Theory of Magnetic Fields of Electrons and Protons

In summary, the electron and proton both possess magnetic moments, which is a measure of their magnetic strength. The electron's magnetic moment is due to its spin, while the proton's is due to its magnetic moment. When in motion, an electron produces both an electric and magnetic field. The interaction of the magnetic fields of the electron and proton in the hydrogen atom causes oscillation between attraction and repulsion, leading to vacuum polarization. The neutron also plays a role in this process, but only when present. The electron has a magnetic field even when not in motion, and its magnetic moment ratio with the proton is -658.2. The magnetic interactions between the electron and proton are not trivial and can dominate in stabilizing the atom. The
  • #1
what_are_electrons
PART 1. Magnetic Field of Electron

The electron and the proton both have Magnetic Moments. By definition (Penguin Dict. of Physics, 1991) the term Magnetic Moment means:

1. SYMBOL, m,: "A property possessed by a permanent magnet or current-carrying coil, used as a measure of the magnetic strength"
2. OF A PARTICLE. SYMBOL: mu : "A property of a particle arising from its spin... The electron magnetic moment..."

In various other texts, we learn and can measure that electrons in motion (an electric current) produce a magnetic field in addition to their electric field (in effect an electromagnetic field). For all intents and purposes this is true based on what is known about (a) currents of electrons in wires or devices, (b) electrons orbiting atoms and (c) electrons in flight in evacuated instruments.

Doesn't this mean that the electron, by itself, has a magnetic field?
Ignoring sub-atomic particles, doesn't this mean that the electron represents the smallest magnet?
Why don't the texts say that the electron has a magnetic field with North and South poles?

If an electron could be stopped dead in its tracks (within our framework), truly "at rest" would it have a magnetic field?
Doesn't the electron have a "permanent" magnetic field even if it is not moving? Or better stated: A permanent "electromagnetic" field?

No matter whether or not the electron has a permanent magnetic field at rest, it clearly has a magnetic field because it is always moving and a moving charge has a magnetic field.


PART 2. Interaction of the Magnetic Fields of the Electron with the Proton (or electrons with protons)

In the same manner, the proton also has a natural and permanent (electro)magnetic field since it has a Magnetic Moment.
Ignoring the measured magnetic moment ratio of the electron and the proton, are the Structures and Shapes of these two (electro)magnetic fields the same or different?

If, at a first pass, we assume that the magnetic fields of the electrons and the proton are, in effect, the SAME in structure and shape, and if we consider the hydrogen atom, and momentarily ignore the electric fields, then we can think about what these two magnetic fields are doing to each other. In this setup we must keep in mind the fact that the electron and the proton are in continuous motion, both on their own axes and around each other.

IF the two rotations of the magnetic fields are NOT aligned, then the two magnetic fields will oscillate between attraction and repulsion, which causes the attached electric fields to produce vacuum or space polarization within the sphere of the atom.

Since vacuum or space polarization seems to be reality, we can imagine that the "magnetic fields" of the electrons and the protons in all atoms are the cause of the local space or vacuum polarization around the atom.

This same interaction, magnetic field based attaction and repulsion between the electron and the proton, is most probably a "major reason / factor" in why the orbit of the electron does not decay.

Neutrons, with their magnetic fields, also play a role in this balancing act, but only when they are present which is in 99% of all the other elements. First things first. Neutrons later...
 
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  • #2
Doesn't this mean that the electron, by itself, has a magnetic field?

From the evidence you have posted... No it does not. In electro-magnetism a magnetic field is associated with a moving electric field.. so a moving electron generating a magnetic field does not imply that the electron itself has a magnetic field.
 
  • #3
But he's asking if the electron has a magnetic field even if it stops moving, and the answer is "yes". Its intrinsic magnetic moment is due to both its charge and its intrinsic spin. But we know that intrinsic spin does not correspond to any real "spinning".
 
  • #4
That is why I specified "from the evidence he presented".
 
  • #5
what_are_electrons said:
PART 1. Magnetic Field of Electron

The electron and the proton both have Magnetic Moments.
<snip>
Doesn't this mean that the electron, by itself, has a magnetic field?

