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## Faradave's View on Quantum Gravity

This is not an everything goes forum, but rather a place to ask questions and request help for developing your ideas.

### Faradave's View on Quantum Gravity

[Mod Note: This thread has been split off from Faradave's Is Gravity Relative? thread, becasue it veered outside of the Physics section guidelines.]

I'm pretty sure this material is repeated over a dozen times by Faradave, in various parts of this forum. I already told Faradave that he appears to be deriving spherical wave mechanics in 3 dimensions, but replacing the textbook orthodoxy with his own neologisms. If he ever gets off the this forum and goes and studies this topic, he will find that indeed the amplitude of the wave falls off with distance, exactly in the way he keeps repeating his argument about "density of rope".

His hijacking of established physics terms (superposition) is making me itch, but there is nothing 'wrong' with it as far as forum etiquette.

By "model gravitation fundamentally", I assume he means he thinks he is deriving a model of Quantum Gravity.

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### Re: Relativistically Inclined

Jorrie wrote:...physicists tend to think of 'real' as the result of measurements ...

The term Taylor & Wheeler used instead of "real", for the magnitude of an invariant 4-vector was "well defined", which I find agreeable.

"Despite this arbitrariness in the means that we use to describe the 4-vector AB, the 4-vector itself is well defined. Not only does the interval AB have the same magnitude in all frames of reference. More significantly, the locations of events A an B themselves...are as well...regardless of what coordinates one uses..."

They consider the 4-vector a unifying idea between invariant spacetime intervals (I) and invariant rest mass (m0). In natural units (c = 1) we see:
ΔI2 = ΔX2 – ΔT2 and Δm02 = ΔE2 – Δp2.

I also find this agreeable, though I prefer their Euclidean representation.

Jorrie wrote:...your idea of renormalization is very different from the mainstream meaning.

Understood. I simplistically interpreted, "Renormalization replaces the originally postulated mass and charge with new numbers such that the observed mass and charge matches those originally postulated. ... If the electron is assumed to be a point, ... the mass diverges, because the field is inverse-square."

Though limited, the rope field analogy is much clearer than QED. Renormalizing reveals some places it could be improved.

You accept that "rest mass" of a system includes the energy of its spin, an intuitive way of representing energy at rest. I push that concept in conceiving a fundamental particle as a spinning field element, which embodies mass-energy equivalence. QED sees the field as a far more convoluted swarm of self-interacting virtual particles. This seems to apply to electric charge but it neglects mass charge (thus "quantum electrodynamics"). Either way, an instance of a field (G or EM) corresponds to a particle's future light cone at that moment.

Tidal forces, which confound the equivalence principle, are avoided by Einstein's "sufficiently small region of spacetime". In the limit, as that region goes to zero, we're left with a single, lightlike field element, from which generation of a particle's field may be imagined with "chronaxial" spin.

Getting back to the OP, Einstein was able to elegantly deduce time dilation (duration contraction) with his imagined light clock. Length contraction follows from SR's 2nd postulate, as the length:duration ratio is preserved by invariant c. I believe "relativistic mass" should be as simply derived. Not finding that, I attempt it below.

Recall the light clock scenario, considering only the half paths needed. Light path t' relates to t by equivalent expressions √(1-v²) and cosθ.

The light clock relates paths t & t' by both Pythagoras and trigonometry.

Now, consider a massive particle, the designated center of a field. It's persistence defines a particle worldline, vertical in the particle's rest frame. Regular instances of that field can be marked along it. An identical particle, seen to be in motion (here 0.71c), has a worldline at 45°, in Euclidean coordinates. A triangle so defined is similar to the light clock’s in that the angle between the vertical and diagonal paths goes to 90° as v goes to c.

Here, worldline angle (θ) indicates speed. A moving particle (m) is seen to accomplish more instances of its native field per unit of rest time of (m0). Thus, observed mass (m) increases with v toward limit c (90°).

Like a tilted stack of checkers, a motion worldline registers more field instances per vertical unit (proper duration) of an observer's rest frame. This holds, even in the limit as that duration goes to zero. A resting observer will therefore measure a greater gravitational field intensity for the moving particle, which implies greater "relativistic" mass. Similarly, more instances of a particle make it harder to push.

But moving clocks run slow. Why should a moving object have more instances of its field?
A diagonal worldline is the proper time coordinate for the moving particle. Like the tilted stack of checkers, it sees nothing amiss, the same density as always. Further, a moving particle is seen to have the energy to supply the extra instances observed. True, a moving clock is seen to run slow, but consider the slowed motions in this video.

This "slow motion" video requires a higher image rate (5,000 fps) than normal cameras (60 fps). Apparent motion slows asymptotically to a stop with increasing fps (frames or "instances" per second).

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### Re: Instant Replay

Faradave » 23 Oct 2016, 09:09 wrote:
hyksos wrote:By "model gravitation fundamentally", I assume he means he thinks he is deriving a model of Quantum Gravity.

Yes, in that the field is modeled as arising from personally characterized quantum spin (i.e. chronaxial). But I don't adhere to string theory or extra dimensions and I do unify G & EM simply (as a Personal Theory). So, there are distinctions from what's found in the literature.

This is exactly why these posts do not belong in the Physics section. It becomes extremely time consuming to filter out (and correct) all the false arguments, of which there are quite a few in the last few posts. Until I have the time, this thread is closed, pending moderation.

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### Re: Relativistically Inclined

Faradave » 23 Oct 2016, 08:59 wrote:They [Taylor & Wheeler] consider the 4-vector a unifying idea between invariant spacetime intervals (I) and invariant rest mass (m0). In natural units (c = 1) we see:
ΔI2 = ΔX2 – ΔT2 and Δm02 = ΔE2 – Δp2.

I also find this agreeable, though I prefer their Euclidean representation.

The problem is that space-time is not Euclidean. Add to that confusing terms like "radiant energy (p)" and "light interval (I)" and you are creating complete confusion. Neither of these terms have the meanings in physics that you attempt to attach to it.
QED sees the field as a far more convoluted swarm of self-interacting virtual particles. This seems to apply to electric charge but it neglects mass charge (thus "quantum electrodynamics"). Either way, an instance of a field (G or EM) corresponds to a particle's future light cone at that moment.

Never heard of "mass charge" - what's that? Please also define "instance of a field (G or EM)" in standard terms (or at least provide a reliable reference).
In the limit, as that region goes to zero, we're left with a single, lightlike field element, from which generation of a particle's field may be imagined with "chronaxial" spin.

What is a "lightlike field element"? And "chronaxial spin" has been refuted by Lincoln, myself and others in the past. Why are you persisting with it?
I believe "relativistic mass" should be as simply derived. Not finding that, I attempt it below.

It has been simplistically derived by Einstein, in its energy form.

I think your next diagrams have the potential to create a lot of confusion. It mixes two reference frame views into one diagram. It is really an Epstein space-propertime diagram, which never caught on due to its confusing mixing of "my space" and "your time".

But moving clocks run slow. Why should a moving object have more instances of its field?

Since I assume you are talking inertial movement here, there are no "moving clocks", only clocks that move relative to reference frames and then the situation is reciprocal - each clock "run's slow" according to the others perspective. Hence moving clocks do not run slow. It is just an observational perspective.

Also, in your scenario, no clock has "more instances of its field". It is only the perception of the "other guy". One of the pitfalls of your diagrams.

The only time you can have an absolute (frame independent) difference between elapsed times is when you consider a two-way situation like in the classical "twin-paradox". We had plenty of threads on that in this forum, so no need to belabor it again. The point is: do not try to build your private theory of quantum gravity on false perceptions.

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### Re: Frame Dependence

Jorrie wrote:false arguments

The numbers work! The interval equation (X² = I² + T²) and energy equation (E² = m² + p²) are analogous. Further, a mass triangle and Einstein's energy triangle must agree, by mass-energy equivalence.

Jorrie wrote:The problem is that space-time is not Euclidean.

I didn't say it was. But Einstein's light clock and energy triangles are Euclidean! That should be sufficient to question naïve acceptance of archaic space and time coordinates to represent the continuum.

Fortunately, we aren't stuck with clumsy spacetime. It has legacy value but it's not taking us anywhere new. As you've informed us, physics also employs light cone coordinates, which entail lightlike and spatial coordinates. It's slowly catching up to my combination of lightlike and temporal coordinates, Times Square (T2).

Jorrie wrote:[Your] confusing terms like "radiant energy (p)" and "light interval (I)" ...are creating complete confusion. Neither ... have the meanings in physics that you attempt to attach

I'm sorry about any confusion. "Radiant energy" is nothing special. Taylor & Wheeler use it for kinetic energy, particularly in the case where a "particle" has zero rest mass. Such radiant energy transmits via lightlike intervals.

We also know radiant energy as the "momentum component" (pc)* of the total energy, even for massive particles. An equivalent term would be"radiant mass".

*just p in natural units, where c=1

Jorrie wrote:Never heard of "mass charge" - what's that?

As I consider energy to be the more fundamental aspect of mass-energy. "Mass charge" is energy in any form. It could also be called "inertial charge" or "gravitational charge" by the equivalence principle. I meant to invoke both latter terms with the former.

Jorrie wrote:Please also define "instance of a field (G or EM)" in standard terms (or at least provide a reliable reference).

An instance of a particle should be understood to be an event along that particle's worldline, i.e. the particle at a particular instant. Each instance of a particle has an associated future light cone, which defines the entirety of its potential causal interaction. That future light cone corresponds to an instance of that particle's field.

