163 replies to this topic

[bgwowk]

Diameter scales linearly with mass...

Indeed. The formula for the Schwarzschild radius of a black hole is r = mG/c²
I'm impressed that you knew that proportionality off the top of your head, Jay.

Edited by bgwowk, 12 November 2006 - 06:58 AM.

[doug123]

Can you guys do this thread in laymans terms? Perhaps a "just for kids" version for dimwits like me?

[jaydfox]

You assume a BH could pass through the earth with little to no resistance and that is patently false.

Patently false? How so? Did you prove it? Or did you just make another uneducated guess."

Gravitational interaction with surrounding matter, for one thing. Slowing of momentum as it absorbs matter for another. Possible interactions by means of electrical charge or other forces. All of this was already discussed, did you miss it?

1. Gravitational interaction
As a black hole starts plunging through the earth, gravitational interactions won't apply a frictive force. Think of the black hole's path through the earth as if you were dropping a ball down a long tunnel that went all the way through the earth and out the other side. If you dropped a ball down such a tunnel, and if that tunnel contained a vacuum (aside from the ball), then would gravity slow the ball down? Neglecting the earth's rotation (which would create a "coriolis" force that pushed the ball into the edge of the tunnel), the ball would fall right through the center of the earth, then decelerate right up to the surface on the other side. It would oscillate back and forth, virtually forever.

2. Possible interactions by means of electrical charge or other forces.
Possible, but negligible. A black hole could not long contain a net charge, because if it did, it would polarize mass around it, stripping electrons and absorbing a slightly higher amount of either electrons/negative ions or positive ions as necessary to get back to neutral. A decent electric charge, dropping through the earth's metal core, could conceivably create a very small EMF that served to slow the BH slightly, but the effect would be rather small compared to the huge mass of the BH, primarily because the BH couldn't collect much charge.

3. Slowing of momentum as it absorbs matter for another.
Actually, I covered that one pretty well, I thought. Saying the momentum "slows" is potentially misleading. The magnitude of the 3-D momentum would stay the same. But the same momentum on a heavier object translates to a reduced speed. Reduced exactly by the ratio of mass absorbed on the way through, to the mass of the BH. Which would be a tiny fraction.

You assumed a lab created BH would have escape velocity when created and not interact with normal matter. And you base that on what exactly? <-- do try to answer that one.

Excellent question. How would we create an artificial black hole in a lab? The only methods I've read about involve smashing particles (typically atomic nuclei) into other particles, at extremely high relativistic speeds.

Well, there are two typical methods. One, smashing a high-speed particle into a stationary target. This is the trivial case. The center of momentum of the decay products of the collision will be moving at a very large fraction of the speed of light (like, >90% of the speed of light). For a stationary black hole to be created, it would have to be "kicked" backwards from the collision site at exactly that fraction of the speed of light, relative to the frame of the center of momentum.

For example, a gold ion travelling at 99.995% of the speed of light smashes into a stationary gold ion. The center of momentum will be moving at about 99% of the speed of light. (In a reference frame moving at 99% of the speed of light, the moving gold ion and the "stationary" target ion would both be moving at about 99% of the speed of light, in opposite directions.) So for a black hole to emerge, stationary, from this collision, it would have to be kicked straight backwards at nearly exactly 99% of the speed of light. Not 99.001%, not 98.999%. Not 99% but at an angle of 0.01 degrees misaligned with the direction of the moving gold ion. The odds of that happening are too low to worry about.

Okay, the trivial case is out of the way. Now for the harder case. Two ions accelerated in opposite directions and smashed into each other. Presumably, the center of momentum would be roughly stationary, and if the black hole was not kicked away from the collision site, then it too would be stationary. This isn't really feasible with large nuclei, since we'd need anti-particle pairs, and anti-gold is hard to come by. So we'll assume protons and antiprotons. I haven't read the latest specs on particle colliders, so maybe they're savvy enough to use anti-gold or anti-lead or something like that. Or maybe the new colliders will use two circular or linear "tracks" to accelerate like-charge particles in opposite directions...

Anyway, using protons and antiprotons, we'll smash them into each other, head on, at 99.99995% of the speed of light. Those would be about 1 TeV. I don't know how big proton-antiproton accelerators are these days; maybe they're more than 1 TeV per particle.

But keeping the math simple, if the proton had 1.0000 TeV of energy, and the antiproton had 0.9999 TeV of energy, then the center of momentum would actually be moving at about 30 km/sec in the direction of the proton. So even a small inaccuracy in the particle energies could result in a huge discrepancy in the collision speed (note that 30 km/sec is almost three times escape velocity).

And even assuming the collisions occasionaly happened in a stationary reference frame (they do enough collisions that it would eventually happen), most particles created by these collisions are expelled at relativistic velocities, so the assumption that the black hole would be stationary is very weak indeed. That's probably the only risk that's numerically high enough to worry about: that the black hole would be stationary relative to the center of momentum. It's a small risk, but one that I can't quantify. Qualitatively, I'd say it's less than 1 in a million, but I'd have to admit I'd be guessing.

[jaydfox]

Can you guys do this thread in laymans terms? Perhaps a "just for kids" version for dimwits like me?

