Need help with maths for new theory of physics

[ddj]

Hi,
I have written a beautiful theory of Physics based on the discredited aether theory. Unfortunately although the written description of the theory is excellent, the mathematical foundation leaves a lot to be desired. If there is any mathematician present at this forum, who disagrees with time dilation and length contraction and is in favour of finding a new theory. I request you to kindly offer your ideas for a mathematical foundation for the theory, which could be worked on, on a partnership basis.

At present there exists no satisfactory theory for the propagation of light. Even the simple case of light travelling from point A to point B is very obscure. Quantum mechanics holds that from the moment that light is emitted at point A, it ceases to exist as something real and exists instead as an abstract mathematical wave function that travels through multiple dimensions. The light only becomes real when it is detected at point B when the wave function collapses and the light becomes real again. It might be argued that the wave function only gives the probability of finding the light at any given point, but this is a far from adequate answer. According to Huygens light exists everywhere on an expanding spherical wave-front.

These are the kind of ideas that my theory attempts to explain. I request anyone interested to not disparage the concept of an aether. After all Dark Matter exists and possess exactly the same properties that the aether was said to possess, it has not been detected. According to my theory Dark Matter is synonymous with the aether. There are new and cogent explajnations for electricity, magnetism and even for gravity.

If anyone is interested in pursuing this further, I will send you a link to download the paper. Thanks ddj

 

[topsquark]

Hi,
I have written a beautiful theory of Physics based on the discredited aether theory. Unfortunately although the written description of the theory is excellent, the mathematical foundation leaves a lot to be desired. If there is any mathematician present at this forum, who disagrees with time dilation and length contraction and is in favour of finding a new theory. I request you to kindly offer your ideas for a mathematical foundation for the theory, which could be worked on, on a partnership basis.

At present there exists no satisfactory theory for the propagation of light. Even the simple case of light travelling from point A to point B is very obscure. Quantum mechanics holds that from the moment that light is emitted at point A, it ceases to exist as something real and exists instead as an abstract mathematical wave function that travels through multiple dimensions. The light only becomes real when it is detected at point B when the wave function collapses and the light becomes real again. It might be argued that the wave function only gives the probability of finding the light at any given point, but this is a far from adequate answer. According to Huygens light exists everywhere on an expanding spherical wave-front.

These are the kind of ideas that my theory attempts to explain. I request anyone interested to not disparage the concept of an aether. After all Dark Matter exists and possess exactly the same properties that the aether was said to possess, it has not been detected. According to my theory Dark Matter is synonymous with the aether. There are new and cogent explajnations for electricity, magnetism and even for gravity.

If anyone is interested in pursuing this further, I will send you a link to download the paper. Thanks ddj

A few points.
1) How can you be sure that you are correct? Your theory must be testable... which typically means you need to do Math in order to check it with any experimental results. So the basic comment here is that you haven't yet verified your "theory" which makes it merely a hypothesis.

2) The "material" that light propagates in used to be called the "luminiferous aether" (a name coined by Newton.) The existence of the aether was pretty much disproven by the Michelson-Morley experiment. Light is actually neither a wave nor a particle though it shares similar concepts of both. It does not need a material to propagate through.

3) Wavefunctions are defined to contain all the information about the object. The Born lemma says that the "square" of the wavefunction gives the probability that a particle will be in a specific location. But the wavefunction contains a lot more than that. Energy, momentum, angular momentum, spin, etc. are several other properties that a wavefunction will contain.

4) Dark matter can be detected by observing the gravitational force acting between it and any "ordinary" matter. One possible explanation for dark matter is the concept of an aether, but really it is nothing like the Newtonian aether. So far as a I know no concept has been successful in explaining what dark matter is or how it works. Many other ideas for dark matter have been proposed (such as WIMPs, which is my personal favorite) but none of them have really been validated.

5) Time dilation and length contraction are verified by experiment. How can you discount them?

I would be happy to give you some ideas about the Math that you are interested in learning. But please bear in mind that dark matter is one of the cutting edges of Physics right now and that the Math involved is going to likely be rather extreme. Please let us know what your ideas are and we can get to work. Be advised, though, that your theory needs to account for not only the experiments that have already been done but it must also make new predictions that the old theory hasn't explained.

-Dan

 

[ddj]

A few points.
1) How can you be sure that you are correct? Your theory must be testable... which typically means you need to do Math in order to check it with any experimental results. So the basic comment here is that you haven't yet verified your "theory" which makes it merely a hypothesis.

2) The "material" that light propagates in used to be called the "luminiferous aether" (a name coined by Newton.) The existence of the aether was pretty much disproven by the Michelson-Morley experiment. Light is actually neither a wave nor a particle though it shares similar concepts of both. It does not need a material to propagate through.

3) Wavefunctions are defined to contain all the information about the object. The Born lemma says that the "square" of the wavefunction gives the probability that a particle will be in a specific location. But the wavefunction contains a lot more than that. Energy, momentum, angular momentum, spin, etc. are several other properties that a wavefunction will contain.

4) Dark matter can be detected by observing the gravitational force acting between it and any "ordinary" matter. One possible explanation for dark matter is the concept of an aether, but really it is nothing like the Newtonian aether. So far as a I know no concept has been successful in explaining what dark matter is or how it works. Many other ideas for dark matter have been proposed (such as WIMPs, which is my personal favorite) but none of them have really been validated.

5) Time dilation and length contraction are verified by experiment. How can you discount them?

I would be happy to give you some ideas about the Math that you are interested in learning. But please bear in mind that dark matter is one of the cutting edges of Physics right now and that the Math involved is going to likely be rather extreme. Please let us know what your ideas are and we can get to work. Be advised, though, that your theory needs to account for not only the experiments that have already been done but it must also make new predictions that the old theory hasn't explained.

-Dan

Hi Dan, I can hardly begin to thank you for this wonderful reception. I have already prepared my reply, I just need to know if yiou would like me to post it here or PM you, Thanks, Dilip

 

[topsquark]

Hi Dan, I can hardly begin to thank you for this wonderful reception. I have already prepared my reply, I just need to know if yiou would like me to post it here or PM you, Thanks, Dilip

I do all of my tutoring help on the open forum. You can get other inputs that way as well.

-Dan

 

[ddj]

Hi Dan,

Thank you for the great introduction to the Maths Help Forum, I am excited that you are willing to consider my proposition. As you had pointed out it is going to be difficult to describe something new. I have been working on some ideas but you would have to say if they are practical or not. I appreciate that you would like to have some idea of what my theory is, before making any commitment.

I was thrilled to get my first computer and log onto the internet (quite a long time ago). Naturally for such an important occasion I had to pick something really important to search for, and the subject I came up with was light. I had studied physics and done a course in engineering and I was wondering what wonderful advances had been made and what new mysteries had been discovered about light. To my amazement, I discovered that far from making advances, theories about light were more obscure now than ever. This must have been the early 2000’s. I was so disappointed that I decided to investigate the subject on my own. As a starting point I decided not to follow the quantum mechanics method of trying to describe light using statistics and probabilities, but to use the methods followed by Crick & Watson in their search for the structure of DNA which had eluded bio-geneticists for a long time. The search for DNA had, previous to Crick & Watson, depended solely upon statistics and theory to come up with a model.

Like, Bio-tech (as it is called now-a-days), quantum mechanics which is the dominant main stream theory in physics, also depended solely upon statistics, to the extent, that no model for the structure of a photon had ever been attempted. In investigating light, my first idea was to study the properties of the photon and to go from there.

