How would a chronologically accelerated/slowed object affect a chronologically normal object?

Question

The world has a kind of magic called chronomancy, essentially time manipulation. It can be done on two scales: local and universal.

Due to how the cost of magic works even the most experienced or skilled of human chronomancers have only ever been capable of stopping, accelerating, or reversing time on a universal scale for a few seconds at most before passing out from exhaustion, so for most chronomancers that's never even an option unless absolutely necessary and as such most time manipulation is mostly done on a local scale on a per-object (or living thing) basis. Chronomancers can slightly cheat the whole universal time manipulation thing by affecting themselves on a local scale, the universe from their perspective slowing down if they accelerate themselves and vice versa, though this carries the usual risks of them aging at an accelerated rate from everyone else's perspective if they abuse time acceleration on themselves throughout their lives.

I've already decided how frozen or time-reversed objects are affected by external forces, in that they are invulnerable or reversed in entropy/damage until they return to a normal or faster-than-frozen time passage, but I'm having a hard time deciding how a chronologically accelerated/slowed object (like an arrow in flight) will be affected by external forces or how it will affect chronologically normal objects when their slowed or accelerated forces interact with them.

How would a chronologically accelerated/slowed object affect a chronologically normal object?

Things I have considered:

• That a slowed down or frozen object would stay where it is relative to the universe instead of the gravitational object it was being affected by, causing all sorts of damage as the slowed down/frozen object goes the opposite direction of the planet's orbit it was affected by.
  To resolve this I've made it so that the slower you go time-wise the more you are 'locked in' to your position relative to the rotation of your local source of gravitation, as if you're stuck in a Lagrange point if that makes any sense.
• That simply affecting an object won't do much and that you've need to slow or accelerate its entire path of travel for it to affect other things differently. Assume this is the case if simply accelerating or slowing the object won't alter any results.

Answer 1

The Object's Mass Changes

Manipulating time, is basically the same thing as manipulating the Speed of Light. The Speed of light is a funny thing though because things that move at 1C have the same apparent speed in all frames of reference whereas things moving slower than 1C have apparent speeds based on their frame of reference. For time-space equations to balance, this means that when an object moves at relativistic speeds compared to another reference frame, everything in front of that object appears closer, and everything behind it appears farther away.

So, to speed up time, you increase the "constant of C" (which I suppose should be called the "variable of C" to a time mage). This makes the distance the arrow perceives equivalent to firing an arrow over a shorter distance. So, if you fire a 50 gram arrow at 60mps at a target 120m away, and raise C around the arrow to double its speed, it will traverse the distance faster as other people see it, but from its own perspective, it will just travel a shorter distance without gaining or losing energy. IE: the arrow only sees itself as only traveling 60m, but facing the same amount of air resistance as though it had traveled 120m.

So what about the impact? Is it more or less energetic? ... Assuming your spell is just trying to manipulate time and not pump more energy into the system, this means you need to change the mass of the arrow as it flies to balance your equation. So, if you accelerate an arrow with time manipulation, E=MC^2 could become E = (M/4) * (2C)^2. So making local time move twice as fast would reduce your mass 4 fold. In this way, your arrow hits just as hard as it would moving slower, but gets to its target much faster. In short, your arrow effectively becomes a 12.5 gram projectile moving at 120mps.

NOTE: it will hit with the same energy, but the terminal ballistics of the system will more closely resemble a bullet impact than an arrow. Low Mass, High Speed objects tend to pernitrate armor better than High Mass, Low Speed objects of equivalent energy.

When you slow things down the opposite becomes true, the arrow moves much slower, but has a higher apparent mass.

This solution will also work very well with:

a slowed down or frozen object would stay where it is

Because a slowed down object is more massive than normal, it can still rest on the Earth and be manipulated sort of normally. You would think that this also means that it would sink into the Earth and become super heavy, but it does not because its reference frame becomes distorted to compensate. The object would fall much slower from our perspective and much farther from its perspective so the total energy interactions over time in each reference frame between the Earth and the object would remain the same. Inversely, If you are time slowed, everything around you would appear farther away and to be moving much faster but with the same total energy. So, if they bump into you, the energy transfer is the same... though their hand may still cut through you because of changes in terminal ballistics if they hit you hard enough.

Someone who is completely or near completely time frozen would become intangible. You would pass right through them like gamma rays. From their perspective, everything would become a very distant far away blur of light. Likewise, if you speed up an arrow fast enough, it will also pass through regular matter like a gamma ray as its mass approaches zero.

Answer 2

A time-manipulated object has a magical aura that affects its surroundings, similar to e.g. a gravitational field: it emanates its time-change.

Let's say a slowed down arrow reaches a bird perched on a branch: as it gets closer, the bird will be caught in the arrow's aura, and slow down gradually. It might be able to perceive the arrow as a threat, and try to escape it, but as the arrow comes closer, the bird will increasingly slow down.

A chronomancer's ability/talent/skill might be decisive for the size of this aura, relative to the quality of the time manipulation (which is the sum of the duration and intensity with which time is changed).

