Omniscience and quantum mechanics

[Adoniram]

No no, nothing like that, though I can see how you got that. No, I'm talking about how Christians who say that God is omniscient are contradicting our understanding of the universe. A quantum mechanical universe is not deterministic: there are inherent limits on what you can know. An omniscience can't exist because the concept makes no sense in an indeterministic, quantum mechanical universe. Since our best understanding of the universe is that it is quantum mechanical (though that's not likely the end of the story), there's a paradox.

One has to give .

But God is not governed by the physical laws of our universe. He is responsible for them however. The Bible says He holds the universe together by the power of His Word, and that without Him nothing exists that exists. That means that all the physical laws that hold this universe together are the product of His intellect. How could He not understand and be aware of all? Even to the infinite degree? God must, to be who He is, know, for example, the exact location of any given particle at any given time. And on top of that, be responsible for it's being there at that time.

And in addition to that, He has the power to circumvent any physical law He chooses at any time He chooses. For example, the physical laws of this universe would support the idea that one cannot raise from the dead, but we know that Jesus and others have, according to God's purposes.

So there is no paradox. There is only the inability of our finite minds to grasp the magnitude of God.

 

[Wiccan_Child]

How can you know this? You've only ever been in the one reality you're working with now.

You have to reference every logic statement to this reality, don't you? I mean, you're in it.

I'm in it, yes, but that's incidental: the statement makes no reference to this reality (unlike, say, quantum mechanics, or evolution). The statement is true solely because of its own internal characteristics; the nature of reality doesn't affect the truth of the statement. In this reality we express the statement in a particular arrangement of symbols or phonemes, but that's different to the statement itself.

Can you explain how a terrasect is 4-dimensional? I only see height, width and length; a cube inside a larger, mishapen cube.

I made a small error: it's a tesseract, not a terrasect .
It is a projection of a 4D hypercube (the next step in the point-line-square-cube series) onto 3D space (the 2D nature of the monitor notwithstanding), just as this cube is actually a projection of a cube onto 2D space:

If you rotate the tesseract about an intersecting plane, this is what happens to its projection:

While it seems to be changing shape, it's actually not.

I agree that a contradiction is impossible, but I don't think that what makes for a contradiction in one time and place has to make for a contradiction in another time and place (or in the absence of time and place: eternity).

Why not?

It doesn't make sense to me because I'm a Christian; I'm a Christian because it makes sense to me.

How did that lead you to Christianity?

 

[Chesterton]

I'm in it, yes, but that's incidental: the statement makes no reference to this reality (unlike, say, quantum mechanics, or evolution). The statement is true solely because of its own internal characteristics; the nature of reality doesn't affect the truth of the statement. In this reality we express the statement in a particular arrangement of symbols or phonemes, but that's different to the statement itself.

Well this should teach me never to enter a thread with the words "quantum mechanics" in the title. I presume you know what you're saying but I can't see how anything, even any thought in your head, does not have to "reference" this reality. There is nothing you can do or say or think which isn't founded in the reality of which your mind is a part.

And it reminds me though of another thing you say: that something can come from nothing. That idea seems wrong in a similar way, because once you have "something" (a universe) that statement is impossible to make. There is no "nothing" for something to come from. Maybe you could have made that claim 14 billion years ago, but it's too late now.

It is a projection of a 4D hypercube (the next step in the point-line-square-cube series) onto 3D space (the 2D nature of the monitor notwithstanding), just as this cube is actually a projection of a cube onto 2D space:

If you rotate the tesseract about an intersecting plane, this is what happens to its projection:

While it seems to be changing shape, it's actually not.

I don't understand this either. I see an interesting optical effect, but I'm not getting how this suggests a fourth spatial dimension. But I'll set the tesseract aside for now, unless you're in the mood to try and explain higher math for dummies.

Why not?

I just simply don't assume the human mind can comprehend everything that could possibly be.

How did that lead you to Christianity?

It wasn't any one or two ideas that led me to Christianity, but there are some ideas which even though I can't understand them, they sort of resonate within this reality, I guess I'd say. Or even though I don't understand it, "the idea of the idea" rings true.

