[Mr. Scientist]

Force due to gravity can be expressed as a particle  with a mass M² moving in a field is given as: F_g=-▼φM_g (1) so:

(F_gvt)²=-▼²φ²(ћ(c/G))_g v²t² (2)

This equation was the first form i considered. It is respectfully using the gravitational charge relationships given (1), just altered slightly to involve an energy due to gravity since equation (2) reduces to E_g. One normally interpretes this as an energy due to a gravitationally-related inertia, hence the possible existence of a small amount of matter for a photon to allow such a charge in your assumptions.

To note, there are a few relations which will help decode eq. (2):

M²=ћ(c/G) (3)

and this take a large value as it is rearranged:

ћc=GM² (4)

As has been interpreted (ref:1), the value ћ=GM²/c is very small and can be seen as a quantized gravitational charge. It is also wise to note for the record that β=v/c and that in relativity, we have the form to consider pc=E(v/c), so you can check the dimensions yourself. Also we will encounter what are called super-complex numbers, which have values which renormalize positively i²=+1, where respectively you can mathematically treat terms like i=k=j as found in quarternion relationships. The super-complex symbol is usually present as a box with a cross inside of it, but for the sake of my incomplete knowledge on how to represent this in latex symbolism, i will represent it as ξ so that i²=ξ=+1.

The equation which describes such a connection for a photon with a considerably small mass and almost negligable charge can be represented by this exausting equation;

The equation which takes into respect permittivity of both gravitational and electric (-magneto) relationships where the energy and force terms found in equation (2) are also taken into consideration:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i ∫d^4 x(½[ξε_0(M²ψ-M²ψ]+½[ξε_g(M²ψ*-M²ψ*]) (5)

where A=e^i ∫d^4 x(½[ξε_0(M²ψ-M²ψ]+½[ξε_g(M²ψ*-M²ψ*]) (6) and since we are dealing with four respective interactions given by the vortex description of k=DψDψ* then the value of k is indeed a squared value. k is given as:

k=(t1<t2)ψ*(t2>t1)ψ*/∫A dt

for one description of a wave interaction. The math itself has retarded and advanced forms, so psi description of ψ* can be classed as an incoming field, whereas ψ can be interpreted as an outgoing field. Naturally, these should obide by normlization so that two quantum psi waves can multiply and create one positive value, which is an amplitude prediction of quantum statistics given as: ∫|ψ|²=+1.

The use of ξ is to represent the ''positive attraction'' (experimentally-proven for gravity and for certain interactions of non-like charges) between the two permittivity constants. It also contains an element of ''likelihood'' so the value of <A> is given as an ''expectational value'', becoming a state vector when defined accordingly. Because all terms on the right hand side remain positive is the same mathematical reason why the left is given as an absolute value |a|=+a. The symbol k is in fact a coupling constant dependant on the rate of A. If A is strong, the exponent of e^iA is itself dependant on the rate of A so the increased factor of A increases the repitious vibrational pattern. The value of d^4 is in fact just a four dimensional configuration with a small value calculating the action within a volume of space we usually associate with the coordinate (x). You could expand the equation to show this four-dimensional configuration under a wave description, but to keep this as simple as possible ffor myself and the reader, it will be confined by the description of d^4.

In equation (5), a photon with a charge due to the presence of a curvature takes into respect the imposed conditions of both ε_0 and ε_g which remain a positive value under the influence of its super-complex coefficients. The presence of the trig-function of β=v/c has an importance when considering particles which travel at light speed.

To finalize, equation (5) yields the contention that a photon has a non-zero but small mass with a corresponding small charge, within the presence of the permittivity of the system in free space. According to the equation itself, a photon cannot magically transform into matter, but rather the matter increases when the intrinsic kinetic energy increases, or due to the strength of (A) mass can increase to have the appearance of a slow restricted inertial body.

[Vern (OP)]

I suspect that you can not get to the photon construct within Quantum theory. A photon has no apparent charge because the electric and magnetic charges that comprise it are equally balanced. Your description does not match the vision of a photon that I see. I'm not sure whether it is because I have not communicated the vision well, or you need to modify it to fit a view you can accept.

