Although it's not exactly a question about writing, it still seems appropriate to ask here... so here goes.
When you're traveling at speeds close to the speed of light, time becomes dilated. My question is this: Are there any solid ideas of exactly how dilated time becomes? Is there a scale? Do you know what that scale is, or where I could find more information on it?
To be a little more clear... if I were traveling at x% the speed of light, and my ship weighed y tons, how much time difference would there be between me and my starting point upon returning?
Does mass even have anything to do with it? Do we know?
I tried to get this question answered like ten years ago, but the general consensus seemed to be "A lot of people have a lot of different ideas on the subject." and I was wondering if there had been any progress.
I'm asking because, in the book I'm writing, there's near light-speed travel.
[This message has been edited by theokaluza (edited March 05, 2005).]
Not being a math or physics major, I'm venturing into nasty waters here, and I probably won't have the best answer. That said, maybe I can help point in the right direction (even by being wrong).
It's my understanding that the general consensus on relativistic travel is that if time freezes, or seems to freeze, completely at the speed of light, then the slowdown must occur at an exponential rate as you approach that velocity. Again, I may be and probably am completely wrong.
While I don't know how to give you anything exact, or how to find it myself, your speed is obviously the first thing to pick--how far under 180k mph do you want to be? (The more fuel the ship carries, the heavier it has to be--I'm not sure how this affects its mass but it definitely affects its velocity--and depending on what type of engine your ship has it may take an enormous amount of fuel, which also affects your ship's size.) Once you have that, you might be able to rope someone into giving you a guesstimate on both the ship's mass, the amount of fuel necessary to make the trip, and the number of light years it would take to go the distance you want your ship to go--if you're talking near-light speeds, the number of (solar) years it would take would diminish down towards light-years. In other words, a trip that might take 150 years at some low sublight speed to go a distance that takes 35 light years might take 40 years at close-to-light speed.
The answer, put simply, is yes. There are very definate equations (known as Lorentz' equations I believe) that Einstein used to precisely predict both the contraction of space and the dialation of time. I've seen them, they're not that complicated. They look like (and probably are) modified distance formulae. I don't quite remember them, though. If you pick up any copy of "Relativity" and look in the appendix they'll be there staring you in the face.
As for mass and velocity, here's my understanding: Time dialation is a function of velocity only, your percentage of the speed of light dictates the time dialation you experience. However, your mass also increases depending on velocity. The higher your mass, the more thrust it takes to accelerate, and so on. When you near the speed of light your mass actually approaches infinite, which would mean it'd take infinite force to accelerate you past that point. That's one way of saying FTL travel isn't possible (there are many, but they're really just restatements of a central fact that only Einstein himself seemed to be able to compute).
Hope this helps. If any of it was confusing say so, I'll see if I can't explain it better.
The one thing that bothered me about Shadow of the Giant was how hard he worked to make it believable that... - - - - - - SPOILERS - - - - - - Petra would stay behind. When he could easily posit that the weight of 6 more people and their food would cripple the mission. Granting that someone with Bean Syndrome would probably want to prolong their life by restricting calories. But maybe they thought of that and discarded it. - - - - - - - - End Spoilers - - - -
Card posits something he calls "Park shift" that essentially allows an advanced starship to somehow ride its own "wake" from a low percentage of c to a very high percentage of c, which is how he is able to make interstellar war possible in the first place.
So in his universe, your solution to that plot point wouldn't work. That's one of the problems with creating your own universe where relativity and effects that totally disregard conventional physics coexist and are even used together like that. Eventually only your real nut-job fans will be able to keep track of even basic stuff like how much space travel costs.
The short answer is: T * sqrt(1-V^2), where T is the time as measured by the "stationary" observer, and V is the velocity measured as a percentage of light speed.
For example, if you have a ship traveling 20 light years at 90% the speed of light, then the trip (as observed by those not on board) will take 22 and 2/11 years. On board ship, that would be: 22.222 * sqrt(1-0.9^2), or about 9.68 years.