 

[Wiccan_Child]

Well this should teach me never to enter a thread with the words "quantum mechanics" in the title. I presume you know what you're saying but I can't see how anything, even any thought in your head, does not have to "reference" this reality. There is nothing you can do or say or think which isn't founded in the reality of which your mind is a part.

Agreed. My thoughts about the statement are grounded in reality, because my thoughts are simply neural pathways. But the statement itself makes no reference to reality. We can talk about cubes, and our brains (which do the thinking) are grounded in reality, but the cube itself is not: it's a mathematical abstraction that can't exist in reality. Nonetheless, it does have six sides, eight vertices, etc.
Likewise, though we use reality to talk about logic (by manipulating the air, say), logic itself doesn't reference reality.

And it reminds me though of another thing you say: that something can come from nothing. That idea seems wrong in a similar way, because once you have "something" (a universe) that statement is impossible to make. There is no "nothing" for something to come from. Maybe you could have made that claim 14 billion years ago, but it's too late now.

When we make a statement about reality, it carries with it all of the baggage, including the temporal nature of events. That's why we say two mutually exclusive things cannot be true simultaneously: they can be true one after the other (something changing colour, for instance), but they can't be true together (like invisible pink unicorns).

That said, it is interesting to note that "1 + 1 = 2" is true regardless of time.

And, just to clarify, I never said (or never meant to say) "something from nothing". Nothing can't do anything, because there's nothing to cause the event. It's more "nothing, then something".

I don't understand this either. I see an interesting optical effect, but I'm not getting how this suggests a fourth spatial dimension. But I'll set the tesseract aside for now, unless you're in the mood to try and explain higher math for dummies.

It's like the 2D shadow of a 3D object. The shadow appears 2D, and it appears to be morphing weirdly as the actual object rotates. It's an illusion, of course: the object is rotating and the projection (shadow) does weird things as it does so.

Now extend that into higher dimensions .

I just simply don't assume the human mind can comprehend everything that could possibly be.

Well, no, obviously. But you don't have to know everything to know that something is false. Bachelor's are unmarried. I don't have to know every single bachelor and unmarried person to know that this claim is absolutely true.

It wasn't any one or two ideas that led me to Christianity, but there are some ideas which even though I can't understand them, they sort of resonate within this reality, I guess I'd say. Or even though I don't understand it, "the idea of the idea" rings true.

So, why Christianity in particular? I don't mean to pry, and I know it's not the right thread for it, but I'm just curious .

 

[Chesterton]

Agreed. My thoughts about the statement are grounded in reality, because my thoughts are simply neural pathways. But the statement itself makes no reference to reality. We can talk about cubes, and our brains (which do the thinking) are grounded in reality, but the cube itself is not: it's a mathematical abstraction that can't exist in reality. Nonetheless, it does have six sides, eight vertices, etc.
Likewise, though we use reality to talk about logic (by manipulating the air, say), logic itself doesn't reference reality.

It seems like you're saying that logic statements are unreal, or extra-natural or supernatural or something like that. When you say making no reference to "reality", are you really meaning to say making no reference to "nature"? That's the only way I can maybe understand what you're saying. I don't know about the math aspect of it, but I know a man can make a cube, and it might not be natural but it is real.

When we make a statement about reality, it carries with it all of the baggage, including the temporal nature of events. That's why we say two mutually exclusive things cannot be true simultaneously: they can be true one after the other (something changing colour, for instance), but they can't be true together (like invisible pink unicorns).

So if we could lose the temporal nature of events, then we'd lose that constraining baggage. So then something which would be a contradiction within the temporal realm might not be a contradiction outside the temporal realm, no?

That said, it is interesting to note that "1 + 1 = 2" is true regardless of time.

What about before time, or outside of time? Are you sure that still has to be true? If spacetime is one thing, then you can't have space without time. And without space, there can't be 2 of anything, right? In that case, either both "1" and "2" would be meaningless, or else they could be meaningful in a way which doesn't rely on space (on things being separate things). Enter the Trinity, wherein "1 + 1 + 1 = 1".

