Help with Math Question: Calculating Time Dilation

[benjonesart]

hello guys I am writing a science fiction novel atm and I am having trouble figuring something out since I am no mathmetician by any means.

Im trying to figure out how fast an object needs to travel faster or slower than local Earth spacetime to receive a 1% time dilation effect. Working theory for the story is to find a planet that has received a 1% difference in time than Earth has with the possiblity of life evolving faster than Earth being because they have expirenced more time than when relative to earth.

 

[DaveC426913]

http://www.1728.com/reltivty.htm
There's a calculator at the bottom.

Play with the velocity input until you get a dilation factor of 1.01. I got 42,500km/s.

 

[DaveC426913]

Wait. Your story logic is completely flawed. In myriad ways.

1] Your planet would have to be rocketing through our galaxy at 1/7 of light speed.
2] Your planet will be pelted with dust and gas traveling at 1/7th light speed. It will glow.
3] All incoming radiation will be dramatically blue-shifted (more energetic). Your organisms will die.
Also
4] The dilation would actually slow down passage of time on your planet (Earthers will observe only 99 million years having passed on your planet for every 100 million on Earth).
5] Why bother? Unless both planets began their evolution at a starter's pistol, there's no reason why their timelines would match at all. Just start your other planet evolving a billion years earlier.
6] There are far, far greater factors that affect the rate of evolution than simply time. Even on Earth, some species evolve orders of magnitude faster than others. (Many species here have not changed appreciably in hundreds of millions of years, whereas others change weekly.)
The list goes on...


Skip the relativity aspect. Your planet simply got its start a billion years earlier than Earth.

 

[benjonesart]

no you are thinking of it backwards than I am. I am using a SLOWER moving planet in relation to earth. If I am correct a planet created in any area devoid of super large gravitational forces and going at speed that could equal a 1% time dilation then it would evolve faster. Yes I know I could easily just have it form 1billion years earlier but I wanted to look atit from a different point perspective.

Though its getting pretty complicated because of speed being a term in relation to a specific object or point. So I might have to use a made up object within our galaxy as our "new' reference point in the future to judge true speeds of objects such as planets and stars with in our local spacetime area.

thanks for the calculator btw that does help but I am finding more stubmling blocks that I wil lhave to navigate through fiction and science.

 

[Dmitry67]

It does not work this way. If Planet X is moving 45000km/s relative to Earth, then Earth is moving at 45000km/s relative to planet X.

 

[benjonesart]

Though its getting pretty complicated because of speed being a term in relation to a specific object or point. So I might have to use a made up object within our galaxy as our "new' reference point in the future to judge true speeds of objects such as planets and stars with in our local spacetime area.

that i have figured out that is why i said this above.

 

[DaveC426913]

no you are thinking of it backwards than I am. I am using a SLOWER moving planet in relation to earth.

There can be no planets moving slower than Earth; Earth is stationary in its own frame. Any planet that is moving relative to Earth will experience dilation, resulting in time appearing to move slower on that planet.

Though its getting pretty complicated because of speed being a term in relation to a specific object or point. So I might have to use a made up object within our galaxy as our "new' reference point in the future to judge true speeds of objects such as planets and stars with in our local spacetime area.

You don't understand; it doesn't work this way. Any planet moving with respect to Earth will be time dilated. It makes no difference if you want to name some arbitrary point in space as a reference; the whole point of relativity is that it's relative.

 

[wolf1728]

Just thought I 'd reply that my relativity calculator has a new URL - it is now http://www.1728.org/reltivty.htm
The reason? My domain name www.1728.com was stolen and I don't know when or even if I'll regain it.
Just thought I'd let people at this forum know about that. It seems you folks like to link to my site quite a bit - and thanks.

 

[DaveC426913]

Just thought I 'd reply that my relativity calculator has a new URL - it is now http://www.1728.org/reltivty.htm
The reason? My domain name www.1728.com was stolen and I don't know when or even if I'll regain it.
Just thought I'd let people at this forum know about that. It seems you folks like to link to my site quite a bit - and thanks.

Yay! It's back!

I wondered where it gone! I use it all the time. There are others, but none I've found are as straightforward. When I couldn't find it anymore, I was lost.

Had no idea it was yours.

Sucks for you, btw.

 

[Ryan_m_b]

Evolution is not teleological, there is no purpose to evolution. If we have two environments both seeded with life they will not "evolve" at the same "rate" and in the same manner.

Organisms pass on mutations to their offspring's genotype, these mutations may result in phenotypic differences. Whether or not these differences are deleterious, neutral or advantageous is strongly contextual with regards to the environment. Natural selection, sexual selection, gene flow and genetic drift will all then act upon these mutations to change the allelic frequency in a population.

If you want to talk about the "speed" of evolution you are going to have to set an appropriate measure. Are you counting mutations per generation? Genetic difference over time? Rate of speciation?

 

[BruceW]

If we assume that the rate of evolution is the same on each planet (not saying it is or isn't, but supposing it is) then:
In the reference frame of the earth, the other planet (planet X) will evolve more slowly. And in the reference frame of planet X, the Earth will evolve more slowly.
Also, in the reference frame of the earth, planet X would have started evolving first. BUT in the reference frame of planet X, the Earth would have started evolving first.
This is due to the fact that simultaneity is relative. (i.e. if someone fired a gun at some time, then the time at which that gun went off depends on your reference frame).

So therefore, in special relativity, one planet would not overtake the evolution of the other. For example, if the two planets were on a collision course with each other, then when the planets collided, they would both have evolved by the same amount.

General relativity is a whole other kettle of fish. Maybe if one planet was in a galaxy that was rotating really fast and the other was in a galaxy that wasn't rotating as quickly, then the planet in the faster rotating galaxy would evolve slower.
But I'm not sure about general relativity, I've only been taught special relativity.

And then there's the issue ryan m b brought up that two planets wouldn't necessarily evolve in the same way.

 

[BruceW]

I should say that in the case of 2 planets with uniform relative motion, if someone from one planet got into a spaceship and went to the other planet, then due to the acceleration of the spaceship, then special relativity no longer holds all the answers, you have to look to general relativity. I think that in this case, the guy who travels in the spaceship will be going to a world which has evolved more than his own.
Am I right here? I'm don't really know the rules of general relativity...

 

[DaveC426913]

By far the best way to wind up with two planets with dramatically different levels of complexity is to drive evolution harder, which can occur in several overlapping ways: an excess of life-supporting properties and nutrients, a dearth of life-supporting properties, extra mutative radiation, geographic isolation, etc.

 

[wolf1728]

DaveC426913
Thanks for your remarks about the relativity calculator and I'm glad I was able to track down some of the places where it was linked.

 

[Ryan_m_b]

By far the best way to wind up with two planets with dramatically different levels of complexity is to drive evolution harder, which can occur in several overlapping ways: an excess of life-supporting properties and nutrients, a dearth of life-supporting properties, extra mutative radiation, geographic isolation, etc.

I agree though it is possible that over time a harsh environment will force specialisation.

An older planet where the plates have fused (no earthquakes, tsunamis or volcanoes) with no axial tilt and with the majority of the surface sporting an archipelago would fit nicely. Throw in a few jovians orbiting further out to soak up any asteroids, provide the excess resources and write the ecology to be heavily focused on symbiosis and sexual selection and you've got one hell of a complex ecosystem.

 

[BruceW]

that post really makes me want to create some planets and see what happens. If only :)