Time and distance at constant C: A sieries of questions for Umbran or other physicists.

[Umbran]

I've tackled this in various ways.

1) You create settings of a size appropriate to your speeds. No FTL, then you stay in the solar system! You can have some amazing space adventures in one solar system.

And if our own solar system seems a bit small, make a bigger one, like Firefly.

2) If nobody else can move faster than light either, it really doesn't matter, as you'll never know what's happening back at home, and it can't affect you. Freeze the PCs for the time required, wake them up. Have some fund with time dilation.

Well, the "fun" in tie dilation is in the interaction with home. Otherwise, relativistic travel is just "one-way trip to another universe" really.

3) Make time and age part of your advancement system. You can "spend" XP in real-time, or "years" in downtime to purchase character advancements, at the cost of growing older.

It still becomes a worldbuilding issue - say some of the PCs take a relativistic jaunt, and others don't. The ones at home advance using years, the ones on the trip by XP. The GM still has to figure out decades worth of world-changes. A system to handle advancing cultures (not just tech, but *cultures*) over time would be a good part of a relativistic travel system.

 

[Scott DeWar]

IF we were to be able to travel at FTL, I recently saw an interesting video on YouTube where it shows travel through our own solar system at light speed for 45 minutes - you do not reach Saturn, but you make it to Jupiter.

but enough of that aside.

As for this:

[sblock=Tom B.]

Do you mean 'C' to be the speed of light? A ship couldn't actually travel at the speed of light, but, in theory, it could travel close to the speed of light.

A ship traveling close to the speed of light will experience time dilation: Clocks on the ship will appear to advance more slowly to an observer which is not in motion (say, someone still on the earth). A clock on a ship moving close to the speed of light will advance quite slowly, and the closer the ships speed gets to C the more slowly the clock will advance.

An observer on the ship won't notice any slowdown of the clock; they are moving more slowly, too. However, an observer on the ship will notice other effects: Distances outside of the ship will shrink in the direction of motion of the ship.

If the ship travels 100 light years away from the earth, then travels back to the earth, both at close to C the speed of light, then, to an observer on the earth, the trip will appear to take 200 years, and the earth will circle the sun 200 times during the journey.

On the other hand, the observer on the ship will notice a much reduced passage of time. How much depends on how long the ship takes to accelerate from a standstill up to C, but in principle the journey can be made arbitrarily short. For the observer on the ship.

Thx!

TomB

There is a discussion here:

https://en.m.wikipedia.org/wiki/Time_dilation

The ratio of elapsed times is represented by the lower case gamma, and is (sorry about the representation):

1/sqrt(1-v^2/c^2)

There is a table here:

https://en.m.wikipedia.org/wiki/Lorentz_factor

For 0.9c, the value is 2.3, for 0.99c -- 7.1, for 0.999c -- 22.

A trip which starts with synchronized clocks, one of which goes on a trip while another stays at home is a version of what is called The Twins Paradox, with clocks and twins exchanged.

Basically, if you put one twin on a rocket and send one on a trip of 11 light years and back (so 22 ly total), at 0.999c, the twin on the rocket will age 1 year while the twin that stays at home will age 22 years.

What happens on the rocket won't affect what happens at home (unless it crashes on return without slowing down!). And other than accelerations, the twin on the rocket won't perceive anything different inside the rocket.

Thx!

TomB

[/sblock]

I will have to write down stuff to get it to process, otherwise it means a lot of dream time and that takes too long.

 

[freyar]

I'm late to the party, but...

Ok, I should have been more detailed of what I was thinking. Sorry.

I meant to say at .99C, but we will go with the theoretical .9 C

Also, I meant to mention two clocks synced on earth - both atomic clocks for accuracy

Also, let us say, for the sake of argument they can "instantly accelerate to C" for passing of time.

