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Offline Mr. Data

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what is Mass?
« Reply #50 on: 06/07/2011 16:40:50 »
Let us take a simple scalar field, with a non-invariant gauge condition - this means there is no symmetry present in the field equations:

∂φ'=[∂φ + iφ(∂θ/∂x)]e

∂φ'*=[∂φ* + iφ*(∂θ/∂x)]e

Multiplying these two terms (which make up the kinetic term of a field), we have:

[∂φ + iφ(∂θ/∂x)]e[∂φ* + iφ*(∂θ/∂x)]e=∂φ∂φ* + i(φ∂φ* - φ*∂φ)∂θ/∂x + φ*φ(∂θ/∂x)

Which has no symmetry at all. So mathematicians needed to make a new mathematical concept, called the Covariant Derivative, and this brought order back into our equations, and it uses the four-vector of electromagnetism:

Dμφ = ∂μφ + A\muφ

Dμφ* = ∂μφ* - A\muφ*

This is just a wee taster... but plugging that term into our field restores invariance and so this is a similar reason why a photon cannot have a mass. Only if there was some breaking of the symmetry could we state such things.



« Last Edit: 06/07/2011 16:42:35 by Mr. Data »
 

Offline Mr. Data

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« Reply #51 on: 06/07/2011 16:43:13 »
Note though that I haven't included a potential term here. You could if you wanted to.
 

Offline Mr. Data

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« Reply #52 on: 06/07/2011 18:16:20 »
Now let us debate on the existence of the Higgs field. It is true that mathematics is an abstraction, and it does not represent the true physical reality. It is merely a tool we use to help us describe the world, but it does not refer to the real world; It can only be like this, since mathematics opens the realm of different interpretations, and thus only through measurement can we adjust the equations to a greater degree of certainty. Whether we will know the entire blueprint of reality at some point in our future horizon is another question up for debate, that is saying if we can even simplify something as complicated as a universe.

There is no clear definition of a Higgs field when it comes to important questions like inertia, a property inherent in systems in which the behaviour of the system is changed intrinsically and in a non-symmetric sense to the more fundamental field (the photon field) and dynamically, meaning that the dynamics of the particle, whether theyn involve observable properties have been changed. Not only is energy a measurable quantity, but mass is also an observable and predicted upon the density of the amplitude of the function.

It is also a strange idea we call the Goldstone Boson, its name, as it is really simply just a photon in the lowest energy state - this often confuses people as it may imply something odd and exotic. But it really isn't, it's just a matter of the least principles of energy on a system - a langrangian, which may take the lowest energy state possible. This state never reaches an absolute zero temperature, which would be denoted simply as T=0, or a zero vacuum state vector Ψ|0> because no such system can exist in the vacuum of space, simply because space is infinitely filled with energetic fluctuations.

So the Goldstone Boson should be (a weakly fluctuated) kinetic packet of energy, around some lower bound potential φ = 0 where φ is your field and 0 refers to the lowest state.
« Last Edit: 06/07/2011 18:32:40 by Mr. Data »
 

Offline Mr. Data

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« Reply #53 on: 06/07/2011 19:19:08 »
But some kind of differential must come into play if we talk about:

'' lower bound potential φ = 0 where φ is your field and 0 refers to the lowest state.''

Since  Ψ|0> ≠ ρ(ee-iθ) we can assume that there is some inherent change in φ which represents the potential scalar. Whether we look for some symmetry breaking, it will be at the cost of either excepting a Higgs phenomenon or believing there is some more unique symmetry in θ which may invoke connections on other terms. This could obviously drastically change our look on the dynamics of

[∂φ + iφ(∂θ/∂x)]eiθ[∂φ* + iφ*(∂θ/∂x)]eiθ=∂φ∂φ* + i(φ∂φ* - φ*∂φ)∂θ/∂x + φ*φ(∂θ/∂x)

Perhaps there are restraints on certain variables which invoke the vanishing of the term which causes the non-invariance. This could only be done by a super-connection in a higher representation of a probability field - the field represented by Ψ should have a conjuugate Ψ* and if coupled to components to the i'th components could alter dimensions in the field sufficiently to fine tune dynamical reasons for matter, rather than appealing to a new field, that being the Higgs Field, of course.

