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Time bubbles: Movement outside time


Kurkistan

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Back when Shardlet asked those questions about time bubbles, I said that "this means that bubbles are almost certainly a straight effect on local space-time, rather than an effect on local objects that happens to be roughly spherical in shape."
 
gnimhey was kind enough to point out that that is a very stupid thing to say (in much more diplomatic terms).
 
I started typing up a reply to him, then started thinking about some other time bubble related stuff, and then...
 
Well, you guys know me well enough by now to guess what happened next.  ^_^
 
Thread:
 
My comment that time bubbles were "a straight effect on local space-time" was specifically getting at an earlier theory of mine where I suggested that time bubbles weren't actually a spherical area of effect, but instead simply an incidentally spherical manifestation of the limits a bubble reaches when it "runs out of the power" making everything around it experience time differently. The fact that the presence and absence of air particles has no impact on how "far" bubbles can reach almost certainly throws such a model out the window, and that was what I was attempting to emphasize.
 
(And yes, I do recognize the irony that the founding post for my overarching theory of everything came to a fundamentally incorrect conclusion on the topic that I had been trying to address from the beginning.)
 
Fuller Explanation:
 
Alternatively, a more nuanced theory can still make bubbles fundamentally spherical, but say that there size is a function of how much "energy" they have to put into altering objects they affect. So a Slider can cast a bigger bubble if it has fewer objects to worry about than if there are a lot. Under that model, there should be a measurable difference in the maximum size of a bendalloy bubble cast around a pool table full of billiard balls versus that same table when its empty.
 
That second theory also goes out the window, since the atmosphere is the fullest pool table you can imagine, chock full of pool balls bouncing around and whatnot. If you can get rid of it and have absolutely zero effect on the size of a time bubble, then that casts near mortal doubt onto any theory that bases the size of time bubbles on how much "energy" they have to put into the objects they affect.
 
--
 
Something energetic is still happening with encompassed objects, though. It's just that the bubble doesn't seem to care at all about the costs of that energy. It follows, then, that time bubbles don't directly affect the objects they contain, but instead affect areas of space-time (here I quite explicitly mean to include that area's Cognitive and Spiritual components), with the effects on objects trickling down.
 
---
 
NOTE: It occurs to me at this very moment that the maximum compression factor (how much it alters the flow of time) of the time bubble could still be affected by the objects it contains. We know that flaring a metal can get you a higher factor, but not necessarily a larger bubble. I've been assuming the energy costs of the two to be somehow proportionate, or at least that larger bubbles cost more energy, but I could be wrong. I'll keep acting like making a bigger bubble is of the same "cost-type" as raising that bubble's compression factor, because I think it reasonable, but that's not a certainty.
 
----
 
Regardless, I phrased myself poorly and misleadingly, and now gnimhey has gone and given me an excuse to discuss the remaining possibilities for how time bubbles work, given our current evidence.
 
Time Bubble Mechanics (not Realmatically, but just on a brute-force Physical level):
 
First, some facts:
 
Time bubble overlap is multiplicative.
 
Time bubbles overlap like Venn diagrams, they don't just "cancel" one another.
 
Atmosphere has no effect on bubble diameter.
 
Aside: Time bubbles accelerate or slow objects as a function of some frame of reference, independent of how they influence the passage of time for that object.
-Just my own reasoning, not WoB. It's solid reasoning, though, and necessary once you think of it.
 
---
 
I infer from these facts about time bubbles that they directly impact an area of space-time (once again including all the Realms), rather than the objects within that area of space-time. Otherwise we would get exploding bubbles when they overlapped, and overlap would really have to be additive rather than multiplicative. Not to mention all my analysis on what the atmospheric answer tells us.
 
Specifically, I would posit that time bubbles essentially alter space-time in the Cosmere such that:
 
Time passes at t*x speed for objects in this area of space; and these objects move at v*x velocity along their vectors relative to <the bubble's frame of reference>.
 
:With 't' defined as the rate of the passage of time before the bubble's existence.
:And 'x' as the bubble's compression factor.
-Either x>1 or x<1 depending on whether it's a Bendalloy or Cadmium bubble, respectively.
 