I reasoned that since the electron is a charged particle, that it most probably mediated its energy by emitting and absorbing short pulses of electric energy:



Since the initial pulses of energy emitted by the electron were stronger than subsequent pulses of energy that are emitted, the pulses of energy became polarised. The fact that the short pulses of energy were separated by gaps, gave the structure a capacitor like formation which meant that this structure could maintain its energy forever. In the next stage, the polarised pulses of energy formed a solenoid field around themselves:



The definition of a solenoid dipole is that there are no open loops all of the loops consist of closed loops. This gave the whole structure a very stable configuration that could be maintained for a long time with no loss of energy.
This model of the photon fulfils all of the properties of the photon:

• The photon has no mass
• The photon is electrically neutral
• The photon always travels at the speed of light, it is never still
• Optical photons are always emitted by bound electrons within the atom.
• There are trillions of possible frequencies, wavelengths and energies that photons can possess
• Photons keep their energy (identity) intact even after travelling for billions of light years.
• Photon can combine to form different colours but always maintain their identity intact.
• Radio-waves also possess the identical properties that have been enumerated above but have a different genesis than optical and high energy photons.
• Photons follow the inverse square law.
• The photon is both wave and particle.

This, in short, is the first part of the basis of my theory. The second part of my theory, is the aether. The aether according to my theory is made up of photons that are identical to the photon described above, but possess such low energy 10^-40 J, that they are to all purposes undetectable, since no atom could possibly ever use, or require, a photon of such low energy. They also, by the provision of the Heisenberg Uncertainty Principle \(\displaystyle \Delta T \Delta E \geq h \) as it applies to energy and time, have life times comparable to that of the proton. These photons permeate the whole of the Universe and were formed at the time of the Big Bang. Thus light is formed , it travels through light and returns into light.

You had asked me why I thought my theory was better. Firstly, as you can probably see, this ‘aether’ has nothing in common with the luminiferous aether. This ‘aether’ consists of electric dipoles that are more or less stationary in space, but possess 360 degrees of freedom. When a real photon is emitted, the virtual photons of the aether form into a line whose ends rest on infinity and the energy of the real photon is conveyed along this line of aligned photons. Note, it is not the ‘physical’ real photon that is conveyed, but its energy. Since Dark matter constitutes 85% of all matter in the Universe and baryonic matter another 5%, the theory of an all pervasive aether is compelling. Also note the very low interaction with matter that this electric dipole aether possesses ; because of the extremely low energy of 10^-40 J that individual virtual photons possess, no atom would need or accept photons of such low energy, therefore, the sun, the planets and the stars can pass through the aether as if it did not exist and vice versa. The Michelson & Morley experiment did not take into account this crucial property of the aether, namely its extremely low interaction with matter: hence the whole concept of the earth dragging the aether to create an aether wind was based on false premises.

This configuration of the ‘aether’ allows for light (EM radiation) to follow the inverse square law while still enabling each individual photon to retain the original energy with which it was originally emitted. This is something that quantum mechanics had failed to do in over a 100 years, while Einstein depended on Mawell's equations. These equations do not work because they are wave equations.

As I had mentioned earlier I had tried to make some forays into a mathematical explanation but these would probably be considered to be farcical. Hope this theory meets the criteria laid down in your post.

 

[topsquark]

First, I am not going to tell you that I'm receptive to your hypothesis. I am a firm believer in teaching the Standard Model in these forums because most students that come here aren't ready to deal with what we don't know if they don't understand what we do know. I am not saying I'm against your ideas.... there is a thread of truth in what you are saying. I am willing to help you but I'm not promising that I'll support your ideas or where they lead.

The main theory of light that we have right now is Quantum ElectroDynamics. This is generally what we use when I speak of charged particles and photons. (Later on we can bring in the weak nuclear force and we then talk about Electroweak theory.) QED is just about the most ridiculously accurate model that you could ever want. It does the job just fine.

You are conceptually moving into QFT. Your idea of particles of light at [math]10^{-40}[/math] J pervading the Universe since the BB is incorrect. That field of light waves is known to exist and has been measured at a temperature of between 2 and 3 K. Any model with the photons you are proposing would have to come from a different source.

The idea about polarizing the vacuum (that's where you seem to be leading to) is more or less in the spirit of the Standard Model, but again you are backing the wrong particles. The concept of a quantum field is based on a second order correction to the field's oscillators. The field is composed of a bunch of quantum harmonic oscillators. A problem arises there because of the sheer number of these things.... it's what forms the "zero point energy" and the calculations based off this give the vacuum an infinite energy density. It's a big problem and no one has come up with a solution to it. (Perhaps String Theory but we can't prove any of it yet.) Either way, the oscillators of the field are not photons in general.

Now a question: What do you mean by saying that photons obey the inverse square law? Are you trying to talk about the intensity of the light from a source? That holds for all radiation, not just light. If you mean the Coulomb force law I have to disagree... photons do not interact in that way. (As you say, they are neutral.)

You need to be careful about how you talk about what a photon (or any other particle) is. A photon is not "both a wave and a particle" it has elements of both but it is neither. At low energies particles are better described as waves whereas at higher energies they are better described as particles. But we can measure either property at any energy given the right equipment. Essentially if we look for a photon to be a wave we find a wave. If we look for a photon to be a particle we find a particle. Many Particle Physicists simply call the thing a "particle" just to get it over with. Some call them "wavicles." This is not about splitting hairs... we need to acknowledge what we can and cannot measure. Quantum particles have no analogue in the macroscopic world.

You have certainly heard of the Schrodinger wave equation. That is a non-Relativistic equation that deals with spin 0 "scalar" particles. There are a number of Relativistic wave equations that deal with other types. For example, the Klein-Gordon equation deals with spin 0 scalar particles as well. The Dirac equation deals with spin 1/2 spinor particles. And, to the point, helicity 1 massless particles are described by the Maxwell equations. (Sometimes referred to as solutions to the massless Proca equation.) The Maxwell equations do just fine.

Last, your extrapolation of your field of low energy photons into dark matter is pretty much just that... an extrapolation. Frankly it isn't even a good one. No one knows what dark matter is (or dark energy, don't go their either). All we know is that there is some kind of gravitational interaction between dark matter and ordinary matter. It has nothing to do with QED or even Electroweak, it has to do with gravity and we have no real idea how to do the calculations about something like that. Your photon field simply doesn't make the grade: photons have helicity 1 and gravitons have helicity 2. The interactions are completely different.

I'm not telling you to give up and I'm not telling you that all of your ideas are wrong. But you need to go back to the basics.
1) The Scientific Method must be followed in any research programme.
2) What you have is, at best, an hypothesis... a statement that explains a few things but one that needs to still be tested.
3) Any good theory will make predictions. You prediction is a field of extremely low energy photons that can't be measured.
4) You have not worked any real Math into this, and I'll tell you why you won't be able to: The Math is excruciatingly difficult. It's Differential Geometry and can be hard even for PhD level Mathematicians. It will take a lot of work on your part to be able to understand how the Math applies to your hypothesis. Again, I'll help where I can but I strongly suspect that this is going to be way harder than you imagined.

-Dan

Addendum: By the way, no one has come up with a construction for an elementary subatomic particle. There are structures for protons, neutrons, and the rest of the hadrons, but they are made of more elementary particles. So far as we know (again, String Theory says something different) elementary particles are singularities.. they are point particles that have no structure. This is a clearly ridiculous statement but it's all we have for now.

 

[ddj]

First, I am not going to tell you that I'm receptive to your hypothesis.

P.S. I have exceeded the number of permissible characters, so I will just quote the first phrase of each of your queries.

