Are there size constraints to Time Bubbles?

Question

I'm creating various artificial Time Bubbles in my universe where time flows faster or slower inside a specified area, typically depicted as a semi-transparent bubble. Before developing any more stories with this feature I need to figure out any hypothetical size constraints.

The bubbles I am after typically do not cause any catastrophic local damage when activated or later deactivated. A little local damage is acceptable. Extinction level events or even city killers are not. Currently, I have only created "small" Time Bubbles on planets, and haven't yet created anything larger than a small hamlet or out in space.

Aside from the varying amounts of energy I assume, I will require (derived from my Unobtainium using applied Phlebotinum), are there any theorized size constraints to having different sized Time Bubbles? If I need to handwave something, I need to have some idea of what it is, right?

I was curious if, at larger/smaller scales, the square-cube law and other parameters would cause the bubble to break down and collapse, OR cause too much catastrophic damage to the surrounding environments. I don't want to accidentally create a black-hole or blast any of my cities with Gamma-rays or accidentally nuke them into smithereens.

Disclaimer: I know that Time Bubbles are hypothetical and that the real answer is "we don't/can't know". I'm looking for answers derived from current theories, both science and science fiction. As I'm not looking for answers in how to create a Time Bubble, I do not see any magic being involved. If there are no current theories about size restrictions, aside from the previously mentioned energy requirements, great! Please do let me know.

Answer 1

If anything, larger bubbles may cause less problems, because your temporal gradient can be less steep (much like how you would be torn apart by tidal forces near the event horizon of a small blackhole, but can pass through the event horizon of a supermassive blackhole quite intact.)

Besides the time gradient, the major concern I think would be the redshift/blueshift of light that is crossing the bubble. In particular, light traveling from the "fast" side into the "slow" side will see a blueshift equal to the relative speeds; if the differential is great, visible spectrum light can be bumped up to dangerous levels (x and gamma rays.) This could result in burns, radiation poisoning, increased rates of cancer, etc, for those in the vicinity. While size of the bubble doesn't qualitatively impact this effect, a larger bubble will be a larger source of damaging radiation.

Answer 2

It would depend greatly on whatever is generating said Time Bubble.

Say we had a machine which had to contain the time bubble inside of its operating radius. Wires running between the pylons containing/generating the bubble would cause synchronization issues, because timing data is still restricted by the speed of light (and sending your timing data through the bubble you're creating can only result in hardware-debugging-related headaches and causality issues). If the pylons are standalone, they would all need their own energy source now, and have to coordinate via other speed-of-light-constrained methods, like satellite uplinks. And in both cases, the pylons would be targets for abuse, whether by the enemy or by bored teenagers. And, of course, these pylons can only operate at either certain key points along the bubble (say every 10 or 36 degrees), or at certain distances from each other (say between 150 to 300 feet), lest the bubble become unstable and collapse.

On the other hand, if the time bubble is generated from the inside, with the pylons pushing the bubble outward with them at the center, then this supposes that these pylons have an operating radius. That radius could be increased with more power, but there would be a exponential drop off similar to how light and sound drop off in intensity. There's a point when that extra foot of bubble radius isn't worth the power it needs. So then you set up a second pylon with its own radius. This then introduces problems with overlap (where two pylons are affecting the same area, causing the time differentials they're producing to add together and get 4x speed when you only wanted 2x speed) and underlap (where you could well get gaps in the time bubble because the pylons aren't close enough, meaning that bit of street corner is moving at 1.5x or 1x speed instead of the desired 2x). This, adding to Gene's answer about temporal gradients, may cause issues with people's health. "Oh my, Timmy and Jenny were so looking forward to getting married, but now Timmy had to check himself into an old-folks home before Jenny could finish High School, all because Timmy's bed happened to be in a temporal pocket caused by 4 overlapping time bubble pylons...."

Basically what it boils down to is this: you must construct additional pylons.

Answer 3

The first implication that comes to my mind is that objects and light that goes into a time bubble will pop out the other side very quickly because they traversed the inside of the bubble quickly. This could allow FTL movement.

Make a time bubble 20 meters wide and with time accelerated 2x. Throw a baseball at the time bubble going 10 m/s. Ordinarily the baseball would take two seconds to traverse the space occupied by the time bubble. But looking from the outside, we see the baseball exit the time bubble only one second after it went in.

So if you've got a time bubble with a 100000x time acelleration, then an object that travels through the bubble will seem to appear on the far side at the same moment it entered the near side.

Imagine you walk into a room with a time bubble between you and a lamp. It's a smallish time bubble so it doesn't obscure the whole lamp from you. When you flick the light-switch on the wall, the photons that travel through the time bubble on their way to you will arrive sooner than the other photons, which is pretty remarkable if you're a physicist.

So if you make a huge time bubble, then it can be used to transfer things, light and information from one side to the other at what appears from the outside to be faster than the speed of light.

Answer 4

Where time flows faster or slower inside a specified area, typically depicted as a semi-transparent bubble

You have a problem there: conservation of energy.

Say that you have a 2X accelerated bubble with a bulb inside pumping out 100 W of infrared radiation with a wavelength of 700 nanometers. 100 W means it gives off 100 J of energy per second local time frame.

When that energy reaches the skin of the bubble, it moves twice as fast, which means you have exactly twice as many waves in the same space; so the bulb, seen from outside the bubble, is emitting 200 W of ultraviolet energy.

A flashbulb in a 20X bubble would hit anything outside with the force of a hard gamma battle laser. This is a plot point in one of Niven's The Long ARM of Gil Hamilton stories.

For the same reason (time differential), heat exchange might be difficult or even impossible (I'd have to think about that), or it might be a problem - either the inside of a time bubble becomes stifling hot, or it grow wondrous cold because heat flows outside twice as fast.

It would stand to reason that a time bubble requires, to be created (or kept existing), at least as much extra energy as it gives out. So, the larger the bubble and the more energetic its contents, the more energy it requires and/or the less it can last. When the "extra juice" is exhausted the time differential drops back to normal.

On the other hand, this would mean that a slower-than-normal bubble would supply energy. When enough energy (light, heat, etc.) is sunk in the bubble, the bubble collapses - this would allow harvesting low-density energy (e.g. heat) to a point where the laws of thermodynamics themselves are apparently challenged; that's why I suspect that heat transfer is going to be difficult. Preventing it from happening looks like it would be Nature's easiest and sneakiest way of keeping things balanced.