On the other hand, if it were going 99.9% the speed of light, then it would come out to about 9/10 of a year.
It doesn't have anything to do with the mass. And, regarding your informants of ten years ago, this has been pretty much accepted (at least by the physicists) for almost exactly a century (as measured on a rotating, orbiting Earth).
[This message has been edited by rickfisher (edited March 06, 2005).]
Okay, well maybe the ship was only built with four seatbelts. I just think the whole "normal life" thing was not as well presented as it might have been. But maybe I would have understood it better if I had read one of the prequels more recently.
Posts: 366 | Registered: Sep 2006
Just a warning, theokaluza: that equation is for special relativity for a constant velocity. And time is symmetrical with those conditions.
What I mean is that the equation is good for the "stationary observer." But per special relativity, anyone travelling at a constant velocity can be considered a stationary observer. So while the guy on Earth sees the spaceship heading away at 99.9999% of the speed of light (c), and time slowing for the guys on the spaceship, the guys on the spaceship see Earth speeding away at 99.9999% of c, and time slowing down for everyone on Earth exactly the same.
The time changes that create the Twin Paradox (look it up on Google), where one twin ages more slowly than the other, occurs when one of the guys accelerates or decelerates. Otherwise, the other twin will always age more slowly than the observing twin, regardless of which twin you are talking about. (Try to wrap you mind around that one... )
The formulas for time dialation for accelerating and decelerating objects are not easy (or, at least they didn't teach me them in my undergraduate courses), so I can't help you there. Just use the special relativity formula as an approximation, and realize it is only an approximation.
For the twin paradox, you need to do multiple accelerations so as to bring the "traveling" twin back into the same frame of reference as the "stationary" twin. But it doesn't really matter what direction the initial acceleration is in, just so that eventually you bring the twins back together with all the subsequent accelerations.
quote:Just use the special relativity formula as an approximation, and realize it is only an approximation.
You can actually use the special relativity formula to calculate time changes involving acceleration (including the twin paradox), so long as you take into account that what the formula evaluates to changes with a changing velocity. If your ship takes a long time to get up near lightspeed, then you might need to factor that in, and it gets harder; but if most of the trip is at a constant velocity, then ignoring the periods of acceleration at the beginning and end will give you a very good approximation indeed. If you accelerate instantly (and manage not to get squashed), the special relativity formula will give you an exact answer.
As an example of this (one which doesn't require getting squashed), assume that you are floating in space somewhere. Spaceship A passes you at 99.9% the speed of light, and you synchronize clocks with the pilot just as he passes you. After traveling 10 light years A passes spaceship B coming toward you at 99.9% the speed of light. A & B synchronize clocks at that moment. When B finally reaches and passes you, you compare your clock with his, and you'll find that his clock reads .895 years, while yours reads 20.02 years.
It seems really strange that this can work, considering that in A's reference frame, YOUR clock is running slow the whole time, and in B's reference frame, YOUR clock is also running slow. The thing is that, when A and B pass each other, each thinks that your clock reads something way different from what the other thinks.
[This message has been edited by rickfisher (edited March 08, 2005).]
quote:The time changes that create the Twin Paradox (look it up on Google), where one twin ages more slowly than the other, occurs when one of the guys accelerates or decelerates. Otherwise, the other twin will always age more slowly than the observing twin, regardless of which twin you are talking about. (Try to wrap you mind around that one... )
I'm familiar with the twin paradox. That's exactly the effect that I'm trying to reflect accurately in my book.
Any idea what the equation would look like with acceleration and deceleration factored in? Should I go grab a graphing calculator soon?
Simplify, simplify. Round numbers. Fuzzy math. Rick's method works okay...except that two ships can't see each other traveling 199.8% of the speed of light relative to each other, so the synchronization gets messed up pretty badly. I prefer getting even simpler.
How many light years did the "traveling" twin traverse from the POV of the "stationary" twin? Subtract that many years from the time the journey took (again, from the "stationary" twin's perspective) to get the approximate time it took from the "traveling" twin's perspective. And there you have it. Plenty close enough.