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I Always love questions along these line and get a good chuckle.

What happens depends on what you accept and what you want to extrapolate into something that you have no data which is always fun.

If GR is your thing then the easiest extrapolation is using Rindler coordinates and it says times stops for the observer not because time really stops just they are unable to detect it in any way. It is well covered in Wikipedia.

http://en.wikipedia.org/wiki/Rindler_coordinates

If Quantum ElectroDynamics(QED) is your thing then you go back to a problem Einstein was struggling with before his death and later extended by Wheeler. The topic gets picked up from time to time but is out of favour with science media at the moment.

http://en.wikipedia.org/wiki/Black_hole_electron

One of the interesting ways to look at your question is what is the minimum size black hole can be.

The "accepted theoretical minimum" size of a black hole is about 21.77 micrograms. That yields a schwarzchild radius of a planck length.

That answer provides a link between the 2 schools of thought above and may help you with thinking more carefully about your question and show you a little problem often forgotten in the argument smile

Black holes can be very small if theory is right and any concept of falling into them means what? No one has seen a microscopic black hole so do they exist and if not why not? Would time stop around a micro black hole and what would that mean anyhow?

The cosmology side of black holes get a lot of science media discussion but micro black holes under the same theory are interesting. Ethan did a good article on cosmology ones a couple of years ago (http://scienceblogs.com/startswithabang/2012/05/02/black-holes-dont-eat-as-much-a/)

When people were concerned the LHC might create a blackhole it spawned a lot of discussion on it and some considered thinking (http://www.newscientist.com/blogs/shortsharpscience/2009/05/black-hole-catching.html)

Last edited by Orac; 08/13/14 06:47 AM.

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Originally Posted By: Orac
The "accepted theoretical minimum" size of a black hole is about 21.77 micrograms. That yields a schwarzchild radius of a planck length.

How long would a minimum sized black hole last? Since the temperature of a black hole is an inverse relation to its size then a black hole with a schwarzchild radius that small should have a very high temperature. The super massive black holes have extremely low temperatures and extremely long lifetimes, so I would expect super small ones to have very short lifetimes.

Also of course there is the question of what the Planck length means. Ethan Siegel discusses this in his blog. The Smallest Possible Scale in the Universe. I don't expect that makes much difference to what you have to say, but it is an interesting discussion.

Bill Gill


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Black holes, entanglement, GR + Quantum mechanics and gravity.

http://www.scienceagogo.com/news/20131105203121.shtml

It does seem to involve string theory though.

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Originally Posted By: Bill
How long would a minimum sized black hole last? Since the temperature of a black hole is an inverse relation to its size, a black hole with a Schwarzchild radius that small should have a very high temperature. The super massive black holes have extremely low temperatures and extremely long lifetimes, so I would expect super small ones to have very short lifetimes.

Did you read => http://www.newscientist.com/blogs/shortsharpscience/2009/05/black-hole-catching.html

It explains what would happen in layman understandable detail assuming you made one it would continue to grow so long as it could absorbs particles.

The article on scale is sort of what I was trying to get Bill S to think about. In cosmology they talk about people falling into a black hole and make weird assumptions not least about the space geometry but they forget the theory must and should hold for a microscopic black hole, unless their theory explains a reason micro black holes can't exist.

Laymen think black holes are like these incredibly dense things that suck everything into them. They aren't anything like that at either a macro level, as Ethan discussed, or if they exist in micro form. As per the above article a micro black hole has no more gravity than an orange and it isn't going to suck you or the earth anywhere and assumptions and theories about what is going to happen to time should be valid for the micro black hole as the large cosmological version.

The two really weird facts about black holes that catch people out.

1.) The Schwarzschild radius formula is linear if you double the mass of a black hole the Schwarzschild radius doubles. However because the thing is a sphere that means it actually gets less dense because volume is 4/3 x Pi x radius cubed. So a microscopic black hole has the highest density you can have and as the black hole gets larger to the cosmological version it's density actually decreases. Catches people out all the time they expect it to get denser like the core of a sun. That is why when they get really large: (http://en.wikipedia.org/wiki/Supermassive_black_hole)

Quote:
The average density of a supermassive black hole (defined as the mass of the black hole divided by the volume within its Schwarzschild radius) can be less than the density of water in the case of some supermassive black holes

2.) Black holes often spin (perhaps always?), and because they distort space, they would drag space around like some wrinkled fabric and that makes simplifications like Rindler calculations fanciful at best.

A third interesting fact is outside the ability of laymen. It is to do with energy calculations with the weird density behaviour of point 1.

Last edited by Amaranth Rose II; 08/14/14 07:29 PM.

