Stopping time, by speeding it up inside a bubble

Question

Imagine I have a device that can stop time for the person who holds it (similar to Bernard's Watch). This device works in a very specific way - it creates a bubble around the user (just large enough to hold the user) in which time flows much faster than in the rest of the universe. The difference is very high but it is finite (say 100,000 times faster). This means that if the person holding the device experience times at "normal speed" the rest of the world outside the bubble appears to him to be drastically slowed down, almost (but not quite) to a standstill. In contrast, anyone outside the bubble looking in would see everything inside the bubble happening at lightning fast speed (almost instantaneously).

The border between this bubble of faster time and the rest of the universe is not infinitely thin - there is a boundary (say a few centimetres thick) where the speed of time changes gradually from one to the other.

My question is what side effects would this bubble cause? For example: any sounds from the outside would sound quieter and deeper, as the wavelengths are "stretched out" at the boundary. Similarly looking out of the bubble the outside world would appear darker and redder, as light is red-shifted. In fact with enough time dilation you would be able to see x-rays with your naked eyes. I'm also positing that waves such as light and sound would also bend at the boundary, as if they had struck a lense, so the outside world would appear distorted. Moving object such as bullets would also be deflected slightly (if they struck at an angle).

Are there any other interesting effects that could arise? What would happen if you walked up to another person, as they crossed the bubble's boundary? Is there anything cool you could do with this device?

For extra credit: would this violate any physically laws in any way e.g. conservation of energy? Show your working!

Answer 1

As you point out, the world outside the bubble will appear darker - much darker. What appears as visible light is actually very, very far infrared (about 0.1 meter wavelength) and the energy available is virtually nil at these wavelengths.

Interface effects make this a superb weapon of assassination. Simply walk up to the victim and position yourself so that only part of his body is within the bubble. The portion inside will have "normal" metabolism, but if the heart is outside the bubble there will be no circulation and the tissue will die in minutes. Simply stand in place for a half-hour subjective, then move on. The effects of massive tissue death will be enormously traumatic for the victim.

Alternatively, stand aside from the victim and point a flashlight at where you you believe him to be, and hold it there for a while. Let's say you have a 10 watt beam, and you hold it for 30 minutes. The result (outside the bubble) will be an 18 kJ (10 watts x 60 x 30 seconds) pulse of extreme gamma radiation directed at the target.

Of course, you'll need SCUBA tanks or something similar, since you'll use up the oxygen in your bubble fairly quickly (subjectively). You'll also need to come up with a method of heat management. On the one hand, you are effectively encased in a black body at 0 K which will suck the heat out of you and leave you frozen solid. If, on the other hand, you posit that the interface characteristics are normally reflective (so you don't freeze) then not only can you not use the flashlight, the longer you operate your bubble the hotter you'll get, since resting human metabolism is about 100 watts, and this has nowhere to go.

Answer 2

Well, let's see how such a field would work. The Hamiltonian equations are $$\frac{\mathrm d x_k}{\mathrm d t} = \frac{\partial H}{\partial p_k} \quad \frac{\mathrm d p_k}{\mathrm d t} = -\frac{\partial H}{\partial x_k}$$ Now we want the field to affect the speed of things happening, so a natural assumption would be that the field just acts as factor of the Hamiltonian: $$H(x,p) = \exp(f(x,t)) H_0(x,p)$$ Here the exponential function mainly is there to make time go normally when the field is zero. It however also makes sure time cannot go reverse.

Now for a constant non-zero field, you'd just get a rate of temporal change proportional to $\exp(f)$, so if the field is positive, things are going faster, as intended.

However what happens in the "bubble wall", assuming a static field? Well, here we have to use the product rule: \begin{aligned} \frac{\mathrm d x_k}{\mathrm d t} &= \exp{f(x)}\frac{\partial H_0}{\partial p_k}\\ \frac{\mathrm d p_k}{\mathrm d t} &= -\exp(f(x))\frac{\partial H_0}{\partial x_k} - f'(x)\exp(f(x))H_0(x,p) \end{aligned} Note the extra term on the second equation. This is an extra force proportional to the derivative of the field and the total Hamiltonian (which more or less gives the total energy). Assuming that energy is positive, this means that this acts like an extra repulsive force. Note that this repulsive force is in addition to the slowing down due to the local factor, and its strength depends on how rapidly the field grows. Note that since the kinetic energy is proportional to the mass, this leads also to a force term proportional to mass, similar to gravitation. Any potential energy would, however, give rise to an extra force that is not mass dependent.

Let's look at the energy, now also with time-dependent field: $$\frac{\mathrm dE}{dt} = \frac{\partial H}{\partial t} = \exp(f(x,t))\frac{\partial H}{\partial t} + \frac{\partial f}{\partial t}\exp(f(x,t))H_0(x,p)$$ So energy change only happens with field change, and proportional to it; that can well be explained as energy going into the field (of which I only included the effect). As long as the field remains constant, energy is conserved.

In effect, the outside world would look colder than would be expected from the slowdown, as the additional force would draw away more energy from incoming particles;on the other hand, outgoing particles would get an extra boost, so to the outside world, you'd be hotter than expected from the speedup.

Indeed, with a sufficiently small border zone (and corresponding rapid onset of the field) the border might even act like a wall for all normal-speed particles coming from outside.

Answer 3

In Larry Niven’s 1975 story, there were several side effects of note, used as clues by the detective to figure out that this was used. Besides the logistics of needing food, water, and medicine for an extended time relative to the outside world, the user had to sit in the dark because the flashlight inside the bubble became a powerful weapon seen from outside and set the wallpaper on fire (and presented as a novel unknown weapon to the M.E.).

