Jump to content

Model for spin


robinpike

Recommended Posts

I have gone some way to reading around the subject in the last three days . One or two things seem to be coming home to me. Angular momentum is a very fundamental thing for the operation of the atom thus elements. The orbital angular momentum is slightly easier to understand and visualize to some extent as demonstrated by the diagram on previous postings. Although even their uncertainty or probability still tempts wonder. Despite their fuzzy clouds one can form a mental picture however approximate or inaccurate these diagrams appear. Then we come to the electron spin itself which is said to have angular momentum of two discrete values up spin and down spin. Here comes the rub! If NOT a simple spinning Top for reasons of maths inconsistencies or problems what is the nearest or nearer approximate model that we can visualize, even if it one to shoot down and move on to a more accurate model. Frank Wilczek in his recent book " the lightness of being" page 114 " in trying to understand complicated concepts or equations its good to have toy models". So is there anyone out there who has a good toy model of :- an electron

A) its movement generally , say in orbit ,

B) its movement in or by itself including the spin bit ,

C) its reality as a point, charge swirl, wiggling small mass energy or whatever lepton

D) its ability or lack of to stand still

E) any possible exclusion or coupling with another electron.

It seems to have originated way back as a fundamental particle within the plasma or shortly after the inflationary start to the Big Bang.

It has been mooted that one needs to penetrate maths to get the full picture. But surely we must cloth maths models with some form of philosophical idea !

Hi Mike,

Here is a video model of an electron spinning - does this help you at all?

Robin

Link to comment
Share on other sites

Hi Mike,

Here is a video model of an electron spinning - does this help you at all?

Robin

Robin I am not ignoring you, please do not think that. I have had a crazy weekend with two dogs. My mind has been addled with unwinding extendable leads about once every two seconds. Trying to get my head around electron spin this weekend will take me over the brink. As you no doubt realise I am very interested in the core drivers of the cosmos, and I definitely think one of the fundamental ones is down there in the two angular momentum ( spins ) associated with atomic particles. So this subject is not going to go away easily. I also think just saying " there's the maths just get on with it " is not sufficient. So I am very interested in discussing or exploring models to do with spin.

 

Although I have looked at a couple of your Video clips , I have not yet grasped YOUR core idea. Probably the dreaded Dogs.

 

If you have Six sentences ( I can Probably take 6 in ok. )

 

How would you describe your model, how the electrons are acting , in principle ?

 

mike

Link to comment
Share on other sites

Hi Mike,

 

Ok, I'll have a go...

 

1) The core feature of the model is constant movement in the shape of a strand of movement.

 

2) The electron, proton and photon are all constructed from the strands of movement.

 

3) Meaning that every explanation is visual, as the electron, proton and photon all have a shape and form (note, although maths is not the starting point, there is nothing to prevent the model being tested using maths).

 

4) The electron's properties of mass, inertia, momentum, spin, electric charge, electric field are all properties that come about from how the electron is constructed.

 

5) All electrons end up with the same amount of movement inside them, which means that they all have the same amount of mass, the same amount of inertia, the same amount of spin, the same amount of electric charge.

6) Without knowing how the electron is constructed, it would be nigh on impossible to explain how those properties have arisen - the best you could do would be to find those properties through experiment and state the results as equations.

 

7) All the explanations come about because of topology, I don't see how any theory which does not use topology as its basis could ever explain why the electron, proton and photon behave as they do - for example, the model shows how the uncertainty principle and quantum mechanics behavior are formed using Newtonian rules.

 

Ok, so I've used 7 sentences - but hope the above is clear and helps.

 

Robin

Edited by robinpike
Link to comment
Share on other sites

Robin

 

GREAT !

 

Just picking on 7

 

7) All the explanations come about because of topology, I don't see how any theory which does not use topology as its basis could ever explain why the electron, proton and photon behave as they do - for example, the model shows how the uncertainty principle and quantum mechanics behavior are formed using Newtonian rules.

 

In the 1980's I read a large tome by Cambridge University Press called " The New Physics. " I might still have it between here and Italy. If you wanted a look. Mind you , you might need to come over to Italy ! . It was all about string theory development as an idea. It featured TOPOLOGY as the base root to the strings. A quasi spherical minute surface with specified features that dictated the string particle. Is this your take too. Strings. ? Or is it just the Topology of a quasi spherical surface that you are featuring.? ( shhhh Going out D & D . don't mention the war ! )

Edited by Mike Smith Cosmos
Link to comment
Share on other sites

Hi Swansont, Can you expand in what way a bit more please...

