"I think I can... say that nobody understands Quantum Mechanics." Save perhaps for other Quantum Mechanics. Thanks for this discussion.

On 9/16/2022 at 3:07 PM, joigus said:

Suppose a civilisation more familiar with both BH's and entropy than our scientist ancestors have been for centuries, and didn't know QM, came to study BH's very much like physicists of the 19th century came to study the black-body radiation. The Planck of this civilisation solves a puzzle for a generation of these physicists. What is their puzzle?: all calculations of a BH's entropy give infinity! Let's call it the ultra-entropic catastrophe, in close analogy to the ultraviolet catastrophe that gave rise to QM.

The solution to the puzzle comes in the form of regularising the entropy by means of quantising the action variables on the denominator so that the entropy doesn't come out infinite. That's what the HB formula for the BH seems to be suggesting.

Now that's what I find very surprising. What is that infinite entropy that the quantum equation is suggesting if we "classicalise" the BH by doing h-> 0?

What are these classical variables, all scrambled up, that QM needs to regularise?

"Formula for black hole entropy
How to express the black hole entropy in a concrete formula? It is clear at the outset that black hole entropy should only depend on the observable properties of the black hole: mass, electric charge and angular momentum."

I posit that trying to bring into the same occupying space like* charges implies an entropic increase because of the inordinate potential force that they be ejected far away and into any other possible degree of freedom but I do not understand entropy.

On 9/15/2022 at 3:42 PM, KosherDill said:

She says the only reason she can drink milk is because the fats in the milk surround the water molecules so they cannot be detected by her immune system.

Uh

On 9/15/2022 at 6:48 PM, KosherDill said:

Intravenous saline doesn't have any additives like chlorine in it.

Uh

On 9/15/2022 at 7:28 PM, KosherDill said:

She's been diagnosed with aquagenic urticaria otherwise known as water allergy, her mother is an MD.

Wondering what MD stands for. Not to put too fine a point on it, but if you have this person's ear, communicate that the observed correlation of water causing an allergic response is not sufficient to conclude causation or make a diagnosis. It is more likely that the inflammation/allergy is caused by histamine from mast cells, that she's likely primed to histamine release from minor irritations, and that this is an inflammatory condition so yes a lot of things are going o be painful.

On 9/15/2022 at 6:43 PM, KosherDill said:

If I started to itch these spots (which I try really really hard not to) then rashes and hives can quickly pop up and persist for a lot longer than this sensitivity.

This is like dermatographia, which again I think is a sign of high tissue histamine. There is no good reason to avoid water, drinking or bathing, dehydration makes just about everything worse. If you really want to help her, source Betaine(TriMethylGlycine) from purebulk.com, or find Source Naturals healthfood store version (750mg chalky pills) or something similar somewhere and grind them up. Or source MethylTetraHydroFolate or MethylCobalamin -- these are 3 methyl donors. I think it's safe to conclude she's undermethylated as in a histadeliac. If you have this person's ear try to disabuse her of this poorly founded notion of aquagenic urticaria.

Presuming there is this histamine, urticaria, reaction she claims, I'd bet on histadelia, a baseline high tissue histamine condition largely unrecognized. 

The terminal acceptor of electrons in the electron transport chain is oxygen. In effect, two hydrogen atoms are tacked on to an oxygen, so you make metabolic water. That and the other context of it being the main solvent in the body would seem to make this scenario unlikely. I for one would badger her youtube or wherever this is from that she needs methyl donors or benadryl to knock down that urticaria.

@bangstrom,

I was mistaken, I'd meant to mention, Extracting the Universe from the Wave Function. In this presentation, S. Carroll makes no bones about making many choices along 'branch points' in developing his physics with the understanding that he may be wrong, but to make the work-up he is going to make certain decisions. What is pertinent here to my recall is that he starts the work-up by discussion of and looking at decomposing Hilbert space. From this it follows that small areas of Hilbert spaces are aggregated to a "bulk" space, and as depicted here at this time-point in the video (you'll have to play the video as the display slide is not the one I'm talking about): 

 he's written out, "in QFT, empty space is a busy place. Modes in a nearby regions are highly entangled, and the closer they are to each other, the more entangled they get. Turn this around! Define "nearby" as "highly entangled."

So, a big part of this presentation's work-up is on getting a handle on Hilbert space, using a certain interpretation, and then examining how that plays into local vs. non-local and entanglement. I'd highly recommend the presentation for viewing. It is not much on the MWI part you seem to find objectionable with regards to multi-dimensional dopplegangers, as I recall, but I don't have all the information properly on file.

Oi, good on you. I'll re-visit it and try to see where I was mistaken. Thanks for the challenge!

On 9/9/2022 at 4:18 PM, hoola said:

I have heard that is "how it works", but that doesn't explain the internal workings of the black box attributed to the idea. I did get the gell mann video to load, and having seen it several times before,  still leaves one with the impression that "it works this way because it works this way" and not a real explanation, nor much of a hint as to what is in the black box. I can  see one option and that is that quantum entanglements are independent from geometric space notions of distance and act as such being composed of i based mathematical numerical structures, and as so, rely on that structured, yet illogical underpinnings to explain their behavior.

Of course I am in favor of this surly  business. I do not think  is so agreeable as to disappear by the conventional squaring of the modulus to obtain Born's probabilistic interpretation. My understanding of a second-hand interpretation is that Schrödinger did not like this either, because it creates a wave with a variable radial component or the interpretation being that squaring  has removed the azimuthal part which should be there and describing a more coherent or classical wave. 

5 hours ago, Ned said:

The connecting particle fields are all converged , for example the Suns quantum field extends to the earths surface and beyond . Energy is always transferred between particles unless those particles are in an equal state . Because everything in the universe is always in motion , kinetic energy is always produced and this energy is transferable . Quantum fields are dependent to the particle and bounded (fixed) to the particle . If a particle is in spin then the field spins with it .

The sun's quantum field, because it is having photons as force carriers? It sounds like the magnetosphere between the two and heliosphere beyond that. I don't uderstand the unbounded vs. bounded energy, perhaps we are dealing in quanta that in large aggregates seems unbounded.

5 hours ago, Ned said:

It depends on your interpretation of energy because in my interpretation and understanding there is several types of energy that are either bounded energy or unbounded energy . A particle for example would be bounded energy and  free to ''wonder about''.

There is also a difference in the transfer of unbounded energy locally and non-locally . In example two objects touching can exchange energy because they are touching .Non-locally transfer of unbounded energy relies on obstruction of the unbounded energies path . In example the exchange of the Suns unbounded energy with the Earth is simply because the Earth obstructs the path (vector) . There is additional an exchange of bounded energy because the Suns QF touches the Earths surface .

So you're talking about radiant energy from the sun, but I do not think it is so simple in this two-body problem that the earth is catching an incident bit of the radiant energy by being in the... vector's path. Since it is an electrically charged and magnetized body there are induced field lines over which charged particles move. Again I do not think a spinning body spins the field...

I fear we've lost the thread or at least I have.

