As a member of that most exclusive group of objects -
"The things which physically exist" - you are imbued with a number of
characteristics. First among them is obviously the matter of existing in
itself, and that is the gateway to enjoying the other benefits of your
membership such as going to the pictures or witnessing crumbs.
Proud owners of a physical forms (or even leaseholders thereof) generally have predilection for keeping tabs on the characteristic of its position, or, where that physical form or "body" is. They will say "I am in Jamaica", "I'm in the bath", or "Most of me is in the bath, but some of me has become entwined in the towel rack due to factors beyond my control". Other body owners may even share your interest in the location and engagement of your body, evidenced by exclamations such as "Where are you?", or in more advanced cases: "Why are you in my bathroom and what are you doing with my towel rack?".
"Where are you?" should be a relatively easy question to answer for most active members and even some distinguished alumni of the things which physically exist. After all, if you can't even point to a space which you are certain that you occupy (generally within arm's reach of your arm) then your existence must be a peculiar thing indeed, and the board of governors may have to review your membership eligibility.
Another characteristic of this "body" you so proudly wear every day is the speed at which it is travelling. A knowledge of this can be used to determine both where you were some time ago, and where you will be at some point in the future. As such, the value of this quantity is displayed prominently in all motorcars so that the driver may ignore it in pursuit of important tailgating commitments.
If you are an electron, this is the stage at which things become a little ropey. Not only can you not reach the pedals or the steering wheel, but if you manage know where you are, then you have no idea how fast you are going and could end up somewhere else entirely in any amount of time. If you are watching your speedometer then you have no idea where you are at the time and will most likely become close friends with a lamp-post, the tail you were so diligently gating, or a discount furniture store. You are a victim of a brutal conspiracy, courtesy of Heisenberg and his unwavering principle of uncertainty.
As a conspirator, Heisenberg is a fairly eminent chap. He hasn't simply driven a sheet of steel into your car such that your head can be either a) above it looking out of the windscreen, or b) below it looking at the speedometer. He's gone one step further and decided that as soon as you so much as glance at one of them then the other is sabotaged; it is ruined in a fit of quantum mechanical spite - the worst kind of spite. Your knowledge or measurement of one observable actively precludes the precise measurement of the other. He has either replaced your windscreen with an elaborate kaleidoscope, or glued a random number generator to your speedo. For these reasons, Mr Heisenberg can be inferred to be both a skilled mechanic, and a terrible choice of MOT provider.
That isn't the only way in which he's been a tinker about people knowing too much about something either. The safeguarding of simultaneous knowledge applies equally to lots of other things, such as the momentum of one object in each of the three spatial dimensions. Should you be so bold, so daring, so ARROGANT as to try and know all three spatial components of your momentum at the same time (god forbid) then you will be mercilessly slapped down. Two components? That's fine. We LIKE knowing two. But all three? You make me sick.
It's not a question of terrible measurement, it's a fundamental characteristic of the universe we live in, which happens to be a Hilbert Space (this is quite distinct from the crawlspace running behind Mr Hilbert's bath). Defining each observable quantity of a system with an operator and combining them within the mathematical constraints of a Hilbert Space, i.e. reality, causes these relations to fall out of the equations like racial slurs falling out of a UKIP party conference. Some of the operators just don't commute with one another, which means that for two operators A and B, AB does not equal BA, or in other words AB - BA is not 0 (Incidentally, this is not how numbers work, so a reassuring consequence of this observation is that we are not numbers. If this doesn't seem to describe you, then please pause to re-evaluate whether you are a human or the final balance of a weekly shop at Tesco getting rather above its station in terms of literacy.). This very roughly translates to the statement that measuring A first and then B gives you a different answer to measuring B first and then A. This is because knowing one of these things defines the system in such a way that the other thing could be one of a number of values. The value of the second thing is uncertain.
