If the universe is donut shaped, what's outside of it? Sugar sprinkles?

Allegro.cc has the answer:

What's outside a donut? (Dizzy Egg)

It's definitely that or, ummm, some rapids. You'd have to ride down them in a barrel. And if you fell in, I guess you'd need to jump from bubble to bubble to make it back to the surface. Of course, you could always stop for some kwik snax.

What is above 'up'?

Higher?

Wolfram|Alpha isn't sure what to do with your input.

Heheh, like that Gnolam.

A hungry person waiting to eat it.

There are higher dimensional beings outside the donut, watching us and this forum.
"Well, it's obvious we should never let them out of the donut!"

The donut is balanced on the nose of a turtle, the turtle below that has a donut on its nose. This also explains how there can be more than one universe in existance.

The donut is the universe.

edit: I'm serious. There is only the donut. There is no outside of the donut, there is no inside of the hole, there is only the donut.

edit2: Well. There is also only the coffee cup. The donut and coffee cup are the same.

I imagine the fish say the same about the ocean. There are schools of fish that assert the universe is rather spherical

No, no, no. The cake donut is a lie.

Didn't we discuss this in the milk thread?

Hopefully they are not on thier coffee break.

Outside a donut are the non-free donuts.

...Homer?

Presumably, higher dimensional space. The question is somewhat misleading because it has an assumption that we are 'inside' the donut; instead, we are on its surface, and the donut is a three (four?)-dimensional surface that curves into a torus in higher dimensions. This, of course, presumes that the donut theory is true; I'm not sure of the current scientific thinking on the topology of the universe.

The universe:

You should be less concerned about what is outside the donut and more concerned about what is with you inside of it.

Hmm.. seems no one read my post.

See here is how i lay it down.

Let's do it compy talk. The universe is the set of all things. What is outside the set of all things. NOTHING. It makes no sense such things as outside the set of everything.

The universe is all the things WE CAN POSSIBLY GET AT! If you could "jailbreak" it, then you'd get access to the other universes.

And probably be able to run linux on it too.

A police car!!! :-)

My yolk filled self has lost sleep over this. How can there be....nothing? You mean like the nothing that is eating up the world in the never ending story? I think I've been using Allegro too long...I'm stuck in 2 dimensions, never mind 3....or even 4.

A guy walks accidentally into the kitchen of Arnold's Donuts and sees a big fat guy making jelly rolls. The guy grabs a chunk of dough with his filthy hands, rolls it against his huge, bare, sweaty belly and places it on the oven plate.
"Eow, after seeing that I'll never eat a jelly roll again!" says our guy. "I wouldn't dare to see him making donuts!"

And thus god created the universe.

Homer Simpson is god?

Did you know Stephen Hawking stole the theory of a donut shaped universe from Homer?

Probably did it when he guest stared.

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If you were right at the edge of this universe (moving with its expansion), what would happen if you tried poking through the edge?

Probably something similar than if you moved with 1 m/s and dropped your speed with 2 m/s.

No. Much more nothing-ish.
What's at the end of a circular road? Not even nothing, because the end itself isn't there; this doesn't mean that the circular road is endless.
Similarly, questions like "what's outside the universe", "what happened before the Big Bang", and such are meaningless.

What about, "What is the universe expanding into?"

Imagine a circular road that's growing. In the road's (1d) space, it's not expanding into anything.

Wouldn't an equivalent way of thinking about it be that everything in the universe is shrinking while the universe itself stays the same size?

Yes, that one is equally meaningless.
When you blow up a balloon, what does the surface area of the balloon expand in?^[1]

That doesn't explain what the entire object is expanding into though.

You are all blowing my mind! What is my mind expanding into?

Umm, "what's outside the circular road?" would be perfectly valid, so how is it not with the universe? Either you have a good analogy there or you dont.

Nice word game there. When you blow up a balloon, it expands into the air. Who mentioned surface area?

In this example, its like the universe.. The universe lives on (or is the surface...) the surface of the donut/toroid. So its the surface they are talking about...

You're all applying the "intuitive" Euclidian lessons you learned as a knee-baby while playing in the yard into the entire universe. You sound like "Why can't we sail off the edge of the world, Columbus?"

I'm not saying you can sail off the edge of the world, or leave the universe. But if it is expanding, it has to be expanding into something.

"Expanding into something" implies there is space (more universe) to expand into.

[EDIT]
There was a PBS show a few years ago about "membranes" that somehow created universes when two of them touched, as the area of contact expanded, the universe grew. This is extremely 2d sounding though. OTOH, maybe you could consider that the "edge of the universe" is merely the farthest part that has "announced" itself to us.

Hey, I'm not one of those crazy physicists who said it was expanding in the first place.

