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# Spiral Structural Fractal Index (SSFi) in QM

## 25 posts in this topic

I want to attach my notes scribbled last night whilst getting inspiration whilst visualising subatomic partcles as fractal helices, or 'spirals made from spirals'. The smallest scale of a mechanical screw helix configuration is the graviton. A spiral of gravitons is a gluon. The next fractal size up in the spiral world is the magnetic field size and after that is the electric field size. This certainly has potential to solve the ambiguities still present when thinking about the latest LHC flocking effect which has been observed, see here LHC - proton collisions appeared to be synchronizing their flight paths, like flocks of birds. Anybody get the picture?

Edited by Humblemun

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Your imagery still fails to provide an origin for the fundamental characteristics of elementary force carriers.

Quantum field theory (QFT) describes the existence of a mathematical abstraction called a "gauge field". These gauge fields have generator operations. If QFT describes reality, than each generator (in a mathematical description) should correspond to a force carrying boson (in a physical description).

What gauge fields exist? Well the three simplest algebras are the SU(1), SU(2), and SU(3) algebras.

• The first, SU(1), is the set of complex numbers (i.e. 1x1 matrices) on the unit circle. This has a single generator (i.e. the number 1. Every other number in the complex plane can be "generated" by multiplying a scalar by this number. This is a really trivial situation).
• The second, SU(2), is the set of complex 2x2 matrices with determinant 1. This has three generators (basically the Pauli matrices - every 2x2 matrix with a non-zero determinant can be constructed by a linear superposition of these matrices).
• The third, SU(3), is the set of complex 3x3 matrices with determinant 1. This has eight generators (the Gell-Mann matrices).

Guess what?

• The electromagnetic field has a single boson (the photon). This is a boson that only possesses a spin (e.g. 1 quantum number).
• The flavor field (weak nuclear force) has three bosons (the W+, W- and Z0 bosons). These bosons have spin (spin-1) and electric charge (e.g. 2 quantum numbers, although note that the Z0 has a charge of 0).
• The color field (strong nuclear force) has eight bosons (the various types of gluons). These have spin (spin-1) and two color "charges" (e.g. 3 quantum numbers).

Now, unlike the other bosons, the flavor bosons (the W+, W- and Z0) have a non-zero mass. As we might expect from this, the flavor force is incredibly weak (hence the common name, "weak nuclear force"). These bosons can also accomplish P- and CP-breaking interactions, while the other bosons cannot.

This oddity can be explained by considering the possible merger of two gauge fields: namely a SU(1) x SU(2) algebra. This would have 4 generators (dubbed W+, W-, W0, and B0 corresponding to triplet and singlet configurations, respectively). If circumstances (such as decreasing below a critical energy) cause this algebra to be broken, i.e.:

SU(1) x SU(2) ---> SU(1), SU(2)

Then the Higg's mechanism (i.e. the action of an SU(2) doublet spinor on these fields) will spontaneously cause the creation of mass factors for the gauge bosons of the SU(2) group (here the combined gauge bosons W0 and B0 combine in a superposition to form the split gauge bosons Z0 and the photon).

-----------------------

Now generators of SU(1), SU(2) and SU(3) algebras are not easy to visualize, unlike spirals. But this treatment of elementary forces provides a lot of simple predictive power.

For example, the color field is still somewhat hypothetical : we have not yet observed individual gluons, and everything we have created in the lab so far has been "color-neutral". However the intranuclear interactions we have observed are consistent with an SU(3) algebra.

As another example, the existence of the three flavor bosons was predicted decades before they were discovered.

Finally, the existence of the Higg's boson (and the energy range where it "should" be) is predicted from consideration of SU(1) x SU(2) symmetry breaking.

Is the gravitational field described by a SU(4) algebra? Some theories consider this possibility (e.g. the "D4-D5-E6" model, see here). Other theories consider gravity to be a second-rank SU(1) field: we know from the description of General Relativity that if there is only one graviton it must be spin-2 (e.g. 1 quantum number, but more possible polarizations than the spin-1 photon).

