Unity of disparate Pieces

damptdweller:

Even if you take the string theorists viewpoint that the energy may “leak” away into a brane instead of actually disappearing I think I’m correct in saying that you still need to ensure that energy is conserved regardless.

Plato:While some might of thought it "dreamy," there is a direct physics correlation to that leaking in the collider. Although it is encompassed, like you said.

So where did it go, and how is "it" encompassed?

Sean:

understanding the unity of disparate natural phenomena.

So some people tried to form "new models" to help extend the way perceptions in science have always existed?

In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings.

While there was "particle states" to consider in terms of fermionic realizations, there was bosonic(force) interpretations that arose as well?

If such states were considered in the colliders, then, what valuation would have seen the extension of what is leaking to have been encompassed? Here the onion signatures are relevant.

Bulk Perceptions?

While the "brane features" seem to answer this, what moved the ideas of bosonic interpetations as features beyond the colliders? This all had to make sense to me. So the history of the expansion of processes, have been altered much as you would look at sound? Gia's example of hitting metal plates, to sound created when billiard balls collide, to exemeplfy a greater understanding of what theoretics is doing here?

Sound in relation to collision had a effect? It was this effect beyond the brane that was considered.

How could such thinking have lead to such abstractions and analogies if the theoretics had not be connected in the consistancies that are required of science?

As Maxwell equations were encompassing. As Einsteins theory of gravity was encompassing. By this methodology what came next? You has to understand this "tree of expression," in the modes of this thinking society "branched" to followed a format?


Time-Variable Gravity Measurements

As well as, the expansion capabilities of our brains?:) Osmosis, would have greater impact then:) From the ground up, as this tree grew? :)

Developement of Disbelief

As you read, hold on to the thought about stringy/M theory developement.

Richard Denton:

I discovered that it was simply philosophy on its own that had played the very much larger role in the gradual erosion of belief.

This is a interesting statement to me since some scientists might think that to have even included this in our "developing perspective" might have showed immediate signs of weakness? Evil?

As if, math came out of all natural things, on it's own?

So how did such views change us if we did not think about them more critically?

See, I am not sure I like to think that there is "no God" that can be substitued by taking this power of belief outside of ourselves to religions and institutions. Crippling us, as to the empowerment we have for such changes in our own life?

While we had seen the topic of "stringevangelism" introduced, there wasn't this concerted effort to make string as a all empowering "theory of everything( what underlying reality was referred too?)", even though, some would try to "invoke" these Godly powers of discrimmination. As a facist group, that would censor any views contrary to their own, as to what seemed, "stringevangelistic?" :)

It then became the same institution, that it despises? Some might know who I mean here. If I stood up to it, could I change reality as well, as to that this group invokes into society?

Anyway while I used Jo-Annes thread, "A little Bit of Heaven," to highlight this quality of earthly senses?

Topo-sense

Plato:

This intuitive feeling that is generated once math processes are understood are realized in dynamical movement revealled in the brains thinking? Had to arrive from lessons it learnt previously? Pendulums, time clocks, great arcs, and gravity?

I sought to internalize Gr's momentums, with Mecuries orbital patterns, or Hulse and Taylors expanding awareness of other things(gravity). I started to ask myself if this internalization was wrong? Is Topo-sense wrong? As too, intuitive unfoldments of the subject, in regards to Genus figures(holes)? Would it perish too? Revelations, leading to maths used?

Internal developement would have revealled a greater core depth of the realities around us. Which are highly abstract, yet, could have lead to insight and convictions held in astronomy happenings in the cosmo(isomorphic relations?)? So this internalization developed conviction, with the basis of Gr's valuation of quantum mechanical things, to cosmological proportions?

Strings as a model then, that could lead to perspectives with "langangian valuations" not only in terms of supersymmetry(concentration of a all pervading "beginning" that we could resort too,) as I espoused in Andrey Kravtsov computer's model.

That such relations in our philosophical orientation of physics would endure in measure, culminate with "fineness" and valuations of gravity perspectives. Could you do this, without some model?

