Definitive Allomantic FTL Theory

[Kurkistan]

Get comfortable, folks. This is the kind of theory thread that I fully intend to save an off-web version of so that I can pull it off of my brain-drive 20 years from now when Brandon writes the third Mistborn trilogy. I do not intend to see any left-out sections at that point in time. Also, slight AoL spoilers.

Background:

I got involved in the FTL discussion after Aiken Frost drew a conclusion about time bubbles affecting the kinetic energy of objects which enter and exit them.

I then concluded that energy gained from traversing the borders of time bubbles gave us possible FTL.

Ulyssessword then challenged me to prove my theories. And so the next dozen or so posts in that thread were dedicated to various people discussing that.

There have been other threads discussing Allomantic FTL, including this one by darniil, but I have yet to see my own model, and I find mine to be the first persuasive model that I have seen, particularly in not relying overmuch on assumptions about the nature of the Metallic Arts. If any others have proposed a theory like my own, then I apologize for not seeing them.

EDIT: I just read through darniil's thread again to make sure I wasn't subconsciously plagiarizing people.

Discipleofhoid actually mentioned that energy gained from bubbles might possibly be harnessed into FTL, but he never went further than a single sentence on it, as far as I can see.

Also, I find Satsuoni's thoughts on an Alcubierre's drive to be plausible, although my own use of bendalloy bubbles is more akin to moving a compressed area of space-time (which just happens to contain a ship) through space by making its movement relative to the time frame experienced within the area, instead of using compression and expansion to propel an area of normal space.

Evidence:

Proof of FTL from Allomancy/Feruchemchy (I only work with Allomancy):
-Actually, looking at this, as well as point 3 of this interview, what Brandon is referring to in the third quote of that source might just be technologically achieved FTL, made possible by increased understanding of physics through the study of Allomancy/Feruchemy.
--I'm going to go on as if this is not the case though, since at that point this theory isn't necessary.
---EDIT: Although, it might be the case that "technological FTL" is simply an artificially created, large-radius speed bubble, so I'll credit myself/Eerongal (credit where credit is due, sadly for my ego) for awesome if that's what it turns out to be.

Hints from Team Sanderson:
 

There's an issue with conservation of momentum with speed bubbles.

Not really. A bullet shot out of a speed bubble IS robbed of kinetic energy—not all of it, but just enough to slow it down to the speed it would have been moving at had it been fired outside the bubble in the first place.

Link
 

ericpeters Mon Nov 14
@BrandSanderson You mentioned friday night in #Seattle Allomacy has "FTL" built into it, any more hints you can share on how that would work

BrandSanderson Mon Nov 14
@ericpeters It involves where the lost energy from thermodynamic issues goes in certain Allomantic interactions.#torchat

EDIT: Book Signing Answer:

At the signing I asked Brandon to personalize the book with a suggestion for a unique or rare effect that could be achieved with a metal. He signed
 

Watch for what happens when something leaves a bendalloy bubble.

He then laughed and said "That won't make any sense for 10 books"

This leads me to believe that this might be related to the FTL travel.

From this, I look at time bubbles as the key to Allomantic FTL, where you can both gain and lose energy by entering/exiting time bubbles.

Assumptions:

• I assume that, just as objects lose energy when leaving bendalloy bubbles, they gain energy when entering bendalloy bubbles, as well as gaining/losing energy inversely for cadmium bubbles.
• I assume, quite fundamentally for propulsion, that when part of an essentially a solid object enters/exits a time bubble, the rest of the object remains within and affected by the time bubble, while the piece outside the bubble attempts to accelerate/decelerate, relative to the frame of reference of the inside of the bubble, to match the speed it "should be" outside of the bubble.
  
  Example:
  
  A uniform metal pole is traveling at 1 m/s inside of a cadmium bubble which is expanding every second passing outside the bubble into 10 seconds within the bubble, for a compression factor (f) of 10.
  
  The front of the pole exits the bubble, putting an infinitesimally small proportion of the pole outside of the bubble for a single instant. That section of the pole, hereby traveling at 1 m/s within the bubble, attempts to momentarily accelerate to 1 m/s outside of the bubble, for an apparent speed of 10 m/s (1 * f) from the perspective of the bubble.
  
  This small section of the pole is still attached to the rest of the pole, resulting in the vast majority of the energy gained from exiting the bubble being used to accelerate the majority of the pole to some infinitesimally greater speed than 1 m/s, x, within the bubble. From an outside perspective, the entire pole appears to be traveling at x/10. Within the bubble, the pole is now traveling at x while the section outside is traveling at an apparent speed of x as well (x/10 * 10 = x).
  
  EDIT 2: Changed the apparent speed to x, instead of x*10, in the last sentence. My mistake.
  
  The rest of the pole exits the bubble in a similar fashion, each moment resulting in a slight increase in the speed of the pole, resulting in an exponential gain of speed proportional to the initial speed of the pole.
  
  /Example
• It would certainly help (a lot) if you could artificially anchor speed bubbles to a location on a ship, but I will also attempt to construct an alternative, less flexible, model for un-anchored speed bubbles.
• A discarding of that whole "no object can meet or exceed the speed of light" theory would vastly simplify the question, but I will dedicate most of my model to assuming that c cannot be exceeded, even with functionally infinite energy.

Main Theory

Note: I'm scavenging this from several of my posts on the other thread, and will try as best as possible to credit others where appropriate. Feel free to call me out if I miss someone.

Goal: Use cadmium bubbles to achieve infinite free acceleration and bendalloy bubbles to achieve FTL travel through real-space while retaining less than 'c' speed from the perspective of the ship.

Propulsion:

The essence of propulsion is in the interaction of time bubbles and solid objects which change the proportion of their mass which is inside/outside of the bubble while the bubble is up. We also benefit using time bubbles, rather than Iron Feruchemy or conventional propulsion, in that we gain energy exponentially as the ship accelerates, with each bubble yielding more energy. The energy gained is directly linked to the relative velocity of the time bubble, though, so the location and movement of the anchor relative to the ship is very important.

