Quantum Mechanics and D&D's Sphere of Annihilation

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Ghouly0104

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I was just contemplating the effect that the Sphere of Annihilation (SoA) would have on our current formulation of Quantum Mechanics (because "It's just Magic, deal with it" isn't good enough for me, and I'm crazy), and I think there are some serious problems here.

In order to produce wave functions in quantum mechanics you need to do an integral over all space in order to normalize the function. (Translation: If you have a particle and you look at the whole universe and ask "Is it here?" you get yes with a probability of 100%)

Herein lies the problem, the SoA is a ball of nothing that takes objects and pulls them out of the multiverse into nothing. So you can't say "The particle I'm looking at has a 100% chance of being in the universe" because it could interact with a SoA and become nothing.

Anyone else have any thoughts on the matter, or other Fantasy/Science things that you think are not reconcilable?
 

Lazarus Long

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You could just say that rather than being destroyed, the sphere breaks matter down into its constituent particles, scattering them through the cosmos.

Unless I misunderstood the question. It's late.
 

Ghouly0104

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I was going under the assumption that the rules represented the actual state of the universe, and that when it says that things that go into a sphere of annihilation go into the void beyond the universe that they are just gone.
 

RavingPenguin

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Lazarus Long said:
You could just say that rather than being destroyed, the sphere breaks matter down into its constituent particles, scattering them through the cosmos.

Unless I misunderstood the question. It's late.
I know nothing of the SoA, but the man said nothingness, meaning your theory has just been completely shot.

OT: Approaching this from a physics stand point, the priciple would have to operate on magic. I believe the second law of thermodynamics states that matter can be neither created nor destroyed (or was it energy? I forget. But seeing as the two are one in the same it works) It is physically impossible to destroy matter. Therefore magic would have to drive the SoA.
 

Ghouly0104

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RavingPenguin said:
OT: Approaching this from a physics stand point, the priciple would have to operate on magic. I believe the second law of thermodynamics states that matter can be neither created nor destroyed (or was it energy? I forget. But seeing as the two are one in the same it works) It is physically impossible to destroy matter. Therefore magic would have to drive the SoA.
This is true only if you assume that the SoA doesn't shoot down thermodynamics in its current state as well, which it does. In fact thermodynamics falls down for a similar reason as quantum, you have probability distributions that can include the SoA and thus fall apart as any state that involves the SoA collapses into nothingness.
 

geizr

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For what you are talking about, you can't just use an integral over space. You also have to use and integral over time, in which case you would also have to introduce a Heavy-side step function over time to enforce the cut-off point at which the object is no longer existent. The result is that you would still get 100% probability of existence, but only over a bounded extent in time. For times beyond that extent, you would get 0% probability.
 

Ghouly0104

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That might just work, but how would you incorporate that time dependence into the proabability distribution without having knowledge of when the object will interact with the SoA? That is, wouldn't you have to know what the probability distribution is first in order to find the expected value of the time of disintegration and thus solve for the probability distribution?
 

geizr

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Ghouly0104 said:
That might just work, but how would you incorporate that time dependence into the proabability distribution without having knowledge of when the object will interact with the SoA? That is, wouldn't you have to know what the probability distribution is first in order to find the expected value of the time of disintegration and thus solve for the probability distribution?
The Heavy-side step function is the component of the probability distribution that takes care of when the object contacts the SoA and becomes non-existent. To make a simple example, you take a normal time-dependent gaussian wave-packet and multiply it by a Heavy-side step function over time that has the appropriate cut-off. This is your total probability distribution over space-time, which you would then perform a full space-time integral over. The Heavy-side step function cuts the probability distribution to zero for all times after the point of contact.
 

Therumancer

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Well, I know this probably isn't what you wanted to hear, but the very idea of having what amounts to a mentally directed portable singularity is by it's very nature scientifically implausible.

The entire discussion exists because your dealing with something created for a game where reality is altered by the will of spellcasters.