Playing with Lie algebra provides definite predictions on how many force carrying bosons one should look for, and how many quantum numbers are required to define them.

Drawing spirals does not. Your models are useful as analogies for certain situations, but they shouldn't attempt to replace the full theory.

------------

[DISCLAIMER: I have made numerous simplifications and even some technical inaccuracies in an attempt to portray the algebraic beauty of QFT to a non-mathematical audience. For example, SU(1) really is U(1), since putting the 'S' is pointless in a scalar group, but I wanted a consistent notation.]

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Your imagery still fails to provide an origin for the fundamental characteristics of elementary force carriers.

Quantum field theory (QFT) describes the existence of a mathematical abstraction called a "gauge field". These gauge fields have generator operations. If QFT describes reality, than each generator (in a mathematical description) should correspond to a force carrying boson (in a physical description).

What gauge fields exist? Well the three simplest algebras are the SU(1), SU(2), and SU(3) algebras.

• The first, SU(1), is the set of complex numbers (i.e. 1x1 matrices) on the unit circle. This has a single generator (i.e. the number 1. Every other number in the complex plane can be "generated" by multiplying a scalar by this number. This is a really trivial situation).
• The second, SU(2), is the set of complex 2x2 matrices with determinant 1. This has three generators (basically the Pauli matrices - every 2x2 matrix with a non-zero determinant can be constructed by a linear superposition of these matrices).
• The third, SU(3), is the set of complex 3x3 matrices with determinant 1. This has eight generators (the Gell-Mann matrices).

Guess what?

• The electromagnetic field has a single boson (the photon). This is a boson that only possesses a spin (e.g. 1 quantum number).
• The flavor field (weak nuclear force) has three bosons (the W+, W- and Z0 bosons). These bosons have spin (spin-1) and electric charge (e.g. 2 quantum numbers, although note that the Z0 has a charge of 0).
• The color field (strong nuclear force) has eight bosons (the various types of gluons). These have spin (spin-1) and two color "charges" (e.g. 3 quantum numbers).

Now, unlike the other bosons, the flavor bosons (the W+, W- and Z0) have a non-zero mass. As we might expect from this, the flavor force is incredibly weak (hence the common name, "weak nuclear force"). These bosons can also accomplish P- and CP-breaking interactions, while the other bosons cannot.

This oddity can be explained by considering the possible merger of two gauge fields: namely a SU(1) x SU(2) algebra. This would have 4 generators (dubbed W+, W-, W0, and B0 corresponding to triplet and singlet configurations, respectively). If circumstances (such as decreasing below a critical energy) cause this algebra to be broken, i.e.:

SU(1) x SU(2) ---> SU(1), SU(2)

Then the Higg's mechanism (i.e. the action of an SU(2) doublet spinor on these fields) will spontaneously cause the creation of mass factors for the gauge bosons of the SU(2) group (here the combined gauge bosons W0 and B0 combine in a superposition to form the split gauge bosons Z0 and the photon).

-----------------------

Now generators of SU(1), SU(2) and SU(3) algebras are not easy to visualize, unlike spirals. But this treatment of elementary forces provides a lot of simple predictive power.

For example, the color field is still somewhat hypothetical : we have not yet observed individual gluons, and everything we have created in the lab so far has been "color-neutral". However the intranuclear interactions we have observed are consistent with an SU(3) algebra.

As another example, the existence of the three flavor bosons was predicted decades before they were discovered.

Finally, the existence of the Higg's boson (and the energy range where it "should" be) is predicted from consideration of SU(1) x SU(2) symmetry breaking.

Is the gravitational field described by a SU(4) algebra? Some theories consider this possibility (e.g. the "D4-D5-E6" model, see here). Other theories consider gravity to be a second-rank SU(1) field: we know from the description of General Relativity that if there is only one graviton it must be spin-2 (e.g. 1 quantum number, but more possible polarizations than the spin-1 photon).

Playing with Lie algebra provides definite predictions on how many force carrying bosons one should look for, and how many quantum numbers are required to define them.