I imagine that the kind of tensions inspired by the pole example in my "assumptions" section would be quite severe, so I do not require that the entire ship be encompassed by a time bubble. I picture a kind of "drive pod" either in front of or behind the main body of the ship, which contains a (heavily padded/inertially protected) Slider or Pulser and is otherwise mostly either solid metal or some kind of strong lattice containing heavy ballast.

Design the drive pod such there is a "safety chambers" to situate the time-bubble (?) in, situated at the center of a sphere whose radius is lesser than or equal to the maximum radius of the time-bubbler's bubbles.

The pod should also be connected to the bulk of the ship by relatively low-mass, low-complexity segments at least as long as the radius of a time bubble so as to minimize interference with the functioning of the pod. This section (engineering challenge!) must also be strong enough to transfer the kinetic energy gained by the pod to the ship which it is propelling.

The "<>" contains the drive pod, to the "O's" of the rest of the ship, with the 'i' as the "safety chamber" for the Slider/Pulser, and '-' as the radius of a bubble (assume maximum bendalloy bubble size for simplicity), in this diagram.

<-i->-OOOOOOOOOO

Spherical model: Assume that the drive pod ('x') has the appropriate safety chambers studded around its rim, as well as being the appropriate size and maintaining an appropriate distance from high-density, fragile parts of the ship.

OOO
OXO
OOO

I say either Sliders or Pulsers because either is theoretically applicable.

Note: I specify only one "safe room" and a drive pod of minimum size assuming that both Sliders and Pulsers will be available, so that both acceleration and deceleration can be achieved. Simply place 2 safe rooms, one on each end of the pod, and cast your bubbles from there if you want acceleration/deceleration (back/front) to use Cadmium for both functions, or the inverse to use bendalloy.

Pulser:

No bubble-anchoring:

Accelerate the ship to a respectable speed (using rockets, Coinshots, Iron Feruchmy, Pewter Compounders on top of a mountain, etc.) such that any cadmium bubble cast from the ship will be essentially motionless for the amount of time it would take the ship to traverse it. Have that Pulser put up a bubble, which the pod will accelerate through until the Pulser exits, which we know pops time bubbles. Rinse and repeat. This can only yield acceleration in the existing direction of travel, although other methods of propulsion could be used to alter course slightly.

Bubble-anchoring; assuming that the anchor can be moved with relative ease:

Situate the anchor anywhere within the ship, cast the bubble, and then move the anchor directly away from the direction which we want acceleration towards, which will also move the bubble. The speed with which the anchor moves will determine rate of acceleration.

Or just leave the anchor directly astern of the motion of travel and move away from it to achieve greater acceleration, if that is cost-effective.

Mild Tangent: This can accelerate the ship in any direction, if we modify the drive pod from a line segment to a sphere, although this might place stress on the connection between the drive pod and the ship. Perhaps the drive pod and the ship could be concentric spheres?

Bubble-anchoring; assuming that the anchor cannot be moved with relative ease:

Perhaps an "engine" similar to the one I initially proposed here, although I would now suggest that the bubble be dropped while the engine is retracted. Honestly, I would refrain from anchoring the bubbles with the ship and just use the un-anchored method for single-directional travel. Perhaps accelerate the anchor in the direction opposite the ship's heading in order to make initial acceleration easier.

Slider:

No bubble-anchoring:

Just cast a bendalloy bubble to accelerate the ship opposite to the direction of travel (aka, decelerate).

Bubble-anchoring; assuming that the anchor can be moved with relative ease:

As with the Pulser, except that you move the anchor towards the direction of travel, not away.

Bubble-anchoring; assuming that the anchor cannot be moved with relative ease:

Use the same engine as the Pulser, only the retraction is now what induces acceleration.

If we can actually break c in real-space in the Cosmere, then this will get you there. Otherwise, you're going to need. . .

Time-Fiddling Movement:

Massive props to Eerongal for inspiring this idea.

Essentially, you establish a bendalloy bubble around the entire ship (or many chained bendalloy bubbles such as to achieve the same effect) such that, to the outside observer, a ship traveling at speed x within a bendalloy bubble with compression factor f appears to be traveling at x*f. This is somewhat similar to how Wayne basically "teleports" using his speed bubbles in fights - moving through space faster from the perspective outside the bubble than he moves within it.

Given this effect, if you have a ship within a bendalloy bubble going at a speed which is infinitesimally less than c, which I'll just call c for ease of use, then that ship will be traveling at an apparent speed of c*f in real-space. A compression factor of 20 will put you at about 20 times the speed of light. FTL.

If we can anchor these bubbles within the ship, then this "super speed" can be maintained throughout the length of the voyage. The problems we encounter are twofold: how to contain a respectably sized space ship within a speed bubble and whether or not we can, in fact, anchor these bubbles.

Also, we need to be sure that not the smallest scrap of the ship is in real-time, since this would necessitate an object in real time traveling at a real velocity greater than c, instead of our goal of having a bendalloy bubble traveling at c*f through space which just happens to contain a ship which is traveling at c.

I assume, by the way, that we use the drive pod (or other methods) to accelerate to c and then use bendalloy bubbles to make use of that velocity to achieve useful FTL.

Assuming ability to anchor time bubbles:

Assuming a maximum radius of r for bendalloy bubbles, which cadmium bubbles can presumably be shrunk down to, make the entire ship out of spherical segments whose radius is <= r, including the drive pod. Attach these segements directly to each other so that it looks like that desert enemy from Mario 64, with any segments which would be abutting the drive pod buffered by special spheres of high-strength, low-density material for at least the hemisphere which abuts the drive pod.

Use the drive pod to accelerate the ship infinitely close to c, and then use separate Sliders situated at the center of each "segment" of the ship, including the drive pod, to cast bendalloy bubbles. There will be some overlap at the junctures of the segments, but this won't cause any odd acceleration/deceleration because the entire ship has zero velocity relative to the anchor.

You now have a stack of bendalloy bubbles flying through space at c*(f of least powerful bubble). You can afford to have less than perfect coordination of the Sliders, it's just that FTL won't kick in until the entire ship is bubbled.

