41 replies to this topic

[forsandifs]

Oh I miss-read years instead of light years. My bad. I'll repost when I've taken that into account.

So bearing in mind that the journey is 10 light years in length as seen from earth we calculate as follows.

The time taken for journey as measured by the observer on earth will be 20 years. And the time taken for the journey as measured by the traveller's clock will be 17.32 years.

EDIT: so szecs post #9 was the first correct calculation, unless I missed some edits. But then iirc he edited post number #7 so that that is now seemingly the first one.

EDIT: Anyway, good to have two separate confirmations of the result. :]

[szecs]

Thanks for the rate-ups, but I'm beginning to think that this new post-rating system is worse than the person-rating system

[forsandifs]

Thanks for the rate-ups, but I'm beginning to think that this new post-rating system is worse than the person-rating system

[offtopic]Hmm, I think it might work out allright. Its easier to go up but its also alot easier to go down. I think the only problem is if people start abusing it with alt accounts, but I guess that could be solved by restricting accounts to one per IP as per the old site. Also, I think people tend to refrain from abusing it with alt accounts because they know it would take the whole point out of the rating system and therefore the whole point of them abusing it in the first place

However I do think the bar for "Excellent" rep status should be raised by a lot (its currently at 20 :/ ), maybe to 100? And also perhaps there should be another bar for "Legendary" at 1000? So, Good at 10, Excellent at 100, and Legendary at 1000? I guess there could be a God status at 10000

EDIT: *Starts getting excited* And maybe we could unlock new gear and super powers at higher re.. err.. no.[/offtopic]

[__sprite]

Last night I kept reading a little more and learned that for a spaceship traveling almost at the speed of light, all the radiations that arrives to the spaceship would be so shifted to the extremes (X-rays, ultra-infra-red) of the spectrum that nothing from the outside would be visible from the inside.

Not that I really understand these things, but I find that a bit strange. Wouldn't this effect depend on direction? So radiation travelling in the same direction as the space-ship will be shifted past infra-red, and radiation travelling the other way past X-rays. But won't light perpendicular to the direction of travel still be observable?

[A Brain in a Vat]

A more interesting question:
How would we relativistically simulate a space-fighting game with all these time dilatations in a multiplayer game? All controls/the behavior of the spaceship would slow down compared to the outside scene? That is an interesting game design question....

See the indie RTS Achron. It's not a space-fighting game, but it involves time-travel. You're asking about how to design a multiplayer game in which the players can be in different temporal frames. This RTS deals with a game design problem that seems similar: how to design a multiplayer game that allows each player to travel back in time and affect the course of game events. It's a very interesting design they came up with.

Sorry to throw the thread off-topic, back to talking relativity BTW, an observer traveling at near the speed of light would be able to see almost nothing. "light perpendicular to the direction of travel", from the frame of reference of the traveler, would necessarily have to emanate from a source that was traveling at near the same speed in near the same direction (i.e. an object that appeared, to the traveler, to be almost at rest). Since this is unlikely, you would see almost nothing.

[Ezbez]

An alternative way to calculate this is from the traveler's reference frame. He will see the destination as nearing at speed of 0.5c, but the distance to the destination is not 10 light years to him. Rather distance contraction (just as time dilation) plays a role here. Lorentz contractions on distance say the distance is now (10light years)/(gamma), where gamma is 1/sqrt(1-v^2/c^2)=1.15. So d=8.65 and we get the time to traverse this distance is 17 years again.

I played with the idea of incorporating relativistic effects into a video game a while back and was unable to come up with anything particularly compelling. The simulation is non-trivial. At relativistic speeds it becomes necessary to not have information transmitted instantly - you must be careful that everything is "seen" after a speed-of-light delay (at least), which makes simulation considerably more complicated. This is necessary, for otherwise you break causality and let things "see" into their future. So it is necessary to keep track not only of the current state, but of previous states. For a suitably simplistic game, this might be practical. I am also interested in the possibilities for a puzzle game to be made where you combine relativity with something like wormholes to create time travel if properly moved. (One of Brian Greene's books has an interesting section on this possibility: take one end of a wormhole on a long, fast spaceship ride and now you have temporally (as well as spatially) separated the ends.)

