In celebration of #sciencesunday trending on Google+, we have the original LOLCAT.
Originally shared by Vic LeFaber
In celebration of #sciencesunday trending on Google+, we have the original LOLCAT.
Originally shared by Vic LeFaber
I have never been sure about what Schrödinger was trying to tell me about with this one, its deeply upsetting and perplexing.
An excellent series, I agree, Rashid Moore (one was featured today on ScienceSunday : is it in your circles?). I hadn’t seen the cat episode, haha. Perhaps as they say in that short clip, Schrödinger was a dog person, Suhail Manzoor.
ScienceSunday is a Google+ Page, Rashid Moore, that you can follow, and any science post can be directed to it using the #sciencesunday . It so happens that I joined the curating team today.
Haha, added another customer 😉 I’m marketing science as a side profession, it appears! Thanks Rashid Moore Any new poems to share?
It is a crime to enclose a so cute cat !
That’s a real problem Bruce Harding!! , we seek it live AND dead
LOL, exactly Fadia Lekouaghet ! I wonder how many people spotted that? 😉
You! for sure 😉
Martin Sacha or Fadia Lekouaghet will have to explain a Schwarzchild sphere to this non-astrophysicist.
More precisely, the Schwarzchild radius for an object of a given mass determines the volume to which that object must be compressed in order to become a black hole. Larger than that and gravitational forces are insufficient to overcome quantum pressures due to the Pauli exclusion principle, which forbids particles (neutrons in this case) from occupying both the same space and the same quantum state. At formation, the Schwarzchild radius is also the event horizon, the altitude below which the escape speed exceeds the velocity of light.
Once a star has collapsed into a black hole, it can continue to accumulate more mass due to infalling matter, so the event horizon can increase in size. A black hole also loses mass due to Hawking radiation, in which case the event horizon shrinks, although for stellar-mass black holes the rate of mass loss is extremely tiny.
So the Schwarzchild radius is strictly dependent on some mass to volume ratio? Is that a fixed value?
Yes, for nonrotating bodies (angular momentum makes things a little more complicated) the necessary radius is 2Gm/c^2, which is dependent only upon the object’s mass, G and c being constants. I love how fairly complicated concepts in general relativity and quantum mechanics sometimes reduce to such terribly simple equations!
It’s also awesome that the Rs for our sun is about 2.5 km, and that for the earth is essentially 0 (I’m guessing some small number?).
A little less than a centimeter, if I’m using Google Calculator right:
((5.9742e24 kg * 2 * G) / c) / c = 8.87134507 millimeters
… nifty, it also works to just type in “(mass of earth) * 2 * G / c^2”. And it does the dimensional analysis for you too. I’m kind of digging Google Calculator.
Argh… don’t you all know cats are an evil joke on the human race?
yes u r right……………..
Martin Sacha Charley Kline Woot! Thanks for the detailed info on the Schwarzchild radius, and the distinction from the event horizon.
I’m trying to wrap my monday brain around this 🙂 Given that you only get a black hole when light can no longer escape, it’s obvious that an object must compress beyond the SR before it turns into a black hole – you said as much. I’m having a bit of trouble, though, with figuring out the circumstances in which the SR and the EH can get different, afterwards. Or is the SR simply no longer particularly relevant after the change?
They aren’t different. Sorry, I think I was confusing because of the way I think of the two concepts, and should have thought out how I phrased my comment before posting it. Think of the Schwarzchild radius as a pre-existing condition: any mass has a particular SR, whether it’s a black hole or not. Compressing the entire mass inside the SR creates certain solutions to the field equations of general relativity which is what creates the singularity and the black hole.
Once it’s formed, it has an event horizon; the sphere at which the mass’s escape velocity equals c. Again because of relativistic effects, all sorts of strange things happen there; to a distant observer time stops, inside the EH there are swaps of space and time dimensions, and so on.
What I failed to make clear was that as the black hole gains mass, the EH grows because the SR is growing due to the mass increase. They are indeed the same thing, but the literature tends to refer to the event horizon because of the physical properties of the black hole, something which doesn’t exist before the mass forms into one.
I hope we are not burdening you with questions, Charley Kline , as I have one more. Once formed, is a black hole permanent or can it lose sufficient mass or undergo fragmentation to allow release of its contents at some time? If not, the number of black holes should be increasing.
Rajini Rao , your question is at the heart of the so called Black Hole War (ISBN 0316016411). In a nutshell, Quantum Theory makes firm predictions on the “Conservation of Information”. But the indomitable Stephen Hawking was able to show that Black Holes can destroy information. Matter falling into a black hole, according to Hawking is radiated back into the Universe. This sounds contradictory. The radiation itself is called Hawking’s radiation. So in that sense, A black hole does decay over an extremely long periods of time. But it caused a problem in that, If a black hole “chewed” up a Mr. Darwin and then spewed out what is essentially “random” radiation due to “random” nature of Quantum Mechanics, then the net information content of the Universe is not conserved and we are all in a big doo-doo. Fortunately, an equally indomitable Mr. Leonard Susskind stepped in to save the day.
