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If you are going fast, time slow down?


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Actually, it's significantly less than "a second or two". Probably less than a nanosecond or two.

Measurable? yes. Noticable to an unaided human? no.

You would have to get going about 5% light-speed or more, for about a year or so. That might make a difference of a second or two.

Nah, it is much closer to a second, many orders of magnitude more than a nanosecond. Around 30microseconds per day, people have stayed on the iss for over a year, that's around 1% of a second (or 13 million times more than a nanosecond)

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Actually that takes you up to about the speed of light. I caught the error because I remember that you need to accelerate at 1 g for about a full year to get up to c, so 10 gs for 1/10 of a year should also get you to c. (Did that fact that 1g is about 10 m/s^2 trip you up? I do that myself frequently- like, I'll read off some acceleration as like "1 g", and then make the dumb mistake of somewhere in my head of turning that into 1 m/s^2, and then wonder why all my numbers are off of reasonable, expected values by like a factor of 10. This is why there should only be one unit for each kind of measurable quantity :))

No, accelerating at 1g would take a year to get to the speed of light.

(3*10^8)/10 =3*10^7

3*10^7/1E5=3*10^2=300 days.

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No, accelerating at 1g would take a year to get to the speed of light.

(3*10^8)/10 =3*10^7

3*10^7/1E5=3*10^2=300 days.

That's exactly what I said, re-read my post :)

I caught the error because I remember that you need to accelerate at 1 g for about a full year to get up to c, so 10 gs for 1/10 of a year should also get you to c.
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No, accelerating at 1g would take a year to get to the speed of light.

(3*10^8)/10 =3*10^7

3*10^7/1E5=3*10^2=300 days.

Sure it would only take 300 days to get to 1 c. But... the energy requirements for acceleration increase as you get closer to the speed of light. So matter can theoretically get to 0.999999999999999999999999 c but never reach 1.00000000000 c without expending the entire energy of the universe.

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General relativity is famously incredibly computationally demanding in general. It is only really possible to compute it in special cases, general relativity is a large set of coupled non linear partial differentials which are incredibly hard to solve numerically. What you have linked only simulates special relativity. Even 'simple' 2 body cases are still very hard to solve numerically in anything other than special cases.

But lets imagine that we want to include the basic aspect of relativity into KSP as time dilation and fuel consumption (I miss something important?), besides only when you overseed 10% lightspeed.

There is not noticeable cpu consumption there.

Edited by AngelLestat
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Absolutely noone would care

I would. Especially since a model that simulated subatomic physics correctly would probably also mean having a comprehensive and very accurate simulation of all the higher level stuff. Imagine a The Elder Scrolls game where everything is simulated at the lowest level - it would not get much more realistic.

Of course, we are way off that mark when it comes to computer power, not to mention we do not grasp the physics involved. It would not only mean running a realistic simulation, it would also mean winning the Nobel prize for years to come :)

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Sure it would only take 300 days to get to 1 c. But... the energy requirements for acceleration increase as you get closer to the speed of light. So matter can theoretically get to 0.999999999999999999999999 c but never reach 1.00000000000 c without expending the entire energy of the universe.

I've always wondered about this. Doesn't the energy of the fuel you carry with you increase proportionally as your velocity increases? I.e. you need an infinite amount of energy to reach c but you actually have an infinite amount of energy flying at c as your fuel has infinite mass?

In other words the faster you move the more energy you need to accelerate but the more energy expending your fuel gives you offsetting the higher energy requirements.

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I've always wondered about this. Doesn't the energy of the fuel you carry with you increase proportionally as your velocity increases? I.e. you need an infinite amount of energy to reach c but you actually have an infinite amount of energy flying at c as your fuel has infinite mass?

In other words the faster you move the more energy you need to accelerate but the more energy expending your fuel gives you offsetting the higher energy requirements.

No, relativistic mass is a very outdated concept (only a couple years after Einstein first introduced it did Einstein say that the concept should be avoided entirely as it is not useful) that is very very rarely used anymore except in popsci where they aren't intending the audience to actually understand. Relativistic mass is just a term that is used to make some newtonian functions still work relativistically, i.e. momentum is mass * velocity. However, relativistic mass is in no way at all 'mass', in that it does not have the properties of what mass is (i.e. inertia and gravitational charge).

