Effects of Special Realitivty on STL vessel

[FreeThinker]

Alright, from my understanding the fast you travel , the more your will get under the influense of Relativity

The effects by relativity can be calculated by R = 1 / SQRT(1 - V^2 / C^2 )

Quote

This was formulated by the German-American physicist and mathematician Albert Einstein (1879-1955) in his Special Theory of Relativity. Basically, an object in motion undergoes 3 relativistic changes:
1) An increase in mass
2) A contraction in the direction of travel (Lorentz Transformation) and
3) A "slowing down" of time. (Time Dilation)

Now from my understanding  effect 2 merely optical effect for external observers and effect 3 only has effect on the aging of the crew and vesel. (making the crew and vessel age slower)

Effect 1 is the most important one because it prevent traveling faster than speed of light as mass becomes infinite.

For KSPI-E Daedaul engine I want these relaitivy effect to effect space travel with the Daedalus engine.

As I see it, this can be achieved by making to overal mass of the engine higher or by adjusting the thrust and ISP  of the Daedalus fusion engine.

Seems to me option 2 is the easiers to achieve, as you need to only adjust THrust and Isp by Ralatively effectily making the engine slower untill it becomes close to zero.

However this would only affect the engine performance and not anything else.

 

My Qyestion is, should the increase in relativistic mass also have an effect other operations, like rotating the ship by RCS?

Edited July 22, 2016 by FreeThinker

[Boris-Barboris]

For a observer (player), piloting that ship, nothing in the ship should change at all, mass included. I would actually recommend leaving the idea for later, there are several hardcoded things in KSP core that will not let you properly account for STR effects.

Edited July 22, 2016 by Boris-Barboris

[Green Baron]

https://en.wikipedia.org/wiki/Mass_in_special_relativity

So i'd say as an answer: observed from on board that ship "no" (reaction mass increases as well). Viewed from outside "yes".

I think ... but i'm sure a specialist will show up soon.

Edit: partly ninja'd :-)

Edited July 22, 2016 by Green Baron

[FreeThinker]

8 minutes ago, Boris-Barboris said:

For a observer (player), piloting that ship, nothing in the ship should change at all, mass included. I would actually recommend leaving the idea for later, there are several hardcoded things in KSP core that will not let you properly account for STR effects.

Well the player is by definition an external observer. So in our context Special Relativity only has an effect on accelating/de-accelating, meaning adjusting the engine effective Thrust & Isp shuold be sufficient to prevent FTL travel

1 minute ago, Green Baron said:

https://en.wikipedia.org/wiki/Mass_in_special_relativity

So i'd say as an answer: observed from on board that ship "no" (reaction mass increases as well). Viewed from outside "yes".

I think ... but i'm sure a specialist will show up soon.

Edit: partly ninja'd :-)

Ah, so vieved externaly, the vessel will appear to turn slower but the overal fuel required to do so remains the same ...

Edited July 22, 2016 by FreeThinker

[Green Baron]

I expect it to be very difficult to model the different time frames of objects moving at relativistic speeds in relation to each other. That'll probably be the most challenging part .... ?

 

 

[FreeThinker]

15 minutes ago, Green Baron said:

I expect it to be very difficult to model the different time frames of objects moving at relativistic speeds in relation to each other. That'll probably be the most challenging part .... ?

 

 

Well it doesn't have to be exact in every way, I just want to want to correct the effects on delta V, making it harder to accelate the faster you travel, effectivly prevent faster than light travel.

Edited July 22, 2016 by FreeThinker

[Boris-Barboris]

Then probably changing thrusts is the best thing to do, judging by what you want to achieve. Masses are better to stay untouched, or you'll mess with too many dependencies and connections, especially part physics. Thrust reduction is enough to simulate what you want i think.

 

upd: isp must change indeed, sorry.

Edited July 22, 2016 by Boris-Barboris
Rusty

[Green Baron]

I see. In that case you're probably fine with the relativistic momentum E https://en.wikipedia.org/wiki/Energy–momentum_relation and relativistic Mass Mrel = E/c² ...

Looking forward to your results :-)

 

[FreeThinker]

32 minutes ago, Green Baron said:

I see. In that case you're probably fine with the relativistic momentum E https://en.wikipedia.org/wiki/Energy–momentum_relation and relativistic Mass Mrel = E/c² ...

Looking forward to your results :-)

 

I'm afraid I do not understand how to apply these equations for my case, perhaps anyone could help?

let's say Relativity  = 1.1

now how to adjust engine thust and Isp ?

My initial first tough was I could apply the effect lineary:

AdjustedIsp = (1 /  Relativity)  * engine Isp

AdjustedThrust = (1 /  Relativity)  * engine  thrust

Is this right or wrong? How to calculate it correctly?

Edited July 22, 2016 by FreeThinker

[Green Baron]

I fear i'm no specialist eithier (hoped one would show up), but from what i read the denominator c² is constant while the enumerator grows quadratical.

