What is the fundamental principle from which we can derive quantum mechanics?
Marco Masi
thermodynamics we get to learn about the two (or three) laws of
thermodynamics. In special relativity it is the principle of
relativity, in general relativity it is the principle of equivalence.
But is there anything alike in QM? Heisenberg uncertainty principle is
of course a principle but as far as i understand it it can't be used
in itself as a foundation from which to build up the entire theory.
The thing I can think of is Max Born probabilistic interpretation, but
it is an interpretation, not a physical principle. The axiomatic
approach via Hilbert spaces isn't a principle too, on the contrary, it
skips them in the first place. So, I'm confused.... can anyone help?
Oh No
usually avoided, because, as John Baez once said, it has a way of
bringing usually mild mannered physicists to fisticuffs. However, asking
this question and looking for answers is very much what s.p.f. is about.
My own approach to the problem is given at
http://rqgravity.net/FoundationsOfQuantumTheory
where I seek to show that the mathematical structure of quantum theory
can be found in formal language about hypothetical measurement. If I
have to reduce it to a physical principle underlying the reasons for
needing this formal language, then I say that it extends the principle
of relativity, i.e. relativity of motion, to relativity of position.
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
eugene_st...@usa.net
For me the most convincing foundation of quantum mechanics is the set
of ideas called "quantum logic"
G. Birkhoff J. von Neumann, "The logic of quantum mechanics", Ann.
Math., 37 (1936), 823
G. W. Mackey, "The mathematical foundations of quantum mechanics", (W.
A. Benjamin, New York ,1963), see esp. Section 2-2.
C. Piron, "Foundations of Quantum Physics", (W. A. Benjamin, Reading ,
1976)
Jay R. Yablon
"Marco Masi" <marco...@gmail.com> wrote in message
news:d609e03e-be44-4a53...@r37g2000yqd.googlegroups.com...
demonstrate in parallel threads, the fundamental principles are the same
as those used for special and general relativity, especially general
coordinate invariance. In my view, quantum theory can and should be and
is something that is largely if not totally deductable from the
principles of relativity.
In the lates posted draft at:
http://jayryablon.files.wordpress.com/2009/05/covariance-electromagnetism-quantization.pdf
I have shown how to derive electromagnetic gauge theory, and energy
quantization, form general relativity. Uncertainty is based on
canonical commutation, and that is the next step.
Nature is all one unity. Separate physics disciplines such as GR and
QM, reflect limitations at present in our approach and understanding.
These will be overcome in time.
Jay.
Peter
Many can help ;-)
As you see from the foregoing answers, there is not only one answer.
As far as I know them, the approaches by Charles, Eugene and Jay are
well founded and developed to quite a mature degree. On the other
hand, they are not easy to understand, because they base their
approach on the difficult task to assign classical properties to
quantum particles not really exhibiting them. For this, I would like
to point to another approach which is conceptually much easier,
because straightforward from classical mechanics.
Imagine a classical oscillator. Are their turning points prescribed by
the basic laws of classical mechanics? What happens, if there are no
turning points? How the mechanics of oscillators without turning
points looks like?
The details of how these questions lead to Schr�dinger's wave
mechanics, you can read in my book published by Springer in 2006 and,
in an incomplete and very abridged version in my paper with Dieter
Suisky in Int. J. Theor. Phys. 2005.
Hope this helps,
Peter
Mike
> In mechanics one hears about Newton's and conservation laws. In
> thermodynamics we get to learn about the two (or three) laws of
> thermodynamics. In special relativity it is the principle of
> relativity, in general relativity it is the principle of equivalence.
> But is there anything alike in QM?
I've been able to derive QM from a definition of reality as the
logical conjunction of all facts so that each fact is the result of
every other fact. See details at:
http://hook.sirus.com/users/mjake/QMfromlogic.htm
If I had to attempt a physical interpretation of this I'd suggest non-
locality, everything is effected by everything else.
Bob_for_short
mechanics? ===
I think it is the de Broglie idea of a wave character of electron,
particles, and even macroscopic bodies.
The rest follows from it: the principle of superposition,
probabilistic interpretation, and statistics of identical particles.
We know many attempts to formalize QM: Dirac's, Von Neuman's, etc.,
but the most fundamental idea is the de Broglie's one.
The problems of QM interpretation origin from attempts to understand
QM experiments and the theory via CM notions.
As I showed in "Atom as a "dressed" nucleus", CM notions are illusory:
they are the inclusive QM picture.
The inclusive means practically the average picture. In other words,
with lost details, with loss of actual variety. Can one explain gas
kinetics in terms of temperature solely?
Bob_for_short.
Materion
1. quantum objects are line-shaped --> we may think of them as
vectors, needles, arrows or any other line-shaped object, kets, in
whatever space is suitable for the analysis. This is Feynman's
principle.
