Neutrinos faster than the speed of light?

I certainly did not pick up the analogy from Brian Greene.



http://jila.colorado.edu/~ajsh/insidebh/waterfall.html
A more insightful way to conceptualize how a black hole works is to picture space as flowing like a waterfall into the black hole. At left is a movie of Boulder Falls that I photographed. Here's the movie with sound.
Imagine light rays, photons, as fishes swimming fiercely in the current. Outside the horizon, space is falling into the black hole at less than the speed of light (or the speed of fishes), and photon-fishes swimming upstream can make way against the flow. At the horizon, space is falling into the black hole at the speed of light. At the horizon a photon-fish swimming directly upstream will just stay there, swimming like crazy, but not going anywhere, the inward flow of space exactly canceling the fish's motion. Inside the horizon, the space waterfall falls faster than the speed of light, carrying everything with it. However hard it tries to swim upstream, the photon-fish inside the horizon is carried by the flow of space inevitably inward to its ultimate fate.

In the image at right, the (happy) fish upstream can make way against the current, but the (sad) fish downstream is swept to the bottom of the waterfall. This picture was drawn by my daughter Wild, and provided the cover image for the June 2008 issue of the American Journal of Physics4.

Doesn't relativity say that nothing can go faster than light? It is true that nothing can travel through space faster than light. However, in general relativity, space itself can do whatever it likes.

The idea of space moving is one that you may have met before in cosmology (the study of the Universe at large), in the notion that the Universe expands.


The picture of spacing falling into a black hole has a sound mathematical basis, first discovered in 1921 by the Nobel prize-winner Alvar Gullstrand2, and independently by the French mathematician and politician Paul Painlevé3, who was Prime Minister of France in 1917 and then again in 1925.
It is not necessary to understand the mathematics, but I do want to emphasize that, because the concept of space falling into a black hole is mathematically correct4, inferences drawn from that concept are correct.

The Gullstrand-Painlevé metric is

ds2=−dt2ff+(dr−vdtff)2+r2(dθ2+sin2θdϕ2)
which is just the Schwarzschild metric expressed in a different coordinate system. The free-fall time tff is the proper time experienced by observers who free-fall radially from zero velocity at infinity. The velocity v in the Gullstrand-Painlevé metric equals the Newtonian escape velocity from a spherical mass M
v=−2GMr−−−−−√
with a minus sign because space is falling inward, to smaller radius.
Physically, the Gullstrand-Painlevé metric describes space falling into the Schwarzschild black hole at the Newtonian escape velocity. Outside the horizon, the infall velocity is less than the speed of light. At the horizon, the velocity equals the speed of light. And inside the horizon, the velocity exceeds the speed of light. Technically, the Gullstrand-Painlevé metric encodes not only a metric, but also a complete orthonormal tetrad, a set of four locally inertial axes at each point of the spacetime. The Gullstrand-Painlevé tetrad free-falls through the coordinates at the Newtonian escape velocity.

It is an interesting historical fact that the mathematics of black holes was understood long before the physics. Einstein himself misunderstood how black holes work. He thought that the Schwarzschild geometry had a singularity at its horizon, and that the regions inside and outside the horizon constituted two separate spacetimes. I think that even today research into general relativity is too often dominated by abstract mathematical thinking at the expense of conceptual understanding.


http://jila.colorado.edu/~ajsh/insidebh/waterfall.html

 

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That's not what is being said.
Using another analogy, it is noted that gravity in regions of space/time such as our local group of galaxies, is decoupled from the overall expansion rate of the Universe/space/time.
The space/time within those regions is still trying to expand, but gravity travelling at "c" overcomes that expansion.
The second point you raised about the Earth dragging space/time around it in its orbit, does in fact happen. This is called the Lense Thirring Effect and was shown by GP-B.

With the photon hovering, of course that depends on ones FoR. The photon is of course moving away from the EH at "c ", but the EH is also chasing the photon at "c " with space/time cascading inwards. Therefor in the photon's FoR, it would indeed seem to be "hovering" just outside that EH.

 

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paddoboy

As I pointed out, I don't think the "Flowing spacetime" is valid, and the "hovering" photon? No, not on this side of the EH. Spacetime is not pulled into a BH, but does warp in it's vicinity so badly that all trajectories are inward and no possible vector is outward. If spacetime flowed for a lot of gravity, it would flow for a little and would appear in experiments testing for an aether, I would think. There is frame dragging, that's been measured, but that is a distortion of the field, not a movement of it caused by high gravity. So, photons do not hover at the EH, at least on this side. They still follow the geodesic.

This is just wrong

"Einstein himself misunderstood how black holes work."

This is a sure sign that there are problems here. And any site that tries to tell you detailed descriptions of what is going on inside a BH Event Horizon without copious "maybes" and "could bes" is blowing smoke. But the "waterfall" of spacetime is just wrong. And Einstein was right that spacetime ends at the EH and that the inside IS a different place.

"The idea of space moving is one that you may have met before in cosmology (the study of the Universe at large), in the notion that the Universe expands."

