Definitive Allomantic FTL Theory

[Kurkistan]

Isn't it stated that objects maintain (subjective) speed when passing through the boundary of a time bubble? If we know what the system is like both before and after the transition, it doesn't matter the exact mechanics.

That statement is possible evidence against the possibility of objects partially transiting the boundaries of time bubbles, but does not apply to how it would function if partial transitioning exists. If it is the case that objects, in their entirety, retain their velocity perfectly upon entering/exiting time bubbles, then my own theory does not work. I hold that they do not, as whole objects, maintain their initial velocity. Each constituent part attempts to accelerate/decelerate to its proper velocity in its new space-time, but is still attached to the rest of the object.

So, to summarize, my own theory holds that we do not, in fact, know that objects, in their entirety, maintain the same velocity before and after transitioning. In fact, I hold that some change in velocity is necessary for anything larger than whatever the "minimum transition size" is which does not have exactly equal proportions of it's mass entering and exiting a time bubble.

Edited January 11, 2012 by Kurkistan

[ReaderAt2046]

Very true.

The train is solidly touching the ground/planet, but not really attached. The track, however, might be attached. But there is the other problem that, if the train does not count as "ground," it should do what I described should logically happen to the ground, with the part enclosed in the bubble tearing away from the rest.

One possible way of getting around some of this is if an object can only be in or out of a bubble in terms of time effects, not partway in and partway out. (This has been proposed before.) Think of it with spren. If the planetspren is not sufficiently inside the area of the bubble (which would likely be impossible because of the planet's size), then none of it is affected by the bubble (thus explaining the ground's stability). Same for the traincar; if the traincarspren is not inside the bubble, the traincar is not affected by the bubble (if the Wayne is standing on top, a few items on the ceiling that were inside of but not part of the traincar might be disrupted, but otherwise it wouldn't rip apart. Actually, a few items might be disrupted anyway as Wayne "traded" them for other things.) This would necessitate your spacecraft being constructed so each section would at least mostly fit inside a bubble, and the sections were not so attached as to merge into one spren.

+1 for "traincarspren"

[Musicspren]

+1 for "traincarspren"

Thanks; I do appreciate having upvotespren (or are they reputationspren?).

(Also, my semester has started, so I am, unfortunately, a bit slower to respond to things requiring long posts. Apologies to Kurkistan in particular for the delay.)

[Kurkistan]

Thanks; I do appreciate having upvotespren (or are they reputationspren?).

(Also, my semester has started, so I am, unfortunately, a bit slower to respond to things requiring long posts. Apologies to Kurkistan in particular for the delay.)

No worries. I'll be the same in a week when mine starts up again.

[Satsuoni]

Hm. Well, sorry I am late. Two problems (for simplicity) with the theory:

1. For a part of an object to leave a bubble, part has to enter, losing energy. Also, creating a cadmium bubble lowers the energy of all objects inside ( velocity drop)

2. By your theory, objects leaving bendalloy bubbles will lose energy. I have done the math , and the loss only depends on velocity. Energy drop is bound by zero. This would lead to two unobserved effects: bullets stopping on the border, and air temperature dropping fast (the velocity of air molecules at room temperature is, afaik, faster than a bullet )

[Kurkistan]

Hm. Well, sorry I am late. Two problems (for simplicity) with the theory:

1. For a part of an object to leave a bubble, part has to enter, losing energy. Also, creating a cadmium bubble lowers the energy of all objects inside ( velocity drop)

2. By your theory, objects leaving bendalloy bubbles will lose energy. I have done the math , and the loss only depends on velocity. Energy drop is bound by zero. This would lead to two unobserved effects: bullets stopping on the border, and air temperature dropping fast (the velocity of air molecules at room temperature is, afaik, faster than a bullet )

Better late than never, that's what I always say.

1. If the object is wholly contained within the bubble upon "bubbling", then no part of it need enter at any point, resulting in pure gain. As for lowering the energy of objects inside, this is only a temporary phenomenon which is reversed upon either leaving or dropping the bubble and which we ultimately gain energy from due to differentials as objects exit the bubble.

2. I don't see why you would think bullets should stop completely. Lose some energy, yes, but not stop completely. My head isn't in the math right now, but off the top of my non-mathing head, only an object with infinite velocity would be stopped dead when leaving a bendalloy bubble.

I don't know if I can speak to air temperature, but my hazy understanding is such that, from the perspective inside a cadmium bubble, temperature stays the same while the outside heats up, but any air molecules crossing over will immediately assume the temperature of the proper environment because there are no indissoluble connections to transfer energy between molecules inside and outside of the bubble.

