Musings on physics in D&D [Archive] - Wizards Community

Musings on physics in D&D [Archive] - Wizards Community

Post/Author/DateTime Post
SoAnIs
07-09-07, 10:45 AM I may have some of this wrong, I'm not a physics major. Just going off of what I do know. I'm trying to avoid doing all the hard math to figure out everything that breaks here, and also to keep it in layman's terms. Also, I know that every time you bring Real Physics into D&D Pun-Pun kills a puppy, but I don't like dogs anyway, so here let's all make puppy pie.

Tau = sqrt((1/(1-(v^2/c^2))))
mass due to acceleration = 1/tau -1

First, assume an Arcane Nova outputting lesser Celerity. This allows a character to achieve infinite speed. The character may either be moving faster than the speed of light, taking an infinite amount of energy to do so (maybe), or may be moving at the speed of light and still taking an infinite amount of energy to do so but breaking things somewhat differently.

If the speed of light is infinite, then the Tau factor for ALL other (non-infinite) velocities is infinitely close to 1. This means that there is no time dilation, no mass change, and no length change due to acceleration. Since there is no mass change there is not an infinite amount of energy needed to reach any given finite speed. This means that any non-infinite speed can be achieved by simple constant acceleration. Good news for the Spelljammers! This also means that travelers over great distances, weather via teleportation magic or other methods do not have to account for time dilation, as it does not exist (unless they travel at infinite velocity, at which point time stops and they can't slow down or ever act again, since time has stopped (well, until the universe they are in ends, externally, at which point they may be destroyed, at that time, though they will still exist at previous times, which are the same time, to them.). If Teleportation spells are truly instantaneous, then all teleportation magic should therefore result in character destruction. Also, D&D is not Lorentz invariant.

Now, since the Arcane Nova requires an infinite amount of energy (to accelerate a character to infinite velocity, the speed of light, limits that character's tau factor to 0, which limits their mass towards infinity. When they hit infinite velocity their mass becomes undefined, but it gets arbitrarily close, which is good enough for this argument.) there must either be an infinite amount of energy in the universe, the universe must not be an Isolated (or even Closed) system, or the First Law of thermodynamics must not work. Because the First law fails (the Laws of Thermodynamics only work on Isolated systems with finite energy) then work can be done to decrease the entropy of the universe continually without limit, so the Second and Third laws also fail. Perpetual motion is possible in D&D, with clear implications for power generation. Absolute zero can also be achieved.

Because it is possible to travel at the speed of light, causality ceases to work. Events can precede their causes. If you can find a way to stop your movement at a later round (though later rounds don't exist, see below) (contingency, perhaps?) then you can, via the stopped time effect, exist at all points in time simultaneously. Because of this you can use the Arcane Nova Lesser Celerity to travel back or forward in time as much as you want.

Infinite Velocity and Free Will
arXiv:quant-ph/0604079v1 (http://arxiv.org/abs/quant-ph/0604079v1)
The Conway-Kochen proof of the free will theorem (above), proves that if Free Will exists for any being, it must exist for the universe as a whole, and if it does not exist for the universe (and every particle thereof) it must not exist for anything. The lack of a finite maximum speed at which information can travel allows for Free Will without universal free will. This is very important from a philosophical perspective within D&D.

The Arcane Novaing character's color will shift from red through blue into the X rays and down into gamma rays, eventually emitting infinite energy, instantly destroying everything within its light-cone. Since light has infinite velocity, using an Arcane Nova of Lesser Celerity instantly destroys the universe. Because of the break in causality, it destroys the universe at all points in time, including before you cast the spell. This is a good way to kill a campaign setting.