The real question here is if the universe is finite or infinite.

"That-a Christopher Columbus, he is-a crazy, no? He-a says the world, she is a round, and-a we can't sail off the edge! So he thinks we can-a sail around and around forever? It's not infinite!"

You're totally missing the point.

You can't poke at the edge of the universe (or get to the other side) any more than you can sail off the edge of the world. That's the point.

I (personally) was talking about expansion, not the edge. I never said there was an edge that you could cross.

The universe is considered to be expanding due to (apparently) farther objects having greater doppler red shift, farthest objects are quasars, which are considered to be early stages of galactic development. If you extrapolate where "zero time" would be, then that could be considered an edge.

[EDIT]
And you need an "edge" to point to if you want to claim the universe is expanding

Stop talking about edges!

That's the response I was looking for... I didn't mean to start an argument about it!

But since one's going anyway...

Is space itself expanding, or is the matter in the universe moving further out into pre-existing space?

Either you understand what people are talking about or you don't.

It's not a "word game".
You don't understand the analogy. When you blow up a balloon the volume expands against the air, but the surface doesn't. I even pointed this out in my original post, so I'm not sure how you missed it.

No, you're just some random person on the internet who doesn't know what he's talking about but thinks he can argue a sensible point anyway.
Objects in the universe are moving apart.^[1] In other words, distances in the universe increase. In other words, the universe expands. The notion that it has to expand "into" or "against" anything is your day-to-day intuition being "off" when you try to apply it to regimes of physics that are far removed from your day-to-day experience. It's analogous to the surface area of the balloon.

The universe is a finite volume in space-time (13.7e9 years old, spanning the same number of light years in all spatial directions) without an edge. It is finite or infinite in the same sense that the surface of a sphere is (where the total area is finite but there are no boundaries).

Technically, it's a horizon. But the only way to "get there" is to travel faster than the speed of light, or to travel backwards in time to the origin of the universe (which is more-or-less the same thing if you work it out).

EDIT:

You're welcome.

Neither did I, but whatever...

Space itself is expanding.
That at least is what the equations of general relativity predict. Observationally I don't think there is a way to tell one from the other, but the observations are that everything is moving away from us. That either means that we are at the centre of the universe with all other objects having a speed that scales with distance (homologous expansion), or it means that the entire universe expands (in which case it doesn't matter where you are, it always looks as though everything is moving away from you).

Isn't there something like Einstein's Butter Knife or similar that says we shouldn't assume that we have a special position in the universe? Like, e.g., being in the center.

I think that's called the cosmological principle.

That's what I thought from everything I've read on it.

How does one wrap one's head around the idea that space expands into nothing?

<head_explodes/>^[1]

It can't be nothing. If it was nothing, nothing could expand into it

That's right.

Yes.

I don't see the problem. Seriously. The universe is just getting bigger on the inside. (EDIT: maybe it helps if one has accepted and gone through the mathematics of things like Lorentz contractions and curved space-time.)
How do you wrap your head around the fact that the surface area of a balloon gets bigger as it's inflated? It's the same question (yes, to stress that again, the surface of the balloon is the analog of the universe in this comparison).

But the balloon lives in a 3d world, and the entire thing grows and fills a larger space in it. Where does our universe do that?

Maybe the universe is curved in 4d.

But the surface of the balloon is a 2D space and the surface of the balloon is the analog. That the balloon itself is a 3D object is irrelevant to the comparison. I should start putting emphasis on surface.

Whoever said that's what it does? It's an analogy, not a one-to-one correspondence.
Anyway, part of what you're asking is: if the universe is analogous to the surface of a balloon, what is it that's analogous to the balloon itself? Is the universe is a hyperspace of something else, what does something else look like? What is the topology of the universe?
The answer to that is: no one knows. They are (mostly) outside the scope of modern physics. Do the eleven dimensions of string theory have something to do with this? Maybe. Maybe not. Is it necessary for the universe to be embedded in some higher dimensional object in order for the notion of "expansion" to make sense? I don't think so, but that doesn't mean it can't be.
Topology is a fascinating but complicated branch of mathematics (it sounds simple at the level of teacups being the same as doughnuts, but it can get really complicated especially if you go to many dimensions and allow some of them to be compact or closed; think of the difference between an infinite cylinder and a torus for the gist of that). It is very relevant to the question of the structure of the universe. It is not a given that our every day notion of what makes sense applies.
That is the best I can do on that topic for the moment.

However, the point I'm trying to make is: the universe is no more expanding "into" anything than the surface area of a balloon is expanding "into" anything.
This is a different type of expansion from that of a hot gas expanding "into" a cool gas - or indeed of the balloon expanding against air. Those are examples of a 3D object expanding in a 3D space.