The photon I describe is not my own invention. It is the way photons were depicted before Quantum theory came along and reduced the photon to a wave function. The photon I see is the same as is described by Maxwell's equations. It is comprised of electric and magnetic amplitude potential. It is charge neutral, but comprised entirely of charge. It has zero mass, but it is mass when it is confined in a local area.

I suspect that you can not get the vision unless you can somehow avoid trying to mix Quantum theory with Reality theory. Hey; that's an idea!I think I'll start calling the photon-only universe scheme Reality Theory.  []

[Mr. Scientist]

I suspect that you can not get to the photon construct within Quantum theory. A photon has no apparent charge because the electric and magnetic charges that comprise it are equally balanced. Your description does not match the vision of a photon that I see. I'm not sure whether it is because I have not communicated the vision well, or you need to modify it to fit a view you can accept.

The photon I describe is not my own invention. It is the way photons were depicted before Quantum theory came along and reduced the photon to a wave function. The photon I see is the same as is described by Maxwell's equations. It is comprised of electric and magnetic amplitude potential. It is charge neutral, but comprised entirely of charge. It has zero mass, but it is mass when it is confined in a local area.

I suspect that you can not get the vision unless you can somehow avoid trying to mix Quantum theory with Reality theory. Hey; that's an idea!I think I'll start calling the photon-only universe scheme Reality Theory.  []

Then i will attempt to modify a quantum explanation as to why they may not be balanced. In theory, the balance is true but there may be some mathematical trick to unbalance this. I'll work on it.

And i like the name

[Vern (OP)]

We can build Reality Theory as we go. It should incorporate as much Quantum theory as possible, but still maintain strict adherence to cause and effect. That doesn't mean we must discover the cause for every effect, it just means that we know there is a cause, we may just not know exactly what it is.

As in the original photon-only universe theory, we can base Reality Theory on just two postulates:

(1)Space-time is flat and non varying in the classic sense.
(2)The final irreducible constituent of all physical reality is the electromagnetic field.

When I apply cause and effect while adhering to those postulates, I get Reality Theory  []

[Mr. Scientist]

I need to ask a question.

Are you saying that they should be balanced or that they shouldn't be balanced in your hypothesis, because if it the first one, then equation:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i ∫d^4 x(½[ξε_0(M²ψ-M²ψ]+½[ξε_g(M²ψ*-M²ψ*]) (1)

is balanced, because it takes into respect the electromagnetic permittivity added with that of the gravitational permittivity with a Langrangian term for M². More interestingly enough, M²ψ is similar to the Klein-Gorden relationship. Here are some interesting reationships:

M²ψ=-∂t(ψ)+ ▼²ψ

which results in plane wave solutions. By substitution, you can reconfigurate eq.(1) into:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i ∫d^4 x(½[ξε_0(=-∂t(ψ)+ ▼²ψ-=-∂t(ψ)+ ▼²ψ]+½[ξε_g(=-∂t(ψ)+ ▼²ψ*-=-∂t(ψ)+ ▼²ψ])

Which is very attractive as a wave equation.

We could manipulate the equation even more to have nuetral components after taking ino account, from a Klein-Gorden relationship, where for manipulative convenience we can rewrite the plane wave solutions in  quantized form as:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i ∫d^4 x(½[ξε_0((∂²-M²)ψ*-(∂²-M²)]+½[ξε_g((∂²-M²)ψ*-(∂²-M²)ψ*])

This is suppose, would cancel them out, or at least, this is my interpretation of the equation.

[Mr. Scientist]

We can build Reality Theory as we go. It should incorporate as much Quantum theory as possible, but still maintain strict adherence to cause and effect. That doesn't mean we must discover the cause for every effect, it just means that we know there is a cause, we may just not know exactly what it is.

As in the original photon-only universe theory, we can base Reality Theory on just two postulates:

(1)Space-time is flat and non varying in the classic sense.
(2)The final irreducible constituent of all physical reality is the electromagnetic field.

When I apply cause and effect while adhering to those postulates, I get Reality Theory  []

To do so, if i have understood you, the big bang would need to have been an event which was ruled by classical rules... but this is not the case on their scales.

[Vern (OP)]

Are you saying that they should be balanced or that they shouldn't be balanced in your hypothesis, because if it the first one, then equation:

Forces should balance resulting in the appearance of neutral charge in a photon. When the path of the photon is bent, the balance is interrupted, the field areas can not be symmetrical in the bend, charge is the result.