Yes, it does. However, the effect of the magnetic field on the orbital of the electron is small. Combined with the very small nuclear magnetic field, it leads to some of the fine and hyperfine splitting of energy levels in hydrogen. The magnetic moment of the electron is certainly not responsible for the stability of orbitals in standard theory. As far as stuff you want to make up as you go along, the sky's the limit :-)

Standard theory fine, hyperfine, and lamb shift splitting is discussed in, for instance

http://www.pha.jhu.edu/~rt19/hydro/node9.html [Broken]
 
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  • #6
Tom. Thanks for the confirmation.

pervect said:
Yes, it does. However, the effect of the magnetic field on the orbital of the electron is small. Combined with the very small nuclear magnetic field, it leads to some of the fine and hyperfine splitting of energy levels in hydrogen. The magnetic moment of the electron is certainly not responsible for the stability of orbitals in standard theory. As far as stuff you want to make up as you go along, the sky's the limit :-)

Standard theory fine, hyperfine, and lamb shift splitting is discussed in, for instance

http://www.pha.jhu.edu/~rt19/hydro/node9.html [Broken]

Correct me if I'm wrong, but the 1998 Codata data tables report that the "electron/proton magnetic moment ratio is equal to -658.2" which hardly seems to be a small number. In point of fact the electron is giving the proton a whoppin! So, let me be contradictory and say that the magnetic interactions, though normally ignored, are not trivial and can quite readily dominate the mechanism for stabilizing the atom.

There is one item that puzzles me. When I multiply the electron-neutron magnetic moment ratio times the neutron-proton moment ratio I get the number: -712.8. There is factor of 1.083... I am missing somewhere.
What have I missed?
...
 
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  • #7
what_are_electrons said:
Tom. Thanks for the confirmation.



Correct me if I'm wrong, but the 1998 Codata data tables report that the "electron/proton magnetic moment ratio is equal to -658.2" which hardly seems to be a small number.

You're not so much wrong as irrelevant here

http://physics.nist.gov/cuu/Constants/index.html

A) The electron magnetic moment is 928 e-26 Joules/Tesla
B) The proton magnetic moment is 1.41e-26 Joules/Tesla

C) But the ground state energy of the hydrogen atom is -13.6 electron volts = 2.17e-18 joules.

A may look big when compared to B, but so what? If you compare A to C, you see that A is a very minor effect. (To compare the two, you do need to know the value of the magnetic field in the atom. All we need to say here is it's much much much less than 10^5 Tesla, which is what would be required to make A equal to C, since the energy stored in a manetic dipole is u dot B.) For reference, the Earth's magnetic field is about .0005 Tesla.

To may things very, very, very, very simple:

A flea may be a lot heavier than a microbe. But no matter how many thousands of times a flea is larger than a microbe, it still won't outweigh an elephant.

As I mentioned previously, the magnetic field in the atom causes fine and hyperfine level splitting, not any major effects. For more details, read the URL in my previous post.
 
  • #8
Very simple question and a very simple answer. An electron cannot 'stand still'. Try doing the Maxwell equation with a stationary electron. [hint, add boundary conditions].
 
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  • #9
pervect said:
You're not so much wrong as irrelevant here

http://physics.nist.gov/cuu/Constants/index.html

A) The electron magnetic moment is 928 e-26 Joules/Tesla
B) The proton magnetic moment is 1.41e-26 Joules/Tesla

C) But the ground state energy of the hydrogen atom is -13.6 electron volts = 2.17e-18 joules.

A may look big when compared to B, but so what? If you compare A to C, you see that A is a very minor effect. (To compare the two, you do need to know the value of the magnetic field in the atom. All we need to say here is it's much much much less than 10^5 Tesla, which is what would be required to make A equal to C, since the energy stored in a manetic dipole is u dot B.) For reference, the Earth's magnetic field is about .0005 Tesla.

To may things very, very, very, very simple:

A flea may be a lot heavier than a microbe. But no matter how many thousands of times a flea is larger than a microbe, it still won't outweigh an elephant.

As I mentioned previously, the magnetic field in the atom causes fine and hyperfine level splitting, not any major effects. For more details, read the URL in my previous post.

Question: Hmmm, How can I be irrelevant when I am the author of this thread? I secede that I can become irrelevant to the discussion in this thread, but if I am truly irrelevant, as noted, then I might decide to leave the human race altogether. Let me ponder that one.


Back to the matter at hand:
The values you quote for magnetic moment are not in the right units for comparison to the BE of the hydrogen atom. After converting to base MKS units, the BE for the Hydrogen electron is: 2.17e-18 kg m/s(2).