[Álvaro]

I've thought about making a game or just a toy where Physics are modified so c is something like 100Km/h, and relativistic effects are taken into account. I don't understand relativity well enough to really know how to make it or what it would look like, and that's precisely why I think it would be an interesting teaching tool to help people gain an intuition for how a relativistic world works.

[owl]

Last night I kept reading a little more and learned that for a spaceship traveling almost at the speed of light, all the radiations that arrives to the spaceship would be so shifted to the extremes (X-rays, ultra-infra-red) of the spectrum that nothing from the outside would be visible from the inside.

Not that I really understand these things, but I find that a bit strange. Wouldn't this effect depend on direction? So radiation travelling in the same direction as the space-ship will be shifted past infra-red, and radiation travelling the other way past X-rays. But won't light perpendicular to the direction of travel still be observable?

I'm not really sure. My guess is that light perpendicular to the direction of travel should arrive at the speed of light and it's wavelength shouldn't "suffer" any change in relation to the velocity of the ship. Maybe some sort of lens effect due to space contraction inside the vessel?

[szecs]

Look at the link I posted. I don't completely get the details, but it seems that light coming from behind the vessel will have infinite wavelength and light coming from the front has zero wavelength. So it's sure it has that red -blue rainbow-halo effect, and I think light perpendicular to the vessel WILL have longer wavelength. I think the more you approach c, the more "compressed" will the visible spot be in front of the vessel. I think... I don't think the perpendicular direction is any special.

[owl]

I don't think the perpendicular direction is any special.

I've been thinking about this and I remembered the famous "elevator" analogy used by Einstein. The light arriving perpendicular will describe a curved path inside the vessel, just as it would do if it passed nearby a very massive body. Traveling at c (or almost), from the perspective of the vessel it'd be like if the light coming from the outside bended downwards following the shape of the container (more or less I think...).

                                 BBBBBBBBBBBB
                                 B          B ^
perpendicular light >----------\     O WTF? B |
                               | B  / \     B |
                               | B   |      B |
                               | B  / \     B |
                               | BBBBBBBBBBBB
                               \------------------------------------>

[szecs]

Yes, that's true. So you'll have your lens effect, and I guess at c the vessel becomes a black hole from it's own point of view. Or something.... Shit, that's exciting stuff!

[owl]

and I guess at c the vessel becomes a black hole from it's own point of view. Or something.... Shit, that's exciting stuff!

It is exciting indeed!

If I'm not wrong, if a body with mass get's accelerated to c, then it acquires infinite mass. Also, for that to happen it'd be required infinite energy. Now, if that's true, either black holes cannot exist or acceleration and gravity aren't completely analogous. (I'm shooting kind of blind here though)

[szecs]

Hmm. I remember a thread about this "black holes cannot exist according to relativity" stuff......

[Álvaro]

You don't need infinite mass to make a black hole. I don't know where you got that idea.

[___]

when you reach 1/2 speed of light you wont speed up?

if not s = v * t




t = s/v




remember to calcuale meters per second with meters and seconds




note that destination point and start point dont change




i wonder is this foruma correct for this kind of speed does anyone can describe the problem if not lol ;o

[A Brain in a Vat]

I don't think the perpendicular direction is any special.

I've been thinking about this and I remembered the famous "elevator" analogy used by Einstein. The light arriving perpendicular will describe a curved path inside the vessel, just as it would do if it passed nearby a very massive body. Traveling at c (or almost), from the perspective of the vessel it'd be like if the light coming from the outside bended downwards following the shape of the container (more or less I think...).