This rather neatly tells us how an area reacts to both "competing" time bubbles (Bendalloy vs. Cadmium) and "cooperating" bubbles (B+B or C+C). Just multiply whatever 't' you find (1 if the area of space is normal, 1*x if one other bubble is affecting the area, 1*x*y if there are 2...) by your bubble's compression factor and that tells you about the passage of time.
-Though you probably have to account for relativistic effects a bit, so far as passage of time goes. Sats, HELP!
 
The movement of objects is a bit more complicated, essentially creating a single vector based on the clash of overlapping bubbles' frames of reference and compression factors. It's end up with objects going off at weird angles (Ex. two competing right angle vectors resulting in the object going off at 45 degrees), I think, but not necessarily being torn apart or the like.
 
---
 
Realmatics of the all:
 
Of course, none of this means anything unless you incorporate something to account for Cognitive aspects determining whether something is in or out of a bubble. Hence why I was careful to phrase everything in terms of "objects" up above, not space.
 
This still leaves room for significant discussion of how exactly the surfaces of time bubbles work: Do they distend, or suck in people who touch them, or something else? Is there even really a "surface" worth talking about? It's an open question, so far as I can think of it at the moment.
 
--
 
But, so far as the bubbles' impacts on all three Realms: Obviously they rely on Cognitive aspects to some extent to determine their occupancy. That judgement can likely to outsourced to the objects that enter the bubble: the bubble queries them to ask whether objects think they're "in" some given area, and gets a reply and reacts accordingly.

So that deals with occupancy. But how do we model the actual effect these bubbles have on objects that are "in" them? I'll call back to the Spiritual again, though using a slightly different implementation than I've historically said (that model was rather off-the-cuff, to be fair).

So we have two fundamental things to alter once an object enters the bubble: Its experience of the passage of time and its movement through space. Now, obviously, the two are rather closely linked the majority of the time. But we can't rely on that anymore because of frame-of-reference shenanigans.

Time is easy enough: Just alter the object's passage through time to be t*X (the totality of all bubble effects) rather than the normal t.

At the same time, though, we'll have to decouple the object's normal movement from the passage of time.

Illuminating Thought Experiments:

Imagine a graph with object j, travelling North at speed 1. All bubbles (b for bendalloy, c for cadmium) will travel at speed 5 and have compression factors of 10.

Scenario 1: j is travelling North, the bubble is travelling South to intersect.

Scenario 1.1: Bendalloy bubble b

When the two intersect, j will be moving North at (5+1)*10 = 60 until it exits the bubble, at which point it will go back to travelling at 1.

Scenario 1.2: Cadmium bubble c

When the two intersect, j will be moving North at (5+1)/10 = 0.6 until it exits the bubble, at which point it will go back to travelling at 1.

-

Scenario 2: j is travelling North, the bubble is travelling from East->West to intersect.

Scenario 2.1: Bendalloy

When the two intersect, j will be moving north at 1*10 = 10 and East at (0+5)*10 = 50, for a 11.31 degree angle up to the East-by-northeast at 51 until it leaves the bubble, at which point j will continue North (but not on the same x-coordinate as before) at 1.
-Just did some (web-aided) vector math for that one.

Scenario 2.1: Cadmium

When the two intersect, j will be moving north at 1/10 = 0.1 and East at (0+5)/10 = 0.5, for a 11.31 degree angle up to the East-by-northeast at 0.51 until it leaves the bubble, at which point j will continue North (but not on the same x-coordinate as before) at 1.

-

Note that I disdained units of distance and time here in order to avoid confusion. Now, to confuse you, all magnitudes are measured on the frame of reference of normal time, the same one that sees j as travelling at 1 m/s (ha! I hid it from you! :P) North. So j appears to be travelling 51 m/s ENE in Scenario 2.1, when it's inside the Bendalloy bubble. That's meters-per-second in normal time, just to be clear.



What this all means for movement:

We can do vector math just as easily for multiple bubbles and three dimensions as we just did for one bubble and two dimensions, so let's leave that for now.

How do we implement all of this, though? We may need some physics-brain for this.

However, I do have a thought, if you'll bear with me for just a few more moments.

Every object sees itself as at rest relative to itself, but that's boring and unuseful. More importantly for us, I think it fair to say that every object (at least on a planet, and likely elsewhere) also sees itself as in motion relative to something else.

