms. But after it's decided what are the most fundamental
properties of nature, doesn't it take a mathematical mind to shape it
into a mature mathematical form?
> It would be nice to think that axioms can be found that nature is
> obliged to follow to construct all natural laws, but nature always seems
> to be throwing spanners into the gearbox. The Greeks had an excellent
> set of axioms that explained everything, because they forced it to fit
> everything. Physics has only progressed because of the laboratory.
Isn't that an obvious overstatement? Didn't Einstein's special and
general relativity require a little imagination?
> Mathematics is an extremely useful tool to explain what is observed, but
> the major chore a physicist has regarding mathematics is trying to
> understand what the mathematics mean.
Mathematicians have no problem understanding the meaning of
mathematics. Perhaps physicists should try to reduce physics to
mathematics.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Shubee
> own exposition on physics. I don't think mathematicians would be doing
> physics; they would be doing mathematics based on problems and ideas
> taken from physics. I'm not quite sure what this mathematician thinks
> physics is, but he appears to me to be one of those individuals who may
> think mathematics and physics is the same.
Physics and mathematics are not the same. Physics is a mere
subdiscipline of mathematics.
> I have met those individuals in the past and found that as
> mathematicians they seem quite good, but as physicists they came up
> wanting. There was a mathematics graduate I knew whose PhD advisor was
> Subrahmanyan Chandrasekhar. His thesis was in GR and was immediately
> grabbed by a Midwestern university physics department. My discussions
> with him about physics lead me to believe his basic understanding of the
> philosophy of physics was lacking, but more disturbing to me was that he
> wasn't interested in physics as an observable science.
I'm absolutely captivated by the beauty of David Hilbert's philosophy
of physics. Would you say that Hilbert's philosophy of physics was
lacking because that remarkable genius wasn't interested in physics as
an observable science?
> I finish with this: I strongly believe that Mathematical Physics is a
> mathematical discipline and is not physics. So a comment that
> mathematicians should re-work physics is wrong-headed if the goal is to
> produce useful physics.
I believe it's an admirable goal for any mathematician to remove from
physics everything that is confused, unnecessary and not amenable to
experimental verification. Why wouldn't the axiomatization of physics
be useful?
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Oh No
>>>
>>>This is exactly why doing math and calling it physics is not productive
>>>physics. To insist on an axiomatic basis for physics puts a major
>>>constraint on understanding nature.
>>
>>The only constraint is that nature must be consistent. Do you dispute
>>it?
>No. However, it is more than a constraint; it is a religious belief. If
>we didn't believe this, there would be no hope to discover the laws of
>nature.
Perhaps true, but whether or not it is "religious", an axiomatic
framework is the only way to ensure consistency. I see no point in
thinking we should explore inconsistent ideas, unless the intention is
to discover why they are inconsistent with a view to producing a
consistent axiom set.
>>>It is, what I like to call, a
>>>religious fundamentalist's approach to science. You don't need a
>>>laboratory if you have axioms.
>>
>>At the frontiers of physics, we do not have axioms. That is, we need to
>>determine what the axioms are.
>>
>
>I don't like the word "axioms". I prefer laws. Axioms can be contrived
>or pronounced self-evident; physical laws can't.
A law may be a theorem not a fundamental. The word axiom is not
appropriate for physics. We may forget the greek connotation of self-
evident truth. An axiom is a defining statement in a mathematical
structure. For the purpose of mathematics, we are only concerned with
whether it is consistent with the other axioms of that structure, but
physics be based on statements about nature, postulates. Ideally the
postulates should be statements which can be seen to be true (to within
experimental error) like Newton's laws, or should be eminently
reasonable statements such that it would be difficult to imagine physics
without them like the general principle of relativity (we clearly cannot
test physical laws in another part of the universe, but we assume they
are the same as here).
>
>>>It would be nice to think that axioms can be found that nature is
>>>obliged to follow to construct all natural laws, but nature always seems
>>>to be throwing spanners into the gearbox. The Greeks had an excellent
>>>set of axioms that explained everything, because they forced it to fit
>>>everything.
>>
>>They only had axioms for Euclidean geometry. Certainly that did not
>>explain everything.
>>
>
>The had the four elements: earth, air, fire and water. These were
>sufficient to explain all nature to the early Greeks.
Those are not axioms. They are not suitable for logical deduction, for a
start.
>
>>>Physics has only progressed because of the laboratory.
>>
>>While I don't dispute the value of the laboratory, or indeed the need
>>for it, the big advances have been conceptual and mathematical, as when
>>Newton wrote down his laws, Maxwell his equations, or when Einstein
>>developed relativity (in particular the general theory).
>>
>
>The mathematics puts the observations into a tidy form. The conceptual
>format is giving physical meaning to the mathematics. Maxwell didn't
>conceive of the displacement current because it was needed
>mathematically. It was needed to keep the mathematics consistent with
>what was known, and he felt necessary, for the physical world.
>
>>>Mathematics is an extremely useful tool to explain what is observed, but
>>>the major chore a physicist has regarding mathematics is trying to
>>>understand what the mathematics mean. Answering these kinds of questions
>>>occupies most of the space in this ng, as one would expect.
>>
>>Indeed, it should. However, I do not see physicists, in the main, trying
>>to understand what the mathematics means. I see them doing experiments
>>and calculations and trying to match results, and I see them denying
>>that there is more to physics than that.
>>
>
>That is where your experience and mine differ. My observation is there
>are those who grind through the formalism and turn out results without
>adding much insight to what is going on, while there are others who rely
>rarely rely on the formalism and produce valuable work. The list of
>physicists that worked that way is long and famous. Much has been
>written about the likes of Fermi, Einstein , Feynman, and so on who
>didn't rely solely on mathematical techniques.
No, but you cite physicists who used mathematics effectively. Einstein
is for me the archetypal mathematical physicist, building a mathematical
theory from fundamental principle, even to the extent that he did not
see the need for the MM experiment. I thought that was what you were
speaking against.
>And then there are less
>famous physicists like Eugene Parker who used to invoke my awe by
>solving electrodynamic boundary value problems without doing anything
>more formal than finding a suitable physical analog and using it for a
>quick solution.
Even that can be described as a mathematical method.
>
>>>And I don't agree that there has been a "stagnation" in the advancement
>>>of physics. Physics is evolving just has its always evolved. The
>>>gathering of new data and the attempt to making it fit a theory.
>>
>>Actually, it is theories which must be constructed to fit data :-)
>>
>>>There
>>>have been lots of dead-ends, but there have also been successes. That
>>>has always been true and will always be true. That's the nature of
>>>science.
>>
>>I do not recall hearing of much successes in the dark ages :-).
>>
>>I cannot think of important advances in the laboratory since Gell-Mann's
>>discovery of the eightfold way and quarks. It is true, there have been
>>enormous advances in observational cosmology, and, as I believe, we are
>>set to make even greater advances with the next generation of
>>telescopes. But those advances have not lead to a deeper understanding
>>of Cosmology than has been derived from general relativity. On the
>>contrary, we have a state of confusion which has been described as a
>>"crisis in Cosmology", because of the mass of contradictions in the
>>observations. Nor is it likely that studying the data will resolve the
>>contradictions, or that theory will come from data. Imv we need a
>>consistent theory of quantum gravity before cosmological data can be
>>properly interpreted and understood. A consistent theory of quantum
>>gravity can only be found mathematically, by seeking out a consistent
>>axiom set.
>>
>
>Dyson once remarked about the state of "what's happening". He noted that
>the 19th Century was filled with spectroscopic experiments. The data
>being produced was as confusing as all hell. There were a myriad of of
>rules to explain certain small region, but there was still no all
>encompassing theory. It wasn't until Quantum Theory and then Quantum
>Mechanics to be discovered before any sense could be made for what was
>observed. The point being, the data gathering precedes the
>understanding, and this understanding may be a long time in coming.
The historical order is not necessarily the same as the logical order,
but I wonder if mathematical theory would ever be accepted if it did not
produce results which are already known. Newton developed mechanics
axiomatically, but would his law of gravity have been accepted if Kepler
had not already identified elliptical motion of the planets?
>
>In many ways, we are in the 19th Century spectroscopic data gathering
>mode. The collection of high-energy data is still ongoing and people are
>still trying to find THE explanation. Right now, I think the
>explanations are still in a "primitive" phase. It may take a revolution
>in thinking, similar to what occurred in the early 20th Century, to pull
>everything together. I don't believe that the revolution will be found
>in an axiomatic approach.
Whereas I believe that is always the form of such a revolution.
>>I do not, btw, mean to suggest that axioms can be chosen without
>>reference to physics. Rather they must be found by studying physics,
>>much as Einstein found axioms for relativity.
>>
>
>I'm still a little uncomfortable with "axioms".
Can we settle on "postulates".
>
>>
>>>Time for a confession: In my earlier years I had a strong interest in
>>>mathematics and had very mathematical approach in my understanding of
>>>physics. Then I was standing next to my thesis advisor who was engaged
>>>in a discussion with another physicist. The other physicist made a
>>>remark that "physics was mostly solving equations". My advisor said "not
>>>quite, it was trying to figure out what the equations mean". The insight
>>>of that remark impressed me greatly. My attitude changed from primarily
>>>trying to understand the mathematics in mathematical way to trying to
>>>understand it in a physical way. Although I was aware prior of the two
>>>approaches, my sophistication in understating needed this "epiphany". I
>>>finally appreciated the physical approach that so many really good
>>>physicists used.
>>>
>>For myself, I see understanding what mathematics says about a given
>>subject as an intrinsic part of mathematics - the distinction between
>>applied maths and pure if you like, but still mathematics. I object to
>>the idea that maths is only calculation of results, and only the results
>>are meaningful physics, a view commonly expressed by quantum field
>>theorists. To understand the mathematics, we must understand and
>>interpret the axioms.
>>
>
>I do not think mathematics is only a calculation device, either.
>Mathematics is a language for writing the physical laws with very a
>precise set of logical rules. But one must no lose sight of the physical
>significance of the quantities because he is buried in the details of
>the logical manipulations.
>
There we agree, but this is precisely why I think that now is the right
time to work on a deeper mathematical structure for physics.
pirillo
not a problem of physics, but of human language. People use
assumptions all the time, and then by ignorance, comfort or
whatever, fail to state their assumptions. Psychologically, these
assumptions can either be well delineated in the mind of the
person working with them, or a nebulous class of fairly similar
assumptions that one uses interchangeably, but that all yield
the same results (eg an equivalence class of assumptions) and
thus they never bother to set down one set, for fear that later
evidence may prove that their pick out of the equivalence class
was the wrong one. Rather recently there are schools of
mathematicians that, used to the axiomatic approach, have wanted
to pin down the axioms a physicist or particular group of
physicists is using. I.e., to pin down as best as possible what the
physicists intenal assumtions are. This has a practical objective.
After all, if one sees a karate person doing a kata, you may immitate
them like a monkey, but for that kata, the practitioner has an
internal
model , an internal story, i.e., a complex of assumtions. And you
by imitating will not truly understand what they're doing--Even though
by immitating you may come up with your own internal story I.e., your
own model. It is a common ocurrence in human communication, that
people do not completely state their assumptions and internal
workings.
It is one of the triumphs of the modern methods of math to clean
some of this up by developing more expressive language and standards
to better express and pin down all relevant assumptions--When pinning
down
an assumption is not essential to the task at hand, at least say
which
equivalence class of assumptions is being worked with.
As far as the argument that "physics is pure observation, while
math is useful only in setting up a theory to explain the
observations" ,
one should notice that be it our schooling or whatever, we in practice
do
not do any "physics" by observation alone. We usually have an
underlying
model that we are using to set up an interpret the observation.
This is certainly the case when we do an experiment--when we use
the experiment to check the validity of an existing theory--which
is probably why most experiments are done. Pure observation is
something that happens more by accident--I see some weird image on the
wall
when i raise my glass. Now, progress in modern physics has been made
by
setting up theories based on earlier results, and then doing
experiments based
on the assumptions of those theories to see if the theory (which
includes its
interpretative scheme) matches with that observed. While the future of
physics
seems to be based more and more on setting up theories. Now one thing
about these theories is that thus far all the theories we've had a
logically consistent
theories fully expressible in the language of mathematics. Most
people, except
the crazy or the ultra philosophically deep seem to think this will
always be the case.
Now, If you see physics as I do--and operationally speaking, as
everybody I've ever
seen do physics--as playing a mathematical game, unless you're very
smart
an a natural Sherlock Holmes, you want to be told the rules of the
game. Also
when someone decides to change some of the assumptions, you want to
know that
also. Hence, its rather important that when someone writes a paper,
they state the
particular assumptions (Axioms seems too "permanent" even though thats
what
they are from the point of view of mathematical logic ) that they are
basing they
development and results on.
Now, this being said, I think there is a certain deep physics
phylosophy that
many mathematicians seem to lack, but this has more to do with
questions
relating to the interpretation scheme of the theory and weighing
various alternatives
when one decides to define what a particular quantity means, and
wheather there's
a more correct or general way to define this or that. I other words
what seems to be
lacking is a deep analysis of the interpretative assumptions and
asking things like
"what do I really want to do with this" which may mold certain
physical definitions.
After that, physics work is pure math, tempered with inflow of ideas
that come from
results you expect to come out of the physical predictions based on
the interpretative
scheme. ...And stopping once in a while and examining you
interpretative scheme, and
repeating this again and again many times forever and ever.
Oh No
>Charles Francis wrote:
>>Thus spake Murray Arnow
>>>Charles Francis wrote:
>>>>Thus spake Murray Arnow
>>>>>
>>>
>>>are those who grind through the formalism and turn out results without
>>>adding much insight to what is going on, while there are others who rely
>>>rarely rely on the formalism and produce valuable work. The list of
>>>physicists that worked that way is long and famous. Much has been
>>>written about the likes of Fermi, Einstein , Feynman, and so on who
>>>didn't rely solely on mathematical techniques.
>>
>>No, but you cite physicists who used mathematics effectively. Einstein
>>is for me the archetypal mathematical physicist, building a mathematical
>>theory from fundamental principle, even to the extent that he did not
>>see the need for the MM experiment. I thought that was what you were
>>speaking against.
>>
>
>physicist. He certainly was a theoretical physicist, at times an
>experimental physicists and sometimes an engineer. My definition of
>mathematical physics is the discipline whose concern is with the
>analysis of mathematical problems posed by physics,
I would have said that was mathematical methods of physics
>and theoretical
>physics is the discipline that creates theories to explain physical
>phenomena.
The distinction usually given by journals is along the lines of saying
that mathematical physics requires greater rigor. Modern theoretical
physics seeks license to work without a well defined mathematical
framework, whereas mathematical physics does not, and is generally more
restricted in scope and less applicable in consequence.
For myself, I make no such distinction or compromise. The aim should be
to construct a real physical model with a well defined mathematical
framework. You have said this is a constraint, and indeed it is a severe
constraint, which I why I think that satisfying the constraint will
provide real insight into physics.
>[...]
>
>>The historical order is not necessarily the same as the logical order,
>>but I wonder if mathematical theory would ever be accepted if it did not
>>produce results which are already known. Newton developed mechanics
>>axiomatically, but would his law of gravity have been accepted if Kepler
>>had not already identified elliptical motion of the planets?
>
>It's not clear to me how Newton derived his laws axiomatically. What
>were his axioms? I'd say he derived his laws the prototypical-theorist
>way.
Newton's laws are themselves the axioms. We do not derive axioms
mathematically, but rather all mathematical proof must proceed from
axioms. The mathematical challenge is to establish precisely the axiom
set which yields a good model of physics. Newton, Einstein, and Maxwell
have made the most important contributions to physics because this is
what they did.
Cl.Massé
news:787d8532-31ef-498b...@79g2000hsk.googlegroups.com...
> Physics and mathematics are not the same. Physics is a mere
> subdiscipline of mathematics.
That's like a blind person saying that space is merely a special type of
sound. It's true that mathematical physics is a tiny subdiscipline of
mathematics (rightly said, a discipline and not a science), but mathematics
is a mere tool of physics. No physics can be made with mathematics only.
--
~~~~ clmasse on free F-country
Liberty, Equality, Profitability.
Cl.Massé
>>>I would say more than that. Not just ideally, but that it is essential
>>>to take such an approach. Typical approaches to physics lose sight of
>>>mathematical structure and consider physics as established facts.
No good physicist consider physics (as a set of law about Nature? as a set
of observations? as a set of method to understand Nature?) as established
facts. Only raw results of experiment are. Every good physicist has this
in mind, and use laws because they best represent raw experimental results,
while hunting hidden assumptions.
>>>But on the frontiers, facts and speculations become blurred.
>>>The issues on the
>>>frontiers are interpretation of quantum theory and unification. The
>>>essential requirement of a resolution to these issues is consistency,
>>>both internal consistency and consistency with observation.
I don't think so. For example QM is completely mathematically consistent
and with observation, while conceptually it isn't. Its axiomization didn't
solve any interpretational problem, but concealed them.
That's why Poincaré failed where Einstein succeeded. One was looking after
a formal description, the other found the interpretation without changing a
iota of the mathematics and its consistency.
>>>Mathematics
>>>can be seen as the study of consistency. Only by applying a
>>>mathematical, axiomatic, approach can one address issues of consistency.
>>>Only by constructing such an approach oneself from first principles, by
>>>doing the logical steps oneself, does one really understand the logical
>>>structures required by physics. The lack of such approaches in modern
>>>physics is to me part and parcel of the stagnation of advance in physics
>>>over the last 50 or so years..
That isn't consistent, since physics has never been so much based on
mathematics.
> The only constraint is that nature must be consistent. Do you dispute
> it?
I do. The other constraint, which is much stronger, is that Nature must be
Nature. That is, observation is the most important, and after all, we don't
know at all whether Nature is consistent or not. Mathematics are a
constraint only for the human mind, that is unable to tackle inconsistency.
Perhaps God finds supersymmetry beautiful, but perhaps He also has quite
different logics and mathematics.
> While I don't dispute the value of the laboratory, or indeed the need
> for it, the big advances have been conceptual and mathematical, as when
> Newton wrote down his laws, Maxwell his equations, or when Einstein
> developed relativity (in particular the general theory).
That is an extremely partial view of the process. What was paramount for
all those great spirits was an extraordinary intuition that put them on the
correct mathematical tracks. Newton had to imagine two masses to then
identify them. Maxwell gave a meaning to the set of already known laws by
grabbing a physical input out of thin air. Einstein only generalized an old
idea of his own that was fertile only because well inspired from the
beginning.
Now, there are emulators of Einstein, who unfortunately fail since obviously
Einstein already chose the good group, and because they don't have the same
creative power. Matter of fact, Einstein was a poor mathematician and
Newton was a geek of occult sciences.
> A consistent theory of quantum
> gravity can only be found mathematically, by seeking out a consistent
> axiom set.
