"Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space." -Douglas Adams
Well, maybe "peanuts" isn't going to do. When you look out at the night sky, all sorts of objects are yours to discover, from our closest neighbors in the Solar System to the billions of stars in the Milky Way to the faint, extended and fuzzy galaxies stretching millions and billions of light years across the cosmos.
But all the flowery language in the world isn't going to help you if you actually wanted to figure out just how far away these things are. Lucky for you, it's science to the rescue!
The closest object to us is actually the easiest one to start with: the Moon!
We already know how big the Earth is: about 12,700 kilometers (or 7,900 miles) in diameter. In fact, that's something we've known for over 2,000 years! Just by knowing that, and by assuming that the Moon is a lot closer to us than the Sun is (as you might've guessed from what you know about Solar Eclipses), you can figure out the size and distance to the Moon!
Because every so often -- including tomorrow night -- you'll get a partial lunar eclipse!
When this happens, you can see part of the Moon blocked out by Earth's shadow! And because you know how big the Earth is, if you assume that the Moon is very, very close to Earth compared to how far away the Sun is, then you know that Earth's shadow on the Moon is roughly the same size as the Earth!
So if you can figure out, from viewing the Moon during a partial eclipse, what the relative sizes of the Moon and the Earth's shadow are, you can figure out the size of the Moon. This is a lot easier if you know how to stitch your images together, as Rod Pommier did in this amazing composite, below.
You can figure out that the Moon is about 27% the diameter of the Earth, more or less. But you can also measure that the Moon takes up about half-a-degree in the sky! And as long as you know a little bit of geometry, you can figure out -- from the Moon's angular diameter and its physical diameter that you just measured -- exactly how far away it has to be!
This is remarkable, because it's a measurement you can make with absolutely no equipment or training. For objects in our Solar System, we can make as accurate measurements of their size as we want, because we can actually go there, and in a great many cases, we actually have!
But we've never been beyond our Solar System. And yet, when it comes to the stars, there are a great many that we can measure exactly how far away they are!
This is Sirius, the brightest star in the night sky and one of the closest. Before the invention of the telescope, the only way to estimate the distance to the stars was to assume that they're very much like our Sun, intrinsically, and then measure their brightness relative to the Sun, and infer how far away they are from that.
If you do that for Sirius, you get an answer of about half a light year, which isn't terrible, but is off by around a factor of 20. Thankfully, we can do better.
The reason you can see in 3D is because you have two eyes -- two inputs -- at two different positions in space! If you alternate winking one eye and then the other, the location of nearby objects will appear to shift more dramatically relative to distant, background objects. This is because the angle your left eye makes connecting to the object is different from the angle your right eye makes. And the closer that object is, the more severe the angular difference is!
This effect is known as parallax. For the stars, our eyes are insufficient; they're too close together. But over the span of six months, we get a much longer baseline!
By seeing how the position of the nearby stars shifts -- ever so slightly -- against the background of much more distant stars, we can determine the distances with amazing accuracy! The Hipparcos satellite and later, the Tycho-2 catalogue, were able to measure hundreds of thousands (and then more than two million) of the nearest stars extraordinarily well, and so we know a great deal about the positions of not only objects within our Solar System, but a great many of the stars that lie beyond.
But what about the distant galaxies? The vast majority of stars in our own Milky Way are far too distant to measure a parallax for; how, then, could we possibly hope to measure the distance to this faint, fuzzy galaxies that lie well beyond the extent of our galaxy?
The key is that we have to find a way to connect what we know about stars that we can measure parallax for with stars that exist in these distant galaxies!
And this key was provided all the way back, more than 100 years ago, by Henrietta Leavitt.
Some stars are intrinsically variable in their brightness! Over well-measured periods of time, their brightness oscillates between maxima and minima. What Leavitt did was catalogue over 2,000 variable stars, as was her job, and she noticed something remarkable about the brightest of these objects: there was a strong relationship between how bright an object was, intrinsically, and how quick its period of oscillation was.
So if you can measure how quickly a star of this type -- a classical cepheid variable -- undergoes this oscillation, you know how intrinsically bright it is!