On 9/9/2022 at 1:14 PM, hoola said:

it does seem that there is a faster than light signalling with quantum entanglement issues, but that it cannot transfer any signal other than the basics used to determine a static outcome. Is this because no information can be "added on" to the basic mathematics that determines what is only allowed to happen in normal nature? Could it be possible to artificially "add on" signalling by building unique entangled structures that have a greater bandwidth?

So, @hoola, what would be the utility here? What information is it that we need to desribe systems with by building structures with greater bandwitdth?

On 9/9/2022 at 3:07 PM, MigL said:

There is no information transfer faster than the speed of light.
Of any kind.
Period.

i want to quibble with you on this point on behalf of Reg Cahill, having re-done the interferometer experiments as well as results on anisotropy of light through fiber optic cable. If we don't have constant speed of light I would undercut SR by extension and question whether we're discussing faster or slower or variable speed but other than that I am unarmed for this fight.

If the c.o.b. I made is valid Wolfram Alpha does not agree with answer. Please demonstrate in maths or words you are boss over Wolfram Alpha, I believe it. Still potential problem with y/x term's appearance but I do not conclude you are wrong. I want to boss Wolfram Alpha around, but I need @Sensei or grasshopper to write computer code for it.

Thanks

On 9/12/2022 at 9:27 PM, bangstrom said:

There is a precise orientation where one electron, and likely under the influence of other electrons nearby, can share a common Schroedinger wave function with another electrons such that strong interactions can occur with the result that remote electrons can function as if side by side no matter what the distance between them. That is entanglement.

Because the interaction is instant and non-local, there is no time between the signal and its reception to alter the orientation of a detected result so that it is anything other than anti-correlated.

Because the entangled electrons are found at different locations on the light cone, we observe a light related time delay. Our observations have a “space like” time delay because the observed events are simultaneous but separated by space rather than happening at different times, in which case the delay would be “time like.”

Is that entanglement, or is it non-locality? I read the thread to come to that non-locality implies faster than light information exchange. My question is, if one of two entangled electrons undergoes an interaction/evolution to flip , is this change conducted to the other electron to induce a change in ,or , supraluminally? Or is the "strict" entanglement broken, and now needing consideration as part of the density matrix alluded to since it is not a closed or unperturbed system and has "evolved"?

On 9/14/2022 at 4:38 AM, joigus said:

Then you certainly don't understand the question. 12√(|↑↓〉−|↓↑〉) independently of the space-time factor of the state. In fact, the space-time factor of the state is completely omitted. Don't you find that peculiar?

No telling if it's the suggestion at play, but yes I found it peculiar; isn't that pointing at the entanglement having a non-local character? I need to re-read, I can figure, I did not understand the whole discussion.

On 9/14/2022 at 2:46 PM, bangstrom said:

This appears to be an overly broad a generalization that may apply to entangled particles or entangled particles in quantum computers but normally particles have a largely predictable nature otherwise there would be nothing but chaos. All electrons may look alike but Nature at least "knows" where they are.

Having recently viewed Sean (MWI) Carroll's, The Big Picture: From the Big Bang to the Meaning of Life, I know that Nature is "knowing" macroscopic objects easily, coherently, but I do not know if Nature is "knowing" quantum objects implicitly, rather, perhaps we have to make the measurements of quantum Nature to determine these uknown knowns. I do not think I understood indeterminancy, as I conceive of the observables as having a value capable of being described but that it is in superposition until actually observed; that the state(CSCO n,l,m_s,m_l?) was in existence  before observation but was indeterminate only insofar as it was unknown.

On 9/15/2022 at 3:49 PM, joigus said:

If φ(x,t) is a scalar (number-valued) field on the real line, φ˙ is its time derivative, dφdx its spatial derivative, and f is an arbitrary numeric function, which one of these models is non-local, which one has propagation at finite speed, which one has no propagation at all, and for which one it depends on some non-specified conditions?

 

φ˙=f(ddx)φ

 

φ˙=f(x,t)

 

φ˙=f(φ)

 

φ˙=dφdx+f(x,t)

I can't get the math in here properly, in fact my formatting is now screwed up, too, which I'm sure is symbolic or an omen of some sort, but I want to attach -> the 1-4 propositions to the 1-4 equations, if I can think of a supporting reason.

4.->1.,2.,3.,4. since you have an arbitrary function they all have non-specified conditions

1.->1. equating time derivative to a function acting on spatial derivative ->  non-local on the rt. side since you've d/dx spatial dimension to be acted upon by f before equality

Are 2.&3. the same equation? Equating time derivative to  and ? Equating time derivative to function acting on psi, wouldn't the function be d/dt?
2.,3.->2 finite speed of propagation, time derivative of x,t = speed

4. equating time derivative to spatial derivative plus function acting on psi. function needs to effectuate to  -  on (x,t). here I'll say no propagtion as I think it's just a time point you're getting with dpsi/dx? 

Let me know what you have to say, I presume there is some trick or illogicality you've made to make a point after trying the workup. Then afterwards you must come help with my math homework, you crank.

LaTeX from last post:

if 

 or  or 

 or   or 

 or 

 

for , the signs coming from exponentiation flip accordingly given that we're using a positive prime:

+i, -1, -i, +1

+, -, -, +

or 

so +, +, -, -, when using the established imaginary unit

so
 to  -, -, +, +, to equate a positive prime number as imaginary

 

 

if  or  or  or

exponentiation cycle, signing similar to

so +, +, -, - :

  

Please critique or make input. Question whether one quaternion could be of form:

 with , , and  and if this is useful. No speculation on octonions as I don't understand quaternions.

 

***PLEASE IGNORE BELOW I NEED TO FIGURE OUT PROPER SITE LATEX***

7 hours ago, Mitcher said:

Yes, vector combination is quite basic. So, having sent a sphere into 3 separate rotations would have the same effect as a simple rotation along a single axis ? This is completely counter-intuitive. How a single axis would be selected in relation to the other 3 ones then ?

4 hours ago, studiot said:

The point being that any number of rotations can be compounded to become a single rotation resultant, just as any number of forces can be compounded to form a single resultant or net force.

Quote

"It must be stressed that the Rodrigues approach to rotations, by emphasizing their multiplication rules and by regarding the entirely as operators, fully reveals the group properties of the set of all proper rotations, the full orthogonal group SO(3), as it is now called. Rodrigues's analysis is astonishingly penetrating. He recognizes that rotations do not commute and then he goes on to define infinitesimal rotations, which commute and from which, he shows, all other rotations can be generated. He thus anticipates the idea of the infinitesimal group generators later fully developed by Sophus Lie. The whole theory of the rotation group is in fact contained in some form in the Rodrigues paper, as noticed by Gray (1980). [...]
Before we leave this subject, and Rodrigues ([ed:paper from]1840), it should be said that this paper goes further than a mere treatment of the rotation group. For Rodrigues is mainly concerned with the Euclidean group, that is the group of all translations and rotations. He shows that translations commute amongst themselves but not with rotations and has the remarkably ingenious idea of realizing translations as infinitesimal rotations around infinitely distant rotation axes."

Altmann, Simon L., Rotations, Quaternions, and Double Groups, Dover Publications, Inc. 1986.

