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Discontinuous and/or granular space vs. continuous, smooth space

All models of the universe are mathematical models. Our conception of the "real world" is based on which model we like better.
But the OP is not asking about a model. It is asking about the real thing.

And we must say that at a certain scale smoothness is not what is happening with electrons.
You are confusing the behavior of bound electrons and space....

When electrons are bound to a nucleus or nuclei a functional unit is formed.

I am talking about functional matter.

It is an example of quantum behavior as opposed to smooth behavior.
Then you are derailing the thread. The thread is about the nature of space, not about the allowed energy levels of bound electrons in atoms.

You didn't answer my question about whether neutrinos have spatial limitations on their position.
 
No, the wavefunction defines both, as related by the Schrödinger equation.

The probability function is just how humans approximate it abstractly.

That is exactly backwards.

You confuse models with the real thing.

The equations are abstractions and approximations of the real thing.

The real thing does not use equations to keep electrons in order.

They stay in specific volumes based on what we call energy levels not because of equations.

Whereas you confuse facts with your terrible intuition. Eh, fuck it, that's my quota for the day.

I'll just leave you with this question that you've dodged a few times already: Do you know what the hydrogen 1s electron density looks like?
 
All models of the universe are mathematical models. Our conception of the "real world" is based on which model we like better.
But the OP is not asking about a model. It is asking about the real thing.
You are confusing the behavior of bound electrons and space....

When electrons are bound to a nucleus or nuclei a functional unit is formed.

I am talking about functional matter.

It is an example of quantum behavior as opposed to smooth behavior.
Then you are derailing the thread. The thread is about the nature of space, not about the allowed energy levels of bound electrons in atoms.

You didn't answer my question about whether neutrinos have spatial limitations on their position.

Trying to examine a concept is not derailing the examination of a concept.

Show me the relevance of your question.

Fear of moving from an arbitrary box when examining concepts is not an argument.

If you really think I am just derailing you should ignore completely.
 
You confuse models with the real thing.

The equations are abstractions and approximations of the real thing.

The real thing does not use equations to keep electrons in order.

They stay in specific volumes based on what we call energy levels not because of equations.

Whereas you confuse facts with your terrible intuition. Eh, fuck it, that's my quota for the day.

I'll just leave you with this question that you've dodged a few times already: Do you know what the hydrogen 1s electron density looks like?

Why do you have so much trouble admitting you are wrong?

Not knowing the difference between reality and the human models, human approximations of reality, is a serious rational error.

It leads one to think things like smoothness and infinity could actually exist.
 
All models of the universe are mathematical models. Our conception of the "real world" is based on which model we like better.
You are confusing the behavior of bound electrons and space....

When electrons are bound to a nucleus or nuclei a functional unit is formed.

I am talking about functional matter.

It is an example of quantum behavior as opposed to smooth behavior.
Then you are derailing the thread. The thread is about the nature of space, not about the allowed energy levels of bound electrons in atoms.

You didn't answer my question about whether neutrinos have spatial limitations on their position.

Trying to examine a concept is not derailing the examination of a concept.

Show me the relevance of your question.

Fear of moving from an arbitrary box when examining concepts is not an argument.

If you really think I am just derailing you should ignore completely.
The relevance of the question? Your argument has been that since (in the model offered) electrons aren't allowed in some positions with respect to the nucleus of an atom that it means space itself is quantized. Although an asinine interpretation, lets assume that is what it means. The question is, could a neutrino pass through that "disallowed" space? If so then it isn't a "disallowed" space, only that an electron, because of other factors, can't be there. However, if a neutrino could pass through there then it would indicate that space is continuous.
 
The relevance of the question? Your argument has been that since (in the model offered) electrons aren't allowed in some positions with respect to the nucleus of an atom that it means space itself is quantized. Although an asinine interpretation, lets assume that is what it means. The question is, could a neutrino pass through that "disallowed" space? If so then it isn't a "disallowed" space, only that an electron, because of other factors, can't be there. However, if a neutrino could pass through there then it would indicate that space is continuous.

If I specifically say as I have just a few pages ago:

It is not a demonstration that space is quantized. It is a demonstration of quantized behavior. Not smooth behavior.

How is your question relevant?
 
