• Member Since 28th Mar, 2016
  • offline last seen Last Thursday

Needling Haystacks


Doctor of Physics and sometime Adjunct Professor. Warning: thinking required.

T

This story is a sequel to The Many Deaths of Twilight Sparkle


Twilight has discovered that Alicorns can 'respawn' when they die. Think of the possibilities! She quickly assembles a crack team of scientists* to test the frontiers of this new power.

*IE whoever was willing to respond to a letter asking for 'suggestions of practical uses for the death of an alicorn'.

An unofficial sequel to "The Many Deaths of Twilight Sparkle".

Rated T for references to death and suicide, though in context those things don't really happen.
Featured on 7/6/2020! W00t!
And featured again on 7/20/2020!

Chapters (5)
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Comments ( 155 )

Yo, this is a dope intro. I'll be following this story with interest. :twilightsmile:

10316837
Thanks! Means a lot coming from OP.

Honestly it would really need a full editing run to be a 'proper' story, but as I'm just tryin' to be silly and teach some scientific method (and maybe a little real-world science) as I go, I'm only doing a spelling/grammar pass.

"I'm assuming this has something to do with the pile of bodies outside your castle?" Sunburst said

Hmmm... probably not.

Spike walked into the lab, carrying a large pile of scrolls. he handed one to Starlight

He

"Just put the rest behind the chalkboard," Twilight said. She smiled sheepishly. "I was expecting more ponies.

Missing quotation mark.

"I don't think so," Sunburst mused, still absentmindedly stroking his beard

I think there can a said instead of mused. Stroking a bread is neat way to indicate that he is musing.

10316850
Ay, nothing wrong with silly little stories.

10316876
Valid points. I'll make those changes.

I really like the word 'mused', but I suppose it isn't terribly helpful in that particular sentence. Back to my quest to work that word into as many stories as possible!

Hey. If respawning is relatively costless, Twi could open up a restaurant.
Hot fresh in Ponyville; "Twilights' Teriyaki".
Best (and only) alicorn meat on equs.

Do you only real issue is that there isn’t more of it

*In the presence of a strong magical field, the traditional Einstein relationship that prevails on Earth ceases to apply. While the full equation is more complicated, that given here is generally a 'close enough' approximation. The 'h' here is the magical 'weight' of an object (typically given in milli-thaums), while 'k' is a natural constant much like the speed of light. Working out k's units is left as an exercise to the reader.

E = mc2 + hk3

Joules = kg.m2/s2 + mT.??3

kg.m2/s2 == mT.??3

To make sense in terms of dimensions mT would be Kg.s/m so that ?? could be (m/s)3

kg.m2/s2 == (kg.s/m).(m/s)3

At least I think that's how it works. 'k' is therefore a velocity, the speed of magic?

(m/s)3 = m3/s3

m/s2 is acceleration, a change of velocity with time. m/s3 is jerk, a change of acceleration with time. So would that mean that k3 is the change of acceleration of magical energy over a volume?

And Celestia only knows how the unholy concept of 'mass time per distance' translates to magical mass equivalence in millithaums.

(Come on, you make a comment like that, you know someone on this site is going to be a big enough nerdlinger to take a stab at it.) :twilightsheepish:

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I think there can a said instead of mused. Stroking a bread is neat way to indicate that he is musing.

Now I'm thinking of a super villian behind sabotaging the MMMM, sitting in a chair pettling a white loaf while Pinkie Pie is strapped to a kitchen table, surrounded by stacks of cake and other treats she can't reach.

"So Bread Finger Roll, you expect me to talk?"

"No Miss Pie, I expect you to diet!"

10316901
Just in this sentence it kinda feels redundant that you write mused and after that, he is stroking his beard. Kinda like you have both telling and showing. On the other hand is entirely possible I'm just looking at it too much.

10316938
I THINK I'll get to that in the next part... of course I thought I'd get to it in the next part and realized the experiments wouldn't logically yield the outcome to get to taht without more data, so we'll see.

10316951
I'll be coming back to this once I've gotten a more serious one-shot out of the way. This and the Flim-Flam one are sort of my palate-cleansers: Silly things I can just have fun with.

