0848: "3D"

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Re: 0848: "3D"

Postby ramparts » Tue Jan 18, 2011 10:29 pm UTC

Kyro wrote:
gmalivuk wrote:
Kyro wrote:Someone please tell the string theorists that dimensions are orthogonal by definition.
No, they're not.

If we're talking about something like curved manifolds (which we probably are when talking about space-time), you only need local homeomorphism to Euclidean space when talking about the dimension of that manifold.

And coordinate bases need not be orthogonal even when describing completely flat Euclidean space. Any set of linearly independent vectors can give a coordinate system for the space they span, which has a dimension equal to the number of vectors.


I should probably shut up before I realize I don't know what I'm talking about...

Even if you use non perpendicular vectors as the basis of your coordinate system, you still draw parallel grid lines. Therefore the dot product of the axes is 0. Therefore the dimensions are orthogonal.

Well, that simply isn't right. If you have non-perpendicular basis vectors, by definition their dot product is non-zero. So you wouldn't draw parallel grid lines. Doesn't stop them from being linearly independent, of course :)

It seems to me the notion of manifolds would suggest very large other dimensions, not small ones. I don't think the process is reversible.

The problem is this all vanishes when curvature comes into the picture, hence the qualifier "local." Think of the surface of a sphere: you can draw latitude and longitude vectors that are, at any given point, orthogonal to each other, but due to the curvature of the surface you have no unambiguous way of comparing a longitude vector at one point to a latitude vector at another.

On the topic of small dimensions, the easiest way to visualize this (as I think someone brought up earlier in the thread) is to imagine you're a tiny (and two-dimensional) ant on the inside surface of a cylinder. The cylinder has two dimensions, which you can look at as one going around and one going backwards and forwards. If the cylinder is really, really thin, you'll barely even notice the "going around" dimension - as far as you're concerned, you're living in a one-dimensional surface where you can only go back and forth. The second dimension is "curled up," much like the compact dimensions in string theory and other higher-dimensional physics theories. As you can see, there's nothing funny going on, much less anything in the definition of a manifold which precludes such a situation.

In response to Kyro (who posted after I started writing this), I hope that helps you understand why very small dimensions aren't necessarily nonsense!

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Re: 0848: "3D"

Postby gmalivuk » Wed Jan 19, 2011 2:08 am UTC

Kyro wrote:I should probably shut up before I realize I don't know what I'm talking about...
Yes, you probably should have.

Even if you use non perpendicular vectors as the basis of your coordinate system, you still draw parallel grid lines. Therefore the dot product of the axes is 0.
No. There is such a thing as a non-orthogonal basis. <1,1> and <1,0> form one for R2, for example, and their dot product is most certainly not 0. Parallel grid lines, sure, but not perpendicular.

Even if we're just sticking with vector spaces, you can have perfectly well-defined dimension without specifying *any* inner product on the space.

Kyro wrote:I'm not saying there aren't more than 4 dimensions, just that describing the other dimensions as "too small to observe" is nonsense.
Funny, then, how people who know what they're talking about disagree, isn't it?
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Re: 0848: "3D"

Postby Lucia » Wed Jan 19, 2011 3:42 am UTC

rcox1 wrote: We all seem to accept that the center of our universe has a black hole that stops time.

:shock: We what? And there's a centre of the universe?
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Re: 0848: "3D"

Postby Tyrannosaur » Wed Jan 19, 2011 3:53 am UTC

Lucia wrote:
rcox1 wrote: We all seem to accept that the center of our universe has a black hole that stops time.

:shock: We what? And there's a centre of the universe?

yeah news to me too....
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Re: 0848: "3D"

Postby gmalivuk » Wed Jan 19, 2011 3:58 am UTC

Even giving the benefit of the doubt and assuming "galaxy" was meant instead of "universe", saying any black hole "stops time" demonstrates a serious lack of understanding of how black holes work.
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Re: 0848: "3D"

Postby jpk » Wed Jan 19, 2011 5:30 am UTC

nitePhyyre wrote:
Felstaff wrote:
MacFreek wrote:I wonder if a real 3D movie is possible...What would that entail?

  • Stage
  • Curtain
  • Actors

Ya, but that setup tends to have really, really crappy special effects.