                         		BBBBBBBBBBBB
                         		B          B ^
perpendicular light >----------\ 	O WTF? B |
                       		| B  / \ 	B |
                       		| B   |      B |
                       		| B  / \ 	B |
                       		| BBBBBBBBBBBB
                       		\------------------------------------>

What are you guys talking about? Light would not follow a curved path. He described an instantly accelerating object. The light would only appear to follow a curved path if the observer was accelerating.

As I said before. Just think about it. In all reference frames, the only incoming light that can strike you at an angle orthogonal to your direction of travel is light that was emitted from a reference frame similar to yours. If you are traveling near c in direction v, only objects traveling near c in direction v could possibly shoot a photon at you in a path that would appear to you to be horizontal.

Edit: snipped out some stuff I had here that on second thought was incorrect.

[Ezbez]

Black holes are actually quite easy to construct in special relativity. We know the famous E=mc^2 derived from special relativity, which gives energy as a function of mass. The gravitational potential energy of a point mass of mass m in a gravitational field made by another mass of mass M at a distance of r is -GMm/r. (G being the gravitational constant.) The total energy stored in mass m is mc^2, so it cannot possibly escape the gravitational field of mass M if GMm/r > mc^2 by conservation of energy. Solving for this, we get that r < GM/c^2 is sufficient to "trap" the mass m in M's gravitational field.

Although we assumed M and m were point masses, the equations hold so long as M is a sphere of uniform density of radius less than r. So if we take a mass M, it must be smaller than GM/c^2 for something to be sufficiently close to it to be trapped within its gravitational field. This gives the event horizon of the black hole. The actual results have general relativity considerations to be taken into account, but IIRC this simple calculation is accurate to about a factor of 2. It should be noted that any mass can make a black hole so long as it's compressed small enough ( by this simple model - at some point quantum mechanics plays a role and I know nothing about that).

@ ___: The correct equations for special relativity have already been given. Yours do not take into account any special relativity: time dilation or space contraction (depending on reference frame).

[Emergent]

Black holes are actually quite easy to construct in special relativity. [...] we get that r < GM/c^2 is sufficient to "trap" the mass m in M's gravitational field.

Yes! I really like this; it's clean, simple, and gets the idea across -- which is important. However, IIRC, this "classical" derivation of the Schwarzschild radius is off by a factor of two... (I have not done the derivation to see why; my fuzzy understanding is that you need to get down into the differential geometry to see it.)

[owl]

I don't think the perpendicular direction is any special.

I've been thinking about this and I remembered the famous "elevator" analogy used by Einstein. The light arriving perpendicular will describe a curved path inside the vessel, just as it would do if it passed nearby a very massive body. Traveling at c (or almost), from the perspective of the vessel it'd be like if the light coming from the outside bended downwards following the shape of the container (more or less I think...).

                     			BBBBBBBBBBBB
                     			B          B ^
perpendicular light >----------\ 	O WTF? B |
                   			| B  / \ 	B |
                   			| B   |      B |
                   			| B  / \ 	B |
                   			| BBBBBBBBBBBB
                   			\------------------------------------>

What are you guys talking about? Light would not follow a curved path. He described an instantly accelerating object. The light would only appear to follow a curved path if the observer was accelerating.

You're right there. That drawing doesn't apply for an object that isn't accelerating.

In all reference frames, the only incoming light that can strike you at an angle orthogonal to your direction of travel is light that was emitted from a reference frame similar to yours. If you are traveling near c in direction v, only objects traveling near c in direction v could possibly shoot a photon at you in a path that would appear to you to be horizontal.

How would light emitted, say, by stars behave in relation to the moving object? For some reason (my fault) I'm having trouble picturing that.

[Álvaro]

In all reference frames, the only incoming light that can strike you at an angle orthogonal to your direction of travel is light that was emitted from a reference frame similar to yours. If you are traveling near c in direction v, only objects traveling near c in direction v could possibly shoot a photon at you in a path that would appear to you to be horizontal.

That isn't right. You can get photons in any direction from a source that is moving in any way.