Well, no, obviously. But you don't have to know everything to know that something is false. Bachelor's are unmarried. I don't have to know every single bachelor and unmarried person to know that this claim is absolutely true.

Of course, but that's an observation which cannot not be true; it's tautological. That's not the same type of claim that you make in the OP.

So, why Christianity in particular? I don't mean to pry, and I know it's not the right thread for it, but I'm just curious .

No you wouldn't be prying at all, I'd love to tell you, but it's just that it's like asking for a small biography really. I thought and read about Christianity (and other religions/philosophies) for almost 20 years before I became a Christian. I can remember the exact moment in November 2007 when I decided, and it really felt like it was decided for me. After many times of praying to God to let me know, there was one time when I prayed and He did; it came into my mind and heart that Christ was the Truth, just like he said he is.

I do want to specifically disavow one idea that's often said of why people are Christians: that people become Christian because they like it; that they like the comfort of eternal life and the promise of paradise. It might be true in many cases, but it wasn't in mine. I never could convince myself of atheism, I called myself agnostic, but atheism was really what I wished could be true. It seemed like the ideal arrangement to live, enjoy life, even be reasonably moral (when it wasn't too inconvenient) and then just go to sleep. But I don't think that's the reality.

There's not one reason, but 1,000 different evidences from life which all point to the ideas contained in Christianity. I'd describe it this way, but someone already has, so I'll quote him (G.K.C.):

"If I am asked, as a purely intellectual question, why I believe in Christianity, I can only answer, 'For the same reason that an intelligent agnostic disbelieves in Christianity.' I believe in it quite rationally upon the evidence. But the evidence in my case, as in that of the intelligent agnostic, is not really in this or that alleged demonstration; it is in an enormous accumulation of small but unanimous facts. The secularist is not to be blamed because his objections to Christianity are miscellaneous and even scrappy; it is precisely such scrappy evidence that does convince the mind. I mean that a man may well be less convinced of a philosophy from four books, than from one book, one battle, one landscape, and one old friend. The very fact that the things are of different kinds increases the importance of the fact that they all point to one conclusion. Now, the non-Christianity of the average educated man to-day is almost always, to do him justice, made up of these loose but living experiences. I can only say that my evidences for Christianity are of the same vivid but varied kind as his evidences against it. For when I look at these various anti-Christian truths, I simply discover that none of them are true. I discover that the true tide and force of all the facts flows the other way."

 

[98cwitr]

According to some, God is omniscient: he knows everything.

But, according to quantum mechanics, there are inherent limitations to just how much can be known about a given system. For example, knowing the position of a particle to a given degree of accuracy places insurmountable limitations on how accurate we can know its momentum (namely, ΔxΔp[sub]x[/sub] ≥ ħ/2).

How, then, can God know everything? This uncertainty principle isn't the result of practical limitations to measurements, but is an inherent property of the quantum mechanical nature of the system. Just what does God know about the physical observables of a particle?
Does this relate to the qualifier, "God knows everything knowable"?

yay...someone into math on this forum!

Doesn't apply for this reason...your little equation there is relative to the speed, position, and momentum of moving particles equal to or less than the speed of light. At a single point in time, we could measure position with a fixed value for the momentum...but it is beyond our human ability, but a piece of cake to God. Keep going though, you seem like a smart guy and I like math

 

[Wiccan_Child]

It seems like you're saying that logic statements are unreal, or extra-natural or supernatural or something like that. When you say making no reference to "reality", are you really meaning to say making no reference to "nature"? That's the only way I can maybe understand what you're saying. I don't know about the math aspect of it, but I know a man can make a cube, and it might not be natural but it is real.

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.

So if we could lose the temporal nature of events, then we'd lose that constraining baggage. So then something which would be a contradiction within the temporal realm might not be a contradiction outside the temporal realm, no?

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.

What about before time, or outside of time? Are you sure that still has to be true? If spacetime is one thing, then you can't have space without time. And without space, there can't be 2 of anything, right? In that case, either both "1" and "2" would be meaningless, or else they could be meaningful in a way which doesn't rely on space (on things being separate things). Enter the Trinity, wherein "1 + 1 + 1 = 1".

'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.

