Skip to content
  • Categories
  • Recent
  • Tags
  • Popular
  • World
  • Users
  • Groups
Skins
  • Light
  • Cerulean
  • Cosmo
  • Flatly
  • Journal
  • Litera
  • Lumen
  • Lux
  • Materia
  • Minty
  • Morph
  • Pulse
  • Sandstone
  • Simplex
  • Sketchy
  • Spacelab
  • United
  • Yeti
  • Zephyr
  • Dark
  • Cyborg
  • Darkly
  • Quartz
  • Slate
  • Solar
  • Superhero
  • Vapor

  • Default (No Skin)
  • No Skin
Collapse
Code Project
  1. Home
  2. The Lounge
  3. Quantum Mechanics

Quantum Mechanics

Scheduled Pinned Locked Moved The Lounge
game-devquestiondiscussion
104 Posts 49 Posters 4 Views 1 Watching
  • Oldest to Newest
  • Newest to Oldest
  • Most Votes
Reply
  • Reply as topic
Log in to reply
This topic has been deleted. Only users with topic management privileges can see it.
  • A achimera

    MichaelGallagher wrote:

    If you knew the position of every single atom in existence at any one point in time , you could without error predict the movement of the entire universe, or the exact, and i mean EXACT path of a marble that has been hit by another marble, that was itself hit by a marble being flicked....

    I believe Socrates already debated that particular argument thousands of years ago. As I understand it, QM provides the exact state of an atom cannot be determined, it can only be estimated or predicted. If so, then there is never any certainty -- thus the uncertain portion would lead to "randomness", would it not?

    S Offline
    S Offline
    SimonRigby
    wrote on last edited by
    #39

    Actually I have to say that's one aspect that I've never quite grasped (among the many in QM that make my brain bleed). I've always wondered whether the fact that exact state can not be determined is a true indication of whether that state actually exists. If the state exists but some property of the system makes it impossible for us to determine or whether state just isn't known (even to itsself). Excellent, I started off this post understanding what I thought I understood .. until I examined it .. (spooky).

    The only thing unpredictable about me is just how predictable I'm going to be.

    1 Reply Last reply
    0
    • S SimonRigby

      And only if one of you is looking at the time :)

      The only thing unpredictable about me is just how predictable I'm going to be.

      H Offline
      H Offline
      Henry Minute
      wrote on last edited by
      #40

      Nah! If you're looking it can't do it. :)

      Henry Minute Do not read medical books! You could die of a misprint. - Mark Twain Girl: (staring) "Why do you need an icy cucumber?" “I want to report a fraud. The government is lying to us all.”

      1 Reply Last reply
      0
      • A achimera

        MichaelGallagher wrote:

        If you knew the position of every single atom in existence at any one point in time , you could without error predict the movement of the entire universe, or the exact, and i mean EXACT path of a marble that has been hit by another marble, that was itself hit by a marble being flicked....

        I believe Socrates already debated that particular argument thousands of years ago. As I understand it, QM provides the exact state of an atom cannot be determined, it can only be estimated or predicted. If so, then there is never any certainty -- thus the uncertain portion would lead to "randomness", would it not?

        H Offline
        H Offline
        Henry Minute
        wrote on last edited by
        #41

        achimera wrote:

        the uncertain portion would lead to "randomness"

        I don't think that that is correct. Being uncertain about the properties something does not correlate to its being, or behaving, randomly. It is entirely possible that its behaviour is pre-determined, although I personally don't think so, but it appears to be random because of our inability to fully understand the forces acting on it.

        Henry Minute Do not read medical books! You could die of a misprint. - Mark Twain Girl: (staring) "Why do you need an icy cucumber?" “I want to report a fraud. The government is lying to us all.”

        S 1 Reply Last reply
        0
        • D Douglas Troy

          Kick him in the shin, they say "Hey! I'm sorry, you were right all along, it's all predetermined, I couldn't prevent it". Then see what he says ...

          C Offline
          C Offline
          cruest
          wrote on last edited by
          #42

          The universe is random fundamentally, but emergently ordered macroscopically because it is bounded by probability. What I mean by that is that at the quantum level there's nothing to stop a particle from ceasing to be here and spontaneously appear over there, it's just very unlikely. In fact quarks and anti-quarks spontaneously appear and anhillate each other all the time. We like to think of an electron as a point. A solid particle. It's not. It's a fuzzy potential field around an atom. Everything in this universe is probability nothing more.