What if, then, it's that simple? Just reach into each object's Spiritual aspect and tweak it to change exactly one thing:

From "you're moving at vector V relative to frame F" to "you're moving at vector V' relative to frame B", with V' as the object's vector as the bubble's frame of reference B perceives it. Can it be that simple? If "motion" is stored in (or at least tweak-able by) Spiritual aspects, I think it can. Maybe throw on a bit of extra oomph to make sure that any Physical or "real Spiritual" whining about "real" vectors is ignored until you get out of the bubble.

Then just let the previous motion-rules come back into force, plus or minus any additional energy that was applied along any vector while the object was contained in the bubble.

Satsuoni? Want to murder it?

Conclusion:

So that's about it. I'm very very open to suggestions on how to Realmatically solve the problem of motion once we decouple it from normal time; I do not have full confidence in my model as it stands. I'm also somewhat concerned that we may be using too much energy still, looking at individual objects rather than trying to change "Realm-space" to get general effects.

P.S. A (rather horrifying, given how sure I've been about the way I model it, so far) thought: What if frame of reference isn't decided by the bubble, but by the object? So the object decides whether and how it's moving, then does a simple velocity*time accordingly.

I don't think that'd end up very pretty (objects with different frames of reference could suddenly start colliding with each other or the like), but it could still work, technically. Any other thoughts?

Edited by Kurkistan
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Ah Kurk, I really think that Brandon would facepalm if he ever read your timebubble theories.  "I just thought it would be cool to have time be faster for this guy when he burns bendalloy!"  I think he would quail at the physics implications that you have pondered, fretted, and obsessed about. :D . Gotta love ya for your dedication to the field though.

Edited by Shardlet
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Thanks?  ^_^

 

I'm fairly sure Peter's actually the one who I'd be giving nightmares to, actually. He's "the math guy" and all.

 

Ooh, I forgot to talk about how, if the bubble overtakes j from behind, it will result in counter-intuitive stuff like the object travelling backwards for a bit...

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I'm sure Peter has similar feelings but for different reasons.  Brandon says,  "Hey, Peter! This character can do this funky business!  How do you reckon that might work scientifically?"  To which Peter answers, "...".  Then Kurk says, "Muckity mucky wump. Ha! So, then wimble womble.  Therefore, ollicka folla drimmy doe!"  To which Peter answers, "Uh...yeah, that's the ticket."

 

Edit: I will eventually finish studying the idea so I can make an intelligent comment on it.  I promise. :D

Edited by Shardlet
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Waah! :blink::(:unsure::wacko: (crying)

No, Kurkistan, I give up. I have no idea how bubbles can work, and, truth to be told, am  not sure what your theory is. So just a few things, only tangentially related.

1. Simply increasing velocity of all system components does not increase system time rate. If you speed up all molecules in a human, you'll get expanding red cloud, not faster human...

2. Could you make a thought experiment about air near the bubble border within your theory, Kurk?

3. "Effect", not "affect", Kurk <_<

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@Shardlet

Okay, I'll be waiting. :)

@Sats

Mostly I just wanted to know if I'd run afoul of science somehow. I'll take your incomprehension as a good sign. ;)

1. I agree. That's why I decouple the passage of time from movement. How much time passes for the object bears only a passing relation to how it moves in a bubble.

2. Nope. :) That's a question about how borders work, which I need some more thought on.

3. Where'd I get it wrong?

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@Sats

Mostly I just wanted to know if I'd run afoul of science somehow. I'll take your incomprehension as a good sign. ;)

Well, there are several things in sciency bits that may be problematic. I just don't feel like addressing them without offering an alternative right now. :P

 

1. I agree. That's why I decouple the passage of time from movement. How much time passes for the object bears only a passing relation to how it moves in a bubble.

Except you can't really decouple time from movement, you know <_< To some extent, time *is* movement. Unless you define global movement as opposed to local heat movement, and the you'd have to define global and local scopes...

You know, here is an interesting thought experiment (I don't remember if you addressed it)- imagine a bubble tied to its allomancer (or any object inside bubble). Now imagine that allomancer running at 0.9c in the bubble time For the outside observer, how fast would the bubble move?

2. Nope. :) That's a question about how borders work, which I need some more thought on.

That is the most important question :) Bubbles without borders are rather trivial ;)  It is only the interface that gives so much trouble.

 

3. Where'd I get it wrong?

Here, and in one other place:

But how do we model the actual affect these bubbles have on objects that are "in" them?