For the proton the magnetic moment is: 28.22e-34 kg m/s(2).
For the electron the magnetic moment is: 18.54e-31 kg m/s(2)

This means that the difference you noted is even larger when the units are adjusted accordingly.

The "Energy" (and I use that term loosely just now)
that holds the electron close to the proton in a single hydrogen atom is defined to be the binding energy (BE) of the 1s electron (ie -13.6 eV or in base MKS units -2.17e-18 kg m/s(2)). This is the value you called "the ground state energy of the hydrogen atom".

The questions are: What does this binding energy value represent?
1. Does it represent the +charge -charge attraction ONLY? No, it does not.
2. Does it represent the energy needed to pull the electron away from physically touching the core? No, it does not or we'd all not be here.
3. Does it represent the energy needed to overcome the angular moment of the electron? Yes, that is part of it.
4. What is left? Since the proton has a magnetic moment and since the electron has a magnetic moment and since magnetic moment is, in effect, just another word for the presence of a magnetic field, we might conclude that there should be some level of interaction between the two magnetic fields.
5. Is it possible that there are other forces at work? Yes, but I don't know of any other forces except those that are either way too strong (gluon type) or way too weak (gravity). And yes, there may be other forces at work that we have not yet realized or observed. This may be the real cause of the binding energy, but we should focus on the known forces that may be responsible for this level of binding energy.

For the moment, let's assume that the magnetic fields do indeed play a major role in keeping the electron in orbit around the proton. Let's also assume that the electron and the proton are actually rotating on their axes, and that the electron and proton are in constant motion around each other as we normally assume. If we also assume that the "permanent" electric field of any particle is intimately connected to a "permanent" magnetic field, then we expect that any movement of the magnetic field would cause the electric field to also move. If the speed of the central rotational axes of the two particles are not 100% matched, as is expected (ie slippage occurs), then we can imagine that the orientations of the N-S magnetic poles are in a constant state of flux between various states that produce physical attraction and physical repulsion. This sort of oscillation between the magnetic poles forces the electric charges, that they are intimately connect to, to also oscillate in space. This sort of oscillation could be the actual source of the vacuum or space polarization around the atom. Since we theorize that vacuum polarization exists, we might conclude that vacuum polarization supports the idea that magnetic fields are a major factor in the stability of any atom.

Your turn.


Side note:
When I convert the negative electric charge on the electron into base MKS units I get -12.82e-2 kg(2)/m(2)s(3). The positive electric charge on the proton must then be +12.82e-2 kg(2)/m(2)s(3) base MKS units. It is clear from our knowledge that a negative is attracted to a positive and vice versa, but what are those units? As I look at the base MKS units, I want to convert the kg(2)/m(2)s(3) units into (1 / s) x (kg / m s)(2), but I can not guess the name of the squared unit that is composed of: kg / m s
Suggestions?
 
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  • #10
After the move, there are no more challenges, so it seems that my Theory is well founded.
 
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  • #11
just curious, Sun spots ,why is there blackness at their point?
 
  • #12
Sunspots are not black. They are less bright than the surrounding surface and only appear black in order to get the proper exposure of the full surface when taking photographs.

The magnetic field inside a sunspot is much greater than the ambient magnetic field and as the sunspot is forming it drags plasma in from the surrounding volume. The plasma immediately surrounding the sunspot is cooled by the expansion (but the interior gets hotter) and what you see is the surrounding plasma.
 
  • #13
Good points!, as in fact your point of view about the magnetic field coincides with my proposal, where we recover that non conservative aspect of a magnetic field which means in a certain sense that the magnetic field is a self-consistent entity as is expressed in Maxwell equation, regarding the non existence of magnetic isolated poles.
The main problem with this is that modern physics decided to take the route of the part, not the whole/part route, taking the electric charge concept as the starting point of view, declaring the magnetic field as a relativistic concept, which does not agree with the certitude of that inherent magnetic field of the electron. Is not this the reason why modern physics has been built with so many patches since then? Is not even the concept of field another "patch" as is used by them today?
Another point is that if we represent the magnetic field by the complex concept I have introduced in my papers, it wil appear naturally as sort of "inherent oscillator", giving reason in this way of its inherent energy, that some ones are now calling zero-point-energy, that can be associated with its intrinsic spinning which is a result of the inherent oscillation of the electron system, not precisely the spinning of a particle around a point.