I suppose the idea is, it's not a space expanding into a larger space; it's the total amount of space getting bigger. That is, the universe is all that there is, in our 3d space anyway, and more of it is being created.

That's right. As I said, it's getting bigger on the inside.

I have had it explained to me (in very patient terms), that space itself cannot be expanding, because it has nowhere to expand to. The expansion we see is simply matter moving into existing space. This concept is very simple, and I should easily get it. Apparently I shouldn't be "glim" because I was "wrong".

I hate things that are hard for humans to visualize. It makes proving your point so much harder.

Is it true, then, that our space is curved in 4d and it's that (sphere, torus, whatever) that's getting bigger? That's the only way I can think of for space itself to be expanding.

I don't know what universe you live in, but when I blow up a balloon it expands. And as it expands, the surface stretches. In turn, the surface area increases.

Nah, stuff in space isn't moving. The distances are increasing, but nothing is moving.

I actually understand how it works (as far as I know) - I'm just not seeing where Evert's explanation makes a whole lot of sense (in fact, the whole balloon analogy sucks IMO because of all the confusion it adds - analogies are supposed to make things simpler).

The way it was explained to me was using numbers. Take the sequence 1 to infinity: 1,2,3,..,inf. Now multiply it by two - 2,4,6,..,inf. The distances "between" the numbers went up (1->2 is 1, but 2->4 is 2) but nothing really expanded here, you still have a set of numbers from 0 to infinity.

But a lot of numbers in the first set are gone in the second set! Numbers can't be created or destroyed!

Just pointing out what someone who doesn't understand would (possibly) say.

Personally, I haven't been able to really comprehend 4D... The best I can do is an array of 3D...

As I said, that can only be true if we are at a very special location, the centre of the universe, because all distant galaxies are moving away from us.

Maybe. You can always embed a (mathematical) space into a larger space though, so it's not exactly a prediction. However, such a model would reproduce the physical characteristics of an expanding universe.

Read my previous post again. I said that.
The balloon expands against the surrounding air. The surface of the balloon does not. It just gets larger. Now forget the balloon and only think of the surface. That's your universe. And it expands, but not "into" something else.

Because you're not getting the analogy with the surface of the balloon and keep going back to the entire thing.

That's where you get to have fun by saying that the two sets have the same size (because there's a one-to-one mapping between them), despite the fact that the original one also contained all the even integers.
I don't think it's a particularly good analogy though (in part because it doesn't capture the increase in expansion rate with increasing distance).

Infinite sets are weird. And I don't think that that set mapping is nearly as good an analogy as the balloon.

I understand this. I'm just kind of playing devil's advocate to the idea. I have a friend who can't wrap his head around the idea of space expanding into nothing and I'm hoping someone will have a better analogy than the balloon (which I've already told to him) that will help him.

Right now he thinks that everything is moving into pre-existing space. He agrees with the idea that the universe curves and has no boundary, and that going in a straight line long enough will lead back to the starting point. He thinks that the observable universe only covers a small portion of the available space in the universe, and that it is expanding out into that space, and that eventually it will go all the way around and come together again.

EDIT:

Evert, why does your avatar always make me think of Sluggy Freelance?

Again, if everything is physically moving, then everything is physically moving away from us and we are in a special location.
The other option is that everything is moving away from everything else, but that can only be the case if the universe itself is expanding (as the surface area of an inflated balloon).

There is no reason to believe that is the case. We don't know what the large-scale topology of the universe looks like. It might be sphere-like (the three dimensional analogue of a spherical surface) or torus-like (the three dimensional analogue of the surface of a torus). Or something else entirely. We don't know.
There are theoretical advantages to periodic boundary conditions though, which effectively gives you a torus (think of a sheet of paper where you identify the left and right edges and the top and bottom edges).

Who?

It's a webcomic.

I'm supposed to take Topology in the fall. I imagine this topic will come up.

It reminds me of the 1978 animated film, The Lord of the Rings

The analogy is often made between galactic distances increasing and the distances between raisins in a rising loaf of raisin bread. Every raisin is increasing in distance from every other raisin no matter if the raisin is near the surface of the loaf or buried deep within.

This Just In: The universe expands as the Flying Spaghetti Monster counts the parsecs from the "center" of the universe to the edge

And I always imagined Evert's avatar came from an early illustrated Alice in Wonderland.

Because the "space" (dough) between them is expanding. That's the three dimensional version of the balloon. It has the advantage that the raisins themselves don't expand (whereas dots on the surface of a balloon do) and the disadvantage that the bread actually does expand against the air.

As for my avatar, I've posted where it came from before, but it's rather cultural specific. See Marten Toonder on wikipedia. There is no English language wikipedia article on this character though (see here for the Dutch entry).

