The Glade 4.0

Amanar:

Are you allowing for deceleration on reaching the destination? Because realistically, you'd probably have to start decelerating about halfway through the trip to said destination, unless you have some way of "stopping" that doesn't involve a reverse direction of your acceleration process.

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Darksiege: You are not a god damned vulcan homie.

You could "stop" by entering into orbit around a large astronomical object.

Depends on how fast you're going, but it's true.

With the kind of acceleration Amanar was talking about at any great distance, however, I'm skeptical.

It would have to be one hell of an astronomical object, and I'm thinking it would be more likely that you'd skim in and out of an orbit rather than actually being able to use it to stop.

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Darksiege: You are not a god damned vulcan homie.

I actually attended a seminar where this was the topic. I can't remember the astrophysicist's name, but the logic went something like this:

It's taken 30,000 or so years for humans to develop our current level of technology. The technology required for travel to other systems is technically available now with our current tech level. (Orion type putt-putts, etc) But even if it takes another 500 years to develop the correct tech level required for interestellar travel, there is a predicted rate of expansion of 'frontier colonies' (holds true for human expansion across the globe) Given the time it takes for a population to get established, then continue to push out and expand into the galaxy, Any given society completely engulfs the galaxy in something like 500,000 years. (I may be wrong--its been 15 years since the seminar)

Given that 550,000 years is a heartbeat in the age of the galaxy.Even if we only factor in the age of Population I stars (metal rich stars; the older Pop II, metal poor stars/systems are unlikely to have sufficient metal content to give rise to technological life)

Now he made a large number of assumptions in his work, but it was at least an interesting theory.


In other words, there's no one out there, because we don't have an alien overlord.

Glad someone agrees!

Yeah, I'm assuming you turn your ship around and start decelerating halfway through. I'm surprised more of you have not heard of this kind of thing. Here's a calculator you can check out and put whatever inputs in you want. Relativistic Star Ship Calculator. I was estimating the size of the universe at 100 billion lightyears and it says it would take 49 years. Now, traveling at 0.999c or whatever may be a bit unrealistic, but hey, we're talking about reaching the other side of the universe here. I don't think it's inconceivable that we could build a ship to travel say, 100 or 1000 lightyears.

I was also just thinking, since accelerating at 1g close to the speed of light would take a ridiculous amount of energy, what a similar calculator would show if instead of holding acceleration constant, you held constant your change in kinetic energy. That might be more realistic.

wait...

The Universe has "sides"?

Depends who you ask :p

This thread needs a TARDIS.

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Raell Kromwell

You're a Tardis.

(j/k)

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I prefer to think of them as "Fighting evil in another dimension"

Was watching pbs and they were claiming that a hefty sized treasure chest full of grains of sand accurately represented the number of stars in our galaxy. Multiply this by a billion more galaxies in our perceived universe, like wow///////

No idea on the accuracy of their source...but...




http://en.wikipedia.org/wiki/Space_trav ... celeration
http://www.whiteworld.com/technoland/st ... rce-01.htm

Seems to me, the sun to the galactic core is not a noteworthy distance, cosmologically, and even it would take 340 years for the occupants of the ship accellerating at 1G (without decelleration!) -- and 30,000 years for an observer on earth.

The entire universe in 50 years seems to contradict that.

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Well Ali Baba had them forty thieves, Scheherezade had a thousand tales
But master you in luck 'cause up your sleeves you got a brand of magic never fails...
...Mister Aladdin, sir, What will your pleasure be?
Let me take your order, Jot it down -You ain't never had a friend like me
█ ♣ █

I think there's probably an error with your source. I've heard similar numbers to what I've given in this thread from a variety of sources, including several books by world renowned physicists.

Here's another site with similar numbers, plus it has all the equations and stuff. I just skimmed it, but it looks a bit more legit than the one you linked.

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

I don't really have time to look into it too much right now (so I could easily be wrong here), but I think the problem with your source is it assumes you accelerate to 1c in about a year, stop accelerating and travel at very close to 1c till you are 1 year out from your destination, and then decelerate. In reality you can continue accelerating at 1g the entire time, from your frame of reference on the ship anyway. Space just keeps getting more and more distorted for you, so the distance between you and your destination keeps getting shorter and shorter, which is how you can get there so fast. Something like that. Relativity is weird.

Quite possibly. Although that's odd, too, because the article seems to take the stance that you can keep accellerating forever.

_________________
Well Ali Baba had them forty thieves, Scheherezade had a thousand tales
But master you in luck 'cause up your sleeves you got a brand of magic never fails...
...Mister Aladdin, sir, What will your pleasure be?
Let me take your order, Jot it down -You ain't never had a friend like me
█ ♣ █

Well, that's the weird thing. It's true that you can't accelerate at a constant 1g according to someone else's inertial reference. At least not for very long since you would exceed the speed of light in less than a year if you did. But weirdly enough, you can accelerate at a constant 1g, 2g, or 900000g according to your own inertial frame. Forever. There's no limit to how much or how long you can accelerate in your own frame precisely because it's impossible to ever exceed the speed of light therein. Special relativity makes the idea of "constant acceleration" rather confusing. In a Newtonian sense, a 1g acceleration is pretty straight-forward: for each second, your velocity increases by 9.8 meters per second. But what is a "second"? Or a "meter"? The answer depends on your inertial frame.

Acceleration in special relativity: What is the meaning of ”uniformly accelerated movement”?