So, the time dilation would be:

a. they wold have traveled a total of 180 light years, round trip

b. it took 7 years to those on the ship

c. Earth has moved through the cosmos the distance it would have after 200 years at the present movement that we are at right now, baring any form of "eternal force"

d. To the earth, It would look like 200 Years had passed

e. (and of course I HAVE to have the humor) it is caused that way because it is a wibbly wobbly timey wimy thing.

Do I have that correct?

Just about, but we have to be a bit more careful, actually (I'd have to mark off a bit in my class ). What we need to know is what the .9c speed of the rocket is measured with respect to. People generally seem to be assuming that the rocket is moving at 0.9c with respect to the earth, but then that means the earth wouldn't move IF the earth weren't accelerating. In other words, all that time passes on the earth, but the earth is sitting still.

But the earth's motion around the sun accelerates, so we don't really want to use that as a benchmark. It's better to say that the rocket moves at 0.9c with respect to the sun, while the earth orbits the sun. That's a much better approximation, since the sun accelerates very little in its motion around the galaxy. Of course, from the point of view of the earth, that 0.9c rocket travel is modulated just a bit by the motion of the earth around the sun.

Or we could say that the rocket moves at 0.9c with respect to the galaxy. Then the sun is moving through the galaxy, too, which sounds closest to what you've described. But then, according to the sun, the rocket isn't moving quite at 0.9c either on the way out or the way back.

Of course, the motion of the sun around the galaxy and the earth around the sun are at very small speeds compared to c, so these are all very minor corrections to the big picture everyone's talked about. But usually in relativity we need to be pretty clear about the question we're asking as the answer can come out quite differently in slightly different situations.

 

[Scott DeWar]

Frrayer, you already mentioned in another thread that you were going to bee scarce, so no worries.

 

[Scott DeWar]

I'm late to the party, but... * * * * *stuff * * * * *Of course, the motion of the sun around the galaxy and the earth around the sun are at very small speeds compared to c, so these are all very minor corrections to the big picture everyone's talked about. But usually in relativity we need to be pretty clear about the question we're asking as the answer can come out quite differently in slightly different situations.

there you go againd messing up my nice neat little world.

SiGH . . . I will think on this. I am not sure of what my answer should be here.

 

[freyar]

there you go againd messing up my nice neat little world.

SiGH . . . I will think on this. I am not sure of what my answer should be here.

Well, in this case it doesn't make a practical difference. In fact, in class, I usually pretend the earth doesn't accelerate. But suppose you said that the rocket is moving at 0.9c compared to a distant galaxy that's moving at 0.5c compared to our Milky Way galaxy (just as a silly example). That would make a big difference.

 

[Umbran]

Well, in this case it doesn't make a practical difference.

There is a phrase often used by physicists (and other hard sciences): "...to first approximation..." It is a useful concept here.

There's an actual technical definition (see Wikipedia, "Orders of Approximation") , but, for our purposes, it means, "Taking the strongest factor into account, and leaving out the smaller factors".

A *lot* of what I say here is really to first approximation, because the secondary (and tertiary, and so on) factors will often seem like major complications, that will typically get in the way of understanding the base concept. If Freyar and I have disagreements, it is usually that I think he's jumped on to secondary effects before we've established that folks understand the primary ones.

So, to first approximation, as compared to the speed of light, the Earth can be considered stationary.

Then, you can lay upon that the motions of the sun through the galaxy, and the Earth around the Sun. Note that, on long average (say, over a trip that will take the Earth around the Sun 90 times) the Earth's motion around the Sun won't mean much, as it is pretty much a closed loop - over the long haul, that loop will average out to almost zero. And yes, the Sun moves a bit, but you already had that in mind. The way you drew it, the Sun's motion was pretty much perpendicular to the ship's motion, which also decreases the impact of that motion to the main picture.

 

[Scott DeWar]

Re: Orders of approximation

I figured there was some sort of saying to go with this. And yes, I am working at the first order her. Especially since I am on day one of caffeine deprivation. Also, considering my level of knowledge and understanding, I think keeping it at the first order is always a safe bet.