It's impossible to understand the concept of "the edge of the Universe" with "common sense". With "common sense" I may be thinking of what my brother does right now in Helsinki, 90 km from me. I understand the distance. I understand what time it is. He might be listening to the radio time signal at the same time as me. If I go visit him, I need an hour to get there, but if I phone him, the feeling of right now will be more obvious, despite the distance.

But if my brother were at the edge of the Universe, the distance would be so huge that the idea of right now doesn't work anymore. There simply isn't any absolute right now. If I'd go there with the speed of light, I'd be there right now, only to discover that my brother had died 13.7E9 years ago. And determining whether he was alive at the time when I started my travel is probably difficult, too. There's simply no way to picture the Universe "from above" at one moment, at least not using "common sense".

There is no such a thing as the end of anything much less the universe, it is all endless. If there was an end to anything we could define it, since we cannot therefore there is no end, and if someone had somehow found it then in that instant he would also define what's outside of it, and whatever that is outside then becomes part of the universe and so on, and so on, and on and on and on...

This is a common Relativity Theory misunderstanding. We can measure the time in the edge of the universe relative to us. What we can not have is a global time for all the universe.

As we speak, there are events taking place in, let's say, 5 billion light years away from us. What we can't have is a common reference frame, and therefore a common time measurement.

Well, my intention was that these two statements meant the same. So if there's a misunderstanding, it's only due to my lack of proper words. The Relativity Theory is absolute. The theory gives absolute values on everything in time-space. The only relative there comes from our "common sense" way of dealing with space as one absolute thing and time as another, while Einstein says they are kind of relative to each other.

Would it be fair to say that 5 billion light-years away there are 10 billion years' worth of events happening right now?

I am not sure that there can not be a global time in the universe, though. Is the speed of light the ultimate limit in information propagation speed? if so, then the speed of gravity should be C (the speed of light).

But then how come our solar system is stable? light takes 8 minutes to arrive from the Sun. If gravity took 8 minutes to arrive from the Sun as well, then Earth would rotate around an empty spot in space. The Sun moves inside space, relative to the Galactic Center, and therefore the Earth's rotation around the Sun would not be elliptical, but parabolic. In the end, the Earth would not have remained attached to the Sun. It would slingshot around the Sun and ejected in a different direction from the Sun.

This means that the speed of gravity is instantaneous (since the Earth has the same elliptical orbit each year around the Sun), which means that there is a medium which allows gravity to propagate through space instantaneously, which means that there can be an absolute global time for the universe...

I'm pretty sure the distance that the Sun travels in eight minutes is negligible.

Yes.
Or rather, as some people put it, there is a fundamental upper limit to the speed at which information can travel. Light just happens to travel with the same speed.

Yes - although this has not yet been experimentally confirmed, as far as I know.

Why wouldn't it be? (Strictly speaking, you have to say on what timescale it's stable. We'll take billions of years for practical purposes).

No it wouldn't. Of course it wouldn't.
What it's seeing is a retarded potential, it "sees" where the sun was 8 minutes ago.
By the same logic it's dark here because the sun has moved since it emitted the light that just got here.

What?
Why?
Also, work out how fast the sun actually moves compared to the speed of light. The smallness of this number may surprise you.

Huh?

Think of it this way: the general theory of relativity has gravity propagating at the speed of light. You'd think one of the many people using it would have noticed by now if it predicted that the Earth would just float off into the black beyond. In fact it doesn't predict that. It predicts an eliptic orbit with a precessing perihelion^[1] - as is observed, most famously for Mercury.

Er... no.

Ultimate Fate of the Universe

Particularly fun read is the "Theories about the end of universe" section of the article.

If the Universe doesn't expand forever, would there still be star births in the deflate phase? Imagine an intelligent life form in that phase. Or imagine that we would now live in that phase. It would give a special scent to the future prospects. We now know that Sun might explode after some 4E9 years (and long before that Earth will steam away) and that's why some lunatics scientists work with theories on how humankind could escape our solar system. But seeing all galaxies moving towards each other, towards some centre, and knowing everything will collapse after some 8E9 years would be even more freaky. Try to escape that.

That does it, I'm moving to the suburbs now!

Hmm. What about if I look at the Universe from a microscopic point of of view as opposed to a macroscopic one; does the topology change? Also if I live on the surface of the donut, what happens if I dig through it?

You're right, of course, but it doesn't hurt to try to think out of context for a minute.

But the general theory of relativity doesn't need to predict that the Earth would float off into the black beyond. As you said, it is not confirmed that the speed of gravity is C. Therefore, it may be that the theory of relativity correctly predicts things like Mercury's orbit, but for the wrong reasons. I.e. it is a formula that that has produced correct results so far, just like Newton's theory of gravity produced correct results until problems like the orbit of Mercury showed up.

