| Topic: |
Science > Physics |
| User: |
"wg" |
| Date: |
19 Jan 2006 12:47:49 PM |
| Object: |
Renormalization revisited |
Renormalization;
While it works, most mathematicians and physicists feel uncomfortable
about using it to get rid of infinities. It appears to be a magic trick
without much solid mathematical basis.
Infinites arise of course by division by 0, which leads to an undefined
answer.
But wait a second; we live in a mathematical universe, math simply
works and is explanatory to the highest degree of precision. Every
aspect of the universe grinds to the precision of math. Why does math
work so well for everything ...but lets us down for this one anomaly
which is division by zero....
Have we got something wrong here, should we be looking at the concept
of zero a little differently?
This is where I'm going to step out on a limb and suggest something
radical.
In the quantum world there is no such thing as zero, only minimum
quantities [i.e. Plank quantities].
Let me explain.
In pure math A-A=0 of course, but we do not live in a pure math world,
we live in a quantum world where heisenburgs uncertainty principle
[HUP] comes into play. In our real world all quantities are measured
quantities and have units associated with them. Because of HUP any
measurement has a degree of uncertainty and can never be known with
complete accuracy at some level.
Take for example a measurement of distance on a line graph;
1 meter - 1 meter = 0 correct???
Wrong. In the quantum mechanics one can never know on the line graph
where the meter starts closer than one Plank length [1.6160 x 10-35 m].
One can never know where that 1 meter measurement ends to within 1
Plank length. Subtraction results in the same conundrum. The answer
1M-1M can never be less than the unknown we started with i.e. [1 Plank
length].
This argument applies to all of measurement since there is a Plank
time, Plank mass and a Plank value for every measurement one can do.
Another possible way to obtain a zero in math is to subtract objects
not measurements. For example say one has an object sitting on a table
and take away that object. 1 apple - 1 apple = 0 apples, correct?
This is certainly true in Newtonian space, but in the quantum universe
HUP introduces a degree of uncertainty to even an apple on a table. HUP
states position and Momentum [and conversely, time and energy] cannot
be know to exact precision at some level.
Also in Einsteins Space time one has to consider non locality,
entanglement and Bells theorem. While one can remove the apple in
Newtonian space, one can never remove all traces of the apple in
Einsteins space time. At some level the apple has left its signature on
the universe from that point [position and time] and continue to effect
the universe from that point on. There has to be a minimum effect [i.e.
Plank quantity].
It seems something of a coincidence that string theory which has been
so successful at eliminating infinities, has done so by constructing
strings which have dimensions roughly equal to Plank dimensions.
Minimum dimensions appear to have done the trick here!
So my challenge to mathematicians and physicists is simple...
-Dust off your favorite unsolvable equation [due to infinities]
-look up the dimensional units associated with [that led to zero]
-plug in minimum values [Plank quantities]
-solve
You will find it works.
WG
Addendum;
Pure Math for the most part deals with the manipulation of
dimensionless pure numbers and symbols, and it is here that we may
frequently experience infinities [division by zero].
But in the real quantum universe we observe no infinities so it should
follow that there can be no divisions by zero in applied math.
Since infinities can't be dealt with, the problem must reside in our
use of zero.
It appears Quantum mechanics and HUP may provide a solution to this
dilemma.
.
|
|
| User: "Spaceman" |
|
| Title: Re: Renormalization revisited |
19 Jan 2006 08:27:03 PM |
|
|
"wg" <wgilmour@i-zoom.net> wrote in message
news:1137696469.709286.320620@g43g2000cwa.googlegroups.com...
| Renormalization;
| While it works, most mathematicians and physicists feel uncomfortable
| about using it to get rid of infinities. It appears to be a magic trick
| without much solid mathematical basis.
| Infinites arise of course by division by 0, which leads to an undefined
| answer.
| But wait a second; we live in a mathematical universe, math simply
| works and is explanatory to the highest degree of precision. Every
| aspect of the universe grinds to the precision of math. Why does math
| work so well for everything ...but lets us down for this one anomaly
| which is division by zero....
| Have we got something wrong here, should we be looking at the concept
| of zero a little differently?
|
| This is where I'm going to step out on a limb and suggest something
| radical.
| In the quantum world there is no such thing as zero, only minimum
| quantities [i.e. Plank quantities].
If you stop at the Planck minimum, you have lost the basics of math again.
since after all,
Planck devided by 2 is very possible in basic math.
so stopping the basic math of such will merely allow error again.