I'm not sure how far off-topic this thread has wandered. It might be better to start with a new thread specifically covering black holes. I'd have to look back to see why we even got on the subject.

Oh yeah, I see now... Xanadu was pontificating about lab-created black holes, and suggested that if hawking radiation didn't occur, then such small black holes (artificial or not) could slowly gobble up the earth, and we'd be doomed. I pointed out that such small black holes would take a very long time (on the order of billions of years, give or take a few orders of magnitude) to do any sizeable damage. Xanadu disagreed. A pissing match ensued, because xanadu thinks he knows a lot about physics, presumably because he's read a lot of pop-sci material about black holes and the related physics, which qualifies him to make authoritative statements about how black holes work.

But anyway, we could try something in another thread. I've been studying SR and GR a lot in my spare time lately, and I myself have several questions I could use help on (from Brian Wowk and others who have a better grasp on the math and the concepts than I presently do).

[jaydfox]

But keeping the math simple, if the proton had 1.0000 TeV of energy, and the antiproton had 0.9999 TeV of energy, then the center of momentum would actually be moving at about 30 km/sec in the direction of the proton. So even a small inaccuracy in the particle energies could result in a huge discrepancy in the collision speed (note that 30 km/sec is almost three times escape velocity).

Damn, forgot to divide by 2. When you take the average of two speeds, you add the speeds and divide by 2. My bad.

The discrepancy in speed would be 15 km/s, not 30 km/s. Still, that's more than escape velocity, from an initial inaccuracy of 1 part in 10,000.

[doug123]

...once it gets all technical and I need to pull out a calculator and textbooks...

I guess with really long threads about theoretical abstractions like black holes, speed of light, etc. it's probably best to get in on the topic when its in its first few pages. I even checked if there were any random lyrics I could throw in there and all I came up with is "add without subtraction."

[caston]

At first I thought Jay was arguing in favor of blackhole experiments because he thought that could help us achieve reverse time dilation but then I realised that wasn't the case at a later post of his.

So why would we actually want to play around with blackholes then?

Anyway I think blackholes are bloody risky and that's why I asked "anyone know how we could do it without the pesky blackhole?"

I started a new thread on the physics forums about reverse time dilation:

http://www.physicsfo...ad.php?t=143200

[jaydfox]

So why would we actually want to play around with blackholes then?

Anyway I think blackholes are bloody risky

We'd want to play around with them to learn more about how physics really works. As for risks, higher energy particle collisions happen all the time in the upper atmosphere, due to cosmic rays, and the earth's still here, so until we can generate collisions more powerful than anything seen naturally, there's nothing to really worry about. I don't recall the exact energies, but I'm pretty sure we're not even close yet.

[caston]

Are you talking about the magnetosphere?

I've seen a few unbacked up claims of "teeny tiny blackholes" forming in our atmosphere. What exactly are we talking about here?

[jaydfox]

I'm talking about particles coming at us from outside the solar system:
http://en.wikipedia....wiki/Cosmic_ray

From the article, I see mention of energies up to 10^20 eV, which is about 10^8 TeV. I'm pretty sure that's at least 5 orders of magnitude above anything we can do in current particle accelerators, maybe even 6-7 orders.

If particles of such energy are constantly bombarding the earth, then anything we could hope to create in a lab is created on a regular basis in nature. If people are worried that we might create something in the lab that will destroy the earth or whatever, we need only observe the fact that we're still here, so the odds of anything in the lab being so dangerous are essentially nil. Not exactly zero, but close enough that there isn't a need to proceed with extreme caution.

[xanadu]

bgwowk wrote:

"You have as much to learn about human relations as you do about physics."

No doubt I have much to learn about many things same as you do. You imply you have a vast amount of knowledge in many fields which gives you the right to put down those who question you.

"Credentials are immaterial since you show no respect for them, as evidenced by your general contempt of any physics that doesn't suit your preconceptions."

Credentials are immaterial? Contempt because I make tough questions which you run from? You have done nothing but shoot zingers my way while showing arrogance more fitting someone recognised as the top expert in the field which you are not. True experts tend to be humble. Einstien was not arrogant but more of a humble person. You will jump in with an answer when you think you know it so your silence on all the tough questions indicates something.

I'm not going to get into a pissing match with you because you are not worth it.

Jay, your reply is full of suppositions and false analogies. Where are your calculations that you used to come up with the diameter of the black holes you spoke of?

[DukeNukem]

Diameter scales linearly with mass...

Indeed. The formula for the Swartzchild radius of a black hole is r = mG/c²
I'm impressed that you knew that proportionality off the top of your head, Jay.

No kidding -- that seems very counter-intuitive.

[bgwowk]

No kidding -- that seems very counter-intuitive.

The radius of a black hole event horizon can be calculated classically (within a factor of 2) from Newtonian gravity. Potential energy of an object of mass m in a gravitational field produced by mass M is given by GMm/r where r is the distance from the center of mass M. Therefore escape velocity v is given by 1/2 mv**2 = GMm/r. Solving for the distance r at which the escape velocity is equal to the speed of light gives

1/2*mc**2 = GMm/r

c**2 = 2GM/r

r = 2GM/c**2

The factor of two disagreement with the actual Schwarzschild radius is due to General Relativity.

