Quantum mechanics shows how the poverty of energy imposes structure....?

[jamie.j1989]

From Frank Wilczek's book 'A Beautiful Question'

'Quantum mechanics shows how the poverty of energy imposes structure' P196

Is he saying the poverty of energy imposes structure in the energy of a quantum system or structure in matter? Or both? If we look at an atom it has ordered structure in both the matter and the energy. But if we look at a particle confined in some potential the energy is structured, not the matter.

Is it also correct to say that classical equations create poverty in energy from the structure of matter? And if so is there a connection?

 

[muscaria]

From Frank Wilczek's book 'A Beautiful Question'
'Quantum mechanics shows how the poverty of energy imposes structure' P196
Is he saying the poverty of energy imposes structure in the energy of a quantum system or structure in matter?

It's very hard to know what he means without more context and I couldn't find a pdf of it, could you scan the page? Or at least state what he means by "poverty".

 

[jamie.j1989]

It's very hard to know what he means without more context and I couldn't find a pdf of it, could you scan the page? Or at least state what he means by "poverty".

Here is the page in which he uses it.

 

[PeroK]

From Frank Wilczek's book 'A Beautiful Question'

'Quantum mechanics shows how the poverty of energy imposes structure' P196

Is he saying the poverty of energy imposes structure in the energy of a quantum system or structure in matter? Or both? If we look at an atom it has ordered structure in both the matter and the energy. But if we look at a particle confined in some potential the energy is structured, not the matter.

It's difficult to know what you can learn from a book like this. It might be entertaining and well-written, with an elegant prose style, but what exactly does any of that mean?

Also, your last question:

Is it also correct to say that classical equations create poverty in energy from the structure of matter?

That's just some random words put together. It's literally a meaningless question.

 

[jamie.j1989]

It's difficult to know what you can learn from a book like this. It might be entertaining and well-written, with an elegant prose style, but what exactly does any of that mean?

That was the point of my first question. What does he mean?

That's just some random words put together. It's literally a meaningless question.

If I use the equations describing how two masses move around each other in space, the equations will immediately impose the rule that the energy of the system would like to be in the lowest energy state. And how it reaches that state depends on the initial structure of the matter in space, so I could have added 'in space' at the end. I would agree that the use of the word poverty is misused in both cases, as poverty in something means you have an insufficient amount of that something, which clearly doesn't make sense. So it might be better to say,

Classical equations impose a minimum of energy from the initial structure of matter in space?

 

[PeroK]

That was the point of my first question. What does he mean?

If I use the equations describing how two masses move around each other in space, the equations will immediately impose the rule that the energy of the system would like to be in the lowest energy state. And how it reaches that state depends on the initial structure of the matter in space, so I could have added 'in space' at the end.

Classical equations impose a minimum of energy from the initial structure of matter in space?

It's still impossible to know what you mean. A classical system, unlike a quantum system, can have any energy level and cannot spontaneously change to a lowest energy state by emitting a photon. The Earth is not in its "ground state" with respect to its orbit round the Sun.

And if the Earth had less energy, it would collide with the Sun, which is a valid classical outcome.

PS Classical systems maximise or minimise the Lagrangian, if that is what you mean.

 

[PeterDonis]

What does he mean?

Based on the excerpt given, I would say he means that, as isolated quantum systems lose energy and thereby reduce their temperature, the presence of discrete energy levels in bound quantum systems means that structure is revealed--the structure of the discrete energy levels. The quantum nature of the systems would be essential because classical bound systems do not have discrete energy levels. But that's just a guess.

 

[jamie.j1989]

Based on the excerpt given, I would say he means that, as isolated quantum systems lose energy and thereby reduce their temperature, the presence of discrete energy levels in bound quantum systems means that structure is revealed--the structure of the discrete energy levels. The quantum nature of the systems would be essential because classical bound systems do not have discrete energy levels. But that's just a guess.

That is how I interpreted the phrase, however after reading it over a few times I just really don't think it makes much sense, if we replace the use of 'poverty' with what it means, he is saying,

Quantum mechanics shows how the insufficient amount of energy imposes structure.

Which I don't think is correct, an atom clearly has a sufficient amount of energy to impose structure in its matter and energy levels.

 

[PeterDonis]

an atom clearly has a sufficient amount of energy to impose structure in its matter and energy levels

You have it backwards. Try it this way: an atom has an insufficient amount of energy to allow its electrons to move freely and have a continuum of states available to them; this insufficiency of energy forces the electrons to reveal structure, namely the discrete energy levels of the bound states within the atom.