Drawing spirals does not. Your models are useful as analogies for certain situations, but they shouldn't attempt to replace the full theory.

------------

[DISCLAIMER: I have made numerous simplifications and even some technical inaccuracies in an attempt to portray the algebraic beauty of QFT to a non-mathematical audience. For example, SU(1) really is U(1), since putting the 'S' is pointless in a scalar group, but I wanted a consistent notation.]

I appreciate you're mathematical and technical expertise to describe the current mainstream understanding sepulchrave. It's the accurate simulation model of a hydrogen bond between two hhydrogen nuclei which is needed imo.

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I appreciate you're mathematical and technical expertise to describe the current mainstream understanding sepulchrave. It's the accurate simulation model of a hydrogen bond between two hhydrogen nuclei which is needed imo.

I have a new picture of the three quarks which make up a hydrogen nuclei, i.e. a proton. See attached. It's the fast spinning ion which creates the hydrogen bond by giving the emitted gravitons a larger helical form!

Edited by Humblemun

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Sure. But:

1. The only way of charge-balancing quarks in neutrons and protons is to give one quark ("up quark") a +2/3 charge and the other quark ("down quark") a -1/3 charge. If the charges are equal, you won't get a neutral neutron and an +1 proton. How does your model explain why different helicities of spirals have different charges?
2. Drawing a proton as three interlinked-rings doesn't give any information about the magnitude of spin, or how they "emit gravitons".
3. In a free proton, how is the central axis of these interlinked-rings defined? We know from experiment that in the absence of external fields a proton does not have a preferred spin axis.
4. The hydrogen bond in H2 is due to electrons. Electrons do not have any fine structure that is on the same scale as quarks.
5. The hydrogen bond in H2 is easily visualized by considering the overlap of s-type electron wavefunctions. This overlap can either be symmetric ("bonding") or anti-symmetric ("anti-bonding"). The potential energy of this overlap, the bond length, and the energy separation between bonding and anti-bonding states can all be calculated from the Schrodinger equation and agree quite well with experiment.
6. I'm not sure that it is wise to post letterheads containing your actual address on the internet.

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Sure. But:

1. The only way of charge-balancing quarks in neutrons and protons is to give one quark ("up quark") a +2/3 charge and the other quark ("down quark") a -1/3 charge. If the charges are equal, you won't get a neutral neutron and an +1 proton. How does your model explain why different helicities of spirals have different charges?
2. Drawing a proton as three interlinked-rings doesn't give any information about the magnitude of spin, or how they "emit gravitons".
3. In a free proton, how is the central axis of these interlinked-rings defined? We know from experiment that in the absence of external fields a proton does not have a preferred spin axis.
4. The hydrogen bond in H2 is due to electrons. Electrons do not have any fine structure that is on the same scale as quarks.
5. The hydrogen bond in H2 is easily visualized by considering the overlap of s-type electron wavefunctions. This overlap can either be symmetric ("bonding") or anti-symmetric ("anti-bonding"). The potential energy of this overlap, the bond length, and the energy separation between bonding and anti-bonding states can all be calculated from the Schrodinger equation and agree quite well with experiment.
6. I'm not sure that it is wise to post letterheads containing your actual address on the internet.

You need to read my essay to get a picture of what I'm talking about Reality Was Born Analog But Will Digital Die? by Alan Lowey. I appreciate your questioning but I'm trying to think abstractly to start with and refine my ideas to fit the experimental results. The 'threeness' of quarks is something I'm starting with combined with stability and longevity. What makes a neutron hang out with a proton for example. The idea of gravitons being emitted at an even smaller scale than the quarks is of paramount importance to understanding where I'm coming from. I think I'm onto something here. Give me some more time coz I'm making progress..Do you have any pictorial representations of the standard model of the nucleus which might aid me sepulchrave?

edit* I just read this from Wikipedia:

Spin is an intrinsic property of elementary particles, and its direction is an important degree of freedom. It is sometimes visualized as the rotation of an object around its own axis (hence the name "spin"), though this notion is somewhat misguided at subatomic scales because elementary particles are believed to be point-like.[53]

