My Math Forum timespace, a quantum analog to spacetime

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May 9th, 2018, 04:29 PM   #41
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Quote:
 Originally Posted by steveupson This is a simplified illustration of the math.
A word to the wise. It's better to post actual mathematics if you want to stimulate discussion. Pictures with no mathematical content are unlike to excite interest.

Also, without the mathematics behind them, they are more or less meaningless.

May 9th, 2018, 07:43 PM   #42
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Or, it looks like the opposite, where a square wave is gradually filtered by tuning a circuit in order to produce a sine wave. In reality, this is the function that is discussed in the proof, and is based on the small circle tridentity.

Take out your globe (I don't know why I think that you would have one) and place a wire loop on it so that the loop touches up against the pole. Now look at the intersections that are made between the wire and the lines of longitude. Now change the diameter of the loop and do this again.

Under careful scrutiny you will see that, as the wire loop gets smaller and smaller, it loses all of its spherical excess and becomes a flat circle, with the corresponding sine function. When the loop expands to become a great circle (lying on a line of longitude), it no longer has that sinusoidal relationship with the lines of the globe. If you were to try and revolve around the wire, you would go from perpendicular to the longitude to parallel with it, in one tiny move. This is the way that space is structured, and this is what is captured in the equation.

Another quote from another member of another forum:
Quote:
 "It just occurred to me that since the essence of the model seems to be relating the loop of the cap to the surface of the sphere (2D to 3D), your model might be a linear example of Stokes' theorem in 3-d (central to Maxwell's equation), and you're insistence that the actual sphere was not a necessary part of the proof is relevant, because Stoke's theorem is general for all loops and surfaces (Greens' theorem is actually a special case of Stoke's theorem that Maxwell applied to calculate the speed of light from Ampere's and Coulomb's laws (charges moving in a loop related to charges at a distance), where charge itself is represented by Gauss's law. "The difference between your model and Stoke's law is that Stokes applies to arbitrary loops and surfaces (Greens theorem applies to gradients - both "linearize" lines, areas, and volumes by using cross and dot products to yield Maxwell's equations in terms of calculus. "So your model might represent a fundamental tenet of electromagnetism (and also loop and string theory which is an attempt to apply Maxwell's proof to fundamental particle physics models. >>>> "Your model uses the sphere and circumference of the cap to express Stoke's law with the caveat that the elements (closed loops and spherical surfaces) are not arbitrary, so the expression of the proof is not general. "However, iIf Stokes law is true for arbitrary lines and surfaces, then it certainly is true for your model... which is quantized by virtue of the the fact that you are using trigonometric functions to express it rather than general surfaces in "space-time."" - BuleriaChk

May 9th, 2018, 07:48 PM   #43
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Quote:
 Originally Posted by v8archie A word to the wise. It's better to post actual mathematics if you want to stimulate discussion. Pictures with no mathematical content are unlike to excite interest. Also, without the mathematics behind them, they are more or less meaningless.
The proof is 18 pages, and I can try and post them all here, but for now the mathematics are presented in the pdf

https://www.steveupson.xyz/wp-conten...identities.pdf

 May 9th, 2018, 08:14 PM #44 Senior Member     Joined: Jul 2015 From: Florida Posts: 147 Thanks: 2 Math Focus: non-euclidean geometry The identities which require three dimensions will be called tridentities in order to distinguish them from all of the other mathematical identities which can be expressed in other forms than exclusively in Euclidean 3-space. An example of a known tridentity is (Chapter XVII (Chapter XIV) – Arcs Drawn to Fixed Points on the Surface of a Sphere (Todhunter)): $\displaystyle \cos^2TA+ \cos^2TB+ \cos^2TC = 1$ (page 133 of this edition: https://www.gutenberg.org/files/19770/19770-pdf.pdf >>>> Solving the spherical isosceles triangle Δabc gives simultaneous equations $\displaystyle \cot\alpha = \cos\upsilon\tan\frac{\phi}{2 }$ $\displaystyle \sin\frac{\lambda}{2 } = \sin\frac{\phi}{2 }\sin{\upsilon}$ which describe a family of functions. If we hold $\displaystyle \upsilon$ constant, the function for each member of the family α = ƒ(λ) is: $\displaystyle \alpha={\cot}^{-1 }(\cos\upsilon\tan{\sin}^{-1}(\frac{\sin\frac{\lambda}{ 2}}{ \sin\upsilon}))$ It is a smooth function that approaches a sine curve when $\displaystyle \upsilon$ → 0, and that approaches a hyperbola when $\displaystyle \upsilon$ → π/2. The simultaneous equations can be rewritten in the form of: $\displaystyle \sin{\upsilon}= \frac{\sin\frac{\lambda}{2}}{\cos\frac{\phi}{2}}$ $\displaystyle \cos{\upsilon}= \frac{\cot\alpha}{\cot\frac{\phi}{2}}$ and since, $\displaystyle \sin^2 \upsilon+\cos^2\upsilon=1$ then this gives the tridentity: $\displaystyle (\cos\frac{\phi}{2}\,\sin\frac{\lambda}{2})^2 +(\cot\frac{\phi}{2}\,\cos\alpha)^2=1$ Last edited by steveupson; May 9th, 2018 at 08:17 PM.
 May 9th, 2018, 08:26 PM #45 Senior Member     Joined: Sep 2015 From: USA Posts: 1,944 Thanks: 1011 What kind of response are you looking for here? Are we supposed to do more than look at your proof and produce oohs and ahhs?
May 10th, 2018, 03:13 AM   #46
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I was hoping for a response that isn't about me. I'd rather discuss the math. But sure, you may have missed all that because, you know, English.