EDIT: Although, you wouldn't know that the other side of the bubble is a different temperature, since you can't meaningfully interact with it. I wonder what a laser thermometer would say if you pointed it at the other side of a bubble, given the weirdness of light's interactions with time bubbles.

Edited January 16, 2012 by Kurkistan

[Satsuoni]

Right... Disregarding for the moment the question of losing energy on bubbling, let's do the math.

OK, the math is relatively simple, and goes completely by your words (correct me if I am wrong).

We assume that once the part has exited the bubble, it is no longer affected by the bubble forces, so only the mass currently exiting is affected by acceleration.

Then, as an infinitely small mass dm attempts to exit, it gains energy sufficient for acceleration from velocity v (inside the bubble) to velocity 10*v (going with 10x cadmium). The energy differential is then: dm*(100*v^2-v^2)/2=dm*99*v^2/2. This energy is instead distributed to the whole object with total mass M, resulting in velocity increase dv, so that we can say: dm*99*v^2/2=M*((v+dv)^2-v^2)/2 (equal energy gain) Expanding and simplifying the equations:

dm*99*v^2=M*(2*v*dv+dv^2),

and, since dv is infinitely small, dv^2 does not count (differential equations making), resulting in:

dm*99*v^2=2*M*v*dv,

dv/dm=99*v/M,

a simple differential equation. With a starting velocity of an object v0, we get:

v=v0*exp(99*m/M), where m is the mass of an object that is outside the bubble. If the whole object exits, m=M, so:

v=v0*exp(99), which mean that any objects going at velocity of, say, 1 m/s will instantly accelerate to near light speed on exit . Which does not seem to happen, and means that your theory have some holes somewhere. Feel free to point out errors in my assumptions.

[Kurkistan]

Right... Disregarding for the moment the question of losing energy on bubbling, let's do the math.

OK, the math is relatively simple, and goes completely by your words (correct me if I am wrong).

We assume that once the part has exited the bubble, it is no longer affected by the bubble forces, so only the mass currently exiting is affected by acceleration.

Then, as an infinitely small mass dm attempts to exit, it gains energy sufficient for acceleration from velocity v (inside the bubble) to velocity 10*v (going with 10x cadmium). The energy differential is then: dm*(100*v^2-v^2)/2=dm*99*v^2/2. This energy is instead distributed to the whole object with total mass M, resulting in velocity increase dv, so that we can say: dm*99*v^2/2=M*((v+dv)^2-v^2)/2 (equal energy gain) Expanding and simplifying the equations:

dm*99*v^2=M*(2*v*dv+dv^2),

and, since dv is infinitely small, dv^2 does not count (differential equations making), resulting in:

dm*99*v^2=2*M*v*dv,

dv/dm=99*v/M,

a simple differential equation. With a starting velocity of an object v0, we get:

v=v0*exp(99*m/M), where m is the mass of an object that is outside the bubble. If the whole object exits, m=M, so:

v=v0*exp(99), which mean that any objects going at velocity of, say, 1 m/s will instantly accelerate to near light speed on exit . Which does not seem to happen, and means that your theory have some holes somewhere. Feel free to point out errors in my assumptions.

I have to admit that that goes so far over my head that my neck hurts looking at it. Perhaps this is another example of me failing physics forever, as you so helpfully pointed out last time.

Not that I doubt you, but could we call in another mathy-person to take a look at these numbers? Barring that, could you use dumb-person-speak to explain each step of this process. Where exactly you get the number 100 at the beginning there? Also, given this:

and, since dv is infinitely small, dv^2 does not count (differential equations making), resulting in:

dm*99*v^2=2*M*v*dv,

doesn't this:

dv/dm=99*v/M,

a simple differential equation. With a starting velocity of an object v0, we get:

mean that dv/dm ~= 0, or just about? AKA, an exceptionally small energy gain?

Edited January 17, 2012 by Kurkistan

[Satsuoni]

Not that I doubt you, but could we call in another mathy-person to take a look at these numbers? Barring that, could you use dumb-person-speak to explain each step of this process. Where exactly you get the number 100 at the beginning there? Also, given this:

doesn't this:

mean that dv/dm ~= 0, or just about? AKA, an exceptionally small energy gain?

You have reasons to doubt: I can make mistakes, you know. Still, I have rechecked this. If you can get anyone else to look at it, I would welcome an opinion. I, however, am alone here (Like in, no friends close enough to talk too when I feel like it).