So, would the "counter of belief in God," be the lesson the valuation of what one holds by introducing atheistic valautions, AS TO ROADS LEADING TO "COMMON SENSE?"

While I used stringy comparison for examination, this leads back again to what models can be used to keep the human beings empowered, without stealing this away from them by such institutionalizations? Continued reflection, thwarted, as to no experimental valuations yet philosphically introduced. You remember the opening statement I used?

I thought about the choices we make then, and the convictions we have. Would this have been irrelevant in our assessments of our own characters? After all, it would be you who walked back into society to think about the Smolins and Susskinds who would debate the essence of the backgrond?? What is understood, and what stringy needs to do?

Music of the Spheres

Strange Geometriesby Helen Joyce

Both spherical and hyperbolic geometries are examples of curved geometries, unlike Euclidean geometry, which is flat. In spherical geometry, the curvature is positive, in hyperbolic geometry, it is negative.

I thought I should add the "ascoustic variation" of the struggle for music in the world of "good and evil" as well.

That such "chaos created" in the minds of our youth, would have been frowned upon in Plato's academy.

By such reasonings and understandings of how such sound valuation may have been taken to spherical proportions? Should be no less then the consolidation points, as poincares distribution of eschers angel and demons pictures describe?

What avenues had been less then discribed on those chaldni plates that they had been reduced to dimensional avenues discriptive of the chaldni plates, as a fifth dimensional understanding? Langrangian discription of points L1 or L2, and a visionary context of Sylvestor surfaces as proponents of B field manifestations as part of genus figures with holes?

See:

Angels and Demons

Heaven's ephemeral Qualities?

"Materialism:

Basically, the view that everything is made of matter. But what is matter? Probably the most innocent and cheerful acceptance of it comes right at the start of materialism with Democratius of Abdera (in Northern Greece) in the fifth century B.C., for whom the world consisted entirely of 'atoms', tiny, absolutely hard, impenetrable, incompressible, indivisible and unalterable bits of 'stuff', which had shape and size, but no other properties, and scurried about in the void, forming the world as we know it by jostling each other and either rebounding (despite being incompressible) or getting entangled with each other because of their shapes. They and the void alone are real, the colours, flavours and temperatures that surround us being merely subjective. This model has lasted, with various modifications and sophistications right down to modern times, though the notion of solidity was causing qualms at least as early as Locke. But, in the last century, all has been thrown into confusion by Einstein's famous, E=mc2 and also by general relativity. Mass, the sophisticated notion that has replaced crude matter, is interchangeable in certain circumstances with energy, and in any case is only a sort of distortion of the space in which it was supposed to be floating. Photons and neutrons have little or no mass, while particles pop out of the void, destroy each other and pop back in again.

'The Oxford Companion To Philosophy', edited by Ted Honderich. Oxford University Press, 1995




Heaven in one sense, as a ephemeral quality(violet or blue), but in the gratification of savoring smell and tastes, these are not true bearers of the "quality of thought" are they? These sense are more.....earthly then?

I struggle. :)


If such senses are to perish, then what shall be everlasting? If intuition, is to only serve it's purpose until the math is adorned, then what shall this math be, in the state of the abstract mind(yellow)?

An equation means nothing to me unless it expresses a thought of God.

Srinivasa Ramanujan

Ramanujan's thought about equation is emotively charged (red), that this too issues from such a mental abstract, as to be from heaven and descending?

Wait! It's about heaven on earth? Really? :) Heaven is only a state of mind? (r/light)?

Am I Okay on analogies then, to confuse the mind about these states of heaven, that I could have mixed heaven up, as to the varities of "time and segments," as our own colorful experiences?

What song sung then, that each musical octave gain, and of loss is its own vibratory tone? Yet, it existed in the very fields of the sun, as a chemist combines?

A Clear Presence

Can one miscontstrue your words even more? :)

Lee Smolin said:

Of course if the theory is right-and we never assume so-we must show more. We must show that the ground state is semiclassical, by solving the dynamics. This is a hard problem, analogous to showing that the ground state of water is a solid. But as this is the focus of attention there are beginning to be significant, non-trivial results on how classical spacetime can emerge from a background independent quantum theory.

