Relativistic Universe, and fourth dimension...

[julesstoop]

Probably there has been discussion about this before (I'm new, you know), but how about displaying two speeds: the speed as it is now, and the relativistic speed (where 1 au/s would be something like 0.96 c, correct me if I'm wrong), the formulae are rather simple. Upon this togglable option, you could later ad time-distortion, and maybe even visible relativistic effects, like doppler shift etc...

My second point, which has probably got to do with the database you're using, is the fact all stars are static, even binaries with known orbital data (at least on my current Mac OS X port of 1.2.2). Is it possible to add 'own-motion' to the stars, at least the known ones. The other stars could get a plausible orbit around the centre of the galaxy, based upon their distance from it.

Are these things possible, Chris? Or are they to difficult within the restraints of the database you're using?

To finish this post: Don't get me wrong, I do like the software very much as is, although I can't seem to get eclipse and ring-shadows to work on my G4 (cntr-E just moves me a little bit closer to the selected object, as if I pressed G)

[Matt McIrvin]

Probably there has been discussion about this before (I'm new, you know), but how about displaying two speeds: the speed as it is now, and the relativistic speed (where 1 au/s would be something like 0.96 c, correct me if I'm wrong), the formulae are rather simple. Upon this togglable option, you could later ad time-distortion, and maybe even visible relativistic effects, like doppler shift etc...

We've batted this idea around on the forums before; the really nifty thing would be to put in aberration of starlight (aka Terrell rotation).

[boertje]

I think with our few knowledge it's difficult to work out the 4th dimension. Like you can travel to a star 1000s of ly's away which definitively isn't where you travelled to, eventually doesn't even exist anymore.
You are actually travelling in a virtual environment which never existed like this and is only based on static human observations since a few hundred years. We can only trust our eye, but our eye is way too slow.
It's like travelling with Lightspeed. You seem to stand still in space.

[Guest]

Ehhmm... 1au/s is about 500 times greater than c, the speed of light, not just 0.96 c!!
I think it would be possible to add some relativistic effect, such as Doppler effect, distortion...
But, to be realistic, consider this example: if you are running at a relativistic speed, such as 0.7 c, stars in front of you will appear bluer, and stars behind you will appear redder, but at the limit of c, when you are running at 299 792 458 m/s, the sky in front of you will appear uniformly white, and the sky behind you uniformly black... not so interesting, isn'it?
Obviously you know that's impossible to go faster than c, so, what should the simulation do in this case?
The really problem is that c is a very low speed to fly through the stars, think, it takes 2.4 years to Alpha Centauri...
Maybe it's better you think yourself on a spaceship like the ones of Star Trek, that curve the space around them and surf a wave of space-time at a subluminal speed...
see you
Anarion

[julesstoop]

Ehhmm... 1au/s is about 500 times greater than c, the speed of light, not just 0.96 c!!
I think it would be possible to add some relativistic effect, such as Doppler effect, distortion...
But, to be realistic, consider this example: if you are running at a relativistic speed, such as 0.7 c, stars in front of you will appear bluer, and stars behind you will appear redder, but at the limit of c, when you are running at 299 792 458 m/s, the sky in front of you will appear uniformly white, and the sky behind you uniformly black... not so interesting, isn'it?
Obviously you know that's impossible to go faster than c, so, what should the simulation do in this case?
The really problem is that c is a very low speed to fly through the stars, think, it takes 2.4 years to Alpha Centauri...
Maybe it's better you think yourself on a spaceship like the ones of Star Trek, that curve the space around them and surf a wave of space-time at a subluminal speed...
see you
Anarion

You don't get the picture alltogether (me neither by the way) but I'll try to explain:
When travelling with a relativistic speed of say 0.96 c, as your speed would apear to say someone on earth, you yourself - in your perception of time - actually cover a lot more distance per 'your' second than about 288,000 Km, 'your' time slows down, so to say (remeber the gravity experiments with the cesium-clocks). When it would be possible to ultimately travel with the speed of light, you would even cover the whole universe in an infinetely short moment, though say someone on the earth - seeing you fly by - would percieve your speed as c.