No ability to anchor time bubbles:

I've given this a fair amount of thought, but can't come up with a reasonable answer for any multi-segment ship. You would have to be casting new bubbles essentially every instant in order to ensure perfect coverage, while we know that it takes several seconds to recharge.

A single segment might be able to make a short hop, but, given the size of bendalloy bubbles, it would amount to an "FTL jump" of a few meters at a time, since the bubble is anchored in space at something considerably less than c. Any greater number of segments would have to have perfect coordination of Sliders to attain that same hop. I had considered detaching the segments and having them make the FTL jump separately, without having to worry about "moving" time bubbles causing issues, but this is as useless as using a single segment.

Ship Design:

Now for some ASCII art ship designing. The examples I gave in the "Propulsion" section, traveling at light speed, would result in a ship which bears the closest resemblance to Swiss cheese that you'll find in the Cosmere.

The key is protection from minute particles which acquire a rather deadly aspect when you run into them while traveling at the speed of light. We need to shield our ship from these particles. So the sphere design is off the table for now, since we would need a massive number of "shield bubbles" in order to ensure complete coverage.

I'm going to assume a world where we need bendalloy bubbles in order to exceed c, and obviously where those bubbles can be anchored, since I haven't figured out un-anchored bubble-FTL yet.

"Arrow"
O - Normal segment, contains supplies, personnel, etc.
B - Buffer segment, the hemisphere abutting the drive pod must be a high-strength, low-mass lattice. Supplies and personel can be stored in the other hemisphere. The one leading to the shield section can contain shield material as well.
D - Drive pod, basically solid lead with a small corridor leading from the main ship to an acceleration room.
S - Shield segment, made of something very shieldy. Sci-Fi books I've read have actually suggested water tanks. Contains a way to access the center for FTL bubbling
'_' - Ignore this. The forum doesn't like spaces.

All segments are of radius r, the maximum radius of bendalloy bubbles, and all segments can be accessed by a Slider in order to allow FTL.

_________SS
OOOOOOOBBBSS
OOOOOOOBXBOS -> Direction of travel.
OOOOOOOBBBSS
_________SS

-Can add extra 'O' pods for as long a length as wanted, as well as as much width as will fit behind the shield. You can also increase depth, as long as the shield becomes deeper to cover it.
--Size is really only limited by the number of Sliders you can find, and extra drive pods can be added at will. You can even use a single, set anchor which is detached from the ship.

EDIT: You might also want to have n+2 layers of shields, depth-wise, where n is the number of layers behind the shield section. You would stick the extra layers at the top and bottom of the arrangement so that no particles with odd directionality could miss the shield but then move enough to hit the other segments.

We can accelerate in any direction using moveable anchors here, although you could just as easily replace the buffers above and below the drive pod with either normal segments or shields, if you only use acceleration along the spine. Obviously, you want to do some attitude correction whenever you alter the direction of travel, so as to keep the shields in front of the main bulk of the ship.

"Golf Ball"

__SS
_OOSS
OBBBSS
OBXBOS
OBBBSS
_OOSS
__SS

This is just in one dimension, along the diameter. I really don't feel like doing a floor diagram right now. Note the massive number of shields to ensure that the entire front hemisphere is covered. Multiply that for all of the necessary levels. You can replace the buffers above and below if you don't want lateral acceleration.

Both of these designs will work without lateral acceleration in a world where we cannot anchor bubbles, although FTL would rely upon smashing relativity with a hammer.

EDIT:

Quick update: This is all wrong. Objects are either totally in or totally out of time bubbles based on their Cognitive aspects and frame-of-reference shenanigans means that anything matching the time bubble's vector will not be accelerated by it.

Edited June 25, 2013 by Kurkistan

[Aradel]

the most difficult part of all of this is finding a way to anchor the bubbles off planet.

in the west jordan signing not long ago brandon revealed the bubbles are anchored the planet because of some kind of spiritial metaphysical superstructure.

other than that difficulty your theory seems sound.

[Aradel]

maybe there's some way to artificially make that kind of superstructure off planet and attach it to the ship not sure how it would work though

[Kurkistan]

the most difficult part of all of this is finding a way to anchor the bubbles off planet.

in the west jordan signing not long ago brandon revealed the bubbles are anchored the planet because of some kind of spiritial metaphysical superstructure.

other than that difficulty your theory seems sound.

*WoK Spoilers*

I had forgotten about that answer. I'll bring over the relevant quote from the transcript:

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.

Considering that we've already seen Surgebinders reassign the spiritual connection that objects feel to Roshar, as the Ars Arcanum puts it, I have hope that either a technological or Allomantic solution to this problem exists.

[Aradel]

I actually think that time bubbles affect the spiritual realm somehow. The temporal metals are closest to Ruin's power (since that's where atium was placed while it was still in use) and hemalurgy (which is Ruin's system) is a spiritual art.

[Eric]

Posit: Once outside the spiritual domain of a planet (i.e., the limits of the gravity well), time bubbles are no longer linked to the planet of origin, but to the strongest source of gravitational pull. Most likely (certainly, with proper planning) that of the ship. So while you can't take off using time bubbles, you can skip around space with them.

[Musicspren]

There are some other oddities to account for with a planet involved. The ground is traveling at some rate relative to the center of the planet. If the Wayne puts up a speed bubble, theoretically the ground ought to continue at the same velocity relative to the center of the planet within the bubble, which, from outside the bubble, would make the ground fly off.

For example:

Imagine Marasi is running and, just as she reaches a point that would be within the radius of a bubble, Wayne puts a bubble up, then, when she is about to exit it, Wayne drops the bubble. Marasi would feel no change, but to an outside observer, she would have gone very quickly for a short distance. Now take the same example with the ground. The ground is moving because Scadrial is spinning (its orbit is irrelevant as the bubble is tied to the planet, not the sun). Logically, the ground should continue at the same velocity within the bubble as it did outside, just like Marasi, causing it to exit the bubble (probably with Wayne still standing on it). But that doesn't happen.

Thus I think we can conclude that, although the connection is to the planet, it actually affects things relative to the "ground" (or "thing solidly attached to the planet") nearest the center of the bubble, not relative to the planet's center of gravity. The same should apply for the FTL spacecraft; bubbles would affect time (and with it, velocity) relative to the "ground," but not the "ground" itself ("ground" in this case meaning "anything solidly attached to the center of the spacecraft").