This is speaking about proper vectors, also known as quaternions, whose combinations as I understand are what translate into rotations as in you don't really select an axis, and they are not so basic to work with and so simple complex number "vectors" were used later instead.

e ^lnsin(x)lnsin(x)=cosx  divide both sides by lnx to recover y

e^lnsin(x)y=cos(x)/ln(x)

(since e^lnsin(x)=sin(x))

(sin(x)/ln(x))y=cos(x)/ln(x), times both sides by ln(x)/sin(x) and

y=cot(x) which is wrong.

back to prior try, I think chain rule gets towards it but I don't quite have it and I'll spare any spoilers.

5 hours ago, Peterkin said:

What, please means "intricating"?

from a search, the present participle of intricate.
I do not think it is confusing or intricating, but a semi-professional sophistry exercise, pinned to the board here for entymology study.

On 8/30/2022 at 3:18 AM, joigus said:

I hope I didn't make any silly mistake.

Same goes for me here:

change of base, 

appreciated your initial manipulation once I saw it.

squaredbases-scalingexponents-QuatExtension-idk.pdf

I'll try to summarize what comes out to me with LaTeX pasted into here. I think the multiplication of the basis elements is going to change from being unital because I'm going to change the definition of the imaginary unit, so and squares come out here and in the periodic/cyclic exponentiations:

if 

   or  or

 so   or ;

 or 

so, +, +, -, -
HOWEVER,, so trying to flip the signs accordingly given that we're using a positive prime: 

so +, +, -, -, when using the established imaginary unit
  -, -, +, +, since the attempt is now to equate a positive prime number as imaginary

but, this is problematic, as it looks like my algebra is falling apart. I'm not too surprised given that I'm trying to equate , which is unconventional; but, there is the aspect that  could be showing here. I don't know about how exponentiation of i can hold; this may well break the idea's viability. What do you think about how this would affect geometry? To me, this is now scaling what was formerly a unit circle, and it is now perhaps an exponentiated shape? A scaled hyperbolic complex graph? Please try to think about it and write back your thoughts or ideas.

  ? What I am equating here is the equivalency of roots I'd mentioned. ++, -- = +-, -+

  ? I think this may be related to +i, -i convention, but, again, this is problematic. See attachment for how I try to use this idea

 

These are examples for a positive and a negative prime. Please write back and let me know what you think. I think there are problems. I have gone too far -- I will claim +1s and -1s are primes, I will say  then put in garbage like  and pull a switch-er-oo to have  follow it. This must offend you so deeply that you will be compelled to respond, having fashioned a dunce cap and able to explain the Lies in my algebra. Or you must lament my wanton signifying.

15 hours ago, AbstractDreamer said:

Is there anything (theoretical or otherwise) that has undefined motion relative to another observer?

If 0 is instead a limit, and our numbers on a line are code for oscillators or vibrational states, is that a Brownian-type motion there? Or are they just a distance from 0? If the former, I'd say their motion is self-contained but I don't know about undefined.

6 hours ago, joigus said:

You're living dangerously here. Time propagates with respect to "something else". And what might that be? And how does it relate to everything else that's known?

Feynman bitterly complained about ideas like this: Maybe time is not continuous. Maybe there are other dimensions. Maybe spacetime is a fractal...

Yes. But how does it relate to everything else we know? What the auxiliary hypothesis that gets you out of this arbitrariness/circularity?

[...]

Could the something else be spatial expanse? Not sure that's a useful or practical theory. If you don't mind, what was Feynman's complaint about--those ideas, or are you listing his complaints?

38 minutes ago, Sensei said:

Speed is distance in meters divided by time in seconds. So it does apply to time curve f(t')=t.. If time at some point, goes faster or slower, then you need another clock, which will tell how much they differ, when they try to synchronize their clocks once again after re-meeting.

So then .

On 8/24/2022 at 4:31 AM, AbstractDreamer said:

is the speed of time constant?

Is not its constancy or periodicity, unless perturbed, its defining characteristic?

@Sensei

14 hours ago, AbstractDreamer said:

(Lets define 1 hour as something which exists unchanging in all time moments, like some probability of emission decay of some particle.)

I have some maths for that?.. Probably not.

14 hours ago, AbstractDreamer said:

I have an idea that time propagates.

Can you explain what that would look like? What is it propagating relative to? An observer outside time?

5 hours ago, studiot said:

 

Do you understand what this is all about and can you relate it to the thread topic of prime numbers and Fields ?

 

As I understand it, if each bit of a complex number had a different root prime, operations would be under certain rules. So, as an example, if 
 and 
, then

.

I am unsure if within a quaternion the root primes should be the same, but I think there's an irreducibility about it that could explain the way translations (i.e. changes in direction) are described. The identity element 1 may be necessary, so NO, I do not understand what this is all about.

6 minutes ago, joigus said:

As to octonions... mmm. I don't know. They are non-associative, which is, right off the bat, quite strange to represent physics. But who knows.

To pick a bone, fwiw,
"[Octonions] are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative."
Octonion handwiki.org

"In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have

for all x and y in the algebra.

Every associative algebra is obviously alternative, but so too are some strictly non-associative algebras such as the octonions."
Alternative algebra handwiki.org
"An algebra (or more generally a magma) is said to be power-associative if the subalgebra generated by any element is associative. Concretely, this means that if an element  is performed an operation * by itself several times, it doesn't matter in which order the operations are carried out, so for instance
"

On 7/31/2022 at 3:12 AM, joigus said:

How?

OTOH, I'm sure you know ad hoc explanation, or "just so" stories, are not good enough in science. They're lacking in the falsifiability aspect.

The only aspect I had a grasp of for that was quantum number interdependences, but no, I'm not sure that's applicable or how quaternions and octonions are used in describing physical systems. From rereading the Quanta Magazine piece about Furey ("The Strange Math..."),

Quote

“I realized that the eight degrees of freedom of the octonions could correspond to one generation of particles: one neutrino, one electron, three up quarks and three down quarks,”

I was thinking of the quaternions to describe the four quantum numbers (i.e. an electron at my QM level), but that would imply that the math operations (are they just changing directions?) correspond to the physical relations and I think that is incorrect. However, being that quaternions are used in computer graphic modeling of 3-D rotations an ad hoc description system could have each atom or quantum object as a sphere that is then acted upon by other bodies in the system, say for modeling collisions or bond formation. I need to read it, but there is the precedent of bi-quaternions being formulated into physics as previously mentioned and again from the QM article there is the octonion numbers being used for physical systems. Last and not least, if instead of being underpinned by the real numbers, the real foundation is the square roots of primes, the 4 normed division algebras and possibly the continued dyadics sedenions[16] trigintaduonions[32]... are the real foundation and are more easily operable than real numbers, if I understood anything about p-adics. I doubt there even needs to be a real number appended to the front of the quaternion or octonion group, which could remove some of the difficulty of real numbers compared to p-adics. It looks as though the real number is the resultant of an i'² or additives thereof that have removed the root operation, whereas the i,j,k or e₁-e₇ have a different prime under operation that creates an incompatibility under multiplication or division and hence the noncommutativity and/or nonassociativity, but, this is just more speculation; I don't know if there is anything here falsifiable or testable for you.