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Well, there are several things in sciency bits that may be problematic. I just don't feel like addressing them without offering an alternative right now. :P

 

Translation: "It's all perfectly sensible, Kurk! Keep up the scientifically-acceptable work!" :P

 

Except you can't really decouple time from movement, you know <_< To some extent, time *is* movement. Unless you define global movement as opposed to local heat movement, and the you'd have to define global and local scopes...

 

Yes. That. :mellow: Let's go with that.

 

You know, here is an interesting thought experiment (I don't remember if you addressed it)- imagine a bubble tied to its allomancer (or any object inside bubble). Now imagine that allomancer running at 0.9c in the bubble time For the outside observer, how fast would the bubble move?

 

0.9c. Kind of the whole point of "movement is relative to the frame of reference of the bubble." And if that runner-bubble encountered a "stationary" object, the object would appear from the outside to move in the opposite direction of the bubble at (compression factor)*.9c until it exited the bubble, and would itself have the experience of the watching rest of the world suddenly lurching away from it at .9c, all without (I don't think) any experience of acceleration.

 

The runner would see an object moving at .9c towards him, as opposed to how the rest of the stationary objects outside the bubble look to be moving towards him at .9c/(compression factor)

 

[border mechanics] is the most important question :) Bubbles without borders are rather trivial ;)  It is only the interface that gives so much trouble.

 

A very important question, I agree, but not the only one. The mechanics I outline are just dealing with what happens to normal objects that get whammied by bubbles. Unless I'm just very much an overblown writer, I would say that figuring out how bubbles affect objects—independent of how they go about "capturing" and "releasing" them—is thus a non-trivial pursuit.

 

Here, and in one other place:

 

A tragic mistake. I shall rectify it post haste!

 

Hm, can't seem to find the other one...

Edited by Kurkistan
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Translation: "It's all perfectly sensible, Kurk! Keep up the scientifically-acceptable work!" :P

 Bah. Close enough :)

0.9c. Kind of the whole point of "movement is relative to the frame of reference of the bubble." And if that runner-bubble encountered a "stationary" object, the object would appear from the outside to move in the opposite direction of the bubble at (compression factor)*.9c until it exited the bubble, and would itself have the experience of the watching rest of the world suddenly lurching away from it at .9c, all without (I don't think) any experience of acceleration.

Ok... Let me see if I get this straight: We have a bubble, with a thing it is attached to in the center, and other, unrelated things (observers) that are stationary relative to the observer outside the bubble. The in-bubble observers see the allomancer go by at 0.9c. Let's say the bubble is large enough that inside observers stay inside, and outside observers outside. So... You say that outside observer would see central Allomancer going past at 0.9c, and the inside observer would see the center go past at 0.9c, with them being in areas where time runs differently. Which... might be possible... I guess? But would imply that the inside observer moved relatively outside observer, implying something like frame dragging effect... Err.. could you describe that in more detail? And did you notice FTL objects? :)

A very important question, I agree, but not the only one. The mechanics I outline are just dealing with what happens to normal objects that get whammied by bubbles. Unless I'm just very much an overblown writer, I would say that figuring out how bubbles affect objects—independent of how they go about "capturing" and "releasing" them—is thus a non-trivial pursuit.

Well, the point is, everything that happens to objects happens on the interface. Inside, the physics is normal. Outside, it is normal. The whole notion of relativity relies on the fact that we have to *observe* another system, and to observe, the light has to pass through the interface. It is like a black hole in that regard :)

A tragic mistake. I shall rectify it post haste!

 

Hm, can't seem to find the other one...

It is the opposite :)
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Ok... Let me see if I get this straight: We have a bubble, with a thing it is attached to in the center, and other, unrelated things (observers) that are stationary relative to the observer outside the bubble. The in-bubble observers see the allomancer go by at 0.9c.

 

That's not quite the whole picture. The in-bubble observer, because of wonkiness, actually sees everything else, including the allomancer, go by at .9c heading in the direction of the allomancer's travel. This'll end up with the in-bubble observer essentially "teleporting" the width of the bubble in an eye-blink, moving at .9c relative to the allomancer and .9c*(cf) relative to the outside-observer (FTL lies there, btw).