As for the number 100: it is simple. If we get time slowdown by the factor of 10, the velocity increase should also be ten, so that 1 m/s on the outside corresponds to 10 m/s on the inside POV. The energy (kinetic) is proportional to squared velocity, so the energy of the piece on the inside is dm*v^2/2, outside is dm*(v*10)^2/2=dm*100*v^2/2

2nd: no. For differentials (dv,dm), the square in the presence of a first-power is considered insignificant, since dv is infinitely small, and its square is essentially multiplied by zero. If only squares are present, then they count, but any power above do not.

Also, in formula: dv/dm=99*v/M, on the right hand side there are only non-differential quantities: total mass of an object, and current velocity of an object. So the result is non-zero. The left-hand side is a derivative of velocity in respect to mass outside the bubble. The solution is classic (exponential increase,as you said)

[Kurkistan]

You have reasons to doubt: I can make mistakes, you know. Still, I have rechecked this. If you can get anyone else to look at it, I would welcome an opinion. I, however, am alone here (Like in, no friends close enough to talk too when I feel like it).

As for the number 100: it is simple. If we get time slowdown by the factor of 10, the velocity increase should also be ten, so that 1 m/s on the outside corresponds to 10 m/s on the inside POV. The energy (kinetic) is proportional to squared velocity, so the energy of the piece on the inside is dm*v^2/2, outside is dm*(v*10)^2/2=dm*100*v^2/2

2nd: no. For differentials (dv,dm), the square in the presence of a first-power is considered insignificant, since dv is infinitely small, and its square is essentially multiplied by zero. If only squares are present, then they count, but any power above do not.

Also, in formula: dv/dm=99*v/M, on the right hand side there are only non-differential quantities: total mass of an object, and current velocity of an object. So the result is non-zero. The left-hand side is a derivative of velocity in respect to mass outside the bubble. The solution is classic (exponential increase,as you said)

Ok then, thanks for trying to explain. I get it a bit more now. I think I'll just sit here quietly until someone else comes along to prove how awesome I was without even knowing it. I feel dumb.

Last effort before I take a break to let my brain cool down before possibly looking at the numbers again: what do I do wrong in my math in this post?

P.S. I think I'll just start PM'ing you before I start any physics-related threads from now on.

Edited January 17, 2012 by Kurkistan

[Satsuoni]

Ok then, thanks for trying to explain. I think I get it a bit more know. I think I'll just sit here quietly until someone else comes along to prove how awesome I was without even knowing it. I feel dumb.

Last effort before I take a break to let my brain cool down before possibly looking at the numbers again: what do I do wrong in my math in this post?

P.S. I think I'll just start PM'ing you before I start any physics-related threads from now on.

Simple, actually: you have not calculated in just how much energy increase that will result. You did use the word exponential, you know. But exponential to the (approximately) square of the time differential (multiplier) will result in the above: any velocity will be multiplied by the number larger that the size of the visible universe, resulting in relativistic bullets . Which is not the case observed in books. So the mechanism of the transfer is then different, sorry. Also, Brandon said:

Q. (Mi’chelle)- If you were to pop up a time bubble and someone were to be stuck halfway in and halfway out, would they go splooch?

A. No, they would be in the time bubble. The time bubbles will move with the planet but not with the train.

Which implies that at least a human is all the way in when he is halfway in

[EDIT] Whoops, didn't see the link. Please wait a bit.

... OK. Two errors: you sum velocities instead of energies, necessary to achieve said velocities. It is like you would have accelerated the outside half (disregarding inside part), and then glued them together.

Second: A whole half is too much Try doing the same thing with quarters - the results will be different, 1/8th - again different, etc. In order to get the real results, you need to take infinitely small parts, and integrate. That is because the speed of the pole changes while it reaches the "half-out" position.

Edited January 17, 2012 by Satsuoni

[Kurkistan]

Simple, actually: you have not calculated in just how much energy increase that will result. You did use the word exponential, you know. But exponential to the (approximately) square of the time differential (multiplier) will result in the above: any velocity will be multiplied by the number larger that the size of the visible universe, resulting in relativistic bullets . Which is not the case observed in books. So the mechanism of the transfer is then different, sorry. Also, Brandon said:

Which implies that at least a human is all the way in when he is halfway in

[EDIT] Whoops, didn't see the link. Please wait a bit.

Perhaps it's only all in or all out, but I have some doubts about what that quote means. I think Brandon might have misheard the question there. Mi'chelle wasn't asking about whether time bubbles move, but what happens when you half-bubble a stationary target. Brandon started talking about trains again in his answer. It's a possibility, at least.