  More complex physical system descriptors I think you'd know better about, although I mentioned compression... but allow me to move to a presentation on some information on the, "...quirks of the quaternions being noncommutative and octonions even nonassociative, they continue to find uses in fields such as algebra, geometry, topology and number theory"

Quaternions and Octonions by James McCusker, supervised by Dr. Thomas Leistner University of Adelaide . When I'm off vacation..

Thanks

On 7/29/2022 at 10:26 PM, studiot said:

In response to the last superlarge dish of word salad I offer a simple analysis, I offered on a maths site to someone who thinks they have discovered a 'pattern' in the occurrence of primes.

Since there are a very large number of primes (the ancient Greeks proved this large number to be transfinite) it is not only not suprising to be able to find not only a pattern but any finite pattern inclusded in that infinity.

 

Yes well I've not figured how to route the obstructionism about number theory's definition and modern developments you're providing succinctly.

How about finite fields have a prime for the modulus? The p-adics systems as equally workable as the reals? How about the derived equation I posited is a function acting on a set of integers? 

Since ancient times we've gone on to complex analysis, unless you're some math luddite or reductionist in your rigor.

On 7/29/2022 at 9:55 PM, joigus said:

What do you mean versors? And what properties of those entities describe interference, polarization, helicity, tunneling, spin-statistics connection, or ground-state energy? All of them known and measured properties of quantum objects.

If you actually described any one of those properties from number theory, I'd take your ideas very seriously.

Versors as I understand are quaternions describing vectors. Using a prime number system that is restricted under operation I think can describe physical properties, ad hoc, but would that interfere with what are supposed to be translations in the vector field? A prime number based system should be able to assign values to variables as well as the real numbers, and I think quantization, irreducibility, or rules for interactions could be indicated by a prime root.

On 7/20/2022 at 2:56 PM, swansont said:

Please don’t play games. If you have relevant information, post it.

Here is the complex graph of y=+(1/x):

Graphing Q1 (+/+) and Q3 (-/-) Cartesian quadrants. Not graphed Q2(+/-) and Q4 (-/+): y=-(1/x). So this complex plane contains a spherical discontinuity at the origin. If we take all square roots of prime numbers to be variables for complex math I think the discontinuity becomes an ellipsoid and the hyperbolas upon rotation are providing conics. I think extensions of complex numbers start running into problems, and what can be done with quaternions, octonions, or sedenions as setting up iterations with more and more "imaginary" components points towards imaginary numbers having a natural extensibility. I think real variables are appended to the i value to create any multiples needed, but it is better math to have each i with a possible set of values. This may create limitations, or the real number multiplier may still be valid, but something would have to change with the exponentiation rules for equating or simplifying iⁿ. Perhaps the i,j,k, or , or  are like polynomials, and since if there were different primes assigned to different values there'd be constraint on how the complexity could be reduced, which could be used to assign quantum states to influence other aspects of states as versors: electron spin state influences magnetic spin state, and azimuthal number and principal number are related; so measuring one collapses some possibilities and the measurement has some inherent uncertainty which I think we need to use to account for the discrepancy in the virial theorem for multi-atom systems.

On 7/20/2022 at 3:58 PM, joigus said:

[...]

Honestly. I see no promising science here.

My summary: No. Monopoles are not dipoles for very much the same reason why monocles are not binoculars: two is not one.

Gravity and electromagnetism are not the same.

Radiation fields decrease with distance as (distance)^-1; monopolar fields decrease with distance as (distance)^-2; dipolar fields fall off as (distance)^-3. That's another reason why they can be told apart. Beside the ones explained by myself and others. Each one varies with distance as the spatial gradient of the previous-order one.

Plus EM doesn't satisfy the equivalence principle. Only repetition, and familiarity with it (the EP) makes you forget how incredibly surprising it is, how much different the world would be if EM and gravity were more like "different versions of the same thing," and how exceptional gravity is. The 1/r² coincidence is but a mirage.

Plus EM is scale-independent while gravity is scale-dependent.

Plus charge is a relativistic invariant, while mass is not.

Plus...

And still I can't see what any of this has to do with number theory, which AFAIK has no relevance to physics,* as the question whether, say, the speed of light, or the mass of a body, or any other physical quantity is a rational or irrational number (or prime, or has any other number-recursion connection) doesn't really make sense, for the very simple reason that any of those are measured numbers, and inevitably go with a range of experimental precision. So any claim that you would want to make in terms of number theory would immediately be whitewashed by the fact that all physical quantities are cut off by virtue of experimental uncertainties.

[...]

* Repeat: Number theory has no relevance to physics as both stand today. If it has, IMO, you should make a strong case why it does, if you think it does. There's nothing written in stone that says that number theory and physics will never be related in the future.

From number theory proposition, we will use versors to describe quantum objects. There's the primary quantum number, electron spin quantum number, induced magnetic quantum number, and azimuthal quantum number. I think primary and aziumuthal quantum number are tied together but I need to review. Electron spin state induces magnetic spin state, but magnetic spin state can have complexity that may be playing into uncertainty.

An aside on the, uh... dipole... we have a brick of metal. If in this brick of metal the electron spin states align pointing the same way, given a... gradient... to measure against, it is magnetized. The magnetic dipole: it is induced by current at the quantum level from electrons, and is consisted of a condensed brick of iron, and, nowadays, neodymium dysprosium or something else and boron-doped bricks. If it's in motion, there may be Magnetohydrodynamics involved and I don't get it yet.
 
With a complex number describing 1 real time dimension and three complex spatial dimensions we describe the transformations that are possible. Measurement of spin number tells of magnetic quantum number. Measurement of primary quantum number tells of azimuthal number. Compression/torsion as described in higher-dimensional algebraic geometry structures encodes potential energy discrepancy and I think needs to be written into as describing a physical field; I think physics here is of course dependent on number theory directly through complex numbers as objects for creating these spaces.

Another aside, I'd say the solutions to Riemann's zeta function and his hypothesis being correct follows from it being literally a geometric series exponentiating (limited) complex numbers in the denominators, and this creates a logarithmically spiraling sinusoid if graphed vertically, and this is tied to Fourier transformation and harmonic oscillators. I think if complex numbers were expanded to include all square roots of primes the trivial zeros at negative even integers and the pole at +1 would change in the zeta function, but I don't know that, and this is perhaps the primary number theory speculation here. The Riemann Zeta function is able to bound prime number distribution with a low error rate because it is creating an algebraic geometric construction to graph them as bounded by a logarithmically distending, vertical sinusoid wave: graphed vertically the +(1/2) real part, "non-trivial" zeros form a vertical pole of point hits just under the bound of the real pole at +1. This is the most accurate point for the "hits" to occur, hence the low error rate. When the sinusoidal wave is traveling in the harmonic oscillator models we are using the complex unit circle trigonometric relations, and so Fourier transformations translate vibrational data by extending the complex unit trigonometric functions but I think they're inaccurate because they need to based on hyperbolic geometry and a wider set of imaginary numbers, which are related by right-angle trigonometry.

