Hard Light Productions Forums
Off-Topic Discussion => General Discussion => Topic started by: Enigmatic Entity on October 30, 2009, 03:29:24 am
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I randomly thought up this the other day; what do you think would happen? :)
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can't open...
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If m= infinity then it would create a blackhole wouldn't it?
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Physics suggests bending, however, you cannot have half of infinity, and a curve which is infinitely long would be an apparent line at any single point, so I'd say, visually, nothing would happen.
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As already stated, there are several conceptual issues that arise from the uses of infinity here.
You've got this apparatus located an infinite distance away from an object with infinite mass, which in itself is quite perplexing. An object with infinite mass would imply a black hole of infinite size, thus the entire universe as depicted would lie within an event horizon. That said, I don't think it should matter (in practice) whether the grav-field were infinitely strong or not, if it is uniform as you show it to be.
Also, I'm not sure by how you show it, but is the length of the beam from pin to the right side infinite or finite? You show an endpoint which implies that it is finite, but a distance marker below it showing infinity. :confused:
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That's not right. It's not even wrong.
Seriously, there are so many infinite and ideal things in your thought experiment that it's not even of academic interest.
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I can't make heads or tails of it. :P
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Assume a massless, frictionless grad-student.
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With all these infinities, you'd think some of them might get...
/me puts on sunglasses.
Twisted. :cool:
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YEAHHHHHHHHHHH
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With all these infinities, you'd think some of them might get...
/me puts on sunglasses.
Twisted. :cool:
Oh, so they will be like a campaign that takes an infinitly long time to finish? :p
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Assume a massless, frictionless grad-student.
Is that possible? I thought the egos of most graduate students would distort the space-time continuum to create an effective mass....
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:wtf:
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Infinity is a bull**** "number" that can't be used in real-world applications, ever, unless it's an intermediate value that gets removed promptly.
A situation with impossible values will yield an impossible result...
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You are ignorant of math if you call infinity 'bull****'.
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*_*
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Infinities in physics are generally the product of mathematical singularities, which are in turn generally the product of incomplete theories (as probable in the case of black holes and the big bang.)
However, the universe could easily be spatially infinite, which is quite a practical infinity with real-world applications.
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Stuff
In this example, infinity is used as a value. One cannot just replace a number with infinity except in the context of the most basic of arithmetic functions (+ and x).
Besides that, the situation in the OP is flawed because it's impossible in the real world and has a solution that is also impossible in the real world -- visualizing such a thing is futile.
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Is that possible? I thought the egos of most graduate students would distort the space-time continuum to create an effective mass....
Theoretically yes, but we're typically so out of touch with our surroundings that spacetime actually forgets to bend.
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Stuff
In this example, infinity is used as a value. One cannot just replace a number with infinity except in the context of the most basic of arithmetic functions (+ and x).
Besides that, the situation in the OP is flawed because it's impossible in the real world and has a solution that is also impossible in the real world -- visualizing such a thing is futile.
Have you done calculus?
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A situation with impossible values will yield an impossible result...
Is it really impossible, or just out of scope of finite beings :D
I guess the whole universe becomes impossible, if you deny infinities.
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If you deny the concept of infinities in reality, you deny the reality of superconductors, superfluids, black holes, and numerous other things.
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Including ourselves :P
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If you deny the concept of infinities in reality, you deny the reality of superconductors, superfluids, black holes, and numerous other things.
Supeconductors have not infinite conductivity (or zero resistance for that matter), superfluids have also not zero viscosity. Black holes represent a singularity in current physics, as in we don't really know what physics to apply within the Schwarschild radius, but that does not automaticvally mean that there's really somthing inifnite in them.
TL;DR In the real world nothing is infinite (the universe maybe, but we don't know)
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Fair enough, I'll concede the point for black holes, though I will stick with my belief that a singularity does exist within them until physics demonstrates otherwise.
As for superconductors, I ask what is the electrical resistivity if it is not zero? I've never found information suggesting that, but perhaps you have better information than myself.
