You asked "How can God know..." is knowledge not an ability to comprehend? Your equation is relative to planck's constant. The problem inherently lies within this statement "It is impossible to measure simultaneously both position and velocity of a microscopic particle with any degree of accuracy or certainty"
Perhaps it would be more accurate to say that it is impossible to measure them with absolute accuracy. But either way, the equation is not relative to the Plank* constant: the point is that the product of the uncertainites must be non-zero.
Originally Posted by 98cwitr
Imagine you could stop time though and possess the fixed measurement for the momentum of a particle. From each fixed point to each fixed point, you are able to accurately measure the position AND velocity of the particle.
Which is impossible, at least according to quantum mechanics: particles don't have a well-defined position and momentum at any given moment in time. Particles exist as a blurry cloud of probability. That's how an electron can tunnel out of a potential well: its wavefunction is mostly in the well, but part of it exists outside the well. There exists, therefore, a small but significant possibility that the electron will behave as if it is outside the well, and thus zip away from the well.
The same is true for momentum: a particle doesn't travel with a well-defined velocity, because it doesn't have a well-defined position from which it is moving from.
Originally Posted by 98cwitr
We are human, we cannot stop time. God can and we wouldn't even realize it if he did, because time is a human construct. God conceives eternity, which does not possess time.
Perhaps, but that doesn't solve the problem. Quantum mechanics doesn't dissapear when you remove time.
There's a reason we have the Time Independent Schrödinger Equation.
*The equations use the Dirac constant, which is a reduced form of the Plank constant.
__________________
A scientific man ought to have no wishes, no affections, -- a mere heart of stone.
- Charles Darwin
"I am a scientist... when I find evidence that my theories are wrong, it is as exciting as if the evidence proved them right."
- Stargate: SG1
What can be asserted without reason, can be denied without reason.
- Anon
"A casual stroll through the lunatic asylum shows that faith does not prove anything."
God created everything including quantum mechanics. Quantum mechanics is just man's interpretation of what God has created. This is what science does. God created ALL things. He isn't mortal and limited but is infinite, immortal and isn't defined by the bondage of time. God is the creator, man is the creature - its that simple.
Nonetheless, man, the creature, has discovered something about this reality: there are fundamental limits to how things behave. Namely, particles have spectra of positions and momenta, rather than the intuitive single position and single momentum. Quantum mechanics tells us that the widths of these spectra obey a particular law: their products must be greater than some finite value.
The question, then, is how can God be omnipotent, if he himself has placed fundamental limits on what can be known about particles? It's not that we humans have a practical difficulty determining the exact location of a particle, but that the very notion of a location becomes blurred at the quantum scale.
To what degree is God 'omnipotent'?
__________________
A scientific man ought to have no wishes, no affections, -- a mere heart of stone.
- Charles Darwin
"I am a scientist... when I find evidence that my theories are wrong, it is as exciting as if the evidence proved them right."
- Stargate: SG1
What can be asserted without reason, can be denied without reason.
- Anon
"A casual stroll through the lunatic asylum shows that faith does not prove anything."
Actually, we can't: we can make objects that approximate a cube, but there are limits. Indeed, since a cube is a mathematical abstraction, it can't exist.
Yes and no. The premises remain unchanged, and the contradiction only exists as a result of these premises being simultaneously true. However, the statements are necessarily false in a world without time. Consider:
Pigs are animals.
Animals can fly.
Therefore, pigs can fly.
If pigs are indeed animals, and if animals can indeed fly, then it necessarily follows that pigs can indeed fly. The premises don't give two hoots whether they're true or not. If you like, the logical argument posits a hypothetical scenario defined by the premises (e.g., one where pigs are animals and where animals can fly), and then says "OK, then what?".
It doesn't matter what exists in reality. Replace 'pig' with 'unicorn', and nothing really changes, even though unicorns don't actually exist.
'1' and '2' don't necessarily get their meaning from real things. We conceptually understand them by thinking about, say, two apples, but we can again use mathematical abstractions to define them (for instance, '2' can be defined as the cardinality of the set {{},{{}}}).
Point is, a statement has a truth value, but not every string of physical symbols is representative of a statement. The pattern of light on my wall isn't a (representation of a) statement, but the symbols on my whiteboard are. Thus, the statement "1 + 1 = 2" is true because we define the symbols '1', '2', '+', and '=', to represent mathematical concepts and abstractions that, when strung together, represent a true statement.
In other words, the statement doesn't refer to anything, yet is true nonetheless.