10316958
As it's only one occurance it's not THAT bad, but it doesn't really add anything so I took it out.


10316957
You can't assume mTh (T is Tesla so I use Th for Thaum) has units of kg*s/m, so you have to leave it as-is. Thus we have:

(J/mTh)^(1/3) = ? You can expand out the Joules if you like but whether that makes sense depends on context.

Strictly speaking it's possible the thaumic mass and inertial mass are related in some way other than this equation, but I haven't thought it out that far. I'm currently operating on the principle that magic is a fifth field-force. However when writing this I thought "You know, that's not quite exotic enough... what if it coupled to energy differently than inertial mass?" So basically the idea here is that there is both kinetic mass and energy and magic mass and energy, but the two energies behave more or less the same with respect to the principle of relativity. However, the masses don't.

Now, I don't think the math on that could BOTH produce a recognizeable universe AND account for the strength of the magic field in Equestria (I haven't worked that out), but it certainly looks neat.

:rainbowlaugh:Bruh now we have more content for Straighttothepoint.

For energy suggestion, see post in prior story.

As for Magic itself, one suggestion, if neutrinos are dark matter, then magic is Dark energy, and is the Octonion Eulerian vector in 5 space, using the fact that Fourier maths utelises complex values to represent scalars in time due to relative phase variations.

Also, its very useful that very recently a spacial planetary object has been observed with a projected density thats 100 times greater than that of water. If Dark energy has collected in the gravity well, enough to counteract it through the planets atmosphere, but not much greater radius, it depends on how far the dark matter equivalent imaginary gravity field extends, if the same inverse square, then the field is the sdame, the core just doesnt collapse as expected.. if its a faster fall off, then orbital parameters can be under far higher gravitational effects?

Still trying to work out if the maths works, but QM=GR(GR) seems to mathematically give the effect of renormalisation, that is, planck mass is self causing gravitational energy object, has no rest mass as we understand it.

An infinite energy singularity physically cannot exist,e ven in approximation, as it would be infinite energy and gravitational field, which would be a black hole of infinite radius, and the current event horizon of the universe is approximately the mass event horizon?

At least Twilight hasnt tried going into Gamer, Horror levels of alicorn sub fatal regeneration, such as the one that Everyone avoids because its a totally OP get out clause, that of Mitosis. :yay:

Hey, your story took the original's place in the cleanbox. Congrats on the feature, dude!

"Write it down! Write it down!" Twilight urged. Starlight found the pen anchored to the table the book sat on and scribbled down the reading.

“Write that down. Write the down!”
Oh the memes.

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Saw the response in other thread, wish you'd have reproduced it here. Hmmm, that's a valid point. Hadn't consider solar conversion rate or accretion rate. Let's do the math here A little math shows that neglecting the thaumic mass you'd get 4.27 x 10^9 kg, whereas your average pony is closer to 10^2 kg. That said, the energy would have to be yoinked from a distance, as at Earth you only get the equivalent of 2 g of mass per second, and with a respawn time of approximately 50 s, you'd thus only have 100 g. Just not enough, and anyway that's spread over the whole Earth. It also draws the question of whether this requires all Alicorns to have a link to the sun, and whether their sun is even a star as we know it, but that's a whole thing.

The accretion rate is around 1.4 x 10^6 kg/year for Earth, so let's assume the same here. That rate comes to 2.6 kg/minute. Too low to match the measured rate (a pony is 40-ish kg), so we are still at a loss. This does neatly solve the problem of the mass accumulation, which I hadn't actually gotten to yet, since so long as Twilight doesn't respawn above once every 20 minutes on average, she is not adding significant mass to the system compared to other mass accretion. Either way, we still have the problem of where the mass-energy is ultimately coming from. Even yoinking the energy at a distance, the body still has to be put into an ordered configuration somehow. Actually that gives me an idea for that but I'll get around to it in a later chapter.

Alright,the rest of this is a bit outside of my usual field but I'll do some research here and see if I can figure out what you're suggesting. ...Assuming it is a serious suggestion, it gets hard to tell at some point.

As for Magic itself, one suggestion, if neutrinos are dark matter, then magic is Dark energy, and is the Octonion Eulerian vector in 5 space, using the fact that Fourier maths utelises complex values to represent scalars in time due to relative phase variations.