Regards
EP


what_are_electrons said:
Question: Hmmm, How can I be irrelevant when I am the author of this thread? I secede that I can become irrelevant to the discussion in this thread, but if I am truly irrelevant, as noted, then I might decide to leave the human race altogether. Let me ponder that one.


Back to the matter at hand:
The questions are: What does this binding energy value represent?
1. Does it represent the +charge -charge attraction ONLY? No, it does not.
2. Does it represent the energy needed to pull the electron away from physically touching the core? No, it does not or we'd all not be here.
3. Does it represent the energy needed to overcome the angular moment of the electron? Yes, that is part of it.
4. What is left? Since the proton has a magnetic moment and since the electron has a magnetic moment and since magnetic moment is, in effect, just another word for the presence of a magnetic field, we might conclude that there should be some level of interaction between the two magnetic fields.
5. Is it possible that there are other forces at work? Yes, but I don't know of any other forces except those that are either way too strong (gluon type) or way too weak (gravity). And yes, there may be other forces at work that we have not yet realized or observed. This may be the real cause of the binding energy, but we should focus on the known forces that may be responsible for this level of binding energy.

For the moment, let's assume that the magnetic fields do indeed play a major role in keeping the electron in orbit around the proton. Let's also assume that the electron and the proton are actually rotating on their axes, and that the electron and proton are in constant motion around each other as we normally assume. If we also assume that the "permanent" electric field of any particle is intimately connected to a "permanent" magnetic field, then we expect that any movement of the magnetic field would cause the electric field to also move. If the speed of the central rotational axes of the two particles are not 100% matched, as is expected (ie slippage occurs), then we can imagine that the orientations of the N-S magnetic poles are in a constant state of flux between various states that produce physical attraction and physical repulsion. This sort of oscillation between the magnetic poles forces the electric charges, that they are intimately connect to, to also oscillate in space. This sort of oscillation could be the actual source of the vacuum or space polarization around the atom. Since we theorize that vacuum polarization exists, we might conclude that vacuum polarization supports the idea that magnetic fields are a major factor in the stability of any atom.
 
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  • #14
what_are_electrons said:
After the move, there are no more challenges, so it seems that my Theory is well founded.

You seem confused as to what makes a theory well founded.
 
  • #15
Paraphrasing Lord Kelvin we can say that:
"I often say that when you... express what you are speaking about mathematically...you know something about it; but when you cannot... your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be."
And what_ what_are_electrons proposes can be expressed mathematically in one of the Maxwell's equations. The point is that this is a different point of view of that taken by modern physics.
Regards
EP

Locrian said:
You seem confused as to what makes a theory well founded.
 
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  • #16
A more general title for this thread can be suggested as follows:

Theory of magnetic fields of fermions (specifically, leptons and baryons).

Electrons are the lightest charged leptons. Protons are the lightest charged baryons.
Other facts:
Electrons are experimentally stable point-particles with no substructures. Protons are composite particles of quarks (3-quark configuration). Yet it is now accepted that protons are stable with lifetime in excess of 10^33 years and quarks can never be isolated at low energy domain, while at high energy, quarks are asymptotically free.

Somehow it can be theorized that there is a direct correlation between magnetic field strength and mass and increasing internal magnetic field intensity seems to indicate heavier mass.
 
  • #17
introducing "patches" in modern physics?

Antonio,

The title you put the thread depends on the framework you are using. If we take the electron as a fundamental energetic entity with no substructures and with an inherent magnetic field with its well-known spin property the title is ok; on the contrary, even the concept of a magnetic field will certainly become another "patch" in yours constructs.
Why insisting in explaining the whole by the part? Why don't we start with a whole/part entity such as the electron(no substructures), and its inherent magnetic field? In this way for sure we will not have so many patches in modern physics.

Regards
EP


Antonio Lao said:
A more general title for this thread can be suggested as follows:

Theory of magnetic fields of fermions (specifically, leptons and baryons).

Electrons are the lightest charged leptons. Protons are the lightest charged baryons.
Other facts:
Electrons are experimentally stable point-particles with no substructures. Protons are composite particles of quarks (3-quark configuration). Yet it is now accepted that protons are stable with lifetime in excess of 10^33 years and quarks can never be isolated at low energy domain, while at high energy, quarks are asymptotically free.

