The Axiomatization of Physics - Step 1
Shubee
http://www.everythingimportant.org/relativity/special.pdf
I see this first step to physics as a distinctly logical approach. I see
no reason why physics shouldn't begin this way, with step 1, in high
school. The time for students to learn spacetime physics is immediately
after they have taken algebra. Only algebra required to get through this
very detailed derivation of the Lorentz transformation.
I don't believe that the principle of relativity and the constancy of
the speed of light should be taken as axioms. I see greater advantages
in beginning with simple toy universes and obvious mathematical assumptions.
Shubee
Jay R. Yablon
news:45D4882B...@yahoo.com...
. . .
> I see this first step to physics as a distinctly logical approach. I
> see no reason why physics shouldn't begin this way, with step 1, in
> high school. The time for students to learn spacetime physics is
> immediately after they have taken algebra. Only algebra required to
> get through this very detailed derivation of the Lorentz
> transformation.
Shubee,
I agree with you. While physics developed in the opposite direction
(starting with, for example, momentum 3-vectors and an energy vector),
the covariant representation in spacetime provides a much clearer
formulation of natural laws.
In my own self-study of physics after I left MIT, I first learned
general and special relativity, which I regard as the geometrodynamic
"gold standard," and then studied particle physics, QFT, etc.
Especially, if one is trying to probe the foundations of physics and
answer new questions, GR is a "gold standard" to keep in mind. The
study of everything else in nature should be approached from the
standpoint of trying to obtain a similarly simple and natural way of
understanding the material world. One's intuitive sense of a "new"
theory can then be compared against a concrete, successful example of a
theory based on the simplest of principles, namely that of geometry and
of natural geodesic motion through geometry. Anything which approaches
the same simplicity stands to be a good candidate; anything which does
not have such a simple logic is more suspect as, at best, a transient,
provisional explanation of nature.
Jay.
_____________________________
Jay R. Yablon
910 Northumberland Drive
Schenectady, New York 12309-2814
Phone / Fax: 518-377-6737
Email: jya...@nycap.rr.com
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm
Christophe de Dinechin
> Here is my perspective on how the foundations of physics should be laid:
> http://www.everythingimportant.org/relativity/special.pdf
>
> I see this first step to physics as a distinctly logical approach.
Why do you believe that this is justified as a "first step". I do not dispute that you can write axioms
and manipulate mathematical symbols, but I have trouble connecting your abstract axioms to the
physical world.
In your article, there are a number of axioms that seem all but obvious to me. For example, when
you refer to "same distance" on page 2 of your article, what physical process are you using? Does it
matter if you translate a metal rod or if you count wavefronts of some electromagnetic wave or if you
count footsteps? Are you certain that they measure the same "distance"? If so, isn't that another
implicit axiom? If not, how do you solve the problem?
On page 5, you write "Because mathematical clocks express time in terms of real numbers". First, I
do not know what a "mathematical clock" is, I only know about physical clocks. Second, my physical
clocks do not express time as a real number, but as discrete counts of cyclic physical phenomena
(e.g. rotations of the moon or earth, number of oscillations of a pendulum, oscillations of a crystal
quartz). That gets translated into another fractional number (number of minutes, seconds, and so
on). Going from there to a real number is a major step. If time is a real number, what physical reality
corresponds to pi * 10^-262144 seconds?
These are pretty difficult problems, which I tried to address in part in http://cc3d.free.fr/tim.pdf. I
believe that your axiomatization work is interesting as a mathematical formalism, but it's already
built on quite a bit of abstraction. In my opinion, there is a lot of additional work needed to actually
connect that to the most fundamental physical "reality", to physical "postulates".
My own attempt at laying down fundamental postulates can be found in the article referenced above.
It boils down to 6 measurement postulates and one axiom. The measurement postulates describe
not what physical reality is, but what we, as human beings, accept to call "measurement" among all
the physical processes. They state that a measurement is:
1. A valid, existing physical process
2. impacting two fragments of the universe chosen in advance
3. repeatable
4. gathering information about the "unknown" (measured) fragment
5. representing information as a change in the "display" fragment
6. which can be given a numeric or symbolic interpretation.