Spin can be represented by a vector whose length is measured in units of the reduced Planck constant ħ (pronounced "h bar"). For quarks, a measurement of the spin vector component along any axis can only yield the values +ħ/2 or −ħ/2; for this reason quarks are classified as spin-1⁄2 particles.[54] The component of spin along a given axis—by convention the z axis—is often denoted by an up arrow ↑ for the value +1⁄2 and down arrow ↓ for the value −1⁄2, placed after the symbol for flavor. For example, an up quark with a spin of +1⁄2 along the z axis is denoted by u↑.[55]

Do you believe elementary particles to be point-like sepulchrave, as the standard model dictates??

Edited by Humblemun

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The 'threeness' of quarks is something I'm starting with combined with stability and longevity.

I trust you realize that `threeness' or quarks isn't unique, it just `happens to be' quite stable. We know of 2-quark states (mesons), and we may have observed 4-quark states (so called tetraquarks).

Particles with an even number of quarks have integer spins, and therefore are massive bosons (but not gauge bosons, as I discussed above). Since bosons tend to form condensates (and therefore can stack up almost infinitely in a nucleus), we don't expect to see even quark states floating around normally.

A 1-quark state is not stable because it can't be color neutral.

A 5-quark state (the pentaquark) is theoretically possible (but the consensus is that it has not yet been observed).

It is expected that the more quarks you cram into a particle, the less stable that particle is.

What makes a neutron hang out with a proton for example.

The common model is Residual Strong Nuclear Force. Even though each proton and neutron is color neutral, since they are so close together they can exchange virtual quark/gluon clusters. This exchange creates an attractive force.

One nice thing about this is that it is analogous to the well-known phenomena of van der Waals bonding in chemistry. In this bonding, even though each atom/molecule may be electrically neutral, they are still close enough that they can exchange virtual electron/photon clusters. This exchange is what holds together the carbon sheets in graphite, for example.

van der Waals bonding is much much weaker than "proper" electrical bonding (covalent or ionic, for example). Similarly, nuclear bonding is much much weaker than "proper" strong nuclear force bonding (i.e. it is much easier to split an atom apart - done every day in nuclear power plants, for example - than it is to break a proton apart - something which I don't think has been clearly observed yet).

In fact, I believe that 2-quark states (mesons) are the force carriers for nuclear bonding.

The idea of gravitons being emitted at an even smaller scale than the quarks is of paramount importance to understanding where I'm coming from. I think I'm onto something here. Give me some more time coz I'm making progress..Do you have any pictorial representations of the standard model of the nucleus which might aid me sepulchrave?

Unfortunately I don't think visual models involve strong nuclear force exist. This is because gluons are self-interacting, so actually calculating the probability distributions of simple quark-gluon states is fiendishly complicated.

All the useful pictures are of extremely simplistic things, like color balancing (see here). I'm not sure how much this will help.

There is some belief that the protons and neutrons in a nucleus stack the same way as electrons do in an atom (i.e. s-, p-, d-, f-type symmetry in n = 1, 2, 3,... energy levels). These wavefunctions are easy to visualize (see here for a 2D picture, or here for a 3D picture), but this hypothesis hasn't been properly proven (or dis-proven), again due to the complexity of calculating things involving gluons.

There is some useful imagery for molecular bonds (much simpler to calculate, just involving photons/electrons/protons). For example the `electron cloud' distribution in H + H --> H2 is visualized here (the bonding arrangement is on the left, the anti-bonding arrangement is on the right).

The energy levels of these bonds can easily be drawn as well, see here.

Do you believe elementary particles to be point-like sepulchrave, as the standard model dictates??

Yes - in the sense that an elementary particle can always be confined to a region of arbitrarily small size. [subject, of course, to the assumption that space is truly continuous. If space is discrete, than elementary particles can always be confined to that quantum of space.]