Somehow it can be theorized that there is a direct correlation between magnetic field strength and mass and increasing internal magnetic field intensity seems to indicate heavier mass.
 
  • #18
Epsilon Pi,

The Millikan's oil drop experiment sets the quantum of charge. But this setup was done by balancing the electric force against gravity.

Until now there is no experiment that determine the quantum of mass. My suggestion is that an experiment can be setup by balancing the magnetic force with the electric force or with gravity to find the quantum of mass.

My hunch is that this quantum of mass might turn out to be the Planck mass.

For leptons, I think, there is a correlation between magnetic moments and mass. If this is true then all the neutrinos have mass since they all possesses magnetic moments.

For photons, since it has no magnetic moment, its mass is zero. But both W+ and W- and Z0 have mass. So for bosons or hadrons (quarks composites), the correlattion between magnetic moment and mass does not hold or could be just more complicated.
 
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  • #19
Antonio,
We certainly have the quantum of charge as an invariant in the universe, but does not it mean that it is related with a quantum of a magnetic field?
As a matter of fact "mass" is not an invariant as it changes with velocity, and it seems after all a derived concept, not a fundamental one.

Is not mass sort of a frozen energy?

Is not energy the real fundamental entity associated in fact with Plank's constant, as with the wave-nature established by Davisson and Germer as well?

Are you not putting too much the accent in a concept such as the particle concept that is but an abstraction in the QM world?

Regards
EP

Antonio Lao said:
Epsilon Pi,

The Millikan's oil drop experiment sets the quantum of charge. But this setup was done by balancing the electric force against gravity.

Until now there is no experiment that determine the quantum of mass. My suggestion is that an experiment can be setup by balancing the magnetic force with the electric force or with gravity to find the quantum of mass.

My hunch is that this quantum of mass might turn out to be the Planck mass.

For leptons, I think, there is a correlation between magnetic moments and mass. If this is true then all the neutrinos have mass since they all possesses magnetic moments.

For photons, since it has no magnetic moment, its mass is zero. But both W+ and W- and Z0 have mass. So for bosons or hadrons (quarks composites), the correlattion between magnetic moment and mass does not hold or could be just more complicated.
 
  • #20
The magnetic force is given by

[tex]F_B= q\vec{v} \times \vec{B}[/tex]

The inertial force is given by

[tex]F_i=ma[/tex]

(instead of using the gravitational force)

when these forces are equal, mass is proportional to the magnetic field by

[tex] m= \frac{v}{\kappa\mu} B[/tex]

where the proportionality constant is a ratio of speed over the product of charge-to-mass ratio with the product of magnetic field and a quantum of length.
 
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  • #21
Yes, thank you, Antonio, which is precisely my point regarding the magnetic field as the fundamental one.
It is right to assume the equality between gravitational and inertial mass; it was Einstein who used this equality in his general relativity.
Regards
EP
Antonio Lao said:
The magnetic force is given by

[tex]F_B= q\vec{v} \times \vec{B}[/tex]

The inertial force is given by

[tex]F_i=ma[/tex]

(instead of using the gravitational force)

when these forces are equal, mass is proportional to the magnetic field by

[tex] m= \frac{v}{\kappa\mu} B[/tex]

where the proportionality constant is a ratio of speed over the product of charge-to-mass ratio with the product of magnetic field and a quantum of length.
 
  • #22
Epsilon Pi,

After some thoughts, I think the quantum of the magnetic field is a current loop. The current is derived from the motion of space charges. Space charges is different fundamentally from color charges or weak charges or electric charges. And since time is linked to this current loop, the magnetic quantum is the same as quantization of spacetime. When two loops are linked together, they formed two distinct structures for a square of energy, H+ and H-. One can be the south pole and the other can be the north pole of the magnetic field. But everything in nature is composed of some number of H+ and some of H-. Therefore it is impossible to isolate just one H+ or one H- (the key reason why magnetic monopole can never be found). For fermions, there are odd number of H+ and odd number of H-. For bosons, there are even number of H+ and even number of H-. I already described extensively other properties of H+ and H- in many other threads of this forum.
 
  • #23
Thank you, Antonio, again you give the opportunity to clarify my own point of view.
The point of view you are expressing is precisely that one prevailing in modern physics that tries to explain the whole by the part, i.e., the magnetic field a self-consistent entity with an inherent structure or polarity, by the charge, whatever it may be.