[Scattered]

Hey guys, I've been lurking for quite some time now, but never created a profile before because I have found that someone has usually already said anything that I would have to say. Today I made a profile specifically to reply to this topic.

If one of the difficulties with time travel is that the time bubbles are anchored to the planet by some sort of spiritual metaphysical superstructure, is it possible that the feruchemist power of investiture will have something to do with this?

I may be way off, but it was just a thought, and for once no one had already said it. ^.~

[Aradel]

Ivestiture is the power of converting one stored attribute to another. Example: The feruchemist converts stored heat into pure investiture then converts it into age with atium. It's possible to convert to and from allomancy, but only if the feruchemist is an allomancer as well.

[Scattered]

I know, but it seems to me that this explanation might be a bit of a red herring. Everything we've seen on investiture says that no one really understands it yet, and I think there might be a little more to it than just that explanation. Since magic in the Cosmere is basically an interaction between the Physical and Spiritual Realms by means of a catalyst, investiture seems like it would have to involve some of this as well in order to be switching metals' attributes around. And since the discussion involves that spiritual metaphysical superstructure, I thought perhaps investiture might be used as a way to alter this superstructure somehow, just as it alters the attributes of a metal, although really I think it's doing something more like altering the spiritual attribute connected to that metal. (Am I explaining this in a way that's making sense? It makes sense in my head.) I'm not sure exactly how this would work, but it just seemed like it might be connected somehow.

Again, as always, I could be totally off, and I probably am, but I thought it was worth bringing up.

[Eric]

Thus I think we can conclude that, although the connection is to the planet, it actually affects things relative to the "ground" (or "thing solidly attached to the planet") nearest the center of the bubble, not relative to the planet's center of gravity. The same should apply for the FTL spacecraft; bubbles would affect time (and with it, velocity) relative to the "ground," but not the "ground" itself ("ground" in this case meaning "anything solidly attached to the center of the spacecraft").

This is a legitimate potential problem, which could be solved architecturally. If the engine is not attached, but is instead inset (think of a ball socket joint, where the protrusion is the direction opposite thrust), you can avert the engine being unaffected by the time bubble.

[Kurkistan]

There are some other oddities to account for with a planet involved. The ground is traveling at some rate relative to the center of the planet. If the Wayne puts up a speed bubble, theoretically the ground ought to continue at the same velocity relative to the center of the planet within the bubble, which, from outside the bubble, would make the ground fly off.

For example:

Imagine Marasi is running and, just as she reaches a point that would be within the radius of a bubble, Wayne puts a bubble up, then, when she is about to exit it, Wayne drops the bubble. Marasi would feel no change, but to an outside observer, she would have gone very quickly for a short distance. Now take the same example with the ground. The ground is moving because Scadrial is spinning (its orbit is irrelevant as the bubble is tied to the planet, not the sun). Logically, the ground should continue at the same velocity within the bubble as it did outside, just like Marasi, causing it to exit the bubble (probably with Wayne still standing on it). But that doesn't happen.

Thus I think we can conclude that, although the connection is to the planet, it actually affects things relative to the "ground" (or "thing solidly attached to the planet") nearest the center of the bubble, not relative to the planet's center of gravity. The same should apply for the FTL spacecraft; bubbles would affect time (and with it, velocity) relative to the "ground," but not the "ground" itself ("ground" in this case meaning "anything solidly attached to the center of the spacecraft").

An excellent analysis which had not occurred to me. I probably should have devoted more time to solving the anchoring problem myself, but at least I left something for other people to discuss after my mega-OP .

While I think that you're on to something, exactly how "ground" is defined is still up for grabs. Remember that Brandon said that a bubble cast in a moving train wouldn't move with the train, despite the fact that the train is "solidly attached" to the planet at the moment of casting. Since even the truly "solidly attached" ground does move slightly, relative to the center of Scadrial (plate tectonics, not rotation), at all times, perhaps there's a certain threshold of motion for when something attached to the main mass can qualify as an anchor.

This is a legitimate potential problem, which could be solved architecturally. If the engine is not attached, but is instead inset (think of a ball socket joint, where the protrusion is the direction opposite thrust), you can avert the engine being unaffected by the time bubble.

I'm having some trouble visualizing how this would work, despite Wikipedia's generous help.

Also, by "engine," do you mean a part that extends and retracts through time bubbles to provide energy, just a drive pod, or the part of the ship where the bubbles are anchored?

[Eric]

I'm having some trouble visualizing how this would work, despite Wikipedia's generous help.

By socketing the engine into the ship, rather than fully attaching it, you get the same effect as putting a train on a set of rails on-planet. The locomotion can be affected by passing through the time bubble.

Think of your shoulder. We'll substitute the bones for the planet to illustrate. The shoulder is the largest body we need to contend with, so it becomes our ground. We can't fuse the arm to it, or we don't gain motion. So we socket the humerus (our engine) into it, and strap tendons (guide wires controlled from the main body of the ship) which the muscles (our astronauts) can pull to direct the bone (our thrust) to the proper direction.

Also, by "engine," do you mean a part that extends and retracts through time bubbles to provide energy, just a drive pod, or the part of the ship where the bubbles are anchored?

It's a general solution that could work with several types of drive engines, even rockets. I suppose I mean the drive pod, but I wasn't really thinking specifics as far as the drive type went.

Edited January 6, 2012 by Eric

[Kurkistan]

By socketing the engine into the ship, rather than fully attaching it, you get the same effect as putting a train on a set of rails on-planet. The locomotion can be affected by passing through the time bubble.

Think of your shoulder. We'll substitute the bones for the planet to illustrate. The shoulder is the largest body we need to contend with, so it becomes our ground. We can't fuse the arm to it, or we don't gain motion. So we socket the humerus (our engine) into it, and strap tendons (guide wires controlled from the main body of the ship) which the muscles (our astronauts) can pull to direct the bone (our thrust) to the proper direction.

