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Quantum Mechanics

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  • 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 ...

    K Offline
    K Offline
    Kastellanos Nikos
    wrote on last edited by
    #4

    Douglas Troy wrote:

    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 ...

    Will most certantly kick you back, claiming entanglement :-D

    J M 2 Replies Last reply
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    • K Kastellanos Nikos

      Douglas Troy wrote:

      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 ...

      Will most certantly kick you back, claiming entanglement :-D

      J Offline
      J Offline
      Jim Crafton
      wrote on last edited by
      #5

      Kastellanos Nikos wrote:

      claiming entanglement

      Nah, that's only if he kicks back simultaneously!

      ¡El diablo está en mis pantalones! ¡Mire, mire! SELECT * FROM User WHERE Clue > 0 0 rows returned Save an Orange - Use the VCF! VCF Blog Just Say No to Web 2 Point Oh

      S 1 Reply Last reply
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      • 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 ...

        Y Offline
        Y Offline
        Yusuf
        wrote on last edited by
        #6

        Douglas Troy wrote:

        Then see what he says ...

        I'll sue you for your random act of violence :laugh:

        Yusuf Oh didn't you notice, analogous to square roots, they recently introduced rectangular, circular, and diamond roots to determine the size of the corresponding shapes when given the area. Luc Pattyn[^]

        1 Reply Last reply
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        • 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
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          Tim Deveaux
          wrote on last edited by
          #7

          Your friend would probably lean towards Bohmian Mechanics[^]. Sorry if there will be a repost.

          D 1 Reply Last reply
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          • 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
            Logan Black
            wrote on last edited by
            #8

            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

            D L A C L 9 Replies Last reply
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            • K Kastellanos Nikos

              Douglas Troy wrote:

              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 ...

              Will most certantly kick you back, claiming entanglement :-D

              M Offline
              M Offline
              Mladen Jankovic
              wrote on last edited by
              #9

              Or supersymmetric :)

              [Genetic Algorithm Library]

              1 Reply Last reply
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              • 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?

                M Offline
                M Offline
                Mladen Jankovic
                wrote on last edited by
                #10

                Yes and it's called Uncertainty Principle[^]

                [Genetic Algorithm Library]

                A 1 Reply Last reply
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                • 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?

                  S Offline
                  S Offline
                  Stuart Dootson
                  wrote on last edited by
                  #11

                  Randomness tends to apply at the individual particle level - once you observe it, thus fixing some set of its properties (but not others - that's the outcome of Heisenberg's Uncertainty Principle[^]). Before that, particle properties can be specified as a probability distribution. As you gather together large numbers of particles, they tend to be statistically distributed according to that probability distribution. Electron diffraction[^] (any diffraction, I guess, presuming you go with a particulate nature for light) illustrates this. If you slow the rate of particles so you can detect individual particles, then diffracted particles appear to be deflected by random angles. Aggregate lots of particles together and you get a smoothly curved distribution of particles, which defines the probability that any individual particle will be deflected at a specific angle. What does that mean for your argument? Well - at an everyday (and also at most cosmological) level, motion of objects is actually pretty predictable - look how well we can predict planetary motion, for example.

                  achimera wrote:

                  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.

                  The second law of thermodynamics (total entropy of an isolated system increases over time[^]) implies directionality of time. What has that to do with randomnss? Well, as far as I can tell, high entropy states are the most likely states for systems to end up in, as (because of the high homogenity of the system) they describe the highest fraction of the possible states of the system. Confused? Yeah, well, I am.

                  Java, Basic, who cares - it's all a bunch of tree-hugging hippy cr*p

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                  • 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

                    D Offline
                    D Offline
                    Douglas Troy
                    wrote on last edited by
                    #12

                    I knew you were going to say that. :rolleyes:

                    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
                      #13

                      At what point does unpredictable determinsim become randomness?

                      Visit http://www.notreadytogiveup.com/[^] and do something special today.

                      M C S 3 Replies 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
                        Luc Pattyn
                        wrote on last edited by
                        #14

                        MichaelGallagher wrote:

                        my atoms are being affected by other atoms

                        affected != determined :)

                        Luc Pattyn [Forum Guidelines] [My Articles]


                        - before you ask a question here, search CodeProject, then Google - the quality and detail of your question reflects on the effectiveness of the help you are likely to get - use the code block button (PRE tags) to preserve formatting when showing multi-line code snippets


                        L S 2 Replies Last reply
                        0
                        • L Lost User

                          At what point does unpredictable determinsim become randomness?

                          Visit http://www.notreadytogiveup.com/[^] and do something special today.

                          M Offline
                          M Offline
                          Mladen Jankovic
                          wrote on last edited by
                          #15

                          Randomness is a lack of order, purpose, cause, or predictability.