Allow me to say, that what you propose is certainly very acceptable. I like the idea of quantum mechanics as long as it is restricted to empirical data. For instance, Max Planck’s discovery that energy was quantized, was as great a discovery as man’s discovery of fire. Einstein’s explanation of Brownian motion practically proved the existence of atoms, or at the very least paved the way for an acceptance of their existence. His explanation of the photoelectric effect, not only vindicated Max Planck’s discovery that energy was quantized but laid the foundations of modern physics, Neils Bohr’s tremendous work (and it was hard back breaking work) on atomic spectra laid open the secrets of the atom, and Rutherford, Soddy and the Curies, with the splitting of the atom and the transmutation of elements paved the way for nuclear energy. All in all, the achievements of quantum mechanics equal or eclipse the achievements of Classical physics. I have no quarrel with that.

My problem starts with the esoteric, unsupported theories of quantum mechanics. Take wave-particle duality, the only thing to support it is speculation and (I am told) atrocious mathematics. Imagine that the speed of the ‘matter wave’ (no-one including De Broglie, or even Einstein for that matter, was able to explain what matter waves were or even what was waving) always exceeds the speed of light by the expression. v_m x v_p = c². Where v_p is the velocity of the particle and v_m is the velocity of the matter wave. This means that if a particle has a velocity of 2.18 x 10⁶ m/s the velocity of the matter wave would be c² / 2.18 x10⁶ = 4.122 x 10¹⁰ m/s . You must excuse me, if I am criticizing long held beliefs, but it seems to me that anything that is travelling at 100 times the speed of light cannot have anything to do with something occurring locally. Yes, it is possible to elude and ameliorate and waffle. But facts are facts. To imagine that the whole edifice of wave-particle duality is based on such waffling is quite horrifying. From this one inclusion of a supposed property come, superposition where an object can be in two or more places at the same time, multiple dimensions (In our Universe, there are only 3 dimensions [if time is added 4 dimensions] it is almost impossible to describe additional dimensions, physicists have been trying for years, with what can only be called limited success, the apparent ability to dematerialize and then to materialize again as happens with light in transit, and so on. I could go on about how wave-particle duality was only introduced to explain why the electron did not radiate away all of its energies and spiral into the nucleus. Today, wave-particle duality has been superseded by gauge theories according to which the electron is constantly emitting and absorbing ‘virtual’ photons and in the process self-regulating its energy so that there is no possibility of its falling into the nucleus.

The main theory of light that we have right now is Quantum Electro Dynamics.

Fine, yes, and if one looks at Feynman diagrams (I am not implying that all Feynman diagrams are correct) it is possible to see that the theory of why electrons do not fall into the nucleus explained at the end of the last paragraph, has some merit. Take two electrons that approach each other. At a certain distance they appear to repel each other. The question is why does this repulsion takes place? According to quantum Electro Dynamics the two electrons are emitting ‘virtual’ photons causing the repulsion.

You are conceptually moving into QFT. Your idea of particles of light at 10⁻⁴⁰ J pervading the Universe since the BB is incorrect.

Pardon me for saying so, but the present explanation of the CMBR and relic radiation is totally incorrect, I say this at the risk of raising umbrage. Think about it logically, atoms are 99.999999999% empty space, yet we are not able to walk through walls. Everything we do is through electromagnetic interactions. Without such interactions we would not be able to walk. Each time we pick up a pencil or touch something trillions of electrons have to re-arrange themselves. EMR does not hang around, it is constantly moving at c, to imagine that this CMBR is just hanging in place is quite unsatisfactory. No the CMBR is more a record of the distribution of matter in the Universe as it exists at present, meaning that the radiation from the massive hydrogen clouds, from which everything in the Universe had its origins (meaning that they are quite active) are the source of the radiation. Until a better explanation is reached as to how the CMBR can hang stationary in place it is unacceptable from the point of view of pure logic. As Galileo once said: “In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.” Galileo Galilei. A far more probable candidate for a Big Bang relic is Dark Matter.

The idea about polarizing the vacuum (that's where you seem to be leading to) is more or less in the spirit of the Standard Model, but again you are backing the wrong particles.

In my version the vacuum does not exist, the whole of space, the whole of the Universe, including all matter (because matter is permeable to the aether) is permeated by the aether (also called dark matter) which consists of infinitesimal electric di-poles, all oriented randomly until a real photon is emitted when they undergo polarization I the direction of the emitted photon.

Now a question: What do you mean by saying that photons obey the inverse square law?

Allow me for now, to assure you that the answer to this question is related to both how the Universe came to be populated by a virtual photon aether and also to how photons can spread out according to the inverse law, still maintain their energy (identity) intact and at the same time result in a reduced intensity of signal of the wave front in keeping with the inverse square law.

You need to be careful about how you talk about what a photon (or any other particle) is. A photon is not "both a wave and a particle" it has elements of both but it is neither.

Allow me to differ. The structure of the photon that I have put forward has a configuration that is absolutely stable. Schrodinger’s wave equation was introduced with a simi8lar aim in mind. If QM had accepted that the photon is a symbiosis of a particle and a wave, instead of (if you will pardon me) putting forward the ridiculous and improbable theory that it is both wave and particle but never possesses both properties simultaneously, it would have been more acceptable.

You have certainly heard of the Schrodinger wave equation. The Maxwell equations do just fine.

Schrödinger came up with the 'wave packet' to represent the electron. Using this treatment an electron appears to be a particle (i.e., possess the properties of a particle). This model had the advantage in that since a wave, any wave, would disperse the question of the electron radiating away its energy did not arise. However, a multi-dimensional space was required for this 'standing wave' model of the electron. Helium required a 6-dimensional space, lithium got 9 dimensions and uranium needed 276.
An almost instantaneous coming together, a localisation at one point in space would have to take place every time an electron was detected as a particle. Secondly when attempts were made to apply the wave equation to helium and other atoms, Schrodinger’s vision of the reality that lay beneath his mathematics disappeared into an abstract multi-dimensional space that was impossible to visualize. The wave function of an electron encodes everything there is to know about its' single three dimensional wave. Yet the wave function for the two electrons of the helium atom could not be interpreted as two three dimensional waves existing in ordinary three dimensional space. Instead the mathematics pointed to a single wave inhabiting a strange six-dimensional space. In each move across the periodic table from one element to the next, the number of electrons increased by one and an additional three dimensions were required. Schrodinger was never able to come to terms with the fact that his construct did not represent ‘reality’. All Max Born did was to shift Schrodinger’s equation out of the atom and into space. Where it took on the name of the wave-function and , if you ask me, it has not fared any better. Sorry for such a lengthy answer but your questions are not easy to answer.

Last, your extrapolation of your field of low energy photons into dark matter is pretty much just that... an extrapolation.

It isn’t an extrapolation, the theory of a Universal aether is something that has existed since before Aristotle. Also, note I have my own theory of gravity which closely echoes Newtonian gravity but avoids the disastrous action at a distance error that is falsely attributed to him.

Lastly, I hope (not in vain, I trust) that due consideration will be given to my answers. My advice is don’t be in a hurry, take your time. Try to apply a rational mind to what I have written. Remember that quantum mechanics is a wonderful theory, except for the esoteric, almost voodoo like parts, that I had mentioned. If you like, just give the word and I will give an account of how photons can follow the inverse square law.

 

[topsquark]

Due consideration is one thing. Saying that experimental results are wrong is another. QM has existed for over 100 years and has only grown, not been invalidated. Einstein put one heck of an effort into doing so and all he managed was to improve the theory. Your comments about why QM is "unsupported" is simply wrong. Everything that has been published has had extensive experimental validation. Just because you don't agree with it doesn't make it wrong.

Phase and group velocities are different entities. It is the phase velocity that is the physical speed of the wave.

There are two kinds of spaces (or space-times if you will) in QM. There is physical space (3 + 1 space-time) and Hilbert space. Hilbert space is an infinite dimensional (complex) vector space and we use finite dimensional subgroups of it. Quantum waves "wave" in these spaces, not real space.