A field is a region of potential force pairing (e.g. potential interaction with a test particle.). As QED sees forces mediated by massless force carriers, an instance of a field is the future light cone of a particle. It is the collection of all potential forces, which can originate from an instance of a particle.

Jorrie wrote:What is a "lightlike field element"?

"A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex... in the case of half-lines, it extends infinitely far. ... The definition of a cone may be extended to higher dimensions." Let the half lines (i.e. rays) be "radial elements". A lightlike field element is a radial element of a future light cone (in 4D).

A more elegant and insightful definition is that a lightlike field element is an unpaired force. This sees force as an object, not unlike its conventional treatment as a vector. I model a force (i.e. field element) more fundamentally, as a particle-interaction wormhole (pinhole). With chronaxial spin, a particle's field is generated.

Jorrie wrote:And "chronaxial spin" has been refuted by Lincoln, myself and others in the past. Why are you persisting with it?

1. You're too intelligent to continue denying one of four available, independent spin axes.
2. It's the least I can do, considering all I've learned from you.
3. With all due respect, said refutations have been insubstantial. (Remind me, if there was a good one.)
4. Chronaxial* spin is the best and only available explanation of quantum spin. QM is woefully incomplete without it.

*More generally, it occurs about a particle's worldline, which parallels proper time in the particle's rest frame.

Jorrie wrote:["relativistic mass"] has been simplistically derived by Einstein, in its energy form.

Good for him! My feeling is that length contraction, time dilation and relativistic mass-energy all occur together and if the light clock example gives us one, it should give us all three.

Jorrie wrote:I think your next diagrams really an Epstein space-propertime diagram, which never caught on due to its confusing mixing of "my space" and "your time".

Yes! My post included a link to Epstein diagrams. He and Minkowski both suffer with spatial coordinates. The simplicity of Epstein diagrams is retained by replacing spatial with invariant lightlike coordinates, agreeable to all observers. As I showed, the geometry is as elegant as with the light clock.

Jorrie wrote:...you are talking inertial movement here, there are no "moving clocks" ... each clock 'run's slow' according to the others perspective. It is just an observational perspective.

Those are equally legitimate "observational perspectives", wrt physical law. As you know, SR allows no privileged inertial frames. There was nothing about Einstein's light clock example nor my analogous diagram that would deny reciprocal perspectives. In fact, that helps legitimize them.

Jorrie wrote:no clock has "more instances of its field". It is only the perception of the "other guy".

I beg to differ. We agreed that gravity is relative. I now provide a mechanism.

Two stacks of coins oriented at an angle to each other, each think the other stack has more coins per its own vertical measure. Do the same for instances of a gravitational field along angled worldlines and you've got relative gravity.

Parallel lines from either stack measure higher coin counts in the other angled stack. Parallel simultaneities measure mutually higher temporal densities of gravitational fields in different inertial frames.
Length, duration and mass (inertial and gravitational) are indeed frame dependent. I take that as the meaning of "relative" in SR. Additional terms like "reciprocal" and "mutual" apply but are redundant.

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### Re: Faradave's View on Quantum Gravity

No machinery has ever been invented that “explains” gravity without also predicting some other phenomenon that does not exist.

-- Richard Feynman. (Caltech, 1963)

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### Re: Faradave's View on Quantum Gravity

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### Re: Reality Check

I love the Feynman lectures, which I own on CDs (several sets) but I especially like his videos.

Richard Feynman wrote:No machinery has ever been invented that "explains"” gravity without also predicting some other phenomenon that does not exist.

So far, yes. Nevertheless, gravity is here along with all the phenomena which do exist. It is thus, also the case for its explanation (my goal).

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### Re: Faradave's View on Quantum Gravity

I hope that my words will not come across as combative or inflammatory. Where ever I say something which might be construed as such, I have placed the qualifier (advice) next to it.

(advice) Wikipedia is for reference, not for learning.

The following wikipedia links should act as 'portals' for your own reading, as jumping-off points to deeper research. There are three main 'thrusts'/'directions' in physics regarding how gravity acts at the smallest scales. Roughly in the order they were introduced in history,

I will include two more notable mentions. I separate these from the 'main three' directions, because in some cases they fit underneath them as subheadings. But the wall-of-text will often obscure these topics, and they would be unfortunate to overlook.

Your posts on this topic in the forum are closest to semi-classical gravity -- as I can see you making references to the "gravitational field". You refer to the field in the classical sense, rather than say, a quantum field. Euclidean QG (number 5 above) may be of interest to you, particularly the part about Wick rotation. You seem to have put a lot of thought into rotations performed in Minkowski space. But don't let that go to your head -- they are using Wick rotations to simplify a path integral. The mathematics is very erudite.

(advice) Speaking in rough terms, it is unlikely you can make any progress in this topic using college-freshman-level mathematics. Claiming that you have a theory of quantum gravity, and then presenting the theory with triangle diagrams (that look like repeated derivations of the Lorentz factor), this will only lead to pain.

Remember what Feynman said,
"Finally, let us compare gravitation with other theories. In recent years we have discovered that all mass is made of tiny particles and that there are several kinds of interactions, such as nuclear forces, etc. None of these nuclear or electrical forces has yet been found to explain gravitation. The quantum-mechanical aspects of nature have not yet been carried over to gravitation. When the scale is so small that we need the quantum effects, the gravitational effects are so weak that the need for a quantum theory of gravitation has not yet developed. On the other hand, for consistency in our physical theories it would be important to see whether Newton’s law modified to Einstein’s law can be further modified to be consistent with the uncertainty principle. This last modification has not yet been completed."

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### Re: Frame Dependence

Faradave » 28 Oct 2016, 07:35 wrote:
Jorrie wrote:false arguments

The numbers work! The interval equation (X² = I² + T²) and energy equation (E² = m² + p²) are analogous.

They may look the same, but they represent totally different concepts. Saying they are analogous is a great way of getting everyone confused. Here's why. The spacetime interval equation embodies the hyperbolic nature of spacetime. Note that $S$ takes the place of your $I$ here.

The spacetime interval definition

If we solve these equations, we get a spacetime diagram like this:

The hyperbolic nature of spacetime

The energy equation has the rest mass $m$ taking the position of $S$ in the interval equation, but they are not related to each other. The other two (total energy E and momentum p are self explanatory, but would a diagram like the hyperbolic spacetime depicted make any sense with mass in place of $s$? Certainly not. Hence, the two concepts are not related.

FD wrote:
Jorrie wrote:[Your] confusing terms like "radiant energy (p)" and "light interval (I)" ...are creating complete confusion. Neither ... have the meanings in physics that you attempt to attach

I'm sorry about any confusion. "Radiant energy" is nothing special. Taylor & Wheeler use it for kinetic energy, particularly in the case where a "particle" has zero rest mass. Such radiant energy transmits via lightlike intervals.

The standard meaning of "radiant energy" is given in this Wiki. I do not know how Wheeler and Taylor got away with that, but I have never seen that in any paper - I presume it is because books are not refereed! In any case, to insinuate that one can use the same term for a massive particle's kinetic energy seems quite absurd.

OK, I'll leave you alone with your quantum gravity effort now, and only comment where I think statements are to detriment of this forum. I see Hyksos has given you great advice.

=J

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### Re: Enlightened Electron

Jorrie wrote:[The interval equation (X² = T² + I²) and energy equation (E² = m0² + p²)] ... may look the same, but they represent totally different concepts. ... The energy equation has the rest mass taking the position of [the spacetime interval] in the interval equation, but they are not related to each other.

Let's think about that. At rest, a mass proceeds along a vertical worldline, corresponding to its proper time coordinate. So, corresponding rest components are m0 and ΔT*. Each equation has a spatial component (E & X) and a motion component (I & p).

Mere coincidence? The geometric representations of space-time-interval separation and total-rest-radiant energy correspond exactly, suggesting the former is the coordinate system upon which the latter occurs.

Each equation also has invariant terms (m0 & I) while angle (θ) corresponds. Perhaps nature is telling us something.

*For simplicity, I omitted Δs from my interval equation, presuming the values are represented from the origin.

Jorrie wrote:The spacetime interval equation embodies the hyperbolic nature of spacetime.

OK. But it's just as well to say that rearranged, the equation represents the Euclidean nature of Times Square (time & light coordinates). It's not unusual for science to get things a bit sub-optimal the first time. Spacetime coordinates have their use but lack a justification so robust as to preempt all others.

Jorrie wrote:If we solve the [conventional] equations, we get a [hyperbolic] spacetime diagram

And if we solve my single rearranged equation: X² = T² + I², we get a simpler diagram. One in which the otherwise inexplicable future "light cone" becomes a simple "light disk". Speed limit c exists as a consequence of the unidirectionality of time and the mysterious quantum spin becomes clearly evident by its spatial projections, exactly as measured.

Jorrie wrote:...to insinuate that one can use ["radiant energy"] for a massive particle's kinetic energy seems quite absurd.

It needn't seem that way. Consider three related scenarios:
1. An electron with kinetic energy (KE) is seen to have velocity (v). As KE increases, v approaches lightlike limit c, suggesting a lightlike influence of KE.
2. The electron's northeast velocity can be said to have components which are north and east, even though it never travels due north or due east. In the same way, an electron worldline which makes an angle with your proper time can be said to have timelike and lightlike components, though it is not seen at rest or at speed limit c.
3. The electron annihilates with positron but their kinetic energy is not lost. It remains lightlike, recoiling away (with the rest energies of the annihilated particles) as gamma emissions.

