Sorcerer

Yes, that's exactly what I was getting at. The example given where time switches places uses an eternal black hole and allows for the complete timeline, to infinity of that BH. Since when measuring space (volume, length, anything), we only measure at one point in time. The infinite nature of the timeline of the BH is irrelevant. Thus when we switch the dimensions as we cross the horizon, and we measure a length of time, we should only be doing so over a finite moment in space. The infinite length of 1 or 3 dimensions of time isn't relevant to a measurement of the finite size of 3 or 1 dimensions of space. The article I was referencing is here: http://www.einstein-online.info/spotlights/changing_places But however if it is demanded that we make either time or space infinite, we must account for the measurement of the corresponding space or time being summed with each corresponding moment/distance so as that too becomes an infinite dimension. We must also be aware that the limits we place on a minimum size for any moment/distance must correspondingly apply to the other half of coordinates. Accordingly, eternal or not, if we choose any two numbers and allow for the minimum to be the infinite series of coordinates between them, infinities can be summed over any length of time or space. Which is a version of Zeno's paradox. Funnily I noticed this stickied on the homepage, I haven't read it yet, but I skimmed over Aleph0 and cardinality briefly about 2 months back. http://blogs.scienceforums.net/pengkuan/2015/12/10/continuous-set-and-continuum-hypothesis/

I was wondering about gravitational lensing as an alternative to inflation to account for the smooth nature of the CMB, If our observable segment of the universe was surrounded by a vast dense patch of matter, couldn't light travelling towards us be lensed by this and spread evenly so that we observed a homogenous background. To clarify, our CMB would in this case be a magnified section of a smaller area, the lensing effect spreading this local point evenly across our view of the universe as we look back in time. IE the CMB is just a small area smudged out across the sky. So rather than inflation spreading the radiation out rapidly, gravitational lensing spread a small section over a wider area. Possible?

I was reading up on gravitational waves at http://www.einstein-online.info/and it states that they propagate at the speed of light. If they are only distortions of space, which therefore have no mass/energy they shouldn't be bound by the rules preventing them exceeding the speed of light. Does this constraint indirectly say that they are composed of particles with mass/energy? If so, why don't they travel slower than the speed of light? So why is the speed of light chosen for the speed of gravitational waves propagation, why not above or below?

By too much energy I assume you mean, that the universe would simply rip itself apart again, correct? I was just reading about gravitational waves and they carry away energy, if there is too much energy in the ground point, could a collapse of a local area where gravitational waves from the merger carry away energy allow for a stable universe?

The size of the earth for what? The earth has its 3D size and you might want that, for a measurement of a particular moment in time. But what if you wanted to know how much space the earth occupied in a year? The earth occupied the entire orbit around the sun. It occupied all those points in space time. So in order to ask how big something is, you must also define over what time you are measuring it. Separating space and time and then reversing the components, but first giving one an eternal infinite label and then having weirdness pop up when trying to describe it, isn't a indicator of a weird reality, it's an indicator of a weird set of conditions. If you give an object infinite time and then only consider length or size of an object under a small fraction of it, you must also then ignore the rest of the time. And thus you must ignore the rest of the space dimension when considering only a finite ammount of time inside the horizon. You can't have both. In the moment you look at the BH and consider the length of the axis, it is only as long as that moment. Space is the same. Space is cut into intervals by arbitrary coordinates, 3 of space and 1 of time. You cannot measure any length without taking a small amount of time to do so, another observer may get another result, because either his length or his time disagreed. They're not separate. Hopefully one day our computing / AI will be good enough that we won't have to dumb things down. This is most likely why we're having so much trouble finding a GUT. If we simplify 2 halves of a whole and exclude the places they interlink, we'll never fit them together. It's like cutting a third of the peg off a puzzle piece and filling in half of it's opposites hole, they'll never line up.