The electron has an inherent magnetic field that can give reason in a most natural way of its spin behavior because of that inherent polarity; please note that this behavior exists even at rest,no electric charge moving, no current loop.

If we use complex numbers in all its full power we can express mathematically that duality you are trying to explain by introducing another concept, space charge, and even we can see why at those levels of the electron behavior time and space are decoupled, as is expressed in the Schrodinger wave equation. On the other hand we can express with them too why there can be no magnetic monopoles.

My main concern since 1968, was not precisely to find a TOE, but to find a mathematical methodology to include the fundamental equations of physics, and this can be done with the basic unit system concept introduced in my papers, being the most relevant thing about it that we do not need to introduce additional strange physical concepts; this seems to me untenable as an engineer, and that claim I've heard so many times about why in modern physics they use such a different language as that one we use in our daily engineering applications, is finally solved.

Regards
EP


Antonio Lao said:
Epsilon Pi,

After some thoughts, I think the quantum of the magnetic field is a current loop. The current is derived from the motion of space charges. Space charges is different fundamentally from color charges or weak charges or electric charges. And since time is linked to this current loop, the magnetic quantum is the same as quantization of spacetime. When two loops are linked together, they formed two distinct structures for a square of energy, H+ and H-. One can be the south pole and the other can be the north pole of the magnetic field. But everything in nature is composed of some number of H+ and some of H-. Therefore it is impossible to isolate just one H+ or one H- (the key reason why magnetic monopole can never be found). For fermions, there are odd number of H+ and odd number of H-. For bosons, there are even number of H+ and even number of H-. I already described extensively other properties of H+ and H- in many other threads of this forum.
 
  • #24
Epsilon Pi,

The space charge are truly zero dimensional point object of spacetime. It will take 8 space charges to form a 3D detectable object like an electron. The reason why there have to be 8 is because there are precisely also 8 directional properties for all 3D objects. If there are less than 8, then the object cannot be 3D.

All neutrinos are composed of only 1 H+ and 1 H-, total 2 space charges, less than 8 required to be 3D.

The up quark is made of 5 H+ and 1 H- total 6 space charges again less than 8.
The down quark is made of 1 H+ and 3 H- total 4 space charges less than 8.

The electron is made of 7H- and 1 H+ exactly 8. The photon is made of 4H+ 4H- exactly 8. The proton is composed of 2 ups and 1 down total 16 space charges are more than 8. The neutron is made of 2 downs and 1 up quarks total 14 space charges more than 8.

Note there are higher levels of existence for H+ and H- that can account for the disparity in mass. The 8 directional properties match the 8 gluons of particle physics.
 
  • #25
Antonio Lao said:
Epsilon Pi,

The space charge are truly zero dimensional point object of spacetime.
Humm...truly zero dimensional point object? how can it be an object of spacetime if it has no dimension? It is beautiful construct, but do we really need it?
Can you express it mathematically?
Does it mean that we have a metaphysical non space time background?

[/QUOTE]

Antonio Lao said:
It will take 8 space charges to form a 3D detectable object like an electron. The reason why there have to be 8 is because there are precisely also 8 directional properties for all 3D objects. If there are less than 8, then the object cannot be 3D.
Quite interesting! I'll think a little bit more about it.
Like an octave?

Regards
EP
 
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  • #26
Epsilon Pi said:
Can you expresses it mathematically?

The space charges H+ and H- can be expressed in two ways: by matrices or vector products.
 
  • #27
Epsilon Pi said:
Like an octave?
I guess so. Now, it seems to indicate that even musical harmony requires 8 directional invariant properties of spacetime.
 
