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Exploratory Mathematics « on: 2022-09-16, 14:13:14 »

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Edit:  Thread split from Telluric Communication as I think exploratory mathematics has enough depth to warrant its own topic.

C is derived from the permittivity(capacitance) and permeability(inductance) at any point in space.  So technically, the speed of light in a vacuum is actually two constants, not one.
This makes the problem more complex, but offers more possible solutions.

For example, if the effective permittivity or permeability can drop below unity, then you might end up with things like negative refractive index and negative impedance.  This is being explored in optics as 'negative index metamaterials':
https://en.wikipedia.org/wiki/Negative-index_metamaterial#Artificial_transmission-line-media
(Note the connection between the Wiki diagram and the Transverse vs Parallel networks thread. >:-) >:-))
« Last Edit: 2022-09-18, 18:26:36 by Hakasays »


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Re: Exploratory Mathematics « Reply #1 on: 2022-09-16, 15:22:16 »

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Quote from: F6FLT on 2022-09-16, 10:15:08
None of them are conclusive, for the reasons already given.

The speed we are talking about is the limit speed c, basis of relativity. It is a locally measured speed, speed limit of matter/energy or information.

Explain to us how apparent velocities > c due to the expansion of the universe could lead to the transmission of matter/energy or information at this speed.

Explain us how quantum entanglement could lead to the transmission of information at a speed > c, when it is precisely proved that it is impossible in the framework of quantum mechanics to which you refer.

Speeds higher than c in science are not impossible. The phase velocity > c of a wave is even commonplace.

Obviously you don't master the subjects at all and mix everything up, you don't understand at all what speed is meant with c.

I added the video because of the title.  I have not viewed it yet.

If the experiments shared are inconclusive, perhaps you can perform a more conclusive one.
   
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Re: Exploratory Mathematics « Reply #2 on: 2022-09-16, 18:27:31 »
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Quote from: Hakasays on 2022-09-16, 14:13:14
C is derived from the permittivity(capacitance) and permeability(inductance) at any point in space.
...

Funny idea. Who tells you that permittivity and permeability are not derived from the speed of light?


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Re: Exploratory Mathematics « Reply #3 on: 2022-09-17, 01:02:55 »

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Quote from: F6FLT on 2022-09-16, 18:27:31
Funny idea. Who tells you that permittivity and permeability are not derived from the speed of light?

Two reasons IMO:

1 - Structural requirements.  Dielectricity and Magnetism can exist independently of each-other, implying that they exist in separate dimensions.
IE: dielectricity and magnetism can both exist without photons, but photons cannot be exist without dielectricity and magnetism.

(In analogy, space and time can both exist without energy, but energy cannot exist without both space and time.  This implies that space+time are more fundamental than energy, or that energy is a ratio or conjugate of the two components)

2 - Many different factors of C and L will arrive at the same propagation result.  For example, if L is divided by 2 and C is multiplied by 2, the result will be the same propagation constant through that medium.    This implies C is more like a natural ratio than a fundamental constant.

(optional) 3 - A lot of interesting solutions fall out when we 'solve' C for its underlying components of permittivity+permeability.   It gives us an entire new realm to explore and experiment, that is still consistent with existing formulas.


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Re: Exploratory Mathematics « Reply #4 on: 2022-09-17, 02:29:15 »

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If "space" is a "medium" there should be a way to move it.
   
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Re: Exploratory Mathematics « Reply #5 on: 2022-09-17, 10:43:05 »
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Quote from: Hakasays on 2022-09-17, 01:02:55
Two reasons IMO:

1 - Structural requirements.  Dielectricity and Magnetism can exist independently of each-other, implying that they exist in separate dimensions.

Unfounded assertion, and obviously false. A single charge at rest ("dielectricity"), viewed from a moving observer, is viewed as a current (magnetism).