That is a truism, but the purpose is to find a theory describing reality.
Before the axioms, purely physical concepts have to be imagined, and for
that there is no mathematical methods. It is only after that mathematical
methods seek for minimal sets of axioms, and then propose a choice of them
to the physicists.
Cl.Massé
> "A great physical theory is not mature until it has been put in a
> precise mathematical form, and it is often only in such a mature form
> that it admits clear answers to conceptual problems." A. S. Wightman,
> Hilbert's sixth problem: mathematical treatment of the axioms of
> physics, in: Proc. Sympos. Pure Math., Vol. 28, AMS, 1976, pp.
> 147-220.
>
> Don't you believe that coming up with "clear answers to conceptual
> problems" is being productive?
I don't think the issue is "precise mathematical form", but rather
"convenient mathematical form", for it would mean that the physicist are
imprecise, which is obviously wrong. Even if the mathematical formulation
lacks rigor, it precisely and consistently describes what is observed, and
it is the only goal.
It often takes years before the theory is conveniently formulated and
spelled out in textbooks. The convenient mathematical form is the one based
on a minimal set of conceivable and insightful postulates. But again, it is
a physical task, and not a mathematical one.
> Mathematicians have no problem understanding the meaning of
> mathematics. Perhaps physicists should try to reduce physics to
> mathematics.
There is nothing to understand in the meaning of mathematics. Either a
theorem is true, either it isn't, period. It would be like trying to
understand true & true = true. It's no news that the mathematicians
consider the physicist as sort of backward people. But the truth is that
both disciplines can't be compared since they have very different purposes
and philosophical status.
Ken S. Tucker
On Aug 10, 7:31 am, "Cl\.Massé" <danielle.be...@gmail.com> wrote:
> "Shubee" <e.Shu...@gmail.com> a écrit dans le message denews:2a7a0dc4-6dfc-40a9...@2g2000hsn.googlegroups.com...
Your last paragraph troubles me, because I think
logic is a discipline, and mathematicians I've met
have always respected the applications of math.
Let me provide an enigmatic example.
Let a vector A have components A_u and set a
covariant derivative (w.r.t "w") as,
(A_u A_v);w = 0 , (1)
which is symmetrical in indice "u" and "v".
Next, watch this, I'll expand Eq.(1) via elementary
*chain rule* to,
A_u;w A_v + A_u A_v;w = 0 meaning
A_u;w A_v = - A_u A_v;w , (2)
where Eq.(2) is asymmetrical in "u" and "v".
((That is important for me because I want to generalize
Eq.(GRCC2) in this article,
http://physics.trak4.com/GR_Charge_Couple.pdf
with the covariant derivative of the metric vanishing)).
How can both identical Eqs.(1) and (2) be the same,
and be symmetrical and asymmetrical?
((J. Baez in week 268 discusses this,
"g(ab,c) = e(a ^ b ^ c) = g(a,bc)
So, it works! But, this algebra is far from semisimple." )).
Based on mathematics, I reason both sides of Eq.(2)
vanish, for both Eqs.(1) and (2) to be consistent.
But I'm still without an effective solution, so I do a bit
of physics induction, as a shot into the math, and
reconstruct Eq.(1) as,
(A_u B_v);w =0 , (1A)
wherein indice "u" and "v" can be asymmetrical, and
A and B are *different* vectors enabling,
A_u;w B_v = - A_u B_v;w , (2A).
Eq.(2A) is very rich, nonsymmetrical in vectors A and B,
and indices "u" and "v".
Once again though, Eq.(2A) will a need a shot of physics
to hone it down to apply more easily in the universe we
inhabit, by the discipline of physics, to distinguish it from
the infinity of universes mathematicians can logically define
and inhabit.
Regards
Ken S. Tucker
kxsxt8
Oh No
>Charles Francis wrote:
>>For myself, I make no such distinction or compromise. The aim should be
>>to construct a real physical model with a well defined mathematical
>>framework. You have said this is a constraint, and indeed it is a severe
>>constraint, which I why I think that satisfying the constraint will
>>provide real insight into physics.
>This is where we part company. I don't see where mathematical rigor will
>produce any valuable insight in physics. I am hard pressed to think of
>mathematical rigor giving any physical insight. You may know that going
>from A to B is completely logical and valid, but this is a mathematical
>statement that doesn't give you any insight of the physical nature of A
>or B, and it gives no information about the physical validity of the
>answer.
In order to find that which is right, we must first eliminate that which
is wrong. I think we can only do this by working from small numbers of
postulates, and by being flexible in adjusting them subject to
requirements of both rigor and sense.
>>>It's not clear to me how Newton derived his laws axiomatically. What
>>>were his axioms? I'd say he derived his laws the prototypical-theorist
>>>way.
>>
>>Newton's laws are themselves the axioms. We do not derive axioms
>>mathematically, but rather all mathematical proof must proceed from
>>axioms. The mathematical challenge is to establish precisely the axiom
>>set which yields a good model of physics. Newton, Einstein, and Maxwell
>>have made the most important contributions to physics because this is
>>what they did.
>>
>
>You may interpret the laws axiomatically, but as I keep repeating, there
>is little physical insight gained from the approach.
I don't agree. I think the fact that the whole of mechanics can be
reduced to the postulates of absolute space and time together with N1,
N2 and N3 is a huge insight. That these can be replaced by conservation
of momentum is another important insight. That conservation of momentum
can be reduced, via Noether's theorem, to a space symmetry principle
contained in the general principle of relativity is again a huge
insight. Vast amounts of physics reduces to the general principle, a
fact which gives the lie to the empirical basis of science since, while
it is difficult to conceive of physics without it, can never be
established empirically.
>The goal of a mathematician isn't not the goal of a physicist. The fact
>the either one has knowledge of the other's discipline doesn't mean that
>a physicist is a mathematician or that a mathematician is a physicist.
>An expert's knowledge of history is extremely beneficial to being an
>American President, but it doesn't mean that a President should be a
>historian.
>
>It is the rare individual who is both a expert mathematician and expert
>physicist. I can think of only one modern-day example, Fermi, and he
>gave up mathematical studies to pursue physics full-time.
>
>At the risk of becoming overly repetitious, the goals of mathematics and
>those of physics intersect; they don't overlap. Neither is a subset of
>the other. I usually get into these disagreements with individuals who
>started as mathematicians, often attaining advanced degrees, and then
>become interested in physics. I have noticed that it is common to see
>there is something missing in their physical insight.
I don't dispute it, but one should not dispute the worth of a discipline
by criticising the individuals who pursue it. I could also point to
things lacking in physicists, in some cases leading to huge wasted
effort. It will be necessary, in my view, for an individual to be able
to embrace both disciplines, and also to have deep insights into
philosophy (a discipline in which the practitioners often have an even
greater lack) to make the next important conceptual step in
understanding nature.
>That is why it is
>rare that mathematicians produce any new physics.
It was not always so. The period of the eighteenth and nineteenth
centuries were perhaps the most fertile in history. At that time the
proponents were both mathematicians and physicists. Newton, Gauss,
Maxwell, were foremost mathematicians. Riemann, who I regard as the
smartest mathematician in history, thought of himself as a physicist.
You may think his contribution to physics was small, but he contributed
the mathematics of general relativity, and not by chance either. He knew
precisely why this mathematics was needed, though of course without the
special theory he could not put all the pieces of the puzzle together..
>
>Let's see how many toes I've trod on with this last statement. I'm
>interested to learn how many people posting here are trained
>mathematicians who are now working in physics.
My undergraduate degree was mathematics, and my doctorate was also
mathematics, though the topic was qed.
Peter
> I've heard these arguments many times before, and its actually
> not a problem of physics, but of human language.
On this level, ie, on use of inaccurate language, the problem is already far
from Hilbert's problem ;-)
> People use assumptions all the time, and then by ignorance, comfort or
> whatever, fail to state their assumptions.
A known effect, unfortunately, yes
> Psychologically, these
> assumptions can either be well delineated in the mind of the
> person working with them, or a nebulous class of fairly similar
> assumptions that one uses interchangeably, but that all yield
> the same results (eg an equivalence class of assumptions) and
> thus they never bother to set down one set, for fear that later
> evidence may prove that their pick out of the equivalence class
> was the wrong one. Rather recently there are schools of
> mathematicians that, used to the axiomatic approach, have wanted
> to pin down the axioms a physicist or particular group of
> physicists is using.
whith which results?
> I.e., to pin down as best as possible what the
> physicists intenal assumtions are. This has a practical objective.
> After all, if one sees a karate person doing a kata, you may immitate
> them like a monkey, but for that kata, the practitioner has an internal
> model , an internal story, i.e., a complex of assumtions. And you
> by imitating will not truly understand what they're doing--Even though
> by immitating you may come up with your own internal story I.e., your
> own model. It is a common ocurrence in human communication, that
> people do not completely state their assumptions and internal workings.
interesting, unexpected analogy :-)
> It is one of the triumphs of the modern methods of math to clean
> some of this up by developing more expressive language and standards
> to better express and pin down all relevant assumptions--When pinning
> down an assumption is not essential to the task at hand, at least say which
> equivalence class of assumptions is being worked with.
How the following propositions are dealt with?
1) Space and time are absolute, and homogeneous and isotropic. (Newton)
2) The object of natural science is the body. The essence (central or
outstanding characteristic) of the bodies is their impenetrability. (Euler)
> As far as the argument that "physics is pure observation, while
> math is useful only in setting up a theory to explain the observations",
obviously, superficial
> one should notice that be it our schooling or whatever, we in practice do
> not do any "physics" by observation alone. We usually have an underlying
> model that we are using to set up an interpret the observation.
> This is certainly the case when we do an experiment--when we use
> the experiment to check the validity of an existing theory--which
> is probably why most experiments are done. Pure observation is
> something that happens more by accident--I see some weird image on the wall
> when i raise my glass. Now, progress in modern physics has been made
> by setting up theories based on earlier results, and then doing
> experiments based
> on the assumptions of those theories to see if the theory (which
> includes its
> interpretative scheme) matches with that observed. While the future of
> physics
> seems to be based more and more on setting up theories.
I don't think so; theory and experiment build a dialectic unity
> Now one thing
> about these theories is that thus far all the theories we've had a
> logically consistent
> theories fully expressible in the language of mathematics.
this is certainly wrong, see above
> Most people, except
> the crazy or the ultra philosophically deep seem to think this will
> always be the case.
>
> Now, If you see physics as I do--and operationally speaking, as
> everybody I've ever
> seen do physics--as playing a mathematical game,
this is very much spread, but, nevertheles, incomplete
> unless you're very smart
> an a natural Sherlock Holmes, you want to be told the rules of the
> game. Also
> when someone decides to change some of the assumptions, you want to
> know that
> also. Hence, its rather important that when someone writes a paper,
> they state the
> particular assumptions (Axioms seems too "permanent" even though thats
> what
> they are from the point of view of mathematical logic ) that they are
> basing they
> development and results on.
yes, of course
> Now, this being said, I think there is a certain deep physics
> phylosophy that
> many mathematicians seem to lack, but this has more to do with
> questions
> relating to the interpretation scheme of the theory and weighing
> various alternatives
> when one decides to define what a particular quantity means, and
> wheather there's
> a more correct or general way to define this or that. I other words
> what seems to be
> lacking is a deep analysis of the interpretative assumptions and
> asking things like
> "what do I really want to do with this" which may mold certain
> physical definitions.
> After that, physics work is pure math, tempered with inflow of ideas
> that come from
> results you expect to come out of the physical predictions based on
> the interpretative
> scheme. ...And stopping once in a while and examining you
> interpretative scheme, and
> repeating this again and again many times forever and ever.
this seems to be a repetition of the foregoring paragraphs, thus, no comment
Best wishes,
Peter
Shubee
> "Shubee" <e.Shu...@gmail.com> a écrit dans le message denews:2a7a0dc4-6dfc-40a9...@2g2000hsn.googlegroups.com...
>
> > "A great physical theory is not mature until it has been put in a
> > precise mathematical form, and it is often only in such a mature form
> > that it admits clear answers to conceptual problems." A. S. Wightman,
> > Hilbert's sixth problem: mathematical treatment of the axioms of
> > physics, in: Proc. Sympos. Pure Math., Vol. 28, AMS, 1976, pp.
> > 147-220.
>
> > Don't you believe that coming up with "clear answers to conceptual
> > problems" is being productive?
>
> I don't think the issue is "precise mathematical form", but rather
> "convenient mathematical form",
All mathematics is precise; I believe that Wightman is emphasizing
detail rich mathematics. The need that some physicists may have for
easy mathematics is irrelevant.
> It often takes years before the theory is conveniently formulated and
> spelled out in textbooks. The convenient mathematical form is the
> one based on a minimal set of conceivable and insightful postulates.
> But again, it is a physical task, and not a mathematical one.
Aren't you overlooking the fact that the mathematician John von
Neumann was the first to axiomatize quantum theory?
> > Mathematicians have no problem understanding the meaning of
> > mathematics. Perhaps physicists should try to reduce physics to
> > mathematics.
>
> There is nothing to understand in the meaning of mathematics. Either a
> theorem is true, either it isn't, period. It would be like trying to
> understand true & true = true. It's no news that the mathematicians
> consider the physicist as sort of backward people.
We finally agree on something.
> But the truth is that both disciplines can't be compared since
> they have very different purposes and philosophical status.
It's very easy to compare mathematicians and physicists. Aesthetics
and beauty guide mathematicians. Mathematicians are usually perfectly
logical scientists. Their discipline is based on the orderly, logical,
systematic unfolding of mathematical knowledge. The exact opposite is
true of physicists. Physicists strongly oppose taking the time to
remove from physics everything that is confused, unnecessary and not
amenable to experimental verification. They happily endorse and are
satisfied with confused-sounding irrationality and agree with
physicist John Stewart Bell, who wrote in "Speakable And Unspeakable
In Quantum Mechanics," that the purpose of the way special relativity
is taught is to shake the students' confidence in common sense. For
these reasons, physicists aren't interested in axiomatizing the
foundations of physics. And they don't even have the time to waste on
such a contemptible task as they see it because they are too busy in
hot pursuit of the Holy Grail of physics.
Shubee
Shubee
> "Shubee" <e.Shu...@gmail.com> a écrit dans le message denews:787d8532-31ef-498b...@79g2000hsk.googlegroups.com...
>
> > Physics and mathematics are not the same. Physics is a mere
> > subdiscipline of mathematics.
>
> That's like a blind person saying that space is merely a special
> type of sound.
Who but a physicist could twist a straightforward fact into a false
physical principle?
> It's true that mathematical physics is a tiny subdiscipline of
> mathematics (rightly said, a discipline and not a science),
Welcome to the new era where all physics is mathematical.
> mathematics is a mere tool of physics.
Merely possessing tools doesn't make anyone a craftsman any more that
possessing a library card makes anyone literate.
> No physics can be made with mathematics only.
The only substantial part of physics is mathematics. Special
relativity, for example, only requires a kindergarten definition of
time. General relativity is likewise virtually all math; that's why
David Hilbert was able to solve Einstein's grand problem in only a few
weeks, while it took Einstein many years even with trying to solicit
the help of less talented mathematicians. According to Richard
Feynman, the entire mystery of quantum mechanics is contained in the
double-slit experiment. How is that experiment not high school level
physics? Now point me to a physics book where a physicist expounds on
the sole implications of the double-slit experiment and draws from it
all the mathematical equations implied by the phenomena.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Peter
> On Aug 10, 9:31 am, "Cl\.Massé" <danielle.be...@gmail.com> wrote:
> > > "A great physical theory is not mature until it has been put in a
> > > precise mathematical form, and it is often only in such a mature form
> > > that it admits clear answers to conceptual problems." A. S. Wightman,
> > > Hilbert's sixth problem: mathematical treatment of the axioms of
> > > physics, in: Proc. Sympos. Pure Math., Vol. 28, AMS, 1976, pp.
> > > 147-220.
> > >
> > > Don't you believe that coming up with "clear answers to conceptual
> > > problems" is being productive?
> > I don't think the issue is "precise mathematical form", but rather
> > "convenient mathematical form",
> All mathematics is precise; I believe that Wightman is emphasizing
> detail rich mathematics. The need that some physicists may have for
> easy mathematics is irrelevant.
> > It often takes years before the theory is conveniently formulated and
> > spelled out in textbooks. The convenient mathematical form is the
> > one based on a minimal set of conceivable and insightful postulates.
> > But again, it is a physical task, and not a mathematical one.
> Aren't you overlooking the fact that the mathematician John von
> Neumann was the first to axiomatize quantum theory?
I guess that my fellow comoderator has read only the upper half of this
posting. While the forgoing sentence is just missing the point (maths/physics
is not necesseraliy that what a mathematician/physicist does), the last
paragraph below violates the charter as, (i), it contradicts well-known and
obvious facts and, (ii), it is a personal attack against a group of people
(including many posters of this group who do the opposite of what is claimed
there).
Please stick with physics and do that better, what you think should be
improved or corrected.
Best wishes,
Peter
Ken S. Tucker
I came into the problem of Eq.(1) and (2) above entirely
open minded but the mathematical contradiction fed-
back into the theory and my understanding of physics.
There is an ongoing controversy about fields reacting
with themselves, such as a charge "self-energizing",
but the *mathematical* contradiction/enigma above
compelled me to re-examine that notion.
The Eqs.(1) and (2) above, using the discipline of tensor
analysis, has NO logical solution, that I know of,
therefore I was compelled to solve the problem by
using interacting charges, extended to A and B
below in Eq.(1A) and (2B).
Well that rendered another problem...
Our friendly mathematicians designed tensor analysis
to analyse static curved surfaces in N-dimensions.
Einstein and his buddy's took that math into a
dynamic spacetime, which I can describe here,
http://physics.trak4.com/modern-spacetime.pdf
compatible with our common definition of the meter,
so that looks ok.
Then the next problem, defining distance in a curved
spacetime. As it happens, using EFE's provided a
simple solution, see Eq.(4) herein...
http://physics.trak4.com/GR_Charge_Couple.pdf
and please examine Eq.(4) to find the differentials.
S dS = X dX
and the increments
S DS = X DX
are both true, to permit either a continuum (dS) or a
quantized solution (DS) respectively, extended from
the Orthogonal quantities X, dX and DX, since those
later values are in linear proportion.
It's my opinion and respect of the EFE's that they
provide a basis for a continuum and/or quantized
solution, based on the examination above.
Regards
Ken S. Tucker
...
refs
> (A_u B_v);w =0 , (1A)
>
> wherein indice "u" and "v" can be asymmetrical, and
> A and B are *different* vectors enabling,
>
> A_u;w B_v = - A_u B_v;w , (2A).
>
> Eq.(2A) is very rich, nonsymmetrical in vectors A and B,
> and indices "u" and "v".