The relevance of the question? Your argument has been that since (in the model offered) electrons aren't allowed in some positions with respect to the nucleus of an atom that it means space itself is quantized. Although an asinine interpretation, lets assume that is what it means. The question is, could a neutrino pass through that "disallowed" space? If so then it isn't a "disallowed" space, only that an electron, because of other factors, can't be there. However, if a neutrino could pass through there then it would indicate that space is continuous.

If I specifically say as I have just a few pages ago:

It is not a demonstration that space is quantized. It is a demonstration of quantized behavior. Not smooth behavior.

How is your question relevant?
Aha, so your whole rant is a derail?

Again, the question is the nature of space, not the behavior of bound electrons in an atom.
 
If I specifically say as I have just a few pages ago:



How is your question relevant?
Aha, so your whole rant is a derail?

Again, the question is the nature of space, not the behavior of bound electrons in an atom.

Again, is trying to examine things a derail?

What can we say of space?

How do you propose we slice it up and examine it?

How wide is an infinitely small slice of space?
 
You confuse models with the real thing.

The equations are abstractions and approximations of the real thing.

The real thing does not use equations to keep electrons in order.

They stay in specific volumes based on what we call energy levels not because of equations.

Whereas you confuse facts with your terrible intuition. Eh, fuck it, that's my quota for the day.

I'll just leave you with this question that you've dodged a few times already: Do you know what the hydrogen 1s electron density looks like?

Why do you have so much trouble admitting you are wrong?

It's OK folks, calm down, that wasn't North Korea setting off a high-yield thermonuclear device, it was just my irony meter.
 
If I specifically say as I have just a few pages ago:



How is your question relevant?
Aha, so your whole rant is a derail?

Again, the question is the nature of space, not the behavior of bound electrons in an atom.

Again, is trying to examine things a derail?
It is if those "things" have nothing to do with the question.

If you want to look at the nature of an electron for a clue to the answer then look at a free electron in a potential well, not an electron bound in an atom. The possible position of such an electron is well described by Schrodinger and that description extends the possible position smoothly with no "granularity". Experiments have shown Schrodinger's equation to be a pretty damn good description of reality. Does this prove that space is smooth? No, but it is a much better "thing" to examine than the allowed energy levels of an electron bound in an atom... which speaks to energy level not position.
How do you propose we slice it up and examine it?
With the new Ginsu slicer... only $19.95 if you order within the next ten minutes. And to get a second Ginsu slicer FREE you only need to pay the extra handling fee.
 
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With the new Ginsu slicer... only $19.95 if you order within the next ten minutes. And to get a second Ginsu slicer FREE you only need to pay the extra handling fee.

You seem to call any examination above the level of this a derailment.
 
Why do you have so much trouble admitting you are wrong?

It's OK folks, calm down, that wasn't North Korea setting off a high-yield thermonuclear device, it was just my irony meter.

Do you also have a problem understanding the difference between reality and the human abstractions and approximations of it?

To not know the difference between human constructed models and reality is a serious rational defect.
 
With the new Ginsu slicer... only $19.95 if you order within the next ten minutes. And to get a second Ginsu slicer FREE you only need to pay the extra handling fee.

You seem to call any examination above the level of this a derailment.

That was a little sarcasm at your failure to understand the difference between what is and how we measure what is.
 
If it's already a continuous entity, it doesn't "turn into an entity" with the help of something else.

How is space chaotic, gravity waves?
I said "is it?" not "is." I imagine the overall structure of space, which apparently evolves through gravitation, is extremely complex (even if it is smooth). So I was wondering if the structure, persistence, and self interaction of space would allow Boltzmann like* brains to evolve out of it over time.

By Boltzmann like, I mean they appear like Boltzmann brains, but are self perpetuating. So particles of matter might have emerged from space's interactions with itself, and might be self supporting individual units of spacetime, that sort of tug on the rest.

That's pure quantum mechanics, no? From what I understand, Boltzmann brains, etc. are possible because QM and vacuum energy. I don't think you can leave QM out of it, or ...
 
If it's already a continuous entity, it doesn't "turn into an entity" with the help of something else.

How is space chaotic, gravity waves?
I said "is it?" not "is." I imagine the overall structure of space, which apparently evolves through gravitation, is extremely complex (even if it is smooth). So I was wondering if the structure, persistence, and self interaction of space would allow Boltzmann like* brains to evolve out of it over time.