Quote
2 - Many different factors of C and L will arrive at the same propagation result.  For example, if L is divided by 2 and C is multiplied by 2, the result will be the same propagation constant through that medium.    This implies C is more like a natural ratio than a fundamental constant.
...

perfectly explainable by the fact that the speed limit exerts a constraint. When either parameter changes (L/µ or C/ԑ), the other prevents c from being exceeded.


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Re: Exploratory Mathematics « Reply #6 on: 2022-09-17, 10:54:10 »
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Quote from: Grumpy on 2022-09-17, 02:29:15
If "space" is a "medium" there should be a way to move it.

I have already proposed a simple experiment to verify this, by the magnetic force on the displacement currents. The loss of balance of the forces on the circuit should make it move to the right. This is not the case.

This means that the "displacement currents" are not real currents in the medium, but the influence of charges at a distance, which do not need a medium to exert it.




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Re: Exploratory Mathematics « Reply #7 on: 2022-09-17, 14:35:09 »

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I should have clarified that I was using dependence logic to describe my view regarding the derivation/ratio of C, and by 'dimension' I am referring to the mathematical definition, an independent parameter of coordinates needed to describe the system.

All phenomena within Electrical Engineering can be deduced from the 4 primary dimensions of Space, Time, Dielectricity, and Magnetism.

Lets take Ohms law as another example.  V=IR;   voltage, current, resistance and try to find the primary dimensions:
* Voltage can exist without current or resistance (charged capacitor)
* Current can exist without voltage or resistance (permanent magnet, or superconducting coil)
* Resistance CANNOT exist without both current and voltage.  Thus, we can conclude Resistance is not a primary dimension but instead a natural ratio or relationship between the other two.

Now lets do something like 'resonant frequency' f = 1 / (2π √L C)
* L can exist without capacitance or frequency (permanent magnet, or superconducting coil)
* C can exist without inductance or frequency  (charged capacitor)
* Frequency (in this formula) CANNOT exist without the factors L and C.  Thus, we can conclude that 'Frequency' is not a primary dimension but a natural or relationship between the other two.

Now lets electrically analyze speed of light (or rather the velocity of a signal in empty space):
* Permittivity can exist without permeability (dielectric constant, as modeled as a capacitor)
* Permeability can exist without permittivity (permeability, as modeled in an inductor)
* 'C' cannot exist without both permittivity and permeability.  Thus we can conclude that C is not a primary dimension but instead a natural ratio between the other two.

This becomes most evident when we look at the electrical characteristics of free space:
Z0 = 376.730313668(57) Ω          https://en.wikipedia.org/wiki/Impedance_of_free_space


The reason I find this POV interesting is because it presents new and unexpected solutions that lead directly to falsifiable experiments.  A whole new region to explore electrically, without rewriting any existing formulas.


PS: I might move this all to a new thread as I find it an interesting side-topic by itself. ;D


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Re: Exploratory Mathematics « Reply #8 on: 2022-09-17, 15:51:25 »

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Quote from: F6FLT on 2022-09-17, 10:54:10
I have already proposed a simple experiment to verify this, by the magnetic force on the displacement currents. The loss of balance of the forces on the circuit should make it move to the right. This is not the case.

This means that the "displacement currents" are not real currents in the medium, but the influence of charges at a distance, which do not need a medium to exert it.

I agree on displacement current.

If I thought that I moved "space", what could give this impression?

For example: Dr. Harold Aspden was experimenting with a permanent magnet motor, vertical magnets, rotational axis also vertical.  He found that the energy required to turn the rotor became less if he started it soon after it stopped.  The effect dissipated if he waited several minutes, decreasing with unit time.  This was the case regardless of the direction of rotation.  He said it seems as though some medium is being rotated by the rotor/magnets, and that it keeps rotating for a short time after the rotor stops. Aspden called it "virtual inertia".

I know the information is limited, but what could give the impression of this rotating space that Aspden called "virtual inertia"?
   