A concept in number theory can be obtained from taking a specific number set under an operation, conceptualized as being derived from 5-D where, perhaps charge seperation effects are equivalent to motion, as in Kaluza-Klein theory which I just read about. However, I think time is simple and limited to one-dimension, and space is complex and needs the more representative part of complex numbers, like with quaternions there could be 3 complex spatial dimensions and one real time dimension. Then, literally reducing dimensionality of the field through the differentiation operation of  to 4-D where the simple time dimension is incorporated, to where making any measurements have an uncertainty to account for the virial deviation for even simple molecules: it should be set at +/- 40% given that the virial theorem cannot account for a simple molecule by a 20% discrepancy (2.0 vs. ~1.61). I conjecture that the complex hyperbolic graph is cutting cones, akin to light cones of radiant light events in spacetime, and that the ellipsoid discountinuity is equatable to an uncertainty in the time-measurement of the system: the displacement out along the x or y-axes (with the x-axis discontinuity narrower and y-axis discontinuity containing the focii of the ellipse once on an exponentiated hyperbolic plane) covers a length which is tied to the uncertainty in the measurement. Also this radiance outwards should be differentiated from emanations, which I envision akin to stored torsion or compression that'd have helical or differently spiraled propagation: and again I think cutting conics from the hyperbolas can be descriptive.

 Fourier transformations which seem inaccurate by being unable to account for uncertainty in vibrational spectra, but, that is just my opinion. I don't know yet how to do the actual math required to check if this works, or to improve the accuracy in spherical/elliptical/hyperbolic harmonic functions which should function as descriptors of molecular orbitals and perhaps also pair or groups of nucleons. But, the juiced up compression/torsion forces encoded by quaternions or further complexifications of specific algebras can perhaps better describe complex quantum systems by having exponentiations in the quantum numbers. Even the primary quantum number for simple absorbance spectra should be scaled, as normal integers do not describe the change in vibrational rate; groups of square roots of primes could be made to be degenerate energy states if necessary for principal quantum number and can better describe the other 3 quantum numbers and their implications upon measurement: a potential energy shift encoded by switching spin states, thereby magnetic spin states, or azimuthal position as encoded by measurement uncertainty with regards to time as to whether the quantum object was at an actual discrete position or undergoes a quantum tunneling wave probabilistic transition to another allowed state (e.g. +1/2 vs. -1/2 spin state, it's implications on magnetic spin state; or principal number 1-6+ excitation, and it's implication on azimuthal number occupancy) which could be like going back in time, or more like the measurement gives a result from a prior part of the interval, akin to antimatter generation speculations. To account for the -20% incorrect measure in virial (2.0 vs. 1.61) we increase the bound to +/-40% potential energy under a rubric utilizing complex hyperbolic or conic harmonic oscillators, and I think this has implications for the physics of accounting for charge/mass/energy.

This speaks to charge potential that is not accounted for properly in the current paradigm. Current accounting alludes to dark matter, dark energy, and also the existence of magnetic monopoles (as yet unseen) as a proof of the quantization of charge. Therefore I think there is insufficient reason to conclude that charge is quantized, but I do not understand that quantization, or what the implications are for total charge density. However, as an explanation, I will try to learn what @joigus is talking about by ^-1, ^-2, and ^-3 decrases in force vis visa gravity and electromagnetism, and to understand the equating of inertial masses with gravitational masses--the equivalence principle! I want to equate mass and charge, and claim that charge is not properly being measured, perhaps as a result of being unable to account for electric field lines actually having no closure and entering singularities like White or blackholes (Q1 and Q3 and Q2 and Q4 for complete quadratics?). So this is also about the issue of monopoles, and if they were supposedly plentiful earlier in the evolution of the universe, or where they've gone, too. I did not equate monopoles to dipoles, I've only just now tried to define a dipole and that probably needs correction.

On physics and math here broadly,

Quote

 

The four-dimensional algebra of hyperbolic quaternions incorporates some of the features of the older and larger algebra of biquaternions. They both contain subalgebras isomorphic to the split-complex number plane. Furthermore, just as the quaternion algebra H can be viewed as a union of complex planes, so the hyperbolic quaternion algebra is a union of split-complex number planes sharing the same real line.

It was Alexander Macfarlane who promoted this concept in the 1890s as his Algebra of Physics, first through the American Association for the Advancement of Science in 1891, then through his 1894 book of five Papers in Space Analysis, and in a series of lectures at Lehigh University in 1900.

 

speaks to some precedent in relevance between physics and number theory, which number theory I think includes complex math as mathematical objects for creating things like Lie algebras, or groups of algebraic expressions that are being used to describe physical fields.

If anyone can talk me out of my mathematical misadventure regarding imaginary numbers, I'd appreciate it. Can the rules of exponentiation that are used to simplify be re-written? As even exponents given multiples (+1 or -1) and odds give multiplies times roots (+1+i or -1-i)? Or does this create inoperability of quaternions or octonions as their division, multiplication, addition or subtraction is complexified? Doubt it makes sense. Do please speak to this vis viva number theory: can we take the set of square roots of primes as the object in complex numbers ()? Might this put legitimacy to complex math as based on the harder to define but equally consistent two products of quadratics +/- and -/+ as opposed to +/+ and -/- which we have short-hand for in normal polynomial roots? Wouldn't expanding the definition of complex numbers in this way effect Fourier transformations in particular, which touches the gradients of fields, expansion of harmonic functions, etc.?

I know there are problems with the Exponentiation: Failure of power and logarithm identities.
I want to re-iterate that the prime number distribution π(X) ∼ X log X ⇐⇒ ψ(X) ∼ X and the Zeta function creating 
 

as seen here  Prime numbers and the Riemann zeta function, Undergraduate Mathematics Seminar, University of Pittsburgh, November 12, 2019. 36 slide presentation, by Carl Wang-Erickson may be due to the availability of all prime numbers to be objects for complex math, and that this is 

Quote

Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers).
[...]
Starting early in the nineteenth century, the following developments gradually took place:

• The rise to self-consciousness of number theory (or higher arithmetic) as a field of study.[69]
• The development of much of modern mathematics necessary for basic modern number theory: complex analysis, group theory, Galois theory—accompanied by greater rigor in analysis and abstraction in algebra.
• The rough subdivision of number theory into its modern subfields—in particular, analytic and algebraic number theory.

is about number theory, and if it is to change imaginary numbers that has direct implications for physics regarding harmonic oscillators, Fourier transformations, and other aspects of what I'd formerly described as quantum chemistry. I think this works towards two other Millennium prizes, but, I can't actually do the math.

"Plus charge is a relativistic invariant, while mass is not." Ought verify understanding of that, EP, ^-1,^-2,^-3, more basic math, EM and mono-/di-pole magnets, actual details of quantum numbers, other speculations. 

Thanks

On 7/17/2022 at 2:46 PM, studiot said:

You know, this is a really interesting game of

Who can make the most irrelevent post to the topic ?

Last night I was struck by an interesting observation in number theory.

What is the next number after 25 ?

Suprisingly the answer I came up with was 24 !