To be honest, this is where I lost the plot. Its on my to-do list though because Susskind might be on to something here. I say this mostly because my own pet interest is Information Theory and Complexity and to answer if Complexity is conserved. BTW, if you have oodles of time, look up Susskind on Youtube. He has a few month’s worth of Modern Physics courses thats quite easy on the head.
Suhail Manzoor , thanks for that thought provoking reply. I had heard of Hawking radiation and it’s now put in context. But, why do you say that the net information content of the universe is conserved? I thought that pertained only to matter. If the entropy of the universe is increasing, and entropy is inherently lower in information (i.e., disordered), then the latter cannot be conserved. I will seek out those Susskind videos and attempt to digest them, thanks!
Rajini Rao , I suffer the bane of Entropy I tell you. I can never escape that demon! Its all down to Herr. Schrödinger’s mystical wave equation actually. Besides, doing evil things to poor cats, its also a profound statement about information. Everything has a wave function that evolves in space and time according to some operator. The weird thing is, this function is time reversible. So what that actually means is that if we have two particles that collide and re-collide in the a myriad of ways, like the dance of Siva, you can play it back and you get to where you started. This is actually one of the fundamental principles of the QM – information is conserved. But a black hole has other ideas via Hawking’s radiation because apparently, its not (or is as per Susskind’s Holographic Principle. Mind you, at this point I should mention Gerard ‘t Hooft who is actually a hero to me of sorts. It was ‘t Hooft and Susskind who took on Hawking and seemingly won), you can lose reversibility.
We are in some sense talking here about Shannon Uncertainty – aka, Entropy because Hawking’s original study was primarily about the Charley Kline ‘s own “Schwarzchild Sphere” being the measure of a black hole’s Shannon Uncertainty. So with matter falling into a black hole, does the information (see how I have switched the terms around) content increase or decrease? Do we lose time reversibility of Schrödinger’s wave function? If you are a relativist, you would nod you head, if you are a particle physicist, you are reaching for a baseball bat!
The universe should have a wave function right? So in that sense, the evolution of the universe as a whole should be time reversible. Its the time reversibility we call the conservation of information. This is true regardless of what Shannon’s uncertainty has in store for us. I think 😉
Suhail Manzoor answered your question, Rajini, way better than I could have, and funnier, too! Beyond the Coding Theorem, Shannon kind of loses me. But I do get that to preserve the direction of entropy, the black hole has to “store” information somewhere, and there’s no place for that storage other than the flat surface area of the event horizon itself.
I was just going to return to something a little more classical-physics-y and point out that Hawking radiation is actual energy radiating out of a black hole, and that energy has to come from somewhere, and that’s where the mass loss comes in. Eventually, the black hole “evaporates” due to the mass loss, vanishing in a final burst of energetic particles. But only the tiniest black holes, the so-called “primordial” ones created at the Big Bang, are small enough for that process to run to completion in anything even close to the age of the Universe.
My, this is an interesting thread. Kind of over my head, but I try to keep up 🙂
Two more questions, then. First off, how come that the amount of Hawking radiation is inversely proportional to a black hole’s mass? I’d assume that, since a larger singularity has a larger event horizon surface, there should be a higer probability of virtual particles emerging exactly on the border.
And, second, if Hawking radiation is basically half of a virtual particle pair blazing off, shouldn’t the other particle get sucked into the black hole, thus INcreasing it’s mass?
Johan De Meersman , it should be noted that Hawking radiation is still unproven so be sceptical about it. The odd thing about it is that if he is right, (and don’t forget Bekenstein who hit upon the idea originally) then black holes have a temperature. This temperature is defined by the equations that govern “black body radiations”. You will find that this relationship has an inverse relationship between temperature and mass.
The whole situation arises because at a very fundamental level the laws of thermodynamics must hold regardless of whether you are talking about black holes or virtual particles.You have to realize that if Hawking and Bekenstein are correct, then black holes are radiating energy. This is proof positive that the rabbit hole is quite bizarre place when you marry Quantum Mechanics and General Relativity.
There are two ways you can think about this radiation. One is to think about it in the manner described by Martin Sacha or you can think of it as a quantum tunnelling process. I prefer the latter model.
Personally, I don’t think any of this is settled science because we are in the realm where general relativity has to be reconciled with Quantum theory. That is by no means a settled matter.
Oh, wow, I totally should have mentioned Jacob Bekenstein! I feel bad, now.
It is really weird how sometimes the science leads the weirdness by the nose. Black hole thermodynamics leads to the notion of a temperature, which leads to black body radiation, which leads to mass loss in something that’s hard to imagine not growing without bound. The closer one gets to that uncomfortable zone between General Relativity and Quantum Mechanics, the more this kind of weird thing happens, mostly because it’s so radically different from the realm where neither GR nor QM effects are noticeable.
Nicely put Charley Kline , couldn’t have said it better myself.
but I like kittens!!!