There is a number of problems that the theory or relativity seems not to be able to explain. For example, the positions of the spacecraft leaving the solar system - they are off from calculations by a tiny amount, but scientists can't say why. Physicists had to introduce dark matter, dark energy and the dark force to explain the many mysteries of the cosmos. And then there is the quantum world: quantum entanglement escapes relativity, and although it can not be used to transmit information (which I don't really believe it can't, as transmission of information faster than light does not really violate causality), it shows that there is spooky action at a distance, indeed. Which means that the very fabric of the universe is interconnected in ways unknown to us. Einstein himself could not believe it.

And then there is the problem of black holes, which have never been observed, and can not exist for Ric = 0. For a black hole to contain an infinite amount of matter in a single point, it means that energy is infinite, which means matter can get the speed of light, which the theory of special relativity does not allow!

Crazy stuff...

Note that I didn't say "outside the circular road", but "at the end of the circular road". Although a circular road is finite and embedded in a 2-dimensional space, it is "endless" when looked at from a 1-dimensional perspective. The 1-dimensional space that the road represents can expand without expanding "into" anything, 1-dimensionally speaking. Assuming a mathematically ideal road that has no width and can make infinitely sharp turns, it would even be possible for a road to expand its 1-dimensional space forever without leaving its original 2-dimensional enclosure (so technically speaking, it is not expanding into anything - it just keeps filling the same space).
Also, without any means of looking or measuring beyond the road's single dimension, we cannot tell what it looks like in 2D - we can only measure its length, and practically only so if it isn't too large; if it expands and there are objects on it that we can observe, we can measure their distance and the speed at which they appear to be moving away from us, and if we assume that the objects keep their relative position on the road, then we can use this information to calculate how fast the road expands.
If the road isn't too long, we can also send some kind of signal into one direction and see if we receive it back at the other end, which would prove that the road is indeed circular; if it's not, but rather actually infinite, we won't receive the signal ever; however, this could also mean that the road is really a closed loop, but too large to receive the signal anytime soon.

Now expand the model from 1 to 3 dimensions (or more if you want to), and you have your analogy. We cannot observe more than the 4 dimensions we live in, so we cannot find out what kind of space the universe is embedded into.

Yes. The idea of a donut might lead us astray. It's not like our 3D world would be inside the donut, but on the surface. They are talking about a hyper donut. The Eukleidean infinite space would be a hyper plane. The curved Universe would be a hyper sphere or a hyper saddle (hyperbolic paraboloid). Or a hyper donut. "Hyper" just adds one dimension to it.

My colleagues and I have just conclusively proved space is positively curved (spherical). Well, it's either that, or my car pulls to the left...

Yes. That's why there's a problem reconciling quantum mechanics and general relativity. The idea that the universe has a well-defined local metric breaks down.

In the analogy you're a flatlander living on the surface of the doughnut. For you, there is no direction "into" or "through" it.

While possible, it is more likely that the answer would be grossly wrong than that it would happen to come out to be correct by accident. General relativity is a far more complicated theory than Newtonian gravity is; any theory that replaces it will need to have it as a special case.

It's not clear that that is a problem that is due to a break down of general relativity. Some people like to think so, but it's by no means clear. It could well be something else entirely.

Dark matter is inferred from galactic rotation curves and gravitational lensing. In a way it's an "intrinsic" curving of space time. General relativity deals with it just fine.
Dark energy enters in the form of the cosmological constant, which is just an extra term appearing in the gravitational field equations. It's manifestly dealt with naturally in the context of general relativity.

It doesn't, because...

Yes. It. Does.
Do a search on the forums, this has been done to death. If you construct Minkovski diagrams for the situation where two observers in relative motion exchange information faster than with the speed of light, you'll see that one of the possibilities has the reply arriving before the question is asked. Someone (SiegeLord?) posted the relevant diagrams in the previous thread where this point came up.
This is apparently a hard point to grasp, since I've had discussions with other scientists who seemed equally unaware that this is ruled out.

What Einstein could or could not believe is as irrelevant to modern physics as whether Darwin believed in evolution^[1] or not is to modern biology.
He did not have some magical insight into the nature of the universe that others lack.

I know a great many people who would disagree with that sentiment.
There are X-ray sources in the sky that can only be explained by accretion disks around black holes. There are regions in the inner part of galaxies where matter is observed to be concentrated within a Schwarzschild radius.
I guess it depends on what you would consider a "black hole observation". Gravitational wave detectors will be very interesting in this sense.

No black hole contains an infinite amount of matter. Either way, whatever happens inside the event horizon of a black hole is causally disconnected from what happens outside. Our physical laws may not apply there at all - but it doesn't matter.