 

Let's say the bubble is large enough that inside observers stay inside, and outside observers outside. So... You say that outside observer would see central Allomancer going past at 0.9c, and the inside observer would see the center go past at 0.9c, with them being in areas where time runs differently. Which... might be possible... I guess? But would imply that the inside observer moved relatively outside observer, implying something like frame dragging effect... Err.. could you describe that in more detail? And did you notice FTL objects? :)

 

You got it (though I'm not up on the mechanisms of frame-dragging). The inside-observer moves, relative to the outside, at .9c*(compression factor of the bubble) in the opposite direction of that travelled by the allomancer/bubble.

 

Well, the point is, everything that happens to objects happens on the interface. Inside, the physics is normal. Outside, it is normal. The whole notion of relativity relies on the fact that we have to *observe* another system, and to observe, the light has to pass through the interface. It is like a black hole in that regard :)

 

The weirdness I posit for motion makes it so that inside motion really isn't that normal, since we're hijacking objects' vectors through space for the duration of their occupancy in the bubble. Is this making sense, or is Science shaking its head? 

 

It is the opposite :)

 

Ha! Got it. :D

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Ok, count me confused :( Moving bubbles creating wakes of ruin and destruction... I'll try to think on it later. I guess the question is - doe anything happen when the object bubble is attached to is swallowed by the bubble? If you make it large enough to cover the planet?

As for your question - well, it is impossible to say whether you are inside the bubble or not without looking outside :) That was AoL plot point, after all. Hence, the laws of physics in both cases are equivalent, but some constants between them are tweaked (it is, in theory, possible to tweak c by changing the nature of the vacuum state)

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Ok, count me confused :( Moving bubbles creating wakes of ruin and destruction... I'll try to think on it later. I guess the question is - does anything happen when the object bubble is attached to is swallowed by the bubble? If you make it large enough to cover the planet?

 

Not quite a wake of Ruin and destruction: objects just get jostled over to the side a bit. They return to normal once the bubble has passed. An object enveloped by running-allomancer's bubble will return to its normal vector once it exits the bubble.

 

I don't think anything weird happens when the anchor is enveloped. It should just experience some extra/less passage of time, but have no movement relative to the bubble's frame of reference by default. This is only if, as I assume, the bubble's anchor defines the bubble's frame of reference. A fair assumption though, I would think:

 

If the bubble can have a different frame of reference from its anchor, then that produces two odd results: Either the bubble is stationary relative to its novel frame of reference (so it isn't actually "anchored" to the anchor, and the anchor is pointless) or the bubble is actually perceiving itself as in motion relative to its own frame of reference, in motion relative to what "at rest" means, but motionless relative to its anchor. I doubt that either possibility is the case.

 

As for your question - well, it is impossible to say whether you are inside the bubble or not without looking outside :) That was AoL plot point, after all. Hence, the laws of physics in both cases are equivalent, but some constants between them are tweaked (it is, in theory, possible to tweak c by changing the nature of the vacuum state)

 

We're on the margin, though. A fundamental point of my theory is assuming moving time bubbles, for Harmony's sake. ;)

 

Everyone in Marasi's bubble was perfectly fine accepting the ground as a frame of reference: no one was being yanked out of their frames of reference by rogue time bubbles or anything.

 

I don't attempt to tweak c. To objects within the bubble, they are going at <c at all times. It's only relative to the interaction of different sets of framed time/motion that objects go traverse space at an apparent speed >=c.

Edited by Kurkistan
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Not quite a wake of Ruin and destruction: objects just get jostled over to the side a bit. They return to normal once the bubble has passed. An object enveloped by running-allomancer's bubble will return to its normal vector once it exits the bubble.

Movement vector, maybe, but not on the same position as before...

(as an aside, is it just me, or do the quotes no longer separate when one hits enter repeatedly?)

Let's consider a simpler case, a (somehow) moving bubble in the room with a chair. As the bubble envelops chair, chair (but not floor) is accelerated, since it was moved relative to bubble. From the outside view, the bubble moves at speed v, so the chair starts moving in the opposite direction at speed v*tcf as it enters -which means it is no longer stationary relative to the floor, since it cannot be compensated by bubble speed (v, relative to floor) - and we have a chair being dragged by force unknown (of the moving bubble), damaging the floor. Or do I misunderstand your system? I might, frame relativity always gave me some difficulty.

 

 

I don't attempt to tweak c. To objects within the bubble, they are going at <c at all times. It's only relative to the interaction of different sets of framed time/motion that objects go traverse space at an apparent speed >=c.