So even classically the predicted "density" of a black hole (mass per volume inside event horizon) depends on the mass, which is why the intuitive expectation of mass varying with the cube of radius doesn't hold.

Edited by bgwowk, 12 November 2006 - 07:00 AM.

[eternaltraveler]

Credentials are immaterial? Contempt because I make tough questions which you run from? You have done nothing but shoot zingers my way while showing arrogance more fitting someone recognised as the top expert in the field which you are not. True experts tend to be humble. Einstien was not arrogant but more of a humble person. You will jump in with an answer when you think you know it so your silence on all the tough questions indicates something.

nothing you've asked qualifies as a tough question. You just seem incapable of accepting simple answers, just as you've demonstrated about yourself on many other occasions in many other subjects.

[xanadu]

elrond wrote:

"nothing you've asked qualifies as a tough question"

If they are so easy, then why are there no answers? I have noticed a pronounced tendency on this site to resort to personal attacks as a first line of defence when confronted by anything. That and the urge to circle the wagons when an oldtimer is opposed by an upstart. Jay does both those things incessantly as do many others. No tough questions? Well then let me rephrase just one of them and you can give it a go. Or whoever wants to.

The unverse in it's early formative stage is believed to have been very small yet it contained all the matter/energy we see today. Was the universe at that time a black hole or closed region of space time? I believe it was due to the extreme density and huge mass. When then did it stop becoming a BH or did it ever?

There were many others but that will do for starters.

If it's true that the density of a black hole varies along with it's total mass with large masses being less dense, that is very interesting and I did learn something. It goes to show this thread has some uses. Although, you could say it's not really the density that varies, just the size of the event horizon in comparison to the mass. The BH itself is likely to be a point.

[jaydfox]

Jay, your reply is full of suppositions and false analogies.

Enumerate, please.

Where are your calculations that you used to come up with the diameter of the black holes you spoke of?

The 2 cm diameter of an earth-massed black hole is a well-known factoid for people who study physics as anything more than a passing hobby. The linear scaling of black hole radius with mass is also a well-known factoid. The fact that you knew neither is indicative of how qualified you are to be telling Brian Work that he's making false assumptions.

I'll admit I didn't go into all the mathematical details of the particle collisions I described. For one, you didn't seem to care when I had done the math previously. For those who care (i.e., not for you, but for the benefit of others), here they are:

For example, a gold ion travelling at 99.995% of the speed of light smashes into a stationary gold ion. The center of momentum will be moving at about 99% of the speed of light. (In a reference frame moving at 99% of the speed of light, the moving gold ion and the "stationary" target ion would both be moving at about 99% of the speed of light, in opposite directions.) So for a black hole to emerge, stationary, from this collision, it would have to be kicked straight backwards at nearly exactly 99% of the speed of light. Not 99.001%, not 98.999%. Not 99% but at an angle of 0.01 degrees misaligned with the direction of the moving gold ion. The odds of that happening are too low to worry about.

I started with the precondition that, in the frame of reference of the center of momentum, the gold ions were approaching each other at 99% of the speed of light. From the stationary reference frame (relative to the lab), the moving gold ion would have "twice" that speed. Using the well-known rule for adding velocities in relativistic terms, we have:
v3 = (v1+v2)/(1+v1*v2)
=(0.99+0.99)/(1+0.99*0.99)
=(1.98)/(1.9801)
=0.9999494975...
~=0.99995, or 99.995% of the speed of light.

Now, working backwards, you can get the first set of numbers from there. Start with a gold ion going 99.995% of the speed of light, and another stationary, and in the frame of reference of the center of momentum, each is approaching the collision site at 99% of c. The rest of the argument followed from simple logic and math. For example, 0.99001c and 0.99000x differ by 0.00001c, or 30 km/s, using naive addition, and by:
(0.99001-0.99000)/(1-0.99001*0.99000) ~= 0.000502763c, or about 151 km/s, using relativistic addition. Either way, 30 km/s or 151 km/s, that's more than escape velocity. In the case of a particle off course by 0.01 degrees, this requires the vector version of the velocity addition formula: v3 = (v1+v2)/(1+v1.v2), where "." is the inner product, dot product, or whatever you like to call it. Note that this formula uses the 3-D velocity vector, not the four-velocity.

Okay, so first we'll take a vector at 99% of the speed of light, and rotate it 0.01 degrees. It doesn't matter which axis, as long as its perpendicular to the direction. So assume the first vector is (-0.99, 0, 0), and rotate around the z axis, to get:
(-0.99*cos(0.01*pi/180), -0.99*sin(0.01*pi/180), 0)
(-0.9899999849, -0.0001727876, 0)

As you can see, the velocity vector has a vertical component of 0.00017c, or about 52 km/s. But who knows, maybe it'll go away, right?
Okay, now for the nitty-gritty stuff. We're subtracting, so just reverse the signs on the second vector and add:
v3 = (v1+v2)/(1+v1.v2)
= (-0.99+0.9899999849, 0.0001727876, 0)/(1+(-0.99*0.9899999849 + 0*0.0001727876 + 0*0)
= (-0.0000000151, 0.0001727876)/(0.019900015)
= (-0.0000007577, 0.008682787)

Wait a minute, that 0.00017c got bigger? Well, I guess I could have tossed an even smaller angle out there...