          H 1 Reply Last reply
          0
          • A achimera

            Does not the physics of QM provide for "true randomness" in the Universe? I'm debating a friend who seems to think everything is predetermined, period. My argument against, is that his proposal would be a finite machine, one which could be moved either forward or back. Additionally, my argument continues, if true randomness exists, then it can't be predetermined nor undone. Am I incorrect? Any thoughts?

            T Offline
            T Offline
            Tomz_KV
            wrote on last edited by
            #43

            Thinking of what science is about, it is to discover or to explain what has been in existence. From this point of view, "true randomness" is just something we have not discovered or explained. It may not be random at all.

            TOMZ_KV

            C 1 Reply Last reply
            0
            • E ely_bob

              I am 1 graduate course away from a phd in Quantum Mechanics.... Dictionary.com says: ran⋅dom   /ˈrændəm/ Show Spelled Pronunciation [ran-duhm] Show IPA –adjective 1. proceeding, made, or occurring without definite aim, reason, or pattern: the random selection of numbers. 2. Statistics. of or characterizing a process of selection in which each item of a set has an equal probability of being chosen. o.k. in order: :doh: 1; quantum particles behave according to their "nature" they usually are "aimed" (at the lowest local energy state), the reason is entropy(usually) and they have a pattern(albeit poorly defined: See Heisenberg uncertenty principle.. which basically says that if a particle is then it exists somewhere in the universe, but you will never know where it is... ) 2; the positions of any given quantum particle can never be know, however it is to all reasonable approximations residing in bounding frustrum in space-time(its physical extent..from a certain perspective). However the exact probability that a quantum particle is ever in any position is 0 (i.e. it doesn't exist). [Check this out^] so to answer your debate: (if you believe in string theory and that there exists a grand unified field theory) everything in the universe is pre-determined by something that is so complicated that we percieve it as random, although were we capable of peering into an alternate dimension we could (knowing absolutely EVERYTHING) possibly account for all particles(assuming that that universe exists of only one sub atomic particle.. (n=9)^27 after that (n=81)^27 the calculation becomes .... unstable or simply to big to compute... but even if you could compute it it wouldn't matter because that universe would have already cooled and you would need to recompute the answer... (if you only go to quantum theory) then yes there is randomness in this universe (below the quantuum classical barrior aproxamatly less then 200 microns ) (if you believe that newton was the last scientist ever) then no there is no randomness. your finite machine depend on scale if it's "pointer" is >200 microns your friend is absolutely correct(sorta) if your below the threshold but still greater then one particle(in a universe)

              T Offline
              T Offline
              Tomz_KV
              wrote on last edited by
              #44

              What a detailed reponse which certainly made me want to read more on this subject.

              TOMZ_KV

              1 Reply Last reply
              0
              • D Delphi4ever

                I'm with your friend here, everything is predetermined. "Random" and "probability" is just mathematical methods used when you are unable to calculate the outcome due to lack of understanding or lack of data.

                T Offline
                T Offline
                Tomz_KV
                wrote on last edited by
                #45

                Agree with you. Before a law of physics (mathematics) is established (discovered), anything governed by this law would appear "random".

                TOMZ_KV

                1 Reply Last reply
                0
                • L Logan Black

                  Yeah that sounds quite logical, but just because an exact state can't be determined, does that mean an exact state doesn't exist? I'll have to read up on Socrates, sounds really interesting. The thing I love about science is that a lot of fundamentals were uncovered by guys in the last couple thousand years, without all the technical abilities and tools we have today, because the principles are all around us, in nature, in many forms, and to have a fundamental understanding of them you don't really need to understand the mathematics, just picture the process in your head. In fact, they may have had an advantage over others today; not having been already brainwashed with certain "facts" about our universe and not having the preassure of religion telling them they are unequivocally wrong (well, not all the time). So simple, yet so complex! Einstein, what a legend.

                  S Offline
                  S Offline
                  Skymir
                  wrote on last edited by
                  #46

                  Actually yes, it does mean that an exact state does not exist. Until an 'observation' causes the probability wave to collapse into something real. The really weird side effect is that some things can only happen when they're not being observed. Don't peek or the universe stops working. The one that depressed me is that above a certain number particles become self observant. So for instance you couldn't really put Schrodinger's cat into a state of flux. Too many atoms. I do still have hopes for creating an entangled cat though. :cool:

                  1 Reply Last reply
                  0
                  • A achimera

                    MichaelGallagher wrote:

                    If you knew the position of every single atom in existence at any one point in time , you could without error predict the movement of the entire universe, or the exact, and i mean EXACT path of a marble that has been hit by another marble, that was itself hit by a marble being flicked....