Same question for superfluids/viscosity.
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Superconductors have very low but still non-zero resistance (although Wikipedia falsely states otherwise), as to which effect causes the small residual resistance is still a topic of research IIRC. But since there's still no definitive theory for superconductors, this is no surprise.
For superfluids the situation is similar.
The name singularity for the center of the black hole, comes from the fact that it represents a mathematical singularity when you try to calculate physical properties at the center of the black hole, leading to a theoretical point with infinity density, infinitely bent space-time, etc. Nowadays physicists call it still the singularity, but it's properties are basically unknown.
*waits for Herr Doktor to lecture us all in detail about it* ;)
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Do you have a source on that claim that superconductors have non-zero resistance?
Given the upper limits for the resistance of superconductors I found during research, it's a little hard to believe that such a low resistance could even be measured.
It's like with quantum teleportation - it's not guaranteed to happen instantly, but iirc there is no proof that it takes more than zero time.
After thinking about arguments for some time I believe that question comes close to religion - we only have a finite accuracy to observe the universe, and as a result can neither prove nor disprove the physical and real relevance of infinities.
(I thought about using Real numbers as an argument against that claim, but you could just evade that by saying that the universe is divided into discrete parts - making this argument useless :/ )
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If you deny the concept of infinities in reality, you deny the reality of superconductors, superfluids, black holes, and numerous other things.
Supeconductors have not infinite conductivity (or zero resistance for that matter), superfluids have also not zero viscosity. Black holes represent a singularity in current physics, as in we don't really know what physics to apply within the Schwarschild radius, but that does not automaticvally mean that there's really somthing inifnite in them.
TL;DR In the real world nothing is infinite (the universe maybe, but we don't know)
Everything you say here is correct. :nod:
Except the TL;DR version. In the real world there is plenty that is infinite: the amount of energy required to accelerate through lightspeed, for instance.
(Although I guess you'd probably say that is a mathematical value, and the fact that it is infinite is why it can't happen in reality...)
Actually, I'm just gonna stick with my original hunch that what you say here is correct. Infinity is very useful in mathematics, and in that sense is very useful for describing reality, but no measurable quantity can be infinite except possibly for things like the number of stars in an open flat universe or the size of said open flat universe.
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no measurable quantity can be infinite except possibly for things like the number of stars in an open flat universe or the size of said open flat universe.
Or the extent of human stupidity :D
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Finite and quantifiable. :p
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Boy, he really sucked the fun out of that reference. :p
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It's easy to make up examples of infinities in real life. Anything that is discontinuous (or more generally, unstable) will have infinite derivatives, for example.
As for infinities that are actually relevant in some way, that depends on the context and is probably a matter of opinion as well.
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Do you have a source on that claim that superconductors have non-zero resistance?
Nothing easily accessible on the net, since last time I've read about the topic was in research papers a few years back. But to prove I'm not making this up ;)
http://www.nist.gov/eeel/electromagnetics/magnetics/superconductor-characterization-2004.cfm
Scroll down to the 3d plot where they measure the resistance in nano-ohms.
Except the TL;DR version. In the real world there is plenty that is infinite: the amount of energy required to accelerate through lightspeed, for instance.
Read that again and think what you typed here ;)
My point is that current cosmology holds that the universe contains a large but finite amount of energy (including matter), therefore any hypothesis that involves an infinite amount of energy (or an infinitely large force, speed, etc) is damned to remain impossible... even in theory.
As for derivatives, they are a mathematical concept and are as much real as the mean value of something. If I define it exists according to my definition, but that doesn't' mean I can touch it.
Plus, can you give me a real world example of a true discontinuity?
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Isn't a Prandtl-Glauert singularity an example of that? (The vapor cloud produced by a sudden pressure drop in a shockwave)
http://en.wikipedia.org/wiki/Prandtl-Glauert_singularity (http://en.wikipedia.org/wiki/Prandtl-Glauert_singularity)
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Except the TL;DR version. In the real world there is plenty that is infinite: the amount of energy required to accelerate through lightspeed, for instance.