To do so, if i have understood you, the big bang would need to have been an event which was ruled by classical rules... but this is not the case on their scales.

We have an easy out on this one. There could have been no big bang within Reality Theory. The natural rules of nature apply, we can not suspend them to allow for a creation event.

[Ethos]

To do so, if i have understood you, the big bang would need to have been an event which was ruled by classical rules... but this is not the case on their scales.

Could we proceed with this without assuming the need for a Big Bang? It is possible that the so-called, "Big Bang", is only an invention that attempts to explain expansion when there are other explanations for the observed red shift.  

[Mr. Scientist]

To do so, if i have understood you, the big bang would need to have been an event which was ruled by classical rules... but this is not the case on their scales.

Could we proceed with this without assuming the need for a Big Bang? It is possible that the so-called, "Big Bang", is only an invention that attempts to explain expansion when there are other explanations for the observed red shift.  

Verns answer, seems to apply directly to your question.

Vern's answer is only a possibility on the effect that there has been no such quantization period in the universe where spacetime literally expanded. On this note, Verns theory will have to evidently require that the electromagnetic singularity he speaks of must be removed, because electromagnetic singularities are usually associated with some infinitely dense point, but as Vern punctually-noted, he does not want a big bang.

[Mr. Scientist]

Are you saying that they should be balanced or that they shouldn't be balanced in your hypothesis, because if it the first one, then equation:

Forces should balance resulting in the appearance of neutral charge in a photon. When the path of the photon is bent, the balance is interrupted, the field areas can not be symmetrical in the bend, charge is the result.

To do so, if i have understood you, the big bang would need to have been an event which was ruled by classical rules... but this is not the case on their scales.

We have an easy out on this one. There could have been no big bang within Reality Theory. The natural rules of nature apply, we can not suspend them to allow for a creation event.

But Vern, what is a neutral charge? - it seems indestinguishable to a system which has no charge at all...?

[Ethos]

Verns answer, seems to apply directly to your question.

Quite right.............he seems to have beaten me to the punch in his last post.

[Vern (OP)]

I suspect that there is a difference between a neutral charge and no charge at all.  A local area would experience a quick succession of electric and magnetic change when a photon passed through. It would experience a half cycle of charge in one direction immediately followed by a half cycle of the opposite.

No charge at all would not experience the brief ripple of cancelling charges. But the charges can cancel to neutral only if the path of the photon is a straight path. Any bending of the path must leave a residual charge.

[Ethos]

I suspect that there is a difference between a neutral charge and no charge at all.  A local area would experience a quick succession of electric and magnetic change when a photon passed through. It would experience a half cycle of charge in one direction immediately followed by a half cycle of the opposite.

No charge at all would not experience the brief ripple of cancelling charges. But the charges can cancel to neutral only if the path of the photon is a straight path. Any bending of the path must leave a residual charge.

I suggest that when the straight line path of the photon is influenced by a gravitational field, it not only responds with a resultant charge, it takes on the property of mass. Mass and charge go hand in hand. Like the gyroscope, the photon wave resists a change in it's trajectory and when this wave is forced to deviate, it responds by taking on the character of mass with charge.

[Mr. Scientist]

I suspect that there is a difference between a neutral charge and no charge at all.  A local area would experience a quick succession of electric and magnetic change when a photon passed through. It would experience a half cycle of charge in one direction immediately followed by a half cycle of the opposite.

No charge at all would not experience the brief ripple of cancelling charges. But the charges can cancel to neutral only if the path of the photon is a straight path. Any bending of the path must leave a residual charge.

I suggest that when the straight line path of the photon is influenced by a gravitational field, it not only responds with a resultant charge, it takes on the property of mass. Mass and charge go hand in hand. Like the gyroscope, the photon wave resists a change in it's trajectory and when this wave is forced to deviate, it responds by taking on the character of mass with charge.

This is almost certainly what the main equation i made in the work implies.

[Mr. Scientist]

I suspect that there is a difference between a neutral charge and no charge at all.  A local area would experience a quick succession of electric and magnetic change when a photon passed through. It would experience a half cycle of charge in one direction immediately followed by a half cycle of the opposite.

