1

New Theories / Time as an observable

« on: 16/10/2021 03:06:15 »

One issue quantum mechanics has is that while space is an observable, time isn't. I'd like to challenge this if we can.

General relativity treats time as quite special, as a leg of the Pythagorean triangle and in fact with it, general relativity was capable of manifesting curvature.

It is by this, that I say, time is manifested an observable from the curvature of space. Space bends because of time. Therefore when we observe curvature, we are seeing time "in" space, or at least, the effects of the warping of time and space.

2

New Theories / The Full Equation of Motion For The Gyroverse

« on: 14/10/2021 15:07:56 »

You can find my derivation here:

[Mod edit: Derive it here if you feel it matters to this topic]

Now let's say something about this. Godel's universe didn't take into account the Hubble expansion but this model does. It is a Lorentz violating model since it has a preferred reference frame. It also explains expansion directly as a centrifugal force. If it hadn't have been for Hoyle and Narlikar, we wouldn't have realized that spin decays and gets slower with increasing linear expansion and solves Hawking's dilemma - that is, if rotation exists today, it must be doing so at an incredibly slow rate. So we solve intuitively the reason of the "axis of evil" (why we don't see axis in background tenperatures) however dark flow can be taken as the residual leftover of the spin.

3

New Theories / A Small Number Hypothesis

« on: 13/10/2021 23:11:08 »

For the work, we will draw only on the similarity of powers and we will derive an approximation of Newtons constant.

Dirac must have been disheartened by the lack of support on his large number hypothesis and I feel some of his pain. There is equally a small number hypothesis that requires attention. The charged ion of nitrogen has a mass approx to 5 * 10^(-26) kg and for oxygen it is the same roughly. Hence Avogadro's number is also approx to the same number for a 24 cubic meter of space for an ideal gas. Hydrogen being an electrically charged proton pulled vertically by an electric field is approx to 2*10^(-27)kg. An alpha particle from radium has a mass approx to 5*10^(-27) kg and a neutron with a mass only slightly bigger has a mass approx to 5*10^(-27) kg. With protons and neutrons in mind, the neutron is slightly bigger and the question of why seems to lye with charge itself contributing to the total mass observed Gm^2 ~ nhc. This was even known to Feymann who stated that while the neutron was electrically neutral it has a more complex configuration involving a charge distribution making it slightly heavier than a proton.

At room temperature for air is 28.8kg for the 24 cubic meter of space. Further the measured density of liquid air is 1000kg/cu.m

The standard calculation for the lattice is

24/(28.8 ))/1000) = 833/1

From here I noticed that when it is divided by 6 it is approximately equal to the fine structure constant

833/6 ~ 137

By noticing this, I further took

(1/833)/6 ~ 8*10^(-6)

Which is further the number relating to the wavelength in meters of red light. Since we where talking about the ideal gas in 24 cubic meters of space, the fact that 6 was used to find the approximate value of the fine structure was a bit of a surprise but understandable as it conveys it self 3+3. In hypothesising this I decided to take the inverse function

3^√833 ~ 1

But stranger if not just a matter of curiosity, adding 833 directly with 137 was nearly the density of liquid air off by a factor of 30.

To note, while many numbers we have noticed approximations to, that fine structure 1/137 is much larger in comparison.


For electric charge to mass measurements, further study has shown remarkable numerical agreement with a small number hypothesis. For instance, the cathode ray for discharged electrons in gas reveals ~ 2*10^(11) while electrons from hot tungsten is the same including electrons from the more general case of the photoelectric effect. There are many more cases of this number obeying fundamental processes involving electrons.

The biggest surprise was the following speculation

833/137*10^(-11) ~ G

The gravitational constant. Notice that we spoke about 10^(11) in electron dynamics

4

New Theories / On The Mass Heirarchy: An Almost Solved Problem

« on: 06/10/2021 20:48:59 »

I'm seeing more and more articles these days about scientists discovering new links to the problem of the mass' of the particles of the quantum zoo.

Before all the refurbished hype on the issue off mass spectrum, I came to realize something a while ago. I've only just now realized that my model needs a tweak. I showed in orbit equations for atoms in another thread here, that the true analogue of charge from gravity to elecectromagnetism, was



https://www.thenakedscientists.com/forum/index.php?topic=82983.0

Whereas Motz' had previously given it as



But theres more.

In natural units, the square of the mass is equal to the fine gravitation fine structure constant!



Why? In natural units, we'd set in accordance with



This looks like a procedure ignoring what is known as
physics.

We see though, arguably the most mysterious of all quantum numbers as a serious statement about its own role in nature. Either way, it is fundamental and mass is a part of spacetime itself, an intrinsic statistical property on the scales of ground state fluctuations and its own interconnection with spacetime in GR states that either one is unthinkable without the other.

Nobel prize winner Weinberg wrote down a mass formula, which has caused many to speculate on its potential. The formula used the Planck charge so I modified it for because of the relationships highlighted above.

His equation now becomes



Weinberg, making now obvious what has made this unusual in the eyes of scholars, he attributes the mass as dependent on the Hubble parameter. Maybe today some might think this is strange, but around the same time other pioneers were wondering the same, especially in context of primordial seeds, which are ground state fluctuations which in theory have been streched in a single parameter and acting as thr first massive gravitational sytems forming the most earliest of galaxies, and thus, playing a role in the universes evolution.