  • #28
The square of energy can be defined by

[tex]E^2=\vec{F_B} \times \vec{r_B} \cdot \vec{F_E} \times \vec{r_E}[/tex]

when expanded by Lagrange's identity

[tex] H^{-} = \left(\vec{F_B} \cdot \vec{F_E}\right) \left(\vec{r_B} \cdot \vec{r_E}\right) - \left(\vec{F_B} \cdot \vec{r_E}\right) \left(\vec{r_B} \cdot \vec{F_E}\right)
[/tex]

[tex] H^{+} =\left(\vec{F_B} \cdot \vec{r_E}\right) \left(\vec{r_B} \cdot \vec{F_E}\right) - \left(\vec{F_B} \cdot \vec{F_E}\right) \left(\vec{r_B} \cdot \vec{r_E}\right)
[/tex]

[tex]\left(\vec{F_B} \cdot \vec{F_E}\right) \left(\vec{r_B} \cdot \vec{r_E}\right)[/tex]
is identically zero if the forces are orthogonal. If this expression does not vanish then its ratio over square of energy can be defined as the coupling constants of the four fundamental forces of nature, and for EM

[tex] \alpha=\frac{\left(\vec{F_B} \cdot \vec{F_E}\right) \left(\vec{r_B} \cdot \vec{r_E}\right)}{\left(\vec{F_B} \cdot \vec{r_E}\right) \left(\vec{r_B} \cdot \vec{F_E}\right)}=\frac{1}{137}[/tex]
 
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  • #29
By 2-order square matrix notations

[tex] H^{+} = \left(\begin{array}{cc}+1 & -1\\-1 & +1 \end{array}\right)[/tex]

[tex] H^{-} = \left(\begin{array}{cc}-1 & +1\\+1 & -1 \end{array}\right)[/tex]

Note that the elements of these matrices are the square of pure imaginary number, i.

[tex] 1 = - i^2[/tex]

[tex] -1 = i^2 [/tex]

and the powers of i show the cyclic permutations of 1, i, -1, -i

[tex] i^0 = 1, i^1=i, i^2=-1, i^3=-i, i^4=1, i^5=i, i^6=-1, i^7=-i, i^8=1 [/tex]
 
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  • #30
Antonio Lao said:
I guess so. Now, it seems to indicate that even musical harmony requires 8 directional invariant properties of spacetime.
Our word octave in reference to music is an artefact of a medieval counting technique, where zeroes were avoided. If we invented the same 12 semi-tone system, we would call the white keys a septet, since 'octave' double-counts the home key. That may sound garbled, but consider that if one octave is 8 keys, 2 octaves is 15 and 3 is 22, etc. The real magic number in music is 12, not 8, or even 7.
 
  • #31
krab said:
The real magic number in music is 12, not 8, or even 7.
The pure imaginary number i to the powers of 0, 4, 8, and 12 all equal to one. Can this cyclic permutation mean anything as far as magic number goes?
 
  • #32
Antonio Lao said:
The pure imaginary number i to the powers of 0, 4, 8, and 12 all equal to one. Can this cyclic permutation mean anything as far as magic number goes?
In music, the 12 comes about because 3^12 is very nearly equal to 2^19. Hence, the "circle of fifths" (each "fifth" represents multiplication by 3/2) closes on itself after 12 notes.
It has nothing to do with imaginary numbers.
 
  • #33
krab,

Thanks for your clarifications.
 
  • #34
Yes, Antonio, complex numbers are fundamental for expressing the laws of nature, and this sense I thought you might be interested in a paper I wrote some time ago

Is the basic unit system a string?
http://arxiv.org/ftp/physics/papers/0010/0010073.pdf

In it the complex basic unit system concept based on Euler relation is presented and it is noted there how that concept behaves as string, that is exactly what you have being presenting in this thread, Antonio, haven't you?
I would appreciate any comments from you and thank you
Regards
EP
Antonio Lao said:
By 2-order square matrix notations

[tex] H^{+} = \left(\begin{array}{cc}+1 & -1\\-1 & +1 \end{array}\right)[/tex]

[tex] H^{-} = \left(\begin{array}{cc}-1 & +1\\+1 & -1 \end{array}\right)[/tex]

Note that the elements of these matrices are the square of pure imaginary number, i.

[tex] 1 = - i^2[/tex]

[tex] -1 = i^2 [/tex]

and the powers of i show the cyclic permutations of 1, i, -1, -i

[tex] i^0 = 1, i^1=i, i^2=-1, i^3=-i, i^4=1, i^5=i, i^6=-1, i^7=-i, i^8=1 [/tex]
 
  • #35
Epsilon Pi said:
Is the basic unit system a string?
Read your paper. Thanks. Will read the other papers at xxx.lanl.gov site.