And if you measure how bright it appears to be, then you can figure out how far away it must actually be!
This is exactly the method that was used to first determine the distances to the galaxies, by Edwin Hubble in 1923, and it's still used today! This is the first "rung" on the cosmic distance ladder, and by measuring other correlations between properties of known galaxies and applying them to more distant observed ones, we can extend our reach to the farthest galaxies seen in the visible Universe.
And that's how we figure out the distances to all the objects in the night sky, from those within our Solar System to the stars, nearby galaxies, and beyond!
And if you liked this story, just you wait... this is just a tiny, tiny bit of the story that's going into the book I'm writing! I know it'll still be a couple years before it's done, but I can't wait to share it with you!
I'll buy it!
Readers who are interested in more details on measuring distances to celestial objects might read lectures in two courses I teach. In an introductory course,
look at lectures 16 - 21. The same material is covered at a higher level in
in weeks 7 and 8 (highlighted by green text).
Ethan, the figure of a stick man looking at the moon, with geometric symbols, is one of mine: see the lecture
Isn't there also a supernova that has a known intrinsic brightness that can be used as a "standard candle"? I thought I read somewhere else about that, and it would seem that it would have a greater intrinsic brightness tahn a cephid variable, and thus be more useful for truly distant galaxies.
The Universe is a big place, perhaps the biggest. - Kilgore Trout
Sean @2: Yes, there is.
Of course, the more rungs in the ladder, the higher the uncertainty. It's only in the last twenty years that people have agreed upon a value for the Hubble constant--when I was a grad student there was a camp which held that it was about 50 km/s/Mpc, and another that held that it was about 100, and each camp had good observational evidence in support of their view. (According to an anecdote I heard at the time, Allan Sandage insisted, only half in jest, that the actual value was 42.) The actual value is closer to 70, as Ethan has mentioned in previous posts. Thus the custom developed among astrophysicists and cosmologists to include a parameter h, representing the value of the Hubble constant in units of 100 km/s/Mpc, to express certain other parameters which depend on the value of the Hubble constant.
"Isn’t there also a supernova that has a known intrinsic brightness that can be used as a “standard candle”?"
Periodic non-destructive novae are standard candles, Sean. I can't remember if they're type 1 or type 2 supernovae, but it doesn't matter.
The one most people think of as novae are destructive: the star no longer exists that can go nova again.
But in a binary system, one star can dump its atmosphere onto another star and that accumulates more and more matter until its atmosphere is enriched to a level that goes nova. Since that depends mostly on mass accrued and it reaches that level from below, it will go nova very quickly after reaching the required mass and therefore, unlike the other type (which may have any mass over the required minimum), goes almost identically nova with each other.
And the star that went bang may still be there and accreting mass from the other star and repeat the event periodically. These events are also used as standard candles.
The nearest star to our Sun is about 5 LY away, and there are many potentially interesting stars within 100 LY. If we can achieve propulsion to 5% of c, a many-generational colony ship could make these trips (one-way, to colonize) in from 500 - 2,000 years. Not impossible according to current science, but beyond current engineering.
The nearest other galaxy to ours is about 25,000 LY away. At a speed of 10% of c, it would take a quarter million years to make the trip. Now we're approaching the boundary between engineering limits and scientific limits. For example one might speculate about using an entire star as a power source for such a trip: but we don't know of any way to "hijack" a star and propel it out of our galaxy, with or without a couple of colonized planets in tow.
Though, I wonder, even just for the proverbial s---s & giggles, if anyone has ever done the math to estimate how one might hijack a star or any mass sufficient to provide fusion power for a trip of between a quarter-million and a half-million years. For that matter is there any decent fiction on the theme of intergalactic travel?
Sean, Wow, I believe you're talking about type 1a supernovae.
Wow, you're talking about one formation mechanism (white dwarf + feeder star). There's a second where two white dwarfs bang together. I think very recently (in the last couple of months), astronomy has advanced enough that the 1a's from the two formation mechanisms can be told apart. So now distance estimates should get even better.