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### Re: Faradave's View on Quantum Gravity

Faradave wrote:OK. But it's just as well to say that rearranged, the equation represents the Euclidean nature of Times Square (time & light coordinates). It's not unusual for science to get things a bit sub-optimal the first time. Spacetime coordinates have their use but lack a justification so robust as to preempt all others.

FD, I've started along the same route (approx your "Times Square") two decades ago and thought that I found an improvement on standard SR representation. In the end I realized the limitations and the potential confusion that it can create. The reason is that whether you regocnize it or not, it mixes reference frame values in a confusing way.

I found that such efforts lead to no valid insights that Minkowski spacetime does not offer (provided one spend the time to understand them properly). Plus, Minkowski offers a whole bunch of thing that your "space-propertime" does not, like half of Minkowski spacetime is spacelike - a quite important domain!
Eventually, I 'saw the light' and I did not have to look back again.

I will leave you with these closing remarks, because I do not intend to continue spending time on the reading of private theories. There is an immense amount of accepted science that I still have to read...
If and when your ideas become mainstream, I'll surely pick up on it again. ;)

Regards, Jorrie

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### Re: Standing Firm on Relativisitic Gravity

hyksos wrote:Wikipedia links The mathematics is very erudite.

Thanks! They're interesting but I have the impression that particles aren't so good at math. That doesn't mean the experts won't derive a workable model for gravitation. But history suggests, a working model with loads of epicycles may actually be yearning for a simple change of coordinates (from geocentric to heliocentric, in that particular case.)

"Any path—periodic or not, closed or open—can be represented with an infinite number of epicycles. ... This is because epicycles can be represented as a complex Fourier series; so, with a large number of epicycles, very complicated paths can be represented in the complex plane."

The methods of your references are going to be far more complicated than with my Times Square coordinates. Currently, an esteemed group are proposing my spinholes (spatial-interconnecting wormholes) as the basis of gravitation. A simple report is below. Here's a more sophisticated lecture.

.
That's fine but since spinholes have internal span, it's going to be hard to create a field which counters dimensional separation, all the way to a point of contact. It's much simpler using my zero-internal-span pinholes (particle-interaction wormholes) instead.

hyksos wrote:Claiming that you have a theory of quantum gravity, and then presenting the theory with triangle diagrams (that look like repeated derivations of the Lorentz factor), ...will only lead to pain.

It didn't hurt Einstein! I allow the "quantum gravity" characterization only because my theory identifies the chronaxial spin upon which it depends as instances of quantum spin (specifically, the spin½ of fermions). There IS a lot of relativity, thus a Lorentz factor must be apparent. Einstein would have gotten to GR faster, had he understood fields in terms of instances, as I illustrated above.

Jorrie wrote:FD, ... whether you recognize it or not, [Times Square] mixes reference frame values in a confusing way.

Adopting lightlike coordinates does not mix different coordinate frames, it employs coordinates common to all of them (inertial or otherwise). That's a major advantage of invariant coordinates.

Jorrie wrote:Minkowski offers a whole bunch of things that your "space-propertime" does not, like half of Minkowski spacetime is spacelike - a quite important domain!

Nonsense! First, Times Square (T2) coordinates are interval-proper time (specifically lightlike intervals), not "space-propertime". Space is derivative in T2.

The spacelike domain is not lost in T2, it's merely shifted down, entirely consistent with the SR assertion that faster-than-light travel is backward in time. That's something that Minkowski diagrams really screw up!
Unlike Minkowski spacetime, T2 correctly depicts the geometric independence of non-aging lightlike intervals by orienting them perpendicular to the aging coordinate (time).

Jorrie wrote:I will leave you ... There is an immense amount of accepted science that I still have to read...

That's perfectly understandable. But it should be equally well understood (by Lincoln as well) that being busy is not a substantive refutation. The same goes for unfamiliarity, dislike, not being mainstream, etc. I've defended Phyxed against all substantive criticisms ventured.

Jorrie wrote:If and when your ideas become mainstream, I'll surely pick up on it again. ;)

You'll be more than welcome Jorrie! Thanks for your (and hyksos's) thoughtful participation.

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### Re: Faradave's View on Quantum Gravity

You have linked a video from the Stanford Institute of Theoretical Physics. https://www.youtube.com/watch?v=WQU9yOtWrQk That lecture is about Maldacena's AdS/CFT correspondence. You claimed you are working on the same thing, (or even that you discovered this before Maldacena found it.)

Are you claiming to this forum that you have been doing mathematical work in the topic of dualities in string theory?

Or are you claiming that you are working on a conformal field theory?

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### Re: Fair Play

hyksos wrote:Are you claiming to this forum that you have been doing mathematical work in the topic of dualities in string theory?
Or are you claiming that you are working on a conformal field theory?

Heck, no! You seem anxious to put words in my mouth. I'm claiming that the esteemed group is taking an unnecessarily difficult path to gravitation. Their approach arises from the realization that entanglement is equivalent to non-traversable, space-like wormholes. [1, 2, 3]

I've previously shown you that I described non-traversible, spacelike wormholes as constituting entanglement in two other public forums (six total postings) three years prior to those authors' first publication. Here's one from PF and one from Amazon. I tried to contact the five authors to offer my term, "spinholes" but got no replies.

Whether I gor spinholes by math or magic is irrelevant! Spinholes were in fact, a logical spin-off of my reasoning toward pinholes.

Note: Penzias and Wilson discovered cosmic microwave background radiation, essentially by accident! (They tried everything they could think of to rid themselves of the signal!) That didn't stop them from getting 1978 Nobel Prize in Physics for their discovery. They got there first.

P.S. T2 is has 3 of 4 coordinates lightlike (invariant). I don't know if that makes fields so represented "conformal".

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### Re: Faradave's View on Quantum Gravity

Okay I'm reviving this thread -- mostly because I saw Faradave's youtube. I watched almost all the videos in one sitting. I guess this will count as my response to the youtube channel.

First things first, Minkowski spacetime is not a literal description of the world. It is a toy model of Special Relativity where space is squashed to 2 dimensions. I notice in the youtube vids, you keep talking about a "cone". Well there is no "cone" in the actual spacetime we are sitting within now. That spacetime is a 4-dimensional subject , with 3 Ds of space and another D that marks off local duration in a reference frame. The D=4 is not "time" per se, (because vis-a-vis ronjanec, the word "time" is fraught with semantic potholes. )

If Minkowski is a toy, then you might want the full description of the theory in 4 dimensions. In my humble opinion, you are at a stage in your physics where you probably need it badly. Ockham's razor is a guideline and a fine tool of justification. But you cannot use Ockham to simply remove actual dimensions of space that are actually there.

4-vectors

You must learn everything about 4-vectors and how they are multiplied by matrices. The basic gist is that all the transformations reduce to multiplying 4-vectors by a Hermitian matrix. I like this link below because they laboriously draw out the whole matrix in every example so you can see exactly what is happening.

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/vec4.html

Learn this material like the back of your hand. Really you will need to apply it to actual problems to get the "hang" of the procedure. You cannot bluster over this material, because eventually every textbook and website you read will stop writing them as a matrix, and instead just show multiplications by a matrix given by greek letter Lambda.

Next you will have to visit and skim (or read carefully) the material in these two articles. Again, this is not for learning, because wikipedia is not for learning. This is so you can familiarize yourself with the terms.

1.) Lorentz Group
https://en.wikipedia.org/wiki/Lorentz_group

2.) Representation Theory
https://en.wikipedia.org/wiki/Representation_theory_of_the_Lorentz_group

In particular , I would like you to familiarize yourself with the word "orthochronous". You will find it numerous times in the above material. Along with the hyperphysics page, consider this another piece of homework : find out what orthochronous means.

We can get into endless arguments about which person "invented" Rock and roll music. Isaac Newton and Leibniz are usually attributed as the people who "invented" calculus. It is true that they were the first people to apply calculus-inspired thinking to mathematics. However, the way calculus is taught at the university level is quite alien from these original formulations , and the college students are actually seeing formalisms invented in the 19th century.

The same is true of Special Relativity. While Hendrik Lorentz and Albert Einstein were the first to formulate it, the way it is taught at universities is very different now. They teach it with the material given above, as matrices (called 'Lorentz Transformations') applied to 4-vectors.

One of the reasons why physics students are forced to wrangle with Representation Theory is because academia is attempting to prepare them to be able to apply S-R to quantum mechanics and QFT. Einstein invented it, yes, but the theory now stands alone with its own jargon. S-R has grown legs and moves around independently of its founders. It is now possible to learn S-R, write books about S-R and teach S-R without ever making any reference to the quote, "...assumptions which Einstein made". You can wrangle with the theory, as a theory.

It is unfortunate that the internet is going to throw a wall of equations at you, and in this regard, you might fall back to habit of Okham's razor simplifying something.

There is nothing here that needs simplifying.

This is the raw depiction of the theory of S-R in the simplest terms. This process of multiplying matrices by 4-vectors neatly captures every aspect of the entire theory. We do not need separate equations to describe time dilation, relativistic mass, and length contraction, and et cetera. The procedure of Lorentz Transformation of 4-vectors captures all the phenomena in one fell swoop. That is truly in the spirit of Okham's principle!

hyksos
Active Member

Posts: 1382
Joined: 28 Nov 2014

### Re: Simple-Minded

hyksos wrote: I watched almost all [Faradave's] videos in one sitting.

Good for you! Thanks. I appreciate the time you invested and your considerable suggestions above and in general.

hyksos wrote:Minkowski spacetime is not a literal description of the world. It is a toy model of Special Relativity where space is squashed to 2 dimensions.