Jacques Distler:

But the mere possibility of such surprises should not reduce us to labelling every as-yet-not-experimentally-verified statement to the status of mere “opinion” or rank “speculation.”

While I am extreme with my "Angels and Demon" such comparative functions had not been limited too, the basics of such assumptions, but had indeed been dressed up by good science woman/man.

We all like a good story. Those, in regards to time travel or Contact like movie(science that is consulted as to the edge of what theoretcial positions had beem pushed).

Yet indeed even within the boundaries of work sciencetists bring here a division of what is hoped for, as a "reduced basis of assumption," could have been misleading as to the real science or not?

Is it illusion that we play with, that we would want the purity of thought manifested on the public scene, as warped mentalities of what many scientists would disgust them? This "clear presence?" An "open heart clear mind."

The story of Angel and demons has been misconstrued in science by very bright scientists, using the nature of right and wrong, as inherent features of negative and positive curvatures?

Taken to mean this theoretics and that, are indcative anomalies of the good and evil in society. Is it political? Or shall we play with the very concepts and misconstrue them for what they really are?

Raphael Rooms

The fog is immmense and greatly hides the idea of this clear presence. Opening good hearts and minds as to the attempts to get rid of the illusions that would take hold of society? Allow the greater vision of perspective, a picture, that had been piecemealed, to raise a reality of what the picutre is painted on, the room it sits in, and what each parts of it, are telling the story about the geometers of the world?

Angels and Demons

Now how could such good thinking minds have not seen that the publics understandings might have been warped by the very underpinnings of good science men/woman, and all the issues become some fictional story for what evils and saints can do for us.



So was it some distant function of creation that we should not recognize the negative effect of all "good things" that will emerge from the actions of what is revealled to us in our "rainbows and aurora's," that we would not seem pleased as to the emissions have to say in the wave forms that surround such things?

Can we hope to use antimatter as a source of energy? Do you feel antimatter could power vehicles in the future, or would it just be used for major power sources?

There is no possibility to use antimatter as energy "source". Unlike solar energy, coal or oil, antimatter does not occur in nature: we have to make every particle at the expense of much more energy than it can give back during annihilation.

You might imagine antimatter as a possible temporary storage medium for energy, much like you store electricity in rechargeable batteries. The process of charging the battery is reversible with relatively small loss. Still, it takes more energy to charge the battery than what you get back out of it. For antimatter the loss factors are so enormous that it will never be practical.

If we could assemble all the antimatter we've ever made at CERN and annihilate it with matter, we would have enough energy to light a single electric light bulb for a few minutes.

So while good thinking men and woman dance with the ideas of Einsteins geometrical propensities to answer thse functions, what spherical relation would have said, that for every sun that burns out, it will rejuvenate itself, by strict geometrical functions in anti-matter creation to bring forth this "new vision" of the world.

Create this wonderful unlimited resource of energies that exist around us now?

So again let's take this back to the Pierre Auger examination of what is taking place outside of the collider expeirments. While it is nice to have these controls, why were we not informed about the potentiality of what exists as you pursue your visons to the very beginnings of this universe? That this beginning would take place right next to you? Is this wrong that we not assign astronomical valuations to the very nature of our world now, as such interactions take place between the sun and earth? That in those compacted dimensions, such calculations would reveal the thinking of relative and mathematical entities, as signals of the events that can take place everyday around us as well.

Einstein was very revealling in what could be taken to a larger scale for what could split apart, so it is not so unlikely that ourvisions have been curtailled,just becuase we did not se the actions that could take plac ein a larger scenario?

So did Heisenberg see what was revealling towards these geometerical propensities, as events unfolded themselves?

Update:

if your foci is "string" enough, you might realize it is less than K=0 :)


All M.C. Escher works (c) 2001 Cordon Art BV - Baarn - the Netherlands. All rights reserved. www.mcescher.com

While some believe in positive curvatures they also understand that the inception could have a negative effect, yet it would not be "angel and demons" they espoused?

