Time Travel Query

[Davka]

OK, so sorta pseudo time travel. No going backwards, I have too much respect for simple logic to even go there, but rather the going-forward-faster-due-to-speed kind of travel that's already engaged in (albeit on a tiny scale) by astronauts orbiting Earth. Relativity, and all that jazz.

What I'm mildly curious about is this: let's say we could build a spacecraft capable of doing some insane speed like 0.1 C. How long - subjectively - would a hypothetical human need to travel at that speed in order to return to Earth one Earth-year later? Is there a formula for determining the relationship between relative speed and relative time?

Because i think there's a short story in there somewhere, at the very least.

 

[none]

I am kind of stumped,
if I create a graph of x being distance and y being time...
and I put a point at "300,000 km and one second" the hypotenuse is the distance traveled in one second but it is a greater distance than the speed of light...

 

[DBT]

OK, so sorta pseudo time travel. No going backwards, I have too much respect for simple logic to even go there, but rather the going-forward-faster-due-to-speed kind of travel that's already engaged in (albeit on a tiny scale) by astronauts orbiting Earth. Relativity, and all that jazz.

What I'm mildly curious about is this: let's say we could build a spacecraft capable of doing some insane speed like 0.1 C. How long - subjectively - would a hypothetical human need to travel at that speed in order to return to Earth one Earth-year later? Is there a formula for determining the relationship between relative speed and relative time?

Because i think there's a short story in there somewhere, at the very least.

Lorenz contraction formula.

 

[Kharakov]

What I'm mildly curious about is this: let's say we could build a spacecraft capable of doing some insane speed like 0.1 C. How long - subjectively - would a hypothetical human need to travel at that speed in order to return to Earth one Earth-year later?

.1c isn't really fast enough. Multiply your time by \(\gamma \).

\(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \,\)

If you're doing some number * c you can eliminate c:

\(\gamma = \frac{1}{\sqrt{1-{v^2}}} \,\)

So, as you can c, .1 will give you 1-.01, which isn't that big, although it gets a bit more embiggened by the sqrt since it is less than 1.

 

[Bomb#20]

.1c isn't really fast enough. Multiply your time by \(\gamma \).

\(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \,\)

If you're doing some number * c you can eliminate c:

\(\gamma = \frac{1}{\sqrt{1-{v^2}}} \,\)

So, as you can c, .1 will give you 1-.01, which isn't that big, although it gets a bit more embiggened by the sqrt since it is less than 1.

Or ensmallened, depending on point of view -- it means the dilation is 1 part in 200 instead of 1 part in 100. Curiously, the dilation factor,

\(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \,\)

is the same as the time dilation you get from flying in a crosswind, when v is the wind speed and c is the plane's airspeed.

 

[Underseer]

What I'm mildly curious about is this: let's say we could build a spacecraft capable of doing some insane speed like 0.1 C. How long - subjectively - would a hypothetical human need to travel at that speed in order to return to Earth one Earth-year later?

.1c isn't really fast enough. Multiply your time by \(\gamma \).

\(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \,\)

If you're doing some number * c you can eliminate c:

\(\gamma = \frac{1}{\sqrt{1-{v^2}}} \,\)

So, as you can c, .1 will give you 1-.01, which isn't that big, although it gets a bit more embiggened by the sqrt since it is less than 1.

If v = kc then

\(\gamma = \frac{1}{\sqrt{1-{k^2}}} \,\)

If k = 0.1 then

\(\gamma = \frac{1}{\sqrt{.99}} \,\)

So the amount of time dilation is 1.00503781526...

As you say, pretty insignificant (half a percent) difference. I just felt compelled to correct that second equation (which I assume was a typo of some sort).

 

[Underseer]

To answer Davka's question, if two observers have a difference of speed of 0.1c and one observer measures 365.25 days, then the other observer will measure 365.25 * 1.00503781526 = 367.090062024 days for a difference of 1.84 days or so.

