Time dilation time travel for novel - I need a calculation

[writer]

Hi!

I've written a novel in which my main character travels through time (into the future) 18 years. While the concept of time travel is necessary to the plot, the details are not. Meaning, the book isn't sci-fi, but contains elements that wouldn't normally exist in a contemporary novel, so while my readers won't (generally) be fact-checking my science, they need to know its possible, it happens, and the amount of time to do so is reasonable. That said, I wanted a generally plausible method of time travel, so I do make mention of time-dilation as it relates to time travel.

Therein lies my question. Setting aside precisely "how", rather, just assuming easy future time travel were to exist (think TARDIS) - that we have the kind of thrust and vehicle available to easily approach the speed of light, and then return to Earth without issue - can someone please give me the plausible amount of time that one would have to travel on board their spaceship/time machine in order to have 18 years of time pass on earth?

Thank you for your calculations and consideration!

 

[Nugatory]

can someone please give me the plausible amount of time that one would have to travel on board their spaceship/time machine in order to have 18 years of time pass on earth?

There's nothing particularly special about time traveling into the future. That's something that we're all doing, at the rate of one second into the future every second (and after five or six decades one gets tired of it, even though it does beat the alternative). So you don't need a time machine at all, just a spaceship that leaves Earth and returns to Earth eighteen years later; the faster the spaceship moves the less time will have passed on the spaceship.

The standard time dilation formula will let you choose any combination of speed of ship and travel time on ship to get to eighteen years on earth: $T_E=T_S/\sqrt{1-v^2/c^2}$ where $T_E$ and $T_S$ are the time elapsed on Earth and on the spaceship. Note that you can make $T_E$ as large as you want by choosing $v$ fast enough, but you can never make either of them negative - no going back in time.

 

[writer]

There's nothing particularly special about time traveling into the future. That's something that we're all doing, at the rate of one second into the future every second (and after five or six decades one gets tired of it, even though it does beat the alternative). So you don't need a time machine at all, just a spaceship that leaves Earth and returns to Earth eighteen years later; the faster the spaceship moves the less time will have passed on the spaceship.

The standard time dilation formula will let you choose any combination of speed of ship and travel time on ship to get to eighteen years on earth: $T_E=T_S/\sqrt{1-v^2/c^2}$ where $T_E$ and $T_S$ are the time elapsed on Earth and on the spaceship. Note that you can make $T_E$ as large as you want by choosing $v$ fast enough, but you can never make either of them negative - no going back in time.

Thank you for your answer... and levity. :)
My character does actually travel in a commercial "pod" returning to Earth after an elapsed earthtime of 18 years. It is gratifying to know this, at least, makes "sense". However, at the risk of sounding stupid... I am not a mathematician in any sense of the word, thus the formula you propose reads like Greek to me. Any chance you could plug in 18 for T_E and give me the result of T_S... (again making the assumption that achieving the necessary V is attainable)? Or do you need to have a set V in order to make this formula work?

 

[PeroK]

Hi!

I've written a novel in which my main character travels through time (into the future) 18 years. While the concept of time travel is necessary to the plot, the details are not. Meaning, the book isn't sci-fi, but contains elements that wouldn't normally exist in a contemporary novel, so while my readers won't (generally) be fact-checking my science, they need to know its possible, it happens, and the amount of time to do so is reasonable. That said, I wanted a generally plausible method of time travel, so I do make mention of time-dilation as it relates to time travel.

Therein lies my question. Setting aside precisely "how", rather, just assuming easy future time travel were to exist (think TARDIS) - that we have the kind of thrust and vehicle available to easily approach the speed of light, and then return to Earth without issue - can someone please give me the plausible amount of time that one would have to travel on board their spaceship/time machine in order to have 18 years of time pass on earth?

Thank you for your calculations and consideration!

One idea is to assume that the spaceship accelerates constantly at our normal gravitational acceleration $g$. This would allow normal gravity on board during the trip. It would then take about a year to get near the speed of light and about a year to decelerate from close to the speed of light. Very roughly, you'd age by two years in this case.

The problem of course, is that you cannot make stops on the way. Or, at least, it costs you about 2 years every time you do. So, if you wanted to make one stop somewhere, then you'd be about 4 years older when you got back to Earth. So, roughly, add two years for every stop along the way!

Edit: I did a quick calculation. It would take 2 years (ship time) to get to 97% of the speed of light. So, you should double those numbers. I.e. minimum of 4-5 years aging on ship for a simple out and back. And, more like 10 years if you make one stop. If you make more than one stop you get very little from time dilation.

Perhaps this is why most sci-fi writers tend to ignore the physics and assume instantaneous acceleration to near light speed!