I think you're either confusing two different theories here or trying to combine them and not explaining it well. Octonion standard model alterations can describe dark matter using a quaternion deconstruction into gravity and electromagnetism, while Kaluza-Klein theory describes the same phenomena using 5 dimensions. In principle they should be combineable but I'm not familiar enough with them to see the implications of that right off. Possibly because of that I'm not clear how a Fourier anlysis relates, though I can see that it might. Got a paper or something to link me to on this?

Also dark matter consists of more than your usual neutrinos. Sterile or Majorana neutrinos may contribute more, but you should specify those when referring to them: they aren't what most people think of when they hear the word neutrino.

And anyway, magic doesn't have the correct properties to be dark energy as we know it. It could enter as the scalar field of the Kaluza-Klein theory I suppose. I'm inclined to think the dark energy angle is a dead end, but I'll respond to the rest.

Also, its very useful that very recently a spacial planetary object has been observed with a projected density thats 100 times greater than that of water. If Dark energy has collected in the gravity well, enough to counteract it through the planets atmosphere, but not much greater radius, it depends on how far the dark matter equivalent imaginary gravity field extends, if the same inverse square, then the field is the sdame, the core just doesnt collapse as expected.. if its a faster fall off, then orbital parameters can be under far higher gravitational effects?

Check your sources on that density. Unless there's an object found within the last 6 months you're referring too, revised data show the densest planet as a 'mere' 26 times the density of water. It's dense, but not so dense as to require new physics.

Again, dark energy or dark matter? I'm a bit unclear. Dark energy, assuming it enters as a cosmological constant, is not per se affected by gravity the way matter is, and so far as it known it doesn't 'clump'. If it did the relative expansion rates of space over distance would vary based on the averaged density viewed along that vector. Space being relatively homogenous, on large scales this would disappear, but I think it would still cause a variation outside the margin of error. Though on the other hand, that margin is pretty large, so I suppose it could be possible within a 5-sigma limit. Still, I'm hesitant to build a theory around this: without such observations there's not that many papers outlining this theory so I'm not sure I can follow it to the degree required.

The imaginary gravity field proposal for dark energy is I THINK what you mean here. If you're using an Octonion the term 'imaginary' stops having its usual meaning, but I suspect that's besides the point. We'd have to assume EITHER dark energy clumps OR that dark matter creates imaginary gravity disproportionately compared to regular matter. Either way we have the same issue mentioned above for a fleshed-out theory, but as a quick-and-dirty approximation your statement is correct. I just don't see what it has to do with the question at hand.

Still trying to work out if the maths works, but QM=GR(GR) seems to mathematically give the effect of renormalisation, that is, planck mass is self causing gravitational energy object, has no rest mass as we understand it.

Ok here I'm lost and I think it might be a language barrier. What's this about the Plank Mass? The rest is a model that exists but I don't see the relation to the rest of the discussion.

An infinite energy singularity physically cannot exist,e ven in approximation, as it would be infinite energy and gravitational field, which would be a black hole of infinite radius, and the current event horizon of the universe is approximately the mass event horizon?

The first part is true (it can't physically exist), the second part is not, and the third might be true but the data is insufficient to say. In any case I'm again not seeing the relevance. FFor the second part, a Schwarzchild black hole only has a true singularity at a point. This does not result in infinite energy and field outside of that point, and if you integrate over space as a whole using the complex time formulation you can then treat any singularities like a pole and more-or-less preserve the math.

I do have to say, I'm not sure if the above is an honest effort from a non-native English speaker or an elaborate prank. Kudos for the effort regardless.

At least Twilight hasnt tried going into Gamer, Horror levels of alicorn sub fatal regeneration, such as the one that Everyone avoids because its a totally OP get out clause, that of Mitosis

Ah so splitting off a separate Twilight? Well respawning rather than regenerating neatly avoids that problem.

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I would be honored.


10317063
...Wow. Think that's my first featured. Feels weird that it's for a silly random piece, but at least it's a Science! one. :P

Working out k's units is left as an exercise to the reader.