I thought they were just going faster than expected, and thus in a different place.

I really want to get high with Evert.

I agree; just like the Theory of Relativity had the Newtonian theory as a special case.

I agree again; it's only a possibility.

Only if spacetime is explained in terms of Einstein's theory. If Einstein's theory is wrong, then dark matter will not be required, provided that a new theory explains the galactic rotation curves and gravitational lensing without the need for dark matter.

In other words, it is just there to make the theory agree with the observations.

I've seen the diagrams but I don't agree with them.

O sends a FTL message to A. A sends an FTL message to B. B sees the O's past; but it can not affect O, because O is not there, and thus causality can not be violated.

In other words, it may be observed that an event A happens before another event B, when A was caused by B, but it doesn't matter: this is not a causality violation, it's only photon play, it's only observation of events in different order that they happened.

The information received by B can not be used to change the course of O, because O is not there: whatever B sees of O, it's in the past of O.

I would never say that what the top physicist of our recent times believed is irrelevant, especially when we are using his works :-).

That is a leap of faith, actually. We found something that seems it fits the theory. It might be it, it might not be it.

Yes, it does. Inside a black hole, according to the theory, all matter is compressed into a singularity. The density of the singularity is infinite. Since the density is infinite, an infinite amount of matter can be stored in the singularity. Since matter = energy (E = mc^2), an infinite amount of energy can exist in a singularity, which means matter, inside a singularity, can obtain the speed of light, which violates the theory of Special Relativity.

They should, if they were correct.

You do know of the Kepler's Laws and the Law of Gravitation? Both allow us to solve the the mass of black holes if they are surrounded by something that orbits them. We've seen things(stars usually) orbit invisible things that are presumed to be black holes, and figured out their mass via those laws.

That's of course beside the other bits of math that describe how the singularity actually seems to work (which is rather unlike the way you are describing it).

There seems to be a problem with observing black holes, because, they're, well, black. I also don't see what the problem with "dark matter" is, since it is after all, dark. Not all matter has to wind up in a body in the proper mass range to produce an glowing thermonuclear furnace.

Your words "can be" doesn't prove "is". 1/0 == ((1.0E+99999999999999)!)/0. The Schwarzschild radius is a direct consequence of the amount of matter within.

No. The cosmological constant is a possible term in the field equations. It empirically gives rise to dark energy. There is a difference between those statements.

It's not open to agreement or disagreement any more than "1+1=2" is open to agreement or disagreement.

B sees O's past, which is B's future. Who says the observer at O and B cannot communicate? The transmission of the message to A is in B's future lightcone. He can influence events there having knowledge from the future. Which part of "causality is violated" didn't you get?

Dark matter isn't required to explain gravitational lensing, dark matter changes the prediction of gravitational lensing by general relativity <i>in a way that can be and has been verified<i>.
I happen to not like dark matter. What I like and don't like doesn't change what's there or not there though.

Einstein's many great contributions not withstanding, it is irrelevant whether he could personally believe in (say) quantum mechanics or not.^[1] Einstein had many great ideas, but that doesn't mean all of his ideas were. In fact, many (most) of them turned out to be wrong.^[2]

Yes, sure.
We have a theoretical prediction saying how an accretion disk around a black hole would behave. We observer said phenomenon (many times under many different circumstances). But it doesn't actually mean anything, it's just a leap of faith to say that theory and observations agree.

No, it doesn't. How does a "10 solar mass black hole" have "infinite mass"?

can be does not mean the same thing as is.

The other way around, actually. Mass is a form of energy.

You're confusing total energy, potential energy and kinetic energy.

There is no reason they have to because the inside of an event horizon is shielded from the outside universe. It's irrelevant either way because you cannot get information out of a black hole.

But it doesn't have to be a singularity. It could be a black star, i.e. massive enough not to let light escape but not with an infinity in its center.

Ok, tell me.

Yes, without a doubt. It still does not mean there is a single point with infinite density in it though.

Indeed. It's there to make the equations agree with observations. Remove that, and the equations are not possible.

It's not valid to compare a theory with an axiom.

B sees O's past, but O can not see B's future, and therefore O can not send information to B regarding B. And therefore B can not receive messages about B's future, and there is no causality violation.

You mean that it fits the mathematics of general relativity. Scientists wondered why the observed gravity can not fit the math, and they came up with dark matter.

So? it still his theory that we are discussing.

Of course it is. Until we go there and observe the black hole, we can't be sure it is a black hole. It's unlike other events we have observed here on Earth.

It can contain infinite mass. It does not have infinite mass.

No, but the math allows it. And by allowing it, it creates the problem I mentioned.

Wordplay. Mass and energy are exchangeable, due to E = mc^2.