 

[Nugatory]

I am not a mathematician in any sense of the word, thus the formula you propose reads like Greek to me. Any chance you could plug in 18 for T_E and give me the result of T_S... (again making the assumption that achieving the necessary V is attainable)? Or do you need to have a set V in order to make this formula work?

You have to choose a $v$. The closer to the speed of light $v$ is, the smaller the time passed on ship is... which is why I said that you dial in pretty much any amount of on-ship time that works for your plot.

A few examples:
- At 99.9% of lightspeed, 294 days on the ship will pass while eighteen years pass on earth.
- At 99.99%, it will be 93 days
- At 99.999% it will be 30 days
- At 99.9999% it will be 9 days

If you can once get that formula into a spreadsheet you can run off your own table in no time at all.

(All of this is assuming a constant speed, ignoring the acceleration as the ship speeds up and slows down at the ends of the journey. That's a completely impractical assumption... but this is fiction, right?)

 

[Nugatory]

You may also be interested to know that the energy required bring a one-ton spaceship up 99.9999% of the speed of light is approximately one thousand time current annual worldwide energy production from all sources.

 

[writer]

(All of this is assuming a constant speed, ignoring the acceleration as the ship speeds up and slows down at the ends of the journey. That's a completely impractical assumption... but this is fiction, right?)

Yes. In which I will also be ignoring the implied G forces a human would have to sustain in order to get to that speed.

Thank you!

 

[writer]

If you make more than one stop you get very little from time dilation.

This is a concern... along with the amount of time it would get to the speed (and the G-forces you'd have to sustain). No stops; just "simple" out/back.

Perhaps this is why most sci-fi writers tend to ignore the physics and assume instantaneous acceleration to near light speed!

Right you are. :)

 

[guywithdoubts]

Thank you for your answer... and levity. :)
My character does actually travel in a commercial "pod" returning to Earth after an elapsed earthtime of 18 years. It is gratifying to know this, at least, makes "sense". However, at the risk of sounding stupid... I am not a mathematician in any sense of the word, thus the formula you propose reads like Greek to me. Any chance you could plug in 18 for T_E and give me the result of T_S... (again making the assumption that achieving the necessary V is attainable)? Or do you need to have a set V in order to make this formula work?

You have to either pick the amount of time the character will spend in the ship (which will give you a velocity) or the velocity (which will give you the amount of time spend in the ship). If you want your character to spend a certain amount of time traveling (say, a day, fifteen minutes, you name it) then do this:

- Divide this amount of time by the 18 years, then square the result
- Substract this number to one (1 - that result)
- Multiply this number by the speed of light squared
- Get the square root of this number

That will give you the speed the ship will need to travel at. Remember to use the same units of length and time (so if you will using the speed of light in km/s, then you can't use years, but seconds, some googling should do.)

ps. I haven't done any math in years, wait until someone makes sure I didn't make any horrible mistakes.

 

[writer]

You may also be interested to know that the energy required bring a one-ton spaceship up 99.9999% of the speed of light is approximately one thousand time current annual worldwide energy production from all sources.

Which is of course why this is set in the future, where energy is abundant and limitless. ;)

 

[Smattering]

You may also be interested to know that the energy required bring a one-ton spaceship up 99.9999% of the speed of light is approximately one thousand time current annual worldwide energy production from all sources.

If the main point is to "send someone into the future", then maybe just freezing him (as in Futurama) is closer to reality than this.

 

[yammy23]

Question for you smart people out there. I'm also working on a novel and was wondering if it's possible for another Planet's time flow to run faster than Earth's.

For instance, approx. 2 years there is 3 days on Earth.

if so how can that work?

 

[Ibix]

Not unless the Earth is moved near to a black hole, probably a supermassive one, or is moving at very very very close to the speed of light.

 

[yammy23]

So it's impossible to work with this idea? Would it differ if the Plant was in a different dimension?

Sorry for my lack of clarity, I'm just not too knowledgeable on these concepts so want to get a better idea on how I can make my idea work. If it's even possible of course.

 

[Ibix]

The clock rate is related to the gravitational potential. The closer you get to a massive body, the slower your clocks run (there are subtleties, but that'll do for this discussion) - but even at the surface of the Sun you only get about a minute less per year spent in intergalactic space. There's nowhere "further up" to be in order to get more time dilation. Sorry.

"Different dimension" is a science fiction concept, not a scientific one. Give it whatever rules you like.

 

[Nugatory]

So it's impossible to work with this idea? Would it differ if the Plant was in a different dimension?

"In a different dimension" sounds more scientific and technical than "All mimsy were the borogoves" but it's just as much nonsense. You can say it means whatever you please.

 

[yammy23]

Thanks! much appreciated!