No charge at all would not experience the brief ripple of cancelling charges. But the charges can cancel to neutral only if the path of the photon is a straight path. Any bending of the path must leave a residual charge.

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i∫d^4 x(½[ξε_0(=-∂t(ψ)+▼²ψ-=-∂t(ψ)+▼²ψ]+½[ξε_g(=-∂t(ψ)+▼²ψ*-=-∂t(ψ)+ ▼²ψ]) (A)


take a look at the exponential function of (A) in the equation. It has the electromagnetic and gravitational permittivity. These where invited to make sense of the need of your theories use of some charge being present.

If we replace both the permittivity of the electromagnetic constant ε_g with the supercomplex coefficient ξ removed since it causes a positive value, (and we want these to be nuetral) with a nuetral charge component, we could for arguements sake, mathematically-express it as: μ_{g,0} for a gravitational charge (1) and one for its electromagnetic form of μ_{e,0}.

These expressions are not too difficult to understand. You can think of the subscript contained with the squibbly brackets as components of both charge and a value of zero, which is a nuetral vector component. μ1,μ2_{g,e,0} so this expression yields both states in nuetral-charge states. So replacing the supercomplex number coupled with the permitivvity constants as ξ1,ξ1_{ε_g,ε_0}, then we have modelled the vibrational patterns to suit your theory hopefully.

So, replacing the functions of ξ1,ξ1_{ε_g,ε_0} with μ1,μ2_{g,e,0}, we would arrive at an equation which i hope you will agree too... if not, as they say, if you first don't succeed, try and try again.

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i∫d^4 x(½[μ_0(=-∂t(ψ)+▼²ψ-=-∂t(ψ)+▼²ψ]+½[μ_g(=-∂t(ψ)+▼²ψ*-=-∂t(ψ)+ ▼²ψ])

(1) - remember, the gravitational charge must also by symmetry to have a neutral charge if indeed such a charge is distinguishable from no charge at all, this is a new reason why its essential to add it.

[Ethos]

If I may be allowed to interject a few thoughts here, I would like to consider the aspect of the wave.

For a long time, I have had trouble understanding the character of charge, but after reviewing the forgoing commentary, I think the concept has taken root in my imagination. Now that the essence of charge has become somewhat understandable to me, I would like to proceed on to the obvious.

How can we developement a reality based understanding of the wave? We know that the wave can not be discribed as a collection of infinitely small particles moving like water on the ocean surface. So what exactly is the electromagnetic wave?

We know that the photon wave can, when disturbed from it's preferred path, give rise to the charged particle. From seemly empty space, the wave transforms itself into  'Localized orbital energy flux' we call matter. This wave, apparently made of nothing but the organized perturbation of space, suddenly becomes localized into an object with radial momentum and mass.

How do we realistically define the electromagnetic wave?

 

[Mr. Scientist]

If I may be allowed to interject a few thoughts here, I would like to consider the aspect of the wave.

For a long time, I have had trouble understanding the character of charge, but after reviewing the forgoing commentary, I think the concept has taken root in my imagination. Now that the essence of charge has become somewhat understandable to me, I would like to proceed on to the obvious. (1)

How can we developement a reality based understanding of the wave? We know that the wave can not be discribed as a collection of infinitely small particles moving like water on the ocean surface. So what exactly is the electromagnetic wave? (2)

We know that the photon wave can, when disturbed from it's preferred path, give rise to the charged particle. (3)

From seemly empty space, the wave transforms itself into  'Localized orbital energy flux' we call matter. This wave, apparently made of nothing but the organized perturbation of space, suddenly becomes localized into an object with radial momentum and mass. (4)

How do we realistically define the electromagnetic wave?

(1)  I'll take that as a compliment.

Thanks.

(2) - An elctromagnetic wave, is really a photon in a quantum wave function.It spreads out over space in many possible locations, but only in a virtual sense. If that's what you meant?