Thanks for your patience, I think I finally understand. That's close to what I suspected you meant, so I'll continue my same objection: an abstract concept is no less a part of this reality than a pig is, and a mathematical set is, and also your imagination which conceives of concepts. So a logic statement need not reference a real thing which exists in nature, but it's simply incorrect to say logic "doesn't reference reality". Actually, I think it would be correct to say it fully references the totality of this reality. And if logic does reference this reality, then saying it has to "play by the same rules" in another reality is just a bald assertion.
But if you insist that logic doesn't reference this reality, it makes me want to ask what does it reference, or what's its foundation? Was there logic before the Big Bang, when there was nothing? That sounds like a contradiction. Before the singularity spat out the first two quarks, there couldn't be any math, because I guess the only number was "1" (the singularity). But if you say math is just how we describe what the Big Bang caused, then you're supporting my idea that logic is grounded in this reality. I know you were Wiccan; do you believe in some kind of super-reality above and beyond us (even though not the Christian one)?
I disagree: the logical technique may be different, but the fact remains that they are both necessarily true.
As far as your claim in the OP being necessarily true: you know why I don't accept the conclusions of science? "For the simple reason that science has not concluded."
Perhaps it would be more accurate to say that it is impossible to measure them with absolute accuracy. But either way, the equation is not relative to the Plank* constant: the point is that the product of the uncertainites must be non-zero.
It's Planck's constant and uncertainty can be zero if you take the change of time relative to the velocity measurement and set it equal to 0, hence stopping time.
Which is impossible, at least according to quantum mechanics: particles don't have a well-defined position and momentum at any given moment in time. Particles exist as a blurry cloud of probability. That's how an electron can tunnel out of a potential well: its wavefunction is mostly in the well, but part of it exists outside the well. There exists, therefore, a small but significant possibility that the electron will behave as if it is outside the well, and thus zip away from the well.
The same is true for momentum: a particle doesn't travel with a well-defined velocity, because it doesn't have a well-defined position from which it is moving from.
probability is not tangible, therefore cannot cannot exist in a cloud, literally; but metaphorically I can see what you mean. Please take into account God does not need to take time into account in any given equation except to give velocity at a stopped time a value to solve these equations
Perhaps, but that doesn't solve the problem. Quantum mechanics doesn't dissapear when you remove time.
No but momentum does become static. Now the equation becomes >=h/2, and thus making possible a certainty to own uncertainty equation
There's a reason we have the Time Independent Schrödinger Equation.
Please elaborate on the TISE, I will research it. I'm not a quantum physicist nor do I claim to be any good at it, as seemingly you are learning. I just like math
*The equations use the Dirac constant, which is a reduced form of the Plank constant.
See comments in bold and italics
__________________ Because I sat down...looked over all the coincidences of my life and realized that while each one of those things in itself was coincidence, when added up, the summation of my coincidences logically points to someone that I can't see or hear being in control.
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Last edited by 98cwitr; 30th July 2009 at 09:20 PM.
okay after looking at the Schrodinger equation it looks like it is only one side of the equation there, bud. Correct me if I'm wrong. Also in my reading I came across this "The exponentially growing solutions have an infinite norm, and are not physical. They are not allowed in a finite volume with periodic or fixed boundary conditions." link. So then I ask...if the solutions are not physical, aren't you referring to abstraction?
__________________ Because I sat down...looked over all the coincidences of my life and realized that while each one of those things in itself was coincidence, when added up, the summation of my coincidences logically points to someone that I can't see or hear being in control.
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Perhaps it would be more accurate to say that it is impossible to measure them with absolute accuracy. But either way, the equation is not relative to the Plank* constant: the point is that the product of the uncertainites must be non-zero.
It's Planck's constant and uncertainty can be zero if you take the change of time relative to the velocity measurement and set it equal to 0, hence stopping time.
Particles move through time at a rate of one second per second (assuming a general relativistic approach. Just as a system can at a particular moment have zero velocity but non-zero acceleration, so too can a particle have non-zero velocity at a particular 'slice' in time. I think you're making the same fallacy as Zeno.
And no, it's the Dirac constant (ħ, ~1.055*10-34 J s), not the Plank constant (h, ~6.626*10-34 J s). True, the former is simply the latter divided by 2π, but still.
Originally Posted by 98cwitr
probability is not tangible, therefore cannot cannot exist in a cloud, literally; but metaphorically I can see what you mean.
The particle is described by a wavefunction, the modulus squared of which gives you the probability of finding it at any given point in space (maybe even time). In that sense, they really do exist as a cloud.