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Re: Exploratory Mathematics « Reply #9 on: 2022-09-17, 16:13:41 »

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Quote from: Hakasays on 2022-09-17, 14:35:09

Now lets electrically analyze speed of light (or rather the velocity of a signal in empty space):
* Permittivity can exist without permeability (dielectric constant, as modeled as a capacitor)
* Permeability can exist without permittivity (permeability, as modeled in an inductor)
* 'C' cannot exist without both permittivity and permeability.  Thus we can conclude that C is not a primary dimension but instead a natural ratio between the other two.


Could "space" ever be a metamaterial?
   
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Re: Exploratory Mathematics « Reply #10 on: 2022-09-17, 16:22:54 »
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Quote from: Grumpy on 2022-09-17, 15:51:25
...
For example: Dr. Harold Aspden was experimenting with a permanent magnet motor, vertical magnets, rotational axis also vertical.  He found that the energy required to turn the rotor became less if he started it soon after it stopped.  The effect dissipated if he waited several minutes, decreasing with unit time.  This was the case regardless of the direction of rotation.  He said it seems as though some medium is being rotated by the rotor/magnets, and that it keeps rotating for a short time after the rotor stops. Aspden called it "virtual inertia".

I know the information is limited, but what could give the impression of this rotating space that Aspden called "virtual inertia"?

This kind of observation is rather light to prove something revolutionary, because the possible experimental artifacts are numerous and much more probable than what is supposed, if only the action of temperature on lubrication and friction.

Aspden can imagine that this is a new effect and call it "virtual inertia", but this is not what is expected of him if he hopes to place himself in a scientific perspective. What is required is an operational and formalized definition of his "virtual inertia", a list of properties, the way in which one can act on them in order to verify experimentally predictions from his theory.
Does he have any?


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Re: Exploratory Mathematics « Reply #11 on: 2022-09-17, 16:53:57 »

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Quote from: Grumpy on 2022-09-17, 16:13:41
Could "space" ever be a metamaterial?

I don't know, but if the permittivity or permeability of free space can be altered in any way, then the speed of light no longer becomes a universal constant. ^-^
That change should be detectable both by interferometry and by electrical circuitry (and may already be documented somewhere in academia).


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Re: Exploratory Mathematics « Reply #12 on: 2022-09-17, 17:36:58 »
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@hakasays

"the 4 primary dimensions of Space, Time, Dielectricity, and Magnetism" : except for time, they are not dimensions. Space alone has 3 dimensions. "Dielectricity" is a term not scientifically defined. Magnetism is another aspect of the same physical reality that is electrostatics, the effect of charges, but when they move.

A resistor can exist without current or voltage, I have boxes full of them. L cannot exist without capacitance for the good reason that like an isolated conductive sphere, every conductor has a capacitance with respect to the rest of the universe.
C cannot exist without inductance, because every conductor has one, including capacitor plates, and if you were working on frequencies > GHz you would know the problem of parasitic inductances of the links between components.

One cannot talk about the "existence" of permittivity since it is not a physical reality but the property of a medium, and permittivity cannot anyway "exist" without permeability since ε=1/μ*c²... etc etc

What you are saying simply does not make sense. This being said, I remain open, and if from your esoteric novel comes an experimental idea capable of demonstrating new effects, I will carefully observe your demonstration.


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Re: Exploratory Mathematics « Reply #13 on: 2022-09-17, 19:03:47 »

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Quote from: F6FLT on 2022-09-17, 16:22:54
This kind of observation is rather light to prove something revolutionary, because the possible experimental artifacts are numerous and much more probable than what is supposed, if only the action of temperature on lubrication and friction.

Aspden can imagine that this is a new effect and call it "virtual inertia", but this is not what is expected of him if he hopes to place himself in a scientific perspective. What is required is an operational and formalized definition of his "virtual inertia", a list of properties, the way in which one can act on them in order to verify experimentally predictions from his theory.
Does he have any?

I have never been able to find detailed information on what he was talking about other than his energy measurements taken during the experiment.