You talk about dark matter but you haven't said what it is! Dark matter is a cover term for a set of observations of the Universe and does not yet have a specific source. There may actually be many different kinds. If you are going to talk about dark matter as being fundamental you really need to tell us what it is. Your photon aether is not enough.

Charged particles exchange photons. The result is that they repel each other (like charges) or attract each other (unlike charges.) They repel or attract due to their nature and what goes into the Feynman diagram. The Feynman diagram is not simply a picture... it represents a number called the "amplitude." For example, if we have an electron and positron exchanging a photon then we must use an electron creation operator and an electron destruction operator for the positron. It is that kind of thing which determines if there is attraction or repulsion.

You missed my point about the background photon radiation. Perhaps I should have been clearer. There is a measured background temperature of 2 to 3 K due to photons from the BB. There are variations in this field over both small and large scales. You are never going to be able to separate out your extremely low photon field from this. It's like trying to measure the height of Mount Everest to within a centimeter in the middle of a snow storm. The storm changes things at so much a larger scale than your background that you can't make out the real height. It could literally take us decades or even more than a century to measure your photon background.

Actually the dimensional calculation of an electron is worse than you know. Even in Classical Mechanics, if we have three spatial dimensions we need 6 dimensions to describe what is happening to a particle... 3 space and 3 momentum. QM particles may have more.. 6 like in CM and there are likely to be Hilbert spaces attached to handle internal properties such as spin.

What I am seeing in your comments is that you are enthusiastic and orderly but not very well read in the Physics. You are making comments against concepts that have been experimentally proven. I offered my help with the Math so let me ask you: what level are you at? QM uses differential Calculus and Group Theory but I am betting that you would probably like to start with Linear Algebra, which talks about your dimensional concerns. The Linear Algebra isn't terribly deep but you do need the basics to understand the Hilbert space material. That's where I would recommend that you start.

-Dan

 

[ddj]

Due consideration is one thing. Saying that experimental results are wrong is another. QM has existed for over 100 years and has only grown, not been invalidated. Einstein put one heck of an effort into doing so and all he managed was to improve the theory. Your comments about why QM is "unsupported" is simply wrong. Everything that has been published has had extensive experimental validation. Just because you don't agree with it doesn't make it wrong.

Fine. There is a point when it is possible to agree to disagree and that point is reached when both theories ‘work’ and what is left is a choice.

Phase and group velocities are different entities. It is the phase velocity that is the physical speed of the wave.

Think of it as distances, the particle in my example is travelling at 2.18 x 10⁶m/s while its associated ‘matter wave is travelling at 4.28 x 10¹⁰ m/s. Logically, is there any point in talking about the difference between phase and group, especially when the phase velocity is supposed to lend the particle its wave like properties?

You talk about dark matter but you haven't said what it is! Dark matter is a cover term for a set of observations of the Universe and does not yet have a specific source. There may actually be many different kinds. If you are going to talk about dark matter as being fundamental you really need to tell us what it is. Your photon aether is not enough.

It is true that not much is known about the properties of dark matter but then not much was known about the aether. What was inferred about the aether in the pre-Maxwell days, is that it was invisible, it had no odour, it was non-tactile, it had extremely low interaction with matter as was evidenced by the sun, the planets and the stars moving through it without the slightest interference, it allowed for the propagation of light, since the speed of light was known to be finite and did not act instantaneously as action at a distance. If now we think about dark matter it can be seen that it possesses exactly the same properties. If it was possible to collect some dark matter (which is highly unlikely) and tried to weigh it, it would not possible because the dark matter would go right through the vessel in which it was collected and would continue to pass through the weighing machine that was used. At the same time it allows for the free passage of light. My model of the structure of the photon and therefore also the basis of dark matter would explain all of these properties perfectly.

You missed my point about the background photon radiation. Perhaps I should have been clearer. There is a measured background temperature of 2 to 3 K due to photons from the BB. There are variations in this field over both small and large scales.

I will just repeat that EMR does not hang around. Further the energies you speak of are a trillion times the value I had mentioned, there is no chance of interaction.

There is little point in getting contentious and arguing about what is right or not. You, justifiably state that QM has been around for a hundred years, although I sense a slight evasion when you refer to my statement that the electron self-regulates it energy around the nucleus through gauge self interactions. The inevitably conclusion is that electrons have a definite shape and are not waves, which must be correct since a wave cannot possess mass. What is important is to find a good starting place for my theory.

I am not really interested in getting into Hilbert spaces as it does not suit my theory. I was thinking more in terms of a mathematical definition of the aether as I see it.

 

[ddj]

I would like to examine your contention that QM is right and cannot be wrong. The reason I say this is that it is easy to say that it has been proved over and over again. But is that really an argument? Could you tell me what quantum mechanics says about how a photon is absorbed? Taking green light from the middle of the optical spectrum, it has a wavelength of 5.5 x 10^-7 m. An atom on average has a size of 10^-10m and the electron has a radius of 10^-18 m. How does quantum mechanics explain how an electron with a radius of 10^-18 m. Absorb a photon with a wavelength of 5.5 x 10^-7 m ? The photon has a wavelength that is a hundred billion times greater than the electron and a thousand times bigger than the atom. Do you see what I mean, quantum theory is so complicated that any answer that is given would be necessarily elaborate.

With my theory of the photon structure, there is absolutely no question about size, the photon retains the same size as that which it had when it was emitted . What the electron has emitted the electron can equally well absorb. It is as simple as that, no question of comparative sizes enter into it.
Another thought that enters my head is this; photons come in trillions of frequencies, wave-lengths and energies. My question is where are all these photons stored, what does quantum mechanics have to say about it? Oh, they are stored in the vacuum energy and appear as needed. Once again, with my theory of photon emission and absorption, there is no question of photons being stored anywhere. The electron regulates it energy very quickly and very exactly by emitting or absorbing photons as needed. The electron is in charge of what photons to emit or absorb, it controls very exactly, the energy needed to mediate its energy.

What I would really like to know is this: With all the advantages that my theory offers, why, can’t it compete as an alternative theory to QM? I will have to demonstrate how light propagates in my theory, you will be surprised at the simplicity and elegance of the concept. As to how light propagates in QM it is difficult to come across any references.

Note, I am not trying to win you over to my way of thinking. I am merely saying nothing is infallible.

​

 

[ddj]

I have just realised that without a description of how light propagates, there would be little point in trying to go straight to a mathematical description of the aether, since there would be no clear idea of what the description was referring to. Further, there appears to be some confusion as to how dark matter can be linked to the theory.

In order To gain some idea of how virtual photons came to permeate the entire Universe, it is first necessary to examine in detail another of the outdated concepts of quantum mechanics. This is the concept of the frequency of a photon. According to quantum mechanics:

Photons don’t have a frequency. Frequency is a wave property and is a property that applies only when you look at light as a wave. A photon has an energy, which is related to, but different from, frequency. So we sometimes use the term ‘the frequency of a photon’ but really as a short hand for “the frequency of the wave that will manifest later as a photon”.

Another way of stating this is by the relation f = e/h this means that if you know the energy of the photon it is possible to determine its frequency by dividing the photon energy by h planck’s constant. Whatever the answer might be it is fairly obvious that the quantum mechanics concept of what the frequency of a single photon might be is shrouded in obscurity; due to the wave-particle duality there can be no definite answer to the question.