Anyway, using protons and antiprotons, we'll smash them into each other, head on, at 99.99995% of the speed of light. Those would be about 1 TeV. I don't know how big proton-antiproton accelerators are these days; maybe they're more than 1 TeV per particle.

But keeping the math simple, if the proton had 1.0000 TeV of energy, and the antiproton had 0.9999 TeV of energy, then the center of momentum would actually be moving at about 30 km/sec in the direction of the proton. So even a small inaccuracy in the particle energies could result in a huge discrepancy in the collision speed (note that 30 km/sec is almost three times escape velocity).

This one's a little more complicated, as it uses less well-known rules (well known to those who do physics as a job, but probably something a hobbyist such as myself would have to look up).

The energy of a particle is given by the following expression:
E = m0/sqrt(1-(v/c)^2)
The kinetic energy would then just be equal to the total energy minus the energy equivalence of the rest mass (m0).

By the way, another couple factoids that I find extremely useful: the rest mass energy of an electron is about 0.5 MeV (~511 keV), while the rest mass energy of a proton is nearly a GeV (~938 MeV).

Okay, to get velocity from kinetic energy, we actually need to rearrange the formula above.
1. E = m0/sqrt(1-(v/c)^2)
2. sqrt(1-(v/c)^2) = m0/E
3. 1-(v/c)^2 = (m0/E)^2
4. (v/c)^2 = 1-(m0/E)^2
5. v/c = sqrt(1-(m0/E)^2)

Okay, so starting with a total energy of 1 TeV, and a rest mass of 938 MeV, we get a velocity of:
v/c = sqrt(1-(9.38e8/1e12)^2)
v/c = sqrt(1-(9.38e-4)^2)
= sqrt(1-8.79844e-7)
= sqrt(0.999999120156...)
= 0.9999995600779... *
~= 99.999956% of the speed of light.

A similar calculation for 0.9999 TeV:
v/c = sqrt(1-(9.38e8/1e12)^2)
v/c = sqrt(1-(9.380938093809e-4)^2)
= sqrt(1-8.8001999519884e-7)
= sqrt(0.99999911998...)
= 0.99999955998991... *
~= 99.999956% of the speed of light.

(* = this is actually slightly off, since 9.38 MeV is only an approximation)

Note that the speeds look very close. However, they are in opposite directions, so we can subtract one from the other to get the difference in speed, using the speed addition formula from above:
difference = (0.9999995600779-0.99999955998991)/(1-0.9999995600779*0.99999955998991)
= (8.799760919942e-11)/(8.79931997e-7)
=0.000100005
0.01% of the speed of light is about 30 km/s. This is where I came up with the 30 km/s. However, the center of momentum would be moving at the average speed of the two particles, which is 15 km/s.

Interestingly, the difference in energies, 0.0001 TeV, or 100 MeV, would be equivalent to much, much more than 30 km/s, for a proton anyway. At lower speeds, the absolute precision (in MeV) is much more important. At high speeds, the absolute precision is not as important. However, the relative precision (as a percentage of the total kinetic energy) is very important. The same is true in Newtonian physics too, of course. Kinetic energy scales as the square of velocity, so at 10 times the velocity, the energy is 100 times higher, meaning you can get away with a 10 times larger absolute inaccuracy to get the same difference in speed (to a first approximation).

[halcyondays]

Isn't the expansion of the Universe kind of like space vs matter? The Volume of the Universe expands faster than the speed of light, but the matter inside the Volume of Space expands at the speed of light? That's always been my understanding of it.

[jaydfox]

Well, locally, expansions of space are somewhat ignorant of velocity, since space expands a certain fraction of its own size, per unit of time. For example, perhaps it doubles in size in a billion years, or alternatively, expands at 1% per ten million years, or one part in a thousand in a million years.

So there's no concept of "speed" for space to violate, locally. Globally, two points can move away from each other at greater than the speed of light, but you can always find a series of midpoints, each of which is moving away from its nearest neighbors at less than lightspeed. So from GR's perspective, no rate of expansion can violate the speed of light.

Quantum mechanically, maybe it's possible, depending on your definitions. The only way I can think of, off the top of my head, to really violate a "speed", when it comes to space expansion, is if two points, a plank distance apart, are suddenly more than two plank distance units apart, in less than one plank unit of time. Since you can't subdivide any finer than the plank scale (in time or distance), then the argument about using midpoints fails.

[bgwowk]

The unverse in it's early formative stage is believed to have been very small yet it contained all the matter/energy we see today. Was the universe at that time a black hole or closed region of space time? I believe it was due to the extreme density and huge mass. When then did it stop becoming a BH or did it ever?

That is actually a good and non-trivial question. I'll attempt to answer it as best as I can (given that I am a physicist, but not a General Relativity or cosmology expert).