 

[Davka]

Well that kinda sucks! You have to be moving like a quantum bat out of multidimensional hell just to get 2 Earth days for every one of yours - looks like around .8c or so - which sort of defeats the whole purpose. I don't think I can pretend we have ships that can do .99c in a ScientiFiction-y type story. It would need to be pure fantasy.

Or Hollywood.

 

[Kharakov]

.1c isn't really fast enough. Multiply your time by \(\gamma \).

\(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \,\)

If you're doing some number * c you can eliminate c:

\(\gamma = \frac{1}{\sqrt{1-{v^2}}} \,\)

So, as you can c, .1 will give you 1-.01, which isn't that big, although it gets a bit more embiggened by the sqrt since it is less than 1.

Or ensmallened, depending on point of view -- it means the dilation is 1 part in 200 instead of 1 part in 100. Curiously, the dilation factor,

\(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \,\)

is the same as the time dilation you get from flying in a crosswind, when v is the wind speed and c is the plane's airspeed.

In that case, I think they do a total velocity (tv) as well, so \(\gamma=\frac {c}{tv}= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\). In other words, it's just the ratio of the planes airspeed to the total velocity, which means the plane's total velocity is a bit greater because of the crosswind velocity addition.

This doesn't work for relativity though!

 Velocity-addition formula sums it up nicely.

 

[Kharakov]

Well that kinda sucks! You have to be moving like a quantum bat out of multidimensional hell just to get 2 Earth days for every one of yours - looks like around .8c or so - which sort of defeats the whole purpose. I don't think I can pretend we have ships that can do .99c in a ScientiFiction-y type story. It would need to be pure fantasy.

Well, there is the hidden ultra-fast computer under the surface of the moon. A string of processors lies a mere 30 meters below the surface of the moon, encircling the whole moon. These processors were accelerated to close to the speed of light, using technology that makes CERN's LHC look like the work of children.

Information can be programmed into the processors at various points, as the processors whip around at .999999762c. I could get into more details, but I have a roof to patch.

The point is this: 2^16 bit encryption takes a certain amount of time to crack: one must send the information to Alice at the Moon, who sends it to one of the Bobs (there are many Bobs encircling the Moon) to crack, who then sends it back to Alice, who sends it to Ralph on Earth. There is sometimes a backlog, but generally one can crack a 2^16 bit key in under 8 minutes.

Keep that in mind when you believe your communications are secure. They are, unless Ralph sends them to the Moon.

 

[Underseer]

Well that kinda sucks! You have to be moving like a quantum bat out of multidimensional hell just to get 2 Earth days for every one of yours - looks like around .8c or so - which sort of defeats the whole purpose. I don't think I can pretend we have ships that can do .99c in a ScientiFiction-y type story. It would need to be pure fantasy.

Or Hollywood.

A difference in gravity can also cause time dilation (general relativity), but one of the observers would pretty much have to be orbiting a black hole to have any noticeable effect.

 

[bilby]

If you want to have someone in your story go 'away' for a small amount of subjective time, and 'return' to find that a large amount of time has elapsed while they were 'gone', why not just put them to sleep?

Save an awful lot of fuel; running a freezer has got to be cheaper than accelerating to a sizable fraction of c.

Sean McMullen made a bloody good show of using this device in 'The Centurions Empire', in which a Roman travels to the 21st century from 71AD by means of a carefully planned collection of cold-storage opportunities and some undisclosed herbal concoction that made being frozen and re-thawed a survivable experience.

 

[DBT]

Thanks Bilby! Based on your recommendation, I'm buying the ebook.

 

[bilby]

Thanks Bilby! Based on your recommendation, I'm buying the ebook.

I like Sean McMullen. He is an Aussie and has written some great sci-fi that is quite different from the run of the mill.