All of the sources so far define constant acceleration the same way: "constant 1g acceleration" is according to the inertial frame of the ship, not earth. Well, almost. Actually, it's 1g acceleration according to an observer with equal instantaneous velocity as the ship, but who is not undergoing 1g acceleration. The reason for this deviation is that acceleration is indistinguishable from gravity, and both have dilating/contracting effects on time/space. It's a somewhat moot point since the effects of being in a 1g field are basically negligible compared to the effects from velocity in this problem. It's just a necessary step for calculating things properly.

The point is this: the people on the ship experience what, to them, feels like a constant 1g force. The back of the ship becomes the floor, and they can go about daily life during the journey in earth-like conditions.

This is the same set of assumptions used here:

http://en.wikipedia.org/wiki/Time_dilation#Time_dilation_at_constant_acceleration

Note that their velocity function v(t) matches equation 6/equation 9 in the source above in the special case where v0=0.

And though it's kind of messy to see, their "proper time" function (i.e. ship time as a function of earth time) is equivalent to the one given in Amanar's source if you work it all out with a=g.

So:

T(t) = (c/g) * arcsinh(gt/c)

Thus using g=1.03 lightyears per year, 113,243 years of earth time would be equivalent to:

T(113,243) = (1/1.03)*arcsinh(1.03*113,243) = 12 years

This precisely matches the value of 12 years given by Amanar's source in case you still have any question that the two formulas are actually the same :p

Observable universe

The edge of the observable universe is about 47 billion light years away. From earth's perspective, the ship will accelerate asymptotically close to the speed of light. Within the first year (according to earth) it will already be travelling extremely close to c. Practically speaking, this means that it will take 47 billion years from earth's perspective for it to get there.

Plugging that into T(t), I get 24.56 years if you just want to zip past the edge of the observable universe on your way to parts unknown. If you actually want to stop and do some sight seeing, you'll need to decelerate halfway through. This gives 2*T(23.5B) = 47.78 years.

But as Amanar's article notes, the universe is expanding, so you'd actually have to travel more than 47 billion LY. Since the rate of expansion isn't exactly known, and may be (probably is?) accelerating, this answer will have to suffice.

It's ultimately somewhat moot. Just as the ship seems to be accelerating asymptotically close to the speed of light from earth's perspective, the distance between stars seems to be shrinking asymptotically close to zero according to the ship. Once it crosses the knee of the relativistic curve, it kind of doesn't matter how vast the distance is -- the time it takes to make the journey is about the same either way. Case in point:

T(10000) = 9.64
T(20000) = 10.32
T(30000) = 10.71
T(10000000000000) = 29.76
T(1000000000000000000000000) = 54.35
T(100000000000000000000000000000000) = 72.24

The problem with the wiki article Talya linked is that the source it is based on didn't properly separate observations according to their inertial frame. Crucially, he claims that time for the people in the space craft is "simply Newtonian d=(1/2)at2. Or by rearrangement: t = sqrt(2*d/a). This isn't wrong, per se. Within their frame, the laws of physics are as Newtonian as ever. However, he makes a crucial mistake immediately after:



He uses a somewhat imprecise definition of 1g = 1 LY/yr2, but that's not the problem. The problem is that he mixed two radically different inertial frames. The 1g acceleration over the entire journey was measured relative to the inhabitants of the ship. However, the 15,000 LY distance (half trip) was measured relative to earth observers. This is where space contraction and their constantly changing inertial frame makes things exceptionally trippy. When they started their journey, the halfway mark was 15,000 LY away. But by even just a couple years or so into the journey (their time), the observed distance to that mark will be dramatically shorter than the expected 14,998 LY.

In fact, they'll cover 15,000 LY (earth measured) in about 10.037 years (ship measured). Plugging that into d=(1/2)at2, it will seem to them that they traversed 51.88 LY to reach the halfway mark in that span of 10.037 years. At first glance, it might seem as though this would require them to travel FTL by their own frame of reference. However, this paradox is resolved by understanding that they didn't possess a single inertial frame throughout the entire journey. It was constantly changing due to their constant acceleration.

Have fun sleeping tonight.

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Sail forth! steer for the deep waters only!
Reckless, O soul, exploring, I with thee, and thou with me;
For we are bound where mariner has not yet dared to go,
And we will risk the ship, ourselves and all.

Brain hurt güd.

That emoticon was designed specifically for this post.

As in, the artist who created it must have had a prophetic nightmare that featured this post, and he happened to have a mouse in his hand while he slept.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

You know, in retrospect I'm not 100% sure that taking their distance as the integral of the relativity-affected distance function and then plugging it into the newtonian d=(1/2)at2 function will actually give you the same result as integrating the "proper time" function over the same range. It seems like it should, but I'm a little wary of relying on intuition with these sorts of problems. Hmmm.

It doesn't really change anything other than last part about their perceived total distance being much 5x as large as their perceived passage of time would allow. I thought I once read something to this effect, but I can't be certain now.

_________________
Sail forth! steer for the deep waters only!
Reckless, O soul, exploring, I with thee, and thou with me;
For we are bound where mariner has not yet dared to go,
And we will risk the ship, ourselves and all.

Also, this thread illustrates quite nicely why I changed my major from Physics to Applied Optics. I still got to play with lasers and a bunch of equations with c involved, but in Applied Optics, there was the very pertinent detail that we didn't care how long the light thought it took to get from place to place.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades