Who Invented the Z Transform

Clay S. Turner wrote:
> <eunometic@yahoo.com.au> wrote in message 
> news:1122873344.917693.210890@g14g2000cwa.googlegroups.com...
> 
>>Hilbert Transforms were ofcourse developed by Hilbert and the Dirac
>>delta by Dirac.
> 
> 
> The "delta function" came before Dirac, but it was little known. He 
> popularized the concept and showed how useful it can be to applications in 
> quantum mechanics.
> 
> 
> 
> 
>>Hilbert incidently had developed relativity before
>>Einstein:  Einstein who had read Hilberts papers simply 'gazzumped' him
>>to publication and has been reaping the publicity since.
> 
> 
> Really? Which aspects of relativity theory did David Hilbert invent?
> 
> 
> Clay
> 
> 


Most detailed histories of almost any scientific activity show that
there was someone who did some piece of work and another who later
realized that it had a much broader scope. The recognition tends
to go to the worker who realizes the importance.

All of the Maxwell equations were know before Maxwell but they had
not been collected into a system to provide a common example of this.

Einstein's special relativity used the known Lorentz transformation.


> 
> 
> 

Actually Maxwell introduced the concept of displacement current. And
with this modification the system became complete. He certainly based
his work on Gauss, Faraday, and  Ampere. But before he did his
modification to Ampere's law, the only theoretical way to produce a
magnetic field was to have a current (charges in motion). He added the
notion that a time varing electric field also produced a magnetic
field. He set up an experiement where a constant current was charging a
capacitor and noted that a magnetic field existed in between the plates
of the cap where there was clearly no current flowing. He also noted
that this magnetic field had the same total flux as the field
surounding the conductors leading to and from the capacitor.

While Einstein used the Lorentz transform, he changed the reasoning
behind its usage and its actual interpretation. However people still
call the Lorentz transform a "Lorentz" transform.  Einstein's greatest
work was in GR. SR is pretty easy to follow, but Einstein had the
forthought to choose the proper two axioms (velocity of light is
constant in vacuo and physics is the same everywhere) and show that
Maxwell's wave equation is invariant under Lorentz transformation. GR
took a lot more vision and the use of tensors. The biggest contributor
would be Poincare'.

His work on GR cost him 11 years of work after SR and his marriage.
Other scientists  warned him to not work on gravity since it is too
hard. Not to take away from Hilbert's mathematical ability, I never
seen his work mentioned in relativity books saying that he predated
Einstein.

Clay wrote:
> Actually Maxwell introduced the concept of displacement current. And
> with this modification the system became complete. He certainly based
> his work on Gauss, Faraday, and  Ampere. But before he did his
> modification to Ampere's law, the only theoretical way to produce a
> magnetic field was to have a current (charges in motion). He added the
> notion that a time varing electric field also produced a magnetic
> field. He set up an experiement where a constant current was charging a
> capacitor and noted that a magnetic field existed in between the plates
> of the cap where there was clearly no current flowing. He also noted
> that this magnetic field had the same total flux as the field
> surounding the conductors leading to and from the capacitor.
> 
> While Einstein used the Lorentz transform, he changed the reasoning
> behind its usage and its actual interpretation. However people still
> call the Lorentz transform a "Lorentz" transform.  Einstein's greatest
> work was in GR. SR is pretty easy to follow, but Einstein had the
> forthought to choose the proper two axioms (velocity of light is
> constant in vacuo and physics is the same everywhere) and show that
> Maxwell's wave equation is invariant under Lorentz transformation. GR
> took a lot more vision and the use of tensors. The biggest contributor
> would be Poincare'.
> 
> His work on GR cost him 11 years of work after SR and his marriage.
> Other scientists  warned him to not work on gravity since it is too
> hard. Not to take away from Hilbert's mathematical ability, I never
> seen his work mentioned in relativity books saying that he predated
> Einstein.

And his Nobel Prize in 1921 was not for relativity, but for explaining 
the photoelectric effect, essentially laying the foundation for quantum 
mechanics.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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"Gordon Sande" <g.sande@worldnet.att.net> wrote in message
news:OjpHe.201853$on1.100332@clgrps13...
>
>
> Clay S. Turner wrote:
> > <eunometic@yahoo.com.au> wrote in message
> > news:1122873344.917693.210890@g14g2000cwa.googlegroups.com...
> >
> >>Hilbert Transforms were ofcourse developed by Hilbert and the Dirac
> >>delta by Dirac.
> >
> >
> > The "delta function" came before Dirac, but it was little known. He
> > popularized the concept and showed how useful it can be to applications
in
> > quantum mechanics.
> >
> >
> >
> >
> >>Hilbert incidently had developed relativity before
> >>Einstein:  Einstein who had read Hilberts papers simply 'gazzumped' him
> >>to publication and has been reaping the publicity since.
> >
> >
> > Really? Which aspects of relativity theory did David Hilbert invent?
> >
> >
> > Clay
> >
> >
>
>
> Most detailed histories of almost any scientific activity show that
> there was someone who did some piece of work and another who later
> realized that it had a much broader scope. The recognition tends
> to go to the worker who realizes the importance.
>
> All of the Maxwell equations were know before Maxwell but they had
> not been collected into a system to provide a common example of this.
>
> Einstein's special relativity used the known Lorentz transformation.
>
>
> >
> >
> >
It was Heviside who wrote the vector form of Maxwells equations - the ones
we recognise - not Maxwell.