> Once again though, Eq.(2A) will a need a shot of physics
> to hone it down to apply more easily in the universe we
> inhabit, by the discipline of physics, to distinguish it from
> the infinity of universes mathematicians can logically define
> and inhabit.
======================================= MODERATOR'S COMMENT:
There is no problem with (1) and (2) at all
Peter
> Charles Francis wrote:
> >Thus spake Murray Arnow
> >
> >>is little physical insight gained from the approach.
I recommend the study of Euler's work on mechanics for realizing how erronous
this claim is
> >I don't agree. I think the fact that the whole of mechanics can be
> >reduced to the postulates of absolute space and time together with N1,
> >N2 and N3 is a huge insight. That these can be replaced by conservation
> >of momentum is another important insight. That conservation of momentum
> >can be reduced, via Noether's theorem, to a space symmetry principle
> >contained in the general principle of relativity is again a huge
> >insight. Vast amounts of physics reduces to the general principle, a
> >fact which gives the lie to the empirical basis of science since, while
> >it is difficult to conceive of physics without it, can never be
> >established empirically.
> There are lots of examples of abstractions not having empirical basis
> but are of extreme value in physics--least action and so on.
Last action has direct roots in the empirical laws of impact
A better example is Euler's efficiacy, the negative of the potential energy
> Abstractions used by physicists don't differ from those used by
> mathematicians as abstractions go. These abstractions, however, are made
> pragmatic in the sense of physical applications. Because a mathematician
> is expert with abstractions, it doesn't follow that he has any physical
> insight to where these abstractions will take him. The concept of
> physical fields is a beautiful abstraction which leads to physical
> models. One of the greatest physicists of 19th Century created these
> useful intuitive models without much mathematical aid.
The concept of field was created by Newton (Principia, Definitions), but
discarded in favor of action-at-distance (which was expressis verbis denied
by Newton)
...
> There may be only one area of physics that can be fit to an axiomatic
> approach. It is thermodynamics.
What about mechanics, electrodynamics? :-o
> In my view, the most difficult field to
> develop a good physical intuition.
I agree
> I'll leave it as an exercise to
> answer why thermodynamics is of such a nature.
Doesn't sound like you know the answer ;-)
> Finally, I see mathematical physics as part of the mathematical
> discipline.
I would rather see it as a border discipline
> Any useful contributions it can bestow on physics is very
> welcome. But I don't see how it can produce anything that can be called
> new physics.
I agree
Best wishes,
Peter
Oh No
>>
>
>>It was not always so. The period of the eighteenth and nineteenth
>>centuries were perhaps the most fertile in history. At that time the
>>proponents were both mathematicians and physicists. Newton, Gauss,
>>Maxwell, were foremost mathematicians. Riemann, who I regard as the
>>smartest mathematician in history, thought of himself as a physicist.
>>You may think his contribution to physics was small, but he contributed
>>the mathematics of general relativity, and not by chance either. He knew
>>precisely why this mathematics was needed, though of course without the
>>special theory he could not put all the pieces of the puzzle together..
>
>math and physics with great facility. There was an explosion in
>mathematics due in great part to the need brought on by physics. But I
>don't see where the participants confused the two.
It used to be generally assumed that mathematics was abstracted from
reality. That lead to problems in the foundations of mathematics, and is
now known not to be true.
>The fact was the
>disciplines were in their infancy compared to what we have today. The
>abstraction of mathematics was far from today's, and most of the math
>then arose from a need to solve physical problems. That a mathematician
>was of tremendous benefit to solve certain physical problems didn't make
>him a physicist (I have no knowledge that Riemann had any understanding
>of thermodynamics or statistical mechanics). His interests were more in
>the mathematical challenge rather than what the physics were.
His interest lay in understanding reality, i.e. physics. The method he
used toward understanding was to develop mathematics.
>(Personally, I would have chosen Gauss over Riemann as an example of
>someone wearing two hats.)
I did, though perhaps my emphasis was not clear. I chose Riemann as
someone who is not generally considered physicist, and yet made an
enormous contribution whose value was only appreciated in the next
century.
>There may be only one area of physics that can be fit to an axiomatic
>approach. It is thermodynamics.
You ignore classical mechanics, classical electromagnetism, the special
and the general theories of relativity, quantum mechanics - in fact all
theory up to qed, which has not as yet been axiomatised.
>Finally, I see mathematical physics as part of the mathematical
>discipline. Any useful contributions it can bestow on physics is very
>welcome. But I don't see how it can produce anything that can be called
>new physics.
Axiomatising classical electromagnetism lead to special relatity. Was
that not new? Was general relativity not new? It was developed entirely
mathematically.
Juan R.
> All mathematics is precise; I believe that Wightman is emphasizing
> detail rich mathematics. The need that some physicists may have for easy
> mathematics is irrelevant.
Is not irrelevant when the goal is to solve complex problems.
Precisely one of main difficulties in theoretical chemistry is that
problems are so complex than most of mathematicians prefer to avoid the
field and focus on 'elegant' and rigorous solutions to simple problems.
This is the main reason why mathematical chemistry is not so well
developed as mathematical physics.
>> It often takes years before the theory is conveniently formulated and
>> spelled out in textbooks. The convenient mathematical form is the one
>> based on a minimal set of conceivable and insightful postulates. But
>> again, it is a physical task, and not a mathematical one.
>
> Aren't you overlooking the fact that the mathematician John von Neumann
> was the first to axiomatize quantum theory?
Massé was right. The axiomatization may be not just mathematically
acceptable, it may be also physically useful.
Von Neumann axiomatization may be fine for mathematicians (I dont know)
but was clearly abandoned by physicists who prefer Dirac approach of 30s.
--
http://www.canonicalscience.org/en/miscellaneouszone/guidelines.html
Juan R.
> Physics and mathematics are not the same. Physics is a mere
> subdiscipline of mathematics.
I recommend a reading of "Common misconceptions". Specially the section
"7.1 Mathematics and physical reality"
in
http://en.wikipedia.org/wiki/Mathematics
Beautiful explanations by Feynman in the difference between
physics and mathematics are also available in his books. I remember nice
Feynman discussion about physical light, geometry, and why physics was
not just mathematics.
In practice physicists (scientists in general) use mathematics as
*approximated* model of physical reality.
And often the mathematics available is not enough to describe parts of
that reality we observe. This explain why so many physicists have
developed mathematics.
One of last examples is Ed Witten, physicist who won the Field medal (The
'Nobel Prize' of mathematics).
--
http://www.canonicalscience.org/en/miscellaneouszone/guidelines.html
Shubee
> While the forgoing sentence is just missing the point (maths/physics
> is not necesseraliy that what a mathematician/physicist does), the last
> paragraph below violates the charter as, (i), it contradicts well-known and
> obvious facts and, (ii), it is a personal attack against a group of people
> (including many posters of this group who do the opposite of what is claimed
> there).
Even if the vast majority of physicists reject John Stewart Bell's
criticism of the way physicists teach physics, I believe that Bell's
statement in "Speakable And Unspeakable" merits respect. I certainly
agree with it and can't imagine why anyone would have difficulty
seeing that it's just plain wrong and counter to the spirit of
mathematics to teach a subject so as to purposely shatter a students'
expectation that elementary physics is based on clear logical
reasoning.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Ken S. Tucker
> compatible with our common definition of the meter,
> so that looks ok.
>
> Then the next problem, defining distance in a curved
> spacetime. As it happens, using EFE's provided a
Thank you moderator's, I wish you all would provide
your initials so I can at least acknowledge your
insights personally. It's good to get confirmation.
Ken
Ken S. Tucker
is that statistics :-).
On Aug 11, 4:15 pm, ar...@iname.com (Murray Arnow) wrote:
> Peter wrote:
>
> >> Charles Francis wrote:
> >> >Thus spake Murray Arnow
>
> >> >>You may interpret the laws axiomatically, but as I keep repeating, there
> >> >>is little physical insight gained from the approach.
>
> >I recommend the study of Euler's work on mechanics for realizing how erronous
> >this claim is
>
> Physics and math prior to the last century were deeply entwined. The
> point I'm having a problem getting across is that more recently they
> have gone separate paths. The path taken in mathematics today is not as
> useful to physics as is advocated here.
A lot of math has been developed apart from physics
(natural science), for example financially, like stats
for insurance, accounting, demographics, military
logistics, architecture that cross pollinate into physics
to some degree such as probability theory was developed
prior to QM applications.
> >> There may be only one area of physics that can be fit to an axiomatic
> >> approach. It is thermodynamics.
>
> >What about mechanics, electrodynamics? :-o
>
> If you are talking about the "axiomatic" basis built in the 19th
> Century, then I'll give a definite maybe. The modern versions are not
> very useful to doing physics.(I should hear squeals about this)
Squeals. What the heck is a "axiom"? I presume it
is a statement that cannot be contradicted.
> >> In my view, the most difficult field to
> >> develop a good physical intuition.
>
> >I agree
>
> >> I'll leave it as an exercise to
> >> answer why thermodynamics is of such a nature.
>
> >Doesn't sound like you know the answer ;-)
>
> Do you care to wager that I don't?;-) I use this question to separate
> the wheat from the chaff when I want to know the level of an
> individual's physical understanding. You may be interested to know, that
> a number of "physicists" stumble here. I think I know why some have
> trouble, and it's related to the question I have with equating math to
> physics. If anyone is interested in another of my ramblings, I may
> summon the strength to continue another thread. BTW, I have more to say
> about thermodynamics in my response to Charles.
Thermodynamics, hmm, 6 degrees of freedom but then
the 4 forces of reactions, gravity, electric, weak and strong,
and then the particle zoo itself as players on that stage.
We study rocket engines, and I figure a rocket is thrusted
photonically by the hot gases outer electron shell in the
Combustion Chamber repelling the outer shell of the CC
material via the exchange of EM force, which I suppose
you might call quantized.
((Isp= Specific Impulse))
A bit OT but lately we've been involved in producing an
algorithm to do soft landings. Two ways exist to throttle
the thrust, (1) is the standard variable thrust but that
has inefficiencies, since the standard engine operates
at a maximum Isp according to it's geometry at a set
thrust level, and (2) pulsing the thrust so that the engine
fires at maximum Isp thrust intermittently. It reminded me
of using a continuous variation or a quantized variation of
thrust, where particle interactions are concerned.
Our current best algorithm uses pulsed (quantized) thrust.
Regards
Ken S. Tucker
Oh No
>>
>>> Charles Francis wrote:
>>> >Thus spake Murray Arnow
>>> >
>>> >>is little physical insight gained from the approach.
>>
>>this claim is
>>
>
>Physics and math prior to the last century were deeply entwined. The
>point I'm having a problem getting across is that more recently they
>have gone separate paths. The path taken in mathematics today is not as
>useful to physics as is advocated here.
On this we agree, but the fault lies not with either mathematics or
physics, but with the practitioners of physics, who do not use
mathematics correctly by first establishing physical postulates as the
axioms of mathematical structure.
Thus spake Murray Arnow <ar...@iname.com>
>Charles Francis wrote:
>> Thus spake Murray Arnow
>
>>>The Nineteenth Century was an interesting time. People engaged in both
>>>math and physics with great facility. There was an explosion in
>>>mathematics due in great part to the need brought on by physics. But I
>>>don't see where the participants confused the two.
>>
>>It used to be generally assumed that mathematics was abstracted from
>>reality. That lead to problems in the foundations of mathematics, and is
>>now known not to be true.
>>
>
>Well, physics must keep in touch with reality. You have recognized why
>physics and math can have conflicts.
Indeed. While there is no such constraint on mathematics, that does not
permit physicists to use mathematics without this constraint.
>
>[...]
>>
>[Responding to the statement about thermodynamics and its
>axiomatization]
>
>>You ignore classical mechanics, classical electromagnetism, the special
>>and the general theories of relativity, quantum mechanics - in fact all
>>theory up to qed, which has not as yet been axiomatised.
>>
>
>I didn't ignore them. It's just that I don't think they have a axiomatic
>basis.
I cannot see how you would think that.
> I think there may be a confusion here between formalism and
>axioms. Formalism, although very nice and powerful, can lead people to
>make some foolish statements about math relative to physics. People can
>rely so heavily on the formalism that they lose sight of the physics it
>encompasses.
That perhaps describes how many physicists abuse mathematics, but not
how it should be used.
>>>Finally, I see mathematical physics as part of the mathematical
>>>discipline. Any useful contributions it can bestow on physics is very
>>>welcome. But I don't see how it can produce anything that can be called
>>>new physics.
>>
>>Axiomatising classical electromagnetism lead to special relatity. Was
>>that not new? Was general relativity not new? It was developed entirely
>>mathematically.
>This is news to me, and from everything I read about the history of
>relativity, would be news to Einstein.
I find that quite extraordinary. To fail to understand general
relativity as a mathematical theory of physics is to fail to understand
it at all, imv.
>I
>am finding it difficult to continue.
Likewise. It seems that there is no correspondence at all between what
we mean by words like mathematics and axiom.
>I don't intend to demean any of the participants in this thread, but I
>am finding it difficult to continue. I am defending something that seems
>obvious to me.
To me it seems you are attacking something which seems obvious to me.
>The best way for me to put it is "where's the physics"?
>This is a question I have been often asked and often heard asked of
>others. An answer of the nature of reference to abstractions such as a
>discourse on the isotropy of space would result in severe criticism. The
>answer has to be what is happening the real physical world; e.g., what
>is happening to atoms, electrons, fields and anything else that's
>happening in the measurable world.
I take it your criticism of "isotropy of space" has to do with the fact
that space is not measurable? Indeed, this is so. The results of
measurement are numbers, the results of measurements of position are
members of R^3. If one correctly applies mathematics, one cannot
conclude, as it seems do most physicists, that space has physical
substance, but rather the use of homogeneous, isotropic mathematical
structure only says that electrons are always electrons, photons are
always photons etc. Of course, one will only apply mathematics correctly
if one first develops a correct philosophy of mathematics and its
relation to physics.
Peter
> Peter wrote:
> >> Charles Francis wrote:
> >> >Thus spake Murray Arnow
> >> >>You may interpret the laws axiomatically, but as I keep repeating,
> there is little physical insight gained from the approach.
> >I recommend the study of Euler's work on mechanics for realizing how
> erronous this claim is
> Physics and math prior to the last century were deeply entwined. The
> point I'm having a problem getting across is that more recently they
> have gone separate paths. The path taken in mathematics today is not as
> useful to physics as is advocated here.
Partially - I agree with Arnol'd's (the 'A' in KAM) criticism, that the
algebraization of maths has brought it rather further away from physics than
supporting its development
> [...]
> >> There may be only one area of physics that can be fit to an axiomatic
> >> approach. It is thermodynamics.
> >What about mechanics, electrodynamics? :-o
> If you are talking about the "axiomatic" basis built in the 19th
> Century, then I'll give a definite maybe.
No, I had in mind Newton and Euler for mechanics, and Fritz Bopp's and my
papers on the principles of electromagnetism; in the latters, I try to realize
the unity of classical physics in putting classical mechanics and elm on equal
footing.
> The modern versions are not
> very useful to doing physics.(I should hear squeals about this)
I agree; textbooks still separate the branches of physics much more than
necessary
> >> In my view, the most difficult field to
> >> develop a good physical intuition.
> >
> >I agree
> >
> >> I'll leave it as an exercise to
> >> answer why thermodynamics is of such a nature.
> >
> >Doesn't sound like you know the answer ;-)
> Do you care to wager that I don't?;-)
No offence intended!
> I use this question to separate
> the wheat from the chaff when I want to know the level of an
> individual's physical understanding. You may be interested to know, that
> a number of "physicists" stumble here.
It is natural that the level of group members (posters) is rather broad; and
also among the PhD's the knowledge is quite different if it comes to different
branches in physics :-)
> I think I know why some have
> trouble, and it's related to the question I have with equating math to
> physics.
I'm against that such statements are passed through, but other moderators are
more liberal here
> If anyone is interested in another of my ramblings, I may
> summon the strength to continue another thread.
This would be great!
> BTW, I have more to say
> about thermodynamics in my response to Charles.
> >> Finally, I see mathematical physics as part of the mathematical
> >> discipline.
> >I would rather see it as a border discipline
> I can see merit in that.
:-)
> >> Any useful contributions it can bestow on physics is very
> >> welcome. But I don't see how it can produce anything that can be called
> >> new physics.
> >I agree
Best wishes,
Peter
> You are losing attributions. Can your newsreader be set to include the
> attribution of the most recently quoted post?
I'm not using a Newsreader, the loss comes from the server www.killfile.org
when making a line break
Cl.Massé
news:13378d57-21ed-4523...@f63g2000hsf.googlegroups.com...
>> I don't think the issue is "precise mathematical form", but rather
>> "convenient mathematical form",
> All mathematics is precise;
I don't think this adjectives applies to mathematics, at best "exact".
Mathematics is rigorous, logical, and that's already very well. Precise
applies to the form, that is, everything should be written mathematically.
But that isn't enough, special relativity written without vector analysis,
although precise, wouldn't allow much insight.
> I believe that Wightman is emphasizing detail rich mathematics. The need
> that some physicists may have for easy mathematics is irrelevant.
Some physicists only need the theorems, not their proofs, and most of the
time, only a sketch of the proof is sufficient for the reasoning.
>> It often takes years before the theory is conveniently formulated and
>> spelled out in textbooks. The convenient mathematical form is the
>> one based on a minimal set of conceivable and insightful postulates.
>> But again, it is a physical task, and not a mathematical one.
> Aren't you overlooking the fact that the mathematician John von
> Neumann was the first to axiomatize quantum theory?
I'm well aware of the axiomatic approach to quantum theory. But I don't
know who made what since it never help me to understand, and it doesn't
solve the mysteries as is sometimes claimed. It is a conceptually
inconsistent theory, and no mathematician can change that, it is a purely
physical issue.
>> But the truth is that both disciplines can't be compared since
>> they have very different purposes and philosophical status.
> It's very easy to compare mathematicians and physicists. Aesthetics
> and beauty guide mathematicians. Mathematicians are usually perfectly
> logical scientists. Their discipline is based on the orderly, logical,
> systematic unfolding of mathematical knowledge. The exact opposite is
> true of physicists. Physicists strongly oppose taking the time to
> remove from physics everything that is confused, unnecessary and not
> amenable to experimental verification. They happily endorse and are
> satisfied with confused-sounding irrationality
Your second portrait is inexact, and from it I surmise that the first one is
intended to be laudatory. But, you know, I never considered order to be
always a quality, and I find also very fun to laugh and levitate like in
_Mary Poppins_. There are so many other things than symbols and diagrams on
paper. Reality for example, the true subject of physics. Never from a real
measure you have a number with an infinity of random decimals, what for
theorems on pi? Imprecision is everywhere, and tackling it is a skill on
its own. The mathematicians can't prove with equations that the physicists
are backward people, so judging them is not in their scope.