It would look something like:

([∂φi + iφi(∂θ/∂x)]eiθ[∂φi* + iφ*i(∂θ/∂x)]eiθ)Ψi = (∂φi∂φ*i + i(φi∂φ*i - φ*i∂φi)∂θ/∂x + φ*iφi(∂θ/∂x))Ψi

The connections are a probability matter: The new function Ψ should measure the probabilities in all measurements in the intrinsic properties of the system. The sub-component relating Ψi with φi which is obviously i can be further translated into tensor products, but we shall leave that kind of thing out in this part. All we should need to know is that the potential of the system (the Goldstone Boson) depends on rotations in it's abstract spacetime to alter the existing non-gauge invariant terms to existing parameters which are allowed. What causes this as of yet could be claimed, as somewhat of a mystery, since this approach has never been fully investigated out the conventional claims of a Higgs Boson. Of course, once we have established this function over all our terms, we can then change the terms to suit some new differential equation. That could be speculated upon how it could form, but such an approach should be possible. It maybe some kind of equation where it takes the space derivative to the second order, whilst the right hand side of an equation represents the time derivative taken to the field to the first order. Such an equation can be allowed, but can only permit the space component, with a vanishing time component (if I have conducted this properly). But either way, that is but an approach.
« Last Edit: 06/07/2011 19:23:11 by Mr. Data »
 

Offline Mr. Data

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« Reply #54 on: 06/07/2011 19:30:43 »
But that is but one way, and there may be many possible ways to approach it, but if you take my way, you find some interesting results.
 

Offline lightarrow

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« Reply #55 on: 06/07/2011 20:39:19 »
Mass is just a concentrated structure of energy.
But where in this statement one can understand that you are considering a region of space which is not moving?
 

Offline yor_on

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« Reply #56 on: 06/07/2011 20:56:38 »
I don't follow Mr Data?  Are you building a field theory depending on some lowest state of energy, that then also would couple to mass?

How do it couple?
=

Vacuum fluctuations that gets dense over 'time's arrow?
And what about Accelerations, as compared to Geodesics.
=

One might assume that as we describe photons as the 'force carriers' of electro magnetism, and as they bend to gravity, they also should be able to bend to a electric field, but I haven't seen that proved in any experiment yet?

Because if they did :) And assuming we all are EM in some way, then ?
But I don't think so myself.
« Last Edit: 06/07/2011 21:12:41 by yor_on »
 

Offline Mr. Data

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« Reply #57 on: 06/07/2011 21:10:38 »
I don't follow Mr Data?  Are you building a field theory depending on some lowest state of energy, that then also would couple to mass?

How do it couple?
=

Vacuum fluctuations that gets dense over 'time's arrow?
And what about Accelerations, as compared to Geodesics.

Coupling the terms is very easy. All you need is to obide by the terms where the function of field comes into play. If you look at the coupled terms in the last equation above, it takes the appearance of:

For all u it represents

(u+u) d+d = ud + (ud - du) + du

where u is the up-down model, where this is ''up'' φ and d is ''down'' φ* - or if you like, you can call both terms as an incoming and outgoing signal. Every time you see these terms, they are the wave operators on the field. All you need to do, is take the wave functions condition and shift the field φ to φ' - θ is the phase and located in the exponential, and it can take many trig metric functions. These shifts can be suited to satisfy an appearance of a spontaneous symmetry breaking if and only if there are terms in the gauge symmetric field which cannot be satisfied.
 

Offline Mr. Data

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« Reply #58 on: 06/07/2011 21:21:34 »
You might notice an antisymmetric part in the representation above (ud - du).

This is a very interesting quantity which can be evolved in a matrix, and seen in light of the hodge star, but that will be later explained when I have more time.
 

Offline yor_on

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« Reply #59 on: 06/07/2011 21:24:21 »
I will have to reread this :)
Several times for sure.

It's interesting.