It does not matter how you label the energy. Energy is energy. I am just stating the obvious, derived from the formula.

But since the matter inside the black hole is of the same kind with the matter outside of the black hole, then the same laws will apply. So if the law applied outside of a black hole gives rise to a paradox inside the black hole, the law applied outside of a black hole is wrong.

Except for quantum information.

I can contain infinite matter, but this means nothing because there is no method by which it would ever acquire infinite matter. The scenario you outlined won't happen in the physical universe. You can add matter to the universe as much as you want, but adding a finite amount of matter into a black hole that already contains a finite amount of matter will never yield an infinite amount of matter.

I made some wildly delicious spaghetti yesterday, and as a result of overeating, can assure you I cannot contain infinite matter.

If the force of gravity is great enough to contain light (if the body is within its own event horizon), then there is no force that will prevent it from shrinking to a singularity.

Assume that there was a first 'true' human, the first one with the brain structures necessary to deal with abstractions like math. Say that this first 'true' human figured out that 1 + 1 = 2. Does this mean that, because of the obvious truth of that equation, we must accept all this cave-man's ideas about mathematics?

You could just as easily make the same claim about (for instance) how stars work. The Sun, after all, could just as easily be a huge light-bulb that a) rotates in time with the Earth, to avoid us seeing the screw part ( ) and b) perfectly simulates a big ball of fusing gas.

But the thing is, it can't violate causality, because of the event horizon.

Huh?

Confucius says: "If you run faster than light, you might blackout."

Yeah. I also hate WIMPs.

Indeed, but I was talking about the fact that the math allows it.

Some of the other 3 interaction perhaps? weak or strong nuclear force or electromagnetism that does not allow matter to be unified in an infinity.

No, but we must consult his wisdom.

We have already sent spacecraft behind the Sun.

Ok, I never said it does, and it seems kind of irrelevant to this discussion.

There is a recent theory that quantum information may escape a black hole.

Thinking about the Minkowski diagram that shows superluminal messaging to violate causality, I discovered its error: it shows one observer being in the future lightcone of another observer. This does not happen in reality: two remote observers are always in each other's past light cone, and therefore superluminal messaging does not violate causality.

EDIT:

Some people in this blog have reached the same conclusion as me, i.e. that no causality violation can take place with FTL travel.

The blog itself disagrees with you. I'm looking over the comments now, and the people who disagree with him don't seem to know what they're talking about.

O is B's future.

That's line OAB in the diagram you linked to. Yes you can.

Messages coming from O are coming from B's future.

You don't seem to actually understand what that diagram is showing.

That's not quite how it works. Measurement of orbits gives you the gravitational mass, measurement of light gives you the luminous mass (ie, stars). These two numbers disagree, indicating that there is a substantial amount of "dark matter" contributing to the gravitational mass of galaxies. That's not the same as "observed gravity not fitting the mathematics".

On the other hand, it's exactly the same as other astronomical phenomena.

That still doesn't make Einstein the ultimate authority on everything. Not even everything relating to general relativity, which has been developed a lot since Einstein's original work.

Hey, you're the one who said differently in the beginning.

Semantics, in part, but it pays to be precise.

They're not interchangeable, they're the same thing (mass is a form of energy). Which is what I said.

Err... no. Go pick up a physics text book and look up the different forms of energy and why it's important to make a distinction.

You don't know that. Considering the conditions inside the black hole are unknown and considering we don't understand how matter responds in an environment of very high density (quark-gluon plasma?), we can't say a thing about how matter would behave inside a black hole.

You don't know that. See above comment.

Wrong. Hawking radiation doesn't contain information from the inside of the black hole.
There are no world lines going from the inside of the black hole to the outside universe. There is no way to transmit information across the event horizon.

The weak and strong forces are only strong at small distances. Electromagnetism is only strong if there is no charge neutrality.
Gravity is the weakest force, but there is a reason that it is the most dominant force in the universe: it cannot be shielded and it has a very long (infinite) reach.

Oh great, you've found some other random people on the internet who think they know what they're talking about. Ok then, find me a peer reviewed paper in a proper scientific journal (physical review, say) that agrees with you.

I'd like to point out, for those who didn't read the previous posts thoroughly, that I am not the one who made the comment this is responding to, A.cc just decided to attribute it to me for some reason.

Matthew's script to automatically attribute quotes to people doesn't seem to be 100% reliable...

He said from the beginning that it wasn't...

I never said he ever claimed otherwise. No need to roll your eyes at that.

I never said you did.

Well, my purpose in pointing it out was to avoid a confusion as to my stance in the argument that could have taken several posts to clear up. But I think you guys took just as long to argue over whether or not the script was perfect and whether or not anyone ever implied that it was, so I might as well have just kept my mouth shut.