> and agree with
> physicist John Stewart Bell, who wrote in "Speakable And Unspeakable
> In Quantum Mechanics," that the purpose of the way special relativity
> is taught is to shake the students' confidence in common sense.
Physics are an eternal challenge to common sense, and win most of the time,
while mathematics are only the navel-gazing contemplation by the humans of
their own spirit, and the eternal satisfaction of agreeing with themselves.
"physics is consistency of theory with reality, mathematics is consistency
with itself."
> For
> these reasons, physicists aren't interested in axiomatizing the
> foundations of physics. And they don't even have the time to waste on
> such a contemptible task as they see it because they are too busy in
> hot pursuit of the Holy Grail of physics.
What for? They have the orderly mathematicians to tidy up behind them,
without being afraid those overtake: they can't read a map.
Cl.Massé
news:394df24a-d428-44a2...@e53g2000hsa.googlegroups.com...
> Who but a physicist could twist a straightforward fact into a false
> physical principle?
Err... A mathematician?
You know the joke. In an train faring over Ireland, there is a engineer, a
mathematician and a physicist. They see a black spot. The engineer: "I
didn't know there were black sheep by here." The mathematician: "You mean,
sheep with at least one black side." The physicist: "stop quarreling,
you're both roughly right. Yet, it isn't a sheep, it's the shepherd."
> The only substantial part of physics is mathematics. Special
> relativity, for example, only requires a kindergarten definition of
> time.
Well, no need to go farther. Why the brilliant Evarist Galois, the not more
clumsy Pascal, the famous Euclide, didn't discovered special relativity?
Even if they had the idea of the Minkowsky space (which they hadn't, before
special relativity precisely), it would have only served as navel-gazing.
They lacked Michelson-Morley, case closed.
As a further proof, the Schrödinger equation existed already with the
eikonal and Hamilton-Jacobi equations. No mathematician had the idea of
postulating a wave of which material particles are high energy
approximations, before De Broglie did it.
> General relativity is likewise virtually all math; that's why
> David Hilbert was able to solve Einstein's grand problem in only a few
> weeks, while it took Einstein many years even with trying to solicit
> the help of less talented mathematicians. According to Richard
> Feynman, the entire mystery of quantum mechanics is contained in the
> double-slit experiment. How is that experiment not high school level
> physics? Now point me to a physics book where a physicist expounds on
> the sole implications of the double-slit experiment and draws from it
> all the mathematical equations implied by the phenomena.
You try and explain me how to discover the geometry of a room by carefully
groping along the walls. It's very kind of you, but I only need to switch
on the light. I've a much better grab of QM than what your shaky sketch
suggests.
Cl.Massé
>>The distinction usually given by journals is along the lines of saying
>>that mathematical physics requires greater rigor. Modern theoretical
>>physics seeks license to work without a well defined mathematical
>>framework, whereas mathematical physics does not, and is generally more
>>restricted in scope and less applicable in consequence.
The definition, given by mathematical physicist is that theoretical physics
is physics. While mathematical physics is mathematics, that is, proving
theorems, in that case in the axiomatic system of physical theories. For
example, some non trivial theorems have been proven in the theory of
turbulence.
Oh No
>
>Some physicists only need the theorems, not their proofs, and most of the
>time, only a sketch of the proof is sufficient for the reasoning.
That depends on the physicist and his interests, not on the requirements
for the overall development of science.
>
>> Aren't you overlooking the fact that the mathematician John von
>> Neumann was the first to axiomatize quantum theory?
>
>I'm well aware of the axiomatic approach to quantum theory. But I don't
>know who made what since it never help me to understand, and it doesn't
>solve the mysteries as is sometimes claimed.
It is a good first step. Certainly, without it, there would be no means
even to address the next step.
>It is a conceptually
>inconsistent theory, and no mathematician can change that, it is a purely
>physical issue.
I don't agree. It is neither conceptually inconsistent, nor is it purely
physical. It only appears conceptually inconsistent because you try to
make it physical, when it is not. The axioms of quantum theory apply to
as much to language as to physics. When the language is understood, it
will be seen to be conceptually consistent. The subjunctive mood
describes counterfactual events in a consistent way. So too does quantum
theory.
>What for? They have the orderly mathematicians to tidy up behind them,
>without being afraid those overtake: they can't read a map.
>
This is now the problem. It is the fashion for physicists to prohibit
the mathematicians from tidying up. I think perhaps they have come aware
that all the big conceptual advances in physics have been made by
mathematicians, and would rather stifle advance than see it happen
again.
Oh No
>"Shubee" <e.Sh...@gmail.com> a écrit dans le message de
>news:394df24a-d428-44a2...@e53g2000hsa.googlegroups.com...
>
>> Who but a physicist could twist a straightforward fact into a false
>> physical principle?
>
>Err... A mathematician?
>
>You know the joke. In an train faring over Ireland, there is a engineer, a
>mathematician and a physicist. They see a black spot. The engineer: "I
>didn't know there were black sheep by here." The mathematician: "You mean,
>sheep with at least one black side." The physicist: "stop quarreling,
>you're both roughly right. Yet, it isn't a sheep, it's the shepherd."
And the joke is a physicist does not know a sheep from a shepherd?
Hendrik van Hees
> I don't think this adjectives applies to mathematics, at best "exact".
> Mathematics is rigorous, logical, and that's already very well.
> Precise applies to the form, that is, everything should be written
> mathematically. But that isn't enough, special relativity written
> without vector analysis, although precise, wouldn't allow much
> insight.
I'd not go that far, although I'm also appreciating the modern
four-dimensional form whose 100th anniversary we can celebrate this
year (or better said we could if physicists would care more about
history ;-)). The physical insight is already very clear and precisely
stated in Einsteins most famous paper on electromagnetism in moving
media from 1905, although there the math is very simple and in a
somewhat indigestible form of writing everything out in components.
>
>> I believe that Wightman is emphasizing detail rich mathematics. The
>> need that some physicists may have for easy mathematics is
>> irrelevant.
>
> Some physicists only need the theorems, not their proofs, and most of
> the time, only a sketch of the proof is sufficient for the reasoning.
>
>>> It often takes years before the theory is conveniently formulated
>>> and
>>> spelled out in textbooks. The convenient mathematical form is the
>>> one based on a minimal set of conceivable and insightful postulates.
>>> But again, it is a physical task, and not a mathematical one.
>
>> Aren't you overlooking the fact that the mathematician John von
>> Neumann was the first to axiomatize quantum theory?
>
> I'm well aware of the axiomatic approach to quantum theory. But I
> don't know who made what since it never help me to understand, and it
> doesn't
> solve the mysteries as is sometimes claimed. It is a conceptually
> inconsistent theory, and no mathematician can change that, it is a
> purely physical issue.
In which respect is quantum mechanics a conceptually inconsistent
theory? It describes with astonishing success all empirical findings so
far. As long as you stick to its essential physical content (i.e.,
Ballentine's minimal statistical interpretation) there is no conceptual
inconsistency whatsoever. The socalled "inconsistencies" are rather
philosophical head aches of some people who have a comprehension of
what's "real", which I never could understand, than a mathematical
problem. Admittedly there are mathematical problems with quantum field
theories like QED which to my knowledge are not solved yet. As long as
you take it as an effective description in a finite energy-momentum
range of applicability in the sense of (resummed) perturbation theory,
there are no physical (maybe not even mathematical) quibbles either.
The real challenge in contemporary fundamental physics is still to find
a satisfactory quantum theory of gravity which I doubt to be found by
pure mathematical reasoning (vulgo known e.g. as string or M
theory ;-)) as interesting that by itself might be.
--
Hendrik van Hees Institut für Theoretische Physik
Phone: +49 641 99-33342 Justus-Liebig-Universität Gießen
Fax: +49 641 99-33309 D-35392 Gießen
http://theory.gsi.de/~vanhees/faq/
maxwell
> >following sentences which I would like to make known to our group.
>
> >"The greatest obstacles to a mathematician grasping the problems
> >that are on the frontiers of physics is his lack of conditioning in the
> >fundamentals and his own overspecialized training and research.
> >Ideally, we mathematicians should write our own expositions of basic
> >physics, so as not to cut our profession off from its historical roots;
> >until then, we can only applaud efforts such as this one that bridge
> >the gap, and hope that more such striking expositions will be written."
>
> >ROBERT HERMANN
> >Bull. Am. Math. Soc. 70 (1964) 5, 658-660,
> >http://projecteuclid.org/euclid.bams/1183526246
>
> >Hoping you enjoy it,
> >Peter
>
> I have a problem with the author saying mathematicians should do their
> own exposition on physics. I don't think mathematicians would be doing
> physics; they would be doing mathematics based on problems and ideas
> taken from physics. I'm not quite sure what this mathematician thinks
> physics is, but he appears to me to be one of those individuals who may
> think mathematics and physics is the same.
>
> I have met those individuals in the past and found that as
> mathematicians they seem quite good, but as physicists they came up
> wanting. There was a mathematics graduate I knew whose PhD advisor was
> Subrahmanyan Chandrasekhar. His thesis was in GR and was immediately
> grabbed by a Midwestern university physics department. My discussions
> with him about physics lead me to believe his basic understanding of the
> philosophy of physics was lacking, but more disturbing to me was that he
> wasn't interested in physics as an observable science. He had a joint
> position in the university's mathematics department, which eventually
> became his full-time interest. He left the physics department without
> making any notable contributions while there.
>
> I finish with this: I strongly believe that Mathematical Physics is a
> mathematical discipline and is not physics. So a comment that
> mathematicians should re-work physics is wrong-headed if the goal is to
> produce useful physics.
Gentlemen: Math is an unconstrained act of the imagination, physics
is the study of nature. Much (ancient) math was inspired by reality
(e.g. geometry, counting etc). Some 18th and 19th century math was
also inspired by SIMPLE toy models of reality (e.g. classical
mechanics, aetherial electromagnetism). The real world is vastly too
complicated for the simplifications of mathematics to apply: vide
chemistry, biology, economics, etc. Let us be happy with the
amusements provided by our head-games; if they approximate reality,
then 'wonderful'. If one's intuition is inspired by thinking about
the world then try doing physics; if it is motivated by more formal,
abstract symbol manipulations then your career will progress faster &
further in the math department. If you are uninspired you will find
thinking about physics very frustrating but you can always teach
mathematics.
Good hunting!
Uncle Ben
....
>
> It's very easy to compare mathematicians and physicists. Aesthetics
> and beauty guide mathematicians. Mathematicians are usually perfectly
> logical scientists. Their discipline is based on the orderly, logical,
> systematic unfolding of mathematical knowledge.
Richard Feynmann would disagree. He argues that mathematicians are
not scientists at all. ("Scientist" is not an honorific term.) His
definition of "science" is an enterprise in whch truth is decided by
external confirmation. The criterion of mathematical truth is utterly
unrelated to the physical world.
Uncle Ben
Shubee
> "Shubee" <e.Shu...@gmail.com> a écrit dans le message denews:394df24a-d428-44a2...@e53g2000hsa.googlegroups.com...
>
> > The only substantial part of physics is mathematics. Special
> > relativity, for example, only requires a kindergarten definition of
> > time.
>
> Well, no need to go farther. Why the brilliant Evarist Galois, the not more
> clumsy Pascal, the famous Euclide, didn't discovered special relativity?
> Even if they had the idea of the Minkowsky space (which they hadn't, before
> special relativity precisely), it would have only served as navel-gazing.
> They lacked Michelson-Morley, case closed.
Cl\.Massé, I'm surprised by your response. I thought that all
physicists understand that Galileo could have derived the special
theory of relativity.
http://adsabs.harvard.edu/abs/1994AmJPh..62..157S
> As a further proof, the Schrödinger equation existed already with the
> eikonal and Hamilton-Jacobi equations. No mathematician had the idea of
> postulating a wave of which material particles are high energy
> approximations, before De Broglie did it.
First of all, the Schrödinger equation is basically just the diffusion
equation (heat equation) with an imaginary diffusion constant. So the
essential physics came from Fourier, a mathematician, who discovered
the heat equation. As far as the axiomatization of quantum theory is
concerned, De Broglie's wave hypothesis was truly irrelevant. The most
original and certainly the most essential contribution to quantum
physics was due to Max Born and his basic rules concerning probability
amplitudes and probability distributions. Born was David Hilbert's
favorite student and Hilbert became Born's mentor.
> > General relativity is likewise virtually all math; that's why
> > David Hilbert was able to solve Einstein's grand problem in only a few
> > weeks, while it took Einstein many years even with trying to solicit
> > the help of less talented mathematicians. According to Richard
> > Feynman, the entire mystery of quantum mechanics is contained in the
> > double-slit experiment. How is that experiment not high school level
> > physics? Now point me to a physics book where a physicist expounds on
> > the sole implications of the double-slit experiment and draws from it
> > all the mathematical equations implied by the phenomena.
>
> You try and explain me how to discover the geometry of a room by carefully
> groping along the walls. It's very kind of you, but I only need to switch
> on the light.
And light to you means observation and the absence of mathematics?
> I've a much better grab of QM than what your shaky sketch suggests.
I wasn't presenting a sketch of QM. I asked a question which you
evidently couldn't answer.
Shubee
http://www.everythingimportant.org/relativity/special.pdf
Peter
> Cl\.Massé, I'm surprised by your response. I thought that all
> physicists understand that Galileo could have derived the special
> theory of relativity.
> http://adsabs.harvard.edu/abs/1994AmJPh..62..157S
Can you provide a copy of this paper? Thank you in advance!
> First of all, the Schrödinger equation is basically just the diffusion
> equation (heat equation) with an imaginary diffusion constant. So the
> essential physics came from Fourier, a mathematician, who discovered
> the heat equation.
I apologize for that this nonsense was overseen by the moderator who has
passed this posting
Best wishes,
Peter
Oh No
>Charles Francis wrote:
>>Thus spake Murray Arnow
>>>Peter wrote:
>>>>
>>>>> Charles Francis wrote:
>>>>> >Thus spake Murray Arnow
>>>>> >
>>>>> >>You may interpret the laws axiomatically, but as I keep repeating, there
>>>>> >>is little physical insight gained from the approach.
>>>>
>>>>I recommend the study of Euler's work on mechanics for realizing how
>>>>erronous
>>>>this claim is
>>>>
>>>
>>>Physics and math prior to the last century were deeply entwined. The
>>>point I'm having a problem getting across is that more recently they
>>>have gone separate paths. The path taken in mathematics today is not as
>>>useful to physics as is advocated here.
>>
>>
>>On this we agree, but the fault lies not with either mathematics or
>>physics, but with the practitioners of physics, who do not use
>>mathematics correctly by first establishing physical postulates as the
>>axioms of mathematical structure.
>>
>
>worry about being judged for the way math is used.
No, you are being judged for not establishing physical assumptions.
> This isn't physics;
>it's pedantry. When the mathematical method gives consistently correct
>answers, that is the only justification necessary.
The mathematical method is tautology. It necessarily gives correct
answers when given correct assumptions. If you do not do that, it is
not mathematics, it is not physics and it is not science. Ramblings
based on false assumptions are simply garbage.
>The end pursuit of
>physics is understanding nature, not validating mathematics.
You may leave validating mathematics to mathematicians, but if you are
not prepared to express assumptions correctly, do not pretend that you
are either understanding nature or doing physics.
>
>> Thus spake Murray Arnow
>>>Charles Francis wrote:
>>>> Thus spake Murray Arnow
>>>
>>>>>The Nineteenth Century was an interesting time. People engaged in both
>>>>>math and physics with great facility. There was an explosion in
>>>>>mathematics due in great part to the need brought on by physics. But I
>>>>>don't see where the participants confused the two.
>>>>
>>>>It used to be generally assumed that mathematics was abstracted from
>>>>reality. That lead to problems in the foundations of mathematics, and is
>>>>now known not to be true.
>>>>
>>>
>>>Well, physics must keep in touch with reality. You have recognized why
>>>physics and math can have conflicts.
>>
>>Indeed. While there is no such constraint on mathematics, that does not
>>permit physicists to use mathematics without this constraint.
>>>
>
>Who is to judge the way math is used and what are the penalties levied?
Anyone with a logical mind can check logic. The penalties for not doing
so are simply wasted time and effort.
>>> I think there may be a confusion here between formalism and
>>>axioms. Formalism, although very nice and powerful, can lead people to
>>>make some foolish statements about math relative to physics. People can
>>>rely so heavily on the formalism that they lose sight of the physics it
>>>encompasses.
>>
>>That perhaps describes how many physicists abuse mathematics, but not
>>how it should be used.
>>
>
>This is where I'm cutting out out of here. We aren't talking physics
>anymore; we are defending math.
Mathematics needs no defence. Either it is established by logic, or it
is not mathematics.
>I don't care if a method can be
>rigorously proved. God only knows, no physicist is happy with
>renormalization theory, but it gives the right answer. If a
>mathematician can prove that the technique is valid, great, but it
>doesn't do anything to better understand the physics.
Untrue. Mathematicians have proved which part of the technique is
correct. Unfortunately most quantum field theory is based on the parts
which are incorrect, and most physicists are wrapped up in a complete
misunderstanding of physics. Hence we have Higgs particles and string
theory, neither of which have any basis in either maths or physics.
>
>>>>>Finally, I see mathematical physics as part of the mathematical
>>>>>discipline. Any useful contributions it can bestow on physics is very
>>>>>welcome. But I don't see how it can produce anything that can be called
>>>>>new physics.
>>>>
>>>>Axiomatising classical electromagnetism lead to special relatity. Was
>>>>that not new? Was general relativity not new? It was developed entirely
>>>>mathematically.
>>
>>>This is news to me, and from everything I read about the history of
>>>relativity, would be news to Einstein.
>>
>>I find that quite extraordinary. To fail to understand general
>>relativity as a mathematical theory of physics is to fail to understand
>>it at all, imv.
>>
>
>I find your statement even more extraordinary. Einstein sweated bullets
>trying to understand the physics of the problem. It was his physical
>insight that reduced much of relativity to the simple form we know now.
Precisely. That is the correct application of mathematics to physics, to
find a few, correct, precisely stated physical postulates, and use them
to construct a mathematical theory. He also sweated buckets to see how
to apply tensors and differential geometry to the problem, btw. In
contrast, other physicists take false assumptions for granted.
>And he still wasn't satisfied with the results for physical reasons;
>e.g., he was very unhappy about using the cosmological constant.
Indeed. The cosmological constant was a fiddle factor, and
unsatisfactory as a physical assumption for that reason. In contrast
cosmologists today say "oh, the observations require it, so it must be
physics", and are not prepared to consider that.there might be some
other false assumption they have not thought of.
>>>am finding it difficult to continue.
