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

[fromderinside]

Gentlemen, I take it you don;t object to being called that, this was resolved in 1967.

To wit:

Mr. McGuire: I want to say one word to you. Just one word.
Benjamin: Yes, sir.
Mr. McGuire: Are you listening?
Benjamin: Yes, I am.
Mr. McGuire: Plastics.
Benjamin: Exactly how do you mean?
Mr. McGuire: There's a great future in plastics. Think about it. Will you think about it?

Update. there will be more placstic objects in the ocean than fish in a few years.

 

[beero1000]

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.

No. Energy levels are not locations. They don't have "space between them". Atoms don't look like microscopic solar systems with electrons in neat orbits around them. That's a popular but seriously out of date model, and has little relationship with reality.

This.

Also, electrons are not intrinsically quantized, it is external conditions that forces bound states in atoms. Unbound electrons can exist anywhere, continuously.

In  quantum mechanics, a bound electron is forced (due to the Schrödinger equation and boundary conditions) to remain in certain quantized states. In  quantum field theory, e.g. the  Standard Model, even this notion of 'particles' is replaced by 'quantum field', which are continuously varying over all space, and can generate any number of particles, with quantized bound states mostly replaced with field resonances.

 

[Kharakov]

Does space have any properties that would allow it to evolve into entities over time, or is it too chaotic (forget the QM bullshit)?

What do you mean chaotic, How is space chaotic, gravity waves? How could space turn into an entity without QM?

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.

 

[Kharakov]

In  quantum mechanics, a bound electron is forced (due to the Schrödinger equation and boundary conditions)

Wait, you're saying the equation itself (combined with boundary conditions) forces electrons to behave according to the equation?

I don't normally see you speak woo!

 

[untermensche]

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.

No. Energy levels are not locations. They don't have "space between them". Atoms don't look like microscopic solar systems with electrons in neat orbits around them. That's a popular but seriously out of date model, and has little relationship with reality.

Energy levels are potential locations. Locations where the electron can possibly be. As you see they are in relation to the center of positive charge.

And there is space between them.

An electron has to be at a location. It cannot exist at no location.

Everything that exists is at a specific location in relation to all other things that exist.

 

[skepticalbip]

No. Energy levels are not locations. They don't have "space between them". Atoms don't look like microscopic solar systems with electrons in neat orbits around them. That's a popular but seriously out of date model, and has little relationship with reality.

View attachment 14084

Energy levels are potential locations. Locations where the electron can possibly be. As you see they are in relation to the center of positive charge.

And there is space between them.

An electron has to be at a location. It cannot exist at no location.

Everything that exists is at a specific location in relation to all other things that exist.

You seem to now be agreeing with the parking lot analogy where there are designated spaces for cars to park but, as you now say, "And there is space between them."

So you now agree that space is continuous?

 

[untermensche]

No. Energy levels are not locations. They don't have "space between them". Atoms don't look like microscopic solar systems with electrons in neat orbits around them. That's a popular but seriously out of date model, and has little relationship with reality.

View attachment 14084

Energy levels are potential locations. Locations where the electron can possibly be. As you see they are in relation to the center of positive charge.

And there is space between them.

An electron has to be at a location. It cannot exist at no location.

Everything that exists is at a specific location in relation to all other things that exist.

You seem to now be agreeing with the parking lot analogy where there are designated spaces for cars to park but, as you now say, "And there is space between them."

But they do not occupy the space between.

They appear to move from one energy level to another without touching the space between.

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

Smoothness is an illusion based on scale of most observations.

 

[beero1000]

In  quantum mechanics, a bound electron is forced (due to the Schrödinger equation and boundary conditions)

Wait, you're saying the equation itself (combined with boundary conditions) forces electrons to behave according to the equation?

I don't normally see you speak woo!

No, I'm not saying that.

 

[skepticalbip]

You seem to now be agreeing with the parking lot analogy where there are designated spaces for cars to park but, as you now say, "And there is space between them."

But they do not occupy the space between.

They appear to move from one energy level to another without touching the space between.

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

Smoothness is an illusion based on scale of most observations.

The thread is not about electrons but about whether space is granular or smooth.

 

[beero1000]

You seem to now be agreeing with the parking lot analogy where there are designated spaces for cars to park but, as you now say, "And there is space between them."

But they do not occupy the space between.

They appear to move from one energy level to another without touching the space between.

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

Smoothness is an illusion based on scale of most observations.

