On Wednesday, February 24, 2016 at 5:23:18 PM UTC-5, snipped-for-privacy@yahoo.com wrot e:
o throw a ball, it would have to achieve escape velocity when it left your hand in order to escape.
y and still escape as long as it had sufficent fuel to continue under power . With enough fuel, it could rise as slow as 1 mile per hour and still eve ntually escape.
objects? In our imaginary space ship (with an engine) , if we crossed 1 fo ot into the the event horizon, why could we not use fuel to turn around and cross back outside the event horizon?
Well no... (I'd have to think hard to do the math right, but it's a 1/r^2 force and 1/r potential... (there must be a wiki article..) as you say, we can show that there is an escape velocity for some potential . You can never go faster than the speed of light, so once the potential, (you can think charge for mass and voltage for (gravitational) potential.) is big enough such that you have to go faster than c... you're stuck... throw your laser up as fast as you can from such a potential and what happens to the light?
The speed of light is invariant. So I believe what happens is that the light is not slowed, but red shifted. In a G field with escape velocity greater than c the light is shifted until the energy is gone.
That is Galilean dynamics where you can increase your speed forever by using more energy to increase your total momentum.
Things only get strange in relativity when you are at c/10 or faster.
Though it would be a terrible way to do it. It isn't for nothing that Saturn V used a three stage solution to go to the moon.
No. Because you are inside a boundary that requires infinite energy to escape. In relativistic dynamics you can increase your energy without limit but you cannot exceed the speed of light c just get ever closer. Light fares no better once it crosses the event horizon.
And I have some more bad news - once you are inside the black hole event horizon your trajectory will inevitably intersect with the singularity at the centre in a finite proper time (by your clock) no matter how hard you try to avoid it. The same fate befalls all light rays that enter into this region too and they can travel at c.
So once you are inside something with escape velocity >c you have had it (although for something the size of our universe the timescale is very long).
The only minor caveat to this it that you could orbit a maximally spinning Kerr metric black hole in the same sense as its spin outside but arbitrarily close to the boundary forever if memory serves. The closest stable orbit is right on the Schwardchild radius Rs.
Counter rotating it is at 9Rs. (and for a non-spinning one at 3Rs).
Because for a large enough black hole nothing special happens to you as you cross the event horizon apart from the inability to return.
Accelerating could be done too given the fudge factor of dark energy but I think at some point the decrease in density would make it not a black hole any more if it is destined to expand forever. This is pushing the limits of my understanding. The theories that hold that potentially every black hole contains a universe are after my time.
Here is an example of the sort of thing.
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Your understanding is wrong. Normally we only consider dropping things into a Black Hole where the rules are simple enough. It falls to the centre in finite proper time. But if everything starts from close to the centre with a large initial velocity it expands until it runs out of kinetic energy (or not) and then falls back in on itself.
No different in principle to throwing a stone up in the air on Earth.
The initial conditions at onset of the Big Bang.
You don't seem to have grasped the fact the a Black Hole is defined by having sufficient mass inside a given region to have an escape velocity from it greater than that of light. It is not compelled to have a singularity until the mass has time to settle down at the centre of it.
For a ray pointing exactly radially away from the BH.
At any other angle ISTR there is a proof that all trajectories will intersect the singularity at some future time. Although I can't find a URL describing this my attempts to find it revealed the series of virtual tours of various Black Hole metrics by university of Colorado supercomputing centre I described in a previous posting:
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Part of the problem here is that some people are using the term black hole to mean the singularity which may or may not be at the centre of the excluded region of space defined by the event horizon.
I think many physicists think that something quantum mechanical related to scales around the Planck length will prevent a pure mathematical singularity but I doubt we will ever know. You can't report your observations if you go to visit one and we haven't a cat in hells chance of reaching the energies needed to probe one in the lab. (although making a femto BH in a collider isn't entirely ruled out)
A black hole is strictly any distribution of matter where the mass enclosed by some bounding spherical surface is sufficient to make the escape velocity equal to the speed of light. The final canonical form of this mass distribution once sufficient time has elapsed in classical GR is a hard singularity at the centre and a semi permeable membrane around it at a radius determined by its mass and spin.
You can check in any time you like but you can never ever leave.
All this talk about escape velocity being greater than c bothers me more than a bit. I mean, the Schwarzschild radius is found by equating the *Newtonian* kinetic energy to the gravitational potential and solving for r with v=c. Shouldn't it use the
*relativistic* kinetic energy instead? There is no place where v reaches c then, no event horizon.
Indeed you should. But using that level of mathematics with covariant and contravariant tensor calculus puts it beyond reach of most people.
You get very similar conservation laws for energy and angular momentum in the full treatment and about the same answers. Notably the deviation of a light ray due to a mass is wrong by a factor 2 in a Newtonian approximate treatment as opposed to correct GR analysis.
The errors made by using Newtonian approximations used judiciously are seldom more than a factor of 2 here and there. eg
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If you do it properly with metric tensors then you can handle a more general case and solve the differential equations of motion eg
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Rs happens to have the same value both treatments.
Why is that not obvious? No light you send out will reach anything outside to be reflected.
Except for that arbitrary and rather absurd initial condition. How does that happen? How do you start that process? How was the start condition not a singularity?
What do you mean "settled"? The initial conditions you propose create a singularity. I think this points out the absurdity of the big bang theory which will only be resolved by a fundamentally new approach to the field not unlike relativity was 100 years ago.
So if an object falls into a black hole and approaches the center with ever increasing accelleration, does it pass through and come up the other side? What happens as it approaches the center?
How much mass is required to create a singularity?