(3) - Only theoretically. This is verns hypothesis, and i'm just attempting to make a mahematical model to help describe it. It's by no means universally-accepted though

..
.... unfortunately

(4) - Absolutely. There From seemly empty space, the wave transforms itself into  'Localized orbital energy flux' we call matter. This wave, apparently made of nothing but the
organized perturbation of space, suddenly becomes localized into an object with radial momentum and mass

Certainly, there is a local phenomena going on. The instrinsic change (or flux) from energy to matter seems to be an instrinsic internal change, but that
doesn't exclude the presence of a gravitational force field that can act as a mechanism for such a flux. It's always been a pet theory of mine to
not accept Higgs Mechanism, but resort to an easier approach using the gravitational field but vern made me realize that in many ways that mechanism was too
magically-inhanced by imaginary terms of course, just because the gravitational fields mechanism was a certain degree of energy did not suggest a reason to
why such a flux would usually happen. I decided it required verns hypothesis that curvature for photons implied a presence of a charge, both of graviational form
and of EM-form... but what i do not agree with is that the charge is constant - meaning constant in the sense it is present all the time, whether it changes
in quantity over time or not. I prefer the contention that charge only appears when there is an acting strong gravitational field associated to the photons
movement in a curved distorted spacetime warp; then as soon as it breaks free, that is if it breaks free, the charge will dissipate, meaning that gravitons
so not couple to the instrinsic properties of a photon when not in a curved geodesic.

This means that the two main equation i have presented:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i∫d^4 x(½[ξε_0(=-∂t(ψ)+▼²ψ-=-∂t(ψ)+▼²ψ]+½[ξε_g(=-∂t(ψ)+▼²ψ*-=-∂t(ψ)+▼²ψ]) ;a

and

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i∫d^4 x(½[μ_0(=-∂t(ψ)+▼²ψ-=-∂t(ψ)+▼²ψ]+½[μ_g(=-∂t(ψ)+▼²ψ*-=-∂t(ψ)+▼²ψ]) ;b

Are two equations with two different charge solutions. Vern's hypothetical neutral decription of photon charge in a respective gravitational field and its associated
charge, and one which solves for the charge-related to the permittivity which is non-nuetral, in fact, its positive.. to attain the negative, just simply remove the
supercomplex coefficient; it's irrational as an equation however, that is equation (a;) to be non-positively attracted, since it would eliminate the connectivity of
both the electromagnetic and gravitational field interactions. Instead of terms:(½[ξε_0(=-∂t(ψ)+▼²ψ-=-∂t(ψ)+▼²ψ]) and (½[ξε_g(=-∂t(ψ)+▼²ψ*-=-∂t(ψ)+▼²ψ]) being
added they would instead be subtracted, eliminating the Langrangian relation and also the vibrational pattern in |(∫F_g vt)²_<A_k²>| where F²_g v²t² is not a gravitational
energy and the expectancy or strength of expectancy of A=(e^i∫d^4 x(½[μ_0(=-∂t(ψ)+▼²ψ-=-∂t(ψ)+▼²ψ]-½[μ_g(=-∂t(ψ)+▼²ψ*-=-∂t(ψ)+▼²ψ]) is no longer valid unless its seen
as an oscillatory system, which still accounts to nothing in the end of any integration.

(5) - How do we realistically define the electromagnetic wave?

Well, my own personal view...

I'd say its the most primal form of information which has had one of the largest impacts in the construction of the universe. But it's still a particle afterall

[Ethos]

 But it's still a particle afterall

Yes, after all the distortions of it's primal state.

In another thread, Vern talks about the rise and fall of amplitudes associated with the wave and discribes this action as referenced to points in space. This notion of points in space relative to the wave is one I'm having trouble with. How can a homogenous wave, in it's pure state, have any particular points? I visualize a wave as the kinetic action on space that the release of energy induces to it. As the wave radiates forth from it's source, each blanketing pulse of energy does distinguish itself with crests and valleys of amplitude but, these crests and valleys are infinitely graduated in power and I can't rationalize any particular and definable points within singular bursts. However, where one blanketing burst meets another, one will find an area of intersecting amplitudes but I still don't visualize any particular points. That is unless, one suggests that along a line of intersecting waves, one must limit things to Planck lengths. In that case, each Planck length would have two points at each end of it's dimension. So maybe yes, I suppose one can talk in terms of points of amplitude.