You are conflating the idea of electrons having quantized energy levels with there being nodes for a given orbital. There is no spatial location where an electron cannot be, and that's even before we take  superposition into account.

 

[untermensche]

You seem to now be agreeing with the parking lot analogy where there are designated spaces for cars to park but, as you now say, "And there is space between them."

But they do not occupy the space between.

They appear to move from one energy level to another without touching the space between.

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

Smoothness is an illusion based on scale of most observations.

The thread is not about electrons but about whether space is granular or smooth.

It was in response to this:

Between the parking spaces numbered 101 and 102 there are no parking spaces

This is not something that has been decided one way or the other.

To me the idea of "smoothness" is like the idea of "infinity".

A mathematical, not real world concept. They are related concepts.

And we must say that at a certain scale smoothness is not what is happening with electrons.

 

[untermensche]

You seem to now be agreeing with the parking lot analogy where there are designated spaces for cars to park but, as you now say, "And there is space between them."

But they do not occupy the space between.

They appear to move from one energy level to another without touching the space between.

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

Smoothness is an illusion based on scale of most observations.

You are conflating the idea of electrons having quantized energy levels with there being nodes for a given orbital. There is no spatial location where an electron cannot be, and that's even before we take  superposition into account.

No. I am describing how an electron might move from one energy level to another should an atom be excited. An instantaneous jump, quantum leap, from one energy level to another. All or none, not halfway in between.

 

[beero1000]

You are conflating the idea of electrons having quantized energy levels with there being nodes for a given orbital. There is no spatial location where an electron cannot be, and that's even before we take  superposition into account.

No. I am describing how an electron might move from one energy level to another should an atom be excited. An instantaneous jump, quantum leap, from one energy level to another. All or none, not halfway in between.

Energy levels are not positions. You are talking about quantized energy levels and the figure you posted is of the probability density functions for each energy level. Those are not the same thing. Do you know what the hydrogen 1s density looks like?

 

[untermensche]

You are conflating the idea of electrons having quantized energy levels with there being nodes for a given orbital. There is no spatial location where an electron cannot be, and that's even before we take  superposition into account.

No. I am describing how an electron might move from one energy level to another should an atom be excited. An instantaneous jump, quantum leap, from one energy level to another. All or none, not halfway in between.

Energy levels are not positions. You are talking about quantized energy levels and the figure you posted is of the probability density functions for each energy level. Those are not the same thing. Do you know what the hydrogen 1s density looks like?

Energy levels are volumes that represent potential locations of an electron.

Volumes have locations in relation to all other things.

And the electron jumps from being in one potential volume to a different potential volume depending on the energy level of the atom.

 

[beero1000]

Energy levels are not positions. You are talking about quantized energy levels and the figure you posted is of the probability density functions for each energy level. Those are not the same thing. Do you know what the hydrogen 1s density looks like?

Energy levels are volumes that represent potential locations of an electron.

Volumes have locations in relation to all other things.

And the electron jumps from being in one potential volume to a different potential volume depending on energy level of the atom.

Energy levels are... levels of energy. The volumes are the contours of the probability density function. The Schrödinger equation relates the two for quantum particles. They are not the same thing.

Do you know what the hydrogen 1s density function looks like?

 

[untermensche]

Energy levels are not positions. You are talking about quantized energy levels and the figure you posted is of the probability density functions for each energy level. Those are not the same thing. Do you know what the hydrogen 1s density looks like?

Energy levels are volumes that represent potential locations of an electron.

Volumes have locations in relation to all other things.

And the electron jumps from being in one potential volume to a different potential volume depending on energy level of the atom.

Energy levels are... levels of energy. The volumes are the contours of the probability density function.

The energy level defines the volume.

The probability function is just how humans approximate it abstractly.

 

[skepticalbip]

The thread is not about electrons but about whether space is granular or smooth.

It was in response to this:

Between the parking spaces numbered 101 and 102 there are no parking spaces

This is not something that has been decided one way or the other.

To me the idea of "smoothness" is like the idea of "infinity".

A mathematical, not real world concept. They are related concepts.

All models of the universe are mathematical models. Our conception of the "real world" is based on which model we like better.

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. Are there any limitations on the position of a neutrino?

 

[beero1000]

Energy levels are... levels of energy. The volumes are the contours of the probability density function.

The energy level defines the volume.

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.

 

[untermensche]

It was in response to this:



This is not something that has been decided one way or the other.

To me the idea of "smoothness" is like the idea of "infinity".

A mathematical, not real world concept. They are related concepts.

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.

 

[untermensche]

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.