The axiom is: there are physical processes like the above.
--
Best regards
Christophe
Thomas Smid
Hi Shubee,
Are you not a little bit over-optimistic by assuming that high-school students
would be able to follow your rather lengthy and abstract derivation?
Anyway, given the title of your paper (and this post), I am actually somewhat
confused by your notion that the principle of relativity and the constancy of
the speed of light should not be taken as axioms. Do you now want an
axiomatization or not?
I personally don't think that physics needs to be more axiomatized than it is
already. From a logical and conceptual point of view, any theory (as well as
any mathematical derivation) needs some kind of axioms to proceed from. The
important question is whether these axioms are strictly adhered to in the
course of the derivation. Only if yes is the derivation actually logically
acceptable. With regard to the Lorentz transformation, this is in my opinion
indeed not the case, as the constraint for the constancy of the speed of light
is changed in the course of the derivation such as to be able to apply the
usual concept of speed (i.e. a velocity dependent transformation) to light
signals (see my page http://www.physicsmyths.org.uk/lorentz.htm ).
Thomas
Oh No
>Shubee <e.Sh...@yahoo.com> writes:
> With regard to the Lorentz transformation, this is in my opinion
>indeed not the case, as the constraint for the constancy of the speed of light
>is changed in the course of the derivation such as to be able to apply the
>usual concept of speed (i.e. a velocity dependent transformation) to light
>signals (see my page http://www.physicsmyths.org.uk/lorentz.htm ).
>
the equations 1a and 1b in your document are inconsistent is plainly
wrong, since they refer to different signals. You follow with a load of
other errors. We don't want this group to degenerate into worthless
discussions about special relativity. It is well established that it is
mathematically consistent, and that the Lorentz transform is quite
straightforward to derive from Einstein's simple premises.
Regards
--
Charles Francis
Moderator
Thomas Smid
As I have indicated above already, the Lorentz transformation only appears
consistent as the original axiom (the invariance principle for the speed of
light) has been correspondingly modified. For a better understanding of the
problem, I have given a simplified mathematical example on my page which I
copy here:
consider the equation
(I) y(x)=ax + b
with the constraints
(C1) y(1) = 1
(C2) y(-1) = -1
The task is to determine the coefficients 'a' and 'b' by applying the
constraints to (I). Now since (C1) results in 1=a+b and (C2) in 1=a-b, it is
obvious that this requires b=0. But since b=0 is not what Einstein likes (as
it would correspond to v=0 in his derivation), he decides to modify the
constraints such that (I) is valid for all b, i.e. he changes (C1) and (C2) to
(C1') y(1) = a +b
(C2') y(-1) = -a +b .
Fine, Einstein says, now I have a system of equations that is consistent for
all 'b' (and 'a' at that), but unfortunately it has nothing to do with the
problem anymore. The task was not to find a set of constraints that are
consistent with (1) irrespective of the value of the coefficients, but to
apply the constraints (C1) and (C2) to (I) and thus to find the coefficients.
Thomas
Jay R. Yablon
. . .
>> I allowed this post, but I think I should not have done. Suggesting
>> that
>> the equations 1a and 1b in your document are inconsistent is plainly
>> wrong, since they refer to different signals. You follow with a load
>> of
>> other errors. We don't want this group to degenerate into worthless
>> discussions about special relativity. It is well established that it
>> is
>> mathematically consistent, and that the Lorentz transform is quite
>> straightforward to derive from Einstein's simple premises.
"Thomas Smid" <thoma...@gmail.com> wrote in message
news:guest.20070217192542$7f...@news.killfile.org...
. . .
> But since b=0 is not what Einstein likes (as
> it would correspond to v=0 in his derivation), he decides to modify
> the
> constraints such that (I) is valid for all b, i.e. he changes (C1) and
> (C2) to
>
> (C1') y(1) = a +b
> (C2') y(-1) = -a +b .
>
> Fine, Einstein says, now I have a system of equations that is
> consistent for
> all 'b' (and 'a' at that), but unfortunately it has nothing to do with
> the
> problem anymore
>. . . .