I prefer to think of a "Minkowski diagram" as a 2D slice from 4D Minkowski "spacetime". In both cases, space and time coordinates are mapped onto the 4D continuum (or manifold) of our existence.

I like toys! So did Feynman, with spacetime the coordinate choice for his ubiquitous Feynman diagrams. As this toy finds extensive utility in both Relativity and QM, it's worth playing with.

hyksos wrote:there is no "cone" in the actual spacetime we are sitting within now. That spacetime is a 4-dimensional subject

The literature is replete with references to "light cones" so, I find the model unavoidable. Of course, you and I know that being a structure in 4D, the referenced "cone" is better described as a 3-cone, incorporating 3D rather than the depicted surface. Any rim (3-conic section) is thus understood to be a surface (e.g. a sphere) rather than just a loop.

hyksos wrote:3 Ds of space and another D that marks off local duration in a reference frame. The D=4 is not "time" per se, (because vis-a-vis ronjanec, the word "time" is fraught with semantic potholes.

Agreed! Dimensions quintessentially provide the potential for separation, three offer bidirectional translational freedom, while one (typically referred to as "time") is unidirectional. This can be modeled from a unique, central, Big Bang event, from which a 4D temporal field emanates and "space" is an enclosing 3-surface.

hyksos wrote:you cannot use Ockham to simply remove actual dimensions of space that are actually there.

A 2D "slice" ignores but does not remove the other two dimensions. It keeps things simple when motion is restricted to one direction. Clearly though, objects like orbitals require 3D & 4D.

hyksos wrote:You must learn everything about 4-vectors and how they are multiplied by matrices.

I expect I will but only to rescue those poor souls who have overlooked the benefits of Euclidean coordinates. I'm not saying they get incorrect answers. I'm saying they work too hard and miss a lot that should be obvious. For example, the absence of massless particles (i.e. Though orbital transitions are indeed quantized, there are no photons).

hyksos wrote:There is nothing here that needs simplifying. This is the raw depiction of the theory of S-R in the simplest terms.

Spacetime is clearly a well-developed legacy with much to offer but that's no reason to neglect the simpler, Euclidean perspective I provide with interval-time coordinates.

With all the emphasis QM places on "locality" vs. "non-locality", it seems especially important to realize the full extent of locality in 4D. Yet, as far as I can tell, I'm the only one. Is it any wonder I'm hesitant to adopt their convoluted methods? It's as if they're trying to be remain ignorant.

"Local" means "contact". While there is no such thing as action-at-a-distance, the majority of contact is spatially remote. This is clearly and undeniably evident with Euclidean coordinates in the limit as ∆s approaches ∆t.

Is it any wonder I'm hesitant to adopt their methods? It's as if they're trying to be remain ignorant.

hyksos wrote:another piece of homework : find out what orthochronous means.

"Lorentz transformations that preserve the direction of time are called orthochronous."

Thanks for the reference. I'll need to do more than just find a quote. Transformations are different from behaviors such as chronaxial spin (i.e. fermion spin½). I was concerned that I might have overlooked some prior art.

Active Member

Posts: 1735
Joined: 10 Oct 2012
Location: Times Square (T2)

### Re: Faradave's View on Quantum Gravity

Spacetime is clearly a well-developed legacy with much to offer but that's no reason to neglect the simpler, Euclidean perspective I provide with interval-time coordinates.

Nobody is neglecting Euclidean coordinates. Nobody is neglecting you. You have posted on this forum for years.

I watched 80% of your youtube videos. You are neglecting the way S-R is taught in the full 4 dimensional versions. If I thought there was absolutely nothing to gain for studying it that way, I would have never mentioned it to you. You will gain the world if you study the full 4D version.

I like toys! So did Feynman, with spacetime the coordinate choice for his ubiquitous Feynman diagrams. As this toy finds extensive utility in both Relativity and QM, it's worth playing with.
==
The literature is replete with references to "light cones" so, I find the model unavoidable. Of course, you and I know that being a structure in 4D, the referenced "cone" is better described as a 3-cone, incorporating 3D rather than the depicted surface. Any rim (3-conic section) is thus understood to be a surface (e.g. a sphere) rather than just a loop.

Yes, I am aware and we are all aware of the "extensive utility" of the chalkboard versions for quick napkin calcs and deep discussions in the professor's office at the white board. Yes. Nobody is arguing these points.

However I am outwardly telling you : you are missing some crucial conceptual points by neglecting the full 4D version. In particular what it says about "time" and "energy" and how they relate to each other.

Agreed! Dimensions quintessentially provide the potential for separation, three offer bidirectional translational freedom, while one (typically referred to as "time") is unidirectional. This can be modeled from a unique, central, Big Bang event, from which a 4D temporal field emanates and "space" is an enclosing 3-surface.

It is this kind of talk that led me to propose a doctor's orders for your remedy. You clearly believe this is what Special Relativity is saying and I'm telling you with complete honesty, mano a mano, that you have it wrong. I am giving you the tools to get it right.

The doctor's prescription is to study the full 4D version with matrices (called Lorentz transformations) and vectors (called 4-vectors).

There are certain geometrical operations that work on vectors in 3D that do not extend or analogize to four dimensions. In short, 4-dimensional space is not something that you get for free by hand-waving. The 4th dimension holds the skeleton key to what S-R is saying about the nature of reality.

Special Relativity is a theory from 1905 -- (and while it clearly is not the end-all-be-all of all physics) it does make assertions about the nature of reality. You will never correct the theory, nor extend upon it, until that time in which you capture its fundamental claims. To abandon a theory , you must first authentically state it.

"time" is very wobbly in S-R. It is far better to begin to conceptualize the 4th dimension as representing energy. Without this conception, you risk rotting away in a cul-de-sac where the theory only makes predictions about a single observer's frame.

But the universe we inhabit is made up of a bunch of different observers. There must be some physical principle that is orchestrating all these allegedly separate observers in their own (allegedly) isolated reference frames. Since the length of durations of time will change from one reference frame to another, the 4th dimension cannot be "time" as normally understood. Energy is what it really is.

S-R strongly suggests that "time" moves in the forward direction because energy starts at 0.0 and increases. In other words, there is no such thing as "negative energy" and so this is why all observers think "time" goes in one direction only. It is not, as you have suggested because we are "emanating away from a Big Bang". (we can argue this point in a different context, but we aren't talking about Quantum Gravity, we are speaking only of physics of 1906 at this juncture).

I can blabber the above points at you and you will read them, then forget them as if I were writing poetry. I can tell you things like "It is an emotional attachment to classical time that must be abandoned." You will think this is a pretty flower to be enjoyed temporarily and moved on.

It is not my calling to use this forum to be your personal physics tutor. This will require elbow grease on your part. If you study the full 4D version, everything I have written above will jump out at you. It will fall in your lap. I cannot make you see it. There is no shortcut. You must see it for yourself.

You have all the tools.

hyksos
Active Member

Posts: 1382
Joined: 28 Nov 2014

### Re: Faradave's View on Quantum Gravity

I can blabber the above points at you and you will read them, then forget them as if I were writing poetry. I can tell you things like "It is an emotional attachment to classical time that must be abandoned." You will think this is a pretty flower to be enjoyed temporarily and moved on.

Unless you happen to have a precise simulation (down to the quantum level) of Faradave's brain, I find it unlikely you can extrapolate his thoughts or actions regarding your posts. Really, it may be best if you don't offer lesson plans and stick with traditional critique. Anything else risks condescension.

Also, are you sure there is "no such thing as 'negative energy'"? That could use a bit more support, perhaps.

Braininvat

Posts: 6703
Joined: 21 Jan 2014
Location: Black Hills

### Re: A Prescription for My "Light" Affliction

hyksos wrote:You will gain the world if you study the full 4D version.

Thanks for your continued time and candor hyksos. I didn't take offence from your post but let's both keep Forum Rules in mind.

I loved Fleisch's little book on Maxwell's equations so much that I'm now finishing his book on wave theory and own his book on tensors to read next. It has some 4D matrix algebra in it and I promise to read it at least twice. I do not however, expect it will change the irrefutable aspects of Phyxed, only the language in which it may be presented.

hyksos wrote:Nobody is neglecting you.

Certainly, I haven't been neglected at SPCF. However, I am having difficulty getting through to the ALPHA team at CERN, regarding the possibility of documenting photo-annihilation. Similarly, with numerous authors as they're busy and I have the profile of a crank.

hyksos wrote:Nobody is neglecting Euclidean coordinates. You've been posting ... for years.
.
If they aren't being neglected, why haven't I found or been referred to such a reference in all those "years"? The closest has been Epstein diagrams but he mistakenly attempted to retain spatial coordinates (when he should have switched to interval coordinates).

Folks like you read and reply to my posts but these fall short of either affirming or substantively refuting the fundamentals presented.

hyksos wrote:You are neglecting the way S-R is taught in the full 4 dimensional versions.

Regardless of the dimension of presentation, vectors are themselves inherently 1D.* That's why they're readily depicted by arrows. An interval occurring in a 2D slice of spacetime (or interval-time) is still a perfectly legitimate 4-vector!** As it turns out, that's all I need to make my point in many cases.

*The degenerate case of a "null vector" may be considered 0D.
**Just add zeros for the two components not presented.

hyksos wrote:you are missing some crucial conceptual points by neglecting the full 4D version

I'll be overjoyed to discover these. In the meantime, I could say the same about anyone who persists in the notion of a photon.

hyksos wrote:In particular what [4-vectors say] about "time" and "energy" and how they relate to each other.