>>
>>I take it your criticism of "isotropy of space" has to do with the fact
>>that space is not measurable? Indeed, this is so. The results of
>>measurement are numbers, the results of measurements of position are
>>members of R^3. If one correctly applies mathematics, one cannot
>>conclude, as it seems do most physicists, that space has physical
>>substance, but rather the use of homogeneous, isotropic mathematical
>>structure only says that electrons are always electrons, photons are
>>always photons etc. Of course, one will only apply mathematics correctly
>>if one first develops a correct philosophy of mathematics and its
>>relation to physics.
>>
>
>That is the kind of answer which would get groans from most of the
>physicists I know.
I think that is because most physicists have no grasp of the fundamental
issues facing modern physics.
>Where's the physics?
In the choice of correct assumptions, or postulates, or axioms. E.g.
mechanics is contained in Newton's laws.
Chalky
>
> Physics and mathematics are not the same. Physics is a mere
> subdiscipline of mathematics.
Careful !
Physicists could argue that chemistry is a subdiscipline of physics,
and chemists could argue that biological systems are a subdiscipline
of organic chemistry.
Speaking as a physicist, mathematics is merely a tool for assisting in
the understanding of physical processes, or in mapping those physical
processes.
Physical processes are discovered by observation and experiment, then
logic (and some creativity) is used to explain those physical
processes as elegantly as possible. Once you have that explanation one
can crank the handle of mathematics to make further predictions.
You, on the other hand, seem to be arguing that the cart (Descartes)
goes before the horse.
This is wrong. To the extent that the importance of empirical
observation can be dismissed, one could more reasonably argue that
both theoretical physics and mathematics are subdisciplines of pure
logic.
Oh No
>>>>
>>>>On this we agree, but the fault lies not with either mathematics or
>>>>physics, but with the practitioners of physics, who do not use
>>>>mathematics correctly by first establishing physical postulates as the
>>>>axioms of mathematical structure.
>>>>
>>>
>>>As a colleague would have put it "What a crock of shit!" Now we have to
>>>worry about being judged for the way math is used.
>>
>>No, you are being judged for not establishing physical assumptions.
>By establishing physical assumptions, I assume you mean mathematically
>justify the assumptions. Well, that's just a part of physics, an
>important part, but it is not the entirety.
Indeed it is not the entirety, but it is an essential part. Nor is it
just mathematical. Mathematically the assumptions must be shown to be
consistent, but simply presenting a consistent axiom set does not
constitute physics. The assumptions, or postulates, should be a
consistent set of statements about the real world, and they should not
contain hidden assumptions which are taken for granted.
>>> This isn't physics;
>>>it's pedantry. When the mathematical method gives consistently correct
>>>answers, that is the only justification necessary.
>>
>>The mathematical method is tautology. It necessarily gives correct
>>answers when given correct assumptions. If you do not do that, it is
>>not mathematics, it is not physics and it is not science. Ramblings
>>based on false assumptions are simply garbage.
>Nonsense. Nature isn't tautological.
Deduction is tautological. Mathematical method is tautological.
Tautology does not add to the physics contained in the assumptions, but
reveals the implications of a given set of assumptions.
>>>The end pursuit of
>>>physics is understanding nature, not validating mathematics.
>>
>>You may leave validating mathematics to mathematicians, but if you are
>>not prepared to express assumptions correctly, do not pretend that you
>>are either understanding nature or doing physics.
>Physicist don't know how to do physics! You are absurd.
I would say rather that Higg's particles and string theory are absurd.
Where is the physics in that?
>
>There are trained physicist who know more math than you seem to give
>them credit for. I admit I started out being almost completely
>mathematical in my approach to physics. It took me more years than it
>should have before I realized that there was something more to physics
>than math and then to realize there was a great deal more than math.
I have always known that mathematical proof proceeds from axioms, and
that if the axioms are not correct for a given application, the exercise
of using them is meaningless.
>
>The great discoveries in theoretical physics come in the physical
>interpretation of the mathematics.
Quite. And if we do not axiomatise the mathematics, we do not know what
is to be interpreted.
>Physics is standardly taught by going
>over the same material again and again in increments of sophistication.
>This is done for a good reason: it requires time to gain sophistication
>beyond the regurgitation of the formalism.
This appears to me a dangerous approach. By repetition one becomes used
to that which does not make sense, and fails to appreciate what it is
that does not make sense. Mathematics is taught by starting from few
postulates, and ensuring that everything based on them makes sense. The
problem which you refer to is that mathematicians are not taught that
one should start by seeing that the postulates apply to the problem in
hand.
>>>> Thus spake Murray Arnow
>>>>>Charles Francis wrote:
>>>>>> Thus spake Murray Arnow
>>>>>
>>>>>>>The Nineteenth Century was an interesting time. People engaged in both
>>>>>>>math and physics with great facility. There was an explosion in
>>>>>>>mathematics due in great part to the need brought on by physics. But I
>>>>>>>don't see where the participants confused the two.
>>>>>>
>>>>>>It used to be generally assumed that mathematics was abstracted from
>>>>>>reality. That lead to problems in the foundations of mathematics, and is
>>>>>>now known not to be true.
>>>>>>
>>>>>
>>>>>Well, physics must keep in touch with reality. You have recognized why
>>>>>physics and math can have conflicts.
>>>>
>>>>Indeed. While there is no such constraint on mathematics, that does not
>>>>permit physicists to use mathematics without this constraint.
>>>>>
>>>
>>>Who is to judge the way math is used and what are the penalties levied?
>>
>>Anyone with a logical mind can check logic. The penalties for not doing
>>so are simply wasted time and effort.
>>
>
>Ok. That has been long practiced in physics. But physicists admit that
>they don't know what "logic" nature will spring on them,
As you rightly said earlier, nature does not spring logic.
>and it may be
>wrong to assume that there is one logical path which connects
>everything;
Normally if there is one logical path, there are many.
>for that matter, that everything can be connected. It would
>be nice if it were so (and everyone hopes it's so), but there is
>disquieting evidence that it may never happen (it looks like that the
>total transition from QM to CM may not be attainable).
If that is so, it is because there is a fault in the assumptions of QM.
A first (mathematical) test of a formulation of QM should be to ensure
that CM may be derived. I do not see physicists interested in such
tests.
>Now, that's a nice mathematical problem. It would be important to know
>if no logic can be constructed which will tie everything together.
>That's one mathematical result I think useful.
On this at least we agree. If you would look at my site you will see
that I start with a (relativistic) formulation of qm at
http://www.teleconnection.info/rqg/RelativisticQuantumTheory
and work to demonstrate classical electromagnetism at
http://www.teleconnection.info/rqg/CEM
>>>>> I think there may be a confusion here between formalism and
>>>>>axioms. Formalism, although very nice and powerful, can lead people to
>>>>>make some foolish statements about math relative to physics. People can
>>>>>rely so heavily on the formalism that they lose sight of the physics it
>>>>>encompasses.
>>>>
>>>>That perhaps describes how many physicists abuse mathematics, but not
>>>>how it should be used.
>>>>
>>>
>>>This is where I'm cutting out out of here. We aren't talking physics
>>>anymore; we are defending math.
>>
>>Mathematics needs no defence. Either it is established by logic, or it
>>is not mathematics.
>Your belief in its ultimate path to truth needs defense.
It may be that we are not as far apart as most of this discussion has
appeared to suggest. I am not saying, as you seem to think, that
mathematics can, on its own, produce physics, but rather that it is an
essential method in producing physics.
>
>> In
>>contrast, other physicists take false assumptions for granted.
>>
>
>Like the assumptions about delta functions and subtracting infinities.
>So they're not rigorous, but they work.
Delta functions can be dealt with rigorously. The only justification for
subtracting infinities is that they should not have been there in the
first place. It is necessary to set the theory up in such a way that
they are not there. In the case of qed, this does require a change in
the physical assumptions. If you peruse further on my site, you will see
that this is an issue which has much concerned me.
>If you think that rigor is the
>path to new physical insight, then you have no idea what physics is
Rigor is a means to eliminate what is wrong. When one eliminates false
assumption, one seeks to replace it with something which has at least a
chance of being right. That may well demand new physical insight.
>
>>I think that is because most physicists have no grasp of the fundamental
>>issues facing modern physics.
>Or maybe it is some mathematicians who don't understand the issues.
Most mathematicians are not even interested. That does not justify a
harangue against all mathematics and mathematicians, or a refusal to
recognise the mathematical nature of the general theory of relativity.
>>>Where's the physics?
>>
>>In the choice of correct assumptions, or postulates, or axioms. E.g.
>>mechanics is contained in Newton's laws.
>But even at the classical and non-relativistic level, Newton's Laws are
>physically flawed. So much for axioms.
Indeed, they are flawed. There never was a physical justification for
absolute space and time. This is why we should use "postulate" rather
than "axiom". I do not see axioms as something which cannot be
challenged. The mathematical method as applied to physics should involve
a willingness to challenge axioms.
>
>And so much for this harangue against physicists because they see the
>world differently.
It is just a response to your harangue against mathematics.
>As I said, mathematics is useful, rigor is nice, but
>it won't get you new physics.
As I have pointed out, it already has. Moreover, there is no other path
to unification.
Chalky
> Time for a confession: In my earlier years I had a strong interest in
> mathematics and had very mathematical approach in my understanding of
> physics. Then I was standing next to my thesis advisor who was engaged
> in a discussion with another physicist. The other physicist made a
> remark that "physics was mostly solving equations". My advisor said "not
> quite, it was trying to figure out what the equations mean".
At a fundamental level I would go even further:- it is trying to work
out what those equations / relationships actually are, in order to
explain observation. This is where great physicists like Galileo,
Newton, Faraday, Planck and Einstein differ from the lesser 'spanner-
men' who merely crank the handles of the equations / relationships
that the greater physicists have already given to them.
> The insight
> of that remark impressed me greatly. My attitude changed from primarily
> trying to understand the mathematics in mathematical way to trying to
> understand it in a physical way. Although I was aware prior of the two
> approaches, my sophistication in understating needed this "epiphany". I
> finally appreciated the physical approach that so many really good
> physicists used.
Chalky
> Newton's laws are themselves the axioms.
Yes, and the axioms were deduced logically from observation.
> We do not derive axioms
> mathematically, but rather all mathematical proof must proceed from
> axioms. The mathematical challenge is to establish precisely the axiom
> set which yields a good model of physics.
Yes, IE good correlation with observation
> Newton, Einstein, and Maxwell
> have made the most important contributions to physics because this is
> what they did.
Well, in terms of applied physics, at least, I would have said that
Faraday's contribution was as great as Maxwell's. Maxwell's equations
gave us radio (via Marconi) and TV (via Baird) Faraday gave us
electric motors and dynamos,hence the electric grid, and Faraday's
education in mathematics and logic was limited to what he learned at
Sunday school.
Ken S. Tucker
An electrician friend of mine, maintained a paper
mill, and would hire new engineers. Well the new
engineer would argue the "book" says bla-bla-bla,
but the friend would counter, "machinery can't read".
Same thing applies to the universe.
The people you cite I would regard as theoreticians.
Just about anyone can memorize the "book" and
be "book smart", but very few can add a page to
that book.
A theoretician is then a technician who employs
mathematics, (and mathematicians) , but those
guys knew the book, and what was important and
sidelined the obvious trivial dogma.
A guy like Newton actually built and invented the
Newtonian reflector telescope by grinding and
polishing his own mirrors etc...those guys were
hands-on people.
So instead of arguing mathematics vs physics
or mathematician vs physicist, we should see
how the eclectic skills of a theoretician evolve.
Regards
Ken S. Tucker
Ken S. Tucker
...
> I said earlier that I want to quit this thread. I will now. I see there
> are others who understand what I'm after and are weighing in. Writing is
> too difficult for me and teaching is even harder. I'll leave the
> educational aspects to those better equipped than myself.
I have found this discussion thought provoking
and inspiring, and I think I can speak for most
of the many readers saying that.
I got a sense of turbelence, possibly from sematics,
circularity or ego, but I actually create a large ego
to compete with the universe, so I understand that.
Cheers
Ken S. Tucker
Peter
> Thus spake Murray Arnow <ar...@iname.com>
Dear colleagues/friends/group members/posters,
Please be wise and stick to dialectics!
The laws of physics must not contradict the laws of logics and of geometry.
Mathematical equations express both quantitative and qualitative
relationships. The latter is often specific to the discipline where it is
applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
necessary, but, nevertheless, auxiliary part of a natural science.
> >>>>On this we agree, but the fault lies not with either mathematics or
> >>>>physics, but with the practitioners of physics, who do not use
> >>>>mathematics correctly by first establishing physical postulates as the
> >>>>axioms of mathematical structure.
How I should understand this statement?
> >By establishing physical assumptions, I assume you mean mathematically
> >justify the assumptions. Well, that's just a part of physics, an
> >important part, but it is not the entirety.
>
> Indeed it is not the entirety, but it is an essential part. Nor is it
> just mathematical. Mathematically the assumptions must be shown to be
> consistent, but simply presenting a consistent axiom set does not
> constitute physics. The assumptions, or postulates, should be a
> consistent set of statements about the real world, and they should not
> contain hidden assumptions which are taken for granted.
Yes, both, physically and mathematically consistent:-)
> >>The mathematical method is tautology.
This cannot be true (I'm trying to avoid modal verbs in science as far as
possible, but, here, I cannot resist to use such one, because I wish to
express a feeling rather than a knowledge)
> >>It necessarily gives correct
> >>answers when given correct assumptions.
This is correct, but: are the answers identical with the assumptions?
...
> >>You may leave validating mathematics to mathematicians, but if you are
> >>not prepared to express assumptions correctly, do not pretend that you
> >>are either understanding nature or doing physics.
Faraday didn't express himself mathematically, neither his assumptions, nor
his conclusions
> >Physicist don't know how to do physics! You are absurd.
...
> >Physics is standardly taught by going
> >over the same material again and again in increments of sophistication.
> >This is done for a good reason: it requires time to gain sophistication
> >beyond the regurgitation of the formalism.
> This appears to me a dangerous approach. By repetition one becomes used
> to that which does not make sense, and fails to appreciate what it is
> that does not make sense. Mathematics is taught by starting from few
> postulates, and ensuring that everything based on them makes sense. The
> problem which you refer to is that mathematicians are not taught that
> one should start by seeing that the postulates apply to the problem in
> hand.
Newton is told to have answered to the question, why he was so successfull,
that he has thought over and over again over the problems :-)
...
> >for that matter, that everything can be connected. It would
> >be nice if it were so (and everyone hopes it's so), but there is
> >disquieting evidence that it may never happen (it looks like that the
> >total transition from QM to CM may not be attainable).
>
> If that is so, it is because there is a fault in the assumptions of QM.
> A first (mathematical) test of a formulation of QM should be to ensure
> that CM may be derived. I do not see physicists interested in such
> tests.
I think, that, first, Schrödinger's (1926) requirement should be obeyed, that
the use of classical expressions within quantum theory should be justified -
otherwise, that requirement becomes a circle-conclusion
Schrödinger's (1926) requirements to the foundation of quantum mechanics have
been fullfilled in my paper with Dieter Suisky, Int. J. Theor. Phys., Feb.
2005, and in my book, published by Springer in 2006
> >Now, that's a nice mathematical problem. It would be important to know
> >if no logic can be constructed which will tie everything together.
> >That's one mathematical result I think useful.
> On this at least we agree. If you would look at my site you will see
> that I start with a (relativistic) formulation of qm at
>
> http://www.teleconnection.info/rqg/RelativisticQuantumTheory
>
> and work to demonstrate classical electromagnetism at
>
> http://www.teleconnection.info/rqg/CEM
In view of Dirac's (1949) approach to relativistic dynamics, its adherence to
the Procrustes bed of Lorentz transformation makes it doubtful
...
> >>In the choice of correct assumptions, or postulates, or axioms. E.g.
> >>mechanics is contained in Newton's laws.
This is somewhat superficial; otherwise, Newton would not have set the
Definitions before theLaws
> >But even at the classical and non-relativistic level, Newton's Laws are
> >physically flawed. So much for axioms.
What is the flaw in them? (This question is not to to defend them, but to
fins out how you are understanding them)
> Indeed, they are flawed. There never was a physical justification for
> absolute space and time.
somebody seems to think to understand classical mechanics better than Newton
;-)
> This is why we should use "postulate" rather
> than "axiom". I do not see axioms as something which cannot be
> challenged. The mathematical method as applied to physics should involve
> a willingness to challenge axioms.
Euler reduced the set of Newton's axioms to the minimum one
Thus, calm down and learn from the masters :-)
Peter
Ken S. Tucker
On Aug 13, 5:26 pm, Peter <end...@dekasges.de> wrote:
...
> Mathematical equations express both quantitative and qualitative
> relationships. The latter is often specific to the discipline where it is
> applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
> necessary, but, nevertheless, auxiliary part of a natural science.
Interesting, photosynthesis...
photon + plant + CO2 => plant + C + O2
Is the weight of C apart from O2 greater than the weight
of CO2?
I think it is because,
C + O2 => CO2 + heat , heat = mc^2.
That's important if you heat with wood, and a very nice
example of how solar fusion using E=mc^2 produces
photons, that are then converted to m=E/c^2 via plants,
to grow trees.
Thanks Peter, better than a cup of coffee.
I'm always interested in a way of finding m=E/c^2
demonstratably, and pair production of taking a
gamma to a positron+electron is fairly hi-brow.
Of course it would be nice to build a solar powered
machine that splits CO2 and H2O neatly and spits
out C8H18 (octane?)...maybe nuclear powered...
Regards
Ken S. Tucker
[snip agreeably]
Oh No
>Dear colleagues/friends/group members/posters,
>
>Please be wise and stick to dialectics!
>
>The laws of physics must not contradict the laws of logics and of geometry.
First one should understand how the rules of geometry arise from
physical processes.
>
>Mathematical equations express both quantitative and qualitative
>relationships. The latter is often specific to the discipline where it is
>applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
>necessary, but, nevertheless, auxiliary part of a natural science.
>
>
>> >>>>On this we agree, but the fault lies not with either mathematics or
>> >>>>physics, but with the practitioners of physics, who do not use
>> >>>>mathematics correctly by first establishing physical postulates as the
>> >>>>axioms of mathematical structure.
>
>How I should understand this statement?
One should understand that mathematical proof proceeds from axioms, and
that it uses only tautology. Anything stated from mathematical proof is
simply a restatement of the axioms. To understand physics it is thus
necessary only to understand the physical content of the axioms, or
postulates. This requires that one is very precise and careful in
choosing postulates which correctly describe the physical behaviour of a
model.
>> >By establishing physical assumptions, I assume you mean mathematically
>> >justify the assumptions. Well, that's just a part of physics, an
>> >important part, but it is not the entirety.