This presents a problem when looked at from a purely mechanical point of view. The problem arises as follows, if one looks at a modern day smart phone one is aware that it is processing data at the rate of several gigabits per second. Consider what the term processing denotes, it means taking input data, evaluating it and outputting the result. The electron is miniscule in size and the distances over which it has to oscillate are even smaller. It is then only natural that the electron should oscillate at frequencies of several hundreds of terahertz and emit photons at that rate. In fact, not to do so would be odd. If further proof is needed all that is necessary is to observe the working of a Caesium 133 atomic clock. In the Caesium 133 atom, the valence electron oscillates between two hyperfine states at a frequency of 9192631770 Hz.6 This is a fairly conclusive indication that all electrons must oscillate at similar frequencies when irradiated. Gestalt Aether Theory, therefore, takes the concept of photon frequency away from the fuzzy abstract notions of quantum mechanics where it is an abstract vague property of the photon and puts it on a sound practical basis. Therefore when we talk of an electron emitting photons with a frequency of 600 THz it means exactly that. The electron is emitting photons at the prodigious rate of 600,000,000,000,000 photons per second. In what direction are these photons emitted? These photons are emitted in a single direction as a line of photons of the same frequency, wavelength and energy. Why? If one looks at the physics behind the emission of a photon, it is apparent that the electron absorbs energy and mediates its energy by emitting that energy in the form of a photon, the process involves the force of recoil. To cope with these forces of recoil the electron rebounds against the nucleus absorbs more energy and again emits this energy at the exact same position as before, hence photons are emitted as a line of photons in a specific direction. Proof that this is indeed the case can be seen in the working of any atomic clock. Frequency is directly related to the rate of emission of photons by the electron or to put it another way by the electron’s rate of oscillation.

This new point of view, makes it possible to understand the concept of a Universe completely submerged or steeped in a sea of virtual photons. Having established that photons are emitted and absorbed at phenomenal rates, it is time to return to the first moments of the Big Bang that is thought to have occurred out of a singularity more than 13.7 billion years ago! Although it is generally accepted that the Big Bang was not a bang in the accepted sense of an explosion but that it involved a rapid inflation or expansion, opinions is almost unanimous that light must have been present also. It is almost a corollary that if matter was present light (or rather photons) must have been present also, although light might not at this early stage of the Universe have been able to propagate. The question is what happened to all that light? Look at the ratio; for every atom of matter, photons were being emitted at the rate of hundreds of Terahertz per second [math](10^{14})[/math] per second. What happened to those photons? Emitted not over seconds but hundreds of thousands, even millions of years? They could not have escaped over the borders of the Universe because by definition nothing exists outside the Universe, so they must have been contained in some way within the Universe.



It is presumed that if light could not escape over the borders of the Universe that the photons linked together, a consequence of their physical structure which allows for such linkage, forming a network that permeated the entire Universe. The scenario of a loosely linked net- work of photons that permeate the whole of the Universe is a very plausible theory. If one examines the model for the structure of the photon proposed earlier, it is possible to see that these photons can link together not only vertically end to end but also laterally.

When photons are linked in this manner their energy is shared. The theory is that as the Universe continued to expand the vast numbers of photons present formed a linked network. As time passed and the Universe continued to expand the network of linked photons expanded with the Universe filling every part of it. One consequence of the expansion of the Universe was that the individual energy of the photons was shared out among the network of linked photons, till eventually they reached such a low state of energy (about [math]10^{-⁴⁰}J)[/math] that they for all practical purposes ceased to exist! Because of this extremely low energy it was possible for this linked network of photons that permeated the entire Universe, to exist for practically ever, with life-times similar to that of the proton or the electron. This process can be attributed to the Heisenberg Uncertainty Principle as it relates to time and energy: [math]\Delta e \Delta t \geq h[/math]
The HUP states that if an event happens in an extremely short period of time \(\displaystyle \leq 10^{-15}\) s or possesses very small energies, it can be ignored by the laws of energy conservation which rule all processes at the macro level. Similarly if a particle or an interaction has such low energy [math]\leq 10^{-40}[/math] J the time over which the particle can exist becomes arbitrary.

These ‘virtual photons’ of the virtual photon aether were almost stationary dipole particles, oriented at random, with which, because of their extremely low energy, no matter would or could interact, thus they could travel through matter as if it did not exist. Eventually when all of the Universe was full of this linked network of photons, light began to propagate in the way that is familiar to us today. When an electron within an atom emits a real photon,the photons of the virtual photon aether, line up forming a line whose ends rest on the shoulders of infinity and the energy of the real photon travels along this line of linked photons.

This explanation of how an aether like medium formed consisting of extremely low energy photons that permeated every part of the Universe and yet was absolutely permeable to all forms of matter and would allow massive objects such as the planets the sun, the moon and the stars to pass through it without the slightest opposition, explains everything that was ever known about light. The aether does not interact with matter because no atom could possibly need or utilise such low energies, thus virtual photons of the aether pass through all atoms as if they did not exist. The existence of such an aether also explains in easily understandable terms, how light can propagate according to the inverse square law and still enable individual photons to maintain the same energies that they possessed at the time they were created. This Aether model explains how and why the speed of light is a constant and invariant and unaffected by the motion of either the source or the observer or of both. This is a perfectly modelled system for light and all of its properties; it makes sense as the quantum mechanics model for light and electromagnetic radiation does not.
To be Contd…….

 

[ddj]

The Gestalt Aether Theory On The Propagation And Dispersion Of Light:

The term ‘light’ is deliberately used in the title instead of ‘electromagnetic radiation’ since according to Gestalt Aether Theory there is a small but significant difference in the manner of production and propagation of high energy, high frequency photons like visible light and x-rays and gamma rays and relatively low frequency, long wavelength, low energy radio-waves.

In order to introduce a new theory or concept it is first necessary to review how the old system worked. Feynman’s is generally considered to be the ultimate theory so here is his theory of light propagation:

“Feynman explains that in QED light sources produce not physical particles or waves, but wavelike “probability amplitudes” that propagate at c in space (not superluminally). The amplitudes spread in all directions and superpose (interfere) just as real light waves do according to the Huygens-Fresnel principle: by spherical wavelets from every portion of the wave front. Feynman restates this principle as light “has a nearly equal chance of going on any path”. As they propagate in space, the probability amplitudes shrink according to the inverse square law and rotate in space according to their frequency (“shrinks and turns”). Adding up all the resultant arrows for all the possible paths light may travel to the receiver renders a final amplitude arrow. Squaring this arrow yields the probability that a detectable light-matter interaction will be observed. Where the probability amplitudes superpose constructively is where events (e.g. photomultiplier counts) are more likely to occur; where they superpose destructively is where events are less likely to occur. Feynman admits that the wave theory of light can account for all the phenomena modelled by QED when the light is intense; but insists that “wave theory cannot explain how the (photomultiplier) detector makes equally loud clicks as the light gets dimmer.” On this basis alone he rejects wave theory and concludes that “light is made of particles.”

Reading the above it is immediately possible to realise that quantum mechanics ( at least as it has to do with wave-particle duality) is a pretty mixed up theory, which apart from complicated maths based almost entirely on imaginary numbers (multiple dimensions) does not offer much of an explanation for anything. Quantum theory has never been adequately able to explain the dispersion of light according to the inverse square law. This is a huge lacuna considering that 400 years have passed since Newton and Huygens and 150 years since Maxwell. We should, by this time, have had a beautiful theory on how light propagates, we don’t. Gestalt Aether Theory offers one such beautiful and unified theory.