 

As not sure in what way you are asking? I've had a quick look at some examples of dipoles, for example as in a molecule of sodium chloride, and the examples discuss a charge separation between positive and negative charges.

 

Do you mean, because the toroidal shape has negative charge spread around the ring?

 

Thanks



Hi Mike,

 

 

GREAT !

 

Just picking on 7

 

 

In the 1980's I read a large tome by Cambridge University Press called " The New Physics. " I might still have it between here and Italy. If you wanted a look. Mind you , you might need to come over to Italy ! . It was all about string theory development as an idea. It featured TOPOLOGY as the base root to the strings. A quasi spherical minute surface with specified features that dictated the string particle. Is this your take too. Strings. ? Or is it just the Topology of a quasi spherical surface that you are featuring.? ( shhhh Going out D & D . don't mention the war ! )

 

Hi Mike,

 

Yes that would be good if you could tell me a bit more about those ideas. A lot of the principles may be the same.

 

Note that the model I use doesn't require hidden dimensions, so as for the topology side of things, it is easy to describe their properties in pictures and videos.

 

Thanks, Robin

Link to comment
Share on other sites

Hi Swansont, Can you expand in what way a bit more please...

 

As not sure in what way you are asking? I've had a quick look at some examples of dipoles, for example as in a molecule of sodium chloride, and the examples discuss a charge separation between positive and negative charges.

 

Do you mean, because the toroidal shape has negative charge spread around the ring?

Yes. The field will not be that of a point charge. The standard model predicts a very small deviation, and experiment limits the distortion of the field. http://www.nature.com/nature/journal/v473/n7348/full/nature10104.html
Link to comment
Share on other sites

Hi Swansont,

 

I've had a look on the web about experiments that measure the electron dipole moment (if there is a dipole moment to find), and some of those mention how its presence would cause CP violation.

 

I found an article which, in its discussion, shows an example of uneven charge across a sphere which would give a dipole moment.

 

 

I can't paste the diagram from the article (it was on page numbered 3, quite a few pages in, which can be found by searching for "Figure 1.2:" in the following pdf file http://jila.colorado.edu/bec/CornellGroup/theses/stutz_thesis.pdf

 

[ Figure 1.2: If an electron EDM exists, the orientation between the electron’s electric (de) and magnetic (µ) dipole moments will change under a parity (P) or time-reversal (T) transformation. ]
The toroidal shape that I am using for the electron, does not in itself have any uneven charge distribution across its surface, but the shape as a whole is obviously not a sphere.
The experiments that measure the electron's dipole moment are complicated - can you describe a basic example of how the electron's dipole moment would show up?
I can then look at the toroidal model to see if it would contradict that example or not?
Also, the aspect of an electron's dipole moment causing CP violation, can that be explained in a simple example for me to consider as well?
Thanks, Robin
Edited by robinpike
Link to comment
Share on other sites

The toroidal shape that I am using for the electron, does not in itself have any uneven charge distribution across its surface, but the shape as a whole is obviously not a sphere.

 

Which means it has a dipole moment. Can you reconcile that with the dipole moment measurements that are thus far consistent with zero?

 

 

The experiments that measure the electron's dipole moment are complicated - can you describe a basic example of how the electron's dipole moment would show up?

 

I can then look at the toroidal model to see if it would contradict that example or not?

 

What do you mean by "how it would show up"? Do you mean the functional form of the field?

 

 

Also, the aspect of an electron's dipole moment causing CP violation, can that be explained in a simple example for me to consider as well?

It causes a CP violation because the electron has a magnetic moment, which does not change under a parity transformation, but an electric dipole moment does.

Link to comment
Share on other sites

 

Which means it has a dipole moment. Can you reconcile that with the dipole moment measurements that are thus far consistent with zero?

 

Still not sure on how the dipole experiments are measuring the dipole moment of the electron. What experiments I have found seem to be measuring the movement of molecules in electric fields. Those are too complicated for me to apply the principal of the experiment to the toroidal shape.

 

However, what the experimenters do say is that the electron's shape must be perfectly spherical for it to have no dipole moment.