> Thomas
It is patently clear to anyone with a reasonable ability at school level
algebra that Einstein did not make elementary algebraic mistakes of this
sort and that 100 years worth of serious physicists and even physics
students somehow failed to catch such mistakes until now. Per the
rules, blocking a post requires agreement by all moderators. The
moderators have agreed to block any further posts in this vein.
Christophe de Dinechin
> Thus spake Thomas Smid <thoma...@gmail.com>
> >Shubee <e.Sh...@yahoo.com> writes:
> > With regard to the Lorentz transformation, this is in my opinion
> >indeed not the case, as the constraint for the constancy of the speed of
> light
> >is changed in the course of the derivation such as to be able to apply the
> >usual concept of speed (i.e. a velocity dependent transformation) to light
> >signals (see my page http://www.physicsmyths.org.uk/lorentz.htm ).
> >
> I allowed this post, but I think I should not have done.
I think that allowing the post (once) and pointing out the mistake was exactly the right thing to do.
Otherwise, it is easily seen as a "cover up" or "censorship" by the original poster.
But that begs the question: what about the inevitable "Einstein was so wrong" posts... How do we teach
relativity? I've tried variations along the line of "it's just perspective with cos theta > 1", which
sometimes helps, sometimes does not...
--
Regards
Christophe
Oh No
>Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:
>
>> Thus spake Thomas Smid <thoma...@gmail.com>
>> >Shubee <e.Sh...@yahoo.com> writes:
>> > With regard to the Lorentz transformation, this is in my opinion
>> >indeed not the case, as the constraint for the constancy of the speed of
>> light
>> >is changed in the course of the derivation such as to be able to apply the
>> >usual concept of speed (i.e. a velocity dependent transformation) to light
>> >signals (see my page http://www.physicsmyths.org.uk/lorentz.htm ).
>> >
>> I allowed this post, but I think I should not have done.
>
>I think that allowing the post (once) and pointing out the mistake was
>exactly the right thing to do.
>Otherwise, it is easily seen as a "cover up" or "censorship" by the
>original poster.
>
>But that begs the question: what about the inevitable "Einstein was so
>wrong" posts...
This was one such.
>How do we teach
>relativity? I've tried variations along the line of "it's just
>perspective with cos theta > 1", which
>sometimes helps, sometimes does not...
In cases like, where "Einstein was so wrong" was based on the complete
inability of the poster to manipulate simple equations, I don't think
relativity can be taught. We just have to ask such posters to discuss
there ideas on sci.physics.relativity where they will find a host of
like minded souls. More generally, I think special relativity can be
very well taught with Bondi's k-calculus. I have a paper describing it
in physics/0110007. Don't pay so much attention to gtr in this paper. My
ideas there actually needed much more development before coming right.
Regards
--
Charles Francis
substitute charles for NotI to email
Peter
Hello Shubee,
I very welcome investigations like yours about the foundations of physics,
because you don't start at a more fundamental level than relativity and
quantum. In particular I'm happy that you refer to masters of the past. And I
guess that you will win when you deepen the definition of what physics is,
ie, what are its subjects and its methods of investigation?
You wrote "Physics is the mathematical study of all conceivable universes."
This throws Faraday's work out off physics, I would not do that. I admit that
I have a vague imagination of a good definition of physics and hope that we
in this group will find one :-)
Best wishes,
Peter
Shubee
> Shubee writes:
>
>> Here is my perspective on how the foundations of physics should
>> be laid:
>> http://www.everythingimportant.org/relativity/special.pdf
>>
>>
> Hello Shubee,
>
> I very welcome investigations like yours about the foundations of
> physics, because you don't start at a more fundamental level than
> relativity and quantum.
I have no clue what you mean by that. I believe that I have started at
the most fundamental level, with the very essence of physics and with
the clearest first step toward the axiomatization of physics.
> In particular I'm happy that you refer to masters of the past.
Thank you Peter. I'm delighted that you noticed that.
> And I guess that you will win when you deepen the definition of
> what physics is, ie, what are its subjects and its methods of
> investigation?