Of course, but that's an observation which cannot not be true; it's tautological. That's not the same type of claim that you make in the OP.

I disagree: the logical technique may be different, but the fact remains that they are both necessarily true.

No you wouldn't be prying at all, I'd love to tell you, but it's just that it's like asking for a small biography really. I thought and read about Christianity (and other religions/philosophies) for almost 20 years before I became a Christian. I can remember the exact moment in November 2007 when I decided, and it really felt like it was decided for me. After many times of praying to God to let me know, there was one time when I prayed and He did; it came into my mind and heart that Christ was the Truth, just like he said he is.

I do want to specifically disavow one idea that's often said of why people are Christians: that people become Christian because they like it; that they like the comfort of eternal life and the promise of paradise. It might be true in many cases, but it wasn't in mine. I never could convince myself of atheism, I called myself agnostic, but atheism was really what I wished could be true. It seemed like the ideal arrangement to live, enjoy life, even be reasonably moral (when it wasn't too inconvenient) and then just go to sleep. But I don't think that's the reality.

There's not one reason, but 1,000 different evidences from life which all point to the ideas contained in Christianity. I'd describe it this way, but someone already has, so I'll quote him (G.K.C.):

"If I am asked, as a purely intellectual question, why I believe in Christianity, I can only answer, 'For the same reason that an intelligent agnostic disbelieves in Christianity.' I believe in it quite rationally upon the evidence. But the evidence in my case, as in that of the intelligent agnostic, is not really in this or that alleged demonstration; it is in an enormous accumulation of small but unanimous facts. The secularist is not to be blamed because his objections to Christianity are miscellaneous and even scrappy; it is precisely such scrappy evidence that does convince the mind. I mean that a man may well be less convinced of a philosophy from four books, than from one book, one battle, one landscape, and one old friend. The very fact that the things are of different kinds increases the importance of the fact that they all point to one conclusion. Now, the non-Christianity of the average educated man to-day is almost always, to do him justice, made up of these loose but living experiences. I can only say that my evidences for Christianity are of the same vivid but varied kind as his evidences against it. For when I look at these various anti-Christian truths, I simply discover that none of them are true. I discover that the true tide and force of all the facts flows the other way."

Fair enough. Thanks for sharing .

 

[Wiccan_Child]

yay...someone into math on this forum!

Doesn't apply for this reason...your little equation there is relative to the speed, position, and momentum of moving particles equal to or less than the speed of light.

Hardly. While the momentum of a particle is relative to the inertial frame from which you measure it, the uncertainty is not. Thus, 'my' equation is not relative to anything: however you measure position and momentum, the product of their uncertainties has a minimum.

At a single point in time, we could measure position with a fixed value for the momentum...but it is beyond our human ability, but a piece of cake to God.

It's not a question of ability. A lot of people seem to make that mistake.

 

[salida]

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.

 

[98cwitr]

Hardly. While the momentum of a particle is relative to the inertial frame from which you measure it, the uncertainty is not. Thus, 'my' equation is not relative to anything: however you measure position and momentum, the product of their uncertainties has a minimum.


It's not a question of ability. A lot of people seem to make that mistake.

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"

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.

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.

 

[Wiccan_Child]

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.

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.

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.

 

[Wiccan_Child]

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'?

 

[Chesterton]

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."

Fair enough. Thanks for sharing .

Thanks for asking.

 

[98cwitr]

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

 

[98cwitr]

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?

 

[Wiccan_Child]

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[sup]-34[/sup] J s), not the Plank constant (h, ~6.626*10[sup]-34[/sup] J s). True, the former is simply the latter divided by 2π, but still.

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.

Please take into account God does not need to take time into account in any given equation

What do you mean?

No but momentum does become static. Now the equation becomes >=h/2

The particle still has momentum.

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:

 

[Wiccan_Child]

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' ).

 

[Wiccan_Child]

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.

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.

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.

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.

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.

 

[98cwitr]

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[sup]-34[/sup] J s), not the Plank constant (h, ~6.626*10[sup]-34[/sup] 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.

 

[Wiccan_Child]

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.

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.

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'?

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.

^^^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.

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 .