Only for people with no imagination. But I guess that's why they make 3D movies, isn't it?

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Re: 0848: "3D"

Postby ijuin » Wed Jan 19, 2011 7:41 am UTC

Pfhorrest wrote:
ijuin wrote:It has been known since James Maxwell's 1873 theory on electromagnetism that heat = infrared = electromagnetic wave = light.


The first identity there is a common misconception. Infrared light is no more "heat" than any other frequency of light, or for that matter, any other manner of energy transfer. Infrared just happens to be the predominant frequency of black-body radiation (i.e. radiation due to temperature) for objects at temperatures common on the surface of the Earth. A blue star is much hotter than any infrared-luminous human body or piece of metal left in the sunlight or what-have-you, but the bulk of its heat is transmitted at frequencies much higher than infrared.

The knowledge that really matters, which the first cave man to ever stand in the sun on a cold winter day (or the shade on a hot summer day) realized, is that light conveys heat. The neat thing about lasers is they let you send a bunch of light all in one direction instead of scattering it around, letting you convey all the heat you can muster with much more precision than just making a big light bulb. But the frequency of that light is much less important; in fact, a visible-light laser puts out much more heat per photon than an infrared-light laser does.

While it is true that any electromagnetic wave can transmit heat, practice shows us that, for materials and temperatures common on Earth's surface, infrared is more efficiently absorbed--i.e. you will get more heating of a target object per joule output of your laser. Wavelengths longer than a few meters will simply diffract around human-sized objects, visible light will reflect more than infrared for the majority of materials, ultraviolet tends to break molecular bonds more than it accelerates molecular vibration, and most materials are at least partially transparent to X-rays and beyond. Furthermore, molecules are most easily excited by electromagnetic frequencies just above their natural resonance frequencies at the current temperature--this is why microwaves in a microwave oven excite water molecules.

Anyway, now that I'm done being pedantic, you are right that most frequencies of laser would deliver a not-insignificant amount of heat, and I apologize for oversimplifying the analogy. My meaning was to convey that the people who first developed lasers were already aware that such a device, if made sufficiently powerful and efficient, could be used as a "heat ray".

gmalivuk wrote:Even giving the benefit of the doubt and assuming "galaxy" was meant instead of "universe", saying any black hole "stops time" demonstrates a serious lack of understanding of how black holes work.

General Relativity tells us that, all else being equal, the stronger a gravitational field, the slower time passes within the strong part of the field. Thus, when you get arbitrarily close to the event horizon of a black hole, time does indeed stop (or rather, gets arbitrarily close to stopping, such that the remainder of the universe's lifespan will be infinitesimally brief). However, this only holds for the space near the event horizon--when you are light-years away, the time dilation is so small as to be irrelevant. This holds true for any black hole, not just supermassive ones at the cores of galaxies.

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Re: 0848: "3D"

Postby ramparts » Wed Jan 19, 2011 9:57 am UTC

ijuin wrote:General Relativity tells us that, all else being equal, the stronger a gravitational field, the slower time passes within the strong part of the field. Thus, when you get arbitrarily close to the event horizon of a black hole, time does indeed stop (or rather, gets arbitrarily close to stopping, such that the remainder of the universe's lifespan will be infinitesimally brief). However, this only holds for the space near the event horizon--when you are light-years away, the time dilation is so small as to be irrelevant. This holds true for any black hole, not just supermassive ones at the cores of galaxies.


Erm... no. It's true that a distant observer will see time "slowing down" as someone falling towards a black hole gets arbitrarily close to the event horizon, but that doesn't mean time is actually stopping: in fact, the observer falling towards the black hole notices absolutely nothing special as he crosses the horizon. He reaches the singularity in finite time.

If you're familiar with the math of GR, you can either look at (e.g.) radial geodesics infalling into black holes (and notice nothing important happens at the horizon) or switch to something like Eddington-Finkelstein coordinates where the apparent singularity at the horizon vanishes (both of which are essentially doing the same thing).

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Re: 0848: "3D"

Postby Brian-M » Wed Jan 19, 2011 10:32 am UTC

phillipsjk wrote:In a movie theater setting, the "fixed position" is assumed to be the center of the theater. The distance between the cameras is chosen with "average" eye spacing in mind. For most people there will be error. You can limit this by limiting the audience viewing angle.