Where IRL we have discussions about science vs. faith, in D&D with enough power you can like open a portal to the home of the gods, walk up to the deity of your choice and say "howdy doood". I don't recommend it within the context of the setting, but the point
is you can do it.

Overall though D&D was inspired by the writings of guys like Michael Moorcock. In Moorcock's writings magic is the stuff of chaos, and technology the stuff of order. The power of each basically waxes and wanes depending on which force holds more sway in a given dimension. So thus in a heavily order based universe it could be argued that a Sphere of Annibilation couldn't exist and might not work based on very closely observed principles of science and physics.

-

At any rate all rambling aside, even if you wanted to argue it within current principles doesn't "Chaos Theory" allow for things that can't even be "explained" by quantum mechanics (which to me seems more like a philsophy than a science, but then again I'm not a physicist)? :)

>>>----Therumancer--->
 

Ghouly0104

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Therumancer said:
Well, I know this probably isn't what you wanted to hear, but the very idea of having what amounts to a mentally directed portable singularity is by it's very nature scientifically implausible.

The entire discussion exists because your dealing with something created for a game where reality is altered by the will of spellcasters.

Where IRL we have discussions about science vs. faith, in D&D with enough power you can like open a portal to the home of the gods, walk up to the deity of your choice and say "howdy doood". I don't recommend it within the context of the setting, but the point
is you can do it.

Overall though D&D was inspired by the writings of guys like Michael Moorcock. In Moorcock's writings magic is the stuff of chaos, and technology the stuff of order. The power of each basically waxes and wanes depending on which force holds more sway in a given dimension. So thus in a heavily order based universe it could be argued that a Sphere of Annibilation couldn't exist and might not work based on very closely observed principles of science and physics.

-

At any rate all rambling aside, even if you wanted to argue it within current principles doesn't "Chaos Theory" allow for things that can't even be "explained" by quantum mechanics (which to me seems more like a philsophy than a science, but then again I'm not a physicist)? :)

>>>----Therumancer--->
You make a fine point, but because of the limits set on gods in D&D (even they look up to Ao who doesn't talk to anyone) there is still room to make these same sorts of arguments on science vs. magic.

What really interests me with this sort of discussion is the attempt to fit something to the given data (which is what science is in reality) as a kind of thought experiment. It is also useful in universe crossover battle discussions (the lowest form of nerd argument I'm sure, but fun nonetheless).

Mostly I just like asking "How does that work?" and since I have my own world to use as a yardstick, that is where I start.
 

NeutralDrow

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Mr.Tea said:
And how do black holes figure in Quantum Mechanics? That's how I've always considered the Sphere of Annihilation in D&D (Minus the ungodly mass and gravitational pull of a black hole, of course)...
You mean Spheres of Annihilation eventually decay due to Hawking Radiation?
 

Ghouly0104

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geizr said:
Ghouly0104 said:
That might just work, but how would you incorporate that time dependence into the proabability distribution without having knowledge of when the object will interact with the SoA? That is, wouldn't you have to know what the probability distribution is first in order to find the expected value of the time of disintegration and thus solve for the probability distribution?
The Heavy-side step function is the component of the probability distribution that takes care of when the object contacts the SoA and becomes non-existent. To make a simple example, you take a normal time-dependent gaussian wave-packet and multiply it by a Heavy-side step function over time that has the appropriate cut-off. This is your total probability distribution over space-time, which you would then perform a full space-time integral over. The Heavy-side step function cuts the probability distribution to zero for all times after the point of contact.
How do you solve Shcrodingers Equation at the cutoff point? It seems like
i*hbar*(dPsi)/(dt)= H Psi
means that you need a continuous time derivative, which a step function violates, or would we have to assume that when the rules say "instantly" they mean "an arbitrarily short but finite amount of time"? Also, how do we deal with the Laplacian in the Hamiltonian Operator? Can we just throw continuity out the window?

Also, when can it be said that the wave function of an object has interacted with the SoA to a degree that we would call "touching"? Can we, in good conscience, make an arbitrary decision on this point? Oh, the humanity of it all!
 

Flying-Emu

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This thread is beyond my knowledge.