The page http://www.mathpages...me/kmath339.htm discusses this issue in depth. Defining black holes on a cosmological scale is a tricky question. But if we define black hole as a region of spacetime that cannot casually affect spacetime outside it, then the universe is composed of not just one back hole, but trillions of different regions of spacetime separated from each other by event horizons ever since the end of inflation. In other words, pick any point in the exanding universe, try to travel elsewhere in the universe at as close to the speed of light as you want, and there will be a limit to how much of the universe you can reach. Every point in the universe is at the center of its own black hole of approximate radius c/H (where H is Hubble's constant), which is just a few billion light years. Note that mass is not scrunched up into point-like singularities at the center of these black holes, but they are still black holes by one of the common definitions.

Addressing your original question more directly-- why wasn't the early universe with large amounts of mass in small spaces obviously a single black hole-- the answer is that conventional (stellar) black holes are formed when critical amounts of mass fall within a critical radius in a larger asymptotically flat spacetime. But the universe is not a blob of mass in a larger empty spacetime, the universe is all of spacetime with mass spattered all through it. Even classically you cannot get a black hole when a high density of matter is inside its Schwarzschild radius if that same high density exists in every direction inside and outside the radius. "Black holes" at cosmological scales are different animals than tiny stellar or galatic mass blackholes.

Still, there are still formulas from General Relativity for calculating whether a universe is an open (infinite) or closed (finite yet unbounded) spacetime based on mass density. A closed spacetime has been compared to the universe being a black hole unto itself. Given that such formulas exist, why wasn't the universe necessarily closed during its early high density moments? In my understanding the answer is that the critical density depends on the expansion rate. As you go back in time, the universe becomes more dense, but the expansion rate was also faster, requiring more density to close the universe, so it is not a priori obvious that there was ever a time when the universe was closed.

Edited by bgwowk, 12 November 2006 - 07:07 PM.

[xanadu]

bgwowk wrote:

"the answer is that the critical density depends on the expansion rate."

Isn't that just a theory? That seems to be a way of saying you don't believe the universe was a black hole so you turn away from other definitions or conditions that lead to BH's and claim the expansion gives it an exception to the rule.

"As you go back in time, the universe becomes more dense, but the expansion rate was also faster, requiring more density to close the universe"

This is just an extention of your premise that expansion neutralises or prevents the BH from existing. It rests totally on the validity of your assumption. The true answer is that we don't know for sure but we do know that these conditions in smaller regions of space do lead to BH's. We can assume that expansion will give an exception to what is the general rule, but the theory that it gives no such exemption seems to be equally valid.

"But if we define black hole as a region of spacetime that cannot casually affect spacetime outside it, then the universe is composed of not just one back hole, but trillions of different regions of spacetime separated from each other by event horizons ever since the end of inflation."

Here you seem to veer off into strange musings. Why can't a BH affect spacetime outside itself? It's gravity does seem to do just that. Observationally, we don't seem to see different regions separated from each other by event horizons except for the BH's we've seen. Where is your data to support that? And last but not least, how do you say that inflation has ended? Continued or accelerated inflation is supposed to be the basis for the belief in dark energy.

That was not a bad stab at answering the question. You did have to assume something totally unproven in order to stick with your belief that the universe is open. That too seems to be a human characteristic. We do not give up easily or casually our long held beliefs. I will admit that I can't prove the universe is closed although I do have the facts on my side that the extreme density of the early universe is a condition that always seems to lead to BH's. I do not need to assume anything unseen, unknown or totally speculative to reach that conclusion. That does not prove me right and we will leave it at that for the moment.

We talk about expansion of spacetime and expansion of the universe as though we know what we are talking about. Objects seem to become farther and farther apart and we assume that the universe is getting larger. Since we can't be outside the universe to measure it, this is merely an assumption. There could be other explanations. We do know that space itself is relative and seems to curve around massive objects. How do we know that the inside of a BH is as large as or smaller than the size of the event horizon? The EH as calculated from outside, defines in our universe the outward boundaries of the BH. How would an observer inside the BH see the boundaries of his universe? He would not see the boundaries at all anymore than we see the actual EH from the outside. Since we know space and time are altered in the presense of high density gravitational fields, it's a sure thing that the apparent size inside the BH is a great deal different than what we calculate from the outside.

If we assume the early universe was a BH, and by extention the later universe, we would be the ones experiencing the warping or alteration of space and time going on inside a closed system or BH if you prefer. Our meaurements and calculations of distance are based on many assumptions. If we are inside a BH like system then our perceptions of distance, expansion and acceleration are all colored by this warping or alteration. It would therefore be impossible to prove or disprove that we are inside such a system by observing things inside it. It would also be impossible to be sure of any apparent expansion in our universe.

[bgwowk]

"the answer is that the critical density depends on the expansion rate."

Isn't that just a theory?

It depends on the universe expansion rate and size, I should have said. Think about it. Suppose you have a universe that is just above the critical density for closure. It continues expanding for eons before it begins collapsing again, and during that whole time the *density keeps decreasing*. Yet even as the density nears zero just before reversal, the density always exceeds the critical density for closure. So obviously the critical density for closure depends on the stage of the universe's expansion. The critical density is higher at earlier times, and lower at later times.

More later.

[xanadu]

bgwowk wrote:

"Suppose you have a universe that is just above the critical density for closure. It continues expanding for eons before it begins collapsing again, and during that whole time the *density keeps decreasing*."

