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Physics Gone Wild: Doggy Style
Walter
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Registered User regular
I was reading up on Newton today (Wikipedia is a terrible thing for procrastinators) and came across Newton's Cannonball. If you haven't heard the story, Newton came up with the idea of placing an object in orbit by realizing that if he shot a cannonball from a mountain at just the right speed the ball would continuously "fall" over the edge of the earth.
It reminded me of an awesome thought experiment I read about some time back. First, you have to assume that the universe is infinite and matter is spread uniformly throughout (rather than all matter just concentrated in our corner of the universe). This is entirely possible and from what I understand there is plenty of evidence that this is true, but lets not debate it. Cosmology is so obtuse and I don't want this thread to become a big bang vs. brane vs. infinite universe arguement.
Imagine a cube so small you can only fit a few hundred atoms inside. Realize that there are an infinite number of these cubes but a finite number of ways atoms inside the cube can be arranged. You can have different numbers of atoms in each cube, different kinds, and different positions but there is a limit to the way the atoms can be placed inside.
Since there are only so many configurations but an infinite number of cubes, eventually they have to start repeating and you get cubes of space that are EXACTLY the same, down to the atomic level. If you think about it, no matter how large these cubes are they eventually have to repeat in infinite space...even cubes as large as our solar system. This means that somewhere very far away there is another one of me typing this exact same post instead of studying for my test tommorow.
Anyone else find this stuff interesting or are you all just posing as nerds to get bitches?
It reminded me of an awesome thought experiment I read about some time back. First, you have to assume that the universe is infinite and matter is spread uniformly throughout (rather than all matter just concentrated in our corner of the universe). This is entirely possible and from what I understand there is plenty of evidence that this is true, but lets not debate it. Cosmology is so obtuse and I don't want this thread to become a big bang vs. brane vs. infinite universe arguement.
Imagine a cube so small you can only fit a few hundred atoms inside. Realize that there are an infinite number of these cubes but a finite number of ways atoms inside the cube can be arranged. You can have different numbers of atoms in each cube, different kinds, and different positions but there is a limit to the way the atoms can be placed inside.
Since there are only so many configurations but an infinite number of cubes, eventually they have to start repeating and you get cubes of space that are EXACTLY the same, down to the atomic level. If you think about it, no matter how large these cubes are they eventually have to repeat in infinite space...even cubes as large as our solar system. This means that somewhere very far away there is another one of me typing this exact same post instead of studying for my test tommorow.
Anyone else find this stuff interesting or are you all just posing as nerds to get bitches?
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As far as we can tell, it's not. I couldn't give you a number off the top of my head, but a scientist could probably give you an estimate as to how much mass is in the universe. It's a huge number, but the odds of there being an exact copy of you on another planet are even huger.
I think the most exciting or interesting topic from the ones I listed above is the missing matter in the universe. According to Newtonian physics, the stars at the furtherst point in the galaxies should be spinning slower since there is less gravity being exerted upon them, from what we observe. We can infer this arguement because we understand that: using our Sun as our basis, we observe Pluto orbiting our sun slower than Mercury. Newton laws of gravity are based on the observations he made back in the 17th century. However, what has been discovered is that these far out stars at the edges of galaxies are moving at the same speed as the stars in the center. There is no logical explanation for this, there isn't enough gravity or matter accountable to answer this, even with variable gravity or MOND(sp?). Scientists still don't know why it happens.
Technically, we can only account for approx. 4% of all the matter in the universe, the other 96% is "missing". Based on our observations, there is not enough gravity or matter in all of the universe to keep any of it together. The planets and galaxies should be in utter chaos, in complete disarray. Since there isn't enough gravity to keep any of it together, our Newtonian physics is obviously flawed. We don't understand how it is being kept together, what is keeping it together, or what the other 96% of the universe is made up of. Scientists think either our physics is wrong, or it's dark matter, or both.
So if dark matter does exist, it has to be on Earth as well, and in huge amounts. It doesn't interact with normal matter either, and so far is unobservable.
Based on all of that, and your thought experiment about the cubes. If you where to see the cubes in action, you'd only have 4% of all the matter accounted for. Inside these cubes, between the spaces of the cubes, and the majority of these cubes would be completely empty and devoid of all matter that we can observe. For the sake of arguement, if you limited it to the amount of cubes you could have, and put all the mass into complete cubes, then out of 100 cubes, only 4 of those cubes would have any matter in it at all. The other 96 cubes would be completely empty and you would have no knowledge why or how any of it is being held together, or why the 96 cubes exist at all.