                          [Genetic Algorithm Library]

                          1 Reply Last reply
                          0
                          • L Luc Pattyn

                            MichaelGallagher wrote:

                            my atoms are being affected by other atoms

                            affected != determined :)

                            Luc Pattyn [Forum Guidelines] [My Articles]


                            - before you ask a question here, search CodeProject, then Google - the quality and detail of your question reflects on the effectiveness of the help you are likely to get - use the code block button (PRE tags) to preserve formatting when showing multi-line code snippets


                            L Offline
                            L Offline
                            Logan Black
                            wrote on last edited by
                            #16

                            But aren't they one in the same? If you played a game of snooker, and slowed it down to one atomic movement per frame, you could see the interaction between all of the molecules, on every level from what you see as the pool ball all the way down to the most finite part, an atom. Each of those interactions, frictions, movements and collisions would all cause a determined reaction on the next atom, and the angle at which that atom flies off would be determined by the angle of approach by the previous atom, just like the white ball hitting another ball, hitting another, and then hitting the black, etc. From a macro view, watching and playing the table, you have a certain amount of control, to put the ball in the hole using other collisions before hand. If you had control at an atomic level, you could direct each ball with 100% certainty in any direction, and DETERMINE exactly where it should go, and therefore know exactly where the hits after that would go also, assuming you had no other resistances such as the pool table itself, etc. Apart from all of that, string theory says that, since there may be something smaller than an atom, randomness may exist after all. If the string theory determines the properties of an atom, or of the nucleus, proton, electrons or something else, then if the absolute smallest element of matter should be studied to see how IT affects the overall nature of energy and mass itself. :confused:

                            L R D 3 Replies Last reply
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                            • L Logan Black

                              But aren't they one in the same? If you played a game of snooker, and slowed it down to one atomic movement per frame, you could see the interaction between all of the molecules, on every level from what you see as the pool ball all the way down to the most finite part, an atom. Each of those interactions, frictions, movements and collisions would all cause a determined reaction on the next atom, and the angle at which that atom flies off would be determined by the angle of approach by the previous atom, just like the white ball hitting another ball, hitting another, and then hitting the black, etc. From a macro view, watching and playing the table, you have a certain amount of control, to put the ball in the hole using other collisions before hand. If you had control at an atomic level, you could direct each ball with 100% certainty in any direction, and DETERMINE exactly where it should go, and therefore know exactly where the hits after that would go also, assuming you had no other resistances such as the pool table itself, etc. Apart from all of that, string theory says that, since there may be something smaller than an atom, randomness may exist after all. If the string theory determines the properties of an atom, or of the nucleus, proton, electrons or something else, then if the absolute smallest element of matter should be studied to see how IT affects the overall nature of energy and mass itself. :confused:

                              L Offline
                              L Offline
                              Luc Pattyn
                              wrote on last edited by
                              #17

                              MichaelGallagher wrote:

                              But aren't they one in the same?

                              No. In an election, your vote will affect the score and may affect the outcome, but (unless you found a way to cheat) you can't determine the outcome. :)

                              Luc Pattyn [Forum Guidelines] [My Articles]


                              - before you ask a question here, search CodeProject, then Google - the quality and detail of your question reflects on the effectiveness of the help you are likely to get - use the code block button (PRE tags) to preserve formatting when showing multi-line code snippets


                              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

                                A Offline
                                A Offline
                                achimera
                                wrote on last edited by
                                #18

                                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?

                                L S H B 4 Replies Last reply
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                                • M Mladen Jankovic

                                  Yes and it's called Uncertainty Principle[^]

                                  [Genetic Algorithm Library]

                                  A Offline
                                  A Offline
                                  achimera
                                  wrote on last edited by
                                  #19

                                  Thanks!

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                                  • 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

                                    C Offline
                                    C Offline
                                    Chris Maunder
                                    wrote on last edited by
                                    #20

                                    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

                                    This is the point of Quantum Mechanics, and more specifically, Heisenbergs uncertainty principle. You cannot know precisely the positions and velocities of anything exactly. You can only know it to within a very, very, very small degree of uncertainty. 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. Hence, you will never, ever have an exact answer on where something is or how fast it's travelling, and hence will never be able to, with certainty, calculate exactly the movement of, say, leaves on a tree. The universe is fuzzy and uncertain and random.

                                    cheers, Chris Maunder The Code Project Co-founder Microsoft C++ MVP

                                    L 1 Reply Last reply
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                                    • L Lost User

                                      At what point does unpredictable determinsim become randomness?

                                      Visit http://www.notreadytogiveup.com/[^] and do something special today.

                                      C Offline
                                      C Offline
                                      Chris Maunder
                                      wrote on last edited by
                                      #21

                                      At the smallest level you are trying to measure, ħ

                                      cheers, Chris Maunder The Code Project Co-founder Microsoft C++ MVP

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                                      • C Chris Maunder

                                        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

                                        This is the point of Quantum Mechanics, and more specifically, Heisenbergs uncertainty principle. You cannot know precisely the positions and velocities of anything exactly. You can only know it to within a very, very, very small degree of uncertainty. 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. Hence, you will never, ever have an exact answer on where something is or how fast it's travelling, and hence will never be able to, with certainty, calculate exactly the movement of, say, leaves on a tree. The universe is fuzzy and uncertain and random.

                                        cheers, Chris Maunder The Code Project Co-founder Microsoft C++ MVP

                                        L Offline
                                        L Offline
                                        Logan Black
                                        wrote on last edited by
                                        #22

                                        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:

                                        M L D 3 Replies Last reply
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                                        • 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?

                                          L Offline
                                          L Offline
                                          Logan Black
                                          wrote on last edited by
                                          #23

                                          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.

                                          L S 2 Replies Last reply
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