Reality Check: Controling time to produce velocity

Question

Background

I recently had some fun watching YouTube videos about redefining the nature of gravity based on the existence and flow or "velocity" of time. (Example) and it got me thinking of an application that I want to build into my world.

The Logic of My World

Technology allows for the control of time in a limited region of space. If you're tempted to ask "how?" let me refer you to L. Ron Hubbard's Battlefield Earth, where Psychlo transportation was based on the teleportation of space from one location to another. Since the space within the engine moved, the vehicle housing the engine had to move with it. In my world, that same small space (the engine housing) is where time is manipulated.¹

The reason, in my world, that this works is expressed by this simplistic graph:

In the "real world," time is always experienced at the same rate (one second = one second). But when we change frame references (i.e., when an observer on Earth sees a hypothetical rocket flying at the speed of light), we can see a difference in time. This is discussed briefly in the above linked video in relation to GPS satellites. From the satellite's perspective, a single second has ticked by. But from ours, there's a minuscule difference that adds up to a measurable GPS error.²

It's important to stop for a moment and point out that I have no honking idea what the shape of the curve shown in the above graph really is. I based it on charts of time dilation like the one seen in this article. Take it as a rule of my world that the chart reflects the basic truth of my world.

Now, using Earth as a quick and convenient point of reference to explain an example "flow of time," consider the following:

The satellite clocks are moving at 14,000 km/hr in orbits that circle the Earth twice per day, much faster than clocks on the surface of the Earth, and Einstein's theory of special relativity says that rapidly moving clocks tick more slowly, by about seven microseconds (millionths of a second) per day. (Source)

Earth rotates at about 1,674 km/hr. Applying the simple logic of my world: when $\Delta{V}=12,326$ then $\Delta{T}=7 \mu{S}$. So, in my world, forcing a particular flow of time ($V_T$) demands an associated velocity vector ($V_{X,Y,Z}$). You can't have one without the other, and the velocity vector's direction can be modified. This results in a difference in the flow of time inside the "engine housing" and outside of it, so to get the (rounding) 11 km/s velocity needed to escape the gravity of a planet equal in size to the Earth, the "engine housing" must experience a flow of time approximately 22.5 ns faster than what's around it.^{3, 4}

Speeding and Slowing Time creates Positive and Negative thrust

An issue on my world is the need to control time gently. If you snapped the "engine housing" to +22.5ns you'd instantly be going 11 km/s. Oof. How fast the flow of time can or should be changed isn't contemplated in this post, it's merely mentioned for the sake of completeness.

However, it must be mentioned that if slowing time gets you to +11 km/s (compared to a velocity of 0 on the planet's surface), then speeding time would get you to -11 km/s (again, compared to a velocity of 0 on the planet's surface).

So it's possible to both speed up and slow down.

The range of thrust is limited

Since the graph has exponential curves toward both maximums, there's a practical limit to the amount of thrust that can be produced. Using the time dilation curve from the article I linked, above, and reproduced below, this solution is only really good to travel up to 90% the speed of light before the control of time becomes too difficult. An argument could be made that there's as much difficulty traveling below 10% of the speed of light due to too little control of velocity — which would nullify the example of escape velocity.

One Problem...

Finally, there's a problem on my world, because forcing a $V_T$ must necessarily cause a $V_{X,Y,Z}$, it's also true that it must necessarily cause a change in gravity. Very generally speaking, in the real world, as velocity increases, time slows down. As gravity increases, time slows down. Said another way by quoting from that last source...

Also, the orbiting clocks are 20,000 km above the Earth, and experience gravity that is four times weaker than that on the ground. Einstein's general relativity theory says that gravity curves space and time, resulting in a tendency for the orbiting clocks to tick slightly faster, by about 45 microseconds per day. The net result is that time on a GPS satellite clock advances faster than a clock on the ground by about 38 microseconds per day.

So, 4X weaker gravity speeds up time by 45 microseconds or 1 microsecond =~ about a 0.09X change in gravity. Slowing by 22.5 ns = 0.0225 us therefore gravity increases by 0.002X, which should be trivially ignorable for escaping Earth-like gravity, right?⁵

The Consequence

The control of time might allow my world to create micro-thrust (or, more accurately, a micro-velocity) with an ignorable amount of change in gravity but can create velocity between 10% and 90% of the speed of light. Gravitational consequences for that range have been skipped in this post.

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About Reality Checks

I've tagged this post "Reality Check" and that's why you don't see an actual question stated anywhere. It's one of the reasons why the tag is so often misunderstood. Another is that the "reality" the tag refers to is the reality of the post's world — NOT the reality of real life. You can think of the tag as expecting respondents to answer the question, "does the scenario I present below fit logically into the rules of my world?" Answers are expected to be of the form "Yes" and "No, and here's why"

The least valuable kind of answer has the form, "No, because in real life X." Remember that the reference for judgment is the world of the post, not real life. The respondent may have pointed out something interesting, but the answer could be intrinsically wrong because the rules of the post's world did away with whatever X was.