This is a physical testable principle, which frees us from
interpretational speculation. You may derive the other "quantum
principles" from this principle, with the help of "common sense". A
simple way to verify this is to think in terms of little needles (some
visuals at wikiversity:
http://en.wikiversity.org/wiki/Making_sense_of_quantum_mechanics/Principles_of_Quantum_Mechanics)
2. when the orientation of a needle evolves, the vector subtraction of
subsequent states of the needle is perpendicular to the needle itself.
With the imaginary 'i' representing the angle 90�, and the needle
represented by symbol |A>, the result of the subtraction is of the
form:
d|A> = i omega |A> dt
This is the generalized form of Schr�dinger / Dirac equation.
3. when two needles interact, the location of the interaction may be
located at any point along the line of the needle. There is intrinsic
indeterminacy in any measurement result. The measure of the
indeterminacy is a fundamental constant: the area swept by the needle
during one cycle. This is Heisenberg's principle.
4. the probability to detect a needle with another needle depends on
the phase of both needles: probability = projection of first needle *
projection of second needle. This is Born's principle.
5. when we have ensembles of needles, the orientation of all needles
are spatially correlated through waves. This is De Broglie / Bohm
principle.
6. the 'particle' needle and its surrounding 'wave-forming' needles
are complementary. Both aspects exist at the same time but refer to
other measured entities. You can never think of them separately. This
is Bohr's / Copenhagen principle.
7. when a needle travels through its surrounding needles, the internal
'energy' (=spinning motion) determines the measure of its 'clinging'
to the environment. This is Higgs' principle.
8. a needle has stable spinning modes depending on the constraints of
the environment...
... and much more which is experimentally testable with ordinary
needles.
This way of investigating quantum mechanics has the advantage to set
experiment (and not theory and interpretation) at the forefront.
"The problem (of paradoxes in quantum mechanics) is an artificial one;
it belongs to imaginative poetry, not to experimental science." ~ L�on
Brillouin.
Kind regards,
Arjen Dijksman
maxwell
> To me the fundamental principle of quantum mechanics is:
> 1. quantum objects are line-shaped --> we may think of them as
> vectors, needles, arrows or any other line-shaped object, kets, in
> whatever space is suitable for the analysis. This is Feynman's
> principle.
>
> This is a physical testable principle, which frees us from
> interpretational speculation. You may derive the other "quantum
> principles" from this principle, with the help of "common sense". A
> simple way to verify this is to think in terms of little needles (some
Your offering is not a fundamental principle, it is a recipe.
Unfortunately, the ''meal" is being cooked by people who only know
where to find the ingredients on the shelf - they have no idea what
they are for or even taste like.
It takes years to be a master chef or a physicist. Cookbooks &
textbooks are just the starting point for students, who need to add
many years of experience to appreciate their art.
Materion
> Your offering is not a fundamental principle, it is a recipe.
> Unfortunately, the ''meal" is being cooked by people who only know
> where to find the ingredients on the shelf - they have no idea what
> they are for or even taste like.
> It takes years to be a master chef or a physicist. �Cookbooks &
> textbooks are just the starting point for students, who need to add
> many years of experience to appreciate their art.
Definition 4 of 'principle at 'thefreedictionary' : "A basic or
essential quality or element determining intrinsic nature or
characteristic behavior"
Definition 2 of 'recipe' at 'thefreedictionary' : "A formula for or
means to a desired end"
The principle (my offering): "quantum objects are line-shaped"
The recipe: the rest of my post? Yes, years are needed to master some
basic facts of physics.
Kind regards,
Arjen Dijksman
rshjr
To trivialize the issue:
As soon as you require a nominally common variable to become a
complex_valued differential operator, then you've "bought-the-farm". The
eigenvectors will be complex exponentials. Eulers equations spits out
sine & cosine no matter what.
And since nobody knows what it means to measure "j"< except in EE classes
where it pushes voltage/current phases about > you must work in some
"energy-like" mode with any variable processed as QQ*.
QM is a clever fudge ... all the way down.
Materion
>
> To trivialize the issue:
>
> As soon as you require a nominally common variable to become a
> complex_valued differential operator, then you've "bought-the-farm". The
> eigenvectors will be complex exponentials. Eulers equations spits out
> sine & cosine no matter what.
>
> And since nobody knows what it means to measure "j"< except in EE classes
> where it pushes voltage/current phases about > you must work in some
> "energy-like" mode with any variable processed as QQ*.
>
That's a defeatist view.
My point of view is that complex values are a precious tool to
describe concrete reality. Scalars can only describe quantities,
proportions, ratios. Complex numbers allow to describe directions,
angles, phases, orientations.
So, as soon as you have managed to get complex values in an
experimental law, you get a step nearer to ordinary reality.