It's a general solution that could work with several types of drive engines, even rockets. I suppose I mean the drive pod, but I wasn't really thinking specifics as far as the drive type went.

Got it. I can see how this would work, and it is more akin to my own initial "engine" concept. This would limit how much energy we could gain from each bubble, since the energy is related to how fast the object passing through a bubble is in relation to the bubble, but would still be workable.

EDIT: This is unrelated to this post, but I would like to note that I edited the OP to add a bit more to the Background, Evidence, and Ship Design sections, as well as clean up some spelling errors.

Edited January 6, 2012 by Kurkistan

[Musicspren]

While I think that you're on to something, exactly how "ground" is defined is still up for grabs.

Very true.

Remember that Brandon said that a bubble cast in a moving train wouldn't move with the train, despite the fact that the train is "solidly attached" to the planet at the moment of casting.

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.

Since even the truly "solidly attached" ground does move slightly, relative to the center of Scadrial (plate tectonics, not rotation), at all times, perhaps there's a certain threshold of motion for when something attached to the main mass can qualify as an anchor.

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.

[Kurkistan]

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.

It needn't tear away from the rest, and the (real) ground doesn't need to tear away either, by my understanding. The section of the train/earth is traveling at speed X, along with the rest of it's components, at the moment of "bubbling." If the bubble is anchored to the object in question, then the bubble will also be traveling at X.

Therefore, the entire structure is traveling at 0 m/s relative to the bubble. To an outside observer traveling at the same velocity as the bubble, the section within the bubble will appear to be traveling at 0*f (compression factor) and the section outside the bubble will be traveling at 0. From within the bubble, the rest of the structure will be traveling at 0/f compared to the 0 of object within the bubble. If the structure as a whole changes velocity, then the same numbers apply, if the bubble is actually anchored to it.

EDIT: Note that this assumes that the bubble is anchored to the structure as a whole, or part of the structure outside the bubble. If the anchor was a point inside the bubble, then bad things will happen as the bubble and the bubbled section attempt to travel at X*f, compared to the X of the rest of the structure.

EDIT 2: Never mind, I think you would be fine even then. EDIT 4: See two posts down for reasoning.

No separation needed or possible. This applies equally well with spaceships and the crust of Scadrial.

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.

I don't subscribe to this particular theory. Perhaps some Physical/Cognitive/Spiritual stuff goes on so that light isn't affected, but I think that the reason why light isn't affected is just because Cadmium/Bendalloy are actually alloys of Handwavium so that a flashlight can't be used to microwave people. Excluding the exemption of light, I imagine that the mechanics of time bubbles are as close to realistic as possible.

I think that the reason for "jostling" for both people and bullets is because of piecemeal acceleration and deceleration as objects enter and exit bubbles. The "unpredictability" of the trajectories of projectiles exiting the bubbles is then because of the high variability of angles of entry and exit relative to the "skin" of the bubble, affecting different parts of the projectile in different orders every time.

People move slowly relative to the bubble and are of high mass, so are only "jostled." Bullets on the other hand, have a very high velocity relative to the bubble and low mass, resulting in large changes of energy in nigh-unpredictable directions as parts of the bullet enter/exit the bubble and impart energy onto the rest of the bullet.

By this model, a projectile fired from the geometric center of a bubble would never be deflected, as would also apply to any projectile which followed the path of a line intersecting that same geometric center. EDIT 3: So long as that projectile was symmetrical and the path it followed was also parallel to its axis of reflection.

Edited January 6, 2012 by Kurkistan

[Musicspren]

It needn't tear away from the rest, and the (real) ground doesn't need to tear away either, by my understanding. The section of the train/earth is traveling at speed X, along with the rest of it's components, at the moment of "bubbling." If the bubble is anchored to the object in question, then the bubble will also be traveling at X.

Well...

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.

Clearly "don't move" is relative, but the trick is whether it is relative to the ground or relative to the center of the planet, and the ground is exempt from time distortion because it is part of the planet and the planet as a whole is not affected by the bubble.

I don't subscribe to this particular theory. Perhaps some Physical/Cognitive/Spiritual stuff goes on so that light isn't affected, but I think that the reason why light isn't affected is just because Cadmium/Bendalloy are actually alloys of Handwavium so that a flashlight can't be used to microwave people.

Handwavium? Nonsense, if it is anything, it must be Wonderflonium. After all, we are trying to

Excluding the exemption of light, I imagine that the mechanics of time bubbles are as close to realistic as possible.

Good sir, whatever makes you believe that the Cognitive and Spiritual interactions are not completely realistic in the Cosmere? Next you'll be telling me that Soothing and Rioting force people to do things.

I think that the reason for "jostling" for both people and bullets is because of piecemeal acceleration and deceleration as objects enter and exit bubbles. The "unpredictability" of the trajectories of projectiles exiting the bubbles is then because of the high variability of angles of entry and exit relative to the "skin" of the bubble, affecting different parts of the projectile in different orders every time.

I would think that the jostling is because of the clothes/other items around a person exit the bubble at different times. If different parts of the body went to normal time exactly as they exited, the person would implode or explode (depending on the bubble type). The bullet deflection, I would think, is because of the odd air currents at the edge of the bubble. As the air currents (or, if you will, windspren), move in and out of the bubble, they move/compress/stretch enough to slightly distort the light entering and exiting.

AofL Chapter 2:

Years of familiarity let Waxillium discern the boundary of the bubble, which was marked by a faint wavering of the air.

In the same way, they will be like sudden brief gusts of wind that will cause a bullet to ricochet in a completely unpredictable way upon entering or exiting (not even refraction laws can help).

[Kurkistan]

I just had a rather large revelation about the nature of time bubbles: I haven't been considering the impacts of frame of reference properly. I was thinking about my answer to the "train as ground" problem that Musicspren raised, and realized that I had stumbled across a rather crucial distinction.