So the thing I'm suggesting is to display two speeds, the 'normal' speed as it would appear towards a 'static' viewer (0.96 c), and the actual perceptional speed of the traveler (1 AU/s, which is identical to the current 1 AU/s). There are simple formulae to calculate those speeds. Another effect of course would be that when you actually travel at such speeds, taking relativistic effects into consideration, time would seem to speed up outside your spacetime. So when you flew by our solar system at a speed of about 1 AU/s, all the planets would seem to move about 500 times as fast in their orbits. Since we have variable time in Celestia, it would be easy to make a toggle between perceptional speed without time-abberation (as it is now) and relativistic speed with time-abberation.

The next step could indeed be visible abberations such as doppler-shift and Terrel-rotation, but thats surely quite difficult (to get a very simplified approximation we could use field of vision, by the way).

Admitedly, these things would only be really interesting if all stars would move as well, so one would get an actual idea of what travelling at such speed - if possible - would really look like.

By the way, the distance to proxima centauri is about 4.3 lightyears.

[dab]

look, the whole point with these twin-paradoxa and what not
is asymmetry in acceleration. the whole concept of "relativity" implies
that if you travel with .96c towards a star, it would take you, yes
even in your personal perception, the same time as if the star was
travelling towards you at .96c. namely practically forever. So, what
you're looking for is an additional display for acceleration.

I know this is tricky shit & I have to watch my wording so I don't
say anything untrue & I wouldn't dare to quote formulas without
digging into the textbooks first. But the gist is that what you are
asking for is _general_ relativity; while time-dilatation of classical
relativity is of no use to you for this. because you see your friend's
clock slowing down as he passes you just as he sees yours slowing
down, but this doesn't get you any quicker to places in anyone's
perception.

dab

[dab]

I think I just posted something stuipd. But since I probably
triggered "Notify me" mails already I just let it stand.

You may be right it could work with just special relativity.
Because the Universe "shrinks" ahead of you. I realize this
is just what you said. Sorry. So there.

I may think this through and get back with a really
annoyingly informed post :-)

dab

[Guest]

Well, if you were going at say... .8c you would see time outside slow down and an outside observer would see your time slow down because you can say that the universe is moving not you.

The way Einstein solved this paradox is that a frame of reference is only valid when it is not accelerating. For you and an observer to confirm the time dialation, you would have to slow down. Thus your frame of reference would not be the correct one.

[Matt McIrvin]

Many frequently asked questions about relativity, the twin paradox, etc. are answered in the Usenet Physics FAQ:

http://math.ucr.edu/home/baez/physics/

The second half or so of the table of contents is all relativity stuff. See especially

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

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

[LionAM]

Hello,
at first I want to say that I love Celestia. I use it for a few days now and read also a little bit in this forum. I think relativity in this program would be interesting.
But here are not all aspects covered. I hope that I'm right, but I've just read something about it.
There is the effect of time dilatation, but you would not be travelling faster than light. In fact, there is also the length contraction, so you would see the distances getting shorter. So you have the same speed in your opinion as any "static" observer would see.
But this means also that you would see the stars compressed in the direction you fly.
If you for example, fly along the x-axis, it would get shorter. But the y- and z-axis would keep their size.

Alex

[Matt McIrvin]

In fact, there is also the length contraction, so you would see the distances getting shorter. So you have the same speed in your opinion as any "static" observer would see.
But this means also that you would see the stars compressed in the direction you fly.
If you for example, fly along the x-axis, it would get shorter. But the y- and z-axis would keep their size.

This contraction does happen in the coordinate frame of a moving observer-- and I suppose that it would be correct to show it reflected in stellar distance measurements for a moving observer, if we had a relativity mode.