Since my goal is Hilbert’s sixth problem (the mathematical treatment
of the axioms of physics), doesn't that automatically contain all its
subjects? And why should I write a historical survey and set a limit to
how knowledge can be acquired? Why must I define what are acceptable
methods of investigation? I think that's the beauty of my definition. If
a physicist wants to consult with a psychic or claims that he's being
taught the equations to the final theory of everything by channeling an
extraterrestrial and receiving messages directly to his brain, then we
can say, "good for you, what are the equations?"
> You wrote "Physics is the mathematical study of all conceivable
> universes." This throws Faraday's work out off physics, I would
> not do that.
I believe that I've already answered that objection in a detailed
response in another thread. Please consider "Why Axiomatize Physics?" as
my reply.
http://groups.google.com/group/sci.physics.foundations/msg/f04dfff1c89b0aa0
Shubee
end...@dekasges.de
> > I very welcome investigations like yours about the foundations of
> > physics, because you don't start at a more fundamental level than
> > relativity and quantum.
>
> I have no clue what you mean by that. I believe that I have started at
> the most fundamental level, with the very essence of physics and with
> the clearest first step toward the axiomatization of physics.
Yes, this is a typo, sorry! Please read "...because you start at a more
fundamental level than relativity and quantum."
> > ...And I guess that you will win when you deepen the definition of what
physics is, ie, what are its subjects and its methods of investigation?
> Since my goal is Hilbert’s sixth problem (the mathematical treatment
> of the axioms of physics), doesn't that automatically contain all its
> subjects?
Do you propose to define the subjects and methods indirectly through the
axioms?
Newton and Euler didn't, but let's see!
> And why should I write a historical survey and set a limit to how
> knowledge can be acquired?
I don't understand this question, because I didn't ask you to write a
historical survey.
> Why must I define what are acceptable methods of investigation?
I don't understand this question, because I didn't ask you to define
acceptable methods of investigation.
> > You wrote "Physics is the mathematical study of all conceivable
> > universes." This throws Faraday's work out off physics, I would
> > not do that.
>
> I believe that I've already answered that objection in a detailed
> response in another thread. Please consider "Why Axiomatize Physics?"
> as my
reply.http://groups.google.com/group/sci.physics.foundations/msg/f04dfff1c8...
Having read this text, I have seen a lot of statements about PEAR and several
accusions against another poster (which should have been commented as not
justified), but nothing about why, say, Faraday's discovery of induction is
beyond physics.
I agree with you that the axiomatization is a cornerstone of the completion
of a physical theory. But it is much more than math.
Best wishes,
Peter
P.S: A. Kent whom you quote seems to be unaware of Newton's and Euler's
axiomatics of classical mechanics, where macroscopic bodies are defined as
exactly as necessary.
Ray Tomes
> I see this first step to physics as a distinctly logical approach. I see
> no reason why physics shouldn't begin this way, with step 1, in high
> school. The time for students to learn spacetime physics is immediately
> after they have taken algebra. Only algebra required to get through this
> very detailed derivation of the Lorentz transformation.
I am not sure that your particular arguments are accurate, but the principle
in the subject line is a sound one.
I wrote this to sci.physics 10 years ago (29-Mar-97):
"What I would like to see done (it is a big job but well worth it I
think) is to basically reduce all science to the form of Euclids axioms
and proofs. That way all the dependencies are shown. Of course there
is a need for lots of accurate definitions."
Often people are confused about the dependencies in physics because
of the sequence of physics history.
To those that have opposed this view and expressed difficulty with
connecting the physics to the real world - this is true regardless of whether
things are axiomitized or not. The definitions of variables needs careful
consideration as that is the connection from the maths to the "real world".
If you think about it, Euclid's axioms were intended to be about the real world.
regards
Ray Tomes
Peter
> I wrote this to sci.physics 10 years ago (29-Mar-97):
> "What I would like to see done (it is a big job but well worth it I
> think) is to basically reduce all science to the form of Euclids axioms
> and proofs. That way all the dependencies are shown. Of course there
> is a need for lots of accurate definitions."