I believe that the `size' of an elementary particle is dictated by it's interactions. For example, I would argue that a 1s electron in a hydrogen atom is relatively large - since the potential from the nucleus is relatively weak. The average radial distribution peaks at about 0.5 angstroms (the ``Bohr radius'', a name from an earlier and cruder model of the atom), so I would argue that 0.5 angstroms (0.05 nm) is the ``characteristic size'' of a 1s electron in hydrogen.

A 1s electron in Uranium, on the other hand, would be about 100 times (very roughly, this isn't an accurate calculation or anything) smaller in size because the potential energy of the nucleaus is about 100 times larger than that of the Hydrogen atom.

The ``characteristic size'' of electrons in a high-energy collision in an accelerator would be considerably smaller than that.

So to summarize my belief: since you can force an elementary particle into a box of arbitrary size, you can think of an elementary particle as ``point-like''. However, unless that particle is actually forced into an extremely small region, it won't necessarily behave as ``point-like''.

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I trust you realize that `threeness' or quarks isn't unique, it just `happens to be' quite stable. We know of 2-quark states (mesons), and we may have observed 4-quark states (so called tetraquarks).

Particles with an even number of quarks have integer spins, and therefore are massive bosons (but not gauge bosons, as I discussed above). Since bosons tend to form condensates (and therefore can stack up almost infinitely in a nucleus), we don't expect to see even quark states floating around normally.

A 1-quark state is not stable because it can't be color neutral.

A 5-quark state (the pentaquark) is theoretically possible (but the consensus is that it has not yet been observed).

It is expected that the more quarks you cram into a particle, the less stable that particle is.

The common model is Residual Strong Nuclear Force. Even though each proton and neutron is color neutral, since they are so close together they can exchange virtual quark/gluon clusters. This exchange creates an attractive force.

One nice thing about this is that it is analogous to the well-known phenomena of van der Waals bonding in chemistry. In this bonding, even though each atom/molecule may be electrically neutral, they are still close enough that they can exchange virtual electron/photon clusters. This exchange is what holds together the carbon sheets in graphite, for example.

van der Waals bonding is much much weaker than "proper" electrical bonding (covalent or ionic, for example). Similarly, nuclear bonding is much much weaker than "proper" strong nuclear force bonding (i.e. it is much easier to split an atom apart - done every day in nuclear power plants, for example - than it is to break a proton apart - something which I don't think has been clearly observed yet).

In fact, I believe that 2-quark states (mesons) are the force carriers for nuclear bonding.

Unfortunately I don't think visual models involve strong nuclear force exist. This is because gluons are self-interacting, so actually calculating the probability distributions of simple quark-gluon states is fiendishly complicated.

All the useful pictures are of extremely simplistic things, like color balancing (see here). I'm not sure how much this will help.

There is some belief that the protons and neutrons in a nucleus stack the same way as electrons do in an atom (i.e. s-, p-, d-, f-type symmetry in n = 1, 2, 3,... energy levels). These wavefunctions are easy to visualize (see here for a 2D picture, or here for a 3D picture), but this hypothesis hasn't been properly proven (or dis-proven), again due to the complexity of calculating things involving gluons.

There is some useful imagery for molecular bonds (much simpler to calculate, just involving photons/electrons/protons). For example the `electron cloud' distribution in H + H --> H2 is visualized here (the bonding arrangement is on the left, the anti-bonding arrangement is on the right).

The energy levels of these bonds can easily be drawn as well, see here.

Yes - in the sense that an elementary particle can always be confined to a region of arbitrarily small size. [subject, of course, to the assumption that space is truly continuous. If space is discrete, than elementary particles can always be confined to that quantum of space.]

I believe that the `size' of an elementary particle is dictated by it's interactions. For example, I would argue that a 1s electron in a hydrogen atom is relatively large - since the potential from the nucleus is relatively weak. The average radial distribution peaks at about 0.5 angstroms (the ``Bohr radius'', a name from an earlier and cruder model of the atom), so I would argue that 0.5 angstroms (0.05 nm) is the ``characteristic size'' of a 1s electron in hydrogen.