>>
>> Indeed it is not the entirety, but it is an essential part. Nor is it
>> just mathematical. Mathematically the assumptions must be shown to be
>> consistent, but simply presenting a consistent axiom set does not
>> constitute physics. The assumptions, or postulates, should be a
>> consistent set of statements about the real world, and they should not
>> contain hidden assumptions which are taken for granted.
>
>Yes, both, physically and mathematically consistent:-)
>> >>The mathematical method is tautology.
>
>This cannot be true (I'm trying to avoid modal verbs in science as far as
>possible, but, here, I cannot resist to use such one, because I wish to
>express a feeling rather than a knowledge)
The application of mathematical reason is tautology. That is not the
whole story. The subtleties lie in the choice of postulates.
>
>> >>It necessarily gives correct
>> >>answers when given correct assumptions.
>
>This is correct, but: are the answers identical with the assumptions?
They are contained in the assumptions, though they might not be visible
without proof.
>> >>You may leave validating mathematics to mathematicians, but if you are
>> >>not prepared to express assumptions correctly, do not pretend that you
>> >>are either understanding nature or doing physics.
>
>Faraday didn't express himself mathematically, neither his assumptions, nor
>his conclusions
Faraday did not consider the structure underlying the concept of a
field. Fields are a useful concept, but not a fundamental one.
>> >Physics is standardly taught by going
>> >over the same material again and again in increments of sophistication.
>> >This is done for a good reason: it requires time to gain sophistication
>> >beyond the regurgitation of the formalism.
>
>> This appears to me a dangerous approach. By repetition one becomes used
>> to that which does not make sense, and fails to appreciate what it is
>> that does not make sense. Mathematics is taught by starting from few
>> postulates, and ensuring that everything based on them makes sense. The
>> problem which you refer to is that mathematicians are not taught that
>> one should start by seeing that the postulates apply to the problem in
>> hand.
>
>Newton is told to have answered to the question, why he was so successfull,
>that he has thought over and over again over the problems :-)
Indeed, Newton was engaged in the matter of choosing postulates.
>> >for that matter, that everything can be connected. It would
>> >be nice if it were so (and everyone hopes it's so), but there is
>> >disquieting evidence that it may never happen (it looks like that the
>> >total transition from QM to CM may not be attainable).
>>
>> If that is so, it is because there is a fault in the assumptions of QM.
>> A first (mathematical) test of a formulation of QM should be to ensure
>> that CM may be derived. I do not see physicists interested in such
>> tests.
>
>I think, that, first, Schrödinger's (1926) requirement should be obeyed, that
>the use of classical expressions within quantum theory should be justified -
>otherwise, that requirement becomes a circle-conclusion
Classical expressions should not appear at a fundamental level of the
quantum theory, but only as quantities and laws which can be derived
from it. The normal practice of introducing quantum theory by quantising
a classical theory is non-mathematical, circular, and should be
prohibited.
>> >Now, that's a nice mathematical problem. It would be important to know
>> >if no logic can be constructed which will tie everything together.
>> >That's one mathematical result I think useful.
>
>> On this at least we agree. If you would look at my site you will see
>> that I start with a (relativistic) formulation of qm at
>>
>> http://www.teleconnection.info/rqg/RelativisticQuantumTheory
>>
>> and work to demonstrate classical electromagnetism at
>>
>> http://www.teleconnection.info/rqg/CEM
>
>In view of Dirac's (1949) approach to relativistic dynamics, its adherence to
>the Procrustes bed of Lorentz transformation makes it doubtful
I am not sure what you are saying. Dirac was certainly not saying that
the Lorentz transformation is false. In any case, the arbiter of
physical theory is nature, not any physicist's approach to understanding
nature, no matter how good the physicist.
>> >>In the choice of correct assumptions, or postulates, or axioms. E.g.
>> >>mechanics is contained in Newton's laws.
>
>This is somewhat superficial; otherwise, Newton would not have set the
>Definitions before theLaws
Newton worked correctly. Definitions form a part of the axioms for a
mathematical structure.
>
>> >But even at the classical and non-relativistic level, Newton's Laws are
>> >physically flawed. So much for axioms.
>
>What is the flaw in them? (This question is not to to defend them, but to
>fins out how you are understanding them)
As stated the flaw is in the assumptions of absolute space and time.
>
>> Indeed, they are flawed. There never was a physical justification for
>> absolute space and time.
>
>somebody seems to think to understand classical mechanics better than Newton
> ;-)
It would be a poor thing, 300 years later, not to understand better than
Newton, the relationship between classical mechanics and relativity, and
between classical mechanics and quantum mechanics.
>> This is why we should use "postulate" rather
>> than "axiom". I do not see axioms as something which cannot be
>> challenged. The mathematical method as applied to physics should involve
>> a willingness to challenge axioms.
>
>Euler reduced the set of Newton's axioms to the minimum one
Imv, he replaced clarity with obscurity, and (perhaps unwittingly)
initiated an approach which incorrectly claims that the physics is in
the results, not in the assumptions.
Peter
> Peter wrote:
> >
> >> Thus spake Murray Arnow
> >
> >
> >Please be wise and stick to dialectics!
> >
> >The laws of physics must not contradict the laws of logics and of
> geometry.
> >
> >Mathematical equations express both quantitative and qualitative
> >relationships. The latter is often specific to the discipline where it is
> >applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
> >necessary, but, nevertheless, auxiliary part of a natural science.
> >
>
>
> Peter, you have to take better measures to correctly record
> attributions. Every response, save one, were aimed at Charles, not me. I
> don't wish to be credited for what Charles writes, and I don't think he
> would like me to be credited for his remarks, either.
>
> Murray
Murray,
I apologize for any confusion! I'm not setting them - what can I do?
You are the first and only writing me about that effect, thus, I would like
to read what other readers say and hope that somebody will response :-)
Thank you and best wishes,
Peter
Cl.Massé
>> don't know who made what since it never help me to understand, and it
>> doesn't solve the mysteries as is sometimes claimed. It is a
>> conceptually inconsistent theory, and no mathematician can change that,
>> it is a purely physical issue.
"Hendrik van Hees" <Hendrik...@theo.physik.uni-giessen.de> a écrit dans
le message de news:g7s73s$lh$1...@news2.open-news-network.org...
> In which respect is quantum mechanics a conceptually inconsistent
> theory?
Quantum systems are described conceptually differently in different frames
of reference. For example, the Aspect's experiment involves different
directions for the causality chain according to the frame moving along the
beam. Even though the choice of description is constrained, that is
conceptually inconsistent with the principle of relativity. It's worth
pointing out that a similar conceptual inconsistency was a rationale to
special relativity, as Einstein wrote in the introduction of his milestone
paper, although classical electromagnetism described all empirical finding
with astonishing success, till MM.
> It describes with astonishing success all empirical findings so far.
That is distinct from (conceptual) self-consistency.
> As long as you stick to its essential physical content (i.e.,
> Ballentine's minimal statistical interpretation) there is no conceptual
> inconsistency whatsoever. The socalled "inconsistencies" are rather
> philosophical head aches of some people who have a comprehension of
> what's "real", which I never could understand, than a mathematical
> problem.
It's precisely here that physics departs from mathematics. And it isn't a
matter of philosophical taste, but of the availability of a better theory.
Like in life, some people resign themselves and find reasons of being
content, while some other people continue to strive for a better world.
> Admittedly there are mathematical problems with quantum field
> theories like QED which to my knowledge are not solved yet.
QED is a failed attempt to solve the inconsistency. In addition, it implies
the Higgs that isn't observed, which is the modern MM.
> As long as
> you take it as an effective description in a finite energy-momentum
> range of applicability in the sense of (resummed) perturbation theory,
> there are no physical (maybe not even mathematical) quibbles either.
I've no opinion on that matter, since QxD isn't the ultimate theory.
> The real challenge in contemporary fundamental physics is still to find
> a satisfactory quantum theory of gravity which I doubt to be found by
> pure mathematical reasoning (vulgo known e.g. as string or M
> theory ;-)) as interesting that by itself might be.
That's not possible as long as quantum theory isn't satisfactory itself.
There are promising approaches that involve solitons in the space-time
geometry, called "geons". There may be a theory containing both QM and
gravity, but finding it means jettisoning much of our favorite ways of
thought, especially corpuscle and wave concepts.
Oh No
>>> I'm well aware of the axiomatic approach to quantum theory. But I
>>> don't know who made what since it never help me to understand, and it
>>> doesn't solve the mysteries as is sometimes claimed. It is a
>>> conceptually inconsistent theory, and no mathematician can change that,
>>> it is a purely physical issue.
>
>"Hendrik van Hees" <Hendrik...@theo.physik.uni-giessen.de> a écrit dans
>le message de news:g7s73s$lh$1...@news2.open-news-network.org...
>
>> In which respect is quantum mechanics a conceptually inconsistent
>> theory?
>
>Quantum systems are described conceptually differently in different frames
>of reference. For example, the Aspect's experiment involves different
>directions for the causality chain according to the frame moving along the
>beam. Even though the choice of description is constrained, that is
>conceptually inconsistent with the principle of relativity.
the inconsistency is not with the principle of relativity, but with
either locality or causality.
> It's worth
>pointing out that a similar conceptual inconsistency was a rationale to
>special relativity,
Indeed.
>
>> Admittedly there are mathematical problems with quantum field
>> theories like QED which to my knowledge are not solved yet.
>
>QED is a failed attempt to solve the inconsistency.
I do not consider it failed, but, just as sr caused us to alter our
views on spacetime, qed requires us to restate locality, and we may have
to alter our views on causality.
>In addition, it implies
>the Higgs that isn't observed, which is the modern MM.
The Higgs is a prediction of the Weinberg-Salam theory, not a prediction
of QED.
FrediFizzx
news:tYUj0wA6...@charlesfrancis.wanadoo.co.uk...
> Classical expressions should not appear at a fundamental level of
> the
> quantum theory, but only as quantities and laws which can be derived
> from it. The normal practice of introducing quantum theory by
> quantising
> a classical theory is non-mathematical, circular, and should be
> prohibited.
That doesn't sound right . If classical fields are emergent from
quantum, why is it not OK to reverse engineer? It should be possible
to tackle from both directions. Especially if we don't know all there
is to know about the quantum? I suspect classical-quantum could be
like a duality. One does not exist without the other.
Best,
Fred Diether
Mike
> This is wrong. To the extent that the importance of empirical
> observation can be dismissed, one could more reasonably argue that
> both theoretical physics and mathematics are subdisciplines of pure
> logic.
You might wish to consider the effort to derive physics from logic at:
http://hook.sirus.com/users/mjake/QMfromlogic.htm
It not a finished effort yet. But it looks promising.
Ken S. Tucker
[...]
On Aug 14, 8:05 am, ar...@iname.com (Murray Arnow) wrote:
> Peter, this isn't a voting issue. One may say it's a historical accuracy
> issue, but I say it's a matter of courtesy. It is discourteous to quote
> a person without identifying him.
I certainly agree. I designate a snip using ... or [...]
or [snip] with a comment. That is to abbreviate the
thread and of course one may return to find what
was snipped. Sometimes a poster might find his
important stuff snipped, so they can reinsert it.
Also, I try to designate the primary person(s) I'm
directing my comments to. Perhaps we should
set-up some guidelines to follow for courtesy but
then we also have persons who have an artistic
poetic style that is fun too.
> You haven't been singled out on this. I am seeing others no longer
> attributing posts. Maybe the moderators can gently remind posters to
> include the attributions.
> Murray
Back to math-physics. I've been admiring your
(and all) philosophy on that subject.
Allow me to present a problem (I sometimes get
ridiculed on :-( ).
In GR the rate of time is "mathematically" defined
at a point by the metric g_00, however in 1983
a finite length and time were "physically" interdefined
using "c". Even looking at the functioning of a Cs
atomic clock, a small finite length is required to
establish the time rate, so physically "g_00" is
defined by a finite length, but mathematically at
an infinitesmal point.
That is a heck of a difference, because the "physical"
definition compells a "quantization" of the tensor
analysis used in GR, which I privately find is doable,
and posted the elementary procedural approach in a
thread in this group, "Flat/Curved SpaceTime", but
it was mocked so I quit the thread. Of course I
learned to improve the reasons for why to do it,
so the criticism was very helpful, and I may add the
complete analysis to my web site here,
http://physics.trak4.com/
that deals with the Modern SpaceTime revision of
1983.
Regards
Ken S. Tucker
Oh No
>
>> Classical expressions should not appear at a fundamental level of
>>the
>> quantum theory, but only as quantities and laws which can be derived
>> from it. The normal practice of introducing quantum theory by
>>quantising
>> a classical theory is non-mathematical, circular, and should be
>> prohibited.
>
>That doesn't sound right . If classical fields are emergent from
>quantum, why is it not OK to reverse engineer? It should be possible
>to tackle from both directions. Especially if we don't know all there
>is to know about the quantum? I suspect classical-quantum could be
>like a duality. One does not exist without the other.
>
While one may, in principle, deduce conclusions (emergent effects) from
assumptions (fundamental effects), it is not generally so that a unique
set of assumptions will lead to a given conclusion. It is logically
incorrect to assume a theorem and try to prove an assumption.
It is possible that we may be able to prove that a unique structure for
the universe exists, but this is because the constraints on a measurable
universe, in quantum theory and relativity, are very severe. As it is we
can prove a great deal of classical behaviour from these constraints,
e.g. conservation of momentum.
Cl.Massé
>> Mathematical equations express both quantitative and qualitative
>> relationships. The latter is often specific to the discipline where it is
>> applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
>> necessary, but, nevertheless, auxiliary part of a natural science.
"Ken S. Tucker" <dyna...@vianet.on.ca> a écrit dans le message de
news:c406c0f8-e806-430b...@a8g2000prf.googlegroups.com...
> Interesting, photosynthesis...
>
> photon + plant + CO2 => plant + C + O2
>
> Is the weight of C apart from O2 greater than the weight
> of CO2?
>
> I think it is because,
>
> C + O2 => CO2 + heat , heat = mc^2.
>
> That's important if you heat with wood, and a very nice
> example of how solar fusion using E=mc^2 produces
> photons, that are then converted to m=E/c^2 via plants,
> to grow trees.
That's true, but the idea is that "mass isn't involved in biology",
especially such a tiny mass difference. In my opinion, using that formula
every time energy is involved it nothing else than pedantic. Einstein's
formula links mass to energy, and is relevant if and only if energy *and*
mass are both relevant.
Peter
> On Aug 13, 5:36 am, Chalky <chalkys...@bleachboys.co.uk>
> > This is wrong. To the extent that the importance of empirical
> > observation can be dismissed, one could more reasonably argue that
> > both theoretical physics and mathematics are subdisciplines of pure
> > logic.
Hardly. Eg, the number 50 is void in physics; relevant is, say, 50kg
'A AND B' is void in physics; relevant is, say, 'mass change AND energy
change'
> You might wish to consider the effort to derive physics from logic at:
>
> http://hook.sirus.com/users/mjake/QMfromlogic.htm
>
> It not a finished effort yet. But it looks promising.
Indeed. But what is 'path'? Have you derived space and time, etc.?
Looking forward,
Peter
Peter
...
> Peter, this isn't a voting issue. One may say it's a historical accuracy
> issue, but I say it's a matter of courtesy. It is discourteous to quote
> a person without identifying him.
>
> You haven't been singled out on this. I am seeing others no longer
> attributing posts. Maybe the moderators can gently remind posters to
> include the attributions.
Murray, I completely agree with you and think that my fellows comoderators
will do as well :-)
Ken S. Tucker
On Aug 14, 1:09 pm, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> "Oh No" <N...@charlesfrancis.wanadoo.co.uk> wrote in message
>
> news:tYUj0wA6...@charlesfrancis.wanadoo.co.uk...
>
> > Classical expressions should not appear at a fundamental level of
> > the
> > quantum theory, but only as quantities and laws which can be derived
> > from it. The normal practice of introducing quantum theory by
> > quantising
> > a classical theory is non-mathematical, circular, and should be
> > prohibited.
Agreed, though "prohibited" might be too strong ;-).
> That doesn't sound right . If classical fields are emergent from
> quantum, why is it not OK to reverse engineer? It should be possible
> to tackle from both directions. Especially if we don't know all there
> is to know about the quantum?
I don't think so Fred, the classical fields are based
on an infinitesmally fine continuum, something that
is useful in macroscopics as an approximation but
can never be measured.
I've been trying to figure out if a regular electronic
oscillator could be designed to continuously vary
in frequency, but then we return to the problem of
measuring the frequency even using the best Cs
atomic clocks, those have incremental accuracy,
in parts of 10^16/sec or so. A classical continuum
would require (oo)/sec, which is unrealistic.
> I suspect classical-quantum could be
> like a duality. One does not exist without the other.
Well that can be a way to express quantum effects
mathematically as compared to a continuum.
> Best,
> Fred Diether
Regards
Ken
Peter
> Thus spake Peter <end...@dekasges.de>
>
> >Dear colleagues/friends/group members/posters,
> >
> >Please be wise and stick to dialectics!
> >
> >The laws of physics must not contradict the laws of logics and of geometry.
> First one should understand how the rules of geometry arise from
> physical processes.
I thought that Euclid's axioms can be - at least on principle - be formulated
without those, is this incorrect?
> >Mathematical equations express both quantitative and qualitative
> >relationships. The latter is often specific to the discipline where it is
> >applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
> >necessary, but, nevertheless, auxiliary part of a natural science.
I hope you agree :-)
> >> >>>>On this we agree, but the fault lies not with either mathematics or
> >> >>>>physics, but with the practitioners of physics, who do not use
> >> >>>>mathematics correctly by first establishing physical postulates as
> >> >>>>the axioms of mathematical structure.
> >How I should understand this statement?
> One should understand that mathematical proof proceeds from axioms, and
> that it uses only tautology. Anything stated from mathematical proof is
> simply a restatement of the axioms.
This is a rather unconventional statement, so you will allow me for some
effort to digest it ;-)
For tautology I have connected with 'nothing new'
> To understand physics it is thus
> necessary only to understand the physical content of the axioms, or
> postulates. This requires that one is very precise and careful in
> choosing postulates which correctly describe the physical behaviour of a
> model.
"necessary only" means 'necessary and sufficient'?
I agree that the appropriate choice of the set of axioms is crucial - and for
this I'm wondering about your judgement about Euler's work below
What means "structure"?
> Fields are a useful concept, but not a fundamental one.
We should open a new thread about what is fundamental :-)
> >> >Physics is standardly taught by going
> >> >over the same material again and again in increments of sophistication.
> >> >This is done for a good reason: it requires time to gain sophistication
> >> >beyond the regurgitation of the formalism.
> >> This appears to me a dangerous approach. By repetition one becomes used
> >> to that which does not make sense, and fails to appreciate what it is
> >> that does not make sense. Mathematics is taught by starting from few
> >> postulates, and ensuring that everything based on them makes sense. The
> >> problem which you refer to is that mathematicians are not taught that
> >> one should start by seeing that the postulates apply to the problem in
> >> hand.