You have already conceded that "time is very wobbly". I believe that "proper time" of SR represents time experienced (i.e. aging) by objects sharing the coordinate frame. If I'm missing some crucial point about that, it's one of philosophy rather than physics.

Energy is a different issue. Physics currently lacks a model for energy from first principles. Phyxed provides one that is consistent with the Standard Model. I'm happy to elucidate but my point is that I can't be "missing a crucial point" of physics, which physics does not itself yet have.

hyksos wrote:Special Relativity …You will never correct the theory, nor extend upon it, until that time in which you capture its fundamental claims. To abandon a theory, you must first authentically state it.

I get what you're saying but one can be a terrific cardiologist without also being a neurosurgeon. It is sufficient to know well, the limited area in which one is contributing. Einstein did a lot with triangles before he understood tensors. So can I.

All physical contact is invariant, interval contact. Remote contact is by far, the most available form of such locality.

Interval-time coordinates are consistent with SR and clearly reveal that for light transmission, no photon is required. Indeed, working models can accommodate photons, but that doesn't make photons necessary.

Respectable textbooks (including yours) define lightlike intervals as representing "zero interval separation". Phyxed simply offers the clarity of calling this direct, physical contact. If you want to play with 4D, you must allow for more than 3D of contact! I'm not asking for tutoring or a prescription but if we’re having a discussion, it's time to affirm or refute.

hyksos wrote: You clearly believe [a curved-space, radial-time model] is what Special Relativity is saying and I'm telling you … you have it wrong.

One step at a time. Curved-space, radial-time can wait.

hyksos wrote:"time" is very wobbly in S-R. It is far better to begin to conceptualize the 4th dimension as representing energy. Without this conception, you risk rotting away in a cul-de-sac where the theory only makes predictions about a single observer's frame.

Length contraction, time dilation and relativistic mass-energy are all part of Phyxed and entirely consistent with Relativity, QM and the Standard Model. Phyxed is just simpler, more complete and more explicit.


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# Tag Info

0

The example by CuriousOne is spot on - we know charged particle will accelerate in static external electric field, so generally, Poynting vector based on the external field does not need to be non-zero when charged particle gain kinetic energy. The apparent problem with local energy conservation is caused by using the wrong expression for the energy flux ...

1

Since $\nabla.B=0$ is true as long as we don't find monopoles one can always define a vector potential for magnetic field whereas $\nabla\times B=0$ is sometimes true ($J=0$ and $\frac {\partial E}{\partial t} = 0$ in the region of inerest) we can sometimes define scalar potential for the magnetic field. If you go by ampere's law you will find that ...

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This is a more general answer. Atoms and molecules are quantum mechanical entities. This means that the "shape" of atoms depends on the solution of quantum mechanical equations, which give probabilities for locating in space the electrons that are bound to the nucleus of the atom with the electric potential provided by the protons of the nucleus. The ...

5

The water molecule is neutral on overall basis, i.e: the water molecule as a whole has no net charge. The water molecule is not linear rather it has a bent shape with two hydrogens on the same side. This happens because of the lone-pair-bond-pair repulsions. The oxygen has is a more electronegative element than hydrogen, i.e: oxygen has high electron-...

1

For simplicity I treat this as a two-dimensional problem. The diagram below shows a dipole of length $l$ and a Gaussian surface of radius R. At point $A$ the dot product $\vec E_{R1}\cdot \vec R$ is positive and at point $B$ the dot product $\vec E_{R2}\cdot \vec R$ is negative where $\vec E_{R1}$ and $\vec E_{R2}$ are the net electric fields at points $A$...

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E=k*p/z^3. This is because usually, the Electric field is calculated at a point whose distance from the midpoint of the dipole(z) is very large as compared to distance between the two opposite charges(say a). That is z>>a. Thus, the original value of dipole at a point on the equatorial line=kp/(z^2+a^2)^3/2. as z^2+a^2=z^2.(z>>a). Thus, E=kp/z^3.

2

A dipole may be represented by a pair of nearby charges of the opposite sign (but the same absolute values), $+Q$ and $-Q$ at a distance $\vec r$ from each other. At the distance $R$ from the dipole (and I will only consider the case when we measure the field on the axis that includes the dipole itself), one adds $E$ going like $+1/R^2$ from $+Q$, and \$-1/(...

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# Get bones associated with specific action in python

Let's say I have a mesh with an armature and I've given it an animation action. I know I can get the action with bpy.data.actions and the bones with bpy.context.selected_pose_bones. But how would I get only the bones that have keyframes set for that specific action? For example, let's say I make a kick action and only bones for the right leg have keyframes, no other bones have any for that action. How would I get the bones for the right leg given the kick action?

Following is one way of getting the bones in a given action.

armature = bpy.context.scene.objects['Armature']
action = bpy.data.actions['ArmatureAction.002']

pose_bones = set()

for fcurve in action.fcurves:
pose_bone_path = fcurve.data_path.rpartition('.')[0]
pose_bone = armature.path_resolve(pose_bone_path)

>>> pose_bones
{
bpy.data.objects['Armature'].pose.bones["R_lower_jnt"],
bpy.data.objects['Armature'].pose.bones["R_hip_jnt"],
bpy.data.objects['Armature'].pose.bones["R_thigh_jnt"]
}

Getting to the actual bone (that belongs to the data of the Armature) is accomplished like below

>>> bone = armature.data.bones[pose_bone.name]
>>> bone
bpy.data.armatures['Armature'].bones["R_hip_jnt"]

References


text:
# zbMATH — the first resource for mathematics

Fibrations, divisors and transcendental leaves. (English) Zbl 1089.32027
Let $$M$$ be a compact complex manifold and $$T(M)$$ the quotient of the group of rational divisors by the group of rational $$S^1$$-flat divisors. The author proves that $$\dim_{\mathbb{Q}} T(M) < \infty$$ and the following results involving $$T(M)$$.
1) If $$D_i$$, $$1 \leq i \leq r \geq 3$$, are connected effective divisors which are pairwise disjoint and whose $$T$$-classes span a linear subspace of $$T(M)$$ of dimension at most $$r-2$$. Then there exists a map $$\rho: M \rightarrow C$$ with connected fibers to a smooth curve which maps the $$D_i$$’s to points.
2) If $$D_1$$ and $$D_2$$ are smooth connected disjoint hyper-surfaces such that $$[D_1]$$ and $$[D_2]$$ lie in the same line of $$T(M)$$, then there exist étale $$\mathbb{Z}/n$$ and $$\mathbb{Z}/m$$-coverings of $$D_1$$ and $$D_2$$ which are diffeomorphic and such that $$m[D_1]=n[D_2]$$, $$m$$ and $$n$$ being positive integers.
3) Let $$F$$ be a codimension-one holomorphic foliation of $$M$$ and $$L$$ a transcendental leaf of $$F$$. Then the cardinality of the set of compact complex irreducible hyper-surfaces of $$M$$ which do not intersect the topological closure of $$L$$ is at most $$\dim_{\mathbb{Q}} T(M) +1$$ and when the equality holds, $$F$$ is given by a closed logarithmic 1-form.
Finally, in the paper one can find an appendix by Meersseman where it is proved that $$T$$ is the suitable object for those theorems, since at least 1) and 2) do not hold for the Néron-Severi group of $$M$$.

##### MSC:
 32S65 Singularities of holomorphic vector fields and foliations
Full Text:
##### References:
 [1] W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. · Zbl 0718.14023 [2] F. Catanese, On the moduli spaces of surfaces of general type, J. Differential Geom. 19 (1984), no. 2, 483 – 515. · Zbl 0549.14012 [3] Étienne Ghys, À propos d’un théorème de J.-P. Jouanolou concernant les feuilles fermées des feuilletages holomorphes, Rend. Circ. Mat. Palermo (2) 49 (2000), no. 1, 175 – 180 (French, with English summary). · Zbl 0953.32016 · doi:10.1007/BF02904228 · doi.org [4] X. Gómez-Mont and L. Ortíz-Bobadilla, Sistemas dinámicos holomorfos en superficies, Aportaciones Matemáticas: Notas de Investigación [Mathematical Contributions: Research Notes], vol. 3, Sociedad Matemática Mexicana, México, 1989 (Spanish). [5] Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. · Zbl 0208.48901 [6] M. Sebastiani, Notes from the Analytic Geometry Seminar at UFRGS, 2003. [7] Burt Totaro, The topology of smooth divisors and the arithmetic of abelian varieties, Michigan Math. J. 48 (2000), 611 – 624. Dedicated to William Fulton on the occasion of his 60th birthday. · Zbl 1078.14508 · doi:10.1307/mmj/1030132736 · doi.org [8] Tetsuo Ueda, On the neighborhood of a compact complex curve with topologically trivial normal bundle, J. Math. Kyoto Univ. 22 (1982/83), no. 4, 583 – 607. · Zbl 0519.32019 [9] Kenji Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Mathematics, Vol. 439, Springer-Verlag, Berlin-New York, 1975. Notes written in collaboration with P. Cherenack. · Zbl 0299.14007 [10] A. Vistoli, Letter to S. Kleiman, 2003.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
### Home > APCALC > Chapter 2 > Lesson 2.3.3 > Problem2-125

2-125.

Determine if the following functions are even, odd, or neither. Explain how you determined your choice.

1. $y = \sin2(x)$

1. $y = \large\frac { x ^ { 2 } + 1 } { x ^ { 3 } - 2 x }$

Even and Odd Functions

A function $f$ is an even function if, for all $x$ in its domain, $f\left(–x\right) = f\left(x\right)$.