A 1s electron in Uranium, on the other hand, would be about 100 times (very roughly, this isn't an accurate calculation or anything) smaller in size because the potential energy of the nucleaus is about 100 times larger than that of the Hydrogen atom.

The ``characteristic size'' of electrons in a high-energy collision in an accelerator would be considerably smaller than that.

So to summarize my belief: since you can force an elementary particle into a box of arbitrary size, you can think of an elementary particle as ``point-like''. However, unless that particle is actually forced into an extremely small region, it won't necessarily behave as ``point-like''.

All very useful info sepluchrave, thanks very much. I'm out of internet time so need more time to digest what you've said. I'm currently toying with fractal helix rings which are twisted into Mobius figure-of-eights. It's looking fruitful..Bye for now..

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All very useful info sepluchrave, thanks very much. I'm out of internet time so need more time to digest what you've said. I'm currently toying with fractal helix rings which are twisted into Mobius figure-of-eights. It's looking fruitful..Bye for now..

This quote from Wikipedia on Bose-Einstein condensates caught my attention:
Compared to more commonly encountered states of matter, Bose–Einstein condensates are extremely fragile. The slightest interaction with the outside world can be enough to warm them past the condensation threshold, eliminating their interesting properties and forming a normal gas. It is likely to be some time before any practical applications are developed...Vortices in Bose–Einstein condensates are also currently the subject of analogue gravity research, studying the possibility of modeling black holes and their related phenomena in such environments in the lab.

and this one from Van der Waals forces:

All intermolecular/van der Waals forces are anisotropic (except those between two noble gas atoms), which means that they depend on the relative orientation of the molecules. The induction and dispersion interactions are always attractive, irrespective of orientation, but the electrostatic interaction changes sign upon rotation of the molecules. That is, the electrostatic force can be attractive or repulsive, depending on the mutual orientation of the molecules. When molecules are in thermal motion, as they are in the gas and liquid phase, the electrostatic force is averaged out to a large extent, because the molecules thermally rotate and thus probe both repulsive and attractive parts of the electrostatic force. Sometimes this effect is expressed by the statement that "random thermal motion around room temperature can usually overcome or disrupt them" (which refers to the electrostatic component of the van der Waals force). Clearly, the thermal averaging effect is much less pronounced for the attractive induction and dispersion forces.

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Here's my latest offerings. They don't look much but I'm making good progress sep.

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I've just clicked a bit..All the forces can be explained by the Archimedes screw representing the structural analogue graviton. All forces greater than the 'gravity force' are due to local irregularities of structure which exaggerate the asymmetry of the graviton-like structure itself. A graviton should be modelled as vector quantity. All the forces can be explained by the relative flux density of gravitons.

Edited by Humblemun

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Ok...

1. What kind of ``asymmetry'' can you have in the spiral structure and still have it able to operate like an Archimedes screw?
2. Why do these asymetries in the graviton result in forces much stronger than gravity?
3. If every force is based on gravitons, why is the magnitude of the electromagnetic field emitted by a proton and an electron the same, while the magnitude of gravitational field emitted by these particles is so different?
4. How is it possible for an object to emit only a graviton moving to the left? Shouldn't they come out in all directions?

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Sep, it can also explain the galaxy rotation curve conundrum!

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Sep, it can also explain the galaxy rotation curve conundrum!

Not really.

The conventional gravitational rotation curve prediction is based on applying Newtonian gravity to the outer halo of the galaxy. In this method, the halo of the galaxy is modeled as a disk in the plane of rotation. If ``in plane'' stars experienced a greater gravitational force that ``out of plane stars'' - as you are suggesting - then the calculated rotation curve would need be scaled, but the basic shape of the curve would not change.

As far as I have seen, there 3 models that quantitatively predict a plateau in the rotational speeds of galaxies:

1. Newtonian gravity is ok, but there is a significant quantity of unseen mass (a.k.a. dark matter) in the halo of the galaxy.
2. Newtonian gravity is not ok, Einsteinian relativistic effects like frame-dragging, and anti-symmetric elements and cross terms in the metric need to be considered.
3. Neither Newtonian gravity nor Einsteinian relativity is ok, but conformal Weyl relativity needs to be considered.