Imagine two systems:

System A:

Two objects, c and d, are at rest 10 meters away from each other in an infinite space, not moving relative to each other. Cast a bendalloy bubble around object c. Wait 1 second. Pop the bubble. Neither object has moved relative to the other

Before bubble: c__________d

After bubble: c__________d

System B:

Two objects, c and d, are moving along the same line in the same direction at 1 m/s, 10 meters away from each other, in and infinite space. Cast a bendalloy bubble with a compression factor of 10 around one of the objects. Pop after 1 second. The object you bubbled just moved 10 meters to the other object's 1, changing their relative positions.

Before bubble: b__________c (10 '_')

After bubble: b_c (1 '_')

How were these two systems meaningfully different?

They are not different in any classical sense. Looking purely at the objects before and after bubbling, they have no relative motion. The speed of "1 m/s" is entirely arbitrary within the c-d system. If you read the descriptions carefully, the relationship between c and d within systems A and B are actually exactly the same before the bendalloy bubble is cast. I could just as easily make a system C that had the objects moving at 1,000 m/s, and it still would have been exactly the same when just looking at the two objects.

Therefore, the bubble itself is the only possible difference. The bubble determines the frame of reference by which the "speed" of the objects are defined, and thus causes changes to what is otherwise a changeless system. The bubble, in turn, presumably borrows its frame of reference from its anchor. If the anchor had been either of the objects in system B, then nothing would have changed because neither object would have had any velocity from the frame of reference of the bubble, and thus would move 0 meters at 0 m/s no matter how many seconds passed.

Therefore, if a bubble is anchored to an object, then that object must necessarily be motionless relative to the bubble, with the velocities of all other objects, both within and without the bubble, defined in relation to that anchor.

This has bad implications for FTL. This means that my time-fiddling won't actually achieve c*f speeds. The bendalloy bubble around the ship will travel at exactly the speed of the ship using this understanding, which will still only be c.

EDIT 1/2:

I'm having a bit of trouble conceptualizing this necessity, though. If you have two objects traveling at the same speed, but one is anchoring a bendalloy bubble with a compression factor of 10, then the anchor object still experiences 10 seconds for every 1 of the other object. So the anchor must be traveling at 1/10 of the speed of the other object, moving 1/10 of the number of meters for every second inside the bubble as the other object moves each second from an outside perspective. So a ship traveling at c in this bubble would actually be traveling at c/10.

This is either a problem with my understanding of how time bubbles actually work or I've found a necessary contradiction built into Cadmium/Bendalloy Allomancy. This second option because it actually reduces the velocity of the anchor while the bubble is up, only to speed it up again when the bubble is dropped, as does not and should not happen with any other instance of time-bubbling. This problem also occurs for anything which matches the speed of the anchor.

EDIT 3: Messed with the examples a bit to clear up possible confusion. Also, it might not be a contradiction, just a limit as objects approach the "0" speed of the anchor. Perhaps time even passes normally for anything which matches the anchor perfectly.

EDIT 4:

Yes, lots of edits. Sorry. I was hoping that someone else would have come along to untangle my brain by now, but instead you get to benefit from a stream-of-consciousness.

Looking at Edits 1/2, I believe I have been mistaken in how I thought about this. Those comments actually contradict my own earlier statements about how important frame of reference is with time bubbles. So what if the anchor was traveling at 1000 m/s from an arbitrary frame of reference? It should still be motionless within a bubble traveling at constant speed. And yet the anchor still needs to experience those same extra seconds.

From the viewpoint of a bendalloy-bubbled anchor, the world, which had been moving about at a normal pace around a stationary anchor, has just slowed down. What is unique about objects within the bubble (excluding the anchor) is that they can travel at "normal" speeds relative to the anchor, while the rest of the universe cannot. So another object which is traveling 1 m/s faster than the anchor, when caught in the bubble, will be moving 1 meter per experienced second relative to the anchor. When that object exits the bubble, it will lose its advantage and slow down like the rest of the universe.

From the viewpoint of the bubble, it as if the entire world is being perceived at a faster rate than normal, while any objects caught within the bubble are perceived normally. So the anchor doesn't move because it never did, assuming the anchor as a frame of reference, while everything else within the bubble does its own thing and the rest of the world glaciates along. When the bubble is dropped, the rest of the world returns to normal, although the anchor never changed.

We must remember that the only valid frame of reference from which to judge a time bubble is that of an anchor. The anchor does not move. Ever. Time may pass, the anchor may be a potted plant that grows into a tree as the world races by around it, but it will never move. The anchor may rotate about it's axis as much as it wants, but can never shift its center of mass in any direction. To say, as I did, that "the anchor is moving at x/f" is meaningless because x is always equal to 0. To accelerate the anchor one direction is to accelerate everything else in the opposite direction, but the anchor will never move - the rest of the world does.

We then have the image of a disc spinning as it moves through space, rotating at 1 Hz. We assume a frame of reference where then disc moves 1 m/s, getting one meter moved for each rotation, but when you put a bendalloy bubble around it, it now rotates at 10 Hz from an outside perspective, despite moving through space at the same rate of 1 m/s.

This appears wrong, but picture another disc rotating at 1 Hz but moving at 2 m/s from the assumed frame of reference, on the same vector as the anchor, getting 2 meters for every rotation. This second disc is caught in the bendalloy bubble, and now rotates at 10 Hz while moving through space only 10 meters, for a 1-1 ratio.

Still wrong? No, it is not. Recall that the speed at which a bubble is traversed is always relative to the speed of the anchor, and that the second disc was only moving 1 m/s relative to the anchor. We have to divorce ourselves from a conception of velocity as distance/time because time is being messed around with. Simply saying "1 m/s over 10 seconds is 10 meters" doesn't cut it anymore. Time bubbles change how space is traversed, as well as time: all motion over time must be made relative to the anchor, because the anchor is pulling along its own little patch of space-time, not just time.

Edited January 7, 2012 by Kurkistan

[Kurkistan]

I would think that the jostling is because of the clothes/other items around a person exit the bubble at different times. If different parts of the body went to normal time exactly as they exited, the person would implode or explode (depending on the bubble type). The bullet deflection, I would think, is because of the odd air currents at the edge of the bubble. As the air currents (or, if you will, windspren), move in and out of the bubble, they move/compress/stretch enough to slightly distort the light entering and exiting.