What you could use ist the Tolman-Expression of mass of a moving body (from the wikipedia articel: m0(1 - v2/c2)^(−1/2), m0 is rest mass and the relativistic version of f=m*a:

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

If that doesn't help then compute the mass for a given case once in intervals of let's say 0.1c until 0.8c and 0.01c for the rest and apply the curve to your spaceship. Kerbal style :-)

Edit: i meant for a mass of 1, in order to obtain factors for multiplication.

 

Edited July 22, 2016 by Green Baron

[FreeThinker]

20 minutes ago, Green Baron said:

I fear i'm no specialist eithier (hoped one would show up), but from what i read the denominator c² is constant while the enumerator grows quadratical.

What you could use ist the Tolman-Expression of mass of a moving body (from the wikipedia articel: m0(1 - v2/c2)^(−1/2), m0 is rest mass and the relativistic version of f=m*a:

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

If that doesn't help then compute the mass for a given case once in intervals of let's say 0.1c until 0.8c and 0.01c for the rest and apply the curve to your spaceship. Kerbal style :-)

 

I guess that mean need to calculate ((1 - v * v^t) * F / R * m ) / ( F/m )

The problem is what is v^t ? It is some sort of 3x3 matrix calculation ...

Edited July 22, 2016 by FreeThinker

[Green Baron]

Edit: the text says the magnitude of v is the speed between 0 and c.

 

Sooo .... very quick and very kerbal, don't blame my style :-)

#include <stdio.h>
#include <stdlib.h>
// #include <math.h>

int main( void ) {
        double gamma = 0.0, i = 0;
        for( i = 0; i < 1.01; i += 0.1 ) {
                gamma = ( 1 - i*i );
                gamma *= gamma;
                gamma = 1 / gamma;
                printf( "At %2fc the mass is %5f\n", i, gamma );
        }
        return EXIT_SUCCESS;
} // main()

 

 

At 0.000000c the mass is 1.000000
At 0.100000c the mass is 1.020304
At 0.200000c the mass is 1.085069
At 0.300000c the mass is 1.207584
At 0.400000c the mass is 1.417234
At 0.500000c the mass is 1.777778
At 0.600000c the mass is 2.441406
At 0.700000c the mass is 3.844675
At 0.800000c the mass is 7.716049
At 0.900000c the mass is 27.700831
At 1.000000c the mass is 20282409603651670423947251286016.000000

I really hope a physicist looks over this.

 

Edited July 22, 2016 by Green Baron

[FreeThinker]

Calculating relatavistic mass from special relativity is very easy, it's the effect on acceleration that is hard.

[Boris-Barboris]

10 minutes ago, FreeThinker said:

Calculating relatavistic mass from special relativity is very easy, it's the effect on acceleration that is hard.

If you want to keep part masses constant, just divide thrust and isp by Lorentz factor. Same can be done for RCS. SAS torque may also be divided by it, just for the sake of consistency.

[Green Baron]

I may be stupid, but isn't it that acceleration for an interval t is ( (1-v*vt)*Thrust ) / ( gamma * restmass ).

Coming close to c, thrust goes down, mass goes up.

But i may be just too naive to see the problem, really ... sorry if this is a misunderstanding from my side.

 

Agian, ninja'd. Shouldn't think so much and rather just write :-)

 

Edited July 22, 2016 by Green Baron

[FreeThinker]

 

3 hours ago, Green Baron said:

I fear i'm no specialist eithier (hoped one would show up), but from what i read the denominator c² is constant while the enumerator grows quadratical.

What you could use ist the Tolman-Expression of mass of a moving body (from the wikipedia articel: m0(1 - v2/c2)^(−1/2), m0 is rest mass and the relativistic version of f=m*a:

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

If that doesn't help then compute the mass for a given case once in intervals of let's say 0.1c until 0.8c and 0.01c for the rest and apply the curve to your spaceship. Kerbal style :-)

Edit: i meant for a mass of 1, in order to obtain factors for multiplication.

 

 

2 hours ago, Boris-Barboris said:

If you want to keep part masses constant, just divide thrust and isp by Lorentz factor. Same can be done for RCS. SAS torque may also be divided by it, just for the sake of consistency.

This looks too simple, perhaps add a quadic factor:  relatavisticThrust = resttTrust /  LozenzFactor ^ 2

Edited July 22, 2016 by FreeThinker

[Boris-Barboris]

11 minutes ago, Green Baron said:

Coming close to c, thrust goes down, mass goes up.

In rocket's frame: thrust stays, mass stays, isp stays.

In Sun frame: mass increases, thrust stays, isp stays. Thrust and isp stays the same, because if you try to redefine them relativisticaly, you get relativistic mass somewhere in numenator and rocket's own time in denominator. Gammas reduced - same expressions as in non-moving frame.

Changing mass is technically difficult, messes with a lot of stuff, so it's easier to change thrust and isp.