This made me laugh out loud. It sounds like a footnote in a bona fide scholarly work, and I would totally try to derive it myself, but I don't know how thaums relate to any other SI unit.

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See other comment: They don't, you have to leave it as Thaums.

That bit was inspired by Terry Pratchett (the definition of a Thaum is from Discworld).

It looks like a scholarly footnote because I'm a teacher and scientist in my day job, so I'm pretty familiar with that style. Especially obtuse textbooks that say things like "it follows naturally" when the result does not follow in any obvious way. That sort of thing has slowed down so many lesson plans and research projects...

10317210
Hey man 75% of my featured stories are silly one shots. The other is also a one shot. That's how it be here.

10317290
...Well this wound up spiraling into a multi-part but I take your meaning. Ironically half the time I struggle to hit 1000 words with one-shots.

***I'm not completely sure that that's correct. It's been awhile since I dealt with trans-finite mathematics in any sort of comprehensive way.

n \rightarrow 2n seems to fit
(for positive whole numbers, obviously)

SRY

10316850
Oh yes, this is so scratching my itch to see more of this and all the implications that would spiral out of it. I liked how you touched on the "quantum immortality" as a potential mechanism too.

Please continue to science the magic horse words.

10317368
When I first wrote that line and accompanying note, before I uploaded it, it looked different. That was actually the example I looked up. But on the infinite sets, n->2n is actually an ordered bijection. It's part of Hilbert's Paradox of the Grand Hotel (https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel). After getting stuck reading up on ordered bijections and set cardinalities I eventually gave up and wrote it like that.


10317388
Actually my immediate example was "The Vat of Acid Episode" from Rick and Morty. I do know about the quantum immortality hypothesis, though.

SRY

10317394
I wondered if that had a Rick and Morty influence to it, the vibe definitely came through with the whole "killing your other selfs bit".

10317394

n->2n is actually an ordered bijection

It doesn't have inverse for odd numbers

Those footnotes give me a scientific-ish vibe.

As a silly pony with no training in thaumaturgy, what if the matter at the respawn point is converted to the matter making up the body? As in, the exact mass of Twilight's body of air is converted. Since air is less dense than fleshy bits, this would cause a dip in air pressure around where she respawns. That's because, to reach the same density air as her body would require a larger volume of air than the volume of her body.

This is what I've always assumed teleportation in the series does. It either disperses air at the destination and leaves a vacuum at the origin, or it swaps the matter between the two locations. That way, if you teleport into a rock or something, you won't get your molecules torn apart. You'd just get stuck in a pony shaped hole.

For how the air is converted to body mass, just blame magic.

Personally if I were Starlight I’d probably be wondering if Twi is getting an endorphin rush or something given the degree of joy she seems to be getting from the act itself.

10317394
In The Vat of Acid Episode, I kinda wondered why nobody mentioned that acid could dissolve everything, but always left the bones intact. Shouldn't it dissolve bones as well?

Reminds me of that Star Trek theory about transportation. The transporter kills you, then makes an exact clone of you somewhere else that just happens to have all your memories.

10317526
We will not talk of how Fimfic stared into that abyss.

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I apologise for the problems, I didnt realise how seriously you were wanting to dig into the required maths etc and what level you were used to working at. In the UK, the education levels are not only different in named level today, they are a lot different today than when I went through them several decades ago. I am a totally native English speaker, just managed, after a lot of years fight, to confuse an expert psych and get certified.

You are also the first pewrson Ive seen who has mentioned Kaluza Kliens 5D equivalence representation between EM and Gravity, before I have. which is one of the things that puzzles me, as its been over a centuary, its the Only thing that even attempts to show a link, and yet it keeps getting lost.

Something that seems to keep being confused, is the difference and relations between physical and mathematical dimentionality. That is, a given physical dimentional region can have far more mathematical dimentions to the numbers describing it, but those mathematical dimentions are just that, descriptions, not physically existant. I first saw this on the Open University, dealing with the navigations matrices for the Voyager spacecraft. They took the rotation matrices in 3 space, and the translation matrices, in 3 space, and showed they were incompatible. But then they added an extra scalar 4th mathematical dimention to the matrices, and showed how the two 3D matrices could be combined in a single mathematical 4D matrix. But it still only described a 3D space. This is what I assumed the KK model did. It took two Quaternion spaces and then combined them in a 5 matrix, that still then only described a 4 Space.