AofL Chapter 2:

Years of familiarity let Waxillium discern the boundary of the bubble, which was marked by a faint wavering of the air.

In the same way, they will be like sudden brief gusts of wind that will cause a bullet to ricochet in a completely unpredictable way upon entering or exiting (not even refraction laws can help).

It wouldn't be as bad as anything requiring the suffix "-plode," I think. The body's constituent parts are rather firmly connected to each other. A bit of math might actually be appropriate here.

I don't think the wind currents are that strong. Recall that Wax and Marasi were right next to Wayne when he changed his disguise at the wedding, but didn't feel a "sudden gust of wind" at any point, which would be the case if the air was circulating quickly enough to deflect bullets.

[Musicspren]

Does this discussion remind you of the iron feruchemy thread?

Okay, I think I agree with you by Edit 4. It assumes you can anchor to anything, or at least that you can when there isn't a planet nearby, but if we make that assumption, I think it makes sense. But your spinning disc made me think: what if you had a disk rotating around a point exactly on the edge of a bendalloy bubble (I'm using what I believe is your theory of bubbles here, not my spren-influenced theory), and the disc were spinning perpendicular to the edge of the bubble, so half the disc was inside and half outside (I'm aware that the curvature of the bubble will mean those won't be true halves, but it doesn't change the point of the thought experiment). The disc is sturdy enough to not be torn apart by time variances. Someone on the outside the bubble starts the disc spinning at 1 Hz. The part of the disc inside the bubble, because it is connected to the rest of the disc, will try to spin at 1 Hz (because the rest of the disc is pushing it out of the way that quickly), but, viewed from outside, that would be 10 Hz. This will cause the part of the disc outside to be pushed to spin faster (in the process slowing the other part somewhat), so the part outside the bubble is spinning at (say) 5 Hz viewed from outside, .5 Hz viewed from inside. But the process will repeat, so the part inside will turn push the outside up to (say) 25 Hz. (How much is lost from the factor of 10 is debatable, but the effect is the same.) Eventually, the disc's Hz would approach infinity. The same thing would work with a cadmium bubble if the disc was started from the inside. Actually, it should work whichever side it was begun from, but starting it from the slower time side would make it faster sooner.

It wouldn't be as bad as anything requiring the suffix "-plode," I think. The body's constituent parts are rather firmly connected to each other. A bit of math might actually be appropriate here.

(Using your model again) If you're running toward a bendalloy bubble, travelling at 5 mph, then when some part of you (say your hand) enters, it will continue traveling at 5 mph. However, because of the time difference, that is equivalent to 50 mph outside. Your arm, trying to keep itself in one piece, will be pulled forward to keep up with your hand. However, that means that when (say) your elbow enters, it is traveling at 10 mph, which, from inside the bubble, is pulling the rest of you forward at 100 mph. This will continue until the speed difference becomes too great and you explode.

[Kurkistan]

Does this discussion remind you of the iron feruchemy thread?

No, not at all, now that you mention it.

Okay, I think I agree with you by Edit 4. It assumes you can anchor to anything, or at least that you can when there isn't a planet nearby, but if we make that assumption, I think it makes sense. But your spinning disc made me think: what if you had a disk rotating around a point exactly on the edge of a bendalloy bubble (I'm using what I believe is your theory of bubbles here, not my spren-influenced theory), and the disc were spinning perpendicular to the edge of the bubble, so half the disc was inside and half outside (I'm aware that the curvature of the bubble will mean those won't be true halves, but it doesn't change the point of the thought experiment). The disc is sturdy enough to not be torn apart by time variances. Someone on the outside the bubble starts the disc spinning at 1 Hz. The part of the disc inside the bubble, because it is connected to the rest of the disc, will try to spin at 1 Hz (because the rest of the disc is pushing it out of the way that quickly), but, viewed from outside, that would be 10 Hz. This will cause the part of the disc outside to be pushed to spin faster (in the process slowing the other part somewhat), so the part outside the bubble is spinning at (say) 5 Hz viewed from outside, .5 Hz viewed from inside. But the process will repeat, so the part inside will turn push the outside up to (say) 25 Hz. (How much is lost from the factor of 10 is debatable, but the effect is the same.) Eventually, the disc's Hz would approach infinity. The same thing would work with a cadmium bubble if the disc was started from the inside. Actually, it should work whichever side it was begun from, but starting it from the slower time side would make it faster sooner.

Sorry for just abandoning your spren-influenced theory. It may be true, but we can't really do any serious thought experiments on the effects of partial entry/exit into bubbles using it, and that's where a lot of the meat is.

As to Edit 4, do you agree with the implications on the impossibility of bendalloy-FTL? I would like it very much if someone could persuade me that my conclusion doesn't apply.

Okay, onto spinning: I believe that you're onto something here, although we have to consider how this works in the real (cough) world.

A cadmium bubble at anything less or a bendalloy bubble at anything more or equal to half "immersion" into a time bubble would achieve momentary infinite acceleration. A cadmium bubble at more/equal or a bendalloy bubble at less would stop rotation instantly.

Less cadmium and more/equal bendalloy bubbles can pour all of their gained energy from the faster section into the slower section, with increasing returns as you noted. More/equal cadmium and less bendalloy bubbles lose all of their energy as they pour more energy into accelerating the slower section than they gain from the faster section.

First of all, unless this half-or-greater disc is secured somehow, it will be near instantaneously yanked inside a bendalloy bubble, or thrown out of a cadmium bubble if it's less than half.

Ideally, if the bubble where to pop the moment the disc moved, disc in a bubble would fly off at a >=45 degree angle (45 degree for 1/2, greater as the immersion changes) either into our out of the bubble, with directionality determined by bubble type and the nature of the initial rotation.

The bubble will most likely not pop in that instant, though, so instead we have the disc shooting off at a 90 degree angle, along the line parallel to it's initial intersection with the bubble and intersecting the position of the center of the disc when its entirety is encompassed by/outside of the bubble (minus an infinitely small portion outside/inside). The path for a bendalloy bubble would intersect the bubble while the path for a cadmium bubble would not.