Two white dwarfs could have a larger range of final sizes (hence brightness of nova) and the result will be a one-off event.
Thank you, Michael, I really appreciate it! I fixed the credit in the post and provided a link to your site; thanks for making these images freely available, even if I couldn't track down the original source so easily!
Sean, Eric, Wow, eric, it is a type Ia supernova that's also a standard candle; these are remarkable because they are by far the most distant standard candles we can observe. How "standard" they are -- given the two (or possibly three) mechanisms that can create them. It may now be possible to go directly from classical cepheids directly to type Ia, bypassing all the other rungs on the distance ladder. How remarkable is that!
I like your stuff, but knock off the exclamtion points. They distract from your message.
The nearest other galaxy to ours is about 25,000 LY away. At a speed of 10% of c, it would take a quarter million years to make the trip. Now we’re approaching the boundary between engineering limits and scientific limits.
Even if the engineering problems could be overcome, how would the possibility of extinction of the crew population's extinction be avoided?
Grrrrr. Not "extinction of the extinction" - sorry about that.
Even if the engineering problems could be overcome, how would the possibility of extinction of the crew* be avoided?
I think if you're undertaking something of this magnitude, you'd probably try and do what G obliqely refers to - use the planet or the entire solar system as your vehicle. If you can move the entire solar system, you are 'traveling in style' and no environmental engineering is really needed. OTOH if you're just moving the planet, the solution to the crew extinction problem might go something like this:
1. Establish big underground ecosystem that utilizes geothermal energy only, not solar. Take a hundred years to do this if you need to. Heck, take a thousand.
2. Wait another thousand years so you can be very confident its stable.
2a: Keep in mind that the 2k years you just spent only increases the time to reach your destination by 0.8%.
3. Then start your acceleration.
*Not a direct quote - I edited.
With strange aeons, even death may die, Dean...
Nice summary of ideas well explained and worth reviewing again. Thanks Ethan.
Of course, my mind wanders, and the idea crossing my mind is that infinite distances, even in some kind of multiverse, cause big problems. My pet peeve is that infinities are much than bigger (philosophically and mathematically) than very very big numbers quantities; and they need to be keep out of physics. And when they appear they signal a serious need for new understanding, in my opinion.
So as I do often, I searched Ethan's blog for "multiverse" and found Ethan saying this, "Based on what we currently think about inflation, this means that the Universe is at least 10^(10^30) times the size of our observable Universe!"
Ethan gives very nice explanations about the multiverse idea and inflation etc. And it is always good to reread what Ethan has clearly explained. But what I was looking for today was to see if Ethan described the mutliverse as very big or infinite.
So well done Ethan (on this speculative but important and interesting topic), you describe the multiverse as very big finite (i.e. non infinite) distance "10^(10^30) times the size of our observable Universe!"
Hence well done Ethan, keeping to finite distances and clear explanations in today's post and your previous multiverse posts.
OKThen: But the universe might really be infinite! If the geometry of spacetime is ultimately flat, or open, then it will be infinite in extent. It is only if it is closed that the universe is finite in extent (though still boundary-less).
If you read the context around Ethan's statement of the universe being 10^(10^30) the size of the observable universe (maybe not in that article, but there is one where he discusses the actual derivation of that value), you'll see that what he's describing is that the universe appears to actually be flat. Very, very, very flat. So flat that our very best measurements put a very tight measurement on the possible degree of non-flatness, such that *IF* the universe is actually closed, then it must be at least that big to appear as flat as it is.
No actual deviation from perfect flatness has been detected, though. It is still quite possible that the universe is actually flat. Or, for that matter, very slightly open.
You are right to be leery of infinities, but you have to take care of the context. If you calculate that something should be producing infinite energy in a finite space, or that something is moving at infinite velocity, then sure, take a step back.
Neither time nor space are situations where infinity should be inherently disturbing.
In short, your pet peeve is misapplied, and your 'well done' is misplaced because Ethan is simply being rigorous and making the strongest statement science can currently make, not conforming to your belief that infinities must be rejected out of hand.