Buncha wizards and their magicks. Give me a stout rod and a connection to a Divine Spirit anyday.

Anyway, if we operate off of the idea that black holes are "wormholes" of sorts to differing dimensions/spaces, couldn't the SoA be a miniature black hole with its gravitational radius confined by some means?
 

Therumancer

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You make a fine point, but because of the limits set on gods in D&D (even they look up to Ao who doesn't talk to anyone) there is still room to make these same sorts of arguments on science vs. magic.

What really interests me with this sort of discussion is the attempt to fit something to the given data (which is what science is in reality) as a kind of thought experiment. It is also useful in universe crossover battle discussions (the lowest form of nerd argument I'm sure, but fun nonetheless).

Mostly I just like asking "How does that work?" and since I have my own world to use as a yardstick, that is where I start.[/quote]

Well, when it comes to Ao it's a little more complicated than that. If you remember at the end of the old Avatar Trilogy Ao reports to his boss just to "blow your mind" however I seem to remember that they covered this basic heirarchy in the old basic D&D Immortals Rules which seemed to be used as a basis. The basic idea being that if your running a campaign where the characters have ascended to Godhood, there needs to be things bigger than they are (requiring 'parties') and the various universal level threats that they apparently contend with in the backround. There were levels above your basic "god" pretty much as described in the books. It's been a long time though.

That said when your dealing with something like a Sphere Of Annihilation it's more or less just a magical item which a deity (or sufficiently powerful wizard, though easier for gods) can create. I seem to also remember a couple of them control Spheres like puppets to use as a weapon in Avatar form (but I haven't used D&D in any form for a while so I can't remember which ones). The exact process hasn't ever been put down I don't believe, but at a guess it would involve basically either creating a small portal to one of the planes of Entropy or taking a piece of that so called "planestuff" and crafting it into a sphere, and then adding whatever it takes to move the portal/blob of planestuff mentally. The whole entropy concept coming from again very old D&D Immortals rules, where the gods empowered by entropy are apparently trying to bring about the cessation of reality. This leading to deities of various alignments with regular spheres of influance fighting them. Again this isn't scientifically plausible, but uses a magical logic.

As far as the specifics of the game system, well a lot of it was based heavily on vintage sword and sorcery. One of the problems even with 1st Edition AD&D was that it worked under the assumption that anyone playing was familiar with the basic concepts taken from those books. Leading to debates and misinterpetations on how terms like "Lawful" were intended to be interpeted since the whole idea of Law/Neutral/Chaos Good/Neutral/Evil (just the former in basic D&D) was based on Michael Moorcock's books. Likewise spell memorization was taken from Jack Vance and it was assumed you were familiar with his writings for some of the explanations of why things worked that way. Of course things have moved away from this over time, but still you can see signs of the foundations from which it was all built. I get a sort of wry amusement from people who write essays about why things work the way they do in D&D (such as the basis for old spell memorization systems) without realizing where the idea was ripped off from for example. Or lengthy descriptions (some actually in the core books nowadays) of how alignments are supposed to be interpeted, with no understanding of Moorcock's multiverse or how it was intended (ie ripped off). D&D was very much intended as a plaything for fans of the fantasy of the era in which it was created.

At any rate, trying to figure things out by current physics is kind of pointless. By the same token applying real physics to magical effects (of which I've seen various examples of over the years) usually tends to limit mages heavily, especially in most adenturing groups where they have a hard enough time already (very weak at low levels, and at high levels everything that they can fight is usually so loaded with magic resistance or has such good saving throws due to it's level that you pretty much need a gimmick for everything to begin with).