 

[dystopian]

Well that kinda sucks! You have to be moving like a quantum bat out of multidimensional hell just to get 2 Earth days for every one of yours - looks like around .8c or so - which sort of defeats the whole purpose. I don't think I can pretend we have ships that can do .99c in a ScientiFiction-y type story. It would need to be pure fantasy.

Or Hollywood.

There are a number of designs that could get us pretty close. Project Valkyrie for instance could theoretically hit .92c

 

[Bomb#20]

In that case, I think they do a total velocity (tv) as well, so \(\gamma=\frac {c}{tv}= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\). In other words, it's just the ratio of the planes airspeed to the total velocity, which means the plane's total velocity is a bit greater because of the crosswind velocity addition.

Actually it's a bit less -- it turns out you have to subtract a component of the crosswind from the velocity, because in order to get to your destination you have to turn and face partly into the wind, or else you'll be blown off course and fly past your destination on the downwind side. This leads to the phenomenon of pilots bitching about facing a headwind in both directions of a round trip.

 

[Davka]

If you want to have someone in your story go 'away' for a small amount of subjective time, and 'return' to find that a large amount of time has elapsed while they were 'gone', why not just put them to sleep?

Save an awful lot of fuel; running a freezer has got to be cheaper than accelerating to a sizable fraction of c.

Sean McMullen made a bloody good show of using this device in 'The Centurions Empire', in which a Roman travels to the 21st century from 71AD by means of a carefully planned collection of cold-storage opportunities and some undisclosed herbal concoction that made being frozen and re-thawed a survivable experience.

The idea of human stasis is problematic - how do we prevent cell deterioration? Even if an object is essentially lifeless (and thus not aging in the sense of living things), there is still aging going on. A chair that is 300 years old is far more fragile than one which is new. I suppose we could build a huge lead-lined underground chamber or something, but entropy is a bitch.

I think I prefer the portable black hole, as posited in the classic film Yellow Submarine.

 

[Keith&Co.]

I don't think I can pretend we have ships that can do .99c in a ScientiFiction-y type story. It would need to be pure fantasy.

Or Hollywood.

Make it an accident, then. Some experiment where they tinker with the building blocks of the universe and hope to increase ship's speed by 10%, they turn it on and FWOOSH! It's a year later and there are all sorts of people trying to explain what happened (and each one is sure they'll be vindicted when the ship is recovered). Is it crucial to the story that the pilot KNOW what happened to his ship, or do you just want to throw him a year into the future?

 

[dystopian]

Any sufficiently advanced technology is indistinguishable from magic. I wouldn't put any sort of hard-limits on what real-world future technology might be capable of; the fact that we can't think of a way to do something today doesn't mean its flat-out impossible. And when you're working with fiction you really shouldn't have to limit yourself; so long as it *sounds* plausible, it works. Of course, getting advanced technology to fit into a near-future story is problematic, since it might not seem realistic for our tech to advance fast enough in the time allotted; but then Keith's suggestion works out well there.

As for the problems with the stasis scenario (although I don't see much of a problem with stasis that only lasts a year as is the suggested time frame in the OP); one could imagine something along the lines of self-repairing cells, which is hardly beyond the limits of what we could plausibly achieve. Or maybe cellular damage has taken place in the story, but the society that revives the protagonist has sufficiently advanced medical technology to repair the damage (either entirely, or imperfectly which could be a whole story seed in itself)

 

[Keith&Co.]

And when you're working with fiction you really shouldn't have to limit yourself; so long as it *sounds* plausible, it works.

For 'plausible' you can also consider that readers will forgive a lot if it doesn't seem too easy (magical). In one SF story, the solution to the duration of the spaceship's flight was a drug that sort of caused stasis. They didn't grow older, though they were still awake. The problem was that the live-long effect of the drug had the side effect of making them dumber than rocks.
The computer turned into their babysitter during that part of the flight.
If there's sufficient cost or difficulty, it might even help 'sell' the story.