By Boltzmann like, I mean they appear like Boltzmann brains, but are self perpetuating. So particles of matter might have emerged from space's interactions with itself, and might be self supporting individual units of spacetime, that sort of tug on the rest.

That's pure quantum mechanics, no? From what I understand, Boltzmann brains, etc. are possible because QM and vacuum energy. I don't think you can leave QM out of it, or ...
Well, I was thinking of classical level phenomena over very large (to us) time scales. So gravitation itself could reflect some sort of giant super-brain's self organization over periods of time that might as well be eternal to beings on our scale. Or it might reflect the dying mind of the first being, slowly decaying, with us feeding on the little tiny sparks of life that still exist as the rest dies or is crushed by death, which is space...the protons and electrons aren't... becoming more distant. They too are dying.. shrinking, as death (or blind, unfeeling, space) consumes everything. :D


lol... we all witness the dying of the first being. The first eternal love, broken by death. Humpty dumptied here on Earth from fragments of itself. QM alzheimer's flickering on the fringes of its dying consciousness, as it descends into eternal sleep, with sentinels (electrons) placed around every dying ember, seeking them like we seek an inn on a foggy night, the light beckoning us in... so we can be added to the stew. :D
 
Maybe the second view is accurate, but the first view lingers still.

When objects get farther and farther apart, the fartherest escape the horizon, but has it been established that space is expanding? Not the objects increasing distance from others but space itself--not the 'space' (or distance) between objects as measurable but the 'blocks' of emptiness.

Without creating a firey storm about relativity, imagine two objects at rest a certain unchanging distance apart. If but a single cubed block of space between them expanded and the two objects were tethered together such that their distance wouldn't increase, then they would not be moving through space per se (since they are rest) but rather space would be expanded beyond them.

To even think of space as if it could be something that is expandable is strange to me, as it's not actually some thing. Sure, we could increase the space between two walls by tearing one down and rebuilding one a foot over, but we would not have actually created some thing. The space in one sense was already there, just taken up by the wall at the time.

I wonder if the ambiguity is seriously understood and considered when sweeping statements are made (not by you).
 
True but irrelevant.

Energy levels are not locations.

They exist in relation to the nucleus.

That is a location.

And electrons do not move in the space between energy levels. They can only exist within them.

That is how "energy shells" were taught to me in the 1970's when I was in Jr. High School. It was a visualization of a concept, not a photograph. Electrons are not, in fact, neatly flying around nucleuses in orderly orbits, like the Newtonian motion of planets.
 
True but irrelevant.

Energy levels are not locations.

They exist in relation to the nucleus.

That is a location.

And electrons do not move in the space between energy levels. They can only exist within them.

That is how "energy shells" were taught to me in the 1970's when I was in Jr. High School. It was a visualization of a concept, not a photograph. Electrons are not, in fact, neatly flying around nucleuses in orderly orbits, like the Newtonian motion of planets.

What happens to an electron when an atom is excited?

Does it smoothly move to a higher energy level or does it make a quantum leap to the next energy level?

Is the behavior of electrons in atoms and molecules smooth or quantized?
 
That is how "energy shells" were taught to me in the 1970's when I was in Jr. High School. It was a visualization of a concept, not a photograph. Electrons are not, in fact, neatly flying around nucleuses in orderly orbits, like the Newtonian motion of planets.

What happens to an electron when an atom is excited?

Does it smoothly move to a higher energy level or does it make a quantum leap to the next energy level?

Is the behavior of electrons in atoms and molecules smooth or quantized?

Are you intentionally moving your goal posts from "space is not smooth" to "the behaviors of electrons are 'jumpy' "?

Assume the expected answers to your questions... now what?

You are talking about energy levels (which I think you were also taught to [incorrectly] visualize as "distances from nuclei"

This thread is about the nature of space-time itself... actually just the space part. That may be why so many participants have accused you of hijacking.

We are talking about a car's odometer and you are talking about its tachometer.
 
There are no goal posts.

There is this invented concept "smoothness".

And at a certain scale things may appear smooth but when we look at something very small, like the behavior of electrons, we see there is nothing smooth about it.

If you have some other very small entity to examine go for it.
 
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