Two more strong pieces of evidence exists which indicates the formulae are what we should be concentrating on. For instance, have you ever heard of Regge trajectories?

As the story goes, the guy speculated, what if we squared the mass of some common particles and graph them, what would he find? It wasn't  unusual for mass square terms in classical for field theory. It even shows up in the classical Klein Gorden equation. So thinking in square mass terms may have been an educated guess Id wager.

What he found was that several particles on their mass spectrum graphed a straight, skew horizontal line. It was so strange, that it remains as a curious discovery which seems to be unrivalled - In effect, something was there that can be explained using a square mass term in solving the Heirarchy Problem.

The final strange bit of evidence, is that Weinbergs formula successfully predicts a wide range of particle masses. Once again I add a little modification where I make use of the string tension T,




The formula can predict 19 or more particles which is much more successful than what you might think.

5

New Theories / A New Kind of Friedmann Equation

« on: 04/10/2021 21:45:33 »

In the past I wrote a theory on a mechanical model for dark energy. In short, if space was a medium that was accurately described by the fluid equation of state, could the flow of spacetime then varies from place to place due to the fluids local pressure inside some quantum entangled bubble. Such ideas of space being entangled with other places in space (and maybe time) is a key idea in  ER=EPR and many of the leading pioneers who original devised it think it holds one last quantum importance in unifying gravity would be those pesky black holes. As GM Jackson admits here:

http://gmjacksonphysics.blogspot.com/2017/02/using-fluid-mechanics-to-explain.html?m=1

Using the Bernolli equation as it is, is largely useless for the dynamics of expanding space. I'll argue he's right in some ways. And while his math looks sound, but it is as clear as mud that he doesn't explain the significance of his results all too well, a bit like me sometime.

If he took a longer thought over it, he should have soon came to the conclusion I reached. Just make a relativistic version. I've seen various derivations of Bernoulli's constraints, believing at least three don't apply to our universe.

When researching sonoluminescense, for two months, I compared many of these equations with the Friedman equation. I noticed, because both theories involve bubble cavity mathematics, which allows bubbles to spin, expand and contract.
I suppose the popping of these analogue bubbles could be associated to a vacuum decay, another hot topic in astrophysics.

Not drifting off to far now, coming back to my investigations of seeing the symmetries of both theories, I derived a specific form of the Reighlegh-Plesset equation as



* we had two R's remaining in the third expression from the left so it has been turned into a gauge. Also, a surface tension appeared, which if we assume no vacuum decay, can be neglected for the cosmological model.

You can read on its derivation in these four articles.

<Mod edit: Plug to personal site violates terms>

Continuing now, Bernoulli's principle can be stated in a few different forms, but at least one of them did first catch my eye. It's a well-known equation, and I reinvisioned, might be a better word, since a I didn't derive it. Like all his fluid equations, they involved the gravitational acceleration.
In order to reinterpret it under a framework for general relativity, I get -- first, let's refresh our mind on Bernoulli's original principle:



At the face of it, it looks all too familiar as an equation satisfying adabatic laws. Adiabatic models preserve the quantum model of conservation, wheteas the Diabatic models entertain violations of the conservation laws, which is a completely unfounded assumption on cosmological models, the late Lloyd Motz once pointed out, and author of the first mathematical model for a non conservstion by use of a third derivative on the Friedmann equation.

EvOLMhJVUiDyAMAohEhMX4AAAA" class="bbc_link" target="_blank">https://www.google.com/search?q=bernoulli+principle&oq=ber&aqs=chrome.0.69i59j69i57j69i59l2j69i61.2044j0j4&client=ms-android-americamovil-gb-revc&sourceid=chrome-mobile&ie=UTF-8#wptab=s:H4sIAAAAAAAAAONgVuLQz9U3yDAtSnrEaMwt8PLHPWEprUlrTl5jVOHiCs7IL3fNK8ksqRQS42KDsnikuLjgmnh2MUm6ppQmJ5Zk5ucl5jjn5yWnFpS45RflluYkLmKVTUotyssvzcnJVC9WKCjKz EvOLMhJVUiDyAMAohEhMX4AAAA

So a relatively simple operation replacing the acceleration notation for the gravitational field itself (ie. The connections of the field in which are described by the Christoffel symbols).

The Bernoulli equation, from its derivation section, is



The funny thing is, if I want a Bernoulli (modified equation) capable of being sufficient to satisfy those that define cosmology, thrn I need redefine the constant as actually the cosmological constant. In itself, as Jackson pointed out, the last equation isn't useful for cosmology and the flows of streams.

So let's make it useful!

We bring back to attention the following equations and suspect them





The first equation is much more superior. Also, by making the constant the cosmological kind, means it should have energy terms. This requires a simple distribution of a mass term on both equations. But since the first is all we care about:



What's interesting about this equation, is because unlike that has been noticed before, viscocity [v] of a fluid which is an interesting factor as it would decrease any uniform flow. Do wr asdume this term is surely approaching zero in the evudence of universal acceleration?
Except, I don't believe the universe is accelerating at all, and I think scientists have misinterpreted the data very badly! This would be out of context here, so if you want me to elaborate, say so and I will in another post.