Any ideas how that can be ?

You were counting down???

On 6/30/2022 at 3:59 PM, swansont said:

How else do you get it to look like gravity, which has monopoles?

Are you familiar with Miles Mathis' work?
 

Quote

That oldest mistake is one that Euclid made. It concerns the definition of the point. Entire library shelves have been filled commenting on Euclid's definitions, but neither he nor anyone since has appeared to notice the gaping hole in that definition. Euclid declined to inform us whether his point was a real point or a diagrammed point. Most will say that it is a geometric point, and that a geometric point is either both real and diagrammed or it is neither. But all the arguments in that line have been philosophical misdirection. The problem that has to be solved mathematically concerns the dimensions created by the definition. That is, Euclid's hole is not a philosophical or metaphysical one, it is a mechanical and mathematical one. Geometry is mathematics, and mathematics concerns numbers. So the operational question is, can you assign a number to a point, and if you do, what mathematical outcome must there be to that assignment? I have exhaustively shown that you cannot assign a counting number to a real point. A real point is dimensionless; it therefore has no extension in any direction. You can apply an ordinal number to it, but you cannot assign a cardinal number to it. Since mathematics and physics concern cardinal or counting numbers, the point cannot enter their equations.

This is of fundamental contemporary importance, since it means that the point cannot enter calculus equations. It also cannot exit calculus equations. Meaning that you cannot find points as the solutions to any differential or integral problems. There is simply no such thing as a solution at an instant or a point, including a solution that claims to be a velocity, a time, a distance, or an acceleration. Whenever mathematics is applied to physics, the point is not a possible solution or a possible question or axiom. It is not part of the math.

Now, it is true that diagrammed points may be used in mathematics and physics. You can easily assign a number to a diagrammed point. Descartes gave us a very useful graph to use when diagramming them. But these diagrammed points are not physical points and cannot stand for physical points. A physical point has no dimensions, by definition. A diagrammed point must have at least one dimension. In a Cartesian graph, a diagrammed point has two dimensions: it has an x-dimension and a y-dimension. What people have not remembered is that if you enter a series of equations with a certain number of dimensions, you must exit that series of equations with the same number of dimensions. If you assign a variable to a parameter, then that variable must have at least one dimension. It must have at least one dimension because you intend to assign a number to it. That is what a variable is—a potential number. This means that all your variables and all your solutions must have at least one dimension at all times. If they didn't, you couldn't assign numbers to them.

This critical finding of mine has thousands of implications in physics, but I will mention only a couple. It has huge implications in Quantum Electro-Dynamics, since the entire problem of renormalization is caused by this hole in Euclid's definition. Because neither Descartes nor Newton nor Schrodinger nor Feynman saw this hole for what it was, QED has inherited the entire false foundation of the calculus. Many of the problems of QED, including all the problems of renormalization, come about from infinities and zeroes appearing in equations in strange ways. All these problems are caused by mis-defining variables. The variables in QED start acting strangely when they have one or more dimensions, but the scientists mistakenly assign them zero dimensions. In short, the scientists and mathematicians have insisted on inserting physical points into their equations, and these equations are rebelling. Mathematical equations of all kinds cannot absorb physical points. They can express intervals only. The calculus is at root a differential calculus, and zero is not a differential. The reason for all of this is not mystical or esoteric; it is simply the one I have stated above—you cannot assign a number to a point. It is logical and definitional.

This finding is not only useful in physics, it is useful to calculus itself, since it has allowed me to show that modern derivatives are often wrong. I have shown that the derivatives of ln(x) and 1/x are wrong, for instance. I have also shown that many problems are solved incorrectly with calculus, including very simple problems of acceleration.

This finding also intersects my first discoveries in special relativity, which I will discuss in greater detail below. The first mistake I uncovered in special relativity concerned Einstein's and Lorentz' early refusals to define their variables. They did not and would not say whether the time variable was an instant or a period. Was it t or Δt? Solving this simple problem was the key to unlocking the central algebraic errors in the math. Once it was clear that the time variable must be an interval or period, at least two of Einstein's first equations fell and could not be made to stand up again.

Next is my Unified Field Theory, just added to this list. I haven't put it above the correction to the point, since the correction to the point determined a part of my UFT. At the heart of my UFT is the discovery that Newton's gravitational equation is a compound equation, one that already includes the foundational E/M field or charge field. This pulling apart of Newton's equation by showing that G is a scaling constant between gravity and charge has become the new centerpiece of my website in the past few years, supplanting the number one spot held by my relativity papers. Since a NASA astrophysicist read my theory on this, recommended it, and wrote the introduction to my new book, this theory has generated a lot of interest worldwide. In it I also show that the current "messenger photon" cannot be virtual and that the field must be both real and mechanical. This means that Einstein's field equations are also compound equations. Einstein already had a UFT and didn't know it. But my theory goes far beyond this, since I don't just pull the lid off Newton and Einstein and then stand back. I segregate and simplify their equations, showing many many new things, including a correction to the perihelion of Mercury, a mechanical solution to the Metonic Cycle, and a new theory of tides. I also show that the universal gravitational constant G is a transform between the two constituent fields of Newton's equation. This allowed me to solve the dark matter problem, including the galactic rotation problem and the bullet cluster problem, by showing that the charge field outweighs normal matter by 19 to 1. Dark matter is not non-baryonic, it is photonic.

As the second part of this Unified Field Theory, I have also deconstructed Coulomb's equation. I show that Coulomb's constant k is tied to the Bohr diameter, and that when applied to quanta we can drop this constant from the equation. Like G, k is a scaling constant, and at the quantum level we have no need to scale. Among other things, this changes the force between electron and proton by a factor of 10-19. The charge part of this unified field has also allowed me to easily solve Bode's Law, resolving all the error, and to show the physical cause of axial tilt. Neither Bode's Law nor axial tilt are coincidences, as we have been told.

More recently I have found a third unified field equation: the Lagrangian. This was my most important discovery of 2010, and it must now rank very high in this list. I have shown that the kinetic energy variable in the Lagrangian is misassigned. Once the variable is properly understood in a fully mechanical two-part field, the Lagrangian becomes mathematically equivalent to my new Unified Field Equation, and I show in that paper how to go from one to the other in a couple of simple steps.

Most recently I discovered a fourth set of unified field equations, that being the equations of Maxwell. Specifically, I discovered that Maxwell's displacement field was hiding the charge field. This allowed me to tie many more things into my unified field, including Gauss' Law.

I haven't updated this paper in a long time, but my nuclear diagrams must certainly place high on this list. I am the first person in history to successfully diagram the nucleus, showing it is not just a bag of marbles. Rather, it is a complex channeler of charge. This has allowed me to also throw out electron bonding theory as unnecessary, as well as the strong force. I have now diagrammed most important elements and many important molecules, showing how their qualities are explained by these channels of charge.

http://milesmathis.com/central.html

Sure, lots of irrelevent material...