If it's above the critical density for closure then it should close. That does not preclude the possibility that it continues to expand or seem to expand. Are you suggesting a universe or system could close and then open itself again because of apparent expansion?

A black hole may have matter inside it compressed into a point. If so, then density would be infinite which seems to be a problem. Could it be that just before it gets to the size of a point, the near infinite density causes all the matter to turn into energy and explode? It would not affect it's closed status and an observer on the outside would see nothing unusual. Inside, we may have something akin to the big bang.

[bgwowk]

bgwowk wrote:

"Suppose you have a universe that is just above the critical density for closure. It continues expanding for eons before it begins collapsing again, and during that whole time the *density keeps decreasing*."

If it's above the critical density for closure then it should close. That does not preclude the possibility that it continues to expand or seem to expand. Are you suggesting a universe or system could close and then open itself again because of apparent expansion?

No. I'm saying that the density of the universe decreases as you look forward in time, and increases as you look back in time. Both these facts are true for open or closed universes. Therefore the fact that the density diverges to infinity as t approaches 0 at the time of the Big Bang says nothing about whether the universe is open or closed.

bgwowk wrote:
A black hole may have matter inside it compressed into a point. If so, then density would be infinite which seems to be a problem. Could it be that just before it gets to the size of a point, the near infinite density causes all the matter to turn into energy and explode? It would not affect it's closed status and an observer on the outside would see nothing unusual. Inside, we may have something akin to the big bang.

That's Lee Smolin's theory for the origin of universes, although technically the expansion occurs in other spatial dimensions that are compactified in our universe. In any case, that's a completely separate issue from what we have been talking about.

"But if we define black hole as a region of spacetime that cannot casually affect spacetime outside it, then the universe is composed of not just one back hole, but trillions of different regions of spacetime separated from each other by event horizons ever since the end of inflation."

Here you seem to veer off into strange musings. Why can't a BH affect spacetime outside itself? It's gravity does seem to do just that.

I was attempting to dumb down the following definition of black hole from the reference I gave

http://www.mathpages...me/kmath339.htm

An asymptotically flat [and strongly asymptotically
predictable] spacetime M is said to contain a black
hole if not every point of M is contained in the causal
past of future null infinity.

The black hole region, B, of such a spacetime is
defined to be the points of M not contained in the
causal past of future null infinity.  The boundary
of B in M is called the event horizon.

Apparently my simplification was not understood. Let me try again: A black hole may be defined as a region of spacetime from inside which you cannot have any effect on the future of spacetime outside. In other words, a black hole is region of spacetime from inside which nothing can escape, not even light.

Observationally, we don't seem to see different regions separated from each other by event horizons except for the BH's we've seen. Where is your data to support that?

A beam of light launched from Earth can never reach any point of spacetime that is now farther than the Hubble distance (about 15 billion light years). NEVER! Yet the oldest farthest glaxies we can see are now more than 40 billion light years from Earth (they were closer when they emitted the light we see today). So not only does theory predict that the universe is much larger than we could ever reach, but we can even observe the early history of galaxies that are now beyond our cosmic event event horizon, and therefore unreachable. Cosmic event horizons are real, and they do conform to one of the definitions of black hole.

And last but not least, how do you say that inflation has ended? Continued or accelerated inflation is supposed to be the basis for the belief in dark energy.

I meant the period of rapid inflation that moved the whole universe out of causal connection with itself into trillions upon trillions of overlapping regions separated by cosmic event horizons.

There is a very good article on the topic of universal expansion, event horizons, and superluminal recession speeds at

http://www.sciam.com...umber=1&catID=2

Edited by bgwowk, 12 November 2006 - 11:39 PM.

[xanadu]

Mathmaticians speak a different language than normal people. You wrote:

"A black hole may be defined as a region of spacetime from inside which you cannot have any effect on the future of spacetime outside."

We have definitions and we now have translations of the definitions. What is the proof that any of these definitions of a BH and the implications thereof are correct? If you are saying that nothing inside a BH nor the BH itself can have any effect on spacetime outside the EH, then what about the effects of gravity from the BH affecting regions of space and time outside it? You can dodge and say it isn't really gravity leaving the BH it's the curvature of spacetime but that is just redefining gravity. Obviously BH's can have a profound effect in our universe far beyond the EH.

"A beam of light launched from Earth can never reach any point of spacetime that is now farther than the Hubble distance (about 15 billion light years)."

Any why is that? You have brought up many theories but theories are cheap. Where is the proof that light can't travel any farther than that? Curvature of space? Or are you using the assumed expansion of the universe? Most likely the latter.

"That's Lee Smolin's theory for the origin of universes"

Very likely everything we have discussed or will discuss has been thought of already.

"In any case, that's a completely separate issue from what we have been talking about."

It relates to my theory that our universe is closed and provides a mechanism for it as well as showing how black holes may function.

"So not only does theory predict that the universe is much larger than we could ever reach, but we can even observe the early history of galaxies that are now beyond our cosmic event event horizon, and therefore unreachable. Cosmic event horizons are real, and they do conform to one of the definitions of black hole."