:)
I am with you all the way on getting rid of the zero stuff,
after all, 0 and nature don't like each other.
:)
.
|
|
|
|
| User: "wg" |
|
| Title: Re: Renormalization revisited |
19 Jan 2006 01:21:40 PM |
|
|
Correction;
In addendum read unitless not dimensionless
.
|
|
|
|
| User: "helloworld" |
|
| Title: Re: Renormalization revisited |
19 Jan 2006 08:19:53 PM |
|
|
Good way to use the values of Planck length, time , mass, charge and
temperature to make sense of phenomena and to use mathematics in a
consistent manner to get meaningful values which can then be compared
with experimental results.
It should work in all cases too.
Congratulations.!
I would like you to apply your fertile mind to see whether
1 Kg mass is equivalent to 7.4 x 10 ^ minus 28 ) mtr .
[ compare this with planck's length :1.61624 =D7 (10^ minus35) m]
I get this value from the expressions for Planck's length and Planck
mass, working out as follows :
Planck's mass, m =3D [ ( hc/G)^1/2] for lumpen matter..........(A) and,
Planck's length, s =3D {hG/c^3}^1/2; ..ie, for empty space ......(B)
eliminate 'h' between (A) and (B) to get,
S=3D {G /(c^2)} x m
Plug in newtonian values for the gravtational const G and einsteinan
value for 'C".to get 1 Kg mass is equivalent to 7.4 x 10 ^ minus 28 )
mtr .
Does it provide a way of converting 'mass' into 'space'?
Implying that Space and Matter ( like space and time .. from s =3D ct or
, energy and mass from E =3D mc^2 ) are physically one and the same and,
convertible to each other.?
Also does it mean that 1 kg mass could only be crunched into nothing
less than
7=2E4 x ( 10 ^ minus 28 ) mtr ( dia or radius or a fractal length???) of
space even in a blackhole?
And, does it indicate that the mass ( or energy content ie, inertia
measured in earthly units ) of a piece of superstring of length 7.4 x (
10 ^ minus 28 ) mtr, is equivalent to 1 kg.?
kindly confirm or clarify to < > directly,please (
besides posting on this page your views also..
.
|
|
|
|
| User: "wg" |
|
| Title: Re: Renormalization revisited |
19 Jan 2006 08:27:18 PM |
|
|
Quote
But no matter how clever the word, it is what I call a dippy process!
Having to resort to such hocus pocus has prevented us from proving that
the theory of quantum electrodynamics is mathematically self
consistent. ... I suspect that renormalization is not mathematically
legitimate. (Richard Feynman)
.
|
|
|
| User: "helloworld" |
|
| Title: Re: Renormalization revisited |
27 Jan 2006 04:55:59 PM |
|
|
will some one kindly ref to my comments at serial 3 above, . helloworld
Jan 19, 6:19 pm and comment on my theory that Planck's constants
could be made use of to anvil out the equivalence of mass and space ?
Secondly, I want to make another valid observation about Planck's
Constants. (PC) .
While maths can model physics , physics cannot model maths. PCs lay
down the physical limits of entities : below those limits the entities
dont exist as stable viable entities in our known three or four or ten
dimensions or whatever dimensions we do our tensors. The entities at
half of plancks length ( for example) may exist as a mathematical
entity but surely not as a physical possibility.Similarly,Infinity or
indeterminancy,is a mathematical concept without any corresponding
physical existence. The state of any "immeasurable" is the same . Other
such immeasurables ( non-quantifiables) are emotions, qualities like
beauty or purely subjective feelings,although these lie in the
reality-fields of individual or even collective human
experience.Therfore, Planck's constants lays down the limits of
meaningful physical measurements which can interact and inter-relate
quantitatively with similar other measurements..Quanta is the "size" of
a quanti-fiable packet: the keythingy is 'quantifiability' of any
quality, entity or phenomena under consideration .Every observable ( if
we take individual or collective experiences also as an observable) is
not quantifiable.Setting limits to the quantifiability of measurables
makes sense. Hence taking into our calculations not zeros but Planck's
constants is an artistic , innovative and effective way of eliminating
infinities..
Now, Can i have comments on my theory that Planck's constants could be
made use of to anvil out the equivalence of mass and space ?( read my
proposition at ser 3 above .)
.
|
|
|
|
|
|
Related Articles |
|
|