Re. CB at #17: I thought that the definitions or descriptors of a flat universe included a) parallel lines remain parallel, and b) the sum of angles of a triangle is always 180 degrees no matter where or when measured. And, that the current consensus is that we are in a very flat, very Euclidean universe.
Re. OKThen at #16: Are you (and Ethan) saying that a multiverse or greater universe, of which our local (observable) universe is a subset, is estimated at 10^(10^30) times the size of our local universe? Then if we can't observe it directly, would that be based on the idea of cosmic expansion, that there is already a very large quantity of "stuff" beyond our scope, much as we expect that at some point in the distant future, we will see far fewer galaxies from Earth? At what point is a "much larger universe beyond our local universe" that and only that (a single universe), and at what point does it become a multiverse?
An obvious practical problem with intergalactic travel is, your destination is receding away from you at a high and increasing rate of speed: so there is a minimum rate of speed (warning: possible foot-in-mouth maneuver ahead!) you'd need to achieve in order to overtake it. If you can't make that velocity, you won't catch your destination galaxy. To my mind the answer to that question defines whether intergalactic travel will ever be possible within the boundaries of any future science.
Eric at #14: Yes exactly. Pick a naturally-occurring object that's large enough, build an ecosystem inside it (presumably powered by fusion reactors), observe long enough to conclude it's stable, and then add humans and attach some kind of thruster to get it moving.
Clearly we are talking about a many-generational voyage. The human crew for an interstellar mission (or an intergalactic mission) would have to be large enough to enable them to reproduce safely along the way, without becoming inbred.
One of the numbers I've seen for a minimum non-inbreeding population of humans is 3,000 adults, but that may be completely wrong. There would have to be rules about reproductive pairings, to keep track of genetics and prevent inbreeding, and additional rules to protect individual rights as far as sexuality and reproductive choice are concerned, so long as the population remains stable.
Ultimately we have to go interstellar or we will go extinct as the Sun expands and eventually becomes a red giant. This is what I call "the cosmic Darwin test." Do we remain in one ecological niche (Earth, and our solar system), or do we boldly go, as our ancestors did when they first spread across the globe?
This ultimately is why sustainability on Earth is essential: so we don't deplete the concentrated energy sources and nonrenewable materials needed to go interstellar. We have a positive moral obligation to preserve the option for our distant descendants to choose whether to accept extinction or reach for the stars: we do not have the right to foreclose their choice by wasteful or otherwise thoughtless actions in the present.
"I thought that the definitions or descriptors of a flat universe included a) parallel lines remain parallel"
No, that's the definition of euclidian space. This isn't the case on the surface of the earth, for example.
Essentially, a flat universe WILL BECOME euclidian after infinite time.
But infinity never turns up, no matter how long you wait, it's just as far away in the future as it has always been.
G: "And, that the current consensus is that we are in a very flat, very Euclidean universe."
Yes, with local deviations where it can only be described by a Guassian metric (and where angles of a triangle won't sum to 180 degrees and parallel lines diverge etc). So technically the universe can't be Euclidean, it is Gaussian but in a way that appears Euclidean on large scales.
Which is just a nitpick, because it is true that the universe is generally viewed as probably being perfectly flat overall. However this was not a foregone conclusion; other geometries are possible.
G: " Are you (and Ethan) saying that a multiverse or greater universe, of which our local (observable) universe is a subset, is estimated at 10^(10^30) times the size of our local universe?"
What *Ethan* is saying is that based on our very best measurements of how flat (or curved) the visible universe at large is, IF it deviates from perfect flatness at all and is in fact actually closed, AND we assume the visible universe is representative of the entire universe, then the radius of curvature of such a closed universe must be extremely large (understatement) to make it appear as flat as it does.
It's a geometrical statement based on empirical data.
Cosmic expansion comes into play in defining the "visible universe". The idea of there being a "visible universe" that is a subset of the total universe goes back to the Big Bang theory -- if the universe is of finite age, but infinite size, then there are parts of the universe which we cannot see because the universe isn't old enough for light to have reached us yet. Cosmic expansion brings a new factor into play: There are parts of the universe which we can *never* see because they are moving away from us faster than light.