"Next is my Unified Field Theory, just added to this list. I haven't put it above the correction to the point, since the correction to the point determined a part of my UFT. At the heart of my UFT is the discovery that Newton's gravitational equation is a compound equation, one that already includes the foundational E/M field or charge field. This pulling apart of Newton's equation by showing that G is a scaling constant between gravity and charge has become the new centerpiece of my website in the past few years, supplanting the number one spot held by my relativity papers. Since a NASA astrophysicist read my theory on this, recommended it, and wrote the introduction to my new book, this theory has generated a lot of interest worldwide. In it I also show that the current "messenger photon" cannot be virtual and that the field must be both real and mechanical. This means that Einstein's field equations are also compound equations. Einstein already had a UFT and didn't know it. But my theory goes far beyond this, since I don't just pull the lid off Newton and Einstein and then stand back. I segregate and simplify their equations, showing many many new things, including a correction to the perihelion of Mercury, a mechanical solution to the Metonic Cycle, and a new theory of tides. I also show that the universal gravitational constant G is a transform between the two constituent fields of Newton's equation. This allowed me to solve the dark matter problem, including the galactic rotation problem and the bullet cluster problem, by showing that the charge field outweighs normal matter by 19 to 1. Dark matter is not non-baryonic, it is photonic.

As the second part of this Unified Field Theory, I have also deconstructed Coulomb's equation. I show that Coulomb's constant k is tied to the Bohr diameter, and that when applied to quanta we can drop this constant from the equation. Like G, k is a scaling constant, and at the quantum level we have no need to scale. Among other things, this changes the force between electron and proton by a factor of 10-19. The charge part of this unified field has also allowed me to easily solve Bode's Law, resolving all the error, and to show the physical cause of axial tilt. Neither Bode's Law nor axial tilt are coincidences, as we have been told.

More recently I have found a third unified field equation: the Lagrangian. This was my most important discovery of 2010, and it must now rank very high in this list. I have shown that the kinetic energy variable in the Lagrangian is misassigned. Once the variable is properly understood in a fully mechanical two-part field, the Lagrangian becomes mathematically equivalent to my new Unified Field Equation, and I show in that paper how to go from one to the other in a couple of simple steps.

Most recently I discovered a fourth set of unified field equations, that being the equations of Maxwell. Specifically, I discovered that Maxwell's displacement field was hiding the charge field. This allowed me to tie many more things into my unified field, including Gauss' Law." ...

This is also regarding your mention of, "it reduces to Newtonian gravity", which I asked for clarification about because I don't understand. I have not heard any new reports from MoEDAL experiment which I think is also up and running.

On 5/21/2017 at 8:17 AM, Randolpin said:

This topic talks about the relationship of philosophy, science and reality.

I will expound it thru questions:

1. Is philosophy more advance than science in understanding reality because it can form ideas even when there is no experiments performed or observations (While science on the other hand can't step forward because it relies on data)?

2. Is philosophy always correct? Are there instance that science prove philosophy?If philosophy always correct, we can rely solely to philosophy than science.

3. Is philosophy as accurate as science?

4. When can we say that a question become philosophical? Can we say that philosophy is an advance science? If yes then we can conclude that the only task of science is to prove philosophy ( is it correct?).

 

I hope you understand my points. If you need clarifications, just ask me. Thank you...

--

 

In answer to your first question it is my opinion that that philosophy is far superior to science.Mainstream science  just thinks it knows best…it doesn’t.

Mainstream science is wrong and failing because it adopts a half philosophy that it has no way of definitively proving.

Half philosophy science suits secular scientists though because it pampers to their hopeful belief systems.All they have is hope you see like everyone else.

If you let unaware secular scientists loose with science it will all go belly up and it has.

Secular scientist don’t even understand consciousness and yet a child could understand it.

What mainstream scientist don’t get is you have to adopt “player” science to understand consciousness.You can’t understand it with “spectator” science.

Its the “easy problem” in “player” science and not the “hard problem”.

Edited July 8 by Jasper10

Speaking to the OP,
1. Here is a false dichotomy, in either science or philosophy I think you're describing forming a hypothesis. Of course observations will follow once you've identified what to observe, just as a philosophical proposition is brought about for the sake of debate.
2. Excessive philosophizing can be characterized as useless, as when there is no test for the hypothesis the philosophical exposition is simply impractical.
3. I think they both get towards accuracy through refinement.
4. I don't know, but I doubt it.

On 7/14/2017 at 4:28 PM, tar said:

Mordred,

 

In the one link though it showed an electron responding to zero point energy like a ball on the end of a spring, with a sine wave type recoil pattern shown.

 

An electron can't become a little more or a little less matter. It has to have a little more or a little less energy to follow the sine wave pattern shown. That would indicate a potential in an energy field, carried by a photon like entity. And my question is, if energy is exchanged in quanta, by a single photon of a certain energy, wavelength and amplitude, does this mean, to get the sine wave pattern shown in the spring recoil model, does an electron need to receive a photon on every up and release a photon on every down?

 

Regards, TAR

On 7/15/2017 at 9:28 AM, Mordred said:

Your looking at the harmonic oscillator via the spring inaccurately. I would like to properly show how the spring via Hookes law relates to the QM oscillator but will need to do so tonight. When I have time to properly answer the above.

 

Its too important to cheapen the answer.

 

However for now think of it this way. In the spring there is an equilibrium point in its range of motion. The equilibrium point being determined by the potential and kinetic energy.

 

So when I have time later I will apply this to Hookes law then step it into QM

Oh, great. How did this get to here? I'll have to read this thread...

Yeah, a particle in a box is like the quantum harmonic oscillator. It's a 1-D string. 

The classical Ideal Hooke spring or Hooke atom is a 2-D harmonic oscillator, related by the spring constant. A spring like that could store potential energy.
In a 3-D electron with spin we have torsion, maybe compression. I for one doubt it needs a photon, and would bet on resonance as a bigger player in a system of harmonic oscillators. Debye's method that is accurate for specific heat of solids models harmonic oscillators in a box as a lattice network. I think a more accurate model than the EM-photon field would be the connected system of oscillators vs. the isolated electron needing a discrete photon, which is similar to Debye's method vs. Einstein's crystal solid conception of specific heat. So the electron could change energy or change rate of vibration through absorbing or emitting a quanta of vibration? I think similar to how the Hooke spring is characterized by the spring constant a 3-D harmonic oscillator network is under the energy storage / mechanical compression force interchangability known as piezoelectricity in electromechanical terms.

On 7/8/2022 at 3:46 PM, mistermack said:

Even if a philosopher managed to "think" himself to Mars, he would still die within seconds. 

I think if I had to go, I'd rather let the scientists organise it. 

Horses for courses

DAMMIT, COHAGEN, ZE AIR! I'M A CESIUM REACTOR, AYEOWHYEAH!