I agree that if he thought he had discovered something, then he should/would/might have explored it further.  Perhaps he did, and the details were not made available.  Who knows....
What is odd is that Aspden was not one to let something curious go by the wayside.  He was a prolific experimenter and writer with a lab at his disposal. So, I would like to think he did explore it further, but whaat were his findings?  Did he make an error, repeatedly, and then laugh about it afterwards?

A short article on the "discovery":
http://newenergytimes.com/v2/archives/fic/N/N199502s.PDF

More details are found here:
http://exo-science.com/aspden.html

It says Aspden went on to develop an OU magnet motor.  I wonder if it actually worked. 
His dual concentric capacitor invention did not work the way he thought it would, he later admitted.

The references are very interesting as I actually know "vortex-1" as "Ion" on this forum and often wondered if he was actually "spherics" who provided details on the TPU.  Not helpful for understanding the motor though.

This has the most detail:
http://www.aetherscience.org/www-energyscience-org-uk/le/Le30/le30.html

So, taking "virtual inertia" on "blind faith":
1. What if you can rotate space and it has an inertial effect?
2. I can rotate something easier, so what?
3. Are moving charges and changing fields relative to "space" as an observer?
4. bottom line: is rotating space useful (assuming it has inertia)?
   
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Re: Exploratory Mathematics « Reply #14 on: 2022-09-17, 21:13:58 »

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Quote from: F6FLT on 2022-09-17, 17:36:58
@hakasays

"the 4 primary dimensions of Space, Time, Dielectricity, and Magnetism" : except for time, they are not dimensions. Space alone has 3 dimensions.

What you are saying simply does not make sense. This being said, I remain open, and if from your esoteric novel comes an experimental idea capable of demonstrating new effects, I will carefully observe your demonstration.

See the discussion on the distinction between metrical and coordinate dimensions:
https://gis.stackexchange.com/questions/115014/whats-the-difference-between-coordinatedimension-and-spatialdimension
and
https://www.quora.com/In-laymans-terms-what-is-the-difference-between-a-spatial-dimension-and-a-time-like-dimension
When I say 'dimension' I am referring specifically to a metrical dimension, not a coordinate dimension.
Don't worry, it confused me for a while too :P


Note in the attached image that E and I are considered the two primary/fundamental metrical dimensions in the table, while every other definition is a derivative or relation that incorporates at least two components.  Of course in the real world there is always a complex mix of everything.

Just to be clear, this perspective is not required to perform experimental mathematics, it's just the perspective that helped led me to some interesting/unexpected solutions (like 1/ϵμ = E/M).   I'm just trying to describe the process and logical techniques that got me there.


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Re: Exploratory Mathematics « Reply #15 on: 2022-09-18, 09:56:11 »
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@Hak

If you don't talk about dimensions as references of coordinate types of a space, then the choice is completely arbitrary, but must respect the rule that a basic dimension must be independent of the others which is also true for the coordinate dimensions. It is in fact the same principle in both cases (the notion of orthogonality).

In the SI system, the 7 basic dimensions are :
length (L)
mass (M)
time (T)
electrical intensity (I)
thermodynamic temperature (θ)
amount of matter (N)
luminous intensity (J)

All other dimensions are expressed from these. You can choose anything as long as the dimensions remain independent of each other, for example you can choose the charge (Q) instead of the current (I).
The choice you made is totally arbitrary too, but it does not correspond to a set of necessary and sufficient dimensions. Most of them share the same basic units as the others (e.g. L and C, or voltage and current), so your dimensions are not independent of each other. It's not so much the question of the dimensions that "confuses me" but the not coherent way you choose them. And even if you choose a correct set of them, as it is arbitrary it would not bring anything new.


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Re: Exploratory Mathematics « Reply #16 on: 2022-09-18, 15:26:54 »

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At least we're more-or-less on the same page now.