G: "At what point is a “much larger universe beyond our local universe” that and only that (a single universe), and at what point does it become a multiverse?"
Most of the time this is just a semantic difference, since "universe" means "everything" and so anything beyond our "universe" would just mean the real universe was something else and we see a subset, though "multiverse" can still be useful to talk about in some theoretical contexts.
Anyway in this particular case the non-visible universe is still part of the same continuous spacetime metric, and the concept of "visible universe" is relative. A planet at the very edge of our visible universe would have in its visible universe both earth and other objects that are far beyond the edge of our visible universe. So I don't think there's any good motivation for calling that a "multiverse".
G: "An obvious practical problem with intergalactic travel is, your destination is receding away from you at a high and increasing rate of speed: so there is a minimum rate of speed (warning: possible foot-in-mouth maneuver ahead!) you’d need to achieve in order to overtake it."
That depends on your target galaxy! If you're heading to Andromeda, then its velocity actually helps you overtake it. In fact, you could "travel" to Andromeda just by waiting a few billion years. Though really "Andromeda" should be in quotes probably too because in this scenario you're just waiting until the Milky Way and Andromeda become whatever we're going to called the galaxy that results from the merger.
While eventually all other galaxies in our cluster will be gone from our visible universe, that's going to be a really, really long time in the future. In the meantime expansion itself probably isn't the biggest obstacle to reaching them if we wanted to.
Here's the thing about intergalactic travel, though. Our galaxy is huge. There are hundreds of billions of stars and most likely trillions of planets. Most of these stars are going to be around for billions or trillions of years, and new ones are going to be formed (though I suspect it's possible that will slow down after the merger with Andromeda temporarily kicks it into overdrive). Unlike our tiny planet, our galaxy is not small or fragile. Nor is it special in a good or bad way.
So as far as motivation, survival of the species doesn't seem compelling to me like it does for intrastellar travel. We have a whole galaxy to play with. If we can't figure out how to live sustainably in the time it takes to use up an entire galaxy's available resources then, well...
If it has the same origin, it's the same universe.
If a universe "budded" from this one, then if the genesis was still a "big bang", then it is a new universe. And the collection of two or more universes could be called a multiverse.
Multiverse, however, usually means more than that.
I.e. the brane idea is a multiverse cosmology, since the method by which any one universe arises is the "multiverse" as it defines the parameters for all of universes.
Parallel universes is a multiverse, since it talks about the universe-as-experienced in terms of multiple universes.
But multiple separate universes which bear no relation to each other, nor interact or depend on each other or have an overarching genesis? Not a multiverse theory.
Just a theory of multiple universes.
Sort of like humanity is not the study of 6 billion humans, but assertions you can make about humans from the features described by (for example) 6 billion humans en mass.
I ponder this often when the expansion of our universe is discussed. As far as we can tell, everything we can see appears to be receding away. I can't help but think that perhaps other parts of the universe un-observable to us could be contracting.
Of course it is completely logical for us to infer, as we do, that other unobservable regions are more then likely expanding because that's what we see in every direction we look; yet I wonder if the whole entirety of the universe could be "giggling". In other words some parts expanding, some contracting. Like a huge chunk of jello [the bulk] that gets vibrated. In some areas the jello is contracting, in others its expanding. Lets pretend that from your frame of reference the jello-verse everything is moving away from you [this would lead you to the big bang theory]. From my frame of reference everything I observe appears to be contracting [big crunch]. Lets also pretend where my universe is no longer visible, your universe begins, therefor we are not connected causally. In the gap of space between your and my observable universes is where Wow lives. From Wows point of view (one half of his universe is shared with me and the other half with you) he would see one side coming towards him and yet another side moving away. So from Wow's frame of reference he might infer that he is traveling at a high rate of speed relative to his observable universe. [sorry to get all Chelle on you guys with the wacky analogy but best I could think of at the moment].