Because the character achieves infinite mass and an infinitely small volume the character becomes a black hole with an event horizon that is infinitely large. The entire universe is destroyed as it is sucked into the black hole. Time stops as this occurs, due to gravitational time dilation, but that is a minor concern as time also ceases to exist, along with everything else. This is still a good way to kill a campaign setting, and should work on energy-immune creatures like Pun Pun. Also, all light bends into the black hole. The character absorbs everything, seeing everything in the universe at once. This may have some effect on knowledge checks, though without a universe they are likely less than useful. All time-space will be absorbed into the black hole, ending the universe. Because of the infinite energy emission, a Big Bang event will occur, creating a new universe (specifically, the energy emission is hawking radiation, the black hole instantly converts all its mass into energy and evaporates to nothing. Some of that energy will become matter and antimatter spontaneously, and since it's all in one place, BOOM. (well, a very, very high probability of BOOM, though the resultant point in phase-space COULD stay still...)) If you want to switch campaign settings in a violent, dramatic manner, this may be just the thing you need.

Ok, it's almost 8 AM and I've been up all night, showing that a character can easily nuke the universe (in yet another way!) is good enough for now.
Lyinginbedmon
07-09-07, 07:30 PM The First Law of Magic: Magic is unaffected by physics, but may affect them.

If you want to violently change campaign settings, cast Reality Maelstrom and fudge the destination to some far-off locale in the Plane of Shadow.
SoAnIs
07-09-07, 10:01 PM Yes, this simply involves a bit of magic that eliminates quite a bit of physics, along with the rest of the universe the magic was cast in.
Callix
07-09-07, 10:46 PM D&D is physically impossible. So what? There's only so much physics in the RAW, and places where the RAW make no physics sense (falling speeds). So physics says an infinite action loop would destroy the universe. It would too, if the Arcane Nova loop was repeated an infinite number of times. But it wouldn't be. The loop would be voluntarily broken when there were no more targets for 7th level or lower spells the caster wanted to cast. Then their velocity would be retroactively calculable, and would not be infinite.
SoAnIs
07-10-07, 01:20 AM Unless the caster wants to cast infinite lesser celerity on itself.

Really, the point of the thread is to point out a somewhat amusing consequence of infinite movement speed and a philosophical consequence of not having a finite speed at which information can travel (disproof of the Free Will Theorem and some causality issues.) Other effects (prepared-action-pass-a-bucket cannon (with or without walrus and theft,) vacuum cannon, etc) may be able to achieve infinite movespeed, and thus destroy everything as well.

If I were GMing a game, I'd just say speed of light is fixed and the same as in the Real World and that the character gets close and then the loop breaks. Or I might use such a loop to make a new campaign setting with the characters rising from the ashes of the old (somehow,) like the Le Shay in the ELH.

As for the Free Will Theorem, that's only important if you are RPing theology and need to have characters/NPCs wondering about the nature of Free Will in the universe.
EDIT: Since people will say this never happens, I had a situation where my (Lawful Good aligned) players used the following reasoning after apprehending a thief:
If he has free will, we must punish him, as he is responsible for his actions and therefore deserves punishment. Punishment may also serve as a deterrent.
If he does not have free will, we must determine weather or not punishment will definitely force him to never commit such an act again, and use the appropriate punishment. Punishment can ONLY serve as a deterrent, it is never Just to punish a being without free will for its actions for any other reason. If an inappropriate or excessive punishment is needed, is it ethical to allow him to go free? He merely stole a magic set of armour from the duke, that does not warrant killing him, but if we must kill him to prevent further thefts, must we do so? Or must we accept that such a killing would be equivalent to murder, and allow him a jail sentence and then let him go free, knowing that he will steal again and be unable to stop doing so. For that matter, is any punishment ethical, as he cannot change his own actions?

With the Free Will Theorem, if one thing has free will, everything has it. There is no need for an independent determination on the presence or absence of free will in any given being, as all beings have free will to some degree. If any being did not have free will, no being would have free will. Without the free will theorem the presence or absence of free will in any given being must be evaluated separately, vastly increasing the burden LG characters face in fighting crime in a truly Just and Good manner.
The Arcane Nova -> Lesser Celerity loop makes the activities of Judicial officials in D&D much harder. Some players may actually choose to roleplay such philosophy.