I disagree with the bolded text anyway. Assuming everybody sits perfectly still is not a valid assumption.

I have to concede that sitting to one side can screw things up for a 3D movie. I hadn't thought about that, because I usually try and sit near the center any time I watch a movie, because even 2D movies can be awkward to watch from an angle.

But the average eye spacing is irrelevant. The end result of different eye spacing is that everything looks a little closer or further away from you than it does for the "average" viewer. The size of the screen and your distance from it will also affect how you see the film in the same way that different eye spacing does, so it's not a big deal.

And while it may not be valid to assume that everyone sits perfectly still, the images they see on the screen while moving are no different than what they'd see if they'd remained still. So my statement that stereoscopic images are effectively the same thing as 3D images viewed from a fixed position remains valid

phillipsjk wrote:Then there is the problem where the audience may not be focusing on the object you expect in the scene. The practice of blurring objects you don't want people to look at is likely headache-inducing for the people focusing on the wrong object (Even with the approximately infinite view distance).

Annoying as it is, I don't see how that has anything to do with 3D. They do it in 2D movies too.

phillipsjk wrote: In closing, not all of us have good depth perception: if I want to see distance without my glasses, I need to physically move my head a few inches. I have seen a video were a bird (of prey) with working stereo vision still moved its head for route planning (navigating an obstacle course).

Ah, I see. I wonder, if circular polarizing glasses were available with prescription lenses, would you still have a problem with it?

I'm not arguing that 3D is great, or even a good thing. I'm just arguing that it's not necessarily a bad thing, nor necessarily a second-rate form of presentation. Sure some people may not be able to enjoy it, particularly people with impaired vision in one eye, or for other reasons, but that doesn't mean it can't be an enjoyable experience for the majority of movie goers.

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Re: 0848: "3D"

Postby Brian-M » Wed Jan 19, 2011 10:34 am UTC

gmalivuk wrote:
gmalivuk wrote:
Tyrannosaur wrote:And do you know how long relativity was around before it was testable?
A decade or so.
Actually, General Relativity was only around 4 years before the famous eclipse observations confirmed at least part of it, and the precession of Mercury was known even before GR came out and gave exactly the same results as had been observed.

But there have been questions raised about the accuracy of Eddington's observations. It's been suggested that the margin of error in his results was too great to actually distinguish between Relativity and Newtonian physics at that time, and so his claims to have confirmed relativity were premature.

(Not that it really matters at this point.)

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Re: 0848: "3D"

Postby phillipsjk » Wed Jan 19, 2011 11:15 am UTC

Brian-M wrote:Ah, I see. I wonder, if circular polarizing glasses were available with prescription lenses, would you still have a problem with it?


My problem with the current crop of "3D" movies is the dishonest marketing, not the technical aspects. The limitations are well-known. I can probably fit most polarizing glasses over my prescription glasses (even if the fit is awkward). I didn't enjoy the last stereoscopic movie I went to because the motorized seat designed to simulate a roller-coaster bumped me around too much.

I suspect the term "3D" is used because it sounds high tech. Stereoscopic images have been around for about 100 years.

When I put on my prescription glasses and see the real world in "3D", the thing I find most impressive is not annoying pop-up effects, but the leaves on trees: each at a slightly different distance and angle.
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Re: 0848: "3D"

Postby gmalivuk » Wed Jan 19, 2011 12:51 pm UTC

Brian-M wrote:
phillipsjk wrote:Then there is the problem where the audience may not be focusing on the object you expect in the scene. The practice of blurring objects you don't want people to look at is likely headache-inducing for the people focusing on the wrong object (Even with the approximately infinite view distance).
Annoying as it is, I don't see how that has anything to do with 3D. They do it in 2D movies too.
Because when we're looking at something in 3D, we expect what we're focusing on to be, y'know, in focus. If it's not, our eyes will keep working at it to make it so. When it's all in 2D and clearly on a flat screen a set distance away, there's not this same eye strain. Instead, our eyes are just drawn toward whatever's in focus, as the cinematographers intended.
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Re: 0848: "3D"

Postby phlip » Wed Jan 19, 2011 1:02 pm UTC

Brian-M wrote:
phillipsjk wrote:Then there is the problem where the audience may not be focusing on the object you expect in the scene. The practice of blurring objects you don't want people to look at is likely headache-inducing for the people focusing on the wrong object (Even with the approximately infinite view distance).

