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

[Staffan]

Talking of time dilation and relativistic speeds, I was wondering if there were games other than my WOIN system which addressed that? GURPS, perhaps? Does Traveller?

There was a sidebar about it in the Spaceships sourcebook for Alternity, but nothing major.

I think most RPGs ignore it because:

1. It's pretty damn complicated.

2. It does not make for good ongoing storytelling. A character going on an expedition somewhere and returning home to a place where decades or centuries have passed? His reaction to that can make for a cool story. So can a relativistic colony ship being caught up to by a FTL ship (that's sort of the backstory to Clarke's Songs of a Distant World, except the ship catching up isn't FTL per se, just a lot faster because of more recent tech). But a bunch of PCs zipping all over the galaxy while centuries or millenia pass at home in between visits? No thanks.

 

[freyar]

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?

Depends on the definition of "year" you want to use. Astronomers use several different "years" to talk about the orbit of the earth (see wikipedia). The main ones I know of are the Julian year which is exactly 356.25 days (at 24 hrs of 60 mins of 60 s) and the sidereal year, which is a bit longer and describes how long the earth takes to return to a set position with respect to "fixed stars."

A lightyear is c times a Julian year.

Incidentally, c is defined at a fixed value, not measured. We measure the length of a second in terms of radiation from a cesium atom and then multiply by c to get the length of a meter.

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?

Well, I think rather than defining an amount of fuel in terms of the time it would last, you'd probably define the amount of fuel by what kind of trip you can take with it. But for food, you're right. For the people in the rocket, time really does pass more slowly, so they only experience the shorter length of time and therefore eat less food. In this example, it would be the amount of food they'd normally eat in 7 years. And, yes, there'd be a whole new generation of people on earth when they returned.

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?

Well, you'd remove the gravitational contribution to the time difference. But that's very small for earth's gravity in comparison to the effect of the speed.

Gravitational time dilation and time dilation due to orbital speed are both about the same size for a satellite around the earth, and both effects have to be included in calculations of position by GPS. So there are real world applications of all this stuff!

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?

OK, the ship is moving at 0.9c compared to earth. So each year that passes on earth, the ship gets 0.9 lightyears farther away. And vice-versa: according to someone on the ship, the ship is sitting still, and the earth is moving away at 0.9c, so the earth gets 0.9 lightyears farther away each year that passes on the ship. But note that a year on the ship is not a year on earth, and a lightyear measured from the ship is not the same as a lightyear measured from earth either!

Just working from the point of view of earth, if the earth sends out a radio signal 1 year after the ship leaves, the radio signal has to travel both the 0.9 lightyears plus however far the ship travels (according to earth) until the radio signal catches up! With the ship moving that fast, it actually takes 9 years for the radio signal to reach the ship (meaning, it reaches the ship 10 years after the ship leaves earth, as according to earth). And that's 9 lightyears away from earth, as measured by earth. This is one of those situations where you have to think carefully about which reference system you're using.

 

[Scott DeWar]

Ok, lets use a less complicated example: Poxima Centari, and theorize an Earth like (M type is it?) at a livable distance of 8:32 light mins away from Centari.

It is 4.3 light years away. We have a thriving colony there and a ship headed there for trade. Sol 3 sends a message via modulated light to the planet to warn them that the ship has an escaped criminal looking to exact revenge on some leader on Centari 3. I do not know how each is moving in reference to each other, so for the sake of argument and simplicity they are close enough to each others movement that no dilation due to velocity occurs, and each planet is nearly the same mass so no gravitational dilation occurs.

Now the ship is traveling at .9 c [chugga chugga chugga]
leaves on 1 October 2115
murderer escaped the week before, and snuck on board

He was discovered to had snuck on board on 2 October 2115, and the message was sent.

message will arrive 4.3 years later, ship will arrive 4.777... years later

those on the ship will have felt aprox .1672 years pass on the trip, or 61 days.

It is now 1 December to them. the criminal barely had time to get settled in and act like a crew member, or what ever, when he is greeted by the centary prime federal forces.

ok, here is what all of this is getting to:

Do I understand this right? or does the message intelligence get scrambled up in timespace?

 

[Staffan]

You're right in concept, except the numbers are off. For 0.9c the Lorentz factor is about 2.3, so while 4.8 years passed on the "outside", the time on the "inside" is more like 2.1 years than 2 months.

 

[Staffan]

You're right in concept, except the numbers are off. For 0.9c the Lorentz factor is about 2.3, so while 4.8 years passed on the "outside", the time on the "inside" is more like 2.1 years than 2 months.

And sending a message between two more-or-less stationary objects does not scramble anything. Sending it to a moving object (or receiving it from one) would lead to blue- or red-shifting (higher/lower frequencies) - basically the same as a moving car sounding more high-pitched when it's moving toward you than when moving away.

 

[Scott DeWar]

of curse, the Doppler effect.

And that can bee remodulated to a corrected factor.

 

[Umbran]

You're right in concept, except the numbers are off. For 0.9c the Lorentz factor is about 2.3, so while 4.8 years passed on the "outside", the time on the "inside" is more like 2.1 years than 2 months.

Aha! Staffan is right. And, I find that my calculator wasn't functioning as expected, such that I was taking a square when intended to take a square root.

On other models I have used that didn't have a specific square root key, it took "inverse x^2" to be square root. This one didn't, and just processed it as a square. Stupid calculator.

This means that my 7 years upthread is off. Apologies.

 

[Scott DeWar]

Aha, I need to revisit my scribbling and scrawling to se if I had gotten it right after all. I had done it on paper and I coul not come up with 7 SY for 200 EY .

 

[freyar]

What Staffan said.

of curse, the Doppler effect.

And that can bee remodulated to a corrected factor.

And Proxima Centauri/any of its planets are moving slowly enough compared to earth that the Doppler effect isn't a concern there.

Of course, if the ship has a receiver, it could receive a very red-shifted version of the "arrest that murderer!" message and could very simply translate it as noted. So the criminal could be arrested long before the ship reaches its destination.

 

[Scott DeWar]

Well, I was thinking of how hard it would be to hit a small target moving at .9c with such a narrow beam like that of laser communications.