                    I believe Socrates already debated that particular argument thousands of years ago. As I understand it, QM provides the exact state of an atom cannot be determined, it can only be estimated or predicted. If so, then there is never any certainty -- thus the uncertain portion would lead to "randomness", would it not?

                    B Offline
                    B Offline
                    byff
                    wrote on last edited by
                    #47

                    thus the uncertain portion would lead to "randomness", would it not? <<<br mode="hold" /> Within limits. The limit is the boundary between the micro and macro perspective. At some point, as we increase in scale from the subatomic level, stoichastic processes become bounded by their peers, in effect becoming statistical rather than real. As has been stated previously, the illusion of determinism isn't really an illusion above a certain scale. Randomness just fades into the background noise. The source of confusion is uncertainty as to where that boundary exists, as well as human inability to perceive it. Without specialized apparatus, we're unable to become privy to the randomness underlying it all, and so all we perceive is the Newtonian reality.

                    1 Reply Last reply
                    0
                    • T Tomz_KV

                      Thinking of what science is about, it is to discover or to explain what has been in existence. From this point of view, "true randomness" is just something we have not discovered or explained. It may not be random at all.

                      TOMZ_KV

                      C Offline
                      C Offline
                      Charvak Karpe
                      wrote on last edited by
                      #48

                      I just read this whole thread and I think the problem we're facing is that there's no good definition of "deterministic". Like, does it make a difference whether the universe is deterministic if there is no way to tell the difference? Maybe particles actually have fixed positions and velocities and interact via deterministic laws of physics like billiard balls (but we obviously cannot observe them because of Heisenberg's principle). Maybe particles are just blurs and they bump into each other going off in "random" directions. There is no way to distinguish the two scenarios. So what is determinism and how does it change anything? Think of it this way. Whatever happens, just happens. Whether it was pre-determined or not is an invalid question because it is ill-defined. The space-time development of the universe just exists and we encounter it moving along the time dimension. When you see the stuff on your desk, you don't ask whether the coffee cup's particular spatial coordinates are "determined" by the monitor's spatial coordinates. You'd ask, what does "determined" even mean in this case? What we do know is that the future state of the universe is not "predictable" because we cannot observe the current state.

                      T 1 Reply Last reply
                      0
                      • L Logan Black

                        My verbage isn't that great, but I think I get my point accross ok... Every action has an equal and opposite reaction. This can be taken as true in any form from an atomic level to a macro level (solar systems and galaxies). As far as I know, you can safely say that each molecule affects the molecule next to it, to some degree, and in the same regard each atom reacts from interaction with other atoms around it. Like a game of marbles, each flick of a marble has an impact on all the other marbles near it; you project the marble with force, and based on so many variables such as gravity, speed, acceleration, mass, velocity, surface area, etc, etc, it hits another marble sending it moving along it's OWN course. Obviously losing energy through other resistances such as friction the second marble may hit a third marble, repeating these effects, but to a lower degree, until all that energy is disipated and the marbles no longer move. You could say that throwing that marble a billion times will NEVER render the exact same results; there will always be some kind of "randomness" associated with the event, and this is completely true. Throw it forever, and you will no doubt never see the same outcome. However, this does not mean that true randomness exists in our universe. Say we were using the big bang as a point of origin for an event. Similar to the marbles, the explosion sends debris, rocks, elements, gasses, energy, etc eminating, rather speeding away from the event horizon heading out into the universe (or as some presume, CREATING the universe itself by expanding at the speed of light). Now at a macro level these bits and pieces hitting each other cause enormous explosions and other major disruptions in space-time, which in turn ricochet off on their own courses, causing more explosions, et al. Imagine, however, what is happening at an atomic level. Atoms changing, breaking apart(?), forming molecules, etc, but importantly, the path of each individual atom is governed entirely by the forces and resistances surrounding it, and of course in large part by other atoms hitting it (or coming close and deterring them electromagnetically(?)). If you knew the position of every single atom in existence at any one point in time :wtf: , you could without error predict the movement of the entire universe, or the exact, and i mean EXACT path of a marble that has been hit by another marble, that was itself hit by a marble being flicked.... You could predict EXACTLY the movement of the leaves on a tree, an