And the different dimension things are spiffy. If you start going into debates about it, everything and anything has had an action and consequence has happened differently in some form or another in another dimension. That means Napolean has won and was never exiled, or Hitler won, or even the dinosaurs never went extinct. It all becomes strange yet interesting. Bizarro worlds.
Edit: damn it, I just realized you where just looking for other interesing theories. How about the use of Nuclear weapons in space travel to approach near speed-of-light velocity?
On the black screen
If you allow for the possibility of neutrinos having rest mass, it can go far in closing this gap (though it depends on the amount). If you allow for relativistic mass to influence gravity, it easily closes the universe (relativistic mass of photons, relativistic mass of neutrinos, etc.)
Honestly, I've never seen any reason why relativistic mass wouldn't influence gravity, nor have I seen any experiments to verify or deny this.
Consider the number: .101100111000111100001111100000...
Even though its decimal representation contains only 0s and 1s and is infinite in length, the series of digits 0110 appears only once in it. Similarly, even if the universe were infinitely large, there's no guarantee that any particular portion of space will be repeated anywhere else.
There's no guarantee, but it would be likely. The odds of that number string being some regular and formulaic string that precludes repeats of digit strings is far less likely than it being truly random.
There are problems with using neutrinos though: neutrinos are very light. It is believed that they move at the speed of light, and since they are so light, they would've spread out evenly amongst the universe, before they could be cold enough to come together in clumps. If this is true, the dark matter made up of neutrinos would've been unable to make the large galactic objects we see. Also, these galaxies appear to be made of large amounts of dark matter which is not fast enough to escape from these galaxies, meaning that neutrinos are believed to only make up a small portion of accountable dark matter. The solar neutrinos we have been able to detect have a very low density, and we haven't been able to detect relic neutrinos that have a rest mass energy in higher density.
So technically speaking, if we account for neutrino's having a rest mass shouldn't it only provide a very small amount of mass that could influence gravity?
I could be all wrong though, my knowledge on neutrinos isn't up-to-par and I had to wiki that information just to re-familiarize myself on the subject.
Isn't Pi's digits random? or at the very least non-repeating?
Maybe. But then maybe our perceptions of gravity are predicated on the convenient coincidence that, in normal matter, the presence of the as yet uncredited sub-atomic particles that are responsible for gravity scale proportionally to our current formula. Where as perhaps neutrinos, and other questionably legal quantum phenomena, actually emit gravitic influence disproportionate to their mass.
What if
man
It's been many years since my cosmology and particle days, but IIRC, there are a fuckton of neutrinos, and they're very weakly-interacting. In fact, some have speculated that the reason that we only see very high-velocity neutrinos is because at lower velocities, their interactions are just too rare and small to be detected with what we can currently do.
They don't need to clump up to have gravitic influence in their broad vicinity. Neutrino emitters (like stars) would have a field of neutrinos that fell off at 1/r^2. If the Big Bang thing is roughly correct, we'd also see a universal field of neutrinos that was denser around the universal origin.
I'm not an expert in this by any means, but I remember wondering about this when I was in school, and never could find a good answer.
Well, it's mainly academic, since as far as I understand the universe doesn't meet the description of infinite matter evenly spread.
As to whether it would be probable (though not guaranteed) that you would have a duplicate somewhere in such a universe, answering such a question would require more knowledge of cardinality and different infinite sets and series than I have.
I'll agree about possibly not being able to detect lower velocity neutrinos because of either rarity (relic big bang born neutrinos) or we just don't have the proper instruments.
I'm not an expert either, espically when it comes to discussing neutrinos: I begin to get lost in the half-spins, right and left types, the higher and lower velocities and densities, how it is clumped into dark matter, etc... It all becomes a bit too technical for a brain to handle in one sitting. I like theory more.
I think we all agree that based on what we can observe, measure and perceive, we obviously are lacking in knowledge of what is holding the universe together as well as, what is the rest of matter in the universe?
Anyone take a look at the Globus Cassus? That thing looks amazing, yet terrifying at the same time. I can't see humans every constructing that thing for earth (because we would destroy earth), but I can see us applying that concept to another planet....without life on it.