It's one of those charming eventualities we all cherish, whereby trying to understand reality by plugging something we know into our equations leads to us learning that we don't in fact know what we thought we did. And when we think we do know it? We not only don't, but actually can't. Or something.
Proud owners of a physical forms (or even leaseholders thereof) generally have predilection for keeping tabs on the characteristic of its position, or, where that physical form or "body" is. They will say "I am in Jamaica", "I'm in the bath", or "Most of me is in the bath, but some of me has become entwined in the towel rack due to factors beyond my control". Other body owners may even share your interest in the location and engagement of your body, evidenced by exclamations such as "Where are you?", or in more advanced cases: "Why are you in my bathroom and what are you doing with my towel rack?".
"Where are you?" should be a relatively easy question to answer for most active members and even some distinguished alumni of the things which physically exist. After all, if you can't even point to a space which you are certain that you occupy (generally within arm's reach of your arm) then your existence must be a peculiar thing indeed, and the board of governors may have to review your membership eligibility.
Another characteristic of this "body" you so proudly wear every day is the speed at which it is travelling. A knowledge of this can be used to determine both where you were some time ago, and where you will be at some point in the future. As such, the value of this quantity is displayed prominently in all motorcars so that the driver may ignore it in pursuit of important tailgating commitments.
If you are an electron, this is the stage at which things become a little ropey. Not only can you not reach the pedals or the steering wheel, but if you manage know where you are, then you have no idea how fast you are going and could end up somewhere else entirely in any amount of time. If you are watching your speedometer then you have no idea where you are at the time and will most likely become close friends with a lamp-post, the tail you were so diligently gating, or a discount furniture store. You are a victim of a brutal conspiracy, courtesy of Heisenberg and his unwavering principle of uncertainty.
As a conspirator, Heisenberg is a fairly eminent chap. He hasn't simply driven a sheet of steel into your car such that your head can be either a) above it looking out of the windscreen, or b) below it looking at the speedometer. He's gone one step further and decided that as soon as you so much as glance at one of them then the other is sabotaged; it is ruined in a fit of quantum mechanical spite - the worst kind of spite. Your knowledge or measurement of one observable actively precludes the precise measurement of the other. He has either replaced your windscreen with an elaborate kaleidoscope, or glued a random number generator to your speedo. For these reasons, Mr Heisenberg can be inferred to be both a skilled mechanic, and a terrible choice of MOT provider.
That isn't the only way in which he's been a tinker about people knowing too much about something either. The safeguarding of simultaneous knowledge applies equally to lots of other things, such as the momentum of one object in each of the three spatial dimensions. Should you be so bold, so daring, so ARROGANT as to try and know all three spatial components of your momentum at the same time (god forbid) then you will be mercilessly slapped down. Two components? That's fine. We LIKE knowing two. But all three? You make me sick.
It's not a question of terrible measurement, it's a fundamental characteristic of the universe we live in, which happens to be a Hilbert Space (this is quite distinct from the crawlspace running behind Mr Hilbert's bath). Defining each observable quantity of a system with an operator and combining them within the mathematical constraints of a Hilbert Space, i.e. reality, causes these relations to fall out of the equations like racial slurs falling out of a UKIP party conference. Some of the operators just don't commute with one another, which means that for two operators A and B, AB does not equal BA, or in other words AB - BA is not 0 (Incidentally, this is not how numbers work, so a reassuring consequence of this observation is that we are not numbers. If this doesn't seem to describe you, then please pause to re-evaluate whether you are a human or the final balance of a weekly shop at Tesco getting rather above its station in terms of literacy.). This very roughly translates to the statement that measuring A first and then B gives you a different answer to measuring B first and then A. This is because knowing one of these things defines the system in such a way that the other thing could be one of a number of values. The value of the second thing is uncertain.
It's one of those charming eventualities we all cherish, whereby trying to understand reality by plugging something we know into our equations leads to us learning that we don't in fact know what we thought we did. And when we think we do know it? We not only don't, but actually can't. Or something.
No comments:
Post a Comment