But what is the actual mechanism by which light propagates in Gestalt Aether Theory? Light propagates as follows. The ‘virtual photons’ of the aether which incidentally resemble a field, of to all purposes stationary di-poles, are oriented at random until a real photon is emitted by an electron, when this happens the ‘virtual photons of the Aether, line up in the direction of propagation of the real photon forming themselves into a line whose ends rest on the shoulders of infinity. The energy of the real photon then travels along this line of virtual photons. However, and this is of significance, as the energy of the line of real photons travels along the line of aligned ‘virtual photons’ it is dispersed not only forward but also laterally so that the energy from the line of real photons spreads out in a cone shape from its point of origin. All of the area covered by this shape is filled with the energy, in sequence, of the original line of photons being emitted at the source. This is why light does not propagate backwards, light reaches a point and passes on. Neither Huygens nor QM have been able to explain why this is so. In order to understand how this dispersion takes place it is necessary to understand the concept of promotion wherein ‘virtual photons’ adjacent and in contact with the energy of the line of real photons are promoted to the status of real photons through a transfer of energy. In order to understand how this happens, look at the lead photon, it has been emitted at the head of a line (ray) of connected photons and it is moving away (its energy) is moving away at the speed of light. Each photon in this line of connected photons possess identical energies. When a photon in this line of connected photons comes into contact with the line of virtual photons aligned in its direction of propagation it results in an energy transfer not only forward but laterally also. This means that a virtual photon in contact moving beside the real photon will acquire all of the energy from the real photon and the energy of the real photon will be replenished from the line of photons behind it. This is why light, as it propagates, follows the inverse square law of dispersion. In incoherent light every receptive electron in the receptive substance will be emitting light at the rate of whatever frequency light is exciting it (i.e. the electron) this results in lines (rays) of photons being emitted in different directions all travelling at the speed of light and all spreading out in keeping with the inverse square law. The direction in which these lines of photons are emitted depends on the laws of reflection as elucidated in classical physics. However, since on average a cubic centimetre of solid material contains about 10^²² atoms the lines of photons emanating from the excited material are virtually innumerable. Thus as each line of photons is emitted by an electron it comes in touch with neighbouring ‘virtual photons’ surrounding it and it passes its energy to these adjacent photons, so each real photon passes all of its energy to its neighbouring ‘virtual photon’ which is immediately promoted to a real photon which in turn can pass its energy along to its adjacent ‘virtual photons ‘ and so on. The energy of the real photon which has passed on its energy is immediately topped up or replenished from the line of real photons behind it. It is important to understand how the transfer of energy takes place during the course of promotion of the virtual photon to a real photon. The ‘virtual photon’ has its fixed energy of 10^-40 J, so when a real photon comes into contact with a virtual photon it is possible for the real photon to pass its energy to the virtual photon with which it has come into contact, in its entirety. There is no loss of energy. The real photon’s energy is fixed by its configuration, its configuration at the time it was emitted determines its energy, as a result it can only pass on or receive whole amounts of this energy, nothing less and nothing more. This is the manner in which light disperses according to the inverse square law. It can now be seen that the inverse square law is a function of the ratio of how many virtual photons come into contact with a real photon. If the real photon is exposed on all sides then it is simultaneously accessible to six virtual photons that will each in turn acquire energy and be promoted to real photons. However, because of the huge number of electrons that are emitting lines or rays of photons, the number of virtual photons that can interact with a real photon is limited. It can be seen that the inverse square law is therefore an approximation of this process of promotion of virtual photons. When the source electron stops emitting and there is no longer any energy, all of the promoted photons lose their energy and turn into ‘virtual photons’, fading back into the virtual photon aether.

Note how natural this version of the propagation and dispersion of light is, it is not the physical real photon that travels but only its energy. In this way the propagation of light is brought into line with the propagation of all other manner of waves such as water waves sound waves etc., with one vital distinction. This distinction is that for as long as light is being emitted, (i.e., for as long as the photon is being excited and emitting photons) every photon in the propagating ‘wave’ front retains the same energy as the originally emitted photon.

As the light moves further from its origin the intensity of the light varies as the inverse of the square of the distance from the source. However, the energy of each individual photon remains intact, thus if it is monochromatic blue-green light with a frequency of 600 THz that is being emitted,
then the energy of each individual photon would be equal to: speed of light x planck’s constant / wavelength. In this case wave-length is equal to c/f = 500nm :

3 x10^⁸ x 6.62607004×10⁻³⁴ /5×10⁻⁷=3.983 x 10^-19J.

Thus at every point, considering that the monochromatic light has been travelling 100 Km, on a 10 billion square metre front, the energy would be 3.98 x 10 ^-19J. Energy from the original line of photons being pumped out by an electron is being dispersed, even as it moves forward at the speed of light, through all the virtual photons immediately surrounding it laterally, these in turn are passing on that energy to neighbouring virtual photons, promoting them to real photons with identical energies to the original emitted photon.
To be continued

 

[ddj]

Hello fellow forum members,

The moderators thought fit to shift my post to the odds and ends forum, deeming it more suitable. I hope they are right and that I will be able to get some help and assistance in framing the mathematics for this theory. This is the last part of my theory on the propagation of light. The mathematics for light is comparatively simple; since, light propagates in a rectilinear manner. More difficult will be the mathematics for my theory of gravity which will require the use of tensors, although apart from that, gravity, at least in my theory and also in Newtonian physics, acts in a rectilinear manner.

It is my intention to end this post, with a practical example on the propagation of light. (it has taken three posts because only 10,000 characters are allowed per post.) [Any mistakes that are pointed out and suggestions made will be appreciated]

Given a non-coherent monochromatic green light source of 600 THz having a power of 1600 lumens from a 100 watt bulb. Calculate:

1) The intensity of the light at a distance of 50 Km.
2)The energy of each individual photon at the wave-front at a distance of 50 Km
3) The area over which the light spreads out, if it has a reflector behind it and is radiating in only a single direction.
Since the power of light at the source is known to be 1000 lumens, its intensity at a distance of 50 Km can be calculated using the relation i = p/r Where r is the distance in metres; p is the brightness in lumens; and i is the intensity, also in lumens.

1a) The brightness at a distance of 50 km from the source is 1000/50000² = 1000/ 2.5 x 10^-8 lumens. Or a luminous flux of 4 x 10^-5 lux.

2a) The energy of each individual photon on the wave front equals \(\displaystyle e = hc/ \lambda\)Where e is the photons energy; h is plancks constant; f is the frequency of the light, and c is the speed of light. It is possible to find the wavelength \(\displaystyle \lambda\) by c/f. In order to find the energy of the individual photons in Joules, the wavelength of the light must first be determined. 3 x 10⁸/600 x 10¹²= 500 x 10^-9 nm.The energy of each individual photon on the wave-front = 3 x10^⁸ x 6.62607004×10⁻³⁴ /5×10⁻⁷= 3.983 x 10^-19J.

3a) The area over which the light would spread after travelling a distance of 50 km, where a = area; and r = distance is simply r²The area over which the light spreads out at a distance of 50 Km from the source is 2.5 x10⁸square metres. (250 million square metres)

The question is, if each photon on the wave front retains its individual energy how can the overall intensity of the light be reduced? In order to answer this question it must be remembered that these photons have been emitted as lines or rays of photons, each line or ray is made up of hundreds of trillions of photons, all of the same value. It is not possible to mix up photons of different frequencies or energies in a single ray of light. As this ray of photons (light) propagates through the virtual photon (aether) medium, each individual photon passes on the whole of its energy to ’virtual’ photons of the aether with which it comes into contact, and the next 'real' photon in the linbe or ray of connected photons (light) takes its place. Thus the number of photons in each ray or line of light, keeps diminishing with distance and the increase in area, and the intensity of the light reaching any spot is also diminished.

Interestingly, this means that, for a fixed source of power, such as described in this problem, it means that a stage will be reached at which the light can no longer be detected. At sufficient distances from the source the light will no longer be detected. If the distance is such that the original energy of each individual photon cannot be maintained the photons at that point on the wave-front are no longer stable and return to the virtual state. The photons behind this invisible line, still maintain their energy. The power at the source can only continually support light over a certain fixed area. There is a fixed amount of energy available. The power available can only sustain light over this area.

Note this is very different from the quantum mechanics view of light, which is that an individual photon will continue to move for ever till it is absorbed by an atom of some substance. According to the theory presented here, yes light from billions of light years distant can still be seen but the power at the source of this light is huge and sustained over millions of years.