But are there any other parameters which might strike the mind important if we want to have an acceptable form of a cosmic safe Bernoulli principle? When I invrstigated mechanical reasons, I used some of the equations we have seen in this post way back in the past. So its ironic to me I'd be dealing with it again.

It's called the Ricci flow. Indid do some massive investigations into in the space. If space is like a fluid, then such behaviour can be found in the Ricci flow, which (is the heat equation) for a Reimannian manifold.

This doesn't actually mean that the flow of heat is attributed simultanously with the glow of space, but it can happen.
Instead, it means that curvature flows, just like heat.

I came to my first attempt at independently deriving the four dimensional case, which seemed easy enough. This was when I realized the temperature was missing. But I couldn't use the math in mind to make ot happen unless I get the radius terms back like R'/R. So that it could be reinterpreted as T'/T due to their symmetries and dimensionlessness. Reareanging my equation we now argue



And so while making a new kind of Friedmann equation, so I made use of the temperature gauge as a coefficient on the viscocity from R/R(0).  This way, the thickness associated to some region of flowing space can slso vary in temperature.
To really finish off neatly, the equation makes time part of the left hand side with the last term on the right have a dependency of time on the pressure, we might ask, what does temperature depend on?
Well, temperature can depend on time, since the scale factor can be invited - We cuttently think it had a very hot and dense past, but we cannot say for sure what happened before it - nevertheless, the viscosity of space may be seen intrinsically related to the density of an element volume of space? All we will be missing is Einsteins curvature constant [k]. The constant in his theory was additive to the RHS



And so in our equation as



And I make a final surprise, not to make temperature time dependent, but as a function of the scale factor.

6

Physics, Astronomy & Cosmology / News report: Spin is looking surprisingly more classical

« on: 02/09/2021 17:07:53 »

Only a half week ago, I said here that we may need to have a revision for particles as being slightly extended ie. Like a corpuscular sphere, and someone replied, "Why do that for an inferior theory?"

I explained it wasn't inferior,  classical spin and quantumspin differ only slighly but the implications are massive for divergence theory issues. A news article came up on  my feed and a new condensus agrees with this. Spin is more and more looking like classical theory.


https://physicsworld.com/a/evolution-of-quantum-spins-looks-surprisingly-classical/?fbclid=IwAR2IxwmEQA6Vnyp5BX2HaUUFy-KC-N87yAY3qUN4rxgB_sGw2f0oAVEyXTY

7

New Theories / Bivector Gravity

« on: 30/08/2021 19:57:02 »

So what motivated me to write a bivector theory of gravity? First of all, it was modelled on electromagnetism. That equation looked like in literature as



Where E and B are the respective electric and magnetic fields. I was massively curious how this would transcend to gravity. I noticed that in bivector gravity, a part of the algebra encodes a spin space and that jumped out to me as important for a theory satisfying a full Poincare group of space symmetries. To start oc I modified the d'Alembertain operator accordingly and it took the form of;



This is just a convienient way to write the operator in terms of curved spacetime where we recognise as the Christoffel symbol. What we notice under bivector gravity is the spin Pauli vector has attached to it an imaginary number. This is the only exception we can allow a complex number into a theory of gravity since gravity is manifestly non-complex. Using these ideas we make a simple theory of gravity with two derivatives



D can be any space ortime derivative. Anyone accostomed to GR will know we just describe curvature and gravity by these "connections." Here ot is vital to understand the importance of the lasr term and I identify it as gravitational torsion



A similar idea of torsion arose in previous work, where I attempted to describe its effects on the particle scale

https://www.thenakedscientists.com/forum/index.php?topic=82903.0

In both cases, torsion there and here are ascribed with dimensions of inverse time. So the LHS has dimensions of inverse length squared, just as it is on the RHS. This cross product if the field and the derivative making torsion is not new, (I think Heaviside might have derived it in this way, but not sure now) but I noticed it falling out of our theory in a natural way, on the spin space of Pauli vectors.

As I said, anyone aquainted with general relativity, we deal with the products of derivatives, frequently. A good example is when deriving the curvature tensor of GR and just looks lije:



In ordinary approach from GR, the torsion is said to arise from this part



Whereas in our theory it arises in



Before I move onto the kinetic energy of spin with the same ideas surrounding the bivector set up, let's investigate a fuller description of the two derivative idea and attach the conventional gamma matrices onto it. A quick reminder of those matrices can be found here

https://en.m.wikipedia.org/wiki/Gamma_matrices

We will quickly note that any timelike gamma matrix is always denoted with a naught and the spacelike ones are denoted with indices (1,2,3). Now we can say the bivector gravity will satisfy



And we can calculate the derivatives in a similar way we would derive the curvature tensor, hence why it was important to feature it earlier. Not just to show the differences of how torsion arises in this theory compared to GR, but how the derivatives are now formally calculated with the gamma matrices.