It's a cute trick. Use it, ignore it, whatever, but it's something to be aware of: Infinite velocity is bad. Free Will may be important.
psly4mne
07-10-07, 11:07 PM The universe of D&D is not a relativistic and/or quantum universe. End of story.
Think0028
07-12-07, 01:24 AM We can illustrate that simply with the good ol' fashioned twin paradox of relativity. Only rules about aging say you get older by one year every year, no stipulations about speed and nearby gravitational fields.

(Note that I say this with a relatively small knowledge of relativity, so I may be wrong/incomplete in my statement. The twin paradox part still stands, though.)
Callix
07-12-07, 05:22 PM But you age 1 year/apparent year on planes with different time traits, so why wouldn't you age 1 year/apparent year in a near-light velocity craft. Note also the twin paradox is not a paradox. The General Theory resolves any outstanding issues. The trick is that in order to come back, the ship has to accelerate. Acceleration slows the accelerating frame, just as gravity slows high clocks. So the twin in the ship is actually younger. This is not a paradox. He just got to "now" via a short cut.
Think0028
07-12-07, 07:30 PM But you age 1 year/apparent year on planes with different time traits, so why wouldn't you age 1 year/apparent year in a near-light velocity craft. Note also the twin paradox is not a paradox. The General Theory resolves any outstanding issues. The trick is that in order to come back, the ship has to accelerate. Acceleration slows the accelerating frame, just as gravity slows high clocks. So the twin in the ship is actually younger. This is not a paradox. He just got to "now" via a short cut.

1) Twin paradox is how it's universally recognized. What was I gonna call it? The twin non-paradox?

2) It says you age differently on other planes, not other velocities. We can construct an explanation with relativity, true, but that doesn't prove that it is based on relativity. I could say since the sun glows, it's full of glowing unicorns, because if it was full of glowing unicorns, it would glow. That doesn't prove anything, though.
Lyinginbedmon
07-12-07, 07:37 PM 2) It says you age differently on other planes, not other velocities. We can construct an explanation with relativity, true, but that doesn't prove that it is based on relativity. I could say since the sun glows, it's full of glowing unicorns, because if it was full of glowing unicorns, it would glow. That doesn't prove anything, though.

In actuality the moon glows because it has been irradiated by secret nuclear tests carried out by the Gnome Confederacy, funded by the Hello Goblin alliance, in an effort to defend the planet from the evil forces of the Half-Orc Empire and it's ally the Halfling Nation.

That's why it's made of cheese, they've had to replace the rocks somehow!
Diplominator
07-16-07, 03:25 AM The universe of D&D is not a relativistic and/or quantum universe. End of story.

Huh. I wonder if it is even possible to create a physics-following set of rules. Well, other than the real world. RPG rules. It might be kind of fun, actually. Figuring out ranges with forces and angles and flight times and such. Magic could be expressed as abilities that modified laws of physics.

Dang. That gives me a great idea for a class.
BillTheManiac
07-16-07, 11:37 AM Newtonian-ly infinite speed would still lead to infinite energy. E=1/2mv^2. How does that destroy the universe?
Lyinginbedmon
07-16-07, 12:35 PM Well, in theory, the enegry would be released in light, heat, ionising radiation...I can certainly see how infinite energy could destroy it (In fact, be definition it probably should) but I'm not 100% sure on whether this is correct or not.
Think0028
07-16-07, 10:16 PM Huh. I wonder if it is even possible to create a physics-following set of rules. Well, other than the real world. RPG rules. It might be kind of fun, actually. Figuring out ranges with forces and angles and flight times and such. Magic could be expressed as abilities that modified laws of physics.

Dang. That gives me a great idea for a class.

Gravity is gonna be a bit of a *****, and you might have a problem with acceleration of characters on foot. Aside from that, you just need really, really detailed rules, and calculus if you want to be really accurate.
Diplominator
07-20-07, 09:11 PM So, like I mentioned, this thread inspired me. Combine that with my love of ToB, and you get this (http://boards1.wizards.com/showthread.php?p=13141431#post13141431). Check it out. Or...y'know, don't.