If a time-altered item would be still relative to the universe, it would be extremely complicated to figure out (or perhaps even imagine) its impact on its surroundings.
Say a cannonball was frozen in time mid-flight. On the surface the earth rotates at around 1000 Mph. This cannonball will cause a lot of damage in very little time, no matter what, but how does the earth move relative to the cannonball? What is the cannonball's position relative to the 'center of the universe'? Will the cannonball actually move towards the chronomancer at that speed, and dive into the earth until it reaches its core at which point it might already be completely crumbled (I know too little about the resistance of metals to external forces to make an educated guess)?

Answer 3

I would say they would interact with an impact of N, where N is the amount of time acceleration one item has. Or in the case of a deceleration, 1/N.

An arrow that moves twice as fast due to time has "trouble" interacting with its surroundings. After all, according to the arrow everything else moves aside twice as slowly, right? So the arrow will need to put in more energy to push the molecules aside fast enough to let it pass. From the air to the target it hits, it doesnt matter. Effectively according to the universe, the arrow simply has twice the energy until the spell fails and the normal time resumes on the arrow. The arrow will have lost more energy during its flight than normal and will go slower than expected because of this.

For an object moving slower the exact same is true. If you were firing an arrow 4x faster than normal and then made it go half speed, it would have the exact same impact as the previous arrow sped up. Only when time resumes it would have more energy left than before.

However you have to be smart about it: if you accelerate an arrow before firing it, it will take twice the energy to launch it at the speed of a normal arrow. The energy of the arrow hasnt changed just because you accelerated it!

Answer 4

Each object interacts according to its perspective on time.

An arrow travelling at a target will be our example. The arrow has had slowing magic cast on it so it moves at .5 seconds for every 1 seconds of ours.

Arrow perspective: everything is now moving twice as fast. It travels the normal travel path and velocity to its destination but, the target has more resistance than expected and penetration is reduced as the target doesn't experience the full impact. The impact damage on the arrow is much higher for hitting the "harder" surface.

Target perspective: the arrow moves much slower and carries less potential energy. the impact registers much less. The arrow despite being slower travels in a normal travel path/arc.

Due to each perspective, the target is less harmed and the arrow is more harmed as it hit a target that experienced it moving slower.

Answer 5

If time-stopped items are invulnerable, and time-reversed items are reversed in entropy, then time-slowed and time-accelerated items are the analogue: they are slowed or accelerated in entropy and internal physical processes. Time-acceleration or time-slowing an object doesn't inherently change how that object interacts with other things. Applying time modification to an area of space is how you get a "slow mo" or "fast forward" effect.

Let's look at some examples:

1. An arrow in flight. A lot of the other answers consider an arrow in flight. If you time-accelerate an arrow and then shoot it, I propose that the flight of that arrow would be almost entirely unaffected. The molecules of the arrow are moving faster. That doesn't affect it's flight or it's movement relative to anything else. It will cause the arrow to decompose faster, but that doesn't occur on a relevant timescale.

2. A crossbow. A time-accelerated crossbow will behave quite differently. Here, the enhanced crossbow will release it's spring energy substantially faster than a regular crossbow and therefore impart more acceleration on the crossbow bolt. Conversely, a time-slowed crossbow will shoot less hard. Be careful just to accelerate the crossbow itself and not the space around it.

3. A person. A time-accelerated person will be able to move faster because all of their biological processes causing muscle movements are accelerated.

4. An area of space. A time-slowed area will cause projectiles to fly slower through it, as the entire process of those things moving (air dispersal, gravity, etc.) are slowed. The same will be true of people entering it and leaving it. As soon as things exit the "slow" area, they go back to normal speed.

Now let's deal with physics problems. There are two doozies:

1. How is energy conserved when objects move into a slow area? This one is pretty easy from a high level perspective; the object has the same mass and velocity, but time is slower, so from the perspective of an outside observer, it will go slower. When it exits the area, it will be going faster again. From the perspective of an observer inside the area, everything outside the area is faster than natural and things move at their actual speed when they enter the area.

2. Motion of molecules equals temperature. If the molecules of an object are accelerated, won't that make the object hotter? Conversely if an object is time-stopped, does that mean that it's at absolute zero and will collapse? My best excuse for this is logic similar to that of objects entering or leaving time-modified areas. A time-accelerated object is just one that exists inside a time accelerated field that is precisely the size and shape of that object. So, while the object might read as very hot on a thermal camera or a remote thermometer, from it's own perspective, it remains it's normal temperature. If something comes in contact with it, that thing would be on the boundary of the time field and so would perceive that item as it's true temperature.

Answer 6

Arrow off time, so it is invisible

Suppose your chronomancers could do this trick with arrows, or spears..

Space time is 4d

Time is the 4th dimension. A shift in time will make you disappear, even a shift in Planck time makes you disappear. You're lifted off from our 3d surface. To explain "off", suppose you'd be a flatlander: a flatlander shifted in time will exist somewhere slightly below, or above the universe plane of the flatlanders.