So aside from using all the fancy gamma matrices, we can still retrieve a theory similar to that obtained by Einstein where the last part

 

Has a structure similar to the torsion in GR. Some algebraic properties you may need to come to know is

and another useful one is . It's also true that . A fun fact is that space and time may not even commute. That is, any product of two classical space derivatives may not be equal to zero. This is called the spacetime uncertainty principle, and there may be evidence of this according to some from scattering experiments.

Ok, so that big formula above with all those gamma matrices atrached to it, we realized looks a lot like a curvature tensor that you might calculate from GR.  If the curvature tensor is just a product of two derivatives, can we not just say



It might be, I even wrote this down in my notes. You might even theorise a stress energy tensor in a similar fashion:



Truth is I don't know if it's right or wrong, a lot of it was guesswork. What I did notice the algebra can fit a number of different physics. For instance, the hydrodynamic time derivative is



You can see how this equation could reinterpretated as



Related to fluid and kinetic motion, I looked at the total angular momentum



I took a really simple approach. Just meddling and merging some ideas together. For instance, similar to the correction term in GR on flat space is just an additive feature in the covariant derivative



Then I looked at some old theories of how the angular momentum L was described interacting with a torsion field. I can't remember who first wrote it, I know Heaviside might gave first written it, but the "moment of forces" equation was



Where was the torsion. By plugging in the total angular momentum and rewriting it like a bivector theory I got



And the last term looks like a torsion, albeit, it's directly written as the connection.

While writing this, I looked into some of the history of Heavisides equations ans found this interesting;

https://en.m.wikiversity.org/wiki/Heaviside_vector

Heaviside in its most simplesr form, said torsion was related to gravity like



Which almost fits my dimensions from



I don't know just by looking at it how he defines his dimensions here, he might be ascribing field as acceleration, in which case the torsion has dimensions of time exactly as opposed to my approach of inverse time. Both ways are just as good. You can define a Christoffel symbol with dimensions of acceleration or as a space or time derivative. Some are even dimensionless.

He was able to define his own vector, ignoring some constants, his vector identified a torsion relationship with the Christoffel symbol as



And I defined it as



Which is very similar. If the derivative D was taken as the torsion directly, then yea, our theories would meet eye-to-eye. Just a recallobration of units and the ideas are the same at the crux of it. I look back on questions I asked a long time ago and it seems I was puzzled by it even back then

https://physics.stackexchange.com/questions/467765/heaviside-vector-units/472807#472807

While searching, I even found myself asking physics exchange on whether there was a functional theory of bivector gravity and we can see some of my preliminary thoughts here

https://physics.stackexchange.com/questions/463682/is-there-a-geometric-algebra-for-gravity


Higher Dimensions

I refer you to wiki's page ob this bivector theory as it speaks about higher dimensions

https://en.m.wikipedia.org/wiki/Bivector

These mathematicians are way over my head. When I was formulating the theory, before this wiki article clearly had tweaks over the years, I made a statement that there was a stringent result on the dimensions, and this is because cross products cannot operate in any other dimensions other than three or seven. Here I go into lengthly detail about a bivector gravity and why it should only work in three or seven dimensions. I ended up answering my own post:

https://physics.stackexchange.com/questions/448809/geometrized-algebra-and-einsteins-equations

I even remark how GR is a theory of curved space and time and how a bivector theory of say three dimensions while not impossible, would be a hard sweet to swallow. I know there are certain physicists out there who meddle with the no-time hypothesis.

But! It just shows you I couldn't have known much back tjen, because since then the wiki article explains how to do deal woth bivectors above four and even more dimensions. It seems I was fixated on the issue of cross products only working in three or seven dimensions and a bit foolishly I guess, just assumed it would extend similarly to a bivector theory of gravity. I wasn't and still not, a big fan of extra dimensions and a limiting case to three appealed to me wthoit fully understanding its complexities. Soyeah, in short I can be wrong. Probably more times than I'd wish to believe!

8

New Theories / Discrete Energy Transitions and Black Holes

« on: 30/08/2021 15:45:55 »

Before we get to the math, I did make a mention how it's possible that electrons inside of atoms really do follow orbits accompanied with waves.

https://www.thenakedscientists.com/forum/index.php?topic=82903.0

While the crux of this theory isn't entirely essential to the work that will follow, I just wanted to highlight we still don't know the full picture, let's get a taster of the Bohr planetary model and why it still gains traction. It never fully diminished even in ligglht of Schrodingers wave mechanics and even back then, Schrodinger eventually became resentful of some physicists trying to do away with particle dynamics soley for a wave interpretation. He even invented his cat in a box thought experiment to highlight the ridiculousness of a purely random statistical model of physics which contrary to them had been taking significant traction.

A Fruitful Theory

A Brief History Of The Bohr Atom

Mamy think Bohr's model correctly predicted the hydrogen atom energy when in reality 8t did so much more.

1. Bohr kept the Rutherford picture of electrons persuing orbits and predicted that it recerved an inverse square law in a Hill diagram.

2. While in collaboration with DeBroglie, he kept the particle model but used Bohr's equations that linked matter to energy and found discrete and simple laws. For instance, the lowest shelf predicted as the smallest allowed orbit and soon after Pauli showed with them that the allowed orbits had to satisfy an exclusion principle, which is the opposite to photon behaviour which tended discrete packages to fall into the same quantum states. This way, several electrons could never occupy a shelf, but two could with opposite spins and gave rise to the periodic table.