But, surprising, the contraction is not actually visible, because of effects involving the finite speed of the light that you use to look at things. What you actually see is described in one of the physics FAQ entries I linked to above: objects get shifted in the forward direction around the apparent celestial sphere, and an extended object like a planet would consequently appear rotated so that the same face still points toward you.

[alexis]

0.96c in the observers inertial frame corresponds to the "experienced velocity" 3.43c, not 499c = 1 AU/s as previously claimed. The formula is very simple:

"experienced velocity" = "true speed"/sqrt(1 - ("true speed"/c)^2)

Conversely, the "true speed" required for "the experienced velocity" 1 AU/s is 0.999998c, not 0.96c:

"true speed" = "the experienced velocity" / sqrt(1 + ("the experienced velocity"/c)^2)

(this is just the inversion of the previous formula)

At this speed, the aberration of light would make an observer see the whole world wrapped up in front of her, all light coming from almost a single point in the direction of travel. Not only that, the spectra from ordinary stars (like, say, the Sun), would be shifted by a factor of 499 to shorter wavelengths. Thus the main part of the radiation would be shifted into lethal (and invisible!) gamma rays in front, and radio (and invisible!) radiation from rear (which would look like it came from the front anyway due to aberration). At 0.99999991c we would start to see some of the black-body radiation of the cosmic background be shifted into the visible.

As you see, all this makes relativistic travel, in real time, impractical. Even with time-dilation, you would get no-where in the universe with (experienced) velocities as low as 1 AU/s, it would take 3 _days_ to get even to alpha Cen. The user would get bored quickly. On the other hand, with the more interesting (experienced) velocities light-year/s, almost all radiation would be shifted either to the invisible far gamma, or the invisible far radio. And, on top of that, all radiation would come from the inside of a single pixel in front, not very entertaining.

The solution to make relativistic space-travel more interesting is of course to introduce a time-scale. In that way you can get the best from both worlds, experience the relatvistic effects of "low" velocities (v < 0.99999c, say), and still get somewhere in a few seconds of simulation time (some light-years).

As this is my first post in this forum, I would like to take the opportunity to thank Chris with co-developers for the excellent (and free) software Celestia. To develop such a software requires hours and weeks and months of hard work (I know!), and to do it for free requires a very dedicated person. In light of all feature-requests, urge for bug-fixes etc, it is easy to forget all the effort that already has gone into Celestia. To implement relativistic effects is not as difficult as it may sound, if you know how to do it, but it takes time. Who is up to the challenge?

/Alexis

[Matt McIrvin]

As you see, all this makes relativistic travel, in real time, impractical. Even with time-dilation, you would get no-where in the universe with (experienced) velocities as low as 1 AU/s, it would take 3 _days_ to get even to alpha Cen. The user would get bored quickly. On the other hand, with the more interesting (experienced) velocities light-year/s, almost all radiation would be shifted either to the invisible far gamma, or the invisible far radio. And, on top of that, all radiation would come from the inside of a single pixel in front, not very entertaining.

The solution to make relativistic space-travel more interesting is of course to introduce a time-scale. In that way you can get the best from both worlds, experience the relatvistic effects of "low" velocities (v < 0.99999c, say), and still get somewhere in a few seconds of simulation time (some light-years).

An excellent point. Maybe in "relativity mode" the observer speed would be yoked to the simulation's overall time scale, unlike the normal situation. That makes some sense, since in this mode velocity is imagined to be a physical parameter rather than an arbitrary imposition on the world.

It also might be interesting to blow around the solar system at relativistic velocities, and near a planet things could happen so fast that you'd want to slow down the time scale.

One thing I don't know is whether OpenGL is up to performing the conformal transformation for the Penrose-Terrell rotation on the image of an extended object in any easy way. Under the transformation, a spherical object would still have a circular disc and shapes are unchanged in the small-size limit, but if an object is of finite visible size, different parts of the image will be magnified to different extents. Maybe you'd have to distort the actual mesh.