"the potential of the system (the Goldstone Boson) depends on rotations in it's abstract spacetime to alter the existing non-gauge invariant terms to existing parameters which are allowed." here we are speaking totally abstractly right?
all in the 'mind sphere', so to speak, although those rotations reminds me of the 'folds' described in the Fractional Quantum Hall (FQH) Effect, which also was related to how that electron needed to 'turn' 720 degrees to get a full rotation.

So, and this is what nags on me, could I relate it to dimensions, or should I strictly think of it as a 'translation' from the mathematics?
==

You have to remember one thing here. It's exactly as JP pointed out, the more exotic your equations the less people will be able to follow them. And some of them might build on definitions you take for granted, but that I miss. Don't let that stop you though :)
« Last Edit: 06/07/2011 21:33:03 by yor_on »
 

Offline yor_on

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« Reply #60 on: 06/07/2011 21:47:03 »
Let us see if I can define a Higgs field in words. It's as you say about a lowest state of energy, the one our vacuum seems to have, a average null. That doesn't state that it is null though everywhere though. The vacuum fluctuates like a sea does but without any wind to help it. And gravity would then be represented by some of the bosons existing inside those fluctuations, they may fluctuate but as they do so over a region their average existence becomes coupled to what we call inertial mass, getting a average value differing from 'null', so it's a very tricky idea in that we can't measure one of those bosons, as all measurements will fail to register such a probabilistic (short timed) 'boson', but the average field created from them will be 'invariant'.

So on one hand you have a classically empty space. On another it's constantly 'fluctuating'. On a third those 'bosons' treated as a average, will have a influence on what we can measure, in this case expressing itself as 'gravity'.
=

the weirdest thing with this idea is that it assumes a value of the Higgs field that somehow seems to be separated from what we observe as 'space'. It's average 'energy' isn't in the same plane, sort of. And that one weirds me out, in many ways. It seems actually to assume a new definition of a 'dimension', not that I'm sure on the old one either :)
« Last Edit: 06/07/2011 22:24:43 by yor_on »
 

Offline Mr. Data

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« Reply #61 on: 06/07/2011 21:53:15 »
You ask a very relative question. What is this rotation in the field? It is a geometrical representation, which would not apply to point like particles. As we have seen from recent news, the electron may indeed have a sphere-like structure, which agrees well with classical idea's. It is up to the reader to decide whether or not the electron has a structure and whether or not the model refers to real rotations in some kind of real geometry or whether it is all just a mathematical representation. Just that, I cannot say.
 

Offline Mr. Data

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« Reply #62 on: 06/07/2011 21:55:45 »
The technical explanation would possibly be described as a special oscillating value between C and R (complex and real) values, which would be part of the U(1) symmetry group. It would then be a special case directly of the U(1) symmetry group.
 

Offline yor_on

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« Reply #63 on: 06/07/2011 22:00:22 »
To me it's all about what a dimension is nowadays Mr Data :) I finally feel that I have gotten some ground rules down for how to see 'frames of reference' relativistically. And 'dimensions' is my new project, I want to see them..

ahem :)
 

Offline yor_on

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« Reply #64 on: 06/07/2011 22:08:37 »
Any 'geometrical representation' seems, to me that is, to build on the idea of 'dimensions'? The way you define it mathematically should either translate to what we see, or stay as a 'ideal idea' of something that doesn't exist. How it then can be accepted to have a real influence I don't know. I could describe the sun as the eye of the mythical Kee, whose rays pierce me with her mystical powers, but I prefer a more prosaic definition. And so those mathematical spaces, if we expect them to influence our day to day experiences, must 'exist' in some more way than just as a mathematical space set. If I now make sense here.
==

You could of course assume us to be some data bits, in some electronic space, or holographic. But that doesn't explain what we are and experience. I prefer a prosaic definition first, a conceptual only when I find my 'prosaic definitions' to end, and I haven't reached that state yet.
« Last Edit: 07/07/2011 00:56:58 by yor_on »
 

Offline Mr. Data

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« Reply #65 on: 06/07/2011 22:21:46 »
u \wedge d = A(u \otimes d)

where A is the anti-symmetric operator. This means

(ui dj - dj ui)

(u Λ v)(a,b) = A(u \otimes d)(a,b)

=1/2(u(a)d(b) - u(b)d(a))

(*1)ijk = εijk

Where * is the hodge star, this relationship can be understood if you know that it is the hodge star of the identity element in 3 dimensions.