No magic, no interaction

Once you displace an object in time, your time-bow (or time-cannon) will never be precise enough to synchronize, or decelerate the projectile back into the timeline it left off from. Your target is in that timeline. Your arrow will miss any target, because the target will only exist in the unique timeline the arrow left off from. This is also the reason why time machines will never cause paradoxes involving your family or friends, because if you travel to the past, you'll affect the time line you'll arrive in, not your own time line. Only trouble is, when you travel in time, you'll never get back home.

Unless.. there is..

Magic

Yes, magic is needed. The chronomancers should take care of time accelleration and decelleration in such a way, that the arrow returns into precisely the same timeline where the target exists. It could reach the target 800x as fast, you would e.g. see your arrow kill a person instantly. For a person being hit by the arrow, it will not go slower or faster, it only arrives unnoticed.

Suppose you do this with a spear. A victim could see a spear coming in and try to dive away.. but a spear thrown by a chronomancer will always be invisible, it will just suddenly be punching your stomach. You did not see it coming in, because the spear was not in your timeline when it was underway.

Impuls will remain the same: for an arrow, don't take your time shift too long

Any shift in time, e.g. a second will do, to make the arrow disappear. But chronomancers found larger shifts have a disadvantage: they will slow down the arrow. The arrow will keep its impuls in space time. A time deviation too large will reduce the impuls left over for 3d space. Some laws of nature even chronomancers must take into account.

Freeze the target with a sub-nano-second time shift

A speculative & magic idea: there could be some minimal time shift that renders an object really invisible and non-interacting. Some delta (far) above Planck time. If you go below that minimal delta time, you'll see effects. The arrow will become vaguely visible, maybe there would be ice crystals forming, or ionization. In the atomic and molecular ranges, there's a lot of interaction between particles. When a time shift is a certain amount, it could affect e.g. the Brownian motion in gases and fluids. It could reverse impuls, or stop particles that exist in both timelines. The effect would be a freezing cold.

The chronomancer's arrow can penetrate armor

The arrow will not be there while it is moving toward the target.

Second speculation: a chronomancer could use a very quick deceleration, to let the arrow kill a knight in steel armor. It will move through armor indisturbed, while still off time. When the deceleration is accurate, the arrow could penetrate any shield and 'materialize' inside the knights's body.

Answer 7

Depends 100% on what is Facilitating this chronological alteration

As mentioned by another, a possible facilitation of this is a sort of "time-envelope" that envelopes the object within a set amount of space for a set amount of time (I'm assuming the effects are temporary) set by the caster.

• Objects within envelope experience time to be the same relative to each other.
• The surface of the envelope is the boundary of chronological field, may be a sharp boundary (perhaps even visible as it would affect light passing through as though slightly refractive) or a more fuzzy boundary where there's a bit of transition between time speeds.
• What happens though if half an object is in this field and the other half is outside? Or does the whole object have to be contained to work? Can I age just my scalp faster than the rest of me to grow hair quickly, fingertips for nails?
• Objects close to the effected object would be slightly affected the closer they came to the object until entering the envelope and being brought up/down to speed. The collision itself wouldn't seem to be impacted by the change in time flow itself, simply occurring sooner/later than normal. (unless part of the collision is to create a new time-envelope on what ever was hit)

Object specific time alteration, where it is not the space taken up by the object, but the object itself that is altered on the time line.

• The matter of the object itself is targeted and the interaction of time with that specific matter are effected.
• Effective changes to time would be visible through other observable phenomenon. Doubling in velocity, squaring of effective mass/inertia, a slight squeezing/stretching of the object to external observations, to whatever ratio matching the change in time speed.
• A one off effect, rather than a persistent field. (Increase/decrease existing qualities to compensate which then becomes its new "normal time" qualities)
• Affect on non-altered objects would be the same as if affected by a normal object with the new qualities (Hits twice/half as hard etc)

Magic - (You basically just write the rules) Time is a magical force that can be manipulated much like heat, light, and physical work.

• Magic can place the affected in a demi-plane bubble with different properties than the normal universe.
• A magical force pushes or pulls against the stream of time like a paddle, pushing your time bubble further up or down stream.
• A time bubble, when colliding with an object of normal time may POP, causing chrono-side effects (potentially wanted effects in the case of arrows etc) or the bubble may remain in tact and cause the object to "bounce" off. Such a bounce may inadvertently Push the normal-time object forward in time slightly. Pushed hard enough, you might send something or someone into next week!

But again, it just depends on how the whole time altering even works. With more details, I'm sure I can give better options.

General Sanity comments:

• A fraction of a second's worth of "absolute position" in a constantly moving universe would be detrimental to any to discover it, instantly slamming you into the earth, space, or nearby structures.
• Gravity is not apart from Time, as gravity is shown to affect the passage of time, so an object frozen in time would not likely suspend itself midair as the non-time stopped earth would still have it's full pull on it (or the envelope of time containing it).
• There's all sorts of fun to be had with the boundary of a time bubble. Imagine a troop of archers lined up for a volley. A bubble is placed around them to make them fast compared to outside. Suddenly that single volley becomes a carpet of every arrow in their quivers as each shot slows at the boundary while they load and shoot the next volley.
• For interactions between time affected and non-effected objects, I would generally treat the acceleration of time as a multiplication of energy, and a slowing of time a division of energy, until time became normalized relative to the two again.