I now take the opportunity to make the first post in about four that doesn't include a smiley rolling its eyes. Note that I never said anything about sticking out its tongue.

Evert, was my WIMP's comment that lame?

Not really, just nothing I felt I had anything to add to.
Ok, it was a bit cheesy.

My work here is done!

Weakly Interacting Mommas Pansy

That's what SHE said!

What's outside a donut? Solar cell ingredients!

http://www.youtube.com/watch?v=bVwzJEhMmD8&eurl=http%3A%2F%2Fwww.wired.com%2Fwiredscience%2F2009%2F03%2Fdonutsolar%2F&feature=player_embedded

God.

There, I said it.

Damn...I missed out on the whole eye roll thing?!
Well...

What does a population of gerbils expand into? You could argue it's bio-mass. But only because you know what the critters are made of.
So analogously, you could say outside the universe is an 0 gravity, 0 electro-magnetism, 0 nuclear force infinite field. (In as much dimensions as you like, starting from 4.) I think... But I also think this is a mathematical and reasoned way of thinking, not encompassing the wondrous nature of all existence, man.

I love threads like this

So, outside a black hole's event horizon, you have freedom to move around in space, but have no choice but to move forwards in time. If you somehow find yourself inside a black hole's event horizon, you have no choice but to travel towards the centre. Do you find yourself free to move back in time?

If you watch something fall into a black hole, it never actually appears to cross the event horizon. As it approaches the event horizon, light takes longer and longer to escape the gravitational pull and reach us. There will never be a time when there isn't still some light on its way from it to you (notwithstanding light coming in quanta etc. etc.). Does this mean it never actually entered the black hole?

Do people walk through walls inside black holes?

Do you mean to say dark matter has the distinction that its gravitational field attracts matter (e.g. planets) but doesn't attract photons?

Is it possible you're thinking of B and O as two separate observers? I think they're actually supposed to be two instants in time for the same observer - so there is ONE observer who was at B (and received the message) and then later was at O (and sent the message). The difficulty is that this observer can then receive the message and deliberately choose not to send it - you get the standard paradox.

(Am I right in thinking the diagram is missing the x=±y lines that represent light speed?)

They used gravitational lensing to try and find what might be dark matter. So far it has popped up some possibilities. So darkmater's gravity effects photons and other matter (well more like it effects space), but the dark matter itself doesn't directly effect anything.

Or thats how I saw it..

I think what he means is that if you take a rough light-emitted-per-mass quotient of a star, then do the same for the galaxy, you get very different numbers, implying that much of the mass in the galaxy is not emitting light.

IIRC, the theory of relativity says that mass warps space, so any gravitational field that attracts matter should also affect photons. The extra mass could be explained by bodies of matter too small to initiate nuclear fusion (self-illuminating stars), whether they're microscopic motes of dust or brown dwarfs.

That was my understanding too. Evert's phrasing made me question it - hence the question.

Earlier he said dark matter was an intrinsic curvature of space-time, not actual matter as we know it.

Error in thread Whats-outside-a-donut OriginalExplanationInsufficientForValidationException

Another thought - wouldn't an intrinsic curvature of space-time be evenly distributed and not cause any concentration in any specific location? How, then, can it explain galaxies staying in one piece?

I think thats the explanation he prefers Noone quite knows what it is, and one of the possibilities is some form of normal or strange matter.

Wouldn't that imply the "energy" of the curvature (in the sense of mass and energy being equivalent) then is more mass? Definition of Recursion: See Recursion

[EDIT]
I suppose it could be a self limiting process, like continuously compounded intrest, which is contradictory on the face of it.

That depends on your frame of reference.

No - because that's not how gravity works. Photons as well as matter follow the curvature of space time. You can't attract one or the other, it's always both.

Yes.

That's right.

Yeah, ok, sorry. Confusing, I know.
The phrase "dark matter" can actually mean two different things. It can mean normal baryonic matter that is not emitting light, and it can refer to an exotic type of matter that doesn't interact with anything except through gravity. To make the distinction, the former is usually called "baryonic dark matter" while the latter is just called "dark matter." This dark matter then enters as a source term for the gravitational field and is in that sense similar to an intrinsic curvature of space-time.
That's what dark matter does: it curves space-time. Other than that... we don't really have a clue.

The problem is that the best estimate of the non-luminous baryonic matter content of the galaxy (or the universe) doesn't give you enough to explain galactic rotation curves.
So yes, there is definitely baryonic stuff out there we don't see, but it seems to not be enough to account for the observed gravitational mass.

Lots of black holes? Of course, then you wouldn't be able to see things behind them...

Inside a black hole Allegro 5 is released.