[Guest]

One thing I don't know is whether OpenGL is up to performing the conformal transformation for the Penrose-Terrell rotation on the image of an extended object in any easy way.

I'm not sure how it's done in Celestia, but I suspect that Open GL's possible transformations won't do, not directly (if they are similar to those in DirectX). For simulating relativistic effects, only the directions to the objects are important, not their distances. These directions have then to be transformed (with a non-linear rational function) into the frame of the observer. After the directions are altered, they can be projected onto the screen. I think in Open GL there is no step in between getting the directions to objects and projecting them onto screen (because usually it's pointless).

Under the transformation, a spherical object would still have a circular disc and shapes are unchanged in the small-size limit, but if an object is of finite visible size, different parts of the image will be magnified to different extents. Maybe you'd have to distort the actual mesh.

Transforming the mesh pointwise for extended objects is a very good idea. In that way the distortion is accurately simulated. However, even in the small-size limit, spheres will not show up as circular discs; they will be ellipses (unless their centre coincides with the travel direction), because the differential contraction/expansion isn't isotropic.

/Alexis

[Matt McIrvin]

Transforming the mesh pointwise for extended objects is a very good idea. In that way the distortion is accurately simulated. However, even in the small-size limit, spheres will not show up as circular discs; they will be ellipses (unless their centre coincides with the travel direction), because the differential contraction/expansion isn't isotropic.

According to that Physics FAQ, at least,

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

circles do map to circles under the Penrose-Terrell transformation, even though it's not isotropic. In the small size limit that's not hard to see because the transformation is conformal (the math is down at the bottom of the page).

Remember, it's not the same thing as the Lorentz contraction, which is only manifest after you factor out the effect of finite light speed delays.

[alexis]

Yes, you're right! In the small-size limit circles are indeed mapped to circles by the transformation. I was skeptical at first but checked it and am now convinced.

The FAQ also claims that circles always map to circles (even large ones), but I really don't see why that should be the case. I noticed the beautiful result that the Lorentz group is isomorphic to the M?bius group, and I know that M?bius transformations preserve circles in the complex plane, but here we are talking about transformations on the Riemann sphere. And when we say circles on the Riemann sphere I suppose we mean those circles that can be described as ordinary intersections between a plane and the sphere (because that is what spheres will look like), not some crazy metric mapped onto the sphere from the complex plane. The question is, will M?bius tranformations map circles on the Riemann sphere (in our "physical" meaning!) onto circles? I think not. In fact, using the formalism from the FAQ I found that circles are not preserved (although I may have made some error, of course).

Are you familiar with these things? Not that it has any direct implications for Celestia (except, perhaps, simplifying the transformation of spheres), I'm just curious to know.

/Alexis

[Matt McIrvin]

Are you familiar with these things? Not that it has any direct implications for Celestia (except, perhaps, simplifying the transformation of spheres), I'm just curious to know.

Unfortunately, that's as much as I know about the subject... I did deal a bit with Lorentz transformations on null vectors as part of some abortive research back in grad school, but it didn't go much of anywhere.

[Guest]

You guys must all have brains the size of watermelons ....
Haven't tried Celestia yet as am experiecing dnld problems so am trying orbiter first...

thanx for your contributions to free sharing of astronomy in the net, through your love of the subject...i think you guys rival us physicists with your friendliness
here's hoping i join you guys in the future on sharing some opinion on the subject....wait a minute....damn, i'm of the grape sized brain variety....

cheers

[alexis]

Hi Matt and others,

Inspired by the Physics FAQ and our discussion, I wrote a contribution to the FAQ on What would a relativistic interstellar traveller see?. Find it on

http://hermes.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/Spaceship/spaceship.html

/Alexis

[Matt McIrvin]

Great FAQ entry! It's always nice to see a new one appear...

By the way, I'm not actually an astronomer, just a programmer who used to be a grad student in particle physics.