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Re: Exploratory Mathematics « Reply #17 on: 2022-09-18, 18:13:19 »

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Fun exercise: calculate the velocity of light through a negative-refractive-index meta-material. ;D :o

https://www.sciencedirect.com/science/article/pii/S1369702106715735

Quote
In addition to a negative index (NI) of refraction, properties such as artificial magnetism, negative permittivity, and negative permeability have been observed in fabricated MM composites; these material properties are either absent from conventional materials or are difficult to achieve over various bands of the EM spectrum

Also: https://www.science.org/doi/10.1126/science.1136481


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Re: Exploratory Mathematics « Reply #18 on: 2022-09-19, 08:38:28 »
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Seriously, do you think scientists would have missed the miracle of a speed > c?

You have to see that n<1 is a macroscopic view. The material is made of resonators between which the light or the radio signal gets trapped in standing waves at certain frequencies, before their re-emission.

The interface between the vacuum (n = 1) and the medium (n<1) acts as a strong resonance scattering center that temporarily traps the wave before gradually re-emitting it. This delay is much longer than the travel time in the medium and explains the apparent paradox of the outer ray propagating faster than the speed of light.

Simplified math formulas like n=c/v are not enough for physics. And if you thought they were enough, then why don't you attach as much importance to the math of relativity which implies a limit speed?



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Re: Exploratory Mathematics « Reply #19 on: 2022-09-19, 14:50:18 »

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Quote from: F6FLT on 2022-09-19, 08:38:28
Seriously, do you think scientists would have missed the miracle of a speed > c?

The scientists working in this field seem to realize that the recorded results are not well-explained by existing models.

https://opg.optica.org/oe/fulltext.cfm?uri=oe-18-2-463&id=194313

Quote
Some of the most striking consequences of the negative index of refraction include the reversal of the direction of the phase velocity with respect to that of the group velocity, the reversal of the Casimir force, the negative refraction, and sub-diffraction-limit imaging, i.e. the perfect lens [1–7]. A complete understanding of the properties of negative index structures requires the re-evaluation of some well-known principles of the electromagnetic wave theory. Application of the usual positive media formula to the analysis of negative index structures may sometimes lead to erroneous conclusions. However, it is clear that fundamental to all NIM(Negative Index Material) is that, as the energy propagates forward, the accumulated optical phase along the light path decreases rather than increases as it does in normal positive index materials (PIM). Recognizing this decreasing optical phase along the energy propagation direction, one can show from the Huygens-Fresnel principle that the refracted beam bends toward the same side of the normal as the incident beam, resulting in the negative refraction.

As 'exploratory mathematics', we simply take the measured results and apply them to other EE formulas to see what else it might infer. ^-^

Negative index materials are simple split electromagnetic resonators scaled down to nano-size.  There's nothing inherently special or magical about them structurally.
I'm curious and am still perusing papers to see if there is a 'lower limit' to this effect....  Perhaps a pair of split resonators several inches in diameter would exhibit similar anomalous characteristics all the way down in the MF/HF/VHF bands? ???


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Re: Exploratory Mathematics « Reply #20 on: 2022-09-21, 12:46:01 »
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There is no 'lower limit'. At low frequencies, it is only a problem of practical implementation, a question of size. A metamaterial must be much larger than the wavelengths and contain a multitude of resonators that are small in comparison to the wavelength.

As for your quote, I don't see anything revolutionary, only truisms (especially the last sentence), and the admission that we must continue to study the subject because we would know so little about it but this quote is already 12 years old and today we already know a little more, with still nothing revolutionary.




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Re: Exploratory Mathematics « Reply #21 on: 2022-09-21, 14:35:40 »

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Quote from: F6FLT on 2022-09-21, 12:46:01
As for your quote, I don't see anything revolutionary, only truisms (especially the last sentence), and the admission that we must continue to study the subject because we would know so little about it but this quote is already 12 years old and today we already know a little more, with still nothing revolutionary.

Did you do any follow-up research on the authors' works to see what kind of progress might have been made since then?