So take that Freyar! :rofl:

 

[freyar]

A *lot* of what I say here is really to first approximation, because the secondary (and tertiary, and so on) factors will often seem like major complications, that will typically get in the way of understanding the base concept. If Freyar and I have disagreements, it is usually that I think he's jumped on to secondary effects before we've established that folks understand the primary ones.

Haha, yes. Either that or we're thinking about slightly different problems with somewhat different distinction between lowest order and higher order effects (see example below). I also have a pretty low tolerance for introducing small errors to keep the focus on the lowest order stuff, which is partly because I teach upper-division university students.

I figured there was some sort of saying to go with this. And yes, I am working at the first order her. Especially since I am on day one of caffeine deprivation. Also, considering my level of knowledge and understanding, I think keeping it at the first order is always a safe bet.

Caffeine deprivation? Horrors! You have my sympathies.

Here's why I brought up that more subtle point. It's true, if you're looking at time dilation effects, that the speed of the earth around the sun (for example) is a totally trivial consideration. But suppose we talk about the motion of the earth while the rocket was gone for 100 years (and let's completely ignore the motion of the sun around the galaxy). There are two cases we might be interested in. One is that the rocket is moving in a straight line with respect to the rest frame of the sun, which is the same as the earth's average rest frame. Then the rocket goes out and comes back and gets to the earth 100 earth years later. But what if the rocket moves in a straight line at 0.9c out and then back as seen from the earth's instantaneous rest frame at the time of launch. At any given moment, the earth is moving about 30 km/s with respect to the sun. If the rocket moves along the same direction, everything is the same as the other case. But if the rocket moves perpendicularly to that, it's path isn't just straight away from the earth and straight back. It's away from the earth and back to where the earth would have been if the earth left its orbit around the sun and went off at a constant velocity. That'd be about 90 billion km away from the earth's position.

Anyway, I looked more carefully at your drawing. Your rocket is moving in straight lines at 0.9c with respect to the sun but as shown from the perspective of the galaxy.

 

[Scott DeWar]

Ok, professors, I am working on paper what you have shown me, but I have a quick question regarding a light year.

given velocity of C is (Apx.) 299,792,458 M/s

how long is one year?

is it:
1. 365 days at 24 hours/ day at 60 mines per hour at 60 seconds/ minute?

2. 365.25 [taking in account leap year to get closer to the astronomical year] 24 hours/ day at 60 mines per hour at 60 seconds/ minute?

or

3. do we use 365.256363004 days here?

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also, I am guessing the ship that traveled for 100 earth years, if given enough fuel and rations to travel 100 years traveling at .9c to get to the star that is 92 light years away would only use a little over 7 years of food and fuel, returning to earth to find a whole new generation of people on earth, right?

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also,
I saw in one of the wiki pages that velocity is not the only effect on time, gravity too.
on this, if the ship is moving at .9 c, it will slow time in reference to Terra, but at 0 g it will speed time, but at an amount way less then the velocity effect is
but if there was a way to produce say a gravity of 1 earth grav, there would be no time disparity . . . Right?

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on communication, radio or light either one moving at C, would anything happen to the signal en-route, time wise?

if the ship has traveled .9 light year, and earth sent a message aimed to intercept the ship at that point and timed to transmit 0.11...[repeat 1] Earth years down the road using the first order of approximation of 100 earth years to 3.5 ship years. Do I understand this right? I figure the ship will have traveled .035 SY. Am I right?

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Anyway, I looked more carefully at your drawing. Your rocket is moving in straight lines at 0.9c with respect to the sun but as shown from the perspective of the galaxy.

by the way, that is correct

As for all of the various movements of the celestial bodies being factored in, that is a couple of orders of complications that is way over what I can handle at my early stages of comprehension.