For those that didn't see it:
A group of astronomers were tracking the stars in the galactic core and found that they orbitted very quickly around a point with eliptical orbits. Yet nothing was detectable at that exact position. They also observed a blast of radiation as the black hole ripped apart and spit out some celestial object. So not only is there one of these bad boys in our galaxy, they're in every other galaxy as far as we can tell. And larger galaxies tend to physically "eat" smaller ones.
In fact, given a string of n digits, no matter how large n is, you will find that string in the decimal expansion of Pi.
I'd imagine that n has to be finite, or at least denumberably infinite. So it's not really no matter how large. Right?
There's a difference between "arbitrarily large" and infinite. But I'd imagine he means "any finite string, no matter how large".
Also, kakos, is this just surmised, or has it actually been proven? Because it makes sense, but I wonder if we actually know it for certain.
Well, if he had just said "arbitrarily large" I would have known what he meant. :P
http://www.angio.net/pi/bigpi.cgi will search up to the first 200,000,000 digits of pi.
My birthday DDMMYYYY appears 31 million places in. The next number is 3, DDMMYYYY4 does not appear in the first 200 million places. But I suppose that its appearance is inevitable given the properties of irrational numbers. You're talking about impossibly slight probabilities, sure, but you're throwing the dice an infinite amount of times.
Not really. Earlier on I gave an example of a non-repeating infinite decimal string which contains only zeros and ones, for example.
If you select each digit 0-9 at random, then as the number of digits you choose approaches infinity then the probability of any finitely large decimal string being contained within your number approaches one. That doesn't mean that any irrational number has all possible decimal strings in it, though.
False. Even with just one atom in the cube, there's an infinite number of places to put the atom.
Or like 3 eyes. Or shit, it would be even creepier if he was ever so slightly taller, so that if we met it wouldn't be like 'whoah that's me' it would be 'holy fuck it's almost me'
Do we have any way of proving that space isn't quantized? That is, can you really place an atom anywhere, or does space have some sort of grid system that particles have to adhere to?
Actually, no we don't. There's Planck length, but that doesn't mean that everything has to adhere to a grid-like placement. I think most people just take space to be continuous because it's easier to deal with mathematically
Even so, even if everything did adhere to a grid-like system, the OP can't conclude that there's a copy of him somewhere, even given infinite particles and cubes. He can only conclude that there exists some cube's placement which is repeated. Not all of them.
You're right, non-repeating non-terminating does not techinically require that it uses all 10 digits let alone lend itself to being a decent random number generator. But I can't help thinking your 010 001100 000111000 pattern is too constrictive to be appropriately compared to a naturally occurring irrational like pi, which seems more functionally random.
And on the other hand, Pi can appear to work to a trillion places, and successfully contain every integer between 0 and 1,000,000; that still won't be proof either way.
Is it really unknowable? I don't care for that at all. Who's big idea was it to measure the number of squares you can fit in a circle anyway?
I'm not certain about that, as quanta tend to make what we think of as continuous values discrete at extremely small scales. I could be wrong about position, though I know that energy, time, and (as a result), velocity quantize.
I dunno. There are an infinite number of variations on that pattern alone.
There are so many infinites here that I really have no idea what the probability of a randomly selected irrational number being any particular way are.
As far as I know, it is not yet known for certain if time (or position, since they are largely the same thing) are quantized. Its fairly likely, since so much other stuff seems to be. Nothing about quantum time has been proven yet, so it remains an open question.
Neutrinos are probably not dark matter. They likely contribute to the effect, but last I heard there definately has to be something else that has a larger influence.
As far as I know, it is not yet known for certain if time (or position, since they are largely the same thing) are quantized. Its fairly likely, since so much other stuff seems to be. Nothing about quantum time has been proven yet, so it remains an open question.
Neutrinos are probably not dark matter. They likely contribute to the effect, but last I heard there definately has to be something else that has a larger influence.[/quote]
Well, I know that the current upper-bound for neutrino rest mass isn't enough to close the equation, but I've never seen any real discussion of whether or not relativistic mass has gravitic effect. I mean - photons bend in gravitic fields, and have relativistic mass. Shouldn't they exert the famous "equal and opposite" gravitic reaction?
I mean - I know that the whole timespace warping thing is a conceptual way to get out of this mutual gravitic interaction, but I don't really see that just because this is a useful conceptual model why it would necessarily be authoritative when it comes to Newton's second law.
Well, I know that the current upper-bound for neutrino rest mass isn't enough to close the equation, but I've never seen any real discussion of whether or not relativistic mass has gravitic effect. I mean - photons bend in gravitic fields, and have relativistic mass. Shouldn't they exert the famous "equal and opposite" gravitic reaction?