Annoying as it is, I don't see how that has anything to do with 3D. They do it in 2D movies too.

The problem here is that the brain sees 2D and 3D as different beasts. It's related to a concept known in CG circles as "photorealism" - the aim in CG isn't to make something that looks real, it's to make something that looks like a photo of something real. (Well, "photorealism" also covers other aspects like realistic style and attention to detail, but it's the looking-like-a-photo thing that's relevant here.)

Take a candle. If you have a candle IRL and look at the flame, it's small and distinctly yellow. But take a photo of a candle, and it'll blow out to white, with a flare, making it significantly larger. But despite this, it still looks "real". Meanwhile, make a CG candle with a small yellow flame, and you can make it look identical to a real candle, but it'll just look wrong and fake. Because your brain is parsing it as a photo, and expecting the flare, and compensating for it... even if it's not flared. It's the same as those old optical illusions where you have two guys the same height on the screen, but one looks in the background, and one's in the foreground, and the one in the background looks huge, and the one in the foreground looks tiny, because your brain is compensating for perspective. Or when there are two pixels the same colour, but one looks like it's in shadow, so your brain corrects for that and it looks a lot lighter than the other. Your brain automatically corrects for things it's expecting to be there that will distort the image... and given enough exposure to photographs and movies and the like, that will include compensating for things like flares and bloom. So, in order to look real, the CG candle flame needs to be white, and flared.

So you get this weird situation where real camera workers try hard to avoid artefacts in shots, like film grain, blooming, focal blur, motion blur, lens flare (or, at least, try to avoid them when they're not being intentionally added for stylistic reasons), but CG camera coders try hard to add all those artefacts in, just so that the watcher's brain will accept it as being real.

The problem comes with 3D... when you're watching a 3D movie, it doesn't seem to trigger the same responses. At least for me. My brain sees a 3D movie and thinks it's looking at something real, not a photo... and so it doesn't apply the same filters, and doesn't have the same expectations. Which means things like lens flare can totally take you out of the movie, and things like motion blur or focal blur, or even common cinematic techniques like crossfades, just end up being confusing and headache-inducing. For 3D CG they just need to find the right balance - figure out which filters need to be kept and which ones need to be dropped in order to make it look "right"... and that will take quite a while (and 3D will need to move from "gimmick" to "staple" before significant effort will be commonly made). But for live-action they don't have much choice... they're going to have all those artefacts regardless. So 3D is going to continue to be the blurry unreal headache-inducing mess for a while, until it becomes commonplace for a while, and everyone's brain is able to re-develop its filters to be able to recognise "oh, 3D-looking thing but with blur and film grain" as a 3D movie and respond appropriately. Because once that happens, then the real experimentation with the format can be done.

Hopefully we'll get to that point before the novelty wears off and its current gimmick status catches up to it.

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Re: 0848: "3D"

Postby The Mighty Thesaurus » Wed Jan 19, 2011 1:47 pm UTC

Lucia wrote:
rcox1 wrote: We all seem to accept that the center of our universe has a black hole that stops time.

:shock: We what? And there's a centre of the universe?

Yes, but everyone in it is all alone.
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Re: 0848: "3D"

Postby Tyrannosaur » Wed Jan 19, 2011 2:46 pm UTC

The Mighty Thesaurus wrote:
Lucia wrote:
rcox1 wrote: We all seem to accept that the center of our universe has a black hole that stops time.

:shock: We what? And there's a centre of the universe?

Yes, but everyone in it is all alone.

Did you know the population of our universe is 0?
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Re: 0848: "3D"

Postby SlyReaper » Wed Jan 19, 2011 2:49 pm UTC

Tyrannosaur wrote:
The Mighty Thesaurus wrote:
Lucia wrote:
rcox1 wrote: We all seem to accept that the center of our universe has a black hole that stops time.

:shock: We what? And there's a centre of the universe?

Yes, but everyone in it is all alone.

Did you know the average population of our universe is 0?