 

So perhaps it would be easier to approach this problem the other way around.

 

In what way would the toroidal shape with negative charge on its surface behave differently to a sphere with negative charge on its surface, when both are in an electric field?

 

Thanks

Link to comment
Share on other sites

In what way would the toroidal shape with negative charge on its surface behave differently to a sphere with negative charge on its surface, when both are in an electric field?

 

In an inhomogeneous field, there could be a torque on the toroid.

Link to comment
Share on other sites

In an inhomogeneous field, there could be a torque on the toroid.

 

Wouldn't that also be true for the sphere? I'm trying to visualize how the toroidal shape would behave differently to the sphere. After all, it's not as if the charge on the toroidal shape is lop-sided?

Link to comment
Share on other sites

Wouldn't that also be true for the sphere? I'm trying to visualize how the toroidal shape would behave differently to the sphere. After all, it's not as if the charge on the toroidal shape is lop-sided?

 

Put a sphere in a 1/r^2 field of a point charge. On any off-axis (line from the point charge through the center of the sphere) point there is a force, there is one that mirrors it. No torque. Put a toroid in that field, oriented at some angle other than 0 or 90º. The force on a point has a corresponding point that is at a different distance, so it feels a different force, and thus a torque. You'd expect the electron to oscillate and radiate as a result.

Link to comment
Share on other sites

Thanks Swansont, that is a good starting point for me to consider.

 

The toroid is made up of strands of movement, whose heads and tails move at fixed speeds. This means that, for the toroid to move, the strands have to bunch up on one side of the ring, and thin out on the other side.

 

The toroid will then move forwards in the plane of its ring. (There are some other points to consider, such as inertia and momentum of this forward movement, but those points are not necessary for this discussion.)

 

If you consider the toroid shown in the video, it can move off in any direction that is in the plane of its ring, that is, it can move off in any horizontal direction.

 

However, for it to move in any other direction, such as upwards, the ring has to twist itself so that the plane of the ring is in that vertical direction.

 

So the toroid is not like a macro gyroscope of circular movement (which can be moved in any straight line direction without changing the plane of the gyroscope).

 

So to the example of the toroid in a field from a point charge.

 

First off, is it possible to perform the experiment using a field from a point charge? To me, that means a field from another electron, which I don't see how that is achieved, as electrons tend to move all over the place and not stay in one place, especially when approached by another electron?

 

Is it the case, that these experiments are done in a macro electric field, such as that between two plates of charge?

 

What exactly is the set up for me to consider?

 

For example,is a stream of electrons passed between, say horizontal plates, with one plate above and the other below the path of the electrons?

 

Can you give me a fuller description of the experiment for me to consider what oscillation is expected?

Link to comment
Share on other sites

Thanks Swansont, that is a good starting point for me to consider.

 

The toroid is made up of strands of movement, whose heads and tails move at fixed speeds. This means that, for the toroid to move, the strands have to bunch up on one side of the ring, and thin out on the other side.

 

I don't know what a strand of movement is.

 

The toroid will then move forwards in the plane of its ring. (There are some other points to consider, such as inertia and momentum of this forward movement, but those points are not necessary for this discussion.)

 

If you consider the toroid shown in the video, it can move off in any direction that is in the plane of its ring, that is, it can move off in any horizontal direction.

 

However, for it to move in any other direction, such as upwards, the ring has to twist itself so that the plane of the ring is in that vertical direction.

 

That would probably be another problem for your model. Any experimental evidence that electrons actually behave this way? (A question that should be asked at all stages of a evaluating a model). Can you reconcile that with Larmor precession? (the precession of the magnetic moment of the electron due to a magnetic field). If the electron precesses due to a magnetic field, but you also have this effect from an electric field, you'd expect that motion to show up too, wouldn't you?

 

So the toroid is not like a macro gyroscope of circular movement (which can be moved in any straight line direction without changing the plane of the gyroscope).

 

So to the example of the toroid in a field from a point charge.

 

First off, is it possible to perform the experiment using a field from a point charge? To me, that means a field from another electron, which I don't see how that is achieved, as electrons tend to move all over the place and not stay in one place, especially when approached by another electron?

 

Is it the case, that these experiments are done in a macro electric field, such as that between two plates of charge?