Read that again and think what you typed here ;)
Read my post again.
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Except the TL;DR version. In the real world there is plenty that is infinite: the amount of energy required to accelerate through lightspeed, for instance.
Read that again and think what you typed here ;)
Read my post again.
Sneaky edit ;) But thanks for the clarification, and in that context you're right.
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Um, that edit was up before you posted anything. It happened less than three minutes after the post went up.
What's with people lately and claiming I sneak edited my posts? :confused:
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Do you have a source on that claim that superconductors have non-zero resistance?
Nothing easily accessible on the net, since last time I've read about the topic was in research papers a few years back. But to prove I'm not making this up ;)
http://www.nist.gov/eeel/electromagnetics/magnetics/superconductor-characterization-2004.cfm
Scroll down to the 3d plot where they measure the resistance in nano-ohms.
To quote from that article:
When the combination of field and temperature are low enough, the sample is in the superconducting state and the resistance is zero
(emphasis added)
The same can be seen at the 3D-graph - in the superconductivity state it's plotted as (indistinguable from) zero. (at a maximum of 0,5 tesla or ~7 Kelvin)
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As for derivatives, they are a mathematical concept and are as much real as the mean value of something. If I define it exists according to my definition, but that doesn't' mean I can touch it.
Anything we can talk about will involve definitions made up by us. As I said, what is physically relevant is a matter of context. A lot of basic things like velocity and acceleration are essentially derivatives.
Plus, can you give me a real world example of a true discontinuity?
That depends on what you mean by real world. The height of your desk surface is discontinuous at its edges. Of course, at the molecular level it's discrete and finite, but it could also be argued that the continuous model of this has more relevance to the real world. :p
As for instability, any kind of turbulence in fluid flow, such as breaking water waves, is like this. In this case, the map from the initial state of the system to the final one is discontinuous. Whether that operator is physically meaningful or not is up to you.
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Finite and quantifiable. :p
Einstein would disagree with you. :P
Einstein >>>>>>>>>>>>>>>>>>>>>>>>> You
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He didn't know what I do.
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Finite and quantifiable. :p
Einstein would disagree with you. :P
Einstein >>>>>>>>>>>>>>>>>>>>>>>>> You
This should be anathema to anyone who actually works with science. The prominence of one's personality matters exactly zilch to science.
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As for infinities, aren't the only thing we're sure about being 'infinite' is quite specifically singularities, and - those things kinda break general relativity anyway?
Though there's some interesting quantum physics on blackholes.
A Singularity having 0 mass and extreme gravity is something that can't exist in our universe based on our current understanding with accepted theories.
Everything else is supposed to be finite, no matter how mind boggling big it is~
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Black holes do have mass, and presumably once we have quantum gravity the 'singularity' will be gone.
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Black holes do have mass
It has a lot of mass, but that mass is also hyper hyper hyper dense.
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Um, yes, it's infinitely dense, thus the singularity.
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Are you sure? Where does that infinite density come from? Doesn't general relativity halt the collapse when it's (almost) reaching the event horizon?
To tell you the truth, I don't know of any scientific theory that says anything about the structure of the inside of the event horizon. Not even the general theory of relativity.
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Doesn't general relativity halt the collapse when it's (almost) reaching the event horizon?
Not remotely.
The event horizon is an imaginary line at the Schwarzschild radius of the black hole. It marks the point at which even light cannot escape the black hole, but if you were falling into the black hole you wouldn’t be able to tell when you’d crossed it.
The entirety of the black hole’s mass is contained within the Schwarzschild radius. It is impossible to hold a constant radial position beyond the event horizon, because that would require a velocity greater than the speed of light, so the mass collapses inexorably inward to an infinitely small, infinitely dense point (the singularity).
General relativity actually tells us quite a bit about what happens inside the horizon. The only thing it doesn’t tell us is what happens at the actual point of the singularity.