Epsilon Pi said:
In it the complex basic unit system concept based on Euler relation is presented and it is noted there how that concept behaves as string, that is exactly what you have being presenting in this thread, Antonio, haven't you?
The H+ and H- formed an algebra of a mathematical field which is a commutative ring of a semigroup under multiplication with no unity nor inverse and an Abelian group under addition with a unity and inverse.
The multiplicative group is used to find the different mass values of both fermions and bosons.
The additive group is used to find the different charge values of both fermions and bosons.
The topological geometric structure of H+ and H- is that of a closed loop of 1D string. But it will take two loops to form an H(+/-) structure. This structure can be said to be isomorphic to a doubly twisted Moebius strip or Hopf ring.

The intermediate level of reality you mentioned I would call it a fractal reality of fractal dimension (fractional dimension) between complete chaos and complete order. The midpoint reality is a theory of complexity (a complex adaptive system). These formed a trinity of physical states of energy (chaos), matter (complex adaptive system) and space (order).

Energy is intrinsically 3D, matter is intrinsically 4D, space can be subdivided into 2D and 1D. The 2D space is called continuous space, the 1D space is called quantized space of closed loops of string. The physical reality of 0D is the spacetime continuum.

Furthermore, the fractal force between 4D and 3D could be the EM force or the weak force, between 3D and 1D could still be the EM force or weak force, between 2D and 1D can be the strong force, and between 1D and 0D is the gravitational force.
 
Last edited:
<h2>1. What is the theory of magnetic fields of electrons and protons?</h2><p>The theory of magnetic fields of electrons and protons is a scientific explanation for how these particles interact with magnetic fields. It states that moving electrons and protons produce a magnetic field, and when these particles are placed in an external magnetic field, they experience a force that causes them to move in a curved path.</p><h2>2. How do electrons and protons create magnetic fields?</h2><p>Electrons and protons have a property called spin, which is a type of angular momentum. This spin creates a tiny magnetic field around the particle, similar to a tiny bar magnet. When many of these particles are moving in the same direction, their magnetic fields align and create a larger magnetic field.</p><h2>3. What is the difference between the magnetic fields of electrons and protons?</h2><p>The main difference is the strength of their magnetic fields. Electrons have a smaller mass and a larger spin than protons, which means they have a stronger magnetic field. Additionally, electrons have a negative charge, while protons have a positive charge, causing their magnetic fields to have opposite orientations.</p><h2>4. How do electrons and protons interact with external magnetic fields?</h2><p>When an electron or proton is placed in an external magnetic field, it experiences a force called the Lorentz force. This force is perpendicular to both the direction of motion and the direction of the magnetic field. As a result, the particle will move in a curved path, known as a cyclotron motion.</p><h2>5. What are the practical applications of the theory of magnetic fields of electrons and protons?</h2><p>The theory of magnetic fields of electrons and protons is essential in understanding and developing technologies such as magnetic resonance imaging (MRI), particle accelerators, and electric motors. It also plays a crucial role in our understanding of the Earth's magnetic field and its impact on our planet.</p>

1. What is the theory of magnetic fields of electrons and protons?

The theory of magnetic fields of electrons and protons is a scientific explanation for how these particles interact with magnetic fields. It states that moving electrons and protons produce a magnetic field, and when these particles are placed in an external magnetic field, they experience a force that causes them to move in a curved path.

2. How do electrons and protons create magnetic fields?

Electrons and protons have a property called spin, which is a type of angular momentum. This spin creates a tiny magnetic field around the particle, similar to a tiny bar magnet. When many of these particles are moving in the same direction, their magnetic fields align and create a larger magnetic field.

3. What is the difference between the magnetic fields of electrons and protons?

The main difference is the strength of their magnetic fields. Electrons have a smaller mass and a larger spin than protons, which means they have a stronger magnetic field. Additionally, electrons have a negative charge, while protons have a positive charge, causing their magnetic fields to have opposite orientations.

4. How do electrons and protons interact with external magnetic fields?

When an electron or proton is placed in an external magnetic field, it experiences a force called the Lorentz force. This force is perpendicular to both the direction of motion and the direction of the magnetic field. As a result, the particle will move in a curved path, known as a cyclotron motion.

5. What are the practical applications of the theory of magnetic fields of electrons and protons?

The theory of magnetic fields of electrons and protons is essential in understanding and developing technologies such as magnetic resonance imaging (MRI), particle accelerators, and electric motors. It also plays a crucial role in our understanding of the Earth's magnetic field and its impact on our planet.

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