Again theory. Saying theory predicts so and so is fine but it proves nothing. Relativity is a theory but has been proven many times in practice. Even if it turned out to be true that light could not reach a point that is now beyond the hubble distance does not mean we are in an event horizon nor that different regions of space are in black holes. It seems to be you who is going off on tangents.

The assumed rate of expansion of the universe and the supposed acceleration in that expansion rests heavily on many assumptions. Many theories are built on top of other theories which rest on assumptions. This creates an edifice that is fragile and top heavy. Any error in one or more underlying assumptions or measurements could cause a chain reaction destroying many complicated and far reaching theories.

Lets look at one of the underpinings of many theories and observations, namely the red shift. It has been a bulwark of cosmology and is relied upon to determine the distance of far away galaxies and other objects such as quasars. It is believed that red shift is caused by a doppler like effect that depends on relative speed between the observer and the observed. Correct me if I'm wrong. By correlating red shift with nearby objects we believe we know the distance to, the theory came up that the farther away an object is the faster it is moving away from us since the red shift seems to be greater in porportion to distance. We then assume that red shift alone tells us not only the speed but the distance from us. Very nice and neat.

I propose to throw a monkey wrench or two into that theory. No doubt prof so and so thought of it first but for the moment this is my theory or group of theories. We know that mass affects light perhaps indirectly and seems to affect spacetime directly. We know the universe is very large and contains mind boggling amounts of mass. This mass affects matter mostly in it's vecinity and has a lesser effect to infinity or propagated at the speed of light. It seems to fall off as the inverse square of the distance. Coud it be that this is the strong gravitational force and there is a weak gravitational force, just to give it a name? This weak force, call it WGF for short, may act over far greater distances than the strong force and attenuate at a much less steep rate, perhaps only linearly to the distance or not attenuate at all. This WGF may not have a noticeable effect or no effect at all upon gravitational attraction but does effect space in the way it transmits light and other energy in subtle ways. It's effects over short distances may be minimal but over intergalactic distances, it may have a much stronger effect. Light that has traveled 1 light year may have a negligable alteration but light that has traveled many thousands of light years may be affected much more. This could explain much of the red shift we see. Even a tiny difference would have a profound effect on many of our theories and may mean the universe is not only smaller but is flying apart much more slowly than we thought.

Another possible explanation is the fact we may be living inside a black hole. We seem to have drifted off from that subject for the moment. If so, then our universe is inside a singularity which may operate under different laws than an open universe. Just as newtonian physics work quite well and accurately here on earth and einstienian physics is needed to explain things on a larger scale, a cosmos wide theory of physics may show that einstienian theories work well on a smaller scale but turn out to be a special case inside the more general laws of the universe just as newtonian physics are like a special case within general relativity.

[bgwowk]

There are so many misconceptions in your post, it is impossible to even begin to address them. All I will say is what I have said before: You don't know what you don't know. Until you actually study some physics at a deep level, you can have no idea of how solid a foundation much of what we know about the universe rests on. (Did you know that the ability of GPS systems to identify locations to within a few feet "proves" much of what is known about modern cosmology inasmuch as the same mathematical formalism known as General Relativity is used in both cosmology and GPS calculations?) Much of what you call "theory" and "assumption" is in fact well-establish reality that you have yet to learn.

You can't see the mountain range, and what may lie beyond, until you have the discipline to climb the mountain. You have far too little respect for those that have done so. Even I am still only in the foothills.

[jaydfox]

What is the proof that any of these definitions of a BH and the implications thereof are correct? If you are saying that nothing inside a BH nor the BH itself can have any effect on spacetime outside the EH, then what about the effects of gravity from the BH affecting regions of space and time outside it? You can dodge and say it isn't really gravity leaving the BH it's the curvature of spacetime but that is just redefining gravity. Obviously BH's can have a profound effect in our universe far beyond the EH.

Let's keep it very simple: light cannot escape a black hole. If we can't agree on that, then you're not discussing the same objects as the rest of the world when we talk about "black holes", so the discussion is over.

If light cannot escape a black hole, and if the effects of gravity propagate at the speed of light, then nothing inside the black hole can ever affect the outside world. So what about the gravity that's left behind? You're correct that it continues to affect the outside universe, and yes, it does admittedly look quite paradoxical that nothing inside a black hole can affect the outside universe, when a black hole very clearly affects the outside universe.

The key is what we define by "affect". Once matter has passed beyond the event horizon, it cannot in any way "communicate with" or "affect" the outside universe. For example, if a lump of matter tried to shift its configuration, so as to alter the effects of its gravity, those effects would propagate at the speed of light, and hence would not leave the black hole.

For example, if you had a big metal sphere, you could determine with some reasonable precision the internal arrangement of its mass. If the mass was configured as concentric shells of material with a constant density, then it would appear gravitationally to be symmetric. On the other hand, if all the mass was located in two small spheres diametrically opposed within the larger metal sphere (say, along an unseen axis, with the circumference between them as an unseen equator), then you would be able to detect where the gravity doesn't always point directly at the center of mass. If you were near one of the larger masses within (which you can't see), the gravity would be slightly stronger. If you were around the equator, the gravity would be slightly weaker. In either case, the direction of gravity would point towards the center of mass. If you were around 45 degrees of latitude, you would detect gravity misaligned somewhat, pointing somewhat away from the center of the sphere, toward the "pole" you were closer to.