We are all better then that, right? There is a "greater whole" we are each part of? To further extend this empowerment beyond "good and evil in religion" think of sound then, and the related entry below. Maybe, it will have a certain resonance for you?

Music of the Spheres

About how the brain's neuronic vitalities of vison are enhanced, and related?

Wunderkammern

Paul Dirac and Geometrical Thinking?

Into the Antiworld was originally staged at CERN inside the underground cavern that houses the Delphi experiment, in which collisions between electrons and their antiparticles - positrons - are studied. That setting must have been awe-inspiring, particularly as the show closed. The audience would have been whisked from the wonder and novelty of Dirac's theory over 70 years ago to the sophisticated particle physics experiments of today that the discovery inspired. At CERN, the curtain behind the stage ripped apart to reveal the Delphi detector the performance ended - but the gigantic photograph of the Delphi experiment that concluded the show at the Bloomsbury worked surprisingly well.

Oh what fanfare and dance is given these genius's that we find the story ends with where the future begins.

The Quantum Theory of the Electron



Paul Dirac

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

Can one distinguish something that is of nature as the basis of reality, and see this before it is algebraically written? Jacques mention where the intuitive lines ends and where the math begins.

So from this statement then, it would have been impossible for Dirac to know what the matrices would look before it was algebraically written?

If there is "no physics" and we are defining things from the horizon or boundary, then what geometry wil be revealing of this nature? Can it be concieved as it was by Dirac?

I was thinking of Lenny Susskinds picture of the rubber band in his mind after working hard to mathematically understand. Did comprehension come by way of his mathe equations or by geometriclaly viewing?

THE LANDSCAPE [12.4.03]
A Talk with Leonard Susskind

Einstein said he wanted to know what was on God's mind when he made the world. I don't think he was a religious man, but I know what he means.

Albrecht Dürer and The Magic Square



So the complexity of geometrical form would have been of value if we had seen the way that it might have taken that vision into the geometrical formations of spin orientated understandings? Isomorphic relations of the orbitals relations in cosmological events?

Oh My God Particle-Revisited

I just wanted to drop this link here for now.

The animation shows schematically the behavior of the gas molecules in the presence of a gravitational field. We can see in this figure that the concentration of molecules at the bottom of the vessel is higher than the one at the top of the vessel, and that the molecules being pushed upwards fall again under the action of the gravitational field.

Gerard "t Hooft:

The Holographical Mapping of the Standard Model onto the Blackhole Horizon

Interactions between outgoing Hawking particles and ingoing matter are determined by gravitational forces and Standard Model interactions. In particular the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the Standard Model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon’s dynamics. The relation between in- and outgoing states is described in terms of an operator algebra. In this paper, the first of a series, we describe the algebra induced on the horizon by U(1) vector fields and scalar fields, including the case of an Englert-Brout-Higgs mechanism, and a more careful consideration of the transverse vector field components.

So we are still looking at the horizon here.

In reference to the God Particle. This was first revealed in the 1991 Fly's eye experiment.

Oh-My-God particle

On the evening of October 15, 1991, an ultra-high energy cosmic particle was observed over Salt Lake City, Utah. Dubbed the "Oh-My-God particle" (a play on the nickname "God particle" for the Higgs boson), it was estimated to have an energy of approximately 3 × 1020 electronvolts, equivalent to about 50 joules—in other words, it was a subatomic particle with macroscopic kinetic energy, comparable to that of a fastball, or to the mass-energy of a microbe. It was most likely a proton travelling with almost the speed of light (in the case that it was a proton its speed was approximately (1 - 4.9 × 10-24)c – after traveling one light year the particle would be only 46 nanometres behind a photon that left at the same time) and its observation was a shock to astrophysicists.

Since the first observation, by the University of Utah's Fly's Eye 2, at least fifteen similar events have been recorded, confirming the phenomenon. The source of such high energy particles remains a mystery, especially since interactions with blue-shifted cosmic microwave background radiation limit the distance that these particles can travel before losing energy (the Greisen-Zatsepin-Kuzmin limit).