Post/Author/DateTime	Post
SoAnIs 07-09-07, 10:45 AM	I may have some of this wrong, I'm not a physics major. Just going off of what I do know. I'm trying to avoid doing all the hard math to figure out everything that breaks here, and also to keep it in layman's terms. Also, I know that every time you bring Real Physics into D&D Pun-Pun kills a puppy, but I don't like dogs anyway, so here let's all make puppy pie. Tau = sqrt((1/(1-(v^2/c^2)))) mass due to acceleration = 1/tau -1 First, assume an Arcane Nova outputting lesser Celerity. This allows a character to achieve infinite speed. The character may either be moving faster than the speed of light, taking an infinite amount of energy to do so (maybe), or may be moving at the speed of light and still taking an infinite amount of energy to do so but breaking things somewhat differently. If the speed of light is infinite, then the Tau factor for ALL other (non-infinite) velocities is infinitely close to 1. This means that there is no time dilation, no mass change, and no length change due to acceleration. Since there is no mass change there is not an infinite amount of energy needed to reach any given finite speed. This means that any non-infinite speed can be achieved by simple constant acceleration. Good news for the Spelljammers! This also means that travelers over great distances, weather via teleportation magic or other methods do not have to account for time dilation, as it does not exist (unless they travel at infinite velocity, at which point time stops and they can't slow down or ever act again, since time has stopped (well, until the universe they are in ends, externally, at which point they may be destroyed, at that time, though they will still exist at previous times, which are the same time, to them.). If Teleportation spells are truly instantaneous, then all teleportation magic should therefore result in character destruction. Also, D&D is not Lorentz invariant. Now, since the Arcane Nova requires an infinite amount of energy (to accelerate a character to infinite velocity, the speed of light, limits that character's tau factor to 0, which limits their mass towards infinity. When they hit infinite velocity their mass becomes undefined, but it gets arbitrarily close, which is good enough for this argument.) there must either be an infinite amount of energy in the universe, the universe must not be an Isolated (or even Closed) system, or the First Law of thermodynamics must not work. Because the First law fails (the Laws of Thermodynamics only work on Isolated systems with finite energy) then work can be done to decrease the entropy of the universe continually without limit, so the Second and Third laws also fail. Perpetual motion is possible in D&D, with clear implications for power generation. Absolute zero can also be achieved. Because it is possible to travel at the speed of light, causality ceases to work. Events can precede their causes. If you can find a way to stop your movement at a later round (though later rounds don't exist, see below) (contingency, perhaps?) then you can, via the stopped time effect, exist at all points in time simultaneously. Because of this you can use the Arcane Nova Lesser Celerity to travel back or forward in time as much as you want. Infinite Velocity and Free Will arXiv:quant-ph/0604079v1 (http://arxiv.org/abs/quant-ph/0604079v1) The Conway-Kochen proof of the free will theorem (above), proves that if Free Will exists for any being, it must exist for the universe as a whole, and if it does not exist for the universe (and every particle thereof) it must not exist for anything. The lack of a finite maximum speed at which information can travel allows for Free Will without universal free will. This is very important from a philosophical perspective within D&D. The Arcane Novaing character's color will shift from red through blue into the X rays and down into gamma rays, eventually emitting infinite energy, instantly destroying everything within its light-cone. Since light has infinite velocity, using an Arcane Nova of Lesser Celerity instantly destroys the universe. Because of the break in causality, it destroys the universe at all points in time, including before you cast the spell. This is a good way to kill a campaign setting. Because the character achieves infinite mass and an infinitely small volume the character becomes a black hole with an event horizon that is infinitely large. The entire universe is destroyed as it is sucked into the black hole. Time stops as this occurs, due to gravitational time dilation, but that is a minor concern as time also ceases to exist, along with everything else. This is still a good way to kill a campaign