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The event horizon is an imaginary line at the Schwarzschild radius of the black hole. It marks the point at which even light cannot escape the black hole, but if you were falling into the black hole you wouldn’t be able to tell when you’d crossed it.
Well, as the event horizon marks the point where time dilation reaches infinity, for an OUTSIDE (meaning: us) observer, it takes an infinite amount of time, meaning it will never cross the event horizon from our POV.
It is impossible to hold a constant radial position beyond the event horizon, because that would require a velocity greater than the speed of light
Ehm.. no.
The Schwarschild radius is defined via the escape velocity, not via a velocity to hold a constant position.
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Ah, reference frames. Yes, the external observer would see infalling objects appear to freeze at the event horizon, at least until they’re redshifted out of view. That doesn’t mean they actually stay there.
Within the event horizon the escape velocity is greater than the speed of light. That means that even light is forced to fall toward the center of the black hole.
Is that clearer?
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Given that our outside universe did only exist for a finite time, and our observation exists only for a finite time, it does mean, yes, for us the collapse stops.
That means that even light is forced to fall toward the center of the black hole.
That conclusion simply doesn't follow. You are assuming the mass is concentrated in the center. How do you know that? What theory does say that?
I don't study physics, so I honestly expect that you could show me such a theory.
But just to say this for everyone: I have used lot of my free time to learn about modern (and not so modern) physical theories and hypotheses, so you don't have to try to teach me the basics. Don't tell me the pop science, tell me the real one :/
[edit]
Added an emphasis.
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The hole actually only has mass, charge, and angular momentum, so technically it doesn't have 'infinite density' in that one could divide the mass by the volume defined by the Schwarzchild radius and get a volume. Nonetheless, the singularity is an infinitely dense point.
It is impossible to hold a constant radial position beyond the event horizon, because that would require a velocity greater than the speed of light
Ehm.. no.
The Schwarschild radius is defined via the escape velocity, not via a velocity to hold a constant position.
Ehm, yes. You're wrong, she's right. There are no stable orbits inside the event horizon. In fact there aren't any within 3 Schwarzschild radii of the center.
That conclusion simply doesn't follow. You are assuming the mass is concentrated in the center. How do you know that? What theory does say that?
No, that assumption is not being made.
You can treat the inside of the event horizon as a homogeneous distribution of mass or as a point source. It doesn't matter. Light must fall towards the center.
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This is a good place to start. (http://en.wikipedia.org/wiki/Gullstrand%E2%80%93Painlev%C3%A9_coordinates) If you want to make a formal study of it, Taylor and Wheeler’s Exploring Black Holes is a text that does not require graduate-level study to understand, though it assumes an undergraduate-level understanding of special relativity and calculus.
The Schwarzschild metric is invalid beyond the event horizon, but the coordinates described in the article I linked have no discontinuity at the Schwarzschild radius and describe the interior of the black hole. Using these coordinates it’s fairly simple to show that any mass that crosses the event horizon will be inexorably pulled inward, like a boat going over a waterfall. Given sufficient time all the black hole‘s mass will indeed be concentrated at the center simply because there’s nowhere else for it to go.
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so technically it doesn't have 'infinite density' in that one could divide the mass by the volume defined by the Schwarzchild radius and get a volume.
And what density does it have non-"technically"?
The original claim was "Um, yes, it's infinitely dense", where does that claim come from?
Ehm, yes. You're wrong, she's right. There are no stable orbits inside the event horizon.
Says who? Results from what theory?
I don't want to calculate the minimum required orbital velocity myself, but after checking the orbital calculator (http://home.att.net/~ntdoug/UCM2.html)
There seems to be a constant factor:
"escape velocity" x 0,7 = "orbital velocity"
So, light could indeed reach the required speed to maintain a stable orbit.
Of course this (probably wrongly) assumes classical physics
You can treat the inside of the event horizon as a homogeneous distribution of mass or as a point source. It doesn't matter. Light must fall towards the center.