[Mr. Scientist]

ince one contention is that electromagnetic fluctuation experience a charge in the presence of following the curved geodesic of a spacetime warp, and then the charge dissipating when beginning to move in a straight line again would mean that the gravitational field is what causes the photon to posses some innate and instrinic charge, whether it be positive, nuetral or propulsive, which all the works equations have attempted to describe these possible states.

The last one on the agenda however, is no charge at all, as described when travelling in a straight line. This derivation was a little harder.


A=(e^i∫d^4 x(½[μ_0(=-∂t(ψ)+▼²ψ-=-∂t(ψ)+▼²ψ]+½[μ_g(=-∂t(ψ)+▼²ψ*-=-∂t(ψ)+▼²ψ]) (1)
 
has no epsilon value. Epsilon is a small value, and when it's used in an equation like this:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i ∫d^4 x(½[ξε_0(M²ψ-M²ψ]+½[ξε_g(M²ψ*-M²ψ*]) (2)

It is itself a tensor so has a factor of √g' which is respectively negative. In mathematical terms, its the determinent of the metric tensor. Replacing this with the epsilon values we have:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i ∫d^4 x(½[ξ√g'_0(M²ψ-M²ψ]+½[ξ√g'_g(M²ψ*-M²ψ*]) (3)

But keeping in mind the supercomplex number (which by the way, hardly no scientist uses, but does respect it as an actual mathematical algebra), we could replace it by (i²), which of course equals the same value of positive +1. This makes the negative value of the metric tensor positive |√g'|.

rearranging the components of equation (1), where A equals the components of all that interesting stuff going on in the exponential function, we now add the D'albertian wave equation ∂²/∂t²-Δ with the mass-squared term and we have:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i ∫d^4 x(½[ξ√g'_0((∂²/∂t²-Δ + M²)ψ-(∂²/∂t²-Δ + M²)ψ)]+½[ξ√g'_g((∂²/∂t²-Δ + M²)ψ*-(∂²/∂t²-Δ + M²)ψ*])

Where (∂²/∂t²-Δ + M²)ψ = 0

→ = g_μν∂^ν∂^μ

Which is perfectly a Klein-gorden solution. Since there is the contraint in the determinent metric tensor quality remaining positively-valued (an unusual approach) requires that any gravitational force will be a resultant vector quantity of compressed (or of pressure-related) forces dependant on a small area of d^4, with a position (x). If the positional change is very minute (AS IN small, ir infinitessimal movements), as the case must imply, then the equation finally can be written as:

|(∫F_g vt)²_<A_k²>|=∫-▼²φ²(ћ(c/G))_g β²t²^(e^i ∫d^4 δ(x-x')(½[ξ√g'_0((∂²/∂δt²-Δ + M²)ψ-(∂²/∂δt²-Δ + M²)ψ)]+½[ξ√g'_g((∂²/∂δt²-Δ + M²)ψ*-(∂²/∂δt²-Δ + M²)ψ*])

The reason why when a small spatial composition is taken into account in a field, there is also a respective amount of small time. This are called the Planck Constraints, they are fundamentally-constant. This would mean we would be measuring the Langrangian Term of the particle in very small confinements.

This final equation, as i promised, is the last of the equations which can take into account a photon could have a zero-quantity of charge when not within the presence of a gravitational field. Though when subject to one, it could be argued it has to, as vern's theory goes.

[Mr. Scientist]

 But it's still a particle afterall

Yes, after all the distortions of it's primal state.

In another thread, Vern talks about the rise and fall of amplitudes associated with the wave and discribes this action as referenced to points in space. This notion of points in space relative to the wave is one I'm having trouble with. How can a homogenous wave, in it's pure state, have any particular points? I visualize a wave as the kinetic action on space that the release of energy induces to it. As the wave radiates forth from it's source, each blanketing pulse of energy does distinguish itself with crests and valleys of amplitude but, these crests and valleys are infinitely graduated in power and I can't rationalize any particular and definable points within singular bursts. However, where one blanketing burst meets another, one will find an area of intersecting amplitudes but I still don't visualize any particular points. That is unless, one suggests that along a line of intersecting waves, one must limit things to Planck lengths. In that case, each Planck length would have two points at each end of it's dimension. So maybe yes, I suppose one can talk in terms of points of amplitude.

Good questions, let me think about it for about 10 mins over coffee