**While Bohr argued certain orbits did not radiate because they didn't follow the usual laws od quantum mechanics, I'll leave as possibly the only ad hoc assumption he made since free fall of orbits answers it sufficiently with accepted laws. Even planets orbiting the sun are in free fall.

3. Bohr predicted the size of the hydrogen atom. There's been a lot of dialogue so far and I just want to get throughthis as quick as possible to the work I wish to present. If yoy would lije mathematical demonstration of this, please just ask in a post. By working out the size of the hydrogen atom, he was effectively calculating the diameter of an electron in the outermost shelf.

4. Arguably his greatest achievement was his prediction of bright spectral lines which at that time was crying for an explanation and had dumbfounded even the brightest minds up till that point.

5. He correctly predicted the fine grating spectrum constant. The value he obtained was experimentally obtained eventually as 3286 trillion compared to his agreement of 3290. For many, the agreement was so precise, it validated his theory to a lot of resistant, suspicious minds.

6. He was capable of measuring the transition of those orbits. In fact, my work below encompasses the same idea, ge write the transition as:



In fact, this equation is called the Rydberg formula and was adopted into his work. Bohr went as far to say, it was a universal equation which was fundamental to a large number of physics which used discrete processes. This is one of the reasons why it will feature a lot later in my own work.

7. Bohr predicted the exact nature of the Helium atom. He presumed that we could envision a Helium atom that had lost two of its electrons and the remaining electeon would emit light when switching orbits. With the one remaining electron, it behaved like an ionized Helium atom which is like a Hydrogen atom with a doubling controlling charge +2e on the nucleus. With Z = 2 (the nuclear charge) the predicted frequences were just 4 times than the Hydrogen frequencies. These lines had been discovered previously, but before Bohr's model, it had been mistakenly takebln for a Hydrogen atom in some strange and special state.

8. Bohr using his model not only predicted this ionized half-stripped Helium but even predicted a minor correction from the nuclear mass from which he was capable of measuring the electron to proton mass ratio as 1/1830.

9. Then his theory predicted the switches of innermost electrons that would produce x-ray frequencies far greater than the visible light spectrum because the constant K had for it Z^2.

So while we might be taught often to drop this planetary model, it is still the only successful theory that has managed to predict all features of quantum physics above. This is why Bohr's model won't be superceded. There has to be some aspect of the planetary model to be true because its highly unlikely he was able to derive these results by pure chance alone. If it had been by chance, then it's been the most successful "accident" ever predicted for atomic physics.

Now To My Theory

When reading Lloyd Motz'wirk on the Uniton (a proposed primirdial particle not too dissimilar to a primordial micro black hole) he stated that Weyl invariance suggested a quantization of mass as



And said it was equivalent to the charge squared analogue. For years I just accepted that, then when doing some preliminary equations to find a charge relationship to the orbitals inside an atom to obey Keplers law of motion which soon brought the analogue into a new light. I first came to hypothesize from derivation



From there I made a suggestion that we set for the special case of a hydrogen atom and then for a sufficiently small electron mass and came to



But then I decided to meddle around, seeked a unification from the inspection of the similarities between electrostatic laws and those with gravity, and found unlike what Motz had claimed, waa not the analogue of charge squared alone, instead I found it must satisfy a slight alteration



In such a case now, we can loosely say that mass is the analogue of the charge and Newtons constant is the analogue of Boltzmann's constant. In cgs units Newtons constant is



In cgs units, Boltzmanns constant is



When I recalibrated my equations, for an electric charge round the nucleus, I eventually derived



And I ended up with a mixture of the two constants, one which measures how gravitational objects interacted and the other how thermodynamics applies to the motion of systems. I went off, took the two and made a new constant out of it, let's call it K and this time the corrected formula for a charge round a nucleus preserving Keplers law and became



A while ago, I submitted a paper in a competition to the gravitational research foundation but I dropped this topic back in 2018-2019 for an attempt on a pseudo quantum picture of gravity which modelled curvature in a Hilbert space without gravitons. The original paper I had outlined in mind was a full translation of the Rydberg constant with DeVroglie wave mechanics and a fully coherent theory of how phase transitions occurred for any system preserving the loss or gain of discrete packets of quanta. I managed to derive that constant with units of inverse length:

*quick note: I was impressed how my original calculations came to that called a Holeum model and gave me insight that at the very least, I derived my own formula from the correct ingredients even expanding it into a relativistic equation, which I had never seen in a transition formula before.



Where the last term managed to pick up DeBroglies famous relationship to matter and waves. I then asked, "What if the Rydberg constant was related to the change in the wavelength using the universal equation" as Bohr had called it?

So I did and I got:



Then to get the energy transition was easy and we pick up



While my theory thus far had nothing to with the Holeum model, my results were very close and told me that instead if a two black hole particle model orbiting each other, this transition formula could describe a single black hole undergoing discrete transitions. Whether the black hole was increasing mass or loosing mass via the evaporation phase, both physics appeared very interesting in light of my formula. What do the limits in the equation mean for discrete transitions of a black hole?