A function $f$ is an odd function if, for all $x$ in its domain, $f\left(–x\right) = –f\left(x\right)$.

Example: If $f\left(x\right)=2x^3+\sin\left(x\right)$, then $f\left(-x\right)=2\left(-x\right)^3+\sin\left(-x\right)$

$=2\left(-1\right)^3x^3+\left(-1\right)\sin\left(x\right)$

$=-2x^3-\sin\left(x\right)=-\left(2x^3+\sin\left(x\right)\right)$

Therefore $f\left(–x\right) = –f\left(x\right)$, so $f$ is odd.

$y=\sin^2x=(\sin{x})(\sin{x})$

$y=\sin x$ is an odd function. Definition of odd functions: $f(−x) = −f(x)$ Therefore, $\sin(−x) = −{\sin}(x)$.

Explore what $y = \sin^2(−x)$ looks like:
$y=\sin^2(−x)$
$=(\sin(−x))(\sin(−x))$
$=(−\sin{x})(−\sin{x})$
$=\sin^2x$

Hence $\sin^2(−x)=\sin^2(x)$.
This is the definition of an even function: $f(−x) = f(x)$.

Test for even: $f(a) = f(−a)$

$f(a)=\frac{a^{2}+1}{a^{3}-2a}$

$f(-a)=\frac{(-a)^{2}+1}{(-a)^{3}-2(-a)}=\frac{a^{2}+1}{-a^{3}+2a}\ ,$

$f(a)\ne f(−a)$; not even

Test for odd: $f(−a) = −f(a)$...


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text:
• ### First limits on WIMP nuclear recoil signals in ZEPLIN-II: a two phase xenon detector for dark matter detection(astro-ph/0701858)

Jan. 31, 2007 astro-ph
Results are presented from the first underground data run of ZEPLIN-II, a 31 kg two phase xenon detector developed to observe nuclear recoils from hypothetical weakly interacting massive dark matter particles. Discrimination between nuclear recoils and background electron recoils is afforded by recording both the scintillation and ionisation signals generated within the liquid xenon, with the ratio of these signals being different for the two classes of event. This ratio is calibrated for different incident species using an AmBe neutron source and Co-60 gamma-ray sources. From our first 31 live days of running ZEPLIN-II, the total exposure following the application of fiducial and stability cuts was 225 kgxdays. A background population of radon progeny events was observed in this run, arising from radon emission in the gas purification getters, due to radon daughter ion decays on the surfaces of the walls of the chamber. An acceptance window, defined by the neutron calibration data, of 50% nuclear recoil acceptance between 5 keVee and 20 keVee, had an observed count of 29 events, with a summed expectation of 28.6+/-4.3 gamma-ray and radon progeny induced background events. These figures provide a 90% c.l. upper limit to the number of nuclear recoils of 10.4 events in this acceptance window, which converts to a WIMP-nucleon spin-independent cross-section with a minimum of 6.6x10^-7 pb following the inclusion of an energy dependent, calibrated, efficiency. A second run is currently underway in which the radon progeny will be eliminated, thereby removing the background population, with a projected sensitivity of 2x10^-7 pb for similar exposures as the first run.
• ### The ZEPLIN-III dark matter detector: instrument design, manufacture and commissioning(astro-ph/0605500)

May 19, 2006 astro-ph
We present details of the technical design and manufacture of the ZEPLIN-III dark matter experiment. ZEPLIN-III is a two-phase xenon detector which measures both the scintillation light and the ionisation charge generated in the liquid by interacting particles and radiation. The instrument design is driven by both the physics requirements and by the technology requirements surrounding the use of liquid xenon. These include considerations of key performance parameters, such as the efficiency of scintillation light collection, restrictions placed on the use of materials to control the inherent radioactivity levels, attainment of high vacuum levels and chemical contamination control. The successful solution has involved a number of novel design and manufacturing features which will be of specific use to future generations of direct dark matter search experiments as they struggle with similar and progressively more demanding requirements.
• ### The ZEPLIN-III dark matter detector: performance study using an end-to-end simulation tool(astro-ph/0603243)

March 9, 2006 astro-ph
We present results from a GEANT4-based Monte Carlo tool for end-to-end simulations of the ZEPLIN-III dark matter experiment. ZEPLIN-III is a two-phase detector which measures both the scintillation light and the ionisation charge generated in liquid xenon by interacting particles and radiation. The software models the instrument response to radioactive backgrounds and calibration sources, including the generation, ray-tracing and detection of the primary and secondary scintillations in liquid and gaseous xenon, and subsequent processing by data acquisition electronics. A flexible user interface allows easy modification of detector parameters at run time. Realistic datasets can be produced to help with data analysis, an example of which is the position reconstruction algorithm developed from simulated data. We present a range of simulation results confirming the original design sensitivity of a few times $10^{-8}$ pb to the WIMP-nucleon cross-section.
• ### The NAIAD experiment for WIMP searches at Boulby mine and recent results(hep-ex/0301039)

Jan. 31, 2003 hep-ex
The NAIAD experiment (NaI Advanced Detector) for WIMP dark matter searches at Boulby mine (UK) is described. The detector consists of an array of encapsulated and unencapsulated NaI(Tl) crystals with high light yield. Six crystals are collecting data at present. Data accumulated by four of them (10.6 kg x year exposure) have been used to set upper limits on the WIMP-nucleon spin-independent and WIMP-proton spin-dependent cross-sections. Pulse shape analysis has been applied to discriminate between nuclear recoils, as may be caused by WIMP interactions, and electron recoils due to gamma background. Various calibrations of crystals are presented.
• ### Study and suppression of anomalous fast events in inorganic scintillators for dark matter searches(hep-ex/0109013)

Sept. 12, 2001 astro-ph, hep-ex
The status of dark matter searches with inorganic scintillator detectors at Boulby mine is reviewed and the results of tests with a CsI(Tl) crystal are presented. The objectives of the latter experiment were to study anomalous fast events previously observed and to identify ways to remove this background. Clear indications were found that these events were due to surface contamination of crystals by alphas, probably from radon decay. A new array of unencapsulated NaI(Tl) crystals immersed either in liquid paraffin or pure nitrogen atmosphere is under construction at Boulby. Such an approach allows complete control of the surface of the crystals and the ability to remove any surface contamination. First data from the unencapsulated NaI(Tl) do not show the presence of anomalous fast events.


text:
Kattis

# Heliocentric

Nicolaus Copernicus, born in Toruń in the Kingdom of Poland in 1473, was the first to develop a view of the universe which placed the Sun, rather than the Earth, at the center of the orbiting planets. Copernicus viewed each planet as revolving in a circular orbit with the Sun as the common center of each circle. This new model, which was later improved by many other astronomers, made it much simpler to understand and predict the motions of the planets. Pictured below is his rendering of the planetary orbits.

Consider two of the planets in Copernicus’ orbital system: Earth and Mars. Assume the Earth orbits the Sun in exactly $365$ Earth days, and Mars orbits the Sun in exactly $687$ Earth days. Thus the Earth’s orbit starts at day $0$ and continues to day $364$, and then starts over at day $0$. Mars orbits similarly, but on a $687$ day time scale. We would like to find out how long it will take until both planets are on day $0$ of their orbits simultanously. Write a program that can determine this.

## Input

Input consists of multiple test cases, at most $10$. Each test case is described by a single line containing two integers $0 \leq e < 365$ and $0 \leq m < 687$. These indicate which days Earth and Mars are at their respective orbits.

## Output

For each case, display the case number (starting at $1$ and incrementing for each case) followed by the smallest number of days until the two planets will both be on day $0$ of their orbits. Follow the format of the sample output.

Sample Input 1 Sample Output 1
0 0
364 686
360 682
0 1
1 0

Case 1: 0
Case 2: 1
Case 3: 5
Case 4: 239075
Case 5: 11679


text:
입력 큐 방식의 ATM 스위치용 면적 효율적인 스케줄러 연구

• Published : 2005.06.01
• 81 0

Abstract

Currently the research on input-queued ATM switches is one of the most active research fields. Many achievements have been made in the research on scheduling algorithms for input-queued ATM switches and also applied in commerce. The scheduling algorithms have the characteristics of improving throughput, satisfying QoS requirements and providing service fairly. In this paper, we studied on an implementation of scheduler which arbitrates the input-queued ATM switches efficiently and swiftly. The proposed scheduler approximately provides $100\%$ throughput for scheduling. The proposed algorithm completes the arbitration for N-port VOQ switch with 4-iterative matching. Also the proposed algorithm has a merit for implementing the scheduling algorithm with 1/2 area compared to that of iSLIP scheduling algorithm which is widely used. The performance of the proposed scheduling algorithm is superior to that of iSLIP in 4-iterative matching.

Keywords

ATM Switch;Scheduler;VOQ;iSLIP;Throughput


text:
# 37 Somers’ D

Somers’ $$D$$ has an asymptotically $$Normal$$ Distribution . It may take any value between -1 and 1. It is used to measure classification agreement between a predictor and outcome variable.

Somers’ $$D$$ is related to a form of a concordance index. Concrodance in measured between 0 and 1 and can effectively be calculated by rescaling Somers’ $$D$$. The rescaling can be accomplished by:

$C = \frac{D+1}{2}$

## 37.1 Theorems for Somers’ $$D$$

### 37.1.1 Theorem: Distribution of Somers’ Derived Concordance

Let $$D \sim$$ Normal$$(\mu, \sigma^2)$$. Then $$C \sim$$ Normal $$(\frac{\mu+1}{2},\frac{\sigma^2}{4})$$.