Q.Zas678- I’ve got a question kind of based off of the train fight. If you have a time bubble, and you were to make it while you are on the train, would the time bubble move with the train, or would it stay at the same spot relative to the planet?

A. Time bubbles don’t move, so it would pull you out of it, then it would vanish.

Q. (Mi’chelle)- If you were to pop up a time bubble and someone were to be stuck halfway in and halfway out, would they go splooch?

A. No, they would be in the time bubble. The time bubbles will move with the planet but not with the train.

Q. Yeah, I always thought it was relative to the person creating the time bubble.

A. No, you’ll see Wayne create one, then he’ll walk up to the perimeter, but if he leaves it, it ruins the time bubble.

Q. Zas678- So is that because it’s linked up to the spiritual gravitational bond between the planet?

A. Yes, and you’re digging very deeply into stuff that I now can’t answer. Time bubbles have some weirdness to them that I don’t want to dig in too deeply, but yes.

EDIT:

[EDIT] Whoops, didn't see the link. Please wait a bit.

... OK. Two errors: you sum velocities instead of energies, necessary to achieve said velocities. It is like you would have accelerated the outside half (disregarding inside part), and the glued them together.

Second: A whole half is too much Try doing the same thing with quarters - the results will be different, 1/8th - again different, etc. In order to get the real results, you need to take infinitely small parts, and integrate. That is because the speed of the pole changes while it reaches the "half-out" position.

I was hoping to sneak using velocities instead of energy past you by using exactly half of the object at a time. If that doesn't work, though, then I suppose that, once again, you have crushed my poor, sad hopes using your cruel "reality."

Edited January 17, 2012 by Kurkistan

[Satsuoni]

Worry not... Brandon himself has stated the he is "not the math kind of guy" in the annotations somewhere. Maybe he didn't calculate that way either.

As for the Q&A, I am not sure. Maybe he misheard, but maybe only the first sentence was the actual answer, and the second clarification for the previous questions. Still, if you can go halfway out of bubble, that means you can stand with half of your brain working 10 times faster than the other. That is bound to feel weird.

[stonetwotwo]

My first post on this forum. I did some searching but couldn't find anything similar.

 

 

I've just finished Shadows of Self and became intrigued by Trell. In the old religions, Trelagism, the people beleived the night was sacred and they mapped the stars, a direct link to space travel perhaps. Brandon also mentioned that a piece of the space travel puzzle is missing. Could the missing piece be the powers of a third Shard?

 

 

Just asking and if this has been discussed it would be great if someone could supply a link to the discussion.

 

Thanks. 

Edited November 10, 2015 by stonetwotwo

[Moogle]

My first post on this forum. I did some searching but couldn't find anything similar (so no shooting )

 

I've just finished Shadows of Self and became intrigued by Trell. In the old religions, Trelagism, the people beleived the night was sacred and they mapped the stars, a direct link to space travel perhaps. Brandon also mentioned that a piece of the space travel puzzle is missing. Could the missing piece be the powers of a third Shard?

 

Just asking and if this has been discussed it would be great if someone could supply a link to the discussion.

 

Thanks. 

 

Hey there, welcome to the forums.

 

What you mention hasn't been directly addressed before as far as I know.

 

Just so you know, if you want to discuss Shadows of Self, you'll want to use the spoiler board for it (which isn't this one). Posts in this board are assumed to not include Shadows of Self spoilers, so if you want to include those you should use spoiler tags like this:

Shadows of Self spoilers:[spoiler]Spoiler text goes here![/spoiler]

The idea you have there is pretty interesting, and probably deserves its own thread, if you want to make one.

[stonetwotwo]

Sorry, didn't think about spoilers. I've updated my post to include tags. I'll also post this in the general cosmere theories section.

Edited November 10, 2015 by stonetwotwo

[Moogle]

Sorry, didn't think about spoilers. I've updated my post to include tags. I'll also post this in the general cosmere theories section.

 

It's not a problem. What you posted barely qualifies as minor spoilers. It was just a friendly reminder in case you didn't know how spoilers work here.

[Shadeshadow227]

http://www.tor.com/2015/07/07/how-can-we-use-mistborns-allomancy-to-travel-faster-than-light/

 

THERE YOU GO. 

[Kurkistan]

http://www.tor.com/2015/07/07/how-can-we-use-mistborns-allomancy-to-travel-faster-than-light/

 

THERE YOU GO.

 

Thanks (though a bit of a necro), but I'll just quote Peter on this:

 

Source:

I'm not very impressed with this one. It gets a lot of things totally wrong. Like when it's talking about how mass works in Feruchemy.