I was reading through this article: http://www.einstein-online.info/spotlights/bh_uniquenessand it stated : What is the need for gravitational waves? Gravity acts uniformly in all directions dependent on distribution of mass, any shaped object would be pulled inwards first at its "complicated features", eventually all features would be scaled down so much that they would be negligible. At some point they would fall behind an event horizon and be pulled into a singularity, which is the most uniform object possible, having no dimensions at all that can differ in any way. Why are gravitational waves needed to remove the "hair", isn't a singularity as bald as it gets. How are features "carried away", why do they need to go "away", why aren't they just integrated into the singularity, since regardless of starting shape, all singularities have exactly the same shape, or lack of it. Why speculate gravitational waves are produced if they're swallowed by the black hole, isn't that redundant and against Occam's razor? What if they're always swallowed, how does that change anything? Isn't it more like how every car that goes to the compactor, no matter how different, comes out a cube? Can you extend the analogy, what would be the gravitational waves, differing forces on the compactor? If gravitational waves remove "hair", could we deduce the shape of the object that created them? Could we create them on purpose to encode and send a message over vast distances? How resistant in the information they contain to degradation, how does it compare to a radio wave? If the concern is the loss of information, why not assume the information is hidden behind the event horizon, trapped in a singularity. If the black hole does evaporate, say via hawking radiation, what prevents that information from being returned. What if Hawking radiation was influenced, by information stored on the horizon? What if we DON'T find gravitational waves, how long should we look?

http://www.einstein-online.info/spotlights/changing_places So this confused the hell out of me: First I don't understand how the black hole has a finite size in space. 1. The black hole is the sum of all it's parts over an infinite time. If we had a 2 meter diameter sphere which was eternal its size would be 4/3 pi^3 summed to infinity. It would be an infinitely large tube in both time and space. To say it's finite in space, just doesn't make any sense, each moment of time is a new moment of space, space is cumulative. 2. If the axis direction inside the even horizon is infinite, but the time direction finite, anything travelling to the center would be travelling at an infinite velocity. v= d/t, since d is infinite dividing it by any finite number will produce an infinite result. The speed of light is the limit for speed, infinite speed is greater than the speed of light. It shouldn't be possible. However if the black hole is infinitely large (as in 1), then infinity divides neatly into infinity....... giving a velocity of 1 using the largest possible unit, meaning travelling at the speed of light. Second, I don't understand why eternal black holes can't have a beginning in time. A timeline is infinite in both directions, if we label an origin, there is still an infinite amount of time in the future. The black hole still existed before the event horizon formed, it's just that it was outside of it. And the universe may (I think must) have also had a beginning in time. Third, why begin with the least likely type, this doesn't make sense and can't be real. Why waste time.

Why don't both horizons move? I thought that horizons are proportional to mass. If one horizon grows surely so should the other. I was looking at the double horizon thing and wondered about it, is it just showing and area of stable eternal orbit inside the first event horizon but before the second, where objects can stay and not join the singularity, but also cannot ever escape back past the first horizon? Assuming your example of event horizons "crossing" is possible. Wouldn't the inner horizon just squeeze, or slowly annex this stable middle region, forcing the matter there out of stable orbit, having to join the singularity eventually? Immediately before the horizons "cross" there would be a point where the event horizons are both of equal size, it would be impossible to tell them apart, they would be a singular horizon. If the 2nd one moved outside the 1st, it would be indistinguishable from the two simply seperating back the way they were. Space and time reversal, if that's one major factor, would be the same as it was. Rather than horizons crossing it would simply be horizons merging and separating again. (I actually never understood that dimension switching thing, does space get 1 dimension and time get 3? And what the hell does that mean anyway, seems more like the math is explaining something which isn't really able to be described in words. Travelling in space is always travelling in time, how does it change anything? Being forced to travel forwards in space is meaningless since the time dimension which has become space-like ensures those previous coordinates, which are "behind" you, are in the past anyway, you could move backwards and be on the same coordinates but in the future..... it really doesn't seem of any special consequence. We can't move backwards in time here outside the event horizon and that's the same as being unable to move backwards in space, we're always moving into a region of space which is in our future. I could break a game of pool and rack them back up, the balls go backwards to where they were in space relative to the table, but they're at another point in time.) It'd be nice if you could answer some of my questions from the previous posts MigL, so far there's more questions than answers.