 

What exactly is the set up for me to consider?

 

For example,is a stream of electrons passed between, say horizontal plates, with one plate above and the other below the path of the electrons?

 

Can you give me a fuller description of the experiment for me to consider what oscillation is expected?

 

You'd have to read the literature to find the details.

Link to comment
Share on other sites

Toroid is unnatural shape.

Everything in nature wants to be sphere as close as possible.

Nature is full of examples: stars, planets, asteroids (with enough time, with enough of collisions they're more and more looking like sphere; liquid, plasma in cosmic space vacuum is quickly forming sphere), molecules, atoms. Sphere is optimal shape.

 

In toroid shape you would have to explain why particles don't collapse to inside.

 

Your theory also doesn't explain what happens to electron bound to nucleus when it's absorbing photon, and what happens when it's emitting photon.

 

You're modeling spin in electron. But every particle has spin, not just electron. Photon, electron, positron, proton, neutron, neutrino, all have spin which we can directly measure in devices.

If toroid shape is causing spin in electron, toroid shape must be also shape of all other Standard Model particles?

 

Do you saw this video?

http://en.wikipedia.org/wiki/File:Quantum_spin_and_the_Stern-Gerlach_experiment.ogv

 

http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment

Edited by Przemyslaw.Gruchala
Link to comment
Share on other sites

I don't know what a strand of movement is.

 

That is the heart of the model, and is as follows...

 

The model uses strands of movement to construct the electron, proton and photon. Each strand is the same as every other strand, and so for the model, it is the elementary particle. The tail of the strand has a fixed speed, as does the head of the strand, but the head moves faster than the tail. This stretches the strand until the head breaks free, the freed head becoming the force conveying strand in the model. After the head breaks free, the original strand repeats the process again and again.

 

The model uses the strands of movement to construct the electron, proton and photon, and the force conveying strands to produce the electric force, magnetism and gravity. So, does the model produce all the different phenomena that we observe? Well, I don't know, but the model does appear to be successful in basic things.

 

 

That would probably be another problem for your model. Any experimental evidence that electrons actually behave this way? (A question that should be asked at all stages of a evaluating a model). Can you reconcile that with Larmor precession? (the precession of the magnetic moment of the electron due to a magnetic field). If the electron precesses due to a magnetic field, but you also have this effect from an electric field, you'd expect that motion to show up too, wouldn't you?

 

In the model, a magnetic field is different to an electric field, and so it does not necessarily follow that there is a contradiction within the model. I have had a look at Larmor precession, but it is too complicated for me to follow through with the model and give you an answer (sorry).

 

In the model, magnetic fields are a lot more complicated than electric fields, and the best I have done so far with regards to magnetism, is to produce the deflection of two wires carrying currents. Of course I would like to say that the model can produce all magnetic phenomena, but at the moment, it is beyond me to know whether the model can do that.

 

To keep it to what I can do, I can discuss some other basic properties of this model of the electron, as well as its spin?

 

Such as mass, inertia, momentum, absorption / emission of a photon, energy of motion, electric charge, movement in an electric field, movement in a gravitational field.

 

In the model, these phenomena are all connected to the spin of the electron. (But for the moment, can we leave out aspects of relativity, as there are many scenarios to relativity, yes, many of which the model can do, but as an example, not sure about the relativistic Doppler shift of light.)

Link to comment
Share on other sites

robinpike, on 08 May 2013 - 09:10, said:

That is the heart of the model, and is as follows...

 

The model uses strands of movement to construct the electron, proton and photon. Each strand is the same as every other strand, and so for the model, it is the elementary particle. The tail of the strand has a fixed speed, as does the head of the strand, but the head moves faster than the tail. This stretches the strand until the head breaks free, the freed head becoming the force conveying strand in the model. After the head breaks free, the original strand repeats the process again and again.

The head goes in a random direction? Why does the force have spherical symmetry in nature while the electron does not, in this model? How do you get attraction?

robinpike, on 08 May 2013 - 09:10, said:

The model uses the strands of movement to construct the electron, proton and photon, and the force conveying strands to produce the electric force, magnetism and gravity. So, does the model produce all the different phenomena that we observe? Well, I don't know, but the model does appear to be successful in basic things.

It has to explain all things that the currently accepted model does. I'm asking about some pretty basic things.