On the issue of distant electric potential energy:

Universite' de Geneve`: De'partement de Physique Nucle'aire et Corpusculaire website: unige.ch
LHAASO Discovers a Dozen PeVatrons and Photons Exceeding 1 PeV and Launches Ultra-High-Energy Gamma Astronomy Era

Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray Galactic sources

12 PeVatron energy level stars emitting from the region of Cygnus

web.archive link to English translation of Chinese Academy of Sciences article (May 24th, 2021):
LHAASO Discovers a Dozen PeVatrons and Photons Exceeding 1 PeV and Launches Ultra-high-energy Gamma Astronomy Era by Liu, Jia. May 17th, 2021

Quote

Although the accumulated data from the first 11 months of operation only allowed people to observe those sources, all of them emit so-called UHE photons, i.e., gamma rays above 0.1 PeV. The results show that the Milky Way is full of PeVatrons, while the largest accelerator on Earth (LHC at CERN) can only accelerate particles to 0.01 PeV. Scientists have already determined that cosmic ray accelerators in the Milky Way have an energy limit. Until now, the predicted limit was around 0.1 PeV, thus leading to a natural cut-off of the gamma-ray spectrum above that.

Zhen C., et al.

Cao, Z., Aharonian, F.A., An, Q. et al. Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray Galactic sources. Nature 594, 33–36 (2021). https://doi.org/10.1038/s41586-021-03498-z

Nature abstract/info.:

Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray Galactic sources

Highest ever energy light captured by Chinese mountain observatory Science.org article by Ling Xin

Quote

Discovered more than 100 years ago, cosmic rays are charged particles, including protons and other atomic nuclei, that have been accelerated nearly to the speed of light. Their sources are poorly understood because interstellar magnetic fields bend them on their path to Earth. However, as cosmic rays rocket away from their sources, they also emit photons, usually about one-tenth as energetic as the cosmic rays themselves, that follow a straight path to Earth. Although Earth's atmosphere blocks this gamma ray light, when the photons slam into air molecules, they create showers of secondary particles and faint blue Cherenkov light that astronomers can look for.

Geneva University - Extended Materials - LHAASO and its core scientific goals

Quote

LHAASO's core scientific goal is to explore the origin of high-energy cosmic rays and study related physics such as the evolution of the universe, the motion and interaction of high-energy astronomical celestials, and the nature of dark matter. LHAASO will extensively survey the universe (especially the Milky Way) for gamma ray sources. It will precisely measure their energy spectra over a broad range—from less than 1 TeV (trillion electron-volts or tera-electron-volts) to more than 1 PeV. It will also measure the components of diffused cosmic rays and their spectra at even higher energies, thus revealing the laws of the generation, acceleration and propagation of cosmic rays, as part of the exploration of new physics frontiers.

Quote

PEVATRONS AND PEV PHOTONS
The signal of UHE photons around PeVatrons is so weak that just one or two photons at PeV energy can be detected using 1 km2 of detectors per year even when focusing on the Crab Nebula, known as the “standard candle for gamma astronomy.” What's worse, those one or two photons are submerged in tens of thousands of ordinary cosmic rays. The 1,188 muon detectors in LHAASO's KM2A are designed to select photon-like signals, making LHAASO the most sensitive UHE gamma ray detector in the world. With its unprecedented sensitivity, in just 11 months, the half-sized KM2A detected one photon around 1 PeV from the Crab Nebula. In addition, KM2A found 12 similar sources in the Milky Way, all of which emit UHE photons and extend their spectra continuously into the vicinity of 1 PeV. Even more important, KM2A has detected a photon with energy of 1.4 PeV—the highest ever recorded. It is clear that LHAASO's scientific discoveries represent a milestone in identifying the origin of cosmic rays. To be specific, LHAASO's scientific breakthroughs fall into the following three areas:

1) Revealing the ubiquity of cosmic accelerators capable of accelerating particles to energies exceeding 1 PeV in the Milky Way. All the gamma ray sources that LHAASO has effectively observed radiate photons in the UHE range above 0.1 PeV, indicating that the energy of the parent particles radiating these gamma rays must exceed 1 PeV. As a matter of convention, these sources must have significances of photon signals five standard deviations greater than the surrounding background. The observed energy spectrum of these gamma rays has not truncated above 0.1 peV, demonstrating that there is no acceleration limit below PeV in the galactic accelerators.

This observation violates the prevailing theoretical model. According to current theory, cosmic rays with energies in the PeV range can produce gamma rays of 0.1 PeV by interacting with surrounding gases in the accelerating region. Detecting gamma rays with energies greater than 0.1 PeV is an important way to find and verify PeV cosmic ray sources. Since previous international mainstream detectors work below this energy level, the existence of PeV cosmic ray accelerators had not been solidly confirmed before. But now LHAASO has revealed a large number of PeV cosmic acceleration sources in the Milky Way, all of which are candidates for being UHE cosmic ray generators. This is a crucial step toward determining the origin of cosmic rays.

2) Beginning an era of “UHE gamma astronomy.” In 1989, an experimental group at the Whipple Observatory in Arizona successfully discovered the first object emitting gamma radiation above 0.1 TeV, marking the onset of the era of “very-high-energy” gamma astronomy. Over the next 30 years, more than 200 “very-high-energy” gamma ray sources were discovered. However, the first object emitting UHE gamma radiation was not detected until 2019. Surprisingly, by using a partly complete array for less than a year, LHAASO has already boosted the number of UHE gamma ray sources to 12.

With the completion of LHAASO and the continuous accumulation of data, we can anticipate to find an unexplored “UHE universe” full of surprising phenomena. It is well known that background radiation from the Big Bang is so pervasive it can absorb gamma rays with energies greater than 1 PeV. Even if gamma rays were produced beyond the Milky Way, we wouldn't be able to detect them. This makes LHAASO's observational window so special.

3) Photons with energies greater than 1 PeV were first detected from the Cygnus region and the Crab Nebula. The detection of PeV photons is a milestone in gamma astronomy. It fulfills the dream of the gamma astronomy community and has long been a strong driving force in the development of research instruments in the field. In fact, one of the main reasons for the explosion of gamma astronomy in the 1980s was the challenge of the PeV photon limit. The star-forming region in the direction of Cygnus is the brightest area in the northern territory of the Milky Way, with a large number of massive star clusters. Massive stars live only on the order of one million years, so the clusters contain enormous stars in the process of birth and death, with a complex strong shock environment. They are ideal “particle astrophysics laboratories,” i.e., places for accelerating cosmic rays.

The first PeV photons found by LHAASO were from the star-forming region of the constellation Cygnus, making this area the best candidate for exploring the origin of UHE cosmic rays. Therefore, much attention has turned to LHAASO and multi-wavelength observation of this region, which could offer a potential breakthrough in solving the “mystery of the century.”

Extensive observational studies of the Crab Nebula over the years have made the celestial body almost the only standard gamma ray source with a clear emission mechanism. Indeed, precise spectrum measurements across 22 orders of magnitude clearly reveal the signature of an electron accelerator. However, the UHE spectra measured by LHAASO, especially photons at PeV energy, seriously challenge this “standard model” of high-energy astrophysics and even the more fundamental theory of electron acceleration.

Off  1 order of magnitude:  0.1PeV estimate <  1.4PeV observed.

I also conjecture that the conclusion that the universe is nearly flat is preposterous if based on observations made from near here -- that until and unless we can position an observation position midway between ourselves and the purported edge the best we can say is that from our vantage it is "locally" flat, to get non-local we would have to measure from half way between or a sufficient vantage point.