The problem with 4 space is that over the decades, more and more experimental and modeling results have turned up which demand a solution in 4 physical dimentions. The simplest of this is the packing of a crumpled shirt fallen on the floor. The last one I know of, is Hawkings last paper, which although the bituary mentioned the article but not the details, I have to assume used the idea of the Flat Torus. Given it collapses to a toroidal singularity.

The trouble with singularities of objects, is the field energy. The classic one is the energy stored in the electric field of a spherical capacitor, where you keep the charge constant, and let the sphere shrink. Because the field strength increases, the energy of the field increases. Eventually, by the time you reach the classical radius of the electron, the energy of the electric field is equal to the mass energy observed of the electron. If this understanding was correct, then electrons have no mass, only charge energy. If you take the same with a neutral charge object that only has mass, and allow to shrink, its gravitational field energy continues to rise, until by the classical planck radius the mass energy of the gravitational field is enough to create the gravitational field of that mass equivalent. Of course, this is only Newtonion calculus, classical maths and so I Know my models and understanding can be widly and totally wrong. But the models do have to simplyfy to Newton eventually. I dislike myself doing mistakes as divide by zero.

One of the simple mistakes I make, at least compared to everything I currently read, is asking a certain question.

Is the reason nothing can travel faster than the speed of light, the same, or similar to the reason nothing can travel faster than the speed of sound?

As for the Hilbert Hotel and infinities, my favourite takeaway from that is that Hilbert not only used it to describe or demonstrate peculiarities in the understanding between real and mathematical objects, but then could easily demonstrate that the infinite cardinal dimention hotel can be carpeted by a cardinal one single carpet, just by the addition of enough stairs?

Something thats bothered me about teh various definitions of teleportation over the decades, is everyone always aims for absolutel perfection in every single quantum particle in each end. Noones ever gone for, hey, we use data compression in computers, and even used to use procedural generation, lets try working out just how Little data we actually need to copy accross for this to work? That, and even in the time Ive been using computers with hard drives, weve gone from 120 Meg to 12 Terrabyte. Im sure I have a 40 Meg somewhere, MFM thing on a hard card for the Amstrad 1640. So thats a million fold. No, the main thing I find intresting is just how Telepods. Using a shell that has a Bose Einstein Condensate layer. So youre only trying to copy a single quantum particle. Something Im really hoping helps with this, are various articles on the measured temperature of dense plasmas at atmosperic pressure, with drive frequency, several of which include a commercial electron beam welder which uses a magnetically confined argon plasma window to seperate the vaccuum of the electron beam generator and the surrounding atmospheric work space, and a medical wound clearer which uses a cold plasma for sterilisation. It also helps that in atmosphere plasma structures are th basis for a whole range of scifi effects such as forcefields. Both physical and energy affecting versions.

For unicorn horns, this to me looks like a good place to start, especially given the Princess Leia and Teapot tactile holograms at CES a few years ago. Are unicorn horns piezoelectric ELF transcievers?

10317625

Is the reason nothing can travel faster than the speed of light, the same, or similar to the reason nothing can travel faster than the speed of sound?

I would say very different. Especially since there is no known physics to allow for faster than light travel, but sound has never been considered an absolute speed limiter. As I understand it, the speed of light isn't really about light (or photons generally); it is the speed of causality, and then the maths works out that all massless particles travel at the speed of causality.

10317648

But where light speed is the speed of causality for light, the speed of sound is the speed of causality for mass, and thers a lot of laboratory experiements that rely on the close relationship in behaviour between sound and light. I would like to think this also extends to high speed motion, but you have to look Very closely at high speed masses. Thats why I say nothing material travels faster than the speed of sound. Heat.

Asking the real questions, and answering them with solid science and maths. You, my dear doctor, have just earned a new student.

10317681
But mass travels faster than sound all the time; it isn't hard. Electrons bounce around in an electric current at near c. Nutrinos go more than 0.99c pretty much all the time. A whip cracking is a mini sonic boom. Many firearms shoot faster than sound. And as the speed of sound approaches zero in higher and higher atmosphere, it becomes easier and easier to propel rockets into even ground level supersonic speeds through that medium.

In contrast, time itself behaves counter-intuitively near light speed. Objects at different relativistic speeds perceive time differently to each other. There is no analogous behaviour for the speed of sound.

And while we use sound metaphors to describe many of the wave-like behaviours of light, that is not the same as sound and light being similar. Light slows down in denser mediums while sound speeds up, which also means they refract in opposite directions when moving between the same mediums of different density (such as air to glass).
Light also has particle-like behaviours that are very different to sound waves.

This makes me think of Star Scribe's Message in a Bottle story where (spoilered as is a twist later in story)
Equestria turned out to be a ring world with a digital afterlife
In such a world, I could see there being a room with a ridiculously large amount of System Admin(Alicorn) clones, and each gets teleported in every death when Twilight wants to respawn. hence the thaum usage being identical

10317427
That isn't n->2n then I don't think... Again been awhile. Now I do know that the odd integers do not have an ordered bijection with the integers, but I think they do have a bijection that isn't ordered. A quick search shows that there is: https://math.stackexchange.com/questions/2107729/bijection-from-the-set-of-odd-natural-numbers-to-integers
The ordered property is irrelevant for the problem considered here.

10317442
That is a perfect experiment, but it's likely not one the ponies would think of since they teleport all the time. Hence, bringing in Sci Twi in the next chapter.

10317510
Also something that must be tested! And probably: If fatigue and hunger transfer, the hormonal state likely does as well, and when the body is injured it releases endorphins. This is to allow action while experiencing the pain signals. Usually the pain means this doesn't feel good (unless your biology is more sensitive to endorphins than pain signals, hence masochists), but if the pain is gone...


10317514
Depends on the acid. Some acids would dissolve bones more slowly, as the calcium matrix present in bone isn't present elsewhere in the body. It isn't a problem in the second vat, since the onlookers wouldn't know, but the first they should have. And indeed in the episode they start to question why the bones weren't dissolving (though not in those words). It really wasn't a very good plan.


10317728
It would make sense, but that's not the direction I'm planning on going with it. Of course, it's gotten away from me once already.

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Pi Man: I'll respond to you at the end so scroll down for that.

I didnt realise how seriously you were wanting to dig into the required maths etc

You read the story, right? :P Over-analyzing is kinda my jam.

I am a totally native English speaker, just managed, after a lot of years fight, to confuse an expert psych and get certified.

Oops, sorry. My third guess was 'outsider who doesn't know the usual jargon'. My friend PsiStarPsi was the same: took a bit to figure out what he was actually saying. My blog links to his theory on the necessity of 2-dimensional time in "The Cutie Re-mark". Actually it's more convenient to describe it as a 2-D embedding in 3-Space, and it's even possible to make it a 1-D embedding in 3-space, but that's another story.

Also I'm in the US so there are even more variations in what different educational levels are called.

You are also the first pewrson Ive seen who has mentioned Kaluza Kliens 5D equivalence representation between EM and Gravity, before I have. which is one of the things that puzzles me, as its been over a centuary, its the Only thing that even attempts to show a link, and yet it keeps getting lost.

My primary field is EM cascades and resulting effects: Thus far generation of anti-matter and gamma-rays in one project, and DNA damage in another. However I dabble in GR (both undergrad and graduate school advisors were GR people, at least partially), and so have come across the Kaluza-Klein theory before. I was unaware of the apparent symmetry between that and the EM-Gravity octonion break-down until I was researching your comment, and while I'd have to check, it certainly LOOKS like there's something there.
Kaluza-Klein wasn't completely lost. It served as a precursor to string theory. IMO the popular 'M-theory' model strays a bit from Kaluza-Klein's elegance, but that's a judgement call.

Something that seems to keep being confused, is the difference and relations between physical and mathematical dimentionality. That is, a given physical dimentional region can have far more mathematical dimentions to the numbers describing it, but those mathematical dimentions are just that, descriptions, not physically existant. I first saw this on the Open University, dealing with the navigations matrices for the Voyager spacecraft. They took the rotation matrices in 3 space, and the translation matrices, in 3 space, and showed they were incompatible. But then they added an extra scalar 4th mathematical dimention to the matrices, and showed how the two 3D matrices could be combined in a single mathematical 4D matrix. But it still only described a 3D space. This is what I assumed the KK model did. It took two Quaternion spaces and then combined them in a 5 matrix, that still then only described a 4 Space.

It's an extension of the Euler method of representing rotation matrixes by Quaternions. You run into a problem above 5-space because it is provably impossible to compose an algebra using objects past octonions. I don't understand the proof myself, but I'll trust the mathematicians.
The KK model used that as a starting point, but actually had to add a 5th spatial dimension to make it work. It's still a 'physical' dimension in the mathematical sense, not a coordinate one, but as usually presented it leaves ambiguous whether that dimension has any reality. It can be made a mathematical nicety.

The last one I know of, is Hawkings last paper, which although the bituary mentioned the article but not the details, I have to assume used the idea of the Flat Torus. Given it collapses to a toroidal singularity.

I need to find this paper, but not right now as I have lunch cooking. I'll have to get back to you on this one.

The trouble with singularities of objects, is the field energy. The classic one is the energy stored in the electric field of a spherical capacitor, where you keep the charge constant, and let the sphere shrink. Because the field strength increases, the energy of the field increases. Eventually, by the time you reach the classical radius of the electron, the energy of the electric field is equal to the mass energy observed of the electron. If this understanding was correct, then electrons have no mass, only charge energy. If you take the same with a neutral charge object that only has mass, and allow to shrink, its gravitational field energy continues to rise, until by the classical planck radius the mass energy of the gravitational field is enough to create the gravitational field of that mass equivalent. Of course, this is only Newtonion calculus, classical maths and so I Know my models and understanding can be widly and totally wrong. But the models do have to simplyfy to Newton eventually. I dislike myself doing mistakes as divide by zero.

Ooooooh, now I see what you're saying. Well that model of the electron is somewhat controversial as it's not clear how to distinguish it from alternatives. On the graviational end, the difficulty there is that all particles in the standard model at least interact weakly, which complicates things. Then you get into spinors and it becomes a whole thing. To isolate gravity, the model you're describing deals with a theoretical 'sterile neutrino', which is one candidate for dark matter. If they exist, we would expect their mass to be precisely what you describe. The problem is they are really hard to detect.

Regardless I also don't think there are physical singularities. I only meant you can avoid some of the mathematical nastiness they cause if you're careful. It's a stop-gap at best.

Is the reason nothing can travel faster than the speed of light, the same, or similar to the reason nothing can travel faster than the speed of sound?

I assume you're referring to Aether Theory. I'll come back to this to address the replies on this specific point.

, but then could easily demonstrate that the infinite cardinal dimention hotel can be carpeted by a cardinal one single carpet, just by the addition of enough stairs?

Not sure why that's a question, but yes that is kind of amusing.

Something thats bothered me about teh various definitions of teleportation over the decades, is everyone always aims for absolutel perfection in every single quantum particle in each end

Because we don't actually know what makes a person themselves. The 'death and clone' problem can theoretically be avoided (see other post that I'm making after this one) by this method, while with compression our current knowledge is inadequate to tell us if that is happening.

Using a shell that has a Bose Einstein Condensate layer. So youre only trying to copy a single quantum particle

That's the trick. You can't actually copy a quantum state precisely: It's Bell's "No Quantum Xerox" theorem. Again I'll address this more in another comment. Already gone on long here and lunch is almost ready.

I'm not sure what the following welder bit is getting at. Is that just for transmitting particle streams without interference?

For unicorn horns, this to me looks like a good place to start, especially given the Princess Leia and Teapot tactile holograms at CES a few years ago. Are unicorn horns piezoelectric ELF transcievers?

I think you linked the wrong article there. That's one's about using VLF for self-driving cars due to the reduction in risk of interference.
From my limited understanding of tactile holograms, though, while they could be such transcievers, that can't be all they are as many magic effects are beyond standard physics. They'd have to also act as magic channelers of some sort.