                        L Offline
                        L Offline
                        Lilith C
                        wrote on last edited by
                        #49

                        So if you created a mechanism for knowing the exact movement of every nanoscopic element of the universe (or any other universes that might impinge on ours) that could calculate the exact result of all of the universe's behavior you'd have to factor in the Heisenberg uncertainty created by it's measurements and it would have to factor in its own existence and any calculations it might potentially make and, of necessity, have to recursively recalculate until it's stack was blown, which would ultimately blow the stack for the universe. So quotes Obi.

                        Windows is a pane.

                        1 Reply Last reply
                        0
                        • C cruest

                          The universe is random fundamentally, but emergently ordered macroscopically because it is bounded by probability. What I mean by that is that at the quantum level there's nothing to stop a particle from ceasing to be here and spontaneously appear over there, it's just very unlikely. In fact quarks and anti-quarks spontaneously appear and anhillate each other all the time. We like to think of an electron as a point. A solid particle. It's not. It's a fuzzy potential field around an atom. Everything in this universe is probability nothing more.

                          H Offline
                          H Offline
                          Hardik Varma
                          wrote on last edited by
                          #50

                          Truer words were probably said, but this is pretty accurate :)

                          1 Reply Last reply
                          0
                          • A achimera

                            Does not the physics of QM provide for "true randomness" in the Universe? I'm debating a friend who seems to think everything is predetermined, period. My argument against, is that his proposal would be a finite machine, one which could be moved either forward or back. Additionally, my argument continues, if true randomness exists, then it can't be predetermined nor undone. Am I incorrect? Any thoughts?

                            R Offline
                            R Offline
                            rbdavidson
                            wrote on last edited by
                            #51

                            The short answer is -- both. QM actually implies that the various properties of sub-atomic particles <b><u>do not have a value until measured</u></b>. It is not that the value is random or unknown, but that it <b><u>does not exist</u></b>. When measured, that property will have a definite value that will fall within an expected range which can be predicted accurately by probabilistic equations. The collection of all possible values is referred to as part of the super-position of the particle. Measurement collapses the super-position. This question actually mirrors the debate between Einstein and Bohr. Einstein maintained that the properties of quantum particles always had definite values and that we simply were unable to determine those values until we measured them. i.e. He maintained that if we had perfect knowledge of all the particles and their current state and how they interacted with each other we could predict their behavior perfectly as far into the future as we wanted. Bohr maintained the values did not exist at all until the moment they were measured. That perfect knowledge of all the particles and their properties was not merely impractical, but fundamentally impossible. Perfect prediction was a pipe dream, and the best you could hope for was a probabilistic model that accurately bounded the range of possible states a particle could achieve. The experiments performed to decide this debate favor Bohr’s interpretation. The end result: At a fundamental level, the current state of the universe can be precisely explained, and the future state can be predicted accurately to a large degree, but the precise details are not determined until the precise moment they are directly observed and measured.

                            1 Reply Last reply
                            0
                            • L Logan Black

                              Chris Maunder wrote:

                              Below a certain threshold the universe is fuzzy. The more you try and measure the position of a particle, the less you will be able to measure its momentum, and vice versa.

                              Ok, this is what I also believe, but isn't that only if WE attempt to measure or intercept a particle? The laws of physics that govern a particle or something so small are different to the laws for objects the size of, say, a human being, or Earth. So trying to measure or observe the characteristics of a particle in our real-time 'macro-verse'(?) could potentially report incorrect results, or missing or contradictory information. Are the properties of the 'fuzzy' parts of the universe not completely defined simply because we cannot measure them effectively? Don't a particles properties exist as a uniform constant regardless of the outcome that the observers best attempts had at defining them? Does a falling tree make a sound if there's no one there to hear it? :-\ Am I completely off track? I have to review every bloody sentence I write! :doh:

                              D Offline
                              D Offline
                              Dan Neely
                              wrote on last edited by
                              #52

                              MichaelGallagher wrote:

                              Ok, this is what I also believe, but isn't that only if WE attempt to measure or intercept a particle?