Why?
@Rian
Thx for the book name, that sounds interesting. (Though it might be a little hard to read it in english :/ )
For the coordinate system... yes, it will be pulled inward, but not within finite time by an outside observer, while it is already a black hole according to an outside observer (that's something I didn't explicitly state before, probably a mistake).
So, for an outside observer, something can (and will) have a finite mass distributed in a non zero space, while still counting as a black hole, and to get back to the original statement:
Um, yes, it's infinitely dense, thus the singularity.
It's not infinitely dense.
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Again, the singularity is indeed infinitely dense because it has no volume.
That's the whole point: it's a singularity.
Says who? Results from what theory?
General relativity.
Your argument is predicated on the fact that you don't know relativity and can't perform the necessary math. For instance:
So, light could indeed reach the required speed to maintain a stable orbit.
Light always travels at the same speed, in all reference frames.
It's not infinitely dense.
The singularity has no volume and thus by definition is infinitely dense. THIS IS WHY IT IS A SINGULARITY.
The black hole has mass, charge, and angular momentum, but no other properties (the no-hair theorem.) The singularity itself has infinite density.
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Of course this (probably wrongly) assumes classical physics
You can’t assume classical physics inside or even near a black hole.
General relativity states that there are no stable orbits inside a black hole. It also predicts that the black hole’s matter will be concentrated in a single central singularity. While this cannot be conclusively proved without actually entering the black hole, the predictions of general relativity are unambiguous here. This has already been explained two or three times in various terms.
For the coordinate system... yes, it will be pulled inward, but not within finite time by an outside observer,
Because an outside observer cannot see inside the event horizon, the perspective of an outside observer is irrelevant. If you want to know what happens inside the black hole, you go to a coordinate system that actually works inside the black hole. One example is described in the article I linked.
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We can argue about this all day but until you do the math you won't fully understand it. I highly suggest learning general relativity and working out a black hole example.
The take-home point for now is that a black hole contains a singularity, which is a point where theory breaks down: an infinitely dense (but finitely massive) entity.
Also, there are no stable orbits within the event horizon; once inside it is impossible to avoid intersecting the singularity.
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To finish this:
It's been news to me that effects inside of black holes (=inside of the event horizon) are considered to be describable accuratly by general relativity, as it starts to conflict with quantum dynamics. As such, literature I read presented those results only as a hypothesis, never as an applicable theory.
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You did not completely misunderstand what you read.
General relativity is required to describe the properties of extremely massive bodies. Black holes are thus largely described by GR, which can make many useful statements about their properties.
Quantum mechanics is required to describe the properties of extremely small bodies. Singularities are very small.
The reason the singularity is a singularity is because QM and GR are incompatible, and attempting to use them together results in a divide by zero error.
If we had quantum gravity, there wouldn't be a singularity. But this doesn't change the fact that black holes are primarily described using the mathematical tools of general relativity, which make a number of predictions about the interior of the event horizon. The math breaks down at the singularity itself.
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And the final answer?
Celestial bodies such as black holes are studied as they are not fully understood. No one here has all of the necessary data to close this argument. ;)
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Here's an application you may find interesting; modelling the orbits of particles close to a black hole, using general relativity. To quote the site,
In Newtonian gravitation, an orbit is always an ellipse. As the gravitating body becomes more massive and the test particle orbits it more closely, the speed of the particle in its orbit increases without bound, always balancing the gravitational force. For a black hole, Newton's theory predicts orbital velocities greater than the speed of light, but according to Einstein's Special Theory of Relativity, no material object can achieve or exceed the speed of light. In strong gravitational fields, General Relativity predicts orbits drastically different from the ellipses of Kepler's laws. This page allows you to explore them.
http://www.fourmilab.ch/gravitation/orbits/ (http://www.fourmilab.ch/gravitation/orbits/)
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Well that killed my phone. :lol:
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Well that killed my phone. :lol:
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DOUBLE KILL!