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http://en.wikipedia.org/wiki/Supermassive_black_hole

“…a person on the surface of the Earth and one at the event horizon of a 10 million solar mass black hole experience about the same tidal force between their head and feet….”

Does that mean they would experience the same gravitational “attraction” in both places?


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Originally Posted By: Bill S.
http://en.wikipedia.org/wiki/Supermassive_black_hole

“…a person on the surface of the Earth and one at the event horizon of a 10 million solar mass black hole experience about the same tidal force between their head and feet….”

Does that mean they would experience the same gravitational “attraction” in both places?

No, it means that the gravitational gradient is the same in both cases, because the radius of the supermassive black hole is about 10^6 km or more, compared to about 6x10^3 km for Earth.


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Quote:
No, it means that the gravitational gradient is the same in both cases, because the radius of the supermassive black hole is about 10^6 km or more, compared to about 6x10^3 km for Earth.


it would be more valid to say that it is the amount of mass
and its density inside the black hole that determines the amount of gravity that he would feel , rather than any measure of distance.

because the density of mass would be a changing inside a
black hole.
the balck hole would be able to pull more
mass inside a given event horizon as it squeezes some energy out of some of its mass.
which increases the diameter of the event horizon because of the increase in mass and the increase in the density of
the mass inside the black hole.


I thought this was normal mainline science hoopla myself.

Quote:
The radius of the central object must be less than 17 light-hours, because otherwise, S2 would collide with it. In fact, recent observations[17] indicate that the radius is no more than 6.25 light-hours, about the diameter of Uranus' orbit. However, applying the formula for the Schwarzschild radius yields just about 41 light-seconds, making it consistent with the escape velocity being the speed of light.


yes , no thing can travel faster than the speed of light... laugh

so it must be a really tiny supermassive black hole
so that it fits in with the hoopla I suppose.



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Originally Posted By: redewenur
No, it means that the gravitational gradient is the same in both cases, because the radius of the supermassive black hole is about 10^6 km or more, compared to about 6x10^3 km for Earth.


And that was the bit I was trying to get Bill S to realize that you therefore end up with a time gradient on you. So when you talk about observers and time it can be the same observers foot versus his head smile

Extrapolation while useful can sometimes be very misleading which is why it is often interesting to look at the thing on every scale micro, normal and extremely large.


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Ok, I found the information about the lifetime of a micro black hole. From The University of Oxford

Originally Posted By: University of Oxford
‘Astronomical black holes are so massive that their evaporation rate is negligible. In contrast, mini black holes are hot: unimaginably hot. The core of our Sun is at around 15,000,000 degrees Kelvin - to get close to the temperature of a mini black hole you would need to add another 42 zeroes.’

‘What this incredible temperature means is that mini black holes of tiny mass ‘evaporate’ into the far, far colder space around them almost infinitely fast. Their expected lifetime is around one octillionth of a nanosecond – so that they pop out of existence again almost as soon as they are created.’


Just about as I thought a micro black hole would have an extremely short life time.

And now that Orac has mentioned it I recall reading a book about black holes where they made an imaginary voyage to several black holes. At the most massive one that they knew of at the time they could orbit comfortably at just above the Event Horizon. If I recall correctly that was at least one place where I got what I know about time at the Event Horizon. What I remember about it is what I used in my first reply to Bill S. And once again I acknowledge that my understanding is very limited since I got it from popular explanations that probably oversimplify it.

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Originally Posted By: University of oxford
‘What this incredible temperature means is that mini black holes of tiny mass ‘evaporate’ into the far, far colder space around them almost infinitely fast. Their expected lifetime is around one octillionth of a nanosecond – so that they pop out of existence again almost as soon as they are created.’

Originally Posted By: Bill
Just about as I thought a micro black hole would have an extremely short life time.

Again warnings about making these sorts of things as facts and trying to put them in your "IN" box they are not facts they are extrapolations hence the words they used were THEIR EXPECTED LIFETIME.

So you understand the problem (http://en.wikipedia.org/wiki/Micro_black_hole)

Quote:
The net result is the black hole loses mass (due to conservation of energy). According to the formulae of black hole thermodynamics, the more the black hole loses mass the hotter it becomes, and the faster it evaporates, until it approaches the Planck mass. At this stage a black hole would have a Hawking temperature of TP / 8π (5.6×1032 K), which means an emitted Hawking particle would have an energy comparable to the mass of the black hole. Thus a thermodynamic description breaks down. Such a mini-black hole would also have an entropy of only 4π nats, approximately the minimum possible value. At this point then, the object can no longer be described as a classical black hole, and Hawking's calculations also break down.

What you got and described is the part in RED what you left out was the warning part in BLUE the calculations break down.