Well, sure - but we don't know if c inside the bubble is the same as outside, or did they raise the speed limit :)  Nor am I sure as to what would happen if c suddenly doubles in our universe.

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Movement vector, maybe, but not on the same position as before...

(as an aside, is it just me, or do the quotes no longer separate when one hits enter repeatedly?)

 

Yeah, position is totally messed with.

 

And no, it's not just you. It's still working occasionally for me, but randomly.

 

Let's consider a simpler case, a (somehow) moving bubble in the room with a chair. As the bubble envelops chair, chair (but not floor) is accelerated, since it was moved relative to bubble. From the outside view, the bubble moves at speed v, so the chair starts moving in the opposite direction at speed v*tcf as it enters -which means it is no longer stationary relative to the floor, since it cannot be compensated by bubble speed (v, relative to floor) - and we have a chair being dragged by force unknown (of the moving bubble), damaging the floor. Or do I misunderstand your system? I might, frame relativity always gave me some difficulty.

 

No, that's about right. It shouldn't damage the floor that much, though. ^_^  

 

Well, sure - but we don't know if c inside the bubble is the same as outside, or did they raise the speed limit :)  Nor am I sure as to what would happen if c suddenly doubles in our universe.

 

True.

 

I'm assuming not, though because, as you said, people inside the bubble don't notice any difference in normal circumstances. I would think that c going up or down would have some effects, and if it does happen in any time bubbles then it seems natural that ought to happen in all bubbles, not just those like the ones I discuss: the ones that force odd frame of reference interactions.

Edited by Kurkistan
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Ok, just to confuse everybody more:

Thought experiment!

 

Wayne creates a time bubble centered around himself, with Wax standing next to him. However, a baddie - let's call him Alceste - happens to have his arm outstretched so that he is touching the outside of the time bubble, but barely. Wax, being properly alarmed at the hulking Thug eager to separate him into several pained components, aims and fires a bullet at Alceste's face - which is outside the time bubble. However, Alceste is still touching the time bubble, and, being alive, is included in its effect. Let's assume for the purpose of brevity that the bullet is deflected into a vector still rather inconvenient for Alceste.

 

Now, Alceste has a free hand. What happens when he tries to move the bullet? 

Wax is still there, in all his badassitude. What happens when he tries to Push on the bullet from within a bendalloy bubble?

 

If this actually happened at any point in the book, sorry - but please give me a page reference.

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Ok, just to confuse everybody more:

Thought experiment!

 

Wayne creates a time bubble centered around himself, with Wax standing next to him. However, a baddie - let's call him Alceste - happens to have his arm outstretched so that he is touching the outside of the time bubble, but barely. Wax, being properly alarmed at the hulking Thug eager to separate him into several pained components, aims and fires a bullet at Alceste's face - which is outside the time bubble. However, Alceste is still touching the time bubble, and, being alive, is included in its effect. Let's assume for the purpose of brevity that the bullet is deflected into a vector still rather inconvenient for Alceste.

 

Now, Alceste has a free hand. What happens when he tries to move the bullet? 

Wax is still there, in all his badassitude. What happens when he tries to Push on the bullet from within a bendalloy bubble?

 

If this actually happened at any point in the book, sorry - but please give me a page reference.

 

Yeah! Thought experiments!

 

First of all, you note the fact that living things are immediately included in the bubble's effect. Now what this means for Alceste is highly debatable: is he yoinked into the bubble, does the bubble expand out to eat him, some combination, some fourth option? What we can be almost certain of, though, is that he isn't just standing there being all Flash without really being "in" the bubble, as that would just be downright odd. We have to answer the question of how bubbles "eat" things to solve your problem, and I'm trying to stay away from bubble-surface questions for now because they're messy. Do you have any particular thoughts that might shed light on the issue?

 

As to the question of Wax pushing: That also has some discussion behind it.

Edited by Kurkistan
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Another thing that bothered me about this was the fact that Alceste is suddenly breathing air moving much slower than him, if he is indeed both touching the time bubble and not part of it. How does that work? Come to think of it, are time bubbles airtight?

Once again, I doubt that there are ever cases where people are "in" time bubbles without being "in" them. And the transmission of air is another fun and interesting problem of bubble surfaces.

Edited by Kurkistan
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