We can change the formula slightly and write it for a change im the mass and write the wavelength as a thermal wavelength,



Then as



Then



So for a black hole, as the thermal wavelength increases, the black holes mass decreases as we would expect. It means that as it looses mass due to Hawking evaporation, the black hole conserves the idea of it getting hotter. We have no exceptions in physics, mass was shown by DeBroglie to always satisfy



And this even applies to tennis balls, not just particles. It's just that the bigger the mass, the smaller associated wavelength there is. It's not impossible to apply the uncertainty principle to the model either. I did so and it falls out like



Where is the invariant time operator. This is just a nice inbetween post as I have been given permission to writeup a thread on bivector gravity. It's one of the most interesting theories I ever looked into and I think I was one of the first to explore it in depth like I had. So expect at some point I'll br writing up about this theory.

9

New Theories / The Cold Big Bang

« on: 22/08/2021 10:02:35 »

In contrary to the hot big bang, the universe can be modelled from a supercool degenerate region all liquid irreversible matter phase. This is a new interpretation I developed where I take older ideas that once explored this type of model which attempted to explain a more valid picture of early cosmology. A hot big bang phase with low entropy appears to violate thermodynamics, but if our universe began in a supercool condensed mattter phase which heated up, it would solve this theoretical problem and I developed the first quantum model for this. Some relevant articles you need to know about is the following:

https://en.m.wikipedia.org/wiki/Entropy_production#:~:text=Entropy%20production%20(or%20generation)%20is,any%20irreversible%20thermodynamic%20cycle%2C%20including

https://en.m.wikipedia.org/wiki/Friedmann_equations

https://en.m.wikipedia.org/wiki/Cold_Big_Bang

https://www.google.com/search?q=planck%27s+law&oq=plancks+la&aqs=chrome.1.69i57j0l4.3877j0j4&client=ms-android-americamovil-gb-revc&sourceid=chrome-mobile&ie=UTF-8

https://en.m.wikipedia.org/wiki/Zero-point_energy#:~:text=Zero-point%20energy%20(ZPE),by%20the%20Heisenberg%20uncertainty%20principle.&text=All%20these%20fields%20have%20zero-point%20energy.

https://en.m.wikipedia.org/wiki/Bose_gas

So let's begin. I was not the originsl proposer of such a model, but I was the first to develop a semi-classical Friedmann equation so satisfy irreversible particle production that implemented the ground state fields for an early cosmology.

In this post, we will show how in principle that temperature can only approach zero, which is best understood when we model the fluctuations into an expanding model, and they can even generate cosmic seeds - before I have done this to accommodate the Sakharov gravitational correction, this time we will accommodate the Planck Law. To ''put in'' the laws of thermodynamics is relatively easy. So I did some calibrating of the modified equation to show Plancks law will hold.

Instead of a fluid expansion coefficient of



We make use of a temperature gauge for the Friedmann equation where



  ∴



The final equation I derived was



We integrate over the frequency to get an energy density



Where entropy can be defined as



Integration over the volume element of the primordial universe will give



We notice in our approach we have combined the gas laws



For the internal energy. The Planck law including a corrective zero point field per oscillator of the ground state for temperatures near T=0



And we invoked a particle expected number as



And has a unique solution for the density volume product in



As the ratio of zeta values



A simple equation of state that will satisfy a particle number creation associated to the temperature and scale invariant



Is



Where is the particle creation number and here, is the thermal wavelength, then when



It will follow the Bose statistics, or if modelled as



Then it will follow Maxwell statistics.

Summary; We rewrote the Friedmann equation, with a temperature gauge directing the fluid expansion while incorporating the entropy production for both reversible and irreversible dynamics to satisfy a Helmholtz irreversible thermodynamic phase transition. It's irreversible because our Friedmann equation has an extra time derivative as opposed to the ordinary Friedmann equation. We incorporated Plancks law and the zero point correction term, invoked the usual gas laws associated to it and then applied statistical thermal particle distances to talk about how the universe evolved from a cold state rapidly heating as it expands to produce the background temperatures we observe today.

10

New Theories / Differentiating The Sakharov Equation

« on: 21/08/2021 15:14:45 »

To a non-physicist, I know some papers can appear very abstract, and Sakharov's equation was one of them. You can follow his ideas from various articles, here's a few to chew on

https://www.atticusrarebooks.com/pages/books/719/a-d-sakharov-andrei/vacuum-quantum-fluctuations-in-curved-space-and-the-theory-of-gravitation-in-soviet-physics

https://dx.doi.org/10.1088/1742-6596/1051/1/012017


As abstract his equation may appear, I'll break it down so it can be understood. It won't take long as the premise is easy to grapple. In his paper, he was attempting to explain how early physics didn't believe in the existence of fluctuations, which is described by a divergent integral series where it is taken over the momentum of the ground state of the field and was presumed zero. In his approach, he showed that this not the case (today, we take the existence of these ground state particles now as a matter of experimental fact) but still remains a very hot topic in physics, because it lies now at the very nature of quantum mechanics, where these fluctuations really do come into and out of existence, governed by the creation and annihilation operators: It's a phenom so engrained in physics that Bogoluibov transformations take place in a wide range of physical systems, even black holes that preserve the idea of Unruh-Hawking radiation.