Proof:

$D \sim Normal(\mu,\sigma^2) \Rightarrow (D+1) \sim Normal(\mu+1,\sigma^2) \\ (D+1) \sim Normal(\mu+1,\sigma^2) \Rightarrow \frac{D+1}{2} \sim Normal(\frac{\mu+1}{2}, \frac{\sigma^2}{4})$

By definition, $$C=\frac{D+1}{2}$$, so $$C \sim Normal(\frac{\mu+1}{2},\frac{\sigma^2}{4})$$.

Note: when the dependent variable is a binary response, the Concordance Index is equal to the area under the Receiver Operator Characteristic (ROC) curve, or AUC.


text:
# Arrays with two different types of indices

Is there a way of having arrays which have, so to speak, two different depths $m,n$? From the point of view of memory usage, it would be the same as an array of depth $m+n$, but I would like to obtain and treat the two depths and the respective dimension lists separately.

To use a mathematical analogy: a tensor (in geometry) of type $(1,2)$ is different than a tensor of type $(0,3)$, it has the same number of components, but the operations defined on the two differ.

How can I do this in Mathematica? Is there such a thing as a "doubly-deep" array? Or can I make a data structure, C-like, in which there is the actual array, plus a couple of int variables to keep track of the two different depths?

Update: Here is an example. Let $X$, $Y$, $Z$ be binary sets (= of 2 elements each). A transition matrix is a matrix whose rows sum to one. A transition matrix $A:X\times Y\to Z$ and a transition matrix $B:X\to Y\times Z$ would be then cubical arrays with the same number of entries (8), same depths (3) and dimensions (2,2,2), but different normalization. In particular: $$\sum_{x,y}A(x,y,z)=1 \quad\forall z\;,$$ but: $$\sum_{x}B(x,y,z)=1 \quad\forall y,z\;.$$ For example I would like to define a command, say "CheckNormal", that checks if $A$ and $B$ are correctly normalized. But the normalizations differ. It's as if $A$ had "depth" (2,1), and "dimensions" ((2,2),(2)), and $B$ had depth (1,2), and dimensions ((2),(2,2)). In both cases, I want the sums to be executed only over the first set of indices, and I would like that information (= how many indices are in the first set) to be encoded in $A$ and $B$ (not in the function CheckNormal).
• ArrayReshape[ ]? – Dr. belisarius Oct 6 '15 at 14:16
• Could you give us a practical example of the structure of an array that would fit your requirements? ArrayReshape as suggested by @belisarius is not limited to two dimensions... – MarcoB Oct 6 '15 at 14:37
• Transpose works in any number of dimensions, and allows any permutation of the different levels. – bill s Oct 6 '15 at 14:57
• My feeling is that the best way to implement this is via the operations on the arrays, not in the arrays themselves; you would need different operations (CheckNormalTypeA, CheckNormalTypeB). Alternatively, use customs Heads typeA and tybeB that wrap your (equal-dimensional) arrays, and then overload the definition of CheckNormal using something like CheckNormal[a_typeA] := ..., etc. However, it certainly seems like ArrayReshape is the way to go, based on your ((2,2),(2) to ((2),(2,2)) example. – march Oct 6 '15 at 15:24


text:
## AC. classical analysis and odes – Alternative characterization of floquet multipliers: Floquet theory

Given an autonomous ode $$dot {x} = f (x)$$ in $$mathbb {R} ^ n$$ which has a periodic solution period-p $$bar x (t)$$, the so-called variational equation can be used on $$bar x$$ to study its stability. This equation satisfies begin {align} dot {y} (t) = A (t) y end {align}, where $$A (t) = D_xf ( bar x (t))$$.

Now the typical definition of Floquet multipliers $$lambda$$ is that they are the values e. of the time flow map-p U (p) of the variational equation, that is, of the matrix / operator U (p) where U (t) satisfies the variational equation, with $$U (0) = I_ {n times n}$$. The exponents of the floquet $$mu$$ then they are defined as $$frac {1} {p} log { lambda}$$.

Apparently, an alternative definition can be given starting with the exponents. Here one defines $$mu$$ as the eigenvalues of the operator $$L (x) (t) = ( frac {d} {dt} -A (t)) x (t)$$ in the space of the p-periodic functions. And then multipliers are defined analogously as $$lambda = e ^ {- µp}$$.

I am looking for proof that both definitions are the same (mod some signs if necessary).

## harmonic analysis – classical singular integral operator

I am working on a problem related to the Biot-Savart law in fluid dynamics. I found a singular integral theorem that is closely related to my research.

Assume that $$K (x)$$ is a Calderón-Zygmund nucleus in $$mathbb {R} ^ {3}$$ Y $$f$$ it's a satisfying smooth function
$$begin {equation} | f (x) | leq frac {1} {(1 + r) ^ {a}} quad text {para} quad 0
Y
$$begin {equation} | nabla f (x) | leq frac {1} {(1 + r) ^ {b}} quad text {para} quad 0
where $$r = sqrt {x_ {1} ^ {2} + x_ {2} ^ {2}}$$. It decomposes only in horizontal directions.

Define $$Tf (x) = int K (x-y) f (y) dy$$. So there is a constant $$c_ {0}$$ such that
$$begin {equation} | Tf (x) | leq frac {c_ {0}} {(1 + r) ^ {d}}, end {equation}$$
where $$d = min {a, b }$$.

My questions:
1. Someone suggested to me that this theorem could be improved. Since it is a point or $$L ^ { infty}$$ estimate the singular integral that was not covered by any existing theory. Is it possible to demonstrate something like this? $$d = frac {a + b} {2}$$ which will help my project a lot.

1. One can change the second condition or add something new like decomposition of $$nabla ^ {2} f$$.

I am not an expert in harmonic analysis. Any advice is welcome. Thank you!

## classical analysis and classical odes: limit of a Fourier coefficient of a non-negative periodic function in terms of its form \$ L ^ 2 \$

This question is motivated by the previous MO question: Show that \$ ( sum_ {k = 1} ^ {n} x_ {k} cos {k}) ^ 2 + ( sum_ {k = 1} ^ {n} x_ {k} sin {k}) ^ 2 le (2+ frac {n} {4}) sum_ {k = 1} ^ {n} x ^ 2_ {k} \$.
It is a clean asymptotic version of that question.

Leave $$f$$ be a non-negative, periodic function with period $$1$$and square integrable in $${ Bbb R} / { Bbb Z}$$. It is true that
$$| { widehat f} (1) | ^ 2 = Big | int_0 ^ 1 f (x) e ^ {- 2 pi ix} dx Big | ^ 2 le frac 14 int_0 ^ 1 f (x) ^ 2 dx ?$$
Equality is achieved, for example, when $$f (x) = max (0, cos (2 pi x))$$.

Note that $$| widehat f (1) | = | widehat f (-1) |$$ and from $$f$$ it is not negative $$| widehat f (1) | le widehat f (0)$$. Thus
$$int_0 ^ 1 f (x) ^ 2 dx = sum_n | widehat f (n) | ^ 2 ge 3 | widehat f (1) | ^ 2,$$
so that the estimate is maintained with $$1/3$$ instead of $$1/4$$. There is a lot of room to improve this argument, and with a more careful application of Bessel's inequality I could get the constant $$1/4 + 1/4 pi$$. But the alleged inequality looks very clean, and I wonder if (i) is true!, (Ii) is known in some context, and (iii) (hopefully) has an elegant proof?

## gr.group theory – Conjugation in simple finite classical groups

Leave $$G_n (q) = mathrm {PSL} _n (q), mathrm {PSU} _n (q), mathrm {PSp} _ {2n} (q)$$, … be a simple classic group. Consider the natural inlay $$G_ {n-1} (q) subset G_n (q)$$. I would greatly appreciate it if you have an argument or a counterexample for the following:

Claim: yes $$x, y in G_ {n-1} (q)$$ such that $$x ^ T = y$$ for some $$T in mathrm {Aut} (G_n (q))$$, then there $$t in mathrm {Aut} (G_ {n-1} (q))$$ such that $$x ^ t = y$$.

## Predictors of linear neuronal branches, exponential classical predictors, in resources?

Wikipedia says:

The main advantage of the neural predictor is its ability to exploit long stories while only requiring linear growth of resources. Classic predictors require exponential growth of resources.

What is the reason for this?

## classical mechanics – Stretch elasticity in terms of main stretches

Suppose we have an indifferent isotropic function
$$W: GL _ + (3) a (0, infty)$$, where $$GL _ + (3)$$ denotes the set of all real $$(3 for 3)$$-matrices with positive determinant.
We can write $$W (F)$$ in terms of the main tranches (i.e. singular values) of $$F$$. More specifically, there is a function
$$f: (0, infty) ^ 3 a (0, infty)$$
such that
$$W (F) = f ( lambda_1 (F), lambda_2 (F), lambda_3 (F)),$$
where $$lambda_1 (F) geq lambda_2 (F) geq lambda_3 (F) geq 0$$ are the singular values of $$F$$.
Assume that $$W$$ Y $$f$$ they are soft I want to write the elastic tensor. $$frac { partial ^ 2 W} { partial F ^ 2}$$ in terms of $$f$$ Y $$lambda_1, lambda_2, lambda_3$$.