Four dimensional analysis can be neglected if you take the idea that the vacuum is spacelike in nature and only timelike in psychological experience. In fact, many papers that have been written on a similar paradox, the time problem of QM seem to indicate that time does not exist.

This is where you can violate Lorentz invariance.
« Last Edit: 06/07/2011 22:24:56 by Mr. Data »
 

Offline Mr. Data

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« Reply #66 on: 06/07/2011 22:29:48 »
Any 'geometrical representation' seems, to me that is, to build on the idea of 'dimensions'? The way you define it mathematically should either translate to what we see, or stay as a 'ideal idea' of something that doesn't exist. How it then can be accepted to have a real influence I don't know. I could describe the sun as the eye of the mythical Kee, whose rays pierce me with her mystical powers, but I prefer a more prosaic definition. And so those mathematical spaces, if we expect them to influence our day to day experiences, must 'exist' in some more way more than just as a mathematical space set. If I now make sense here.
==

You could of course assume us to be some data bits, in some electronic space, or holographic. But that doesn't explain what we are and experience. I prefer a prosaic definition first, a conceptual only when I find my 'prosaic definitions' to end, and I haven't reached that state yet.

Yes it should relate to something physical, and if you work out the equations for a Hamiltonian that satisfies E=δMc^2 where the two possibilities lead two positive solutions and negative solutions. It may, as I have suspected, refer to an energy density of two states of measure as found in the Dirac Equation, which means the equations could be readily used to satisfy that equation by merging the idea that there is some abstract space which is a dynamical change in the structure of a particle.
 

Offline yor_on

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« Reply #67 on: 06/07/2011 22:39:06 »
Ah okay, then we agree on that one :)
And welcome to the forum, if now nobody have said it.

The Hodge star is a geometric function related to the metric you define, if I understands it right? You define reality as 'time-like psychologically' here? Assume you are in a coma, also define it such as I do from 'locality', meaning that I'm the sole representation of this unique 'frame of reference' that psychologically follows me around, by me defined as the one invariant 'thing' that never changes consisting of a 'intrinsic' time experience and 'c'. Why would the translations of others fit the experienced 'time' I find when I wake up? If time can be defined as a 'psychological state'?

Of course it depend on how you define that state as 'psychological', but that's also where I find it hard to see.
 

Offline Mr. Data

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« Reply #68 on: 06/07/2011 22:48:50 »
In short, it seems that it can be acceptable to assume that potential energy can create mass. To explain mass, you need to explain it as a charge from the potential field φ. To do this you need to evaluate the field density to a refined part of space. Calculating this would have a value of:

ρ ≈ g(Mφ)

where the local parameters exist on both sides, so ρ equals a local density energy parameter. Because we have allowed ourselves to take some arbitrary value of φ, this potential energy could be contributed to real mass! There is even a process which should fundamentally explain if the potential actually contributes to anything real, through the confinement potential. This is a quark potential smush of information. It all conrtibutes to inertial mass when reaching a certain energy on ∫|ψ|, which would be some interaction. The interaction of φ and M would imply it's own charge conservation: this means an interaction term may be constructed from: ψ*ψM . Whatever or however we construct this field is irrelevent at this time. All that needs to be known is that the mass of a particle is a charge in itself, and that the mass of most particles involve the potential gradients of quark interactions. So in principle, expecting energy from a potential φ has been given a stamp of approval.
 

Offline yor_on

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« Reply #69 on: 06/07/2011 22:58:20 »
If I'm reading you right you define it the same way I treat 'frames of reference', as strictly locally? It's a 'psychological identifier' defining each one of us intrinsically, from where we observe 'reality', (as in all other 'frames of reference'). Is that a correct statement? If so :)

That's interesting, didn't know that one.

I need to read up on Hodge stars Mr Data :)
It's a new one to me.
 

