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Hamilton's Equations; Physics Models

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Posted by Alan on September 23, 2003 02:42:53 UTC

Hamilton's Equations

(Referring to page 209 Penguin Dictionary Of Physics 3rd Ed. 1990)

The book says there are twice as many Hamiltonian equations as Langrarian equations but only first order instead of 2nd order differential equations. It says they involve the Hamiltonian function H which in ordinary cases is the total energy expressed as a function of the generalised coordinates qi and momenta pi:

dqi/dt = delta H/ delta pi

dpi/dt = -(delta H/ delta qi)

My interpretation;

total energy = total alternatives (counted)

coordinates = self-referent reference (background placement of item)(defining a background which can contain the item)

generalised coordinates qi = referent self-referent reference (choice of backgrounds which can contain item, so item as a background (e.g. if item moving) to changing backgrounds.

function = group variable (still relationship against potentially changing backgrounds)

time = self-referent reference (clock-hand self-refers as center stationary; pendulum re-calibrates same path)

distance = uncertainty

directed distance = relatively certain uncertainty (self-referent)

observed directed distance = self-referent reference

momenta pi = mass x velocity = 'uncertainty' x directed distance/time
= 'uncertainty' x directed uncertainty/ self-referent reference =
'uncertainty' x referent self-reference/ self-referent reference
= negotiation space (the uncertainty in common ground references of meeting self-references)

So have Hamilton function H as in ordinary cases the total alternatives expressed as a still relationship against potentially changing backgrounds (i.e. a function) of the item as a background (stillness) against changing backgrounds (i.e. generalised coordinates qi) and the negotiation space (uncertainty on common ground of alternative backgrounds)(i.e. momenta pi).

So Hamilton function in ordinary cases expresses the accessibility a third party has to participate in negotiating between two negotiating parties say.

That is because: the conserved or overlap region in changing backgrounds
(stillness) is under review but the total alternatives are expressed as a still relationship (so every way this meeting can happen in terms of defining its participants).
dqi/dt = differentiate item as background against changing backgrounds/ differentiate self-referent reference = chose a background and be able to keep to it while moving = delta H/ delta pi = partially differentiate every way this meeting can happen in terms of defining the participants (i.e. defines movement of fixed item against fixed background!)/ partially differentiate uncertainty of common ground of alternative backgrounds (is choice of background! As by partially differentiating the uncertainty of common ground you define region of possible certainty)

So dqi/dt = delta H/ delta pi becomes

choose a background and be able to keep to it while moving = maintaining an agreement between defining your movement consistent with defining your chosen background to your movement

dpi/dt = -(delta H/ delta qi) becomes

choose a possible background that you can move against =

minus (define movement of fixed item against fixed background/ differentiate item as background against changing backgrounds)

= minus (partially differentiate every way this meeting can happen in terms of defining the participants/ partially differentiate item as background against changing backgrounds

= minus (many views of each other, space to negotiate /one view of many, space to negotiate)

= minus one agreement on how you could meet other parties

So: Choose a possible background you can move against = minus common ground as to move requires space and by definition "space to move over" requires giving up some common ground to create that space.

So by definition of "what you can move against": a piece of common ground must be subtracted to create that space to move.

In Dr. Stafford's system:

If you dream up "imaginary data" and add it to so-called known data; you SHARE it between you and the known data (part of its history remains with you?)

You've potentially gone: (you + k data) to
(you and event of - i data) + (k data + i data)

This makes the RULE (group variable) bigger contents as can do this any way (can end out with you sharing a lot with many known datas). So can express any group variable structures on the data (and the "unknown data")

What is number?

Define "one": one
Define "two": divide the "one". The division seems to define the "two" group without specifying in what way the items differ; only that they differ and are grouped as "two".

Define "three": a new division is made. But by assuming the new division (to give 3) agrees with the old division (to give 2); requires blurring roles of "past" (first-ness) and "future" (second-ness). As the way assumed-equal-spaced-units-in-number MATHS works is it makes the roles of "what division occured first" swappable?

Also the role of "two group" becomes swappable.

This ambiguity and self-reference effect in how numbers are defined: when two scientists compare measurements but build a theory to define "linear time sequence" (first-ness and second-ness) they are generating a virtual MATH with projected geometrical structure from their two maths inherent ambiguities in time; by defining ways "time" can happen in a common geometry?

So we have math; math; math: agree on structure (math from math) (on ways three-ness can come from three-ness)(giving a stereo-view 3-D geometry which defines time as geometry of 3-D space).

If we regard this as a fixed four axis (Dr. Dick's system):

we have apparently split "time" as have: (math + math) + math; and math + (math + math).

"Known data" is simply "bracketed" (fixed association); "unknown data" is "non-allocated" (associates with both bracketed items).

known data: (math + math).
add "unknown data": (math + math) + math

add "unknown data" so that any one item can be removed and still unique (still fixed asociation):

involves shifting the brackets to give: math + (math + math).

Now we have mixed the definition of "relativity" (where the brackets are placed) and "quantum (meeting of the items).

This allows Dr. Dick to construct a no-conflict system for relativity and q.m. because he has blurred them already?

He has "split time' in to a generalised beginning; ending?

This allows "cause" and "effect" to appear mixable in his system.

In his system the "unknown" can re-define the known and the previous added "unknown".

Einstein's system:

If we regard the construction of math from math structure; from a meeting of math and math:

as 3 space 1 time:

gives a variety of places to put the brackets (that define the self-reference or say group aspect of time-construction):

math as "m" :

(m + m) + m + m

m + (m + m) + m

m + m + (m + m)

(m + m + m) + m

m + (m + m + m)

this gives many patterns:

possibly (needs checking):

the three options of (m + m) as three quark colours;
the three "outside the brackets" views of those as three quark anti-colours
the eight m's in the two options involving bracketing three m's with one outside: 8 gluons

the individual m perspectives of the m's outside brackets in the rows involving bracketing two m's: 6 quark flavours.

The five rows as 5-fold symmetry; seen as 4 (as space-time) gives mixing (5 views of 4) minus current view: gives 20 - 1 = 19 constants in physics standard model.

See "4" again (conserve space-time definition (make it linear) get projection of particle structures and freedom surfaces (forces) as 10-D string (two views of 5; projecting particles and forces from 10-D string)

See 10-D string again: projects an 11th dimension (re-distribute definitions through interaction exchange)

Yanniru mentioned a theory "loop quantum gravity":

centrifugal force: if I swirl an object attached to a string; in a circle: its tendency to fly off in a chosen direction comes from my pulling it in that direction a 1/4 turn ago.

gravity: if I compare two patterns; and make a new comparison: the old patterns may seem to attract in their old comparison in the context of the new comparison (when I count: as apparently counting (choosing a base for making fixed association) makes gravity seem fixed .

Pattern, pattern: compare: gives "definition".

Make a new comparison: gives "rule" (conservation of definition).

But what is in role of "rule" and what is in role of "definition"?

Dr. Stafford's conserved generalised 4-geometry appears to say blur these roles?

Make a new comparison (5-ness) (structure within Dr. Stafford's 4-geometry) and have "gravity" (re-defining of 4-ness)(curvature of space-time).

But of 5 roles: which is providing the 5th (gravity)? Alternative definitions of gravity gives "quantum gravity" (supposed apparent dividing of gravity; gravity meets gravity).

But the price to pay is the alleged gravity quantum has to form a loop (as the 5-ness distributes over 4).



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