FTFY
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Re: 0848: "3D"

Postby Tyrannosaur » Wed Jan 19, 2011 8:04 pm UTC

SlyReaper wrote:
Tyrannosaur wrote:
The Mighty Thesaurus wrote:
Lucia wrote:
rcox1 wrote: We all seem to accept that the center of our universe has a black hole that stops time.

:shock: We what? And there's a centre of the universe?

Yes, but everyone in it is all alone.

Did you know the average population of our universe is 0?

FTFY

yes but 0 as an average implies 0 as total.
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Re: 0848: "3D"

Postby phillipsjk » Wed Jan 19, 2011 8:08 pm UTC

I would argue, but the person who corrected you neglected to include units.
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Re: 0848: "3D"

Postby gmalivuk » Wed Jan 19, 2011 8:39 pm UTC

Tyrannosaur wrote:yes but 0 as an average implies 0 as total.
Or (asymptotically) infinite denominator. If the universe is infinite, but the number of people finite, then the average population per [any unit of space] is obviously 0.
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Re: 0848: "3D"

Postby Brian-M » Wed Jan 19, 2011 9:55 pm UTC

phillipsjk wrote:Stereoscopic images have been around for about 100 years.
That's an understatement. They've been around for 172 years, according to Wikipedia. [/nitpick]

phlip wrote:The problem comes with 3D... when you're watching a 3D movie, it doesn't seem to trigger the same responses. At least for me. My brain sees a 3D movie and thinks it's looking at something real, not a photo... and so it doesn't apply the same filters, and doesn't have the same expectations. Which means things like lens flare can totally take you out of the movie, and things like motion blur or focal blur, or even common cinematic techniques like crossfades, just end up being confusing and headache-inducing.

I'll have to keep an eye out for that next time I see a 3D film, I don't watch very many of them. The last one I saw was Alice In Wonderland, and that was a mix of live-action and CG.

phlip wrote:Hopefully we'll get to that point before the novelty wears off and its current gimmick status catches up to it.

The novelty of 3D has worn off more than once, but keeps coming back. So even if the current craze does wear off before it's perfected, there's always next time.

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Re: 0848: "3D"

Postby phillipsjk » Thu Jan 20, 2011 5:31 am UTC

gmalivuk wrote:
Tyrannosaur wrote:yes but 0 as an average implies 0 as total.
Or (asymptotically) infinite denominator. If the universe is infinite, but the number of people finite, then the average population per [any unit of space] is obviously 0.


Is the universe infinite though? The observable universe is only about 24-30 billion light-years across.

Edit: what is an order of magnitude between friends?
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Re: 0848: "3D"

Postby NumberFourtyThree » Thu Jan 20, 2011 7:56 am UTC

For those questioning whether 3D movies add enough to a movie experience to be worthwhile, does it seem to have good applications in video games? How will people feel about 3D in a couple months when the Nintendo 3DS comes out (which has the added benefit of not needing glasses).

phillipsjk wrote:
gmalivuk wrote:
Tyrannosaur wrote:yes but 0 as an average implies 0 as total.
Or (asymptotically) infinite denominator. If the universe is infinite, but the number of people finite, then the average population per [any unit of space] is obviously 0.


Is the universe infinite though? The observable universe is only about 12-15 billion light-years across.


According to inflation the universe is larger than the observable universe. We then raise the question of whether something can be real yet be unobservable and unable to cause anything in anything we can observe. What exactly does it mean to be "real"?

By the way, that conversation earlier reminds me about there being a passage explaining that the universe has 0 population in the Hitchhiker's Guide to the Galaxy.
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Re: 0848: "3D"

Postby phlip » Thu Jan 20, 2011 8:06 am UTC

NumberFourtyThree wrote:By the way, that conversation earlier reminds me about there being a passage explaining that the universe has 0 population in the Hitchhiker's Guide to the Galaxy.

I'm pretty sure that whole tangent started with that HHGTTG reference, so yeah...

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Re: 0848: "3D"

Postby ijuin » Thu Jan 20, 2011 11:50 am UTC

ramparts wrote:Erm... no. It's true that a distant observer will see time "slowing down" as someone falling towards a black hole gets arbitrarily close to the event horizon, but that doesn't mean time is actually stopping: in fact, the observer falling towards the black hole notices absolutely nothing special as he crosses the horizon. He reaches the singularity in finite time.