This brings me to my question: What conclusions would Wow draw and what predictions would he make observing a universe that appears to be traveling in one preferred direction? Would he ever be able to piece together the big bang theory we use or anything remotely close to it? I'm guessing no, but want to know what theory for the origin of his universe he would formulate based off observation. What other implications, if any, would this have on his view of the universe?
@ #11: I find it odd that acceptable use of punctuation marks distracts you. Perhaps you had a traumatic experience with the ! as a child. Ethan is extremely passionate about this stuff. Why can't you let him share his enthusiasm? If it ends with ! its usually an amazing and interesting fact. There's one in the name of the blog itself b/c the big bang is an amazing and interesting fact!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
" I can’t help but think that perhaps other parts of the universe un-observable to us could be contracting. "
They could be plaid too.
No reason for the invisible universe to be plaid, but it could be.
You're just rehashing Russel's Teapot, crd2.
@ Wow: I understand you point. Just curious is all. I've heard the implication of an accelerating universe, a contracting one, and want to know about the implications of one that appears to have everything within it moving in the same direction. This is not some quack pot theory I have or how I believe the universe is or should be, simply fun to me to think about. Nothing more, nothing less. I assume you'd not be able to piece together the big bang theory, learn of dark matter, or the expansion.
You must be tired today Wow. That's all you got for me?! Plaid?? Normally you'd say something like "plaid elephants riding tiny pink golf-carts with pizzas for wheels all humming the Benny Hill theme song whilst eating chap stick." I prefer the lengthier ones. Much funnier. Go brew a pot of coffee and quit slacking on your sarcasm! (sorry if I distracted anyone with my punctuation marks.)
"Just curious is all. I’ve heard the implication of an accelerating universe, a contracting one, and want to know about the implications of one that appears to have everything within it moving in the same direction"
Problem is that the question is nonsensical.
If everything is moving in the same direction, then there is no reference point to which you can point to to determine this.
Moreover, this isn't what you stated before. Before it was "if some bits are expanding and some contracting".
The first point of skepticism is to look at your own ideas and go "So how can it be wrong".
And on this thread, things to put "ideas" like that (and I really DO have to use "scare quotes" around that word, please realise this) is over on the "you are responsible for what you say" topic on this blog.
Clearly we are talking about a many-generational voyage.
Not necessarily. Borrowing from Ethan's more recent 'cosmic speed limit' post, if we got the speed of our ark ship up to our current world record for electron beams (299,792,457.9964 m/s), you're talking about a 1.2 year trip according to internal clocks.* Now you only need to figure out how to build an engine that can do that and some sort of protective measure to prevent your ship from disintegrating from the friction. :)
*It is interesting that sci-fi fans often bemoan the speed liimt of relativity and think FTL as a wonderful thing. But think about this: in a Newtonian universe, at that speed it would take you 4.2 subjective years to reach Proxima Centauri, our nearest neighbor. You have to take 8.4 years of food, etc. to make it there and back. Your life support system has to be able to run for 8.4 years. You need 8.4 years of spare parts. And so on. In a relativistic universe, that journey takes under two hours. You could literally do it in an airtight can with an engine and a shield...if you can build the engine and the shield...
CRD2 @23 and Wow:
Regarding the 'expanding and contracting' thing, something somewhat like that happened at the end of the inflationary period. As expansion slowed down, more parts of the universe came into our light cone. Stuff that was literally outside a particle's observable universe became part of it's observable universe.
I suppose something like that could happen again if our current expansion rate slowed. But there would be no effect on human civilization; an gravity and light from the newly-observable regions would propagate towards us from the current edge of the observable universe at light speed, so it would take billions of years to reach Earth. New stars would not just suddenly start appearing in the sky, the Milky Way would not alter course or get pulled apart, etc., etc.
eric, whether things came back into our light horizon depends on when inflation stopped and how much slower it got.
And it may be I understood incorrectly, but it seems the idea was that some bits of the universe beyond our light curve were contracting whilst the bit we can see is expanding. Not that everywhere slowed down the expansion rate.