If you start going into Spelljammer as Canon, I mean even the way "space" works is entirely differant. Your solar system could actually turn out to be being juggled by a giant jester or something equally bizzare, bringing to mind images out of some acid inspired cartoon like the old "Yellow Submarine" or whatever. :p

I suppose if you use OLDER definitions of things like say putting Blackmoor in the past of the D&D Known Worlds, and then using "normal" space and the whole plotline involving "The City Of The Gods" (ie Crashed Aliens in a space ship), or the 2E "Tale Of The Comet" campaign, you could start argueing for some scientific elements. But even then, magic is all about altering reality, not playing by it's rules, which is what puts your fantasy adventurers into those scenarios as a major force (even the non-spellcasters being loaded with magical gear by the intended level).
 

geizr

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Ghouly0104 said:
geizr said:
Ghouly0104 said:
That might just work, but how would you incorporate that time dependence into the proabability distribution without having knowledge of when the object will interact with the SoA? That is, wouldn't you have to know what the probability distribution is first in order to find the expected value of the time of disintegration and thus solve for the probability distribution?
The Heavy-side step function is the component of the probability distribution that takes care of when the object contacts the SoA and becomes non-existent. To make a simple example, you take a normal time-dependent gaussian wave-packet and multiply it by a Heavy-side step function over time that has the appropriate cut-off. This is your total probability distribution over space-time, which you would then perform a full space-time integral over. The Heavy-side step function cuts the probability distribution to zero for all times after the point of contact.
How do you solve Shcrodingers Equation at the cutoff point? It seems like
i*hbar*(dPsi)/(dt)= H Psi
means that you need a continuous time derivative, which a step function violates, or would we have to assume that when the rules say "instantly" they mean "an arbitrarily short but finite amount of time"? Also, how do we deal with the Laplacian in the Hamiltonian Operator? Can we just throw continuity out the window?

Also, when can it be said that the wave function of an object has interacted with the SoA to a degree that we would call "touching"? Can we, in good conscience, make an arbitrary decision on this point? Oh, the humanity of it all!
Your questioning is definitely along the right lines as I realized, after posting, that I had oversimplified the problem(it was too late at night for me to correct my mistake). You would, in fact, have to start from the Schrodinger equation and directly solve for it to obtain the correct wave function. In solving the Schodinger equation, you would have to account for the fact there is a region in space over which the wave function is zero; then you would have to match across the boundary of that region in order to maintain continuity. There are many mathematical techniques for doing this, my favorite of which is the Green's function. However, there may be further issues involving the continuity equation, d(rho)/dt + div(J) = 0, as this is a case where there is current flowing out of the universe, something that, to my knowledge, doesn't normally occur in a real physical situation, through the bounding surface of the SoA.



Therumancer said:
At any rate, trying to figure things out by current physics is kind of pointless. By the same token applying real physics to magical effects (of which I've seen various examples of over the years) usually tends to limit mages heavily, especially in most adenturing groups where they have a hard enough time already (very weak at low levels, and at high levels everything that they can fight is usually so loaded with magic resistance or has such good saving throws due to it's level that you pretty much need a gimmick for everything to begin with).
A friend and I were discussing this very thing at one point and came to the conclusion that magic is a breaking of the natural laws or rules of the universe. Any time you apply rigorous rules to magic such to make it appear derivable from known natural laws or to be some kind of super-set from which the natural laws can be derived, it ceases to be magic and becomes mere science and technology. At this point, a new level develops that we call magic that simply breaks those rules. Our conclusion is that no matter what you do, in order to call it magic, it has to break the rules in order for it to work properly as magic. This may be why mages, sorcerers and wizards can get overpowering; everyone else is stuck obeying the rules while the mages, sorcerers, and wizards do not.
 

ace_of_something

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This thread is possibly one of the nerdiest things I have ever seen.
and with that a quote from a favorite web satirest

It's always nice when a magic item's name is also its description and warning label. Nobody mistakes a sphere of annihilation for an ice cream maker, unless one of your players likes to play a half-orc with an intelligence of three just for the comic possibilities. At that point a ball of absolute destruction is the least of your concerns. According to the rules if you touch the sphere only your deity can bring you back to life, but if your deity cared that much about you, it probably would have imbued you with enough sense not to touch the damn sphere - Lore Sjöberg
 

Agent Face

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I'm glad that there are people who do more constructive things on the internet other than watch porn. Well done.

Now, if you'd excuse me...