                              No it does not. This is probably the worst misconception that comes out of attempts to popularize QM. While observations can affect the state of a system, uncertainty is an inherent component of physics and exists completely independently of what an observer does.

                              Today's lesson is brought to you by the word "niggardly". Remember kids, don't attribute to racism what can be explained by Scandinavian language roots. -- Robert Royall

                              1 Reply Last reply
                              0
                              • C Charvak Karpe

                                I just read this whole thread and I think the problem we're facing is that there's no good definition of "deterministic". Like, does it make a difference whether the universe is deterministic if there is no way to tell the difference? Maybe particles actually have fixed positions and velocities and interact via deterministic laws of physics like billiard balls (but we obviously cannot observe them because of Heisenberg's principle). Maybe particles are just blurs and they bump into each other going off in "random" directions. There is no way to distinguish the two scenarios. So what is determinism and how does it change anything? Think of it this way. Whatever happens, just happens. Whether it was pre-determined or not is an invalid question because it is ill-defined. The space-time development of the universe just exists and we encounter it moving along the time dimension. When you see the stuff on your desk, you don't ask whether the coffee cup's particular spatial coordinates are "determined" by the monitor's spatial coordinates. You'd ask, what does "determined" even mean in this case? What we do know is that the future state of the universe is not "predictable" because we cannot observe the current state.

                                T Offline
                                T Offline
                                Tomz_KV
                                wrote on last edited by
                                #53

                                You have a valid point.

                                TOMZ_KV

                                1 Reply Last reply
                                0
                                • A achimera

                                  Does not the physics of QM provide for "true randomness" in the Universe? I'm debating a friend who seems to think everything is predetermined, period. My argument against, is that his proposal would be a finite machine, one which could be moved either forward or back. Additionally, my argument continues, if true randomness exists, then it can't be predetermined nor undone. Am I incorrect? Any thoughts?

                                  F Offline
                                  F Offline
                                  feanorgem
                                  wrote on last edited by
                                  #54

                                  Then there is no point in arguing with him about it. He's already lost.

                                  1 Reply Last reply
                                  0
                                  • A achimera

                                    Does not the physics of QM provide for "true randomness" in the Universe? I'm debating a friend who seems to think everything is predetermined, period. My argument against, is that his proposal would be a finite machine, one which could be moved either forward or back. Additionally, my argument continues, if true randomness exists, then it can't be predetermined nor undone. Am I incorrect? Any thoughts?

                                    L Offline
                                    L Offline
                                    Lost User
                                    wrote on last edited by
                                    #55

                                    I think you are incorrect in this case, but so is your friend, kind of. QM does not provide for "true randomness". Regular predeterminate formulas don't make sense either. When a formula "approaches infinity", what happens is the solutions get so compressed together the reach a point where the possibilities are too numerous for us or our computers to comprehend, so it is "infinite enough". At the level of quantum physics, the structures are so delicate even human thoughts, or invisible, unseen forces can affect them. "Sub-matter" has "possibility states" but the resulting cow, pig or donkey, of all those "random states" is not random, or it could end up a broom... This is not the same as randomness. Even quantum physics follows formulas, but add in "random factors" for what we do not comprehend. Following quantum physics to it's absolute root, the universe is constantly shifting around and essentially all matter is being recreated every microsecond. The resulting universe, or how those pieces "fall back together" every micrsecond certainly isn't random.

                                    1 Reply Last reply
                                    0
                                    • A achimera

                                      Does not the physics of QM provide for "true randomness" in the Universe? I'm debating a friend who seems to think everything is predetermined, period. My argument against, is that his proposal would be a finite machine, one which could be moved either forward or back. Additionally, my argument continues, if true randomness exists, then it can't be predetermined nor undone. Am I incorrect? Any thoughts?

                                      C Offline
                                      C Offline
                                      Chris Trelawny Ross
                                      wrote on last edited by
                                      #56

                                      What if the universe is a finite state machine? That would mean what people say about God being "outside time" - knowing everything, of all of time, at once - be correct. What if randomness, as we currently know it, and with our knowledge limited by our participation in the universe that we are observing, is actually (on some grander scale) not random? Then our universe would, in fact, be a finite state machine. Further, even if the universe is a finite state machine, that doesn't change the fact that to our perceptions we have a distinct future and past. Perhaps our experience is like a finger moving along the edge of a ruler: the entire ruler exists all the while, but the finger has a past and a future experience of the scale it progresses along. If, then, the universe is a finite state machine, the interesting question is: "How come our experience of it occurs as a cursor moving unidirectionally through it?" ~Chris

                                      W 1 Reply Last reply
                                      0
                                      • A achimera

                                        Does not the physics of QM provide for "true randomness" in the Universe? I'm debating a friend who seems to think everything is predetermined, period. My argument against, is that his proposal would be a finite machine, one which could be moved either forward or back. Additionally, my argument continues, if true randomness exists, then it can't be predetermined nor undone. Am I incorrect? Any thoughts?