Each of these methods ``fixes'' the galactic rotation curves with roughly the same accuracy. There is more additional evidence in favour of dark matter though (uniformity of WMAP background, large-scale structure of the Universe, the dynamics of the bullet cluster, etc.).

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No, it really does. You just haven't given it enough thought Sep.

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No, it really does. You just haven't given it enough thought Sep.

Perhaps.

Can you elaborate on this issue?

First, while your model suggests that the forces involved galaxy rotation would be different than that predicted by Newtonian gravity, is it still acceptable to use Newtonian mechanics to describe the rotation of stars in the new gravity field?

In other words, the galaxy rotation curves are modeled using FN = ma, where FN is Newtonian gravity. Can we simply replace Newtonian gravity with ``Lowey gravity'' (FL, perhaps) and solve for a new rotation curve?

Second, existing galaxy rotation curves are modeled by assuming that most of the mass of the galaxy is in the ``centre bulge''. Is this assumption still valid?

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Perhaps.

Can you elaborate on this issue?

First, while your model suggests that the forces involved galaxy rotation would be different than that predicted by Newtonian gravity, is it still acceptable to use Newtonian mechanics to describe the rotation of stars in the new gravity field?

In other words, the galaxy rotation curves are modeled using FN = ma, where FN is Newtonian gravity. Can we simply replace Newtonian gravity with ``Lowey gravity'' (FL, perhaps) and solve for a new rotation curve?

Second, existing galaxy rotation curves are modeled by assuming that most of the mass of the galaxy is in the ``centre bulge''. Is this assumption still valid?

You make some good points and I've just had some additional insights just of last night:

The helical screw model gives matter a new fundamental shape and dynamics which the standard model lacks imo. This non-spherical emission of gravitons is in stark contrast to the Newtonian/Einsteinian acceptance that "all things exert a gravitatinal field equally in all directions". This asymmetry of the gravitational field allows for the stars to experience a greater pull towards the galactic plane, due to their rotation giving more order to the inner fluid matter of the stellar core. Both the structure of the emitter and the absorber of the gravity particles is important. It also has implications for hidden matter at the centre of the galaxies..

I've given the idea some more thought and come to the conclusion that the stars furthest from the galactic centre must have a more 'bipolar nature' than the matter of stars of the inner halo presumably. This is the reason they have wandered towards the galactic plane whilst the halo stars have not. The outer stars' configuration means they experience a greater interaction with the flux pattern of the graviton field. Are the stars of the outer arms simply spinning faster?? We are on the outer edge of a spiral arm and so this would fit with this hypothesis. Our sun could have spin which is higher that that of the average halo star. This relationship between spin and distance from the galactic centre is a fundamental feature which ties in with the suggested mechanism of their creation.

All that is needed is an additional factor of stellar spin speed as well as it's mass and distance from the galactic centre. The relationship should then give calculated values which match those of the observed. Is this something you could do Sepulchrave?

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All that is needed is an additional factor of stellar spin speed as well as it's mass and distance from the galactic centre. The relationship should then give calculated values which match those of the observed. Is this something you could do Sepulchrave?

Yes I think it is. It should be possible to model the Newtonian dynamics from an arbitrary gravity field, and use that to find a field that fits the observed data.

I've been thinking about this a bit, but I don't have the time right now to get into it properly. Maybe in a week or so, though.

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Yes I think it is. It should be possible to model the Newtonian dynamics from an arbitrary gravity field, and use that to find a field that fits the observed data.

I've been thinking about this a bit, but I don't have the time right now to get into it properly. Maybe in a week or so, though.