The nice thing about studying large negative refractive index cavities in the HF band is that it makes experimentation and analysis much more accessible to the amateur.  Also provides more opportunity for switching/parametrics. ^-^


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Re: Exploratory Mathematics « Reply #22 on: 2022-09-22, 10:45:48 »
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Quote from: Hakasays on 2022-09-21, 14:35:40
Did you do any follow-up research on the authors' works to see what kind of progress might have been made since then?

I rarely follow an author but only areas of physics. Evanescent waves, tunneling and meta-materials are among them. The truth cannot come from a single author, it must at least be confirmed by others.

Quote
The nice thing about studying large negative refractive index cavities in the HF band is that it makes experimentation and analysis much more accessible to the amateur.  Also provides more opportunity for switching/parametrics. ^-^

I agree. The disadvantage is the practical realization.
A meta-material must indeed appear as a homogeneous medium at the wavelength scale, i.e. the dimension of the resonant elements must be small compared to the wavelength, and in order to be able to speak of a "medium", they must be very numerous because they must occupy a large volume compared to the wavelength.
Even at 1 GHz, we would need a volume of 2 or 3 m3 with a few hundred resonators if we want to do things properly. It's still feasible but I don't tell you the work that it represents... :(. At 10 MHz, the same number of resonators but larger, so in a volume 106 times larger!



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Re: Exploratory Mathematics and Large Negative Index Resonators « Reply #23 on: 2022-09-27, 04:04:53 »

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Quote
A meta-material must indeed appear as a homogeneous medium at the wavelength scale, i.e. the dimension of the resonant elements must be small compared to the wavelength, and in order to be able to speak of a "medium", they must be very numerous because they must occupy a large volume compared to the wavelength.
Even at 1 GHz, we would need a volume of 2 or 3 m3 with a few hundred resonators if we want to do things properly. It's still feasible but I don't tell you the work that it represents... :(. At 10 MHz, the same number of resonators but larger, so in a volume 106 times larger!


It's an interesting hypothesis, but I suspect the result has to do more with surface area than with bulk volume (since a negative-index meta-material can be mere atoms thick).
IE: More like a skin effect.

A good test/challenge would to predict the possible results for a resonator that did not cover a significant volume relative to its frequency (for example, a TPU-sized negative-index resonator).

As negative-index resonator volume (or surface area) increases:
Possibility 1 - Wave interaction means that the bulk wave impedance approaches unity and gradually becomes negative as resonator volume is increased.
Possibility 2 - Waves split (some refract, some reflect), so a percentage of a given wave is negative-refracted while the remaining wave continues conventionally.
Possibility 3 - Both 1+2 are true, but the complex interactions results in a solution that approaches possibility 1.

I suspect possibility 1 or 3 are the most likely as they'd also fit with the extra-luminal property observed in Bell's inequality, as well as the complex VNA results I've observed in air-gapped solenoid coils.


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Re: Exploratory Mathematics and Large Negative Index Resonators « Reply #24 on: 2022-09-27, 07:39:41 »
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Quote from: Hakasays on 2022-09-27, 04:04:53
It's an interesting hypothesis, but I suspect the result has to do more with surface area than with bulk volume (since a negative-index meta-material can be mere atoms thick).
IE: More like a skin effect.
...

It's not a "hypothesis", it's the obvious conditions for it to work, known by everyone in the field.
You don't seem to know what you are talking about, nor do you understand the principle of a metamaterial.
A wave cannot propagate in a "medium" smaller than the half-wave, it would no longer be a "medium".  If it is larger than the volume, it would also propagate outside the metamaterial.
And if we have propagation phenomena along the resonant elements, the element itself becomes a "medium", in fact an antenna, and the whole becomes an array of tuned antennas, permeability and permittivity are no longer uniform, it is no longer the same principle.
So: global volume>> lambda and element size << lambda are the conditions to be able to talk about a "medium", i.e. with homogeneous permeability and permittivity seen from the EM waves.


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