Stasis fields were a staple of Niven’s work during that period, so read the Known Space universe and others written during the some years for more ideas.

Answer 4

There is one effect that is derived directly from special relativity. It is remarkably surprising no-one has noticed it. This is based on the fact that the speed of light will always be constant in all frames of reference.

If time inside the 'quick-time' bubble is passing 100,00 times than in the outside world, and since the speed of light must be constant inside the bubble, then lengths in the bubble must increase by a factor of 100,000. This is the inverse of the Lorentz-FitzGerald length contraction. Effectively this is a length expansion.

For example, if the 'quick-time' bubble has a diameter of two metres in its frame of reference, then due to length expansion its size will have expanded out to two hundred kilometres in the frame of reference of the outside world.

This suggests someone inside a 'quick-time' bubble can't sneak into art galleries and museums to steal their treasures. As, for example, in Arthur C Clarke's SF short story "All the Time in the World". Any fast-moving giant can be easily detected and just as easily stopped with a few flashlights.

Of course, the Flash would have the same problem. What a pity. I rather liked the Flash as a good example of a superhero with a singleton super-power and who had to exploit it to the utmost.

Answer 5

To me, the biggest worry beyond those already mentioned is heat transfer. Heat energy is effectively the kinetic energy belonging to individual molecules, which is proportional to the square of the molecule's speed. Within the bubble, the average speed of a molecule is 100000x faster; the average kinetic energy is therefore magnified by a factor of $10^{10}$, or ten billion.

The human body clocks in at about $310$ Kelvin. Scaled up - and bearing in mind that we have no need to account for heat of vaporization or other phase changes - from outside the bubble the individual inside would seem to be upwards of three trillion Kelvin. For comparison, the core of the Sun is less than thirty million Kelvin, and its surface is only six thousand. Standing near a person inside such a bubble would be like standing inside a hundred thousand suns. The heat transfer would be virtually instantaneous and catastrophic. The average person is $62$ kilograms and has a specific heat of $3470$ J/kgC; three trillion Kelvin then means that the person's body contains about $6.5 \cdot 10^{17}$ Joules of energy. Transferring all that energy would amount to about the energy output of a $150$-megaton nuclear weapon, three times the power of the largest nuclear weapon ever detonated.

Answer 6

It seems to me that the volume inside the bubble would quickly become near-vacuum unless the border somehow actively maintained pressure. If the air molecules outside the bubble are effectively moving 100,000 times slower than inside, then air molecules would exit the bubble 100,000 times more often than enter it. This would have the effect of making the effective "air pressure" outside the bubble 100,000 times less than inside.

If the border somehow actively exchanged air with the outside environment at a rate needed to simulate a 1 km/h breeze, outside the bubble there would be a 100,000 km/h wind. A category 5 hurricane is 251 km/h, so this would cause immense wind (and probably heat).

I suppose a solution would be to make the border impervious to air and have any molecule that comes in contact with the border simply be displaced to the opposite side. But then how does the user interact with their environment at all? A molecular whitelist?

Answer 7

Nice idea. I guess the idea comes partly from the "Bobbles" from some other book that work the other way round (stopping time inside).

You could use this if you have a difficult problem to solve => enclose yourself in the bubble with the fastest computer or whatever (and some energy source and all that), and think it through real neat. Then you can come out a second later and would have solved whatever would have taken someone else a dozen years to solve.

This throws up a problem though: you need to bring everything with you, and can't really get rid of stuff either. This means, energy (for light, or a computer or whatever you want to use), food, etc.; there is no point entering the bubble unless you want to achieve something in there.

As you say the border is a few cm think, and things can cross it - I guess you mean that the border consists solely of the time effect; no boundary otherwise, that would keep stuff in or out. This would make it absurdly complicated. If you put your hand through it, the part of your body inside would skeletify and turn to dust long before the rest would enter (without invoking any real science here; just going from the stated time effect). So you would have a way to let the bubble spring into existence around you at an instant (or at least at the same speed for the whole volume).

For comparison: said "Bobble" (from Vernor Vinge) works by enclosing a spherical volume in a metallic/shiny border; neatly slicing through everything. The border is completely impervious to anything - no tool can scratch it, no amount of energy whatsoever can influence it in any way, light reflects perfectly, etc.

Inside, time stops. At a pre-set time, the bobble disappears (in an instant) and time flows normal again. It just "works", there are no side effects. It is an absurdly neat solution to the time travel problem - at least in one direction (the correct one :) ). It is used to great storytelling effect to let people and items (rockets :-) ) skip over events in the real world. He even builds a working spaceship out of them at a later time, you can easily see how.

I believe you can make it work just like that, if you get rid of your "thick" border and replace it by an infinitely thin one that is absolute uncrossable from both sides. You don't need to explain anything (unless you want to make the technical explanation how it works a main part of your story) and get loads of material out of it. It's just a little less practical, as everything "interesting" happens inside the bubble, and thus in a very confined space. You have no outside benefit to enbubbling something (unlike the freeze-bobble).

Answer 8

There's a pretty damn good miniseries called The Lost Room which featured a device (The Comb) that stopped time for the user. It had some very interesting and unique rules:

• A person using the device could not interact with anything. Everything else in the world was locked in place - he couldn't pick up anything, or open a door.
• Momentum was preserved. If the user was running when he used The Comb, if he didn't start running again, in the same direction and speed, when time started up again, he would lurch in the direction he was travelling before its use.
• Light behaved very strangely (everything looked washed out and gray), and there was no sound.

I always thought these were neat takes on the very often used concept.