Because of its mass the Oh-My-God particle would have experienced very little influence from cosmic electromagnetic and gravitational fields, and so its trajectory should be easily calculable. However, nothing of note was found in the estimated direction of its origin.

Why was it necessary to invoke God here as you did Wolfgang? This was around for some time, and now, such references have found their way into particle collisions perspectives? :)

Quantum gravity is the field devoted to finding the microstructure of spacetime. Is space continuous? Does spacetime geometry make sense near the initial singularity? Deep inside a black hole? These are the sort of questions a theory of quantum gravity is expected to answer. The root of our search for the theory is a exploration of the quantum foundations of spacetime. At the very least, quantum gravity ought to describe physics on the smallest possible scales - expected to be 10-³⁵ meters. (Easy to find with dimensional analysis: Build a quantity with the dimensions of length using the speed of light, Planck's constant, and Newton's constant.) Whether quantum gravity will yield a revolutionary shift in quantum theory, general relativity, or both remains to be seen

One needs to keep perspective on what is happening here, and as a layman, it is extremely difficult. Yet, do I seem to understand what these season vets are doing? More then just reading the NYT times for sure :)

The Fly's Eye and the Oh My God Particle John Ellis was instrumental in opening up perspective here. What is happening outside of collision reductionist processes of the colliders

Laying the Foundation with Respect

It is most certain that at this point the public would have been left behind, so is there a way to bring perspective at this point on where you are now?

I recognize the generalization and roads that lead to blackhole as a basis for considerations. What would draw ones atyemtion to this horizon. Lee Smolin in his book gave adequate discription that I just pointed out here.

Three Roads to Quantum Gravity, by Lee Smolin, pg 171


I know it might seem that if this conversation is now highlighting the intricacies of blackhole dynamics, then what exactly are you doing?



By giving a visual map of the Bekenstein Bound this help to direct my attention to the mapping that had been going on theorectically here.

Mine would definitiely be generalizations, but work by others lead to deeper insights.

Conformal Field Theory

A conformal field theory is a quantum field theory (or statistical mechanics model at the critical point) that is invariant under the conformal group. Conformal field theory is most often studied in two dimensions where there is a large group of local conformal transformations coming from holomorphic functions.

So what "tidbits" had already been out there then that would help.


Black Holes and Beyond:
Harvard's Andrew Strominger on String Theory

Quantum Micostates?

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did.

While this is a past issue for most of you it is leading in the direction you are talking I assume.


Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of the event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondance between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinquish which discription is more fundamental.

Pg 198, The Universe in Nutshell, by Stephen Hawking

Gary T. Horowitz and Juan Maldacena,

The purpose of this note is to provide a possible answer to this question. Rather than the radical modification of quantum mechanics required for pure states to evolve into mixed states, we adopt a more mild modification. We propose that at the black hole singularity one needs to impose a unique final state boundary condition. More precisely, we have a unique final wavefunction for the interior of the black hole. Modifications of quantum mechanics where one imposes final state boundary conditions were considered in [6,7,8,9]. Here we are putting a final state boundary condition on part of the system, the interior of the black hole. This final boundary condition makes sure that no information is “absorbed” by the singularity.

While there is no "apparent relationship(?)" between microstate blackhole production and blackholes what would make one think that particle collsions can be written as dual blackholes?

Dmitri Ivanovich Mendeleev: The Law of Octaves

Dmitri Mendeleev in 1897

Courtesy Edgar Fahs Smith Memorial Collection, Department of Special Collections, University of Pennsylvania Library

Dmitri Ivanovich Mendeleyev (Russian: Дми́трий Ива́нович Менделе́ев listen ▶(?)) (8 February (O.S. 27 January) 1834 in Tobolsk – 2 February (O.S. 20 January) 1907 in Saint Petersburg), was a Russian chemist. He is renowned for being one of the two scientists who created the first version of the periodic table of elements. Unlike other contributors to the table, Mendeleyev managed to predict the properties of elements yet to be discovered. In several cases he even ventured to question the accuracy of the accepted atomic weights, arguing that they did not correspond to those predicted by the Periodic Law, and here too subsequent research proved him correct.