Shytot

Clay wrote:
> Actually Maxwell introduced the concept of displacement current. And
> with this modification the system became complete. He certainly based
> his work on Gauss, Faraday, and  Ampere. But before he did his
> modification to Ampere's law, the only theoretical way to produce a
> magnetic field was to have a current (charges in motion). He added the
> notion that a time varing electric field also produced a magnetic
> field. He set up an experiement where a constant current was charging a
> capacitor and noted that a magnetic field existed in between the plates
> of the cap where there was clearly no current flowing. He also noted
> that this magnetic field had the same total flux as the field
> surounding the conductors leading to and from the capacitor.
> 
> While Einstein used the Lorentz transform, he changed the reasoning
> behind its usage and its actual interpretation. However people still
> call the Lorentz transform a "Lorentz" transform.  Einstein's greatest
> work was in GR. SR is pretty easy to follow, but Einstein had the
> forthought to choose the proper two axioms (velocity of light is
> constant in vacuo and physics is the same everywhere) and show that
> Maxwell's wave equation is invariant under Lorentz transformation. GR
> took a lot more vision and the use of tensors. The biggest contributor
> would be Poincare'.
> 
> His work on GR cost him 11 years of work after SR and his marriage.
> Other scientists  warned him to not work on gravity since it is too
> hard. Not to take away from Hilbert's mathematical ability, I never
> seen his work mentioned in relativity books saying that he predated
> Einstein.
> 

I suppose the OP was referring to Hilbert's action principle (for
gravitation as a consequence of space-time curvature).  According
to Misner, Thorne, and Wheeler (see section 21.2 of their book
_Gravitation_) Hilbert published this all of 5 days before Einstein
published his field equation, but in their words "animated by
Einstein's earlier work".  The Einstein field equation (for empty
space-time at least) follows from Hilbert's principle, which is
basically the principle of least action applied to a Lagrangian
proportional to the Ricci curvature scalar.  I don't think there's
any doubt that credit for the field equation (and so for general
relativity) belongs solely to Einstein, but Hilbert's work also
seems to me to be worth noting.

Hope that clears things up.

Robert E. Beaudoin

..

> which is basically the principle of least action 
> applied to a Lagrangian proportional to the Ricci 
> curvature scalar. 

To just read that felt surreal!

--Bhooshan
		
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Robert E. Beaudoin wrote:

(snip)

> I suppose the OP was referring to Hilbert's action principle (for
> gravitation as a consequence of space-time curvature).  According
> to Misner, Thorne, and Wheeler (see section 21.2 of their book
> _Gravitation_) 

I haven't seen a copy for many years.  The story I used to
hear was that only three people really understood the book.

-- glen

Hello Robert,

Thanks for the response. My interpretation of the OP's statement was
Hilbert beat Einstein to the result and then Einstein stole all of the
glory. Hilbert's approach is certainly notewothy since least action
principles abound in physics and alternative mathematical methods often
prove to be illuminating on their own[1]. However I suspect Hilbert was
familiar with Einstein's result and therefore not only had the problem
but also had the solution. This is quite different than working out a
solution where the destination is unknown.  But even if Hilbert found
this solution without knowing the field equation (a great feat the
principle of equivalence is bypassed yielding a theory without an
obvious physical basis (The few references I've found so far give
little to no detail). I don't have Wheeler handy. Einstein's approach
is rooted in a physical basis. And today most who study his work
celebrate his acheivements.

Clay

[1] Hamilton's modification to the LaGrangian method of classical
mechanics turns out to be the usual approach in quantum mechanics.

Clay wrote:
> Hello Robert,
> 
> Thanks for the response. My interpretation of the OP's statement was
> Hilbert beat Einstein to the result and then Einstein stole all of the
> glory. Hilbert's approach is certainly notewothy since least action
> principles abound in physics and alternative mathematical methods often
> prove to be illuminating on their own[1]. However I suspect Hilbert was
> familiar with Einstein's result and therefore not only had the problem
> but also had the solution. This is quite different than working out a
> solution where the destination is unknown.  But even if Hilbert found
> this solution without knowing the field equation (a great feat the
> principle of equivalence is bypassed yielding a theory without an
> obvious physical basis (The few references I've found so far give
> little to no detail). I don't have Wheeler handy. Einstein's approach
> is rooted in a physical basis. And today most who study his work
> celebrate his acheivements.
> 
> Clay
> 
> [1] Hamilton's modification to the LaGrangian method of classical
> mechanics turns out to be the usual approach in quantum mechanics.
> 

Hi Clay,

Just in case it wasn't clear:  I agree with you on all of this.

Bob Beaudoin

"bhooshaniyer" <bhooshaniyer@gmail.com> writes:
> ...
> 
> > which is basically the principle of least action 
> > applied to a Lagrangian proportional to the Ricci 
> > curvature scalar. 
> 
> To just read that felt surreal!

What's the problem?  What he said is intuitively obvious
to the least informed!  :-)