Thus light is created it travels through light, in turn creating more light, and in the end returns back into light. This is exactly similar to the manner in which a wave disperses its energy. It is possible to see how simply and naturally dispersion is explained using the aether model. Light waves spread out naturally and in the same manner as when a stone is dropped into a still pool of water. To those who have read this theory carefully it will be apparent how effortlessly and exactly the manner of propagation of light has been explained. It has been explained in plain language how light is able to travel as a wave, obey the inverse square law of dispersion and at the same time retain its individual identity in the form of its original energy. No mathematical abstract wave function, no disembodiment and travelling through unworldly dimensions, no superposition, no being in two places at once. Here is an extremely realistic view of the propagation of light that continues the tradition of Newton, Descartes, Lorentz, Maxwell, Poincare and others who passionately pursued the existence of an aether simply because it answered all possible questions about light and its propagation as both quantum mechanics and relativity could not.

 

[topsquark]

I did not intend to have a discussion about whether QM is right or not. I intended to try to help you with the Math, which you don't seem to have any of. If you disagree with QM and are not interested in trying to understand the Journal submissions (which contains pretty much all of Physics now a days) then I'm not your man. I have better things to do with my time than try to make all the multitude of corrections needed in your posts. Especially since you don't seem to be interested in asking questions but telling me that I (or Physics) is wrong.

Learn something about the field before you try to dismiss it.

-Dan

 

[ddj]

Dan,

At the outset, let me thank you for your offer of help. I will also state that you are probably right and I do not really care for the quantum mechanics description of reality. So, I am not interested in learning about QM, unless by chance you can answer some of the perfectly simple questions that I had asked:

1) How can you justify the use of Schrodinger’s wave function when it necessitates the use of multiple dimensions? Especially when the theory I have put forward, does not need any of these non-existent and alien multiple dimensions.

2) How can an atom possessing a radius of 10^-10m, or for that matter an electron with a radius of 10^-18 m, absorb a wave-length of 5 x 10^-7m ? In the former case the difference in size is 10³ (one thousand times) times larger and in the latter instance the wave is 10^-11 times larger, or one hundred billion times larger.

3) Where are these trillions upon trillions of photons stored? How are they available at such short notice?

Before you take umbrage about what I have written, and note that I don’t mind if your explanation is in mathematics rather than in words, please take the time to understand that I have given perfectly logical and workably consistent answers to all of the above questions. Where, it is easy to understand where I am coming from.

An allegory can be drawn here between your very strong belief in Standard Theory and QM and religion. Just because someone has a strong belief in something, does not make it right; just as someone with a more compelling answer as to why things are the way they are, is not wrong.

You have also chosen to ignore my reference to gauge interactions where the electron as it travels around the nucleus, is continually self-regulating its energy by emitting and absorbing ‘virtual’ photons. This is the basis of gauge theory, and completely does away with the need for wave particle duality.

When I ask: How does a matter wave moving at a speed that is one hundred times the speed of light, affect the properties of a particle locally? No answer is given except for the statement that this is the accepted state of affairs and is widely supported by theory, experiment and mechanics. Ask yourself, would I the receiver of your purported wisdom, be morally right in accepting without question what you say?

I can anticipate your answer - you don't have the time to teach me. Well if you can't do that, then at least answer any two of the questions I have asked. Use as much mathematics as you need to get the idea across. Thanks.

 

[ddj]

Dan,
I must seem like a complete philistine, which is true, at least as far as maths is concerned, because imaginary numbers seem to be involved at almost all stages. The difference is that the imaginary parts of the solution are usually thrown away. Schrodinger's wave function is different because it actually embraces the imaginary numbers (or dimensions) and makes them a critical part of its theory on the propagatioon of light. Which is totally unacceptable. My questions still need answers, if you are interested.

 

[topsquark]

In general when someone starts making posts like yours the member is not actually trying to learn something they are trying to either get into an argument or they are trying to convince others that they are right. Maybe you aren't in that category but long odds say that you are. You asked about the Math and none of your subsequent posts is about that.

The question right now is not that you are right or wrong, you need to focus on some way to prove your ideas. Simply describing them is not enough... the Scientific Method insists that you be looking for some experiment to prove your assertions. Since you apparently haven't calculated anything and since your post title asks about the Math I am willing to help there. But I'm not going to get into the guts of your hypothesis because the overwhelming odds are that you aren't correct.

QM is not an easy field. The Math can be quite difficult but that's just the mechanics of how it works. The principles are what is truly a problem. I don't think it's an overstatement to say that no Physicist is at all comfortable about the Philosophy behind QM. But the rules we know are rather like a cookbook: we know how to do the calculations even if we don't know why things should be this way. Classical Mechanics is actually in the same boat but unlike QM the principles are easy to observe so it's easier to accept them as correct.

So if you want to talk about the Math behind QM I am more than happy to give you an overview. For that I need to know what level of Math you are already at. If you don't want to learn about the Math then I guess we are done. Your call.

-Dan

 

[ddj]

As I had stated at the beginning of this post my skills in mathematics are from poor to non-existent. However, by careful examination of the equations I deemed to be relevant to my theory, I have selected a few possible openings:-

A wave can be described just like a field, namely as a function \(\displaystyle {\displaystyle} F(x,t)\) where \(\displaystyle {\displaystyle x}\) is a position and \(\displaystyle {\displaystyle t}\) is a time. The value of \(\displaystyle {\displaystyle x}\) is a point of space, specifically in the region where the wave is defined. In mathematical terms, it is usually a vector in the Cartesian three-dimensional space \(\displaystyle {\displaystyle \mathbb {R}^{3}}\).

The value of \(\displaystyle {\displaystyle F(x,t)}\) can be any physical quantity of interest assigned to the point \(\displaystyle {\displaystyle x}\) that may vary with time. For example, if \(\displaystyle {\displaystyle F}\) represents the vibrations inside an elastic solid (e.g., the aether). The value of \(\displaystyle {\displaystyle F(x,t)}\) is usually a vector that gives the current displacement from \(\displaystyle {\displaystyle x}\) of the material particles that would be at the point \(\displaystyle {\displaystyle x}\) in the absence of vibration.

In preparing a mathematical definition of my new theory of physics, I felt that a good place to start would be with a spherical wave in an
infinite three-dimensional medium. This is a wave that is independent of the angles \(\displaystyle {\displaystyle\theta}\) and \(\displaystyle {\displaystyle\mu} \) when it is described in terms of spherical coordinates. The wave function depends on \(\displaystyle {\displaystyle t}\) and \(\displaystyle {\displaystyle r}\) only, and it moves either toward larger values of \(\displaystyle {\displaystyle r}\) --- an outgoing wave --- or toward smaller values of an incoming wave .