Now of course I have made some inferences here and who hasn't when it came to sound and it's values? I've explained this here.

But by exploring the value of the geometric forms, of the square, and the triangle these were simplistic analogies to earth(matter) and the triangle (energy) By simple addition of both these forms, and by looking at the value of Octave=do, re, mi, fa sol la ti do, etc. There had to be a injection point for this octave to ascend?

Now just take this as a story of the plot and look at what this plot is producing, not where science is, but of the easily converted analogies to the thinking of that sound in our universe can make to the elemental structure Mendeleev first sought out to map.

So by joining the square and the triangle, we see where "four triangles" are produced inthe form of the pyramid.

It also asks how can this idea of matter and energy have been sent to another octave, and hence an idealization of the Law of Octaves. So between mi and Fa, such injection would have lead any thinking to have wondered this associative function to what could transpire, if such a completion could have been modelled in the pyramid shape.

Four primary triangles that reprsent the basis of the transmutation of energy from the four lowers states of matter considerations to the triangles, and the ascension of vibrations readily asseted to be in the most rarified of "matter forms (particle reductionism)" associative with energy at this peak?

Proceedings of Societies [Report on the Law of Octaves]

Mr. JOHN A. R. NEWLANDS read a paper entitled "The Law of Octaves, and the Causes of Numerical Relations among the Atomic Weights."[41] The author claims the discovery of a law according to which the elements analogous in their properties exhibit peculiar relationships, similar to those subsisting in music between a note and its octave. Starting from the atomic weights on Cannizzarro's [sic] system, the author arranges the known elements in order of succession, beginning with the lowest atomic weight (hydrogen) and ending with thorium (=231.5); placing, however, nickel and cobalt, platinum and iridium, cerium and lanthanum, &c., in positions of absolute equality or in the same line. The fifty-six elements[42] so arranged are said to form the compass of eight octaves, and the author finds that chlorine, bromine, iodine, and fluorine are thus brought into the same line, or occupy corresponding places in his scale. Nitrogen and phosphorus, oxygen and sulphur, &c., are also considered as forming true octaves. The author's supposition will be exemplified in Table II., shown to the meeting, and here subjoined:--

Now such a colorful model of the pyramid to me in such oscillations mode seemed to reveall a dynamic form of color and it's variations. Is this what sound values of had left for us in our hydrogen spectrum mapped to see what energy valuation had occurred? The blacklines.

So it was not long, that such idealization about the value of sound might reveal it's consolidational effect, as we compared low and high sounds of value, to this spectrum. That low sounds were very matter orientated(consolidated), while high sound were very revealing of the vibratory function of energy valuations seen at the peak of that pyramid? The height of enrgy valuations in relation to particle reductionism. So what would this pyramid reveal in the thoughts of all humanity then? Simple deduction form from model participation is all. It gave insight into the outward expression of these matters(body) fluid emotive forces, to mental states of energy valuations?

I am not saying this is the way of it either, just that such a platform and model developememnt could have sparked other ideas, as Smolin so hopes might be revealled for further explorations into the new theoretical idea developement, to help us look at the way nature is.

Mendeleev example is a case in point where such ideas and sound valuation seem to penetrate the mind as to the essence and nature of matter. How strange then I might be, to say, that in our very own hearts is the transition point between the lower centers of man(his earth nature), that such ascension of this vibratory thought formsanaogy of the triangle to energy) would be, held in the clear mind?

But let's not forget some real science here.

The beam of positively-charged ions generates a slight magnetic field that interacts with an externally-applied magnetic field. The net result is that the trajectory of a charged particle is curved to an extent that depends on its speed (determined by its mass). When the beam of a mixture of isotopes of different masses falls on a photographic plate, the different isotopes converge at different points, corresponding to the different radii of their semicircular paths.

The mathematical equation that describes this phenomenon is: m/e = H2 r2 /2V, where m is the mass of the ion, e is the charge of the ion, H is the magnetic field strength, r is the radius of the semicircle, and V is the accelerating potential.