That's entirely wrong, Expansion is each point in spacetime seeing itself as stationary, spacetime does not move to expand, it stays still in it's own frame of reference and everything else expands away from it. Spacetime does not move, it is the stage upon which ENERGY moves.

"It is not necessary to understand the mathematics, but I do want to emphasize that, because the concept of space falling into a black hole is mathematically correct4, inferences drawn from that concept are correct."

And that's exactly backwards, math can "prove" anything but if the concept is flawed the math proves nothing relevant to reality.

Grumpy

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http://en.wikipedia.org/wiki/Propagation_of_light_in_non-inertial_reference_frames

"The description of motion in relativity requires more than one concept of speed. Coordinate speed is the coordinate distance measured by the observer divided by the coordinate time of the observer. Proper speed is the local proper distance divided by the local proper time. For example, at the event horizon of a black hole the coordinate speed of light is zero, while the proper speed is c.[1] The coordinate speed of light (both instantaneous and average) is slowed in the presence of gravitational fields. The local instantaneous proper speed of light is always c.
In an inertial frame an observer cannot detect their motion via light signals as the speed of light in a vacuum is constant. This means an observer can detect when their motion is accelerated by studying light signals."

 

OK Grumpy, Not sure that you are correct in saying it is wrong. The site itself, would be one of the best BH sites there is in my opinion and the opinion of others I know who visit there regularly.
I see it more as an analogy and perhaps just a difference in interpreting a particular scenario.

The same effect is used when discussing gravitationally bound galaxies and their decoupling from the overall expansion of space/time...The gravity in that scenario, overcomes the space/time expansion.
With the photon emitted radially away from the BH, the apparent "hovering" aspect would depend on the FoR, would it not?
But more Importantly, the photon emitted radially away, is certainly seen as never quite escaping from a local frame.
So I cannot see why that cannot be interpreted as hovering, from a local FoR.
I have no problem in visualising the waterfall analogy as applicable to that.

Brian Cox, another reputable science populariser also uses the waterfall analogy.

Black holes

Using Zambia's spectacular Victoria Falls, Prof Brian Cox demonstrates what happens as you near a black hole.
http://www.bbc.co.uk/science/space/universe/sights/black_holes#p00frjln

I'm also inclined to believe you are not entirely correct, when you say the Lense Thirring effect does not make space/time flow.
This is more then just curvature and is a great example of a mass with angular momentum, dragging space/time around with it.

In saying all that, let me add that I do agree with the more correct aspect of critically curved space/time.
I just think its a way to relay a picture of what a BH is, and what it does as simply as possible.

 

paddoboy

The Brian Cox site is verboten in the US, but I have seen him on the BBC chanel. I didn't agree with his analogy either, for the same reason. The thing is we see lots of light coming from just outside the EH and in jets, none of it travels any slower than anywhere else. And space and time do not initiate events, though they are effected by them and are the "where and when" for those events occur. I have no doubt that matter flowing into a BH can resemble a waterfall, but doubt seriously that spacetime acts the same way. Imagine a photon not quite hovering, being just a smidge above that point, creeping away from the EH over a long period of time. What process accelerates that photon to lightspeed instantly and what "smidge" is enough for that to happen, at what distance from the BH does this effect cease?(because we don't see light traveling at any other speed than lightspeed through the rest of space, even from just outside the EH), and why would such an extreme effect in an extreme level of gravity not be visible as a small effect under a small force of gravity. A bias in spacetime toward flowing into gravity fields would be little different from the aether effects that were not found. Spacetime is not something that flows, it is a characteristic of spacetime(IE the Universe) that allows ENERGY to flow. I think the waterfall concept is flawed.

Grumpy

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Grumpy, don’t shoot the messenger, your going to love this from Nasa…

My bold.
Besides ‘funky’ what else would you call it?

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http://www.nasa.gov/vision/universe/starsgalaxies/bh_roadshow.html

 

*shrug*
As I said Grumpy, I don't entirely agree with what you say, and I don't entirely disagree. I see it as an analogy, and certainly doesn't take away or refute the accepted notion science has regarding GR BH's.

 

You need to do some more reading. He's predicting the speed of light is a variable in the gravitational field. He scoffed at my explanation about the differentiable manifold that includes a tangent space for doing the local physics while the rest of the manifold is where the physics of GR is conducted. In the local tangent space the speed of light is an invariant. c. Always. What you said has been said in several different ways in this thread. He's not even a member of this forum anymore.

Solve the Minkowski metric for the local invariant speed of light. Solve the metric for a clock attached to the Schwarzschild remote bookkeeper coordinates. The local prediction is an invariant. The remote prediction is frame dependent. This was never acknowledged during the discourse. Just that Einstein predicts the speed of light is a variable in the gravitational field. The key is he's no longer a member so we don't have to go through this again.

 

Guys and gals, I've been on a hunt for some helpful videos of great worth, and boy did I find the jackpot! This video, and the other two, explain Relativity much better than I can, with much more ability to explain the math in simple terms. Amateurs(like me)should watch them until they have them memorized.

[video=youtube;Cxqjyl74iu4]http://www.youtube.com/watch?feature=player_detailpage&v=Cxqjyl74iu4[/video]

Grumpy

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Very nice!!