Well ok, on further reading the shape of the ergosphere is given simply by the difference in angular momentum between the poles and the equator. At the poles the distance of travel is 0 and hence the BH angular momentum is 0, the point is not spinning it is stationary and the ergosphere extends 0 distance, the ergosurface perpendicular with the axis of rotation. But as we move from the pole to the equator, the distance of travel over the same time interval, and hence the angular momentum increases, where it comes to be at a maximum at the equator. This forms the oblate sphereoid shape. The shape is not due to the distribution of mass at the center of the black hole, although the ring shape could be shaped as such because ofo a similar reason. The ring being the 1D equivalent of the oblate sphereoid, a singularity, or point spinning on its axis, is its axis and its equator. Therefore, during formation, the moment immediately before it collapses to a singularity, it will distribute its mass in a ring perpendicular to and centering on its axis. Otherwise as it approaches a point the speed at which it rotates approaches the speed of light. From Wiki: What confuses me here is the statement: "The size of the ergosphere, the distance between the ergosurface and the event horizon, is not necessarily proportional to the radius of the event horizon, but rather to the black hole's gravity and angular momentum." I'm guessing the event horizon is determined by the total mass/energy and a (1), small black hole spinning fast, with equal mass energy, to a (2), large black hole spinning slow, would produce equal sized event horizons. While instead the ergosphere would be more angular momentum dominated, (given it's shape is governed by the distribution of angular momentum), so comparisons between 1 and 2, 1 would have a larger ergosphere than 2. Is this correct? Also, is this how the angular momentum of a black hole is calculated? Is it from the ratio of the event horizon to the ergosphere? Or is it estimated in other ways?

The pedantry is strong with this one. OK, without people delegated people managing multi-skilled labour processes the inefficiencies would make otherwise simple production logistics unsustainable when put in direct competition with those managed efficiently. There's always exceptions, but these would be the normal outcomes, wouldn't they? I mean I know you can min/max calculus on this, but that's quite taxing, I know the burden of proofs on me, but what's the basis of your disagreement? The point is that everyone contributes and everyone benefits, and it is a system that facilitates growth by having a selective pressure for those who use the best strategies. Profit split unevenly is better than no profit split evenly.

Fermions must all be assigned a seperate spatial coordinate. If the uncertainty principle prevented me however from knowing both which state and which position though, the possibilities reduce. If we use pool balls though, one black one white to show the 2 states =n. And assign them 3 seperate positions =r. Then it's the permutation nPr. Bosons also aren't excluded from having seperate positions, but are allowed to have the same. So only in one special case is the number of ways reduced to 4. If we use only 3 of the 1D coordinates of a line on the table surface, this is when the balls are stacked vertically. And I haven't even accounted for a change in coordinates, this is only when position swaps exactly. This was useful, I understand his assumptions now. I'll read up further to see how they model reality. Got it! NO INTERNAL DEGREES OF FREEDOM

*Facedesk* 3 positions with 2 energy states to choose from, because the order matters spatially, is the permutation 2x2x2=8. I can distinguish between each energy state in each position.

If they had different energy levels. Why are you reducing it to 2 and removing the energy states, the example was given with 3 with 2 states. Being able to determine their position in space and measure 1 of 2 energy levels makes them distinguishable, therefore only Bosons can be indistinguishable. Otherwise there are permutations formed by variations in energy level. 1. ... 2. :.. .:. ..: <------spatially distinguishable, it does matter 3. .:: :.: ::. 4. ::: How do we observe a non-interacting gas?

The geometric distribution of mass directly relates to the geometric distribution of the effects of gravity. But looking at it, the event horizons are spherical, so I probably am missing something.

Without seeing a working example, I would say that only individual ie self employed people could effectively do this and even then they would benefit from a 3rd party/broker/agency connecting them with clients, but have greater freedom on what they share of their wages that 3rd party gained. That 3rd party could have many clients themselves though. I think under a large scale cooperative venture that individual management would cause inefficiencies from bureaucracy to multiply exponentially. Too many cooks spoiling the broth so to speak. Delegating decisions to a representative would be vastly more efficient. There's also the problem that the means of production isn't owned by the workers, so they only have their labour as a collective bargaining tool. It isn't uncommon for a labourer to become a manager, but merit should be the deciding factor, democracy votes idiots in like Hitler and Bush. The guy who was smart enough to make the company, has the merit to make the choice of manager (or delegate that to someone he feels has the merit to do so, like an employment agency). The guy running the ball bearing machine at a car manufacturing plant doesn't necessarily have any knowledge about any other step in the production line, he lacks the knowledge to make an informed choice as to who would be best to manage all steps. To make it work, everyone would basically have to be trained how to be a manager to understand who would manage them best.

Huh? both particles have a different set of co-ordinates. I can almost grasp the bosonic form, but fermionic doesn't seem possible. Does uncertainty prevent me from doing this?

I see how an object would bulge at the equator, much like the earth, due to centrifical effects. But a point cannot bulge, and a ring doesn't seem like an analogous shape. An effect like frame-dragging shouldn't bulge, because of centrifical effects (unless the fabric of space can be acted on like matter), but the geometry of the ergosphere would be dependent on the distribution of mass. As a ring, mass is distributed unevenly from one axis to the other, it seemingly is quite logical to see the ergospheres shape as a direct dependent result.