1 minute ago, FreeThinker said:

this looks too simple, perhaps add a quadic factor:  relatavisticThrust = resttTrust /  Lozenz ^ 4

You can, but then nerds will come and ask questions.

[FreeThinker]

3 minutes ago, Boris-Barboris said:

You can, but then nerds will come and ask questions.

Well I hope they do.

Edited July 22, 2016 by FreeThinker

[Green Baron]

9 minutes ago, Boris-Barboris said:

In rocket's frame: thrust stays, mass stays, isp stays.

In Sun frame: mass increases, thrust stays, isp stays. Thrust and isp stays the same, because if you try to redefine them relativisticaly, you get relativistic mass somewhere in numenator and rocket's own time in denominator. Gammas reduced - same expressions as in non-moving frame.

Changing mass is technically difficult, messes with a lot of stuff, so it's easier to change thrust and isp.

Yep, but in terms of game loop the formula does just what you proposed, it applies Lorentz to mass and thrust. It leaves the restmass unchanged.

Too simple ? Einstein found out: E=m*c and reported that at lunch to a friend, a marketing person. He said: Come on, be bold ! How am i supposed to sell that ? E=m*c .... no we make it E=m*c². That sounds way better !"

Einstein was deeply impressed.

:-)

 

Edited July 22, 2016 by Green Baron

[Boris-Barboris]

17 minutes ago, FreeThinker said:

Well I hope they do.

Will you have an answer for them though? I can only recommend sticking to something with at least some scientific basis, I still remember resistance in KSPI community when I crutched solar panels heating on earth orbit, wich made all probes explode in early game.

12 minutes ago, Green Baron said:

Yep, but in terms of game loop the formula does just what you proposed, it applies Lorentz to mass and thrust

It does, but it's the matter of game loop efficiency to keep 100 parts untouched and change only a couple.

 

Edited July 22, 2016 by Boris-Barboris

[Green Baron]

Yes, i forgot KSP works that way :-)

 

[FreeThinker]

I create created a post at the Physics Relativity forum, if anyone should be able to answer this question is should be there.

Edited July 23, 2016 by FreeThinker

[PB666]

To answer the question IRL.

 

First, IRL, everything in the universe is traveling around in its comoving space-time, with transitions to other space time. It tends to be more true on large bodies because they tend to warp local space-time more than their local space-time is warped by distal energy sources. This all has nothing todo with relativity, until you have clashing, as occurs in space, a prime example is when two black holes merge a billion light years away and our LIGO sees a blip-blip. Thats relativistic. IOW if you keep your distance from energies that can be described in other inertial reference frames, your safe.

So you are traveling close to the speed of light, your interaction with other objects begin to change, namely because you have some much intrinsic energy. And those things also will begin to disrupt you, not just big things, but smallest objects become cosmic radiation.

Second. Assuming we elimintate the first. How did you reach that point, to get to the speed of light, your propulsion system is relativisitic. dV = ISP_vel Ln(M_i/M_f). To get a dV that approaches c, ISP_vel also has to approach c. The ship is the observer, and the reaction mass is accelerated to c, from the ships perspective as the mass goes faster it gains mass and accelerates more slowly.

Third. Now lets suppose to have a magical drive that delivers infinite dV and you are in magical completely empty space. From your perspective in that completely empty space you have created your own local space-time, its pretty much defined by the quantum inputs of gravity in which your ship defines it as such. When you enter an area where gravity is primarily extrensic, so lets imagine what happens. Imagine your are traveling at the speed of light close to event horizon close to a black hole. So this is where space time comes into play.

Lets imagine. The forces that hold your ship together are in a structural equilibrium, part of that equilibrium is a thing called quantum foam. its basically an ill-defined representation of cellular space. We of course can't see the cells, our eyes lack the resolution or the transmission speed by a factor of 10⁴⁰ on both accounts. But despite the fact you can't see it, the atoms in your ship are in eqilibration with this foam. The distance between them is dependent on the structure of the foam itself and electrostatic forces that operate in it. Now lets compress the foam along one dimension until one dimension disappears, as this occurs the molecules in part of your ship are now moving apart from molecules in other parts of your ship at the speed of light.  Not so good. So that when you are traveling around close to the speed of light, you have to be somewhat mindful of other matter (space-time) in the universe, otherwise it could have relativistic effects on your ship. Or to put it otherwise, light speed travel is only meaningful if the traveler defines the space he/she is traveling through, the definition of the space-time is shared between many massive disequilibriated particles, you tend to have a large hadron collider instead.

[WestAir]

If mass increases is it possible to induce a singularity by increasing the velocity of an object?

[DaMachinator]

On 7/22/2016 at 2:24 PM, WestAir said:

If mass increases is it possible to induce a singularity by increasing the velocity of an object?

I think this is what happens from the point of view of an outside observer were a ship to travel at the speed of light. From the point of view of an inside observer, everyone would be blind.