Please provide your intuitive, common sense, non-weird explanation of the double slit, and Aspect experiments, on the lines below, in a form accessible to Don Trump supporters:
The usual analogy is with light, but when you think about it, the behaviour of light is also deeply mysterious.
Cheers
Phil Hobbs
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Dr Philip C D Hobbs
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curvature of space directly dependent upon its mass-energy distribution, and vice versa? How can an expanding universe occur when it was as dense as our observations show? (You can't use kinetic energy as an excuse, because there was apparently a superluminal expansion phase. But since that's apparently not understood at all, we can mutually ignore that wrinkle...)
Or have I misunderstood the term "metric", and it's more as the name suggests: just a way of _measuring_ an expanding universe? In which case, it provides absolutely no explanatory value whatsoever, just a handy way to measure and speak about our observations. In the same way that it's more useful to speak of geography in terms of spherical coordinates (lat/long) instead of using, say, an R^3 Cartesian system. But then, why is it talked about like fundamental knowledge, if it's just a coordinate system?
Part 2: if the universe is within an event horizon, then how would the observations be explained? That is, if the mass of the known universe is constant, then back just a few billion years when it was smaller, it should've been even more dense and unable to expand at all, and so on going back in history until, apparently, it was a perfect singularity to begin with! (It seems to be a black hole running in reverse..!)
Surely, if the universe was more dense, its Swartzchild radius was more than proportionally smaller (the Swartzchild volume goes as rho^-3/2, so it shrinks faster than linear), and therefore contained less mass (assuming a similar distribution of mass outside the event horizon as well), and therefore the universe is not closed but is gaining mass as r_s somehow happens to increase!
I'm sure I've confused or abused a number of properties of the system, but it doesn't seem to be explained in a consistent, high-level manner anywhere, including whether the gaps are limitations of theory, observation or what. (The Wikipedia page on The Big Bang is about as good as other articles I've read, and like them, it constantly commits the sin of presenting poorly understood hypotheses as hard facts. I HATE IT when 'scientists' do that. It makes it look more like religious dogma than scientific theory.)
Tim, if I'm reading correctly, you're asking, "where did the big bang come from?" and then "what's that inflation BS Guth and others made up?" I'm guessing you know as much as I do, (never studied it deeply.) my limited understanding is that if things start too small and hot there's too much "noise" in the mix, so it had to start out bigger or have some... inflation.
It's a theory to fill in the gaps, I haven't heard of any way to test it.
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Grin... I think metric is just a different name for curvature.
There is lots of data for a big bang, and for dark matter, dark energy has only two pieces, distant supernova, and fitting to the noise spectra of the cosmic background radiation.
I read some of the "starts with a bang" blog.
He does an OK job of explaining why neutrinos can't be dark matter. But there are no equations! lots of stuff in cosmology has simple equations.
Young's optical double slit experiment is easy enough, treating the light as waves, but its interaction with the detector as quantized. It's harder with particles. Does anyone have a reference to a double slit experiment with zero-charge particles with vanishing dipole moments?
Aspect's experiment is harder. Some sleazy statistics to be dealt with.
Actually the only thing that is certain is that these properties that you object to are real and have been verified experimentally.
The problem with both light and particles is that under the right experimental conditions either one can behave like the other.
The experiment that broke classical light as a continuum wave was the wavelength dependence of metal workfunctions. Explaining that strange observation resulted in Einstein's Nobel Prize for quantum mechanics. (I know you know all this Phil)
Continuum classical theory of light emitted by a black body was at the time a bit of a mess see "UV catastrophe" and Plancks constant. eg
But I'm not objecting to the results of the experiments. I'm objecting to the interpretation that describes light as a stream of discrete quanta with mystical properties, even though we *do* have a wave theory that explains it better.
The point is: Do you accept that light is quantized, or that only its interaction with matter is? How would you tell the difference? No, the photo-electric effect is not decisive.
And in the case of a universe there is also the possibility of no time or space at all prior to the initial expansion.
Guth's exponential expansion phase is the least liked ad hoc fixup but it does have the merit of predicting the isotropic background radiation we see left over from the big bang and the flatness.
It is a coordinate system and there is a choice of them depending on what you want to do but fundamentally it allows you to define what you mean by a straight line (aka geodesic) inside the spacetime.
On the surface of the Earth it would be a great circle path which is the shortest distance between two points. These are important because they represent the path that light will take through a spacetime.
If it started out expanding at just under the speed of light then it can grow until it runs out of kinetic energy. If there isn't enough mass to close the universe it keeps on going forever. If there is too much mass then a point will come when it stops expanding and implodes under free fall leading to a big crunch.
The Rs depends on the volume of space in the universe that is inside the radius at which stuff is moving away from us at the speed of light and the average density at that time.
You have to be very careful about definitions of the edges of the observable universe as a function of time. Cosmologists make careful definitions of the various horizons for an observer in spacetime.
These were first defined by Rindler in 1956:
event horizon: light from distant object receding at c particle horizon: light path from new particle to observer in expanding universe absolute horizon: combination of the above allowing the observer to accelerate within the limitations of the laws of physics.
They don't matter too much in ordinary observations since we are unable to accelerate ourselves to anything like light speed, but they do matter when you are talking about cosmologies or you get confusion.
I expect a better theory will eventually come along but I doubt if it will look simpler to a layman (or even to a present day cosmologist). If it turns out the string theorists are right and the universe really is
11 dimensional with 7 tightly curled ones then it may be that only a handful of people in the entire history of the human race are gifted enough to imagine and understand it. I am not holding my breath.
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