With a bendalloy bubble, the disc spinning clockwise into the bubble/counterclockwise out of it or a disc spinning opposite using a cadmium bubble would shoot down at 90 degrees, while a disc spinning counterclockwise into a bendalloy bubble/clockwise out of it or a disc spinning opposite using a cadmium would shoot up.

Infinite gained energy assumes some infinitely strong axle anchored in the anchor for the time bubble, as well as an infinitely strong disc, which do not exist. So either the disc shatters and releases its energy every which way, possibly depopulating a few planets, or the axle breaks and the disc will yank its way off of its axle at a 90 degree angle, with its energy determined by how much was necessary to break the axle. You gain energy either way, but I imagine that this would be rather hard to control properly, and very risky at high energy levels. In the "real world" of Scadrial, I imagine that most instances where this happens simply result in the rotating section being pulled into/shot out of the bubble at relatively low speeds.

(Using your model again) If you're running toward a bendalloy bubble, travelling at 5 mph, then when some part of you (say your hand) enters, it will continue traveling at 5 mph. However, because of the time difference, that is equivalent to 50 mph outside. Your arm, trying to keep itself in one piece, will be pulled forward to keep up with your hand. However, that means that when (say) your elbow enters, it is traveling at 10 mph, which, from inside the bubble, is pulling the rest of you forward at 100 mph. This will continue until the speed difference becomes too great and you explode.

Fear not! Remember that the energy from the exiting the bubble has to try and accelerate the entire body, so as the arm is pulled forward, the body will also pulled forward, taking a significant amount of energy from the arm/hand. Remember that the hand's acceleration most likely doesn't actually provide enough energy to accelerate the arm to 10 mph, also, so the scaling effects you mention will be mitigated each stage.

Edited January 10, 2012 by Kurkistan

[Odium's_Shard]

That. Is. Cool?

So from and outside POV, you would just watch a person be thrown into the bubble and then into pieces? It'd probably be best if you just entered flat, ie arms to your side, back straight, etc. Would want to throw you back into pieces and have to pay for an expensive chiropractor.

[ulyssessword]

I see a huge problem with your proposed method of propulsion, though I may have missed some subtleties. Here is a counterexample to gaining speed by passing through the boundary of a time bubble:

You shoot a bullet (muzzle velocity 1000 m/s) out from a Cadmium bubble (20x compression). before the bullet leaves the bubble, it travels with an apparent velocity of 1000 m/s from the perspective of someone inside of the bubble, or 50 m/s from the perspective of someone outside of the bubble.

I do not know what exactly happens at the boundary (I hold that entire objects transition out, all at once), but I'm not sure if the exact mechanics matter, as we know what the results are.

After the transition the bullet is travelling at 20 000 m/s from the perspective of someone inside of the bubble, or 1000 m/s from the perspective of someone outside of it.

Note that from the bullet's perspective there was no change in velocity, it went from 1000 m/s inside the bubble to 1000 m/s outside of the bubble. No velocity is gained that I can see.

I have a few ideas kicking around for Allomantic FTL, but none are quite as developed as this one.

[Kurkistan]

I see a huge problem with your proposed method of propulsion, though I may have missed some subtleties. Here is a counterexample to gaining speed by passing through the boundary of a time bubble:

You shoot a bullet (muzzle velocity 1000 m/s) out from a Cadmium bubble (20x compression). before the bullet leaves the bubble, it travels with an apparent velocity of 1000 m/s from the perspective of someone inside of the bubble, or 50 m/s from the perspective of someone outside of the bubble.

I do not know what exactly happens at the boundary (I hold that entire objects transition out, all at once), but I'm not sure if the exact mechanics matter, as we know what the results are.

After the transition the bullet is travelling at 20 000 m/s from the perspective of someone inside of the bubble, or 1000 m/s from the perspective of someone outside of it.

Note that from the bullet's perspective there was no change in velocity, it went from 1000 m/s inside the bubble to 1000 m/s outside of the bubble. No velocity is gained that I can see.

I have a few ideas kicking around for Allomantic FTL, but none are quite as developed as this one.

We'll just have to agree to disagree about the entire object transitioning at the same time. I believe that it doesn't make sense for an arbitrarily defined "object" to transition all at the same time after some proportion of its mass exits/enters the bubble.

Given my assumption of partial transition, though, I believe that I've shown that the energy gained from exiting cadmium bubbles can be harnessed, looking both at my example in the Assumptions section of my OP and at my initial response back in the original thread.

To reiterate, the energy is gained when the portion of an object outside of the bubble attempts to accelerate to its "proper" speed, but is still attached to a segment inside the bubble. Because of this attachment, a large part of the energy which the bullet, in this case, gains from the perspective of the section inside the bubble is fed back into the bulk of the bullet.

To use a simple example, let's picture a 2 meter pole traveling at 1 m/s within a cadmium bubble with a compression factor of 10. This magical pole transits the edge of the bubble 1 meter at a time. We will assume an outside perspective at all times.

Step 1: Entire pole within bubble, traveling at 0.1 m/s.

Step 2: First half of pole exits bubble, attempts to travel at 1 m/s while rest travels at 0.1 m/s.

Step 2.5: Energy divided evenly between halves, both travel at (1 + 0.1)/2 = 1.1/2 = 0.55 m/s

Step 3: Second half of pole exits bubble, attempts to travel at 5.5 m/s while rest travels at 0.55 m/s

Step 3.5: Energy divided evenly between halves, both travel at (5.5 + 0.55)/2 = 6.05/2 = 3.025 m/s

This 3.025 m/s compared to the 1 m/s that we would expect the pole to be traveling if we simply dropped the bubble without any transiting of the edge. I had to ponder this a bit to be sure I was actually right, but this math makes a fair amount of sense to me.

Note: I changed the example in the Assumptions section as "Edit 2." Thanks for pointing that out, and I can now understand your confusion.

EDIT: I'm not positive about how the energy transfer should work between "spaces." It seems as if 0.1 m/s worth of energy from real space should be enough to accelerate an equal mass by 1 m/s within a x10 cadmium bubble, but I may be reading it wrong.

Edited January 11, 2012 by Kurkistan

[ulyssessword]

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.