Offline Mr. Data

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« Reply #70 on: 06/07/2011 23:05:34 »
If I'm reading you right you define it the same way I treat 'frames of reference', as strictly locally? It's a 'psychological identifier' defining each one of us intrinsically, from where we observe 'reality', (as in all other 'frames of reference'). Is that a correct statement? If so :)

That's interesting, didn't know that one.

I need to read up on Hodge stars Mr Data :)
It's a new one to me.

Think more on the EM-field ''way of things''. A particle only experiences a charge due to EM effects as it moves through an EM-field. Think now of applying this idea to mass, as a charge itself on the system. A particle moving in a gravitational field will experience a mass. You know, in a classical criteria, Nordstrom predicted the same thing by saying the density of mass depended on the gravitational field

box φ = ρ

Taking this literally, there should be intrinsic conditions in why certain parts of an equation disappear. Thus it is understood in terms of learning the limits of this process.
 

Offline Mr. Data

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« Reply #71 on: 06/07/2011 23:10:46 »
If you want charge in this, you must make sure if you ever write it in terms of density, it is a squared quantity:

ψ*ψe2M

I'm wondering if M needs to be extended a power, but I am not sure right now. I'm stuck between several things right now.



 

Offline yor_on

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« Reply #72 on: 06/07/2011 23:17:45 »
Yes, I can see the analogue, but in a geodesic there is no weight? So we need to define it to inertia, as I understands it, not 'gravity' as the overall term. As when you resting in your bed being 'still', still will feel that 'gravity' acting on you. That is if you accept that we relativistically can define Earth as being at rest for this? Or is there a definition that defines it otherwise?
=

If you define a uniform motion as taking you from 'A' to 'B' in some positional system (in deep space), then you will find 'inertia' existing, but you won't find gravity? Maybe that's the best example of how I think. There is naturally the question of invariant mass moving with you, but you will still find yourself weightless. Still, if you imagine that all invariant mass (particles) always is coupled to a 'gravity', however weak it may be in a uniform motion, then we may agree. But using that definition we now have destroyed the idea of all uniform motions being equal (in a black room scenario)? I'm not sure there? Can one keep the definitions, the invariant mass was there before too, wasn't it? But in Einsteins universe gravity is a result of geometry, not 'forces' and 'quanta'? It's a hard nut to crack this one.
==

And even then I have severe trouble seeing why the Higgs boson/field would threat uniform motion differently than a accelerating? How can it define the difference there, assuming that their 'speeds' are identical at some 'instant', they should be treated the same by the Higg mechanism, that is if we define them as 'clinging to motion'? I need to look this one up.
=

Then you would have inertia as the invariant definition of a Higgs particle (relative rest mass), with 'gravity' as ? Potential? And thinking some more, it would also question the definition of all uniform motions being relative, as Einstein defined it. That as we now would have a universal frame acting upon us at all times. In Einsteins definition inertia has nothing to do with a uniform motion, only with the change of it into some acceleration/deceleration.
« Last Edit: 07/07/2011 00:49:40 by yor_on »
 

Offline Mr. Data

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« Reply #73 on: 06/07/2011 23:35:21 »
Assume you are in a coma, also define it such as I do from 'locality', meaning that I'm the sole representation of this unique 'frame of reference' that psychologically follows me around, by me defined as the one invariant 'thing' that never changes consisting of a 'intrinsic' time experience and 'c'. Why would the translations of others fit the experienced 'time' I find when I wake up? If time can be defined as a 'psychological state'?

Of course it depend on how you define that state as 'psychological', but that's also where I find it hard to see.

As painfully as I want to answer this - I can only appeal to authority, that QM and genetic testing seems to imply an dependance on how our evolution plays a part if not the whole thing of why anything experiences a time-frame. I don't state this in a frivilous nature: If we experience time or any duration which can be called a frame of time, then there exists the gene capable of making that happen. If we had no sense of time (absent of the Suorachiasmatic Nucleus) then what theory of relativity would we readily assume, noting also that only a very small curvature has been noticed in the universe.
 

Offline yor_on

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« Reply #74 on: 06/07/2011 23:41:29 »
You are introducing new terms here.
Now I will have to check up the Suorachiasmatic Nucleus too :)
 

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