Originally Posted by 98cwitr
Please take into account God does not need to take time into account in any given equation
What do you mean?
Originally Posted by 98cwitr
No but momentum does become static. Now the equation becomes >=h/2
The particle still has momentum.
Originally Posted by 98cwitr
Please elaborate on the TISE, I will research it. I'm not a quantum physicist nor do I claim to be any good at it, as seemingly you are learning. I just like math
Particles are described by wave vectors, which evolve in time according to the Schrödinger equation. The time-independent Schrödinger equation is just that: time-independent. The classic particle-in-a-box system can be described using the TISE, becuase it doesn't evolve in time. Some systems do change in time (the potential could osscillate, or the particle is hits a barrier and does funky things), and they require the full time-dependant equation. In its most general form, the Schrodinger eqution states that the time differential of a a particles wavefunction Ψ(r, t) is related to the Hamiltonian by:
It's basically the equation which governs how quantum particles behave. In everyday quantum mechanics, the equation simplifies to:
__________________
A scientific man ought to have no wishes, no affections, -- a mere heart of stone.
- Charles Darwin
"I am a scientist... when I find evidence that my theories are wrong, it is as exciting as if the evidence proved them right."
- Stargate: SG1
What can be asserted without reason, can be denied without reason.
- Anon
"A casual stroll through the lunatic asylum shows that faith does not prove anything."
okay after looking at the Schrodinger equation it looks like it is only one side of the equation there, bud. Correct me if I'm wrong. Also in my reading I came across this "The exponentially growing solutions have an infinite norm, and are not physical. They are not allowed in a finite volume with periodic or fixed boundary conditions." link. So then I ask...if the solutions are not physical, aren't you referring to abstraction?
That's just an explanation for why some of the terms are discarded: since the wave doesn't increase exponentially, the coefficients of exponentially increasing terms are necessarily zero. That's why we're left with terms for exponential decay and oscillation, which are physical (for given values of 'physical' ).
__________________
A scientific man ought to have no wishes, no affections, -- a mere heart of stone.
- Charles Darwin
"I am a scientist... when I find evidence that my theories are wrong, it is as exciting as if the evidence proved them right."
- Stargate: SG1
What can be asserted without reason, can be denied without reason.
- Anon
"A casual stroll through the lunatic asylum shows that faith does not prove anything."
Thanks for your patience, I think I finally understand. That's close to what I suspected you meant, so I'll continue my same objection: an abstract concept is no less a part of this reality than a pig is, and a mathematical set is, and also your imagination which conceives of concepts.
I disagree. An abstraction is just that: abstract. It doesn't actually exist.
Originally Posted by Chesterton
So a logic statement need not reference a real thing which exists in nature, but it's simply incorrect to say logic "doesn't reference reality". Actually, I think it would be correct to say it fully references the totality of this reality. And if logic does reference this reality, then saying it has to "play by the same rules" in another reality is just a bald assertion.
True, but again, I disagree that it does.
Originally Posted by Chesterton
But if you insist that logic doesn't reference this reality, it makes me want to ask what does it reference, or what's its foundation? Was there logic before the Big Bang, when there was nothing? That sounds like a contradiction. Before the singularity spat out the first two quarks, there couldn't be any math, because I guess the only number was "1" (the singularity). But if you say math is just how we describe what the Big Bang caused, then you're supporting my idea that logic is grounded in this reality.
The laws of logic (which includes mathematics) were as true then as they are now; three is greater than two, regardless of whether anyone exists to know what 'two' and 'three' are. We use maths to describe reality, but we also use it to describe a lot of other things, such as that tesseract.
Originally Posted by Chesterton
I know you were Wiccan; do you believe in some kind of super-reality above and beyond us (even though not the Christian one)?
I think it's entirely probable that humanity has yet to uncover the true nature of reality. Despite my fondness for quantum mechanics, and my belief that it is far closer to the truth that classical mechanics ever was, I believe it is ultimately false. At least, in the details, much how classical mechanics was.
When I was Wiccan, I didn't believe that there was some 'higher' reality (except for a belief in the afterlife, which I didn't really ponder too much). I believed that even the gods were the result of natural phenomena; there were no creator deities, but there were deities nonetheless.
So, yeah, lol.
Originally Posted by Chesterton
As far as your claim in the OP being necessarily true: you know why I don't accept the conclusions of science? "For the simple reason that science has not concluded."
Hah, indeed . The OP is meant to question how classical concepts of God and philosophy stand up to modern knowledge. We know some things are true now that were summarily dismissed by previous scholars, such as heliocentricism.