PiMan: Booster Spice is not explaining himself well here. I think he's referring to luminiferous Aether theory. Of course the classical form has largely fallen out of style. However, certain forms of it are still around. Here light 'waves' the aether, and classically it is the properties of the aether that determine the speed. The fact that it moves at light speed is somewhat coincidental: Different aether properties could make it move slower. The additional assumptions that are therefore required are the main reason it has fallen into disfavor.
It wouldn't affect the other weird things about light speed, but for instance:

In contrast, time itself behaves counter-intuitively near light speed. Objects at different relativistic speeds perceive time differently to each other. There is no analogous behaviour for the speed of sound.

The moniker 'light speed' is a historical relic. Any massless particle (or wave!) transmits at that speed, including gravity waves. It's just that of those objects, light is the easiest to measure the speed of.

There is, however, a modern theory called quantum loop gravity whereby there is a quantum 'foam' that acts much like a lumineferous aether. The properties of this foam determine certain things about spatial curvature, and thus about things like time dilation. Thus they link both those effects and the speed of light to the same thing, removing one objection to the aether theory. I think this is what Booster Spice was referring to. Mind you, there's currently no data supporting this model, but with the detection of gravity waves there is some how that there may be a way to do so in the next 20 years or so.

And lunch is done so I'll respond to the teleportation issue later.

It's not very often that an otherwise silly and hilarious story promotes intellectual comments that would make even Twilight "Egghead" Sparkle proud, and give Rainbow Dash headaches.

Well done!

The many oofs of purple princess pone

10317526
Now this is an interesting discussion. Many discussions of teleportation involve reassembling the same configuration of molecules. This of course overlooks Bell's No Quantum Xerox theory, which shows that it is impossible to precisely copy a quantum stage (under certain assumptions which are pretty reasonable). Now if consciousness has no quantum component at all, this is hardly a limitation, but then we have that the 'received' object is effectively a copy and not the original.

However, Pensrose and Hammerhoff's model of Orchestrated Objective Reduction (https://en.wikipedia.org/wiki/Orchestrated_objective_reduction) would provide an out, if true. It's highly controversial, and may well not be true, but it's still plausible. It was taken up by the Alicization arc of "Sword Art Online", though they didn't get it quite right.

Won't go into the whole thing here, but the upshot of the hypothesis is that consciousness would have a quantum component. It wouldn't be the whole of it, but it doesn't need to be. The quantum component of consciousness would thus be unreplicateable. However, while Bell's theorem demonstrates that you can't replicate a quantum state, you CAN, in principle, transfer it from one particle to another. I'm not actually sure if that's possible in practice but in theory it could be (https://en.wikipedia.org/wiki/Quantum_teleportation). This means that your 'received' person is not a copy but is the exact same as the original.

10317960
Would you really take that risk, though?

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Not with the current state of knowledge. We'd have to both know that consciousness is quantumly encoded and that we could move the complex state from point A to point B without errors. And maybe human testing on the terminally ill whom the transporter could fix. Last part is ethically iffy but that's a whole debate on access to experimental procedures for the terminally ill.

10318065
Fair enough, although I would probably just take the train.

10318065

Trouble is with the demand of unique conciousness, are, neural firing rates, physical complexity, sleep, and vegetative states.

The problem with the idea of continous conciousness is the 1 kHz firing rate of neurons, cameras that have normal frame rates over 100 times faster, and the demonstration of being able to PEEK at the Quantum Kitten without killing it. Effectively freezing it in time, or to me a possible theoretical description of a stasis field.

10317853
Any injection is a bijection between it's domain and it's image.
n \rightarrow 2n map chops countable \mathbb{N} into countable set of disjoint oriented chains (each odd number k starts it's own chain containing numbers k 2^{i}), i.e. does exactly what is required.

10318222
Ah. Yeah that checks out. Told you it's been too long since I had that class.
Sunburst in the story was right, then.

10318143
None of those affect the uniqueness, only the continuity, and I deliberately avoided that because I have no resolution for that issue with the knowledge I have. It is an issue, just not one I have a resolution to either way.

Average neural firing rate I think is like 10 Hz... I guess the kHz is the max rate?

Sharp observers may note I have altered the tags. And changed the rating to teen to match "Many Deaths", but it's the tags that'll give you a bit of a hint as to the next chapter.

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