 

robinpike, on 08 May 2013 - 09:10, said:

In the model, a magnetic field is different to an electric field, and so it does not necessarily follow that there is a contradiction within the model. I have had a look at Larmor precession, but it is too complicated for me to follow through with the model and give you an answer (sorry).

Electrons precess in a magnetic field, but your model seems to predict a different precession in an electric field, which, because they are separate effects, would seem to say that your model predicts something different if both fields are present.

 

robinpike, on 08 May 2013 - 09:10, said:

In the model, magnetic fields are a lot more complicated than electric fields, and the best I have done so far with regards to magnetism, is to produce the deflection of two wires carrying currents. Of course I would like to say that the model can produce all magnetic phenomena, but at the moment, it is beyond me to know whether the model can do that.

 

To keep it to what I can do, I can discuss some other basic properties of this model of the electron, as well as its spin?

 

Such as mass, inertia, momentum, absorption / emission of a photon, energy of motion, electric charge, movement in an electric field, movement in a gravitational field.

A bare electron can absorb a photon in your model?

Link to comment
Share on other sites

That would probably be another problem for your model. Any experimental evidence that electrons actually behave this way? (A question that should be asked at all stages of a evaluating a model)..

 

That was in reply to this point: If you consider the toroid shown in the video, it can move off in any direction that is in the plane of its ring, that is, it can move off in any horizontal direction. However, for it to move in any other direction, such as upwards, the ring has to twist itself so that the plane of the ring is in that vertical direction.

 

Here is an animation of an experiment called the Quantum spin and the Stern-Gerlach experiment. Could this be an example of the electron only being able to move forward in a direction that is in the plane of its ring?

 

http://en.wikipedia.org/wiki/File:Quantum_spin_and_the_Stern-Gerlach_experiment.ogv

 

When electrons are used, they only ever hit the top and bottom of the rear screen, never the middle of the screen (unlike when normal magnets are used).

 

This result could be explained by using the toroid model for the electron.

 

When electrons are fired between the magnets in the experiment, the electrons have their spins orientated in any direction. Because of the shape of of the top and bottom magnets, the electrons cannot be deflected sideways by the magnets, only up or down.

 

This means that the electron has to align itself so that the plane of its ring is vertical - giving it only two possible orientations for every electron: its spin is 'up' or its spin is 'down'.

 

Since all electrons have the same, fixed amount of spin, they then are always deflected by the same amount, hitting the same spot at the top or the bottom of the screen, but not in the middle.

 

Swansont, what do you think? Is this a reasonable explanation of the results of this experiment using the toroid model to describe the electron's spin?

 

Is this evidence for the toroid model?

Link to comment
Share on other sites

That was in reply to this point: If you consider the toroid shown in the video, it can move off in any direction that is in the plane of its ring, that is, it can move off in any horizontal direction. However, for it to move in any other direction, such as upwards, the ring has to twist itself so that the plane of the ring is in that vertical direction.

 

Here is an animation of an experiment called the Quantum spin and the Stern-Gerlach experiment. Could this be an example of the electron only being able to move forward in a direction that is in the plane of its ring?

 

http://en.wikipedia.org/wiki/File:Quantum_spin_and_the_Stern-Gerlach_experiment.ogv

 

When electrons are used, they only ever hit the top and bottom of the rear screen, never the middle of the screen (unlike when normal magnets are used).

 

This result could be explained by using the toroid model for the electron.

 

Aye, there's the rub. You are adding an effect from electric fields as well, a complication not observed in nature. It isn't enough to simply explain one experiment with a model. You need a model that's consistent with all observations. To do otherwise is like building a boat in your garage and worrying only that it's small enough to fit in lengthwise, and ignoring that it's too tall and too wide for the door.

 

 

When electrons are fired between the magnets in the experiment, the electrons have their spins orientated in any direction. Because of the shape of of the top and bottom magnets, the electrons cannot be deflected sideways by the magnets, only up or down.

 

This means that the electron has to align itself so that the plane of its ring is vertical - giving it only two possible orientations for every electron: its spin is 'up' or its spin is 'down'.

 

Since all electrons have the same, fixed amount of spin, they then are always deflected by the same amount, hitting the same spot at the top or the bottom of the screen, but not in the middle.

 

Swansont, what do you think? Is this a reasonable explanation of the results of this experiment using the toroid model to describe the electron's spin?