If I've done my thinking well enough, then the goal is to get someone to say "yes" and have it up voted a lot.

But, nothing's perfect, right? So the most valuable answer has the form, "yes, but... [or] no, because... in real life X, but if we adjust the rules of your world Y, we have an uber cool solution that makes the scenario consistent with your rules and would make Larry Niven wish he'd had access to Worldbuilding.SE."

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_{¹ And it's a good thing that it's in a small region of space. If we assume the field encompassed the entire space ship, then you could enjoy attending Julia Davenport's 59th birthday and retirement party, celebrating 125 years of dedicated shuttle service. She'd appreciate gifts of coins minted on her birthday.}

_{² This begs a second question, which I might ask. Remember, rules of my world and not necessarily Real Life, right? If you force the flow of time to its theoretical maximum, meaning that all motion has stopped, do you get a form of stasis? Meaning, is it kinda the same as time "stopping" because matter, all matter, in the affected region has stopped moving completely (no electron orbits, no nothin' folks) and therefore cannot age or change despite the fastest flow of time compared to any other reference frame. It brings to mind the Dr. Who void ships. But it's an interesting bit of symmetry that aging (for lack of a better reference) would stop at both ends of the curve. It suggests that the turning point or "knee point" on the curve is the only truly useful reference frame — but I digress.}

_{³ The astute reader will note that what I just did was apply a linear extrapolation to my curve. I assert that the differences in speed and time are so small that I can approximate the curve with a very short straight line. I could be wrong.}

_{⁴ BTW, if you didn't just notice, this idea would lend incredibly well to a bomb. "Detonating" a time bomb by offsetting time by mere microseconds would, I think, level cities. If there's ever to be an argument against the viability of time travel, this is it. The moment you turned on a time portal to travel one second into the past you just created an extinction-level event, which is why Earth has never seen a verifiable visitor from the future (boom!). Or, at least it's fun to think of it that way. Just don't mess with my engines without a responsible parent present.}

_{⁵ Go re-read footnote #2. What we could be saying here is that when you hit the maximum flow of time, you've not only stopped moving entirely, you've also nullified all gravitational influences and set your own to zero. In wonderful SciFi parlance, just as FTL could be thought of as moving backward through time (negative time) or through "imaginary time," exceeding the maximum flow of time would crate anti-gravity or "imaginary gravity." Oh, there's some fun to be had with that idea....}

Answer 1

It passes my reality check, but the theory of Relativity will be very different in your world. Here's my guess about your world's theory. I don't have the foggiest idea of how the actual Relativity equations will change!

Let's limit movement to only one spatial dimension, and plot it against time (time on x axis, distance on y axis).

In your world, a trajectory (aided by the engine) is actually a parametric curve on the space-time. The curve's parameter is the time inside the engine (t_i), the x axis is the time outside (t_o), and the y axis is the space dimension.

What your engine does is to rotate the tangent vector (t_o, s) of the trajectory, corresponding to the speed and time displacement outside the engine. The trajectory curve can go in any direction, but with limited vector length, no more than a constant.

Without the engine, t_i = t_o, and the trajectory curve points somewhere to the right, as in our world, and the vector length is < c, where c is the light speed. Our Relativity becomes a special case of the theory.

Your world's gravity turns to be the curvature of the trajectory curve, making negative gravity not only possible, but a occasional consequence of the equations.

Answer 2

Instead of a drive perhaps consider a Wormhole.

The classical problem with most FTL drives and wormhole models (WH) is that they can violate causality. For example they let travelers arrive at their destination before the photons announcing their departure do. Which in Einsteinian Spacetime means effectively means traveling into the past (non causality breaching drive and WH models excepted).

Since WH link two distant points in space time by shortening the distance between them you could maintain and have (apparently - to an outside observer) relativistic travel speeds by specifying a type of WH where time inside it slows in proportion to the length of the wormhole. So that a 10 light year trip still take 10 years to complete, even if the 'apparent distance' (to the extent that term would have any meaning) inside a WH between it's two ends only 1000 meters!

Time starts out flowing at the normal rate until a ship passes over through its lip/horizon. Then as the ship 'falls' through the WH the rate at which time slows accelerates along a predictable curve until it reaches the center of the wormhole where time has slowed to its maxima. After that point the curve reverses and time flow returns back towards its 'normal' rate, reaching it as the ship exits.

The plus side is that depending on how 'long' the inside of a wormhole is you get to speeds almost equivalent to that of light. The really BIG plus however is that the wormhole is your engine. As long as it has provisions for the crew/hibernation chambers etc it theory any ship can travel to another star system with the simplest of engines, even just a simple rocket drive i.e. something with just enough thrust to propel it into the mouth of the wormhole and then brake when it exists at the other end.

The big downside is f course is that all trips are still slower than light (but only just).