> >Newton is told to have answered to the question, why he was so successfull,
> >that he has thought over and over again over the problems :-)
> Indeed, Newton was engaged in the matter of choosing postulates.
I'm happy that you agree that your foregoing posting was self-contradictory
;-)
> >> >for that matter, that everything can be connected. It would
> >> >be nice if it were so (and everyone hopes it's so), but there is
> >> >disquieting evidence that it may never happen (it looks like that the
> >> >total transition from QM to CM may not be attainable).
> >> If that is so, it is because there is a fault in the assumptions of QM.
> >> A first (mathematical) test of a formulation of QM should be to ensure
> >> that CM may be derived. I do not see physicists interested in such
> >> tests.
> >I think, that, first, Schrödinger's (1926) requirement should be obeyed,
> >that
> >the use of classical expressions within quantum theory should be justified
> >- otherwise, that requirement becomes a circle-conclusion
> Classical expressions should not appear at a fundamental level of the
> quantum theory, but only as quantities and laws which can be derived
> from it. The normal practice of introducing quantum theory by quantising
> a classical theory is non-mathematical, circular, and should be
> prohibited.
I'm not yet convinced that your approach - despiteof its various merits - is
obeying that
> >> >Now, that's a nice mathematical problem. It would be important to know
> >> >if no logic can be constructed which will tie everything together.
> >> >That's one mathematical result I think useful.
> >> On this at least we agree. If you would look at my site you will see
> >> that I start with a (relativistic) formulation of qm at
> >>
> >> http://www.teleconnection.info/rqg/RelativisticQuantumTheory
> >>
> >> and work to demonstrate classical electromagnetism at
> >>
> >> http://www.teleconnection.info/rqg/CEM
> >In view of Dirac's (1949) approach to relativistic dynamics, its adherence
> >to the Procrustes bed of Lorentz transformation makes it doubtful
> I am not sure what you are saying. Dirac was certainly not saying that
> the Lorentz transformation is false.
Not, of course, but he was saying, that it is not the appropriate starting
point (as you do)
> In any case, the arbiter of
> physical theory is nature, not any physicist's approach to understanding
> nature, no matter how good the physicist.
Exactly this makes Dirac's approach superior to any other approach which *a
priori* *postulates* the Lorentz transformation which, however, lacks
dynamical foundation (a deficiency not disproved by you)
> >> >>In the choice of correct assumptions, or postulates, or axioms. E.g.
> >> >>mechanics is contained in Newton's laws.
> >This is somewhat superficial; otherwise, Newton would not have set the
> >Definitions before theLaws
> Newton worked correctly. Definitions form a part of the axioms for a
> mathematical structure.
I agree, where his set of definitions exceeds the usual amount...
> >> >But even at the classical and non-relativistic level, Newton's Laws are
> >> >physically flawed. So much for axioms.
> >What is the flaw in them? (This question is not to to defend them, but to
> >fins out how you are understanding them)
> As stated the flaw is in the assumptions of absolute space and time.
This is not explicit part of his Laws
> >> Indeed, they are flawed. There never was a physical justification for
> >> absolute space and time.
The effects of rotation are the same on the shelf and on a ship with constant
speed against the shelf
> >somebody seems to think to understand classical mechanics better than
> >Newton ;-)
> It would be a poor thing, 300 years later, not to understand better than
> Newton, the relationship between classical mechanics and relativity, and
> between classical mechanics and quantum mechanics.
This was not the issue, the point is classical mechanics on its own
> >> This is why we should use "postulate" rather
> >> than "axiom". I do not see axioms as something which cannot be
> >> challenged. The mathematical method as applied to physics should involve
> >> a willingness to challenge axioms.
> >Euler reduced the set of Newton's axioms to the minimum one
> Imv, he replaced clarity with obscurity, and (perhaps unwittingly)
> initiated an approach which incorrectly claims that the physics is in
> the results, not in the assumptions.
I don't know, where you have drawn this conclusion from, certainly not from
his 'Anleitung zur Naturlehre', where he derives large parts of classical
mechanics from the single statement that classical bodies are impenetrable
(where it is assumed, of course, that they move in space and time which are
independent of the bodies in them). (For myself, I'm first trying to reach
such a masterpiece of 'physical logics' before criticizing it ;-)
Best wishes,
Peter
Mike
> > You might wish to consider the effort to derive physics from logic at:
>
> >http://hook.sirus.com/users/mjake/QMfromlogic.htm
>
> > It not a finished effort yet. But it looks promising.
>
> Indeed. But what is 'path'? Have you derived space and time, etc.?
>
A "path" is just a sequence of events. A sequence of one event leading
to another event leading to the next event is an ancient concept. Its
incorporated in every story. And the history of argument has also
shown that other people describe alternative sequences of events to
explain how we got from one fact to another. So naturally we end up
consider how probable each path of events is. All this argues for the
real truth being somehow derived from the disjunction of all these
sequences of events. So it should come as no surprise that the laws
of physics could be derived from such a formulation.
Each step in a path, each event in a sequence, could stand as a fact
on its own. And different people could describe different events that
precede it and led to that event. It is not the case that because one
event was the cause of a second event that a third event consequently
resulted. A path means that it is a sequence which only mean that at
each value of some parameter (usually time) you are associating two
events, one as the premise, and the second as a consequence. The
entire path is the conjunction of the steps.
FrediFizzx
> Thus spake FrediFizzx <fredi...@hotmail.com>
>>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message news:tYUj0
>>wA6j9...@charlesfrancis.wanadoo.co.uk...
>>
>>> Classical expressions should not appear at a fundamental level of
>>>the
>>> quantum theory, but only as quantities and laws which can be derived
>>> from it. The normal practice of introducing quantum theory by
>>>quantising
>>> a classical theory is non-mathematical, circular, and should be
>>> prohibited.
>>
>>That doesn't sound right . If classical fields are emergent from
>>quantum, why is it not OK to reverse engineer? It should be possible
>>to tackle from both directions. Especially if we don't know all there
>>is to know about the quantum? I suspect classical-quantum could be
>>like a duality. One does not exist without the other.
>>
>
> While one may, in principle, deduce conclusions (emergent effects) from
> assumptions (fundamental effects), it is not generally so that a unique
> set of assumptions will lead to a given conclusion. It is logically
> incorrect to assume a theorem and try to prove an assumption.
By reverse engineering though, we can figure out better what assumptions we
might want to make in the first place. Pretty much the whole of particle
physics was done this way. And physicists are spending billions to still do
it this way. ;-) The LHC is just a bigger and better microscope.
> It is possible that we may be able to prove that a unique structure for
> the universe exists, but this is because the constraints on a measurable
> universe, in quantum theory and relativity, are very severe. As it is we
> can prove a great deal of classical behaviour from these constraints,
> e.g. conservation of momentum.
Sure.
Best,
Fred Diether
Oh No
>
>> Thus spake Peter <end...@dekasges.de>
>>
>> >Dear colleagues/friends/group members/posters,
>> >
>> >Please be wise and stick to dialectics!
>> >
>> >The laws of physics must not contradict the laws of logics and of geometry.
>
>> First one should understand how the rules of geometry arise from
>> physical processes.
>
>I thought that Euclid's axioms can be - at least on principle - be formulated
>without those, is this incorrect?
We can formulate the axioms of a mathematical structure, but unless one
relates the axioms to physical processes there is nothing to say that
the structure applies to physics.
>> >Mathematical equations express both quantitative and qualitative
>> >relationships. The latter is often specific to the discipline where it is
>> >applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
>> >necessary, but, nevertheless, auxiliary part of a natural science.
>
>I hope you agree :-)
I am not clear what you mean. E=m*c^2 is true in any field, though it is
not an equation one would be likely to use in biology.
>> >> >>>>On this we agree, but the fault lies not with either mathematics or
>> >> >>>>physics, but with the practitioners of physics, who do not use
>> >> >>>>mathematics correctly by first establishing physical postulates as
>> >> >>>>the axioms of mathematical structure.
>
>> >How I should understand this statement?
>
>> One should understand that mathematical proof proceeds from axioms, and
>> that it uses only tautology. Anything stated from mathematical proof is
>> simply a restatement of the axioms.
>
>This is a rather unconventional statement, so you will allow me for some
>effort to digest it ;-)
It is not an unconventional statement for anyone who has studied logic
and the foundations of mathematics.
For example, we can formally develop mathematics using only the
deductive method modus ponens
If P, then Q.
P.
Therefore, Q.[
We may write this formally as a tautology
(P -> Q) ^ P ) - > Q
>For tautology I have connected with 'nothing new'
Tautology has a formal meaning
http://en.wikipedia.org/wiki/Tautology_%28logic%29
but one may consider for example, that, for SHM of a simple pendulem,
there is "nothing new" beyond the statement that Newton's laws hold in
each part of the motion.
>> To understand physics it is thus
>> necessary only to understand the physical content of the axioms, or
>> postulates. This requires that one is very precise and careful in
>> choosing postulates which correctly describe the physical behaviour of a
>> model.
>"necessary only" means 'necessary and sufficient'?
yes
>
>
>> >Faraday didn't express himself mathematically, neither his assumptions, nor
>> >his conclusions
>
>> Faraday did not consider the structure underlying the concept of a
>> field.
>
>What means "structure"?
I refer to the need for a physical structure to give rise to the
mathematical structure
>
>
>> >> >Physics is standardly taught by going
>> >> >over the same material again and again in increments of sophistication.
>> >> >This is done for a good reason: it requires time to gain sophistication
>> >> >beyond the regurgitation of the formalism.
>
>> >> This appears to me a dangerous approach. By repetition one becomes used
>> >> to that which does not make sense, and fails to appreciate what it is
>> >> that does not make sense. Mathematics is taught by starting from few
>> >> postulates, and ensuring that everything based on them makes sense. The
>> >> problem which you refer to is that mathematicians are not taught that
>> >> one should start by seeing that the postulates apply to the problem in
>> >> hand.
>
>> >Newton is told to have answered to the question, why he was so successfull,
>> >that he has thought over and over again over the problems :-)
>
>> Indeed, Newton was engaged in the matter of choosing postulates.
>
>I'm happy that you agree that your foregoing posting was self-contradictory
> ;-)
I see no contradiction.
>> >> >for that matter, that everything can be connected. It would
>> >> >be nice if it were so (and everyone hopes it's so), but there is
>> >> >disquieting evidence that it may never happen (it looks like that the
>> >> >total transition from QM to CM may not be attainable).
>
>> >> If that is so, it is because there is a fault in the assumptions of QM.
>> >> A first (mathematical) test of a formulation of QM should be to ensure
>> >> that CM may be derived. I do not see physicists interested in such
>> >> tests.
>
>> >I think, that, first, Schrödinger's (1926) requirement should be obeyed,
>> >that
>> >the use of classical expressions within quantum theory should be justified
>> >- otherwise, that requirement becomes a circle-conclusion
>
>> Classical expressions should not appear at a fundamental level of the
>> quantum theory, but only as quantities and laws which can be derived
>> from it. The normal practice of introducing quantum theory by quantising
>> a classical theory is non-mathematical, circular, and should be
>> prohibited.
>
>I'm not yet convinced that your approach - despiteof its various merits - is
>obeying that
I do not use canonical quantisation. Instead I derive the commutation
relation, and derive also cem.
>> >> >Now, that's a nice mathematical problem. It would be important to know
>> >> >if no logic can be constructed which will tie everything together.
>> >> >That's one mathematical result I think useful.
>
>> >> On this at least we agree. If you would look at my site you will see
>> >> that I start with a (relativistic) formulation of qm at
>> >>
>> >> http://www.teleconnection.info/rqg/RelativisticQuantumTheory
>> >>
>> >> and work to demonstrate classical electromagnetism at
>> >>
>> >> http://www.teleconnection.info/rqg/CEM
>
>> >In view of Dirac's (1949) approach to relativistic dynamics, its adherence
>> >to the Procrustes bed of Lorentz transformation makes it doubtful
>
>> I am not sure what you are saying. Dirac was certainly not saying that
>> the Lorentz transformation is false.
>
>Not, of course, but he was saying, that it is not the appropriate starting
>point (as you do)
Lorentz transformation is not my starting point. It is derived from the
physical processes used to define coordinates.
>
>> In any case, the arbiter of
>> physical theory is nature, not any physicist's approach to understanding
>> nature, no matter how good the physicist.
>
>Exactly this makes Dirac's approach superior to any other approach which *a
>priori* *postulates* the Lorentz transformation which, however, lacks
>dynamical foundation (a deficiency not disproved by you)
Since Lorentz transformation is derived from the processes used to
define coordinates, it is kinematic not dynamic. I make no claim to be
responsible for the proof. That is Einstein's. Since you are so casual
in refuting Einstein's work, can you justify yourself?
>> >> >>In the choice of correct assumptions, or postulates, or axioms. E.g.
>> >> >>mechanics is contained in Newton's laws.
>
>> >This is somewhat superficial; otherwise, Newton would not have set the
>> >Definitions before theLaws
>
>> Newton worked correctly. Definitions form a part of the axioms for a
>> mathematical structure.
>
>I agree, where his set of definitions exceeds the usual amount...
I don't claim that Newton has used a minimal set of axioms.
>> >> >But even at the classical and non-relativistic level, Newton's Laws are
>> >> >physically flawed. So much for axioms.
>
>> >What is the flaw in them? (This question is not to to defend them, but to
>> >fins out how you are understanding them)
>
>> As stated the flaw is in the assumptions of absolute space and time.
>
>This is not explicit part of his Laws
The laws make no sense without the prior definitions of space and time,
which are therefore a part of the axioms.
>> >> Indeed, they are flawed. There never was a physical justification for
>> >> absolute space and time.
>
>The effects of rotation are the same on the shelf and on a ship with constant
>speed against the shelf
???
>> >somebody seems to think to understand classical mechanics better than
>> >Newton ;-)
>
>> It would be a poor thing, 300 years later, not to understand better than
>> Newton, the relationship between classical mechanics and relativity, and
>> between classical mechanics and quantum mechanics.
>
>This was not the issue, the point is classical mechanics on its own
That is a rather strange point in a discussion of the fundamentals of
modern physics, and in particular with reference to what we now know of
space & time..
>> >> This is why we should use "postulate" rather
>> >> than "axiom". I do not see axioms as something which cannot be
>> >> challenged. The mathematical method as applied to physics should involve
>> >> a willingness to challenge axioms.
>
>> >Euler reduced the set of Newton's axioms to the minimum one
>
>> Imv, he replaced clarity with obscurity, and (perhaps unwittingly)
>> initiated an approach which incorrectly claims that the physics is in
>> the results, not in the assumptions.
>
>I don't know, where you have drawn this conclusion from, certainly not from
>his 'Anleitung zur Naturlehre', where he derives large parts of classical
>mechanics from the single statement that classical bodies are impenetrable
>(where it is assumed, of course, that they move in space and time which are
>independent of the bodies in them). (For myself, I'm first trying to reach
>such a masterpiece of 'physical logics' before criticizing it ;-)
I have read what you say in papers on this, and find it obscure. I do
not know what you mean by "physical logic". Logic is the study of
tautology. If a physical argument is used not formally contained in the
axioms, then that argument just another axiom. If it is not stated as
such, it is a hidden axiom, which is means we have a poor treatment of
physics.
Oh No
Yes, but I think we are somehow at cross purposes. This is a measurement
of quantum behaviour.
>
>> It is possible that we may be able to prove that a unique structure for
>> the universe exists, but this is because the constraints on a measurable
>> universe, in quantum theory and relativity, are very severe. As it is we
>> can prove a great deal of classical behaviour from these constraints,
>> e.g. conservation of momentum.
>
>Sure.
>
>Best,
>
>Fred Diether
>
maxwell
Stories work because they follow a limited number (usually one) of
protagonists. Story events usually involve several actors, so the
implicit world becomes an 'exploding' network. We make sense of it by
tracking ONE path through the maze. I suggest that a single 'target'
electron can play the role of the hero in our 'physics story'.
Ken S. Tucker
On Aug 15, 7:45 am, "Cl\.Massé" <danielle.be...@gmail.com> wrote:
> On Aug 13, 5:26 pm, Peter <end...@dekasges.de> wrote:
>
> >> Mathematical equations express both quantitative and qualitative
> >> relationships. The latter is often specific to the discipline where it is
> >> applied. Eg, E=m*c^2 is void in biology (I guess). The former one is a
> >> necessary, but, nevertheless, auxiliary part of a natural science.
>
> "Ken S. Tucker" <dynam...@vianet.on.ca> a écrit dans le message denews:c406c0f8-e806-430b...@a8g2000prf.googlegroups.com...
>
> > Interesting, photosynthesis...
>
> > photon + plant + CO2 => plant + C + O2
>
> > Is the weight of C apart from O2 greater than the weight
> > of CO2?
>
> > I think it is because,
>
> > C + O2 => CO2 + heat , heat = mc^2.
>
> > That's important if you heat with wood, and a very nice
> > example of how solar fusion using E=mc^2 produces
> > photons, that are then converted to m=E/c^2 via plants,
> > to grow trees.
>
> That's true, but the idea is that "mass isn't involved in biology",
> especially such a tiny mass difference. In my opinion, using that formula
> every time energy is involved it nothing else than pedantic. Einstein's
> formula links mass to energy, and is relevant if and only if energy *and*
> mass are both relevant.
You are, of course, correct, and though pedantic, it
is foundational, just as when sunlight is absorbed by
an object, the object is warmed, and due to more
temperature and kinetic energy, the objects mass
(and weight) will increase.
In the greater scheme of things we're seeing the transfer of
quantized power, in the form of photons / time, converting
into mass.
Regards
Ken S. Tucker
Peter
> On Aug 15, 1:50 pm, Peter <end...@dekasges.de> wrote:
> > > You might wish to consider the effort to derive physics from logic at:
> >
> > >http://hook.sirus.com/users/mjake/QMfromlogic.htm
> >
> > > It not a finished effort yet. But it looks promising.
> > Indeed. But what is 'path'? Have you derived space and time, etc.?
> A "path" is just a sequence of events. A sequence of one event leading
> to another event leading to the next event is an ancient concept. Its
> incorporated in every story. And the history of argument has also
> shown that other people describe alternative sequences of events to
> explain how we got from one fact to another. So naturally we end up
> consider how probable each path of events is. All this argues for the
> real truth being somehow derived from the disjunction of all these
> sequences of events. So it should come as no surprise that the laws
> of physics could be derived from such a formulation.
You have not, because one cannot derive the notions of physics from logics
> Each step in a path, each event in a sequence, could stand as a fact
> on its own. And different people could describe different events that
> precede it and led to that event. It is not the case that because one
> event was the cause of a second event that a third event consequently
> resulted. A path means that it is a sequence which only mean that at
> each value of some parameter (usually time) you are associating two
> events, one as the premise, and the second as a consequence. The
> entire path is the conjunction of the steps.