My ansatz is as follows: symmetry of $$frac { partial ^ 2 W} { partial F ^ 2}$$ reduce the degrees of freedom from 81 to 45. In addition, each rotation $$R in SO (3)$$ can be written exclusively as a product
$$R = R_z ( alpha_3) R_y ( alpha_2) R_x ( alpha_1),$$
where $$R_w ( alpha_i) in SO (3)$$ with $$w in {x, y, z }, i in {1,2,3 },$$ denotes rotation around the $$w$$-axis by angle $$alpha_i$$. By framework of indifference and isotropy we have for each matrix $$F in GL _ + (3)$$
$$W (F) = W (R_z ( alpha_6) R_y ( alpha_5) R_x ( alpha_4) F R_z ( alpha_3) R_y ( alpha_2) R_x ( alpha_1))$$
for each $$alpha_1, dots, alpha_6 in (0.2 pi)$$.
In particular,
$$0 = frac { partial} { partial alpha_i} W (R_z ( alpha_6) R_y ( alpha_5) R_x ( alpha_4) F R_z ( alpha_3) R_y ( alpha_2) R_x ( alpha_1))$$
for each $$i in {1, points, 6 }$$. This relationship produces an additional reduction in the degrees of freedom of $$frac { partial ^ 2 W} { partial F ^ 2}$$. However, I am not sure how to continue from here. The resulting linear system seems to be very complicated and I suspect there is a more efficient way to determine all the inputs of $$frac { partial ^ 2 W} { partial F ^ 2}$$ in terms of $$f, lambda_1, lambda_2, lambda_3$$.

by $$(3 for 2)$$-Matrices the answer to my question was presented by Pipkin in this document: https://academic.oup.com/imamat/article-abstract/36/1/85/762621?redirectedFrom=fulltext
The result is a very compact expression. Unfortunately, there are no details of the calculation provided.

Hence my question: Can anyone tell me how to calculate $$frac { partial ^ 2 W} { partial F ^ 2}$$ in terms of $$f, lambda_1, lambda_2, lambda_3$$ (or how to improve / simplify my previous ansatz)? Or does anyone know any literature where you can find the desired result?

Note: I posted this question on math.stackexchange.com a few months ago, but it received very little attention:
https://math.stackexchange.com/questions/3421016/elasticity-tensor-in-terms-of-principal-stretches

## Does Abstrac Algebra use classical logic?

I didn't know there was something called classical logic. If there is a monetary logic, does the book "Dummit's Abstract Algebra, Foote" use classical logic?

## Process: What would be the difference between classical and quantum computers?

I'm not sure that this is the right place for this question (that's why I think it's for tags), but if not, can anyone say which site is?

Recently, as any of you know, Google achieved quantum supremacy. That is, they built a quantum computer that performed the work given approximately 1.5 billion so fast.

Although they are millions or more;) times faster in the execution of programs (the programming is done here in principle in the same way as in the classic computers, or not?) The condition under which you can use a quality control it's very different. You (maybe very far in the future, if Nature still exists) cannot make them very small and portable, for example.

Will the type of programs, in other words, the jobs that will be sorted, for example, be different? I guess so due to the fact that quality control is superfast in testing millions (or even more) different combinations of any type of object (such as a random combination of bits, as in the case of the Google experiment). I heard that quality controls can be used in meteorology, but (as a secondary question) how is there a question about the combinations? In more general terms, for what type of work are quality controls designed or programmed?

Does anyone have more thoughts on this?

## ag algebraic geometry: derived categories and classical theorems in homological algebra

So far I have studied a fundamental part of the theory of derived categories, for example, the existence of derived functors, the "composition of derived functors", etc.

Now I have some questions about derived functors in the sense of derived category theory.

(one) Are categorical derivative functors universal derivatives in the classical sense?
Leave $$mathscr {A, B}$$ be two abelian categories, $$f: mathscr {A} to mathscr {B}$$ an exact left functor, and suppose that $$mathscr {A}$$ You have enough injection.
Then there is "the" right derived functor $$mathbb {R} ^ + f: D ^ + ( mathscr {A}) to D ( mathscr {B})$$ from $$f$$,
And it is $$i$$-th cohomology of an object $$X$$ in $$mathscr {A}$$ (considering as the complex that has $$X$$ to $$0$$-th grade) is the classic $$R ^ yes (X)$$.
So $${H ^ i ( mathbb {R} ^ + f (X)) } _ i$$ it is universal, in the sense of Hartshorne's AG, chapter III, that is, for each $$delta$$-functors $${g ^ i } _ i$$ from $$mathscr {A}$$ to $$mathscr {B}$$ (i.e., a collection of additive functors that satisfy the following condition: for each exact sequence it cuts $$0 a X a Y a Z a 0$$ in $$mathscr {A}$$, there is the "connection map" $$g ^ iZ to g i + 1} X$$, doing the exact long sequence.), if we have a natural transformation $$f to g ^ 0$$, there is a unique natural transformation $$R ^ if to g ^ i$$.
Is there now a categorical interruption derived from this phenomenon?
That is, for such $${g ^ i }$$ Y $$f to g ^ 0$$there is $$delta$$-functor $$g: D ^ + ( mathscr {A}) a D ( mathscr {B})$$ (such that for each $$X in mathscr {A}$$, $$H ^ i g (X) = g ^ i (X)$$) Y $$mathscr {Q} f to g mathscr {Q}$$?
($$mathscr {Q}$$ is the location functor).
If so, then by universality (in the derived categorical sense), we have $$mathbb {R} ^ + f to g$$.
(I read this post, but it seems to be a little different from my question).

(2) Can we display the "Grothendieck Tohoku" easily using the derived category?
This theorem says that, in particular, for a $$delta$$-functor $${g ^ i }$$Yeah $$g ^ i (I) = 0$$ for each $$i gt 0$$ and each injectable object $$I$$, so this is universal, that is, $$g ^ i cong R ^ i g ^ 0$$.
If (1) is true, then I believe that this theorem can be translated as follows:

Leave $${g ^ i }$$ be a $$delta$$-functor and $$g: D ^ + ( mathscr {A}) a D ( mathscr {B})$$ be "morphism" as in (1).
Yes $$g ^ i (I) = 0$$ for each $$i$$ and injective $$I in mathscr {A}$$, then $$g$$ is the right derived functor of $$g ^ 0: K ^ + ( mathscr {A}) a K ( mathscr {B})$$.

Is this true?

(3) How can we use derived derived categorical functors to show propositions around spectral sequences?
I am studying categories derived from "Waste and duality" of Hartshorne.
In this text, the author says "What used to be a spectral sequence is now simply a composition of functors. And, of course, one can retrieve the old spectral sequence …" (see observations after Proposition 5.4.)
I think the author means that we can show "all" the propositions that the spectral sequence argument used to show using derived categories.
For example:

leave $$mathscr {A, B, C}$$ be abelian categories, $$f: mathscr {A} a mathscr {B}, g: mathscr {B} a mathscr {C}$$ left exact functors, and suppose that $$mathscr {A, B}$$ has enough injectables and that $$f$$ take each injectable object of $$mathscr {A}$$ yet $$g$$– acyclic object.
Leave $$X in mathscr {A}$$.
Yes $$R ^ if (X) = 0$$ for each $$i gt 0$$, then $$R ^ n (gf) (X) cong (R ^ ng) (f (X))$$.
(This is obvious. I could show it.)

b) More generally, in the situation of (a), if $$R ^ ifX = 0$$ for $$0 lt i lt q$$, then there is an exact sequence $$0 a R ^ qg (f (X)) a R ^ q (gf) X a g R ^ q f X$$.

c) Leave $$f: X a Y$$ be a morphism of appropriate schemes on a field, $$mathscr {F}$$ a coherent sheaf in $$X$$.
So $$chi ( mathscr {F}) = sum_p (-1) ^ p chi (R ^ p f_ * mathscr {F})$$.

d) Leave $$f: X a Y$$ be a morpshim of schemes, and $$mathscr {F}$$ a bundle of modules in $$X$$.
Suppose for everyone $$q$$, $$dim operatorname {supp} R ^ qf _ * mathscr {F} = 0$$.
So $$H ^ 0 (Y, R ^ nf _ * mathscr {F}) cong H ^ n (X, mathscr {F})$$.
(This proposition is used in Mumford's Abelian varieties, $$S$$8, theorem1.)

(All propositions are trivial if we use the Grothendieck spectral sequence).

I think there are many of these propositions related to the Grothendieck spectral sequence, but if I understand these (a) ~ (d), it seems similar to show any other type proposition.

Related publication: this

Finally,
(4)Easier test of classical homological propositions
I have heard that we can show Kunneth's formula more easily using derived categories.
I want to know such propositions.
Would you give me references?
I also want references to categorical evidence derived from cohomology and base change theorems (see III.12 of Hartshorne & # 39; s AG or here.
The subsequent statement is too abstract for me.
I prefer Hartshorne's concrete statement).

Thank you!

## Is there any non-relativized separation between a class of quantum complexity and a classical one?

I am familiar with the results of the relativized separation for BPP-BQP, BQP-PH and NPC-BQP. I am also aware that, p. The factoring is not believed to be in BPP, it has not been tested and, therefore, we are not close to demonstrating BQP! = BPP.

My question is, do we have any true, theoretical and non-relativized proof that quantum computers are "superior" to classical ones in any specific problem? Where here, I define superior to include any type of superiority of runtime complexity, for example, a quadratic improvement would qualify in this regard.

I would expect Grover's algorithm to qualify for this criterion, but despite being supposedly "obvious", I am not sure if it has been shown that classical computers cannot solve it also in sqrt (n) time, in a case model black (that is, not relativized).