In this way, the masses inside the sphere could communicate some information to the outside world, gravitationally.

However, for the black hole, once the matter has crossed the event horizon, if it tries to reconfigure itself, the changes in gravity will not register to the outside world, because the changes cannot propagate back up to the event horizon and beyond. The state of gravity as the matter crossed the event horizon is effectively "frozen". You said, "You can dodge and say it isn't really gravity leaving the BH it's the curvature of spacetime but that is just redefining gravity." Well, call it a redefinition, but the point is, whether you call it gravity or spacetime curvature, it's not leaving the mass inside the black hole. The gravity is what was left over as the mass passed through the event horizon. In fact, changes in the mass configuration that were happening as the mass was falling through the event horizon will continue to propagate out slowly forever (or until more mass falls in and the event horizon swallows up those changes before they can make it out, which is the more likely case). But the changes would be so miniscule after a few seconds or minutes that the spacetime configuration (gravity configuration) will effectively be stable after a few seconds or minutes. In effect, when a black hole swallows a lump of mass, it would very briefly become nonspherical, since gravity was larger where the lump was swallowed. But it will quickly reconfigure itself to be spherical, in a well-defined manner, regardless of whether the lump of matter stayed intact as one lump or reconfigured itself into multiple lumps after crossing the event horizon, e.g., if it "blew up".

For example, if we were running an experiment, and we dropped a large chunk of matter into a black hole, and we set a nuclear device on the chunk of matter to detonate immediately after crossing the event horizon. Say we wanted to use the nuclear explosion to force two large chunks of matter away from each other at high speed, so we could test if we could detect the different gravitational "signature" from outside the event horizon. GR predicts we could not. If we could, we could prove GR wrong. Of course, no experiment to date has proven it wrong, so I'm not going to bet the farm on this experiment either.

"A beam of light launched from Earth can never reach any point of spacetime that is now farther than the Hubble distance (about 15 billion light years)."

Any why is that? You have brought up many theories but theories are cheap. Where is the proof that light can't travel any farther than that? Curvature of space? Or are you using the assumed expansion of the universe? Most likely the latter.

Yes, it would be the latter, the expansion rate of the universe. xanadu, do you even know what Hubble's constant is? I don't mean the numerical figure, but what it represents? Are you even aware that it was first discovered over 70 years ago that galaxies are moving away from us, at a speed roughly proportional to their distance from us? Do you realize that this is still the prevailing result of observations made today, and that no one worth taking serious within the physics community disputes this view? If you're questioning the expansion of the universe by throwing the word "assumed" out there, then you have such deep problems with your understanding of modern physics that the best I can do is refer you to some introductory reference materials. Forget the deep stuff, you don't even understand the basics, and you're making yourself look like an idiot by declaring such ignorant remarks with an air of authority. I hate to be blunt, because you'll just use it against me to say that I'm being defensive and trying to change the subject because I don't know what I'm talking about. But so far in this discussion, it's clear that only one of us has no idea what he's talking about, and that person is you.

[jaydfox]

If we could, we could prove GR wrong. Of course, no experiment to date has proven it wrong, so I'm not going to bet the farm on this experiment either.

I should be clear here, for everyone's benefit, that at the scale of quantum mechanics, general relativity doesn't mesh well with QM, so I suppose in some sense there are predictions at the extremely small scale that might be "wrong". A black hole's surface is large enough in scale to make QM effectively immaterial to the equations of state, outside of the Hawking radiation that is predicted by QM (but which, as xanadu points out, has not been observed).

[xanadu]

Jay wrote:

"A black hole's surface is large enough in scale..."

Black holes have no surface. You of course pepper your remarks with personal attacks but that has always been your trademark. I will not address you further.

bgwowk, you have apparently thrown up your hands and given up. Naturaly, you toss out some personal attacks as you go. I did read that article which was dumbed down a lot and I see where you got most of your material.

You wrote:

"I'm saying that the density of the universe decreases as you look forward in time, and increases as you look back in time. Both these facts are true for open or closed universes. Therefore the fact that the density diverges to infinity as t approaches 0 at the time of the Big Bang says nothing about whether the universe is open or closed."

This is all you were able to come up with to address the tough question I put out. If the density of the known universe at one time was close to infinite, then clearly the conditions necessary to form a closed system were present. You speculated about how expansion might give an exception to that known rule but could show nothing to support your speculation. If the conditions were present to form a black hole then a black hole was there. Most likely the universe has been a black hole since long before the most recent big bang.

Over and out.

[DukeNukem]

If light cannot escape a black hole, and if the effects of gravity propagate at the speed of light, then nothing inside the black hole can ever affect the outside world. So what about the gravity that's left behind?

It seems to me that gravity cannot be particle-based (i.e. graviton) merely by the fact that gravity itself "escapes" a black hole. Instead, it seems to me that gravity itself doesn't exist, just as there is no time particle. Gravity and time are both high-level manifestations. Gravity is truly a warping of space-time, and doesn't actually exist as a separate entity. I do not think we'll ever find a gravity particle.

Also, wouldn't an object entering a black hole release a gravity wave that could be measured, and tell you something about the object (its mass)?