If you're familiar with the math of GR, you can either look at (e.g.) radial geodesics infalling into black holes (and notice nothing important happens at the horizon) or switch to something like Eddington-Finkelstein coordinates where the apparent singularity at the horizon vanishes (both of which are essentially doing the same thing).

http://en.wikipedia.org/wiki/Gravitatio ... e_dilation

The deeper you are in a gravitational energy well, the more time dilates. Consider that GPS has to compensate for the fact that time on Earth passes several parts per billion more slowly than time in geosynchronous orbit. Now, increase the depth of the gravity well. As the depth of the well approaches infinity, so does the ratio of time dilation.

You are correct that the person falling into the black hole would perceive time as flowing normally--but that is because his perceptions are equally dilated. He would meanwhile see the rest of the universe speeding up.

Let us perform a quick thought experiment. You have a set of triplets. One performs a close flyby of a massive black hole. The second stays at home within our "stationary" reference frame. The third flies a course that, from the perspective of the second, has equivalent acceleration to the first but stays away from any deep gravity wells. According to the concept of gravitational time dilation, when the fist and third triplet return to meet the second, the first one will have aged less than the third one.

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Re: 0848: "3D"

Postby Pfhorrest » Thu Jan 20, 2011 6:59 pm UTC

ijuin wrote:
ramparts wrote:Let us perform a quick thought experiment. You have a set of triplets. One performs a close flyby of a massive black hole. The second stays at home within our "stationary" reference frame. The third flies a course that, from the perspective of the second, has equivalent acceleration to the first but stays away from any deep gravity wells. According to the concept of gravitational time dilation, when the fist and third triplet return to meet the second, the first one will have aged less than the third one.

I'm not sure that this works quite like you think it does, because acceleration and gravity are equivalent. Say triplets 1 and 3 both head off in straight lines away from Earth, decelerate to their respective destinations, and then fly back to Earth. One of them flies in a straight line to a relatively empty part of space; the other flies in a straight line toward the nearest black hole. They both travel at the same speed under the same initial acceleration. But it will take less acceleration for the first to slow down, stop, and turn back in empty space, than it will for the third to slow down from falling into the black hole, stop while hovering above the black hole, and then accelerate back away from it toward Earth. You could make the first one accelerate away proportionally harder in the first place, thus requiring more acceleration to stop and turn around at the endpoint, with both of them returning to Earth at the same velocity and thus requiring the same amount of acceleration to stop, and thus undergoing the same amount of acceleration overall, but I'm pretty sure you'd get the same amount of time dilation for both of them in that case.

Maybe a better example would be twins travelling from Earth to some distant destination, both along geodesics besides the initial acceleration and terminal deceleration; but one travels the shortest geodesic he can find (i.e. as "straight" as possible through mostly empty space), and the other plots a course that slingshots him close around a black hole before sending him toward their destination, and lets say it works out that he doesn't gain or lose any speed from this slingshot effect, just changes vector, so there's no difference in their terminal deceleration. The first twin arrives first of course, taking the shorter path and both travelling at the same speed; but when the second twin arrives, and they meet up, how do their ages compare? My intuition thinks you're right and the one who passed by the black hole will be younger, but I have a suspicion that there's still something in the math to negate that...
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gmalivuk
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Re: 0848: "3D"

Postby gmalivuk » Thu Jan 20, 2011 9:58 pm UTC

Pfhorrest wrote:acceleration and gravity are equivalent
In some ways, sure. But hovering just above the ground on Earth for a year will sure has hell result in a different amount of time going by than accelerating at an apparent 1g for a one year proper-time round trip where you actually move from and back to some initially comoving point here in our solar system.
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Re: 0848: "3D"

Postby ifer » Sat Jan 22, 2011 11:43 am UTC

Technically, it IS a 3-D movie regardless of string theory, since time is a dimension. This explanation requires less geekery, though.

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Re: 0848: "3D"

Postby sportsracer48 » Sun Jan 30, 2011 1:54 am UTC

I said brains! All they have there are string theorists.

Randall agrees. I know because he said that once.


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