Ultraviolet divegence is very old problem and is not solved completely
yet. I thought we might approach this problem through introducing new
quantisation into Lorentz space which is different from that on
quantum mechanics.
For details:

http://139.134.5.123/tiddler2/c21508/relativity.htm

(tontoko hirorin) wrote in message . com...
Ultraviolet divegence is very old problem and is not solved completely
yet.

Yes it was; centuries ago: Plant your vegetables in a greenhouse with
ordinary glass windows. The glass will absorb most of the UV, solving
your deveging problem.

Paul Cardinale

(tontoko hirorin) wrote in message . com...
Ultraviolet divegence is very old problem

Presumably you're talking about the "ultraviolet catastrophe"
that motivated Planck's work on blackbody radiation.

and is not solved completely
yet.

It's not? What are we missing?

I thought we might approach this problem through introducing new
quantisation into Lorentz space which is different from that on
quantum mechanics.
For details:

http://139.134.5.123/tiddler2/c21508/relativity.htm

Blank page on my browser.

- Randy

tontoko hirorin:
Ultraviolet divegence is very old problem and is not solved completely
yet. I thought we might approach this problem through introducing new
quantisation into Lorentz space which is different from that on
quantum mechanics.


Uh, the uncertainty relations are not just defined. They are derived
from the definitions of the operators (which are also canonical conjugates).
You can't simply define an uncertainty relation between two variables
and create a value for the commutator based upon dimensional analysis
(and your dimensional analysis isn't even correct area/momentum does not
give meter-seconds). You have a "commutation relation" for t and x, but t
isn't an operator, nor did you define an operator for t.

tontoko hirorin wrote:
Ultraviolet divegence is very old problem and is not solved completely
yet. I thought we might approach this problem through introducing new
quantisation into Lorentz space which is different from that on
quantum mechanics.

I am not quite so sure you can dismiss renormalization that quickly. The
divergence is cancelled by counter terms in the bare coupling constant which
is itself assumed divergent. All you need to assume is the exact form of
the bare coupling constant is not known at this stage. If it was known when
combined with the other divergent terms they would cancel. From page 505 of
Weinberg Quantum Theory of Fields he considers some rather interesting
integrals:

i(q) = integral 0 - infinity (dk/(k+q)). Now di/dq = integral (0 -
infinity) -dk/(k+q)2 = -1/q or i(q) = -In q + c where c is divergent.

Now if we have terms like the above in the Lagrangian then by adopting the
effective field theory approach we can say that at this stage we do not know
the full form of the bare coupling constant. If we assume it has a form
like the above so that when summed together the divergent terms (which also
have a form like the above) cancel then we are ok.

At first I thought this was taking infinity from infinity but after thinking
a little bit I realized it really was not the case because:

1. If we group the terms before taking the limit (which is what we are
really doing in an indefinite integral) then they cancel before reaching
infinity.
2. We can take the view we are only dealing with approximations to a more
accurate theory that do not yield divergent terms but only very large
numbers then the subtraction is ok.
3. We can assume the theory only applies to a certain cutof in energy. This
leaves finite terms but strongly dependant on the cutoff. Again if we can
assume that the greater the cutoff is taken the more we approach energies
where the theory does not apply the more uncertain we become. So what we
can do is beyond a certain energy say the theory does not apply - put it in
the form above and the terms we do not want go.

The most elegant alternative seems to be 1.

Now I learnt Quantum field Theory from Weinberg's book so all I know is this
effective field theory approach. It is my understanding that this is a new
approach so critics of renormalization (of which I there have been many -
even perhaps including Feynman) may not have considered how this resolves
the issue.

Thanks
Bill

(Bilge) wrote in message ...
tontoko hirorin:
Ultraviolet divegence is very old problem and is not solved completely
yet. I thought we might approach this problem through introducing new
quantisation into Lorentz space which is different from that on
quantum mechanics.


Uh, the uncertainty relations are not just defined. They are derived
from the definitions of the operators (which are also canonical conjugates).
You can't simply define an uncertainty relation between two variables
and create a value for the commutator based upon dimensional analysis
(and your dimensional analysis isn't even correct area/momentum does not
give meter-seconds). You have a "commutation relation" for t and x, but t
isn't an operator, nor did you define an operator for t.

My supposition for the uncertainty relations on my webpage:

http://139.134.5.123/tiddler2/c21508/relativity.htm

is very simple, i.e. x(meter)*t(second)-t(second)*x(meter) =
constant(meter*second) (please forget Plank constant!)
Since in the special relativity 1 second = 3e10^8 meter, that constant
has the unit of area.
As well as quantum mechanics, there are several ways to express t and
x as operators such as matrices or differential operators. One of them
is to make x correspond to identity mapping and t correspond to
(constant)*(partial deriavtive by x) as described in the webpage shown
above.

Additionally recently I found the clue to determine the concrete value
of that constant. For details how to calculate that constant, please
visit:

http://139.134.5.123/tiddler2/lepton/lepton2.htm

My rough estimate for that constant is around 1e-38 meter^2 as shown
in the above webpage.

In my Astronomy news group I posted how ultraviolet photons can create
photolysis,and this seperated water into its two elements,and that is a
big reason Mars has no surface water. Bert

"Bill Hobba" wrote in message ...
tontoko hirorin wrote:
Truly currently the ultraviolet divergence may be regarded as not
"problem" but "solved problem" by most of people since no actual
"divergence" appearing through the calculation owing to
renormalization. However I think the ultraviolet divergence is more
fundamental problem that that solved by renormalization.

Which is the whole idea of effective field theory - we do not assume we have
the final theory.

Thanks
Bill

Practically QED is a complete theory since every calculation coincides
with experimental result as long as dealing with electron and its
electrical interaction.
However mathematically some inconsistency is still remaining. For
example, on the perturbation development the mass of bare electron is
supposed as finite, neverthless when cancelling out the divergence, it
is supposed as infinte.
About the final theory - actually I'm not sure what the final theory
you've said is, though - isn't it impossible to reach "final" theory
until physicists abandon pursuing physics?