setting, and should work on energy-immune creatures like Pun Pun. Also, all light bends into the black hole. The character absorbs everything, seeing everything in the universe at once. This may have some effect on knowledge checks, though without a universe they are likely less than useful. All time-space will be absorbed into the black hole, ending the universe. Because of the infinite energy emission, a Big Bang event will occur, creating a new universe (specifically, the energy emission is hawking radiation, the black hole instantly converts all its mass into energy and evaporates to nothing. Some of that energy will become matter and antimatter spontaneously, and since it's all in one place, BOOM. (well, a very, very high probability of BOOM, though the resultant point in phase-space COULD stay still...)) If you want to switch campaign settings in a violent, dramatic manner, this may be just the thing you need. Ok, it's almost 8 AM and I've been up all night, showing that a character can easily nuke the universe (in yet another way!) is good enough for now.
Lyinginbedmon 07-09-07, 07:30 PM	The First Law of Magic: Magic is unaffected by physics, but may affect them. If you want to violently change campaign settings, cast Reality Maelstrom and fudge the destination to some far-off locale in the Plane of Shadow.
SoAnIs 07-09-07, 10:01 PM	Yes, this simply involves a bit of magic that eliminates quite a bit of physics, along with the rest of the universe the magic was cast in.
Callix 07-09-07, 10:46 PM	D&D is physically impossible. So what? There's only so much physics in the RAW, and places where the RAW make no physics sense (falling speeds). So physics says an infinite action loop would destroy the universe. It would too, if the Arcane Nova loop was repeated an infinite number of times. But it wouldn't be. The loop would be voluntarily broken when there were no more targets for 7th level or lower spells the caster wanted to cast. Then their velocity would be retroactively calculable, and would not be infinite.
SoAnIs 07-10-07, 01:20 AM	Unless the caster wants to cast infinite lesser celerity on itself. Really, the point of the thread is to point out a somewhat amusing consequence of infinite movement speed and a philosophical consequence of not having a finite speed at which information can travel (disproof of the Free Will Theorem and some causality issues.) Other effects (prepared-action-pass-a-bucket cannon (with or without walrus and theft,) vacuum cannon, etc) may be able to achieve infinite movespeed, and thus destroy everything as well. If I were GMing a game, I'd just say speed of light is fixed and the same as in the Real World and that the character gets close and then the loop breaks. Or I might use such a loop to make a new campaign setting with the characters rising from the ashes of the old (somehow,) like the Le Shay in the ELH. As for the Free Will Theorem, that's only important if you are RPing theology and need to have characters/NPCs wondering about the nature of Free Will in the universe. EDIT: Since people will say this never happens, I had a situation where my (Lawful Good aligned) players used the following reasoning after apprehending a thief: If he has free will, we must punish him, as he is responsible for his actions and therefore deserves punishment. Punishment may also serve as a deterrent. If he does not have free will, we must determine weather or not punishment will definitely force him to never commit such an act again, and use the appropriate punishment. Punishment can ONLY serve as a deterrent, it is never Just to punish a being without free will for its actions for any other reason. If an inappropriate or excessive punishment is needed, is it ethical to allow him to go free? He merely stole a magic set of armour from the duke, that does not warrant killing him, but if we must kill him to prevent further thefts, must we do so? Or must we accept that such a killing would be equivalent to murder, and allow him a jail sentence and then let him go free, knowing that he will steal again and be unable to stop doing so. For that matter, is any punishment ethical, as he cannot change his own actions? With the Free Will Theorem, if one thing has free will, everything has it. There is no need for an independent determination on the presence or absence of free will in any given being, as all beings have free will to some degree. If any being did not have free will, no being would have free will. Without the free will theorem the presence or absence of free will in any given being must be evaluated separately, vastly increasing the burden LG characters face in fighting crime in a truly Just and Good manner. The Arcane Nova -> Lesser Celerity loop makes the activities of Judicial officials in D&D much harder. Some players may actually choose to roleplay such philosophy. It's a cute trick. Use it, ignore it, whatever, but it's something to be aware of: Infinite velocity is bad. Free Will may be important.