 

Is this evidence for the toroid model?

 

It's agreement but not scientific evidence because it disagrees with other observations.

Link to comment
Share on other sites

The head goes in a random direction? Why does the force have spherical symmetry in nature while the electron does not, in this model? How do you get attraction?

 

 

Yes, true the model has the electric field emitted mainly in the plane of the electron’s ring and in the direction that the electron is moving, so it is not emitted spherically.

 

But what are the examples that show that the electron’s field is spherical?

 

In atoms, the electrons are in cyclic orbitals and the atoms themselves are constantly tumbling, so atoms will show spherical fields even if the fields from the electrons are not spherical.

 

In the model, when atoms move, the atoms contract in the direction of movement because the fields from their nuclei change to be more forward facing.

 

Here is a video that shows the electron’s field inside the electron...

 

 

And here is a video that shows the repulsion and attraction forces produced by the model (the attraction force is shown about half way through).

The video also includes a bit at the end that shows the attraction force slightly stronger than the repulsion force, could this be the reason for gravity?

 

http://www.youtube.com/watch?v=ppiC1p4BEn0

Link to comment
Share on other sites

Yes, true the model has the electric field emitted mainly in the plane of the electron’s ring and in the direction that the electron is moving, so it is not emitted spherically.

 

But what are the examples that show that the electron’s field is spherical?

The dipole moment experiment I linked to. It shows that the field is incredibly spherical.

 

In atoms, the electrons are in cyclic orbitals and the atoms themselves are constantly tumbling, so atoms will show spherical fields even if the fields from the electrons are not spherical.

But we can spin polarize atoms, which is a magnetic effect, and they can remain spin polarized for quite some time (minutes in some cases). How would they do so if they also had this electric field acting in a different direction?

 

 

could this be the reason for gravity?

No.

 

The underlying issue is this: Science is a little like a jigsaw puzzle. But a jigsaw puzzle piece is not correct simply because one side fits with another piece. You're focusing one one side, and ignoring the other three that don't match. Using a mallet to try and force it to match doesn't make it the right piece.

Link to comment
Share on other sites

Yes. The field will not be that of a point charge. The standard model predicts a very small deviation, and experiment limits the distortion of the field. http://www.nature.com/nature/journal/v473/n7348/full/nature10104.html

 

Hi Swansont,

 

I'm reading though the D.M. Kara's thesis on the electron dipole moment experiment, to try and understand why the toroid model raises issues.

 

In his thesis, Kara defines a dipole as:

 

 

"The usual definition of a dipole is that of two charges, +q and −q, separated by a vector, ~r, producing a moment, ~d = q ~r, where ~r originates at the negative charge.
For a single particle a more general description is used: that the dipole originates from a displacement between the particle’s centre of charge and its centre of mass."
If the above general description of a dipole is used, then the toroid will have no dipole, since the centre of mass and centre of charge are in the same position.
Is this relevant to remove your objection on the toroid shape?
As I'm still struggling to see why the toroid shape will oscillate in an electric field.
Link to comment
Share on other sites

 

Hi Swansont,

 

I'm reading though the D.M. Kara's thesis on the electron dipole moment experiment, to try and understand why the toroid model raises issues.

 

In his thesis, Kara defines a dipole as:

 

 

"The usual definition of a dipole is that of two charges, +q and −q, separated by a vector, ~r, producing a moment, ~d = q ~r, where ~r originates at the negative charge.
For a single particle a more general description is used: that the dipole originates from a displacement between the particle’s centre of charge and its centre of mass."
If the above general description of a dipole is used, then the toroid will have no dipole, since the centre of mass and centre of charge are in the same position.
Is this relevant to remove your objection on the toroid shape?
I think you're right, and no. If there's no dipole then you will have a quadrupole (and/or higher-order multipoles) which you don't get from a point charge. If the field doesn't look exactly like 1/r^2 (i.e. a monopole), there must be other contributions, and the field of a ring of charge doesn't look exactly like 1/r^2.

 

As I'm still struggling to see why the toroid shape will oscillate in an electric field.

 

Do you see why there's a torque? That the force on one side of the ring is smaller than on the other side, because the external field is smaller when the charge is further away?

Link to comment
Share on other sites

  • 5 months later...

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.