I'm really pleased you see some merit in the idea Sepulchrave. The deadline for comments on the competition essays is Tues 15th march at 11.59am. If at all possible, an equation in LateX would be most useful! I could then post it for posterity in the essay competition. You could be famous as being the first person to write a mathematical equation which describes the galaxy rotation curve using the additional spin term. I'm pursuing something else to do with climate cycles and in particular the 1,500 year climate cycle which I think is related to the dynamics of the Sun's innermost core. Wish me luck..

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Based on the following assumptions:

• Galaxies exist for billions of years, so the stars in the outer halo must be in relatively stable orbits,
• Almost all of the visible mass in the galaxy is at the galactic core,
• There is no ``hidden mass'' (i.e. dark matter), and
• Newtonian mechanics (F = ma) are valid for analyzing halo star trajectories,

We have the following assertions:

• The motion of the halo stars must be centripetal, and
• Any gravitational field exerted by the galaxy must be almost completely divergenceless in the halo.

The first assertion implies that there is a center-pulling force (F) on the halo stars (of mass m) creating a velocity (v) of:

F = mv
2
/ r

Where r is the distance the halo star is from the galactic core. For standard Newtonian gravity the force is:

F = GMm / r
2

Where G is the Gravitational constant, and M is the mass of the galactic core. The velocity of a halo star is then:

v = (GM / r)
0.5

To match to experimental data, we want the velocity of the halo start to be a constant - i.e. not depend on r. The easiest way of achieving this is to set the gravity to:

F = GMm / r

And then we have:

v = (GM)
0.5

This theory has two major problems with it:

• This force would ``break'' all existing planetary orbits, and
• This force has a non-zero divergence.

The second easiest approach is to add a term to Newtonian gravity. There is no ``spiral force'' that will work, such a force would constantly speed up the rotation of halo stars (or constantly slow down, depending on the direction), and the halo would either be flung off into space or collapse into the core. Since we do not observe this happening, we can rule it out.

We can't simply add rn terms to Newtonian gravity either, because they are not divergenceless, and would never cancel out the 1/r2 from Newtonian gravity unless they canceled out the force entirely (i.e. no centripetal motion).

The simplest solution that I can think of is to add some sort of gravitational equivalent to the Lorentz force as follows:

F = m (GM / r
2
+ bvr
n
)

Where b and n are to be determined.

This gives us a velocity of:

v = b / 2 r
n+1
+ r / 2 ( b
2
r
2n
- 4 GM / r
2
)
0.5

If we set n = -1, we then have a velocity of:

v = b / 2 + ( b
2
- 4 GM )
0.5

Which is independent of r, as desired.

Unfortunately... the only Lorentz-type field that is divergence-free has 1/r3 dependence, no 1/r.

If we don't use divergenceless fields, then we are basically postulating dark matter all over again.

It's in!

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It's in!

I am almost afraid to ask... what is ``in'' ?

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I am almost afraid to ask... what is ``in'' ?

The FQXi physics essay competition of course. FQXi Essay Contest - Is Reality Digital or Analog? \$10,000 1st prise. Thanks for our help.. Edited by Humblemun

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Oh my.

You didn't even read the post, did you?

Look: Any form of physics (Newtonian, Quantum, Relativity, etc.) is based on rules of the form:

influence
defines
motion

In you case, we were operating under the idea that Newtonian influence (i.e. the force of gravity) was incorrect, but the motion part (i.e. the ``dynamics'') was correct.

In my previous post I showed my reasoning that there is no way of getting a new force of gravity to match the galactic rotations without requiring some ``hidden'' mass (i.e. Dark matter).

Since I assume you don't agree with conventional Dark matter, the only recourse is to change the rules for motion. There are already (at least) three theories for this:

Each of these has unresolved problems that the Dark matter model does not.

The other problem with changing the rules for motion of course is that it has NOTHING do to with your model for the graviton.

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I've deduced that gravity is stronger on the equatorial plane of the Earth due to the difference in nature of the proton and neutron and the fluid dynamics of the inner core. It's too much to explain any longer Sepulchrave. It's a new way of thinking altogether derived from the discipline of simulation modelling rather than mathematical modelling. Thanks for the professional yet mainstream input you've given me. Best wishes, Humblemun.

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