Writing the Laplacian operator in spherical coordinates. In spherical coordinates the Laplacian operator is given by:

\(\displaystyle {\displaystyle} \nabla^2 f = \frac{1}{r^2} \frac{\partial}{\partial r} \bigg( r^2 \frac{\partial f}{\partial r} \bigg) + \frac{1}{r^2\sin\theta} \frac{\partial}{\partial \theta} \bigg( \sin\theta \frac{\partial f}{\partial \theta} \bigg) + \frac{1}{r^2\sin^2\theta} \frac{\partial^2 f}{\partial \phi^2}\)


Writing the Laplacian operator in spherical coordinates, and eliminating the angular derivatives, the wave equation becomes:

\(\displaystyle {\displaystyle 0 = \Box \psi = -\frac{1}{v^2} \frac{\partial^2 \psi}{\partial t^2} +\frac{1}{r^2}\frac{\partial}{\partial r} \biggl( r^2 \frac{\partial
\psi}{\partial r} \biggr)}\)

\(\displaystyle {\displaystyle \partial \psi/\partial r = r^{-1} \partial u/\partial r - r^{-2} u}\)

so that

\(\displaystyle {\displaystyle}r^2 \partial \psi/\partial r = r \partial u/\partial r - u\)

After differentiation

\(\displaystyle {\displaystyle\frac{\partial}{\partial r} \biggl( r^2 \frac{\partial \psi}{\partial r} \biggr) = r \frac{\partial^2 u}{\partial r^2} + \frac{\partial u}{\partial r} - \frac{\partial u}{\partial r} = r \frac{\partial^2 u}{\partial r^2}}\)

Gives

\(\displaystyle {\displaystyle\frac{1}{r^2}\frac{\partial}{\partial r} \biggl( r^2 \frac{\partial \psi}{\partial r} \biggr) = \frac{1}{r} \frac{\partial^2 u}{\partial r^2}}\)

for \(\displaystyle {\displaystyle \nabla^2 \psi} \) in spherical coordinates. On the other hand, differentiation with respect to \(\displaystyle {\displaystyle t}\)

yields \(\displaystyle {\displaystyle\frac{\partial^2 \psi}{\partial t^2} = \frac{1}{r}\frac{\partial^2 u}{\partial t^2}} \)

and this gives

\(\displaystyle {\displaystyle \Box \psi = \frac{1}{r} \biggl( -\frac{1}{v^2} \frac{\partial^2 u}{\partial t^2} + \frac{\partial^2
u}{\partial r^2} \biggr)}\)

for the wave operator acting on \(\displaystyle {\displaystyle \psi(t,r)}\)

\(\displaystyle {\displaystyle-\frac{1}{v^2}\frac{\partial^2 u}{\partial t^2} + \frac{\partial^2 u}{\partial r^2}}\)

This is recognized as the one-dimensional form of the wave equation, presented in a different notation, with {\displaystyle r}. The general solution to this equation is

\(\displaystyle {\displaystyle\psi(t,r) = \frac{1}{r} A(r-vt) + \frac{1}{r} B(r+vt)}\)

This represents the superposition of an outgoing wave described by \(\displaystyle {\displaystyle r^{-1} A(r-vt})\) and an incoming wave described by
\(\displaystyle {\displaystyle r^{-1} B(r+vt)}\).The functions \(\displaystyle {\displaystyle A}\) and \(\displaystyle {\displaystyle B}\) are arbitrary. Just as
in the case of the infinite string, and they can be the initial conditions imposed on the wave. The factor of \(\displaystyle {\displaystyle r}\) in front of \(\displaystyle {\displaystyle A(r-vt)}\) indicates that the wave's amplitude decreases as the wave expands toward \(\displaystyle {\displaystyle r=\infty}\), the wave becomes increasingly attenuated, a familiar phenomenon in the context of sound waves. On the other hand, the factor of
\(\displaystyle {\displaystyle r^{-1}}\)in front of \(\displaystyle {\displaystyle B(r+vt)}\)reveals that the amplitude increases as the wave converges toward \(\displaystyle {\displaystyle r=0}\) .

While this concept is useful, it seems to lack in certain areas. For instance according to my theory, the ‘real’ photon travels through the ‘virtual’ photons of the aether, spreading our according to the inverse square law as it travels and transferring all of its energy to ‘virtual photons’ with which it comes into contact and being replaced by ‘real’ photon from the line or ray of aligned photons that the electron is emitting. . I therefore thought a mathematical description involving vector propagation might be more useful.


A perfect one-dimensional traveling wave follows the equation:

\(\displaystyle {\displaystyle \psi (x,t)=A\cos(kx-\omega t+\varphi )}\psi (x,t)=A\cos(kx-\omega t+\varphi )\)

where:

1) \(\displaystyle {\displaystyle x}\) is position,

2) \(\displaystyle {\displaystyle t}\) is time,

3) \(\displaystyle {\displaystyle \psi }\) (a function of \(\displaystyle {\displaystyle x and t } \) is the disturbance describing the wave (for example, for an ocean wave, {tex]{\displaystyle \psi }[/tex] would be the excess height of the water, or for a sound wave, \(\displaystyle {\displaystyle \psi }\) would be the excess air pressure).

4) \(\displaystyle {\displaystyle A}\) is the amplitude of the wave (the peak magnitude of the oscillation),

5) \(\displaystyle {\displaystyle \varphi }\) is a phase offset describing how two waves can be out of sync with each other

6) \(\displaystyle {\displaystyle \omega }\) is the temporal angular frequency of the wave, describing how many oscillations it completes per unit of time, and related to the period \(\displaystyle {\displaystyle T}\) by the equation \(\displaystyle {\displaystyle \omega =2\pi /T}\),

7) \(\displaystyle {\displaystyle k}\) is the spatial angular frequency (wavenumber) of the wave, describing how many oscillations it completes per unit of space, and related to the wavelength by the equation \(\displaystyle {\displaystyle k=2\pi /\lambda }\) .

8) \(\displaystyle {\displaystyle k}\) is the magnitude of the wave vector. In this one-dimensional example, the direction of the wave vector is trivial: this wave travels in the \(\displaystyle {\displaystyle +x}\) direction with speed (more specifically, phase velocity) \(\displaystyle {\displaystyle \(\displaystyle {displaystyle\omega /k}\). In a multidimensional system, the scalar \(\displaystyle {\displaystyle kx}\) would be replaced by the vector dot product \(\displaystyle {\displaystyle {\mathbf {k} }\cdot {\mathbf {r} }}\), representing the wave vector and the position vector, respectively.

Still working on it……….\)

 

[topsquark]

Looks okay. In general you are talking about a free particle in 3D. The Schrodinger differential equation is
[math]-\dfrac{ \hbar ^2}{2m} \vec{ \nabla ^2} \Psi (x, t) = i \hbar \dfrac{ \partial \Psi }{ \partial t}[/math]
The best way to attack this is to look for a solution that can be separated: [math]\Psi ( \vec{x}, t) = \psi ( \vec{x} ) \cdot T(t)[/math]. This gives a solution [math]T(t) = A e^{i \omega t}[/math] and [math]\vec{ \nabla ^2} \psi ( \vec{x} ) = 0[/math]. Then you can take your solution from there. (Actually we can separate things again: [math]\psi ( \vec{x} ) = R(r) \cdot \Theta ( \theta) \cdot \Phi ( \phi)[/math]. This gives angular solutions called "spherical harmonics" [math]Y_l^m ( \theta , \phi ) = \Theta ( \theta ) \cdot \Phi ( \phi )[/math], which are very useful. You can look these up.)

-Dan

 

[ddj]

Dan,

Thank you for your encouragement and suggestions. I am not too keen on trying to adapt Schrodinger’s equations to my theory, since his wave function essentially deal with isolated systems which is diametrically opposite to the requirements of my theory.

I had followed your valuable suggestion and looked up spherical harmonics, which looks promising and can be utilized at a later date.

Most of the aether theories which were formulated by Descartes, Euler, Hooke, Huygens and others were vortice theories which implied some kind of circular movement of the aether. Maxwell had rigorously examined these theories but was unable to apply them to his theory. This view also does not correctly describe the theory I have in mind.

I am therefore considering opting for a travelling wave equation, which can incorporate four or five different variables.

1) Frequency of the wave. (An approximate frequency can be used since optical photons are all in the hundred terahertz range.

2) The intensity of the wave will have a reciprocal relationship with the square of the distance, but will also depend on the number of photons available.

3) Area over which ray spreads out, will vary directly with the square of the distance.

4) Time over which the signal lasts.

5) Inverse square law following a cone type of spread.

6) Energy of the individual photons e = fh

I will work on it and post after some progress is made.