Is it possible from earth to measure the extent of a spinning black holes ergosphere. Does the frame dragging effect have a visible signature for us here on earth, or is it only something observed by objects within the ergosphere? By knowing the shape of a spinning black holes ergosphere, and using it as an already complete part in Kerr's solution for Einsteins Field Equations, could we reverse engineer the mathematics and adjust the equation accordingly? Or would it rather just alter another part of the solution? If instead it exactly matched Kerr's solution, would this tell us anything else? Could we be confident enough in our other measurements of the BH to get any certain results? It seems to me that IF the BH has angular momentum > 0 AND Kerr's solution is correct THEN the ergosphere must be an elipsoid. Any other shape, even with uncertainty of mass or angular momentum, would tell us the solution is wrong.

Well, a point moving in 4D about a 3D axis is a ring. It may not be a point on the central axis under this solution, but that doesn't mean it isn't, we can test it. The ergosphere is OUTSIDE the event horizon, it is the area in which frame dragging occurs. I am only intuiting that it is an elipsoid because of the ring, there is greater extension in the plane perpendicular to the axis of rotation. By the same thinking, if it was a point on the axis, the ergosphere would be spherical. I guess it probably extends into the BH too, but I'm having trouble visualising it in the middle of the ring. Also the double event horizon thing gets my head a bit buzzing too. IF we did test it, and IF the ergosphere was another shape or ideally a sphere, could we use the result to reverse engineer from the solution, to the equation? Would this be useful in finding a GUT?

Being a point and considering other point particles normally act as waves, wouldn't hertz, or wavelength be more appropriate. A 1d wave around an axis of a 4d time-space? And that leads me to ask, why the need for a ring? Point particles can have angular momentum, or "spin", why not a Black Hole, why does the maths give a ring shape? (why is probably the wrong question, is there something particular about the solution, that when altered, would produce an answer which allowed for a point?) Could we test whether it was a ring or a point by measuring the extent of the ergosphere, a ring would produce an elipse and a point a sphere. It is possible to do that from outside the ergosphere, eg from earth with a telescope?

Good point, so when wiki says: What part of it are they meaning? Wouldn't an object in synchronous orbit just above the event horizon be a good point to measure from, can such an orbit be achieved? and Strange points out: What is the diameter of the ring? Because that would determine how fast it is "spinning", right? I use "spinning", because it's actually moving in a closed curve trajectory and that's not really spinning. But to be fair I guess that's like how only the central axis of the earth "spins" and everything else moves around it in a closed curve. Shouldn't there be other ways? The moon is moving away from the earth and the earths rotation is slowing down. I'm still confused as to how: "the infalling piece has negative mass-energy". It seems unnecessary to me. I have another topic on bremsstrahlung radiation (which would probably apply more to charged BH's). Similarly, shouldn't an object passing through the gravitation field and accelerating or decelerating, but not crossing the event horizon reduce mass, like how voyager was sling shot? Since mass-energy is related to momentum through E=mc^2, what would determine a preference for mass over rotation? Which leads to another question, if there is no preference what stops all the mass evaporating leaving "nothing" rotating. So long as there was enough warping of gravity by rotation to maintain an event horizon. We can tell there's mass-energy, by gravity, and we can tell there's rotation by frame dragging. Isn't that hidden information posing a problem, surely the must be something to rotate, to drag the frame.

Without people managing those who do manual labour it would never get done. Without people effectively managing those who do manual labour it is done less efficiently. Efficiency is gained by those who devote their time to researching better tools for doing the labour and also by those who educate the labourers on the most effective way to do their labour. Those who invest their money into facilitating and expanding these processes help with manual labour. Manual labour may be the backbone, but there's a body and a brain, I've never see a backbone of much function by itself. Maybe the larvae of Tunicates come close.....

Yes I understand that, but the gas includes 2 energy states. If one was up the other down they wouldnt be identical right? Is it, if I turn my back and you transfer the energy, how could I tell if you switched them or transferred the energy? Or am I unable to measure individual particles energy, only the total system, there's something missing. I could ask you

So I'm confused as to why they're not different. But the particles permuations represented spatially are clearly distinguishable. ::. Mirrors .::

Most of the string theories I've read about have dimensions "below" ours, curled up tight. I never got that analogy.