If you go to in a spaceship to a high velocity your ship does not appear to have more mass, nor does it appear to have any more energy in your frame of reference. Otherwise nothing would be consistent, you could just get energy by just considering yourself in a different frame of reference.

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I agree about gravitational charge, since that's stress-energy, anyways. In fact, I'd simply avoid thinking of mass as ever being the gravitational charge. But inertia? Relativistic mass completely agrees with concept of inertia. A particle moving at relativistic velocities requires disproportionately higher impulse to deflect it. That happens to scale precisely with relativistic mass, and precisely because p = mrelv. I agree that one should be very careful with the concept, but it's not "useless" if you know what it really means. Relativistic mass provides some neat algebraic shortcuts for these who know what they are doing.

Frame-dependent quantities aren't bad. They are still important. You just have to be aware of how they transform from a frame to frame. When you are dealing with relativity, keeping track of your frames is important anyhow. There is no added complexity here.

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No, relativistic mass is a very outdated concept (only a couple years after Einstein first introduced it did Einstein say that the concept should be avoided entirely as it is not useful) that is very very rarely used anymore except in popsci where they aren't intending the audience to actually understand. Relativistic mass is just a term that is used to make some newtonian functions still work relativistically, i.e. momentum is mass * velocity. However, relativistic mass is in no way at all 'mass', in that it does not have the properties of what mass is (i.e. inertia and gravitational charge).

If you go to in a spaceship to a high velocity your ship does not appear to have more mass, nor does it appear to have any more energy in your frame of reference. Otherwise nothing would be consistent, you could just get energy by just considering yourself in a different frame of reference.

Ok, I get that. But still, my understanding is that the amount of dv a ship has is a property of that ship and is not dependent on anything else. Let's assume that we are moving at c - 1000 m/s relative to Earth in a ship that has 1000 m/s dv or more. We turn on the engines, facing the direction of our speed vector. What happens from our perspective? After burning the fuel does our speed change by less than 1000 m/s? Of course this would take an infinite amount of time from an outsider's perspective but for us?

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Ok, I get that. But still, my understanding is that the amount of dv a ship has is a property of that ship and is not dependent on anything else. Let's assume that we are moving at c - 1000 m/s relative to Earth in a ship that has 1000 m/s dv or more. We turn on the engines, facing the direction of our speed vector. What happens from our perspective? After burning the fuel does our speed change by less than 1000 m/s? Of course this would take an infinite amount of time from an outsider's perspective but for us?

Velocities don't add like that in relativity. See this link.

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Velocities don't add like that in relativity. See this link.

I apologize for being stupid but please bear with me.

I don't want to add velocities from different frames, I simply want to change my own velocity. I know you are right and that there is a fallacy somewhere in my thinking but my question is where.

Assume some reference frame.

1) I assumed that ship with x dv at rest at 0 m/s in such a reference frame, after expedning the fuel, has a velocity of x m/s.

2) Likewise ship at c - x dv, after expedning the fuel, has a velocity of c.

Now this is obviously wrong but if 2) is wrong then 1) is wrong too (even though the effect is negligible).

This means that there is no absoulte dv of a ship, correct?

Thanks

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Well, yes. 1) is also wrong. The rocket formula is not strictly correct, once you take relativity into account. Your actual dV will be slightly less than you expect. But at "normal" speeds, the deficiency is negligible. When you get close to light speed, discrepancy becomes huge. But the reason it's wrong still goes back to the velocity addition formula.

The correct formula is kind of ugly. But the key to derivation is recognizing that proper acceleration is frame-independent. Which allows you to integrate proper velocity over time. Once you correct for the fact that fuel is expended at a rate proportional to proper time, you can integrate for total velocity gained as function of classical dV. And yes, you always end up with less than dV.

Edit: Special Relativity tends to be pretty straight forward, but once accelerations get involved, some formulae get ugly and derivations tedious. Rocket formula is definitely one of these.

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