Sakharov's natural insight allowed him to show that higher powers of the metric curvature could sometimes allow virual particles to become real, the contribution of background curvature to the fields.

Sakharov explained that you could expand a Lagrange equation in a geometric series that satisfies



It was so fruitful that he not only obtained a gravitational action



Where but that the geometric series which produced the infamous fine structure. It was further discovered that by integration of the wave length yielded the value of , corresponded to the inverse of a Planck length, an indication that the wavelength of the particle was that corresponding to its smallest smearing in space.

In Sakharov's equation, he didn't specify all to clearly what the constants of and where, but its full translation has been written out, the first authors I read who made this equation clear in the context of quantum mechanics came from Arun and Sivaram, they explain the nodes of the field will satisfy Sakharov's Lagrangian in the following way



A quick inspection from dimensional analysis upholds this. If is the curvature from Einstein's theory, then it has units of inverse length squared, so inspection from the first part



we see is like saying the energy is



With one extra wave length node and the curvature $R$ is equivalent to a density, so it has units of energy density, exactly what a Lagrangian density should have.  Now here is where I invite the "new" physics from some application of calculus.

Since we are blessed with the prospect of knowing that the nodes of the field are described by the relatively simple formula using as the wave lengths, the inverse can be characterized as the length of the wave, which in physics is given by the speed of the particle by a frequency term. As physicists, we often call it and has units of length. We now say that the curvature is a function associated to these waves, so we write a general formula



and its differentiation will yield



Physicists are often more than not pure mathematicians, we can be quite different animals, but the result is standard enough that to a mathematician, it should be clear that becomes our length that has been differentiated like it was in respect to . Now we can also define it as



So long as we recognize that and we see now that Sakharov's equation satisfies the differentiation written as



Where we have rewritten as the differential logarithm (and in calculus known as elasticity) of the wave number, and we have replaced with its differential equivalent form of

11

New Theories / Some Photons Have Mass! New Physics Report

« on: 21/08/2021 02:30:38 »

"And the scientists’ measurements back that up, says laser plasma physicist Stuart Mangles of Imperial College London, who was not involved with the new study: “Everything they’re measuring about it makes it look like a real photon.” However, Mangles notes that the photons are still virtual by some definitions: Unlike normal photons, which have no mass, these photons do have mass."

https://www.sciencenews.org/article/colliding-photons-matter-particle-physics?fbclid=IwAR0xZeM1idBMmZ4pSLJ-1pa5ulemphxW1KWdHWj6O3E19cEFovrUgV0PdMo



Virtual particles are usually ground state particles. Virtual particles are mediator particles just as ordinary photons are. A good example of virtual particles is their interactions with other particles like muons. They exist around the muon in a haze fleeting in and out of existence. Virtual particles should not be mistaken for meaning they are not real, its just that they do not follow the ordinary Hermitian matrices making them strictly observsble, but thry can be obseved indirectly. In a way, they are very much a candidate for a type of dark matter in this sense. Virtual particles have a rich history. Yukawa predicted a hypothetical model where the virtual photon might bind nucleons, at the nuclear range, byt being massless he found it wouldn't provide the correct binding energies. This may be revised now that virtual photons do carry mass. Nevertheless, using the uncertainty principle he was able to calculate the mass of these virtual photons and they were soon vindicated as Pion exchanges that carried the strong force. His rudimentary calculation for the mass was a bit iff, but further experimentation gound there were other Pions and at least one class of these partickes did fit his mass prediction. They were detected in cloud chambers.

htt
p://hyperphysics.phy-astr.gsu.edu/hbase/Forces/exchg.html#c4

If Pions hold quatks together, the picture soon became more complicated because the Quarks had also another exchange particle, called the gluon. Sometimes articles gloss over the role of Pions being the strong force mediator and concentrate on the gluon phenonenon. But now, with it being confirmed that virtual photons can carry mass, they may actually play a role for binding that Yukawa once predicted.

Some intellectual discussions on Pion vs gluon exchange forces https://physics.stackexchange.com/questions/9663/is-it-pions-or-gluons-that-mediate-the-strong-force-between-nucleons

Yukawa wanted to find out what binding agent held a nucleus together. He knew it followed a distance law of 1/r ˛  with it dropping from huge values inside the nucleus to negligible values at the rim. He first speculated it coukd have been a photon, possibly a virtual photon then presumed to have zero mass, but he soon found if it had no mass it could not act as the binding agent. The exchange particle had to have sone mass to fit the experinental knowledge of forces.

To form an orbit its DeBriglie wave would have to form a standing wave ring if radius r and the simplest ring was

λ = 2πr

but for any particle

λ = h/mv

 ∵ mv = h/2πr

if we say v = c that is an overestimate unless it was a photon with zero mass, but if we say m = m' the rest mass of a meson, that was an underestimate.