__________________
A scientific man ought to have no wishes, no affections, -- a mere heart of stone.
- Charles Darwin
"I am a scientist... when I find evidence that my theories are wrong, it is as exciting as if the evidence proved them right."
- Stargate: SG1
What can be asserted without reason, can be denied without reason.
- Anon
"A casual stroll through the lunatic asylum shows that faith does not prove anything."
Particles move through time at a rate of one second per second (assuming a general relativistic approach. Just as a system can at a particular moment have zero velocity but non-zero acceleration, so too can a particle have non-zero velocity at a particular 'slice' in time. I think you're making the same fallacy as Zeno.
acceleration and velocity still involve time, one with respect to change in direction. I'm not seeing your point
And no, it's the Dirac constant (ħ, ~1.055*10-34 J s), not the Plank constant (h, ~6.626*10-34 J s). True, the former is simply the latter divided by 2π, but still.
But still what? If you divide each side by 2pi you still get the same result...I don't see the difference.
The particle is described by a wavefunction, the modulus squared of which gives you the probability of finding it at any given point in space (maybe even time). In that sense, they really do exist as a cloud.
What do you mean?
I took you comment at "cloud" literally, as "any similar mass"...but did you mean it that way?
The particle still has momentum
I totally agree, but it is static and not dynamic when you set time = 0. If you stop time, both position and momentum can be measured. Each are completely inequivalent to the other at a single point when considering an elemental state.
Particles are described by wave vectors, which evolve in time according to the Schrödinger equation. The time-independent Schrödinger equation is just that: time-independent. The classic particle-in-a-box system can be described using the TISE, becuase it doesn't evolve in time. Some systems do change in time (the potential could osscillate, or the particle is hits a barrier and does funky things), and they require the full time-dependant equation. In its most general form, the Schrodinger eqution states that the time differential of a a particles wavefunction Ψ(r, t) is related to the Hamiltonian by:
It's basically the equation which governs how quantum particles behave. In everyday quantum mechanics, the equation simplifies to:
^^^still dont see how the last few statements support your theory...please elaborate...I'm sorry for my ignorance in this matter but rather intrigued. You have been on this site for quite some time...I pray that you will come to Christ at some point in your life and be faithful. For someone with a scientific mind, it is exponentially difficult to accept, and I can understand and respect that...please see sig.
__________________ Because I sat down...looked over all the coincidences of my life and realized that while each one of those things in itself was coincidence, when added up, the summation of my coincidences logically points to someone that I can't see or hear being in control.
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
acceleration and velocity still involve time, one with respect to change in direction. I'm not seeing your point
My point is that particles can still have velocity and acceleration even when you stop time.
Originally Posted by 98cwitr
But still what? If you divide each side by 2pi you still get the same result...I don't see the difference.
The difference is that it's the Dirac constant, not the Plank constant. It's irrelevant to our conversation, but it's a distinction I wanted to point out.
Originally Posted by 98cwitr
I took you comment at "cloud" literally, as "any similar mass"...but did you mean it that way?
What do you mean, 'any similar mass'?
Originally Posted by 98cwitr
I totally agree, but it is static and not dynamic when you set time = 0. If you stop time, both position and momentum can be measured. Each are completely inequivalent to the other at a single point when considering an elemental state.
But that's just it: there can't be measured with pin-point accuracy. Doing fancy things to time doesn't change that.
Originally Posted by 98cwitr
^^^still dont see how the last few statements support your theory...please elaborate...I'm sorry for my ignorance in this matter but rather intrigued.
I'm just saying that there exists a specific equation for dealing with quantum mechanical systems that don't change over time. Nonetheless, they still have velocities and momenta.
Originally Posted by 98cwitr
You have been on this site for quite some time... I pray that you will come to Christ at some point in your life and be faithful. For someone with a scientific mind, it is exponentially difficult to accept, and I can understand and respect that...please see sig.
As a scientist, I go where the evidence leads. If have evidence of God, or Jesus, or Vishnu, let me know .
__________________
A scientific man ought to have no wishes, no affections, -- a mere heart of stone.
- Charles Darwin
"I am a scientist... when I find evidence that my theories are wrong, it is as exciting as if the evidence proved them right."
- Stargate: SG1
What can be asserted without reason, can be denied without reason.
- Anon
"A casual stroll through the lunatic asylum shows that faith does not prove anything."
). 
. The OP is meant to question how classical concepts of God and philosophy stand up to modern knowledge. We know some things are true now that were summarily dismissed by previous scholars, such as heliocentricism. 
. 
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