You have, perhaps, demonstrated the logical structure behind Huygens'
principle es expressed through the Chapman-Kolmogorov equation (cf my papers
in Eur. J. Phys. 1996 and Icfai J. Optics 2008). This is a nice example of
the fact that the laws of physics comply with that of logics. If you are
interested, we can think about a common paper :-)
Looking forward,
Peter
Mike
>
> You have not, because one cannot derive the notions of physics from logics
You know I've put some effort in providing some mathematical proof of
my claims. If you are going to claim otherwise, I'd appreciate more of
an explanation of what is wrong with the theory. Your statement above
sounds more like a prejudice than anything else.
>
> You have, perhaps, demonstrated the logical structure behind Huygens'
> principle es expressed through the Chapman-Kolmogorov equation (cf my papers
> in Eur. J. Phys. 1996 and Icfai J. Optics 2008). This is a nice example of
> the fact that the laws of physics comply with that of logics. If you are
> interested, we can think about a common paper :-)
>
I'd love to have my theory on the arXiv so they can at least be
discussed in forums that require at least publication in the arXiv.
But my ideas are maybe just a little premature at this point. Yet I am
already thinking about how to extend it to General Relativity. If
you'd like to converse, my name is Mike, and my email is
mjake(at)sirus(dot)com. My theory to date is at:
http://hook.sirus.com/users/mjake/QMfromlogic.htm
And the extended ideas to be developed are at:
http://hook.sirus.com/users/mjake/PhysicsDocHistory.htm#To_do_list
Thanks.
Peter
> On Aug 20, 3:45 am, Peter <end...@dekasges.de> wrote:
> >
> > You have not, because one cannot derive the notions of physics from
> > logics
> You know I've put some effort in providing some mathematical
exactly, but no physical
> proof of
> my claims. If you are going to claim otherwise, I'd appreciate more of
> an explanation of what is wrong with the theory.
please read my comment carefully
> Your statement above
> sounds more like a prejudice than anything else.
not at all, see my following comment
> > You have, perhaps, demonstrated the logical structure behind Huygens'
> > principle es expressed through the Chapman-Kolmogorov equation (cf my
> > papers
> > in Eur. J. Phys. 1996 and Icfai J. Optics 2008). This is a nice example of
> > the fact that the laws of physics comply with that of logics. If you are
> > interested, we can think about a common paper :-)
Look, the Chapman-Kolmogorov eq. as used by Feynman (1948) in his pioneering
path integral paper reads
P_ab = Sum(c) P_ac P_cb
One cannot derive that it applies to quantum mechanics without having got the
Schrödinger equation. Thus, without the latter (and logics doesn't give you
any equation of motion), one could at most postulate that this equation for
the transition *probabilities* of Markov processes applies to quantum
transition *amplitudes*.
Generally speaking, logics doesn't provide any *physical* content of its
relations
> I'd love to have my theory on the arXiv so they can at least be
> discussed in forums that require at least publication in the arXiv.
> But my ideas are maybe just a little premature at this point. Yet I am
> already thinking about how to extend it to General Relativity. If
> you'd like to converse, my name is Mike, and my email is
> mjake(at)sirus(dot)com. My theory to date is at:
>
> http://hook.sirus.com/users/mjake/QMfromlogic.htm
>
> And the extended ideas to be developed are at:
>
> http://hook.sirus.com/users/mjake/PhysicsDocHistory.htm#To_do_list
>
> Thanks.
I have not yet published on arXive, one needs an endorser...
Looking forward,
Peter
Mike
>
> Generally speaking, logics doesn't provide any *physical* content of its
> relations
Are you denying that everything physical is logical? What in all
reality are you suposing to be not logical? Or at what scale of
measurement do things stop complying with logic as we know it?
If everything IS logical, then it remains to be shown how to derive
everything from logic. For if something physical exists that cannot be
derived from logic, then this is the same as saying that it does not
comply with logic and all reason breaks down.
Some object because they say logic equally applies to fictitious
things as well. So the laws of physics that could be derived from
logic would be completely general and would not predict specifics such
as my writing this post, etc. Just as we have it today, the laws of
physics are generalities, or hypotheticals. They predict that IF
something, THEN something else. They don't necessarily say that the
premises do exist, only that IF the premises did exist, THEN the
consequences will result. These laws of physics apply equally well to
fictitious situations as they do to what is actuall measured.
Peter
> Mike wrote:
> > On Aug 21, 10:49 am, Peter <end...@dekasges.de> wrote:
> >
> > Generally speaking, logics doesn't provide any *physical* content of its
> > relations
> Are you denying that everything physical is logical? What in all
> reality are you suposing to be not logical? Or at what scale of
> measurement do things stop complying with logic as we know it?
You have understand the opposite of what was said, I'm afraid
Please derive any physical notion, eg, force, from your formalism, after
that, we can continue
Looking forward,
Peter
Mike
You're kidding, right? If I derive the Feynman path integral, then I
derive all the physics usually derived from the PI. I don't see the
problem?
Ken S. Tucker
On Aug 22, 8:01 am, Mike <mj...@sirus.com> wrote:
> On Aug 22, 4:55 am, Peter <end...@dekasges.de> wrote:
>
>
>
> > > Mike wrote:
> > > > On Aug 21, 10:49 am, Peter <end...@dekasges.de> wrote:
>
> > > > Generally speaking, logics doesn't provide any *physical* content of its
> > > > relations
> > > Are you denying that everything physical is logical? What in all
> > > reality are you suposing to be not logical? Or at what scale of
> > > measurement do things stop complying with logic as we know it?
>
> > You have understand the opposite of what was said, I'm afraid
>
> > Please derive any physical notion, eg, force, from your formalism, after
> > that, we can continue
>
> > Looking forward,
> > Peter
>
> You're kidding, right?
I'm in fair agreement with Peter.
>If I derive the Feynman path integral, then I
> derive all the physics usually derived from the PI. I don't see the
> problem?
I admire your approach, you're among friends :-).
I and Murray have stated attempts like that, however
I needed to derive "fundamental charge" as a integration
constant ( $ 0 dx = q) , which is a static invariant and
then fill in "c" as a maximum rate of change, which is
the dynamic invariant. How can pure logic derive them
and also a fundamental relation of those two invariants?
Have you been able to do that?
Regards
Ken S. Tucker
Mike
>
> - Show quoted text -
Not yet. I suspect that such constants will only be recognized in
relation to each other, and not derived separately. I also suspect
that things like the speed of light will not be derived until the
particle math is connected to the metric math, in other words, not
until QM and QG are united. Thanks for the encouragement.
PS. Do you have a link to your efforts?
Ken S. Tucker
On Aug 22, 11:55 am, Mike <mj...@sirus.com> wrote:
> On Aug 22, 12:27 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
...
> > I admire your approach, you're among friends :-).
> > I and Murray have stated attempts like that, however
> > I needed to derive "fundamental charge" as a integration
> > constant ( $ 0 dx = q) , which is a static invariant and
> > then fill in "c" as a maximum rate of change, which is
> > the dynamic invariant. How can pure logic derive them
> > and also a fundamental relation of those two invariants?
> > Have you been able to do that?
> > Regards
> > Ken S. Tucker- Hide quoted text -
>
> > - Show quoted text -
>
> Not yet. I suspect that such constants will only be recognized in
> relation to each other, and not derived separately. I also suspect
> that things like the speed of light will not be derived until the
> particle math is connected to the metric math, in other words, not
> until QM and QG are united. Thanks for the encouragement.
My pleasure. Anyone who takes a serious shot at
such a tough and obscure problem as you demo at
your web-site and calculations has my respect!
> PS. Do you have a link to your efforts?
Yes, Fred and I assembled this article, in which
Eq.(4) is interesting...
http://physics.trak4.com/GR_Charge_Couple.pdf
I'll post here,
S^2 = X^2 + ab , Eq.(4) .
That is an electrical expression of the Einstein
Field Equations "Guv=Tuv".
That same equation(4) can be generated by pure
logic...
By generating successive dimensions, beginning
with "0" produces,
$ 0 dX = e , $ e dX = eX , $ eX dX = eX^2 /2...
unit length "e" followed by indefinite area "eX", etc.
The unit length "e" is perpendicular to all successive
dimensions, thus scalar product e.X= 0, as the use
of integration developes more dimensions with "e"
being the "fundamental unit length".
Set up a Pythagorean vector distance S = X + e,
and then relate two points "a" and "b" that have a
magnitude +/- |e| parallel to "e" to enable,
S(a) = X+a , S(b) = X+b .
X is the orthogonal distance between "a" and "b".
At that point, the scalar product S(a).S(b) yields
S^2 = X^2 + ab,
to reproduce Eq.(4), and the electrical EFE's.
The EFE's can be processed electrically provided
the relation to generic mass is defined, and it is.
We have the electric and gravitation effects explained
but I'm uncertain as to how the invariant "c" can be
derived.
Regards
Ken S. Tucker
kxsxt8
Hendrik Boom
> Mathematics needs no defence. Either it is established by logic, or it
> is not mathematics.
>
Looking at history, there have been quite a few disputes as to the logic
that can be used for mathematics. The logics we have now (and there
are more than one that still survive, and no, they're not all
equivalent) are the result of centuries of experiment, as the ones
that have proved inconsistent have been discarded. No one really
knows which ones used now will have to be discarded and modified in
the future.
In this way, mathematics is itself an experimental discipline.
-- hendrik
.
Hendrik Boom
> I take it your criticism of "isotropy of space" has to do with the fact
> that space is not measurable? Indeed, this is so. The results of
> measurement are numbers, the results of measurements of position are
> members of R^3.
Technically, they're members of Q^3. Actual measurements are all rational
numbers. You get the idea that measurements are real only by inagining
the average of infinitely many rational measurements.
-- hendrik
.
Hendrik Boom
> Thus spake Murray Arnow <ar...@iname.com>
>
>>There
>>have been lots of dead-ends, but there have also been successes. That
>>has always been true and will always be true. That's the nature of
>>science.
>
> I do not recall hearing of much successes in the dark ages :-).
>
The dark ages were a chaotic, inventive period. Much of what was invented
was low-grade technology, creating an industrial base and a mercantile
class that was to revolutionize society centuries later.
And the first seeds of the scientific method itself was propounded by
Roger Bacon, who argued that the correct interpretation of obscure
passages of Aristotle's writings could be determined by experiment. If
you don't know the correct translation of some ancient Greek work, don't
waste time reasoning about it by astrological analogies -- just try out
the various meaning and see what works.
-- hendrik
.
Hendrik Boom
>
> I'm still a little uncomfortable with "axioms".
>
Ken Armstrong, one of mathematics professors in the sixties, was at
first also uncomfortable with the idea of axioms. But he told me his whole
understanding of mathematics changed when he realized axioms weren't
self-evident truths. They were defining conditions. When he taught real
analysis, he pointed out that anything you find lying around that
satisfied the axioms could be what the course was about. It is a
physicist's job to determine whether these axioms are related in any way
to physics.
That said, it is ofcourse also physics that provided the original
motivation for mathematicians to study real numbers and formulate the
axioms. It is good for mathematics to be useful; otherwise it
would be, well, useless.
-- hendrik
.
Hendrik Boom
> Charles Francis wrote:
>
>>On this we agree, but the fault lies not with either mathematics or
>>physics, but with the practitioners of physics, who do not use
>>mathematics correctly by first establishing physical postulates as the
>>axioms of mathematical structure.
>>
>
> As a colleague would have put it "What a crock of shit!" Now we have to
> worry about being judged for the way math is used. This isn't physics;
> it's pedantry. When the mathematical method gives consistently correct
> answers, that is the only justification necessary. The end pursuit of
> physics is understanding nature, not validating mathematics.
Physics being an experimental discipline, it is not unusual for physicists
to treat their mathematical inventions experimentally, at lest when they
are rushing in to new domains where rigorous mathematicians fear to tread.
(It I just assume these infinities cancel, I get the right answer). This
approach gets results (often accompanied with snide remarks about
mathematicians who are such slaves to rigor that they can't
accomplish anything practical)
When he careful mathematicians do come in later and explain what's going on
mathematically, (sometimes making snide remarks about mathematically
careless physicists along the way) they create new room for further
progress in both mathematics and physics.
-- hendrik
.
Oh No
reduced to modus ponens. There is only one logic, and no experiment is
involved.
Oh No
>
>> Charles Francis wrote:
>>
>>>On this we agree, but the fault lies not with either mathematics or
>>>physics, but with the practitioners of physics, who do not use
>>>mathematics correctly by first establishing physical postulates as the
>>>axioms of mathematical structure.
>>>
>>
>> As a colleague would have put it "What a crock of shit!" Now we have to
>> worry about being judged for the way math is used. This isn't physics;
>> it's pedantry. When the mathematical method gives consistently correct
>> answers, that is the only justification necessary. The end pursuit of
>> physics is understanding nature, not validating mathematics.
>
>Physics being an experimental discipline, it is not unusual for physicists
>to treat their mathematical inventions experimentally, at lest when they
>are rushing in to new domains where rigorous mathematicians fear to tread.
> (It I just assume these infinities cancel, I get the right answer). This
>approach gets results (often accompanied with snide remarks about
>mathematicians who are such slaves to rigor that they can't
>accomplish anything practical)
It also gets wrong answers. Or do you think that proving that 1=2 is
accomplishing anything practical.
>
>When he careful mathematicians do come in later and explain what's going on
>mathematically, (sometimes making snide remarks about mathematically
>careless physicists along the way) they create new room for further
>progress in both mathematics and physics.
On this I agree. It is, of course, perfectly legitimate for physicists
exploring the boundaries of knowledge to be careless. Physicists who
think that incorrect mathematics should be preserved, and used as a
basis for further theory are another matter.
Oh No
technically they are members of an interval, since real measurements do
not yield perfectly precise results.
Oh No
>
>>
>> I'm still a little uncomfortable with "axioms".
>>
>Ken Armstrong, one of mathematics professors in the sixties, was at
>first also uncomfortable with the idea of axioms. But he told me his whole
>understanding of mathematics changed when he realized axioms weren't
>self-evident truths. They were defining conditions. When he taught real
>analysis, he pointed out that anything you find lying around that
>satisfied the axioms could be what the course was about. It is a
>physicist's job to determine whether these axioms are related in any way
>to physics.
Indeed.
>
>That said, it is ofcourse also physics that provided the original
>motivation for mathematicians to study real numbers and formulate the
>axioms.
Actually the first major branch of mathematics, geometry, was motivated
originally by surveying, not by physics. Much of the mathematics
developed in the 18th century had to do with navigation. Gambling
motivated probability theory, statistics is motivated by such
applications as quality control, and computer science has motivated
study in discrete mathematics and logic (to name a few non-physics
applications).
>It is good for mathematics to be useful; otherwise it
>would be, well, useless.
>
I agree. Mathematics is a tool, and like any tool, it should be used
properly. Determining axioms which apply to physics should be a first
step.
Hendrik Boom
> Thus spake Hendrik Boom <hen...@topoi.pooq.com>
>>On Tue, 12 Aug 2008 16:39:20 -0600, Oh No wrote:
>>
>>
>>> Mathematics needs no defence. Either it is established by logic, or it
>>> is not mathematics.
>>>
>>Looking at history, there have been quite a few disputes as to the logic
>>that can be used for mathematics. The logics we have now (and there
>>are more than one that still survive, and no, they're not all
>>equivalent) are the result of centuries of experiment, as the ones
>>that have proved inconsistent have been discarded. No one really
>>knows which ones used now will have to be discarded and modified in
>>the future.
>>
>>In this way, mathematics is itself an experimental discipline.
>>
> Mathematics has been reduced to set theory and logic.
There are several set theories. There are controversies whether one
should accept the axiom of choice, or alternatively, Solovay's axion that
every function of a real variable is measurable.
Further controversies about continuum hypotheses, large cardinal axioms,
etc.
Further controversies about whether mathematics should be constructive.
Historically, differentials were quite controversial, until they
discovered that you could model them via linear approximations, thereby
forming a foundation for differential geometry.
I won't even go into the infinitesimals of nonstandard analysis,
And category theory has trouble fitting itself into the regular set
theories.
> Logic has been
> reduced to modus ponens. There is only one logic,
Nope, there's constructive and nonconstructive logics, there's type
theories, there's modal logics, there's quantum logics, ...
> and no experiment is
> involved.
And every now and then one turns out to be inconsistent. That's the
experimental result.
>
>
> Regards
>
.
Oh No
>On Sun, 24 Aug 2008 11:48:55 -0600, Oh No wrote:
>
>> Thus spake Hendrik Boom <hen...@topoi.pooq.com>
>>>On Tue, 12 Aug 2008 16:39:20 -0600, Oh No wrote:
>>>
>>>
>>>> Mathematics needs no defence. Either it is established by logic, or it
>>>> is not mathematics.
>>>>
>>>Looking at history, there have been quite a few disputes as to the logic
>>>that can be used for mathematics. The logics we have now (and there
>>>are more than one that still survive, and no, they're not all
>>>equivalent) are the result of centuries of experiment, as the ones
>>>that have proved inconsistent have been discarded. No one really
>>>knows which ones used now will have to be discarded and modified in
>>>the future.
>>>
>>>In this way, mathematics is itself an experimental discipline.
>>>
>> Mathematics has been reduced to set theory and logic.
>
>There are several set theories. There are controversies whether one
>should accept the axiom of choice, or alternatively, Solovay's axion that
>every function of a real variable is measurable.
>Further controversies about continuum hypotheses, large cardinal axioms,
>etc.
The possibility of choosing different axiom sets does not affect the
truth of what I said.
>Further controversies about whether mathematics should be constructive.
This is a matter of philosophy, not empiricism.
>
>Historically, differentials were quite controversial, until they
>discovered that you could model them via linear approximations, thereby
>forming a foundation for differential geometry.
>
>I won't even go into the infinitesimals of nonstandard analysis,
>
>And category theory has trouble fitting itself into the regular set
>theories.
Imv category theory claims to address an issue which was shown, by
Dodgson (aka Lewis Caroll) in various rather amusing, light hearted, but
actually much ignored and very deep treatises, on language and logic in
mathematics, to be unaddressable. I see it as doing little more than
burying the issue under convoluted language so that it can no longer be
easily seen.
>
>> Logic has been
>> reduced to modus ponens. There is only one logic,
>
>Nope, there's constructive and nonconstructive logics, there's type
>theories, there's modal logics, there's quantum logics, ...
This is the issue raised by Dodgson. One should not confuse the step of
deduction, which is a process of thought, with the forms of
mathematical structure which we call logics.
See http://www.ditext.com/carroll/tortoise.html
http://www.ditext.com/carroll/tortoise.html