                                        W Offline
                                        W Offline
                                        Waylon Flinn
                                        wrote on last edited by
                                        #57

                                        Contrary to popular opinion quantum mechanics doesn't actually answer the question of whether or not the universe is deterministic. Bell's Theorem shows that it cannot be both local and deterministic. Most physicists today elect to give up the deterministic part and keep the locality. However, there are interpretations which do just the opposite. The Bohm Interpretation is currently the most popular among these. This theory is an example of a Hidden Variable Theory. While these theories have fallen out of favor with the physics community the very first documented explanation of quantum phenomenon was of this kind. The Matter Wave interpretation, proposed by Louis de Broglie in his 1924 PhD thesis, preceded the currently fashionable Copenhagen Interpretation by several years. Interestingly enough the Copenhagen Interpretation denies physical meaning to the central construct in quantum mechanics, the Wave Function, while the nonlocal theories tend to embrace it.

                                        1 Reply Last reply
                                        0
                                        • L Logan Black

                                          My verbage isn't that great, but I think I get my point accross ok... Every action has an equal and opposite reaction. This can be taken as true in any form from an atomic level to a macro level (solar systems and galaxies). As far as I know, you can safely say that each molecule affects the molecule next to it, to some degree, and in the same regard each atom reacts from interaction with other atoms around it. Like a game of marbles, each flick of a marble has an impact on all the other marbles near it; you project the marble with force, and based on so many variables such as gravity, speed, acceleration, mass, velocity, surface area, etc, etc, it hits another marble sending it moving along it's OWN course. Obviously losing energy through other resistances such as friction the second marble may hit a third marble, repeating these effects, but to a lower degree, until all that energy is disipated and the marbles no longer move. You could say that throwing that marble a billion times will NEVER render the exact same results; there will always be some kind of "randomness" associated with the event, and this is completely true. Throw it forever, and you will no doubt never see the same outcome. However, this does not mean that true randomness exists in our universe. Say we were using the big bang as a point of origin for an event. Similar to the marbles, the explosion sends debris, rocks, elements, gasses, energy, etc eminating, rather speeding away from the event horizon heading out into the universe (or as some presume, CREATING the universe itself by expanding at the speed of light). Now at a macro level these bits and pieces hitting each other cause enormous explosions and other major disruptions in space-time, which in turn ricochet off on their own courses, causing more explosions, et al. Imagine, however, what is happening at an atomic level. Atoms changing, breaking apart(?), forming molecules, etc, but importantly, the path of each individual atom is governed entirely by the forces and resistances surrounding it, and of course in large part by other atoms hitting it (or coming close and deterring them electromagnetically(?)). If you knew the position of every single atom in existence at any one point in time :wtf: , you could without error predict the movement of the entire universe, or the exact, and i mean EXACT path of a marble that has been hit by another marble, that was itself hit by a marble being flicked.... You could predict EXACTLY the movement of the leaves on a tree, an

                                          M Offline
                                          M Offline
                                          Mark_Wallace
                                          wrote on last edited by
                                          #58

                                          MichaelGallagher wrote:

                                          Every action has an equal and opposite reaction. This can be taken as true in any form from an atomic level to ...

                                          I take it you're not too familiar with probability distribution. Say hi to Heisenberg for me.

                                          I wanna be a eunuchs developer! Pass me a bread knife!

                                          1 Reply Last reply
                                          0
                                          Reply
                                          • Reply as topic
                                          Log in to reply
                                          • Oldest to Newest
                                          • Newest to Oldest
                                          • Most Votes


                                          • Login

                                          • Don't have an account? Register

                                          • Login or register to search.
                                          • First post
                                            Last post
                                          0
                                          • Categories
                                          • Recent
                                          • Tags
                                          • Popular
                                          • World
                                          • Users
                                          • Groups