timespace, a quantum analog to spacetime

timespace, a quantum analog to spacetime

timespace, a quantum analog to spacetime

timespace, a quantum analog to spacetime

timespace, a quantum analog to spacetime

From the OP:

Quote:
 "We need help with proving/disproving this theory. We’re not quite sure how to go about it. The underlying math seems very solid. Any help or criticism will be greatly appreciated."

 May 10th, 2018, 08:17 AM #47 Senior Member     Joined: Sep 2015 From: USA Posts: 1,944 Thanks: 1011 So you're unsure how to go about proving your theory but have an 18 page proof that you want us to review, for free. Well good luck with that. I'm sure there are lots of people with nothing better to do than look at your rehash of spherical trig.
May 16th, 2018, 06:51 PM   #48
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It has become apparent that there is a very common misunderstanding of the math behind the tridentities. The tridentities that are the foundation of this geometry are mathematical expressions of characteristics of Euclidean space. These characteristics of space are completely disregarded by current models and current geometries. In the small circle tridentity, we aren’t mapping a 2D circle to the 2D surface of a sphere, we’re mapping a circle in space to space itself.

Here’s another update from the other conversation. We are still trying to recruit help, just in case anyone here enjoys math or physics or science in general.

Quote:
 “This will no doubt take multiple revisions. It doesn't all need to be perfect the first time, and there's a lifetime of work left to go on this basic model. More than a lifetime, if the experiments to test all the nooks and crannies are included. ”I'm surprised enough at how far we've come in a very short time. I didn't expect to see a GUT this complete in my lifetime, let alone be one of those responsible for a small piece of it. ”It looked like simple spherical geometry at first, not a template to a complete discrete energy localization model and the geometry to go with it, with timespace and quantum spin enhanced relativity as a bonus. ”Didn't break even one of Einstein's original assumptions. The speed of light is still the limit for velocities, even if time is not proportional to it. There still is no aether or aether wind of the kind Michaelson-Moreley had expected. There is unlimited spin inertia in the quantum foam. It would only be that way if the net spin were zero, but that's inertia enough, just not of the kind of inertia most aether theorists expected to find. Matter itself is what converts the spin inertia of the quantum foam to linear inertia in all directions. Pretty cool trick. Can't wait to grasp the math that does that. It's coming... ”I think quantum spins of identically zero for Higgs, ±0.5 for fermions and ±1 for bosons are really all that are needed. The nominal angular momenta are all relative motion dependent as well, but it doesn't really need a lot of range in order to limit the speed of light / mass / energy to <= c. The spins for matter are discrete for good reason, but for Doppler shifts to work continuously as they do with other matter, the spin couplings of matter to the quantum foam must be continuous. ”Best of all, there is no way to make a reactionless drive out of the spin inertia of the quantum foam. If this were not true, I would worry that the model had derailed somehow. Conservation of mass / energy is still the supreme law of physics, in the quantum scale as well as cosmological ones. ”That should help.” - danshawen

 May 17th, 2018, 03:31 AM #49 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,591 Thanks: 546 Math Focus: Yet to find out.
May 17th, 2018, 04:14 AM   #50
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Quote:
 Originally Posted by steveupson Here’s another update from the other conversation. We are still trying to recruit help, just in case anyone here enjoys math or physics or science in general.
Why are you posting this again? This looks like those raving reviews you find at the back of books and that are obviously made up:

"A must read for old and young"

"The debuting author has completed a work that will soon be the gold standard."

 Tags analog, quantum, spacetime, timespace

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