This goal is old, because extremely seducing, indeed. But already Huygens
rejected it. If physics could be reduced geometry, there would be no physics.
> If you think about it, Euclid's axioms were intended to be about the real
> world.
Yes, 'geometry' means measuring the earth.
Best wishes,
Peter
Robert
> rejected it. If physics could be reduced geometry, there would be no physics.
>
General Relativity is a geometrical explanation of gravitation, and
yet I think it certainly qualifies as physics.
Rob
Oh No
>Hello Ray,
>
>> I wrote this to sci.physics 10 years ago (29-Mar-97):
>> "What I would like to see done (it is a big job but well worth it I
>> think) is to basically reduce all science to the form of Euclids axioms
>> and proofs. That way all the dependencies are shown. Of course there
>> is a need for lots of accurate definitions."
>
>This goal is old, because extremely seducing, indeed. But already Huygens
>rejected it. If physics could be reduced geometry, there would be no physics.
I don't think the point is to reduce all of physics to geometry, but to
reduce physics to axioms, as Euclid did for geometry. It is a goal I
agree with and which I seek to apply in my own research.
Peter
Hello Ray, hello Charles,
I apologise to Ray for having perhaps misunderstood his intention and to
Charles for clarification. That their should be fundamental principles on
which all scientific disciplines are built, Huygens had surely signed. What
he pointed out is that -- due to the different nature of their subjects --
the nature of these axioms and the sureness of the proofs and conclusions in
natural sciences are less than in geometry. In geometry, you don't need
comparisons with experiment.
Indeed, Huygens itself has founded the translatoric motion of bodies onto 4
principles (see Simonyi, The Cultural History of Physics, § 3.6.5). Descartes
has formulated 3 laws (Le Monde, Ch. VII) and 7 rules (Principia
Philosophiae, II, pp.46ff.) for elastic collisions. Since he didn't conduct
experiments he didn't realize the errors involved. These errors led Leibniz
to favour the living force, while Newton overcame the errors in realizing the
vector nature of the 'quantity of motion' (linear momentum).
Both Descartes' and Huygens' basic laws concentrate on the conservation of
(stationary) states, and Newton's Laws start with the same. This view is lost
when an action principle is set on top...
Is Newton's system od axioms irreducible, or does it contain axioms which can
be removed without touching the other ones like Euclid's 5th axiom? As a
matter of fact, it can. Euler has deduced Law 2 and Law 3 from Law 1 and the
general properties of the bodies. This is not well known, but it removes the
difficulties Bohr, Heisenberg and Schrödinger faced when generalizing
classical mechanics.
Good definitions are crucial, indeed. The Principia starts with a set of
comprehensive definitions. Euler has completed this in defining 4 general
properties of mechanical bodies, extension, moveability, inertia and
impenetrability. Together with an axiom about state conservation, that's all
what is needed to build classical point mechanics (Euler, 1750). And you need
little more to build quantum mechanics, special relativity and classical
electromagnetism.
This demonstrates the power of good axiomatics. Roy, have you worked in this
way?
Looking forward,
Peter
Oh No
>Both Descartes' and Huygens' basic laws concentrate on the conservation
>of (stationary) states, and Newton's Laws start with the same. This
>view is lost when an action principle is set on top...
I confess, I have never been a fan of action principles. It was the
point in my undergraduate career when I moved away from applied maths
and took mainly pure math courses, which are, of course, rigorously
axiomatic. I'm afraid it always reminded me of the children's game.
Think of a number, do various arithmetic operations, take away the
number you first thought of, and the answer is..
Peter
Yes, it does, because it is not a mathematical theory on Riemannian geometry,
but exploits Riemannian geometry to built a model for gravity.
Peter
Peter
You are right in that it is better to underestimate than to overestimate
them. They are very powerful and valuable as heuristic tool, and they can
contribute to the unity of physics. A drawback consists in that they are not
unique, since the Lagrangian isn't. In quantum physics, h represents a
minimum of action, this makes the application of a minimum principle for the
action doubtful.
Peter