@ 28-19: Mind officially blown. Never heard that b/f. I will study this topic further. Thanks. You two are my fav. commenters. You always give valid points and great insight. Cheers. The two of you have a good cop, bad cop vibe going on. Guess who's the 'bad' cop. :)
*amend 28-19 to read 28-29.
**Never had a comment section tell me relax before.
"Your posting too quickly. Slow down."
" Guess who’s the ‘bad’ cop"
seems to me you are mixing relativity and Newtonian mechanics in a way they don't match. 8 years vs 2hours? In which reference frame? You can't accelerate an arc ship to even 90% of c.
SL, under the assumption of 1g acceleration, you can get arbitrarily close to the speed of light and time dilation can ensure you can reach andromeda in (IIRC) a month or so, accelerating at g.
Now, engineering-wise, the ability to move that mass that quick for that long may not be possible because the energy cannot be contained within the original ship, but a ramjet design will do it.
Take the reaction mass from the interstellar medium.
Wow @29: AIUI its a continuous effect. I.e., if the expansion slows a little bit, the observable universe gets a little bit bigger (in theory - in practice, we probably won't be around to see the difference).
CRD@30: the idea is pretty simple in principle. Think of the universe as a 2-D rubber sheet that's being stretched (that's the expansion). Think of someone walking toward you on it (that's light). If the stretching between you and that person is happening faster than their walking speed, they never get to you.The edge of the observable universe is that distance point at which a walker will just barely get to you. (But don't use this analogy to think he takes an inordinately long time, the analogy falls apart on that point.)
Sinisia @33: I wasn't mixing, I was contrasting subjective travel times for a certain speed under a 'no relativity' universe and a 'relativity' universe. But I did forget to mention one fairly important thing, which is the force required to achieve that speed is much much higher in the relativity system (i.e. the real world). So just assuming equal speeds is probably unfair to our fictional newtonian-universe-dwellers. To be fair we should probably assume equal force applied to the ship - i.e., equal engines. Then compare what that gets us in terms of subjective travel time. I leave that to someone else. :)
the issue is you can't talk about Newtonian universe if you're talking about speeds of 99% c.
"Wow @29: AIUI its a continuous effect. I.e., if the expansion slows a little bit, the observable universe gets a little bit bigger"
That's incorrect, eric.
The universe is big, remember. So the bits that are a long way away are moving away hugely fast and are already around three times further away than the light was when it left.
Which approximately means to see that come back into our light cone it would have to reduce by one third for about 13 billion years.
the issue is you can’t talk about Newtonian universe if you’re talking about speeds of 99% c.
I think we are still miscommunicating. Let's say I'm a novelist. I'm making up a fictional universe for my story. This is make believe - I am not trying to say anything about the how the real universe behaves right now. In this fictional universe, there is no law of relativity. Ignoring all the other stuff that this pretense will throw out of kilter, one of the results of this fictional physics is that when the characters in my story go somewhere on a spaceship, they experience Z seconds of subjective travel time where Z = travel distance / spaceship speed Y, no matter how high Y gets.
My point was, for Y= 299,792,457 m/s, the Z for the characters in my fictional universe is actually going to be significantly longer than the subjective travel time that people in the real universe would experience if they were moving at Y = 299,792,457 m/s. Do you agree?
Or more succinctly: "In a Newtonian universe" means if the universe operated according to Newton, not Einstein. Pretty common hypothetical, particularly when comparing the predictions of the two theories.
The problem with time dilation is that the short travel time is only for your reference frame, while the people back on earth see your journey take the whole 8 years (or millions of years if you're heading to Andromeda).
So you can reach a distant location in reasonable time, but your ability to trade or communicate with your departure point is not reasonable. You're still separated by a gulf of years.
This means that while interstellar colonization is possible in Einstein's universe, an interstellar *civilization* is not. There can be no United Federation of Planets when by the time the message reaches Earth to say the Klingons are attacking Vulcan, Earthlings no longer understand the language in the message, and by the time they respond, the Klingons took over but have evolved into something that doesn't look Klingon anymore.
Which (aside from the challenge of working out actual relativity versus magical FTL travel) is part of why sci-fi authors like FTL so much.