However, we make such exchanges in hope to find they will compensate, so Yukawa gave

m'c = h/2πr

by using

m' = h/2πrc we can now predict the value of m from the known values of h and c and the estimate of the nuclear radius r which is approximately 1.4 x 10^(-15) m. We get a value of

0.9 x 10^(-30) kg.

Comparing this with the rest mass if an electron, the exchange particle had to have roughly several hundred electron masses! This makes it five or ten times light than a single atom. At first, it wasn't believed, but a meson were soon experimentally varified inside of cloud chambers. The mass at first wasn't right but further experiments found more and one of them did fit his predicted mass.
​​​​​​​
So hopefully, you can see the opening of new doors to Yukawas originally binding hypothesis using photons, since he rejected that idea because he was using a now outdated idea of them containing "no mass."

12

New Theories / On Kepler Orbitals For Atomic Physics

« on: 20/08/2021 06:50:28 »

Its been long assumed the electron follows a probability fuzz around a nucleus, but the work of Bohr showed remarkable success that orbitals for the hydrigen atom became to be called stationary orbitals that did not radiate. I independently came to the conclysion that these special orbitals could in fact be folliwing the weak ewuivelence of free falling physics, which means the particle free falling would not accelerate in such a way to give off radiation. I later found out that a free falling orbital model was investigated a while ago but appears not to have gained much traction.

First of all, why did I pursue a free falling model of an electron the in the stable orbits of an atom?

1. Electrons cannot be at rest in a stable equilibrium

2. Electrons cannot be in motion pursuing ellipitical orbits

These two basic premises of quantum theory are at odds with each other. One thing was certain, if electrons had motion then Bohr was right:

3. Only non-stable orbits with motion can allow atoms to radiate.

So with the help of quantum theory, Bohr created a model of the atom where electrons followed ''special orbits'' and these ''special orbits'' where the ones where electrons had been able to whizz around without giving off the usual radiation we would expect from a moving charge. Later, the planetary model was superseded by wave mechanics, the idea was simple enough

4. That electrons did not move around the nucleus, instead they existed as a wave spread out statistically in space.

But with this, there was a catch. DeBroglie, the true inventor of the wave particle duality model, for all states of matter, never said that his wave mechanics specifically said this. From experiments, like the photoelectric effect and gamma scattering, we knew the particle had to exist both sometimes as a particle, other times a wave. The inseparability of the wave from the particle, lead to his famous wave hypothesis, stating that the particle was accompanied by wave. The wave itself was unobservable however, only today using very special techniques, computers and special equipment have been able to indirectly see the wave nature inside of particles. It still doesn't tell us at what time the electron would act as a particle, unless directly observed, by which time the wave would collapse and all that would remain, would be the particle. Yeah, quantum theory was weird.

In spirit of deBroglie, I'd like to carry on his strong assertion that particles where guided by waves, so that we can  in some way rationalise the weird nature of quantum mechanics into a regime that is more acceptable for a willing and rational mind. Certainly, why cannot a particle be guided by its wave? Matter was guided by curvature in space, and it was this correspondence of the two ideas where I linked perhaps a unity between the strange wave mechanics of deBroglie to that of GR. One stated that matter told space how to curve and space told matter how to move, whereas particles told waves how to spread, and the waves told particles how to move. Maybe wave mechanics and curvature where closely related. This was my first motivation. We'll learn as my theory progresses, that the orbits described by the moving particle also contain their own curvatures, their own geometries. By inviting the weak equivalence principle, we would further learn how to allow a particle to move in an orbit without giving off any radiation.

So a natural conclusion under the DeBroglie model is that electrons do in fact follow paths inside an atom accompanied by the wave. The waves are not observable but the electron is.

In order to model an electron with any arrangement of orbits, requires the eccentricity. So in my work we will model this eccentricity for a more accurate spin orbit equation.

Quite a bit of a calculus goes into the derivation, of eccentricity, but it wasn't my derivation. My contribution is its direct application to a spin orbit equation, two final forms came as



where is the gravimagnetic field, we identify torsion as encoded in this as being part of the central potential , its full form is



and



and



Is the eccentricity. In a later post Ill show how you derive the full result from calculus, but its ugly and complicated so I'm not doing that today. The main point is we have a correction term on the spin orbit equation, the deviation of the orbit described by the eccentricity. It shows how much it will deviate from a perfect circle so has real world applications, even inside of the interior of atoms.

The alternative formula is



And is the total angular momentum. You get the first equation by plugging in the inverse Bohr mass



into the standard spin orbit equation, which is,



Ironically, I found that it didn't matter whether I used Bohrs inverse mass or inverse radius, they both produced the same equation, so they are not too much different animals.

In this post I'll explain quickly the calculus used to derive the eccentricity. Its all standard, it's not something I derived myself, whoever did, was doing this stuff at high level university stuff, it was the insight I had where we could use it to describe the radius of curvature. Hopefully I put it here in an understandable way, my only contribution, as its a bit complicated. We start off with a Langrangian



We are able to define the shape of the orbit from



The angle is defined by a succinct integral equation as



The r-integration is followed by making



and



This gives



So pretty complicated stuff tracking these variables, a lot more complicated than Id mess around with normally outside of mathlab. Next we can make from this,



and also



So that the final orbit of curvature can be taken, with eccentricity as