It is not anywhere near a fact that a micro black hole would have an incredibly short lifetime it is an extrapolation that leads to an expectancy that it is probably so. I can't even imagine what confidence level a scientist would put on that.

When I drop a ball the laws of gravity extrapolate the ball falls smoothly until it reaches the center of the earth ... see the problem? You need to understand what bounds exist for your extrapolation and they are only valid within those bounds.

That is why Einstein wondered if micro black holes were actually stable and were what an electron is and why you don't have different size electrons. Any bigger size would evaporate very quickly back to the standard electron size, his work is actually rather interesting.

So there are many possibilities open for micro black holes because our understanding is incomplete and if you like that they would last a very short time that is fine but it is not the only answer possible and can not be treated as a fact. I don't have an answer or even a preference on the answer.

You only have to look at Superconductivity to see the dangers in making the sort of leaps on extrapolation of the sort you have done.

Last edited by Orac; 08/15/14 05:59 AM.

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Quote:
And that was the bit I was trying to get Bill S to realize that you therefore end up with a time gradient on you


I believe that pointing to a gradient of gravity and now
time will only tend to exacerbate the degree of mental comprehension.

Bill S has asked a valid question in my opinion and does not need to have invalid responses directed at him as a reply to his question.

ie...

Quote:
Does that mean they would experience the same gravitational “attraction” in both places?


the offered answer ..

Quote:
No, it means that the gravitational gradient is the same in both cases, because the radius of the supermassive black hole is about 10^6 km or more, compared to about 6x10^3 km for Earth.


"No" is correct

however to explain the why in such a manner is incorrect.
it would be extremely and most highly inaccurate to claim
that the gravitational gradient might possibly be the same
in both cases and base that claim only on the radius of each
case in question.

Bill S like myself seems to be more of a observer who is trying to understand why people think the way they think
about physics even if he does not support the way and ways
that the people think about physics.

the diameter of the mass at the center of a black hole may
be as large as the orbit of Uranus or larger or it may be really small.

but the gravity gradient produced by any black hole is
due to the amount of mass and the density of the mass
inside the black hole , therefore any equal distance from
any two black holes in the universe would not
be presented with the same gravity gradient or attraction from any direction.

likewise any two unequal distances from
any two black holes in the universe would not
be presented with the same gravity gradient or attraction from any direction.

the universe is not uniform when talking about gravity.
there are no two places in the universe where gravity is
exactly the same even if the two places are only a centimeter
apart.

we can add that there are no two galaxies that are exactly the
same anywhere in the universe.

to that we add that there is absolutely no "same" gravity gradient anywhere in the universe.



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I think I left out something in my statement up above. That would be: "If micro black holes exist or can exist". The actual fact is that there is no clear consensus that they can exist. If we don't even know whether they exist we can't really be sure how they would work. That comes right down to the need for a theory of quantum gravity. As it is I think that the best guess is that they would have very short life times.

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And now we are in complete agreement Bill smile

We don't know there isn't a boundary condition that means that micro black holes can't exist.

So just like our ball that extrapolates to hit the center of the earth and runs into the ground the black hole mathematics may hit a condition that restricts there size to a range.

There is also a lesson in that for Bill S original question despite fanciful answers many scientists may like to spruik.

Last edited by Orac; 08/16/14 03:04 AM.

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I thought one of you might have crossed the boundary and actually started to think but it appears not so lets see if we can prompt some thinking.

There is a really good article posted by Assaf Shomer in 2007 which was not a novel work but summed up the status of play with black holes and gravity and remains valid today.

http://arxiv.org/pdf/0709.3555v2.pdf

Really all you need to concern yourself with is the conclusions if you can't follow the technical detail.

Quote:
It seems that gravity is a low energy effective field theory description of something else that is not a quantum field theory


So if gravity is not a quantum field theory then the extrapolation of Quantum theory that predicts micro black holes is totally invalid (Some may want to ponder the implication for quantum gravity but that is another story).

So now you have a series of nasty choices in an attempt to answer the question Bill S posed.


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Originally Posted By: Orac
if gravity is not a quantum field theory

And that bit right there opens a huge can of worms. If gravity is not a quantum field theory then we have the huge problem that the universe seems to be divided into 2 mutually incompatible domains, which nevertheless have to work together. Building that bridge is going to be a huge problem.

And I'm not going to bet either way on the matter, although I have a tendency to think that a quantum view of gravity will be developed.

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Not incompatible but different remember gravity is still showing as an effective field theory just not a quantum one but a very low energy one acting on a very different definition of time.

That insight itself is somewhat interesting.

Now go back to the black hole and think what it would mean smile

Now you possibly understand why quantum gravity is becoming a little like string theory.

Last edited by Orac; 08/21/14 10:48 AM.

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