I mean - I know that the whole timespace warping thing is a conceptual way to get out of this mutual gravitic interaction, but I don't really see that just because this is a useful conceptual model why it would necessarily be authoritative when it comes to Newton's second law.[/quote]
You're right, relativistic mass does have a gravitational effect.
In fact, due to mass-energy equivalence, energy itself can produce a gravitational field. The energy of the Sun is enough to cause a gravitational effect that was thought to be a small planet inside Mercury's orbit before Einstein explained it.
Are you sure-sure? Because when I was in school, I went around asking that question to every professor I could find for years, and never got a straight answer. In studying the neutrino thing and universal closure, the implicit assumption was that relativistic mass had no gravitic influence.
Are we talking high school or college?
All mass will create a gravitational field (according to general relativity), but with a photon it's immeasurably small. Here's a fairly short explanation.
College. I was a physics/ math major. I don't know that the photon thing is generally accepted - there are a lot of photons (4 K background, etc), even though the individual contribution is minor. If neutrinos' relativistic mass were allowed for gravitation, cosmologists wouldn't be so hung up on finding the rest mass (since the energy of neutrinos is well known).
Also, relativistic mass influences of massive objects would be a huge influence on the closure of the universe. AFAIK, they do not take these into account when calculating these models.
I saw that and I nearly shit myself at how terrible and beautiful the concept was. I also (finally) got a handle on what a black hole really was: an object of such intense mass that it folded space and light to impossible degrees. The "hole" is in fact the well of gravity created by the "invisible" matter.
And I loved the one physicist who wanted to die by getting fired into a black hole; that's hardcore.
As for the 'scopes being powerful enough, I thought all they did was put an infrared filter on the lens to wash out all the crap at the center of the universe? I could be wrong.
As far as I know, neutrino mass was never accounted for because:1) it was believed that a neutrino had no mass at all, 2) it was believed that if the combined contribution of all the neutrinos in the universe exceeded 50 electronvolts the universe would fold upon itself. However, I believe recently(I'm not sure when, but it was this year), neutrinos where found to have an electronvolt of .03electronvolts, and combined are far below the 50 limit. As well as the existence of neutrinos that have a non-zero mass.
I think cosmologists are hell bent on finding relic bigbang born neutrinos which technically should be littered out in the universe(everywhere), who's rest mass density is larger than the ones we already can observe, like solarborn neutrinos. That or discovering and defining what dark matter really is.
I thought that they discovered the supermassive blackhole at the center of our galaxy by detecting the huge amounts of radiation it was emitting, as well as the speed of the objects approaching the blackhole. It really is awesome if you think about how a blackhole is both the creator and destroyer of galaxies.
Perhaps by taking this seemingly simpler approach, you are actually complicating things. For example, as we approach the atomic and subatomic levels, we add the complexities of quantum physics such as the Heisenberg Uncertainty Principle and a potentially uncollapsed wavefunction which means we can't even begin to think of asking whether the arrangements in two different cubes are identical.
However, as we increase the complexity of the matter in the cube, it may become more likely that we will arrive at identical outcomes. For example, if we have two atoms in a cube that will bond to form a molecule, the atoms in one cube don't have to be in identical locations in the second cube, they just have to be close enough to each other in each cube to bond. Perhaps the biggest issue is that of chaos since the example above is a deterministic system governed by the fundamental forces that allows for small changes in the initial conditions.
If I'm understanding your argument correctly, it seems to reduce to an absurdity. What if we were to take a look at the universe from the rest frame of one of these neutrinos. In that case we would see massive objects such as stars travelling close to the speed of light which would make their relativistic mass absurdly large. Additionally, the relativistic mass is direction dependent which makes it seem unlikely to be directly applicable to a gravitational effect. I'll have to think about this more, but I think you are somehow 'double counting' the relativistic mass. That is, relativistic mass may manifest itself in some other way in general relativity, such as the warping of space time, so that some equivalence principle holds.
I suspect there's reciprocity/ equivalence in both frames, as relativistic mass is a scalar product dependent on relative velocity ( m1*m2*f(v) ). So the gravitational force is the same in both frames. On the other hand, I never got a good handle on general relativity, and acceleration makes relativity a lot harder and often pretty squirrely.
Honestly, I can't even think of a good way to formulate an experiment to measure this effect, though I think it's of critical importance for something like cosmology.