psly4mne 07-10-07, 11:07 PM	The universe of D&D is not a relativistic and/or quantum universe. End of story.
Think0028 07-12-07, 01:24 AM	We can illustrate that simply with the good ol' fashioned twin paradox of relativity. Only rules about aging say you get older by one year every year, no stipulations about speed and nearby gravitational fields. (Note that I say this with a relatively small knowledge of relativity, so I may be wrong/incomplete in my statement. The twin paradox part still stands, though.)
Callix 07-12-07, 05:22 PM	But you age 1 year/apparent year on planes with different time traits, so why wouldn't you age 1 year/apparent year in a near-light velocity craft. Note also the twin paradox is not a paradox. The General Theory resolves any outstanding issues. The trick is that in order to come back, the ship has to accelerate. Acceleration slows the accelerating frame, just as gravity slows high clocks. So the twin in the ship is actually younger. This is not a paradox. He just got to "now" via a short cut.
Think0028 07-12-07, 07:30 PM	But you age 1 year/apparent year on planes with different time traits, so why wouldn't you age 1 year/apparent year in a near-light velocity craft. Note also the twin paradox is not a paradox. The General Theory resolves any outstanding issues. The trick is that in order to come back, the ship has to accelerate. Acceleration slows the accelerating frame, just as gravity slows high clocks. So the twin in the ship is actually younger. This is not a paradox. He just got to "now" via a short cut. 1) Twin paradox is how it's universally recognized. What was I gonna call it? The twin non-paradox? 2) It says you age differently on other planes, not other velocities. We can construct an explanation with relativity, true, but that doesn't prove that it is based on relativity. I could say since the sun glows, it's full of glowing unicorns, because if it was full of glowing unicorns, it would glow. That doesn't prove anything, though.
Lyinginbedmon 07-12-07, 07:37 PM	2) It says you age differently on other planes, not other velocities. We can construct an explanation with relativity, true, but that doesn't prove that it is based on relativity. I could say since the sun glows, it's full of glowing unicorns, because if it was full of glowing unicorns, it would glow. That doesn't prove anything, though. In actuality the moon glows because it has been irradiated by secret nuclear tests carried out by the Gnome Confederacy, funded by the Hello Goblin alliance, in an effort to defend the planet from the evil forces of the Half-Orc Empire and it's ally the Halfling Nation. That's why it's made of cheese, they've had to replace the rocks somehow!
Diplominator 07-16-07, 03:25 AM	The universe of D&D is not a relativistic and/or quantum universe. End of story. Huh. I wonder if it is even possible to create a physics-following set of rules. Well, other than the real world. RPG rules. It might be kind of fun, actually. Figuring out ranges with forces and angles and flight times and such. Magic could be expressed as abilities that modified laws of physics. Dang. That gives me a great idea for a class.
BillTheManiac 07-16-07, 11:37 AM	Newtonian-ly infinite speed would still lead to infinite energy. E=1/2mv^2. How does that destroy the universe?
Lyinginbedmon 07-16-07, 12:35 PM	Well, in theory, the enegry would be released in light, heat, ionising radiation...I can certainly see how infinite energy could destroy it (In fact, be definition it probably should) but I'm not 100% sure on whether this is correct or not.
Think0028 07-16-07, 10:16 PM	Huh. I wonder if it is even possible to create a physics-following set of rules. Well, other than the real world. RPG rules. It might be kind of fun, actually. Figuring out ranges with forces and angles and flight times and such. Magic could be expressed as abilities that modified laws of physics. Dang. That gives me a great idea for a class. Gravity is gonna be a bit of a *****, and you might have a problem with acceleration of characters on foot. Aside from that, you just need really, really detailed rules, and calculus if you want to be really accurate.
Diplominator 07-20-07, 09:11 PM	So, like I mentioned, this thread inspired me. Combine that with my love of ToB, and you get this (http://boards1.wizards.com/showthread.php?p=13141431#post13141431). Check it out. Or...y'know, don't.