Connection between Quantum and Classical worlds

In summary, the Correspondence Principle states that as the quantum number n goes to infinity, the discrete energy levels of a quantum system become continuous and approach the classical energy levels. This means that the difference between two adjacent levels becomes smaller and smaller until it is practically zero. In the case of a quantum harmonic oscillator, n goes to infinity as well, resulting in the disappearance of discrete energy levels. It is not clear when exactly the classical world starts and the quantum world ends, as our experiments are purely classical and we do not yet fully understand the connection between the two worlds. However, science aims to eventually understand and "see" how the world works through careful observation. For now, it is easier to think of the two worlds as separate entities
  • #1
Josh Coswell
1
0
According to the Correspondence Principle Discrete Quatum levels become Continous Classical levels when n goes to infinity, meaning that the difference between two adjacent level goes to zero.

Questions;

1)
What does infinity mean here? How for do we to go from the center of the atom that infinity is realized and the Quantum World becomes Classsical?


2)
Or in case of a quantum Hormonic Oscillator when does n go to infinity and discrete energy levels disappear?



In Hydrogen Atom

E(n) ~ 1/n(squared)
E(n-1) ~ 1/(n-1)(squared)

At what point in space the classical world starts and quantum world is finished.

Or we do not know how the two world are connected or there is no quantum world because we cannot see it. All of our experiments are purely classical and never quantum so where is the quantum world?
 
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  • #2
Josh Coswell said:
...At what point in space the classical world starts and quantum world is finished. ...

... All of our experiments are purely classical and never quantum so where is the quantum world?
You pretty much have it. As you said:
"we do not know how the two world are connected"
Sure you can say;
"there is no quantum world because we cannot see it."
Just recognize that as a philosophical statement not a scientific one.
Science hopes that we should be able to understand (therefore “see”) how our world works through careful scientific observation.
We just don’t know enough currently to know how to “look” at the world we are in, so for now we find it easier to think of it as "two worlds".
 
  • #3


I can provide the following response to the connection between Quantum and Classical worlds and the Correspondence Principle:

1) Infinity in this context refers to the concept that as the quantum number n increases, the energy levels in a quantum system become closer and closer together until they merge into a continuous spectrum in the classical world. This does not necessarily mean that we have to physically go to infinity in order to observe this phenomenon. Rather, it is a mathematical concept that helps us understand the relationship between the discrete quantum levels and the continuous classical levels.

2) In the case of a quantum harmonic oscillator, n can go to infinity as the potential energy increases without limit. However, the energy levels will never truly disappear as they will always be infinitely close together. This is consistent with the Correspondence Principle, as the classical harmonic oscillator also has a continuous energy spectrum.

In regards to the point in space where the classical world begins and the quantum world ends, it is important to remember that these are not two separate and distinct worlds. Rather, they are two different ways of describing and understanding the behavior of particles and systems. The classical world is simply a macroscopic description that emerges from the underlying quantum behavior of particles. Therefore, it is not a specific point in space where one ends and the other begins, but rather a gradual transition.

Lastly, it is true that we cannot directly observe the quantum world, as our experiments are limited to the classical scale. However, this does not mean that the quantum world does not exist. The laws of quantum mechanics have been extensively tested and have been shown to accurately describe the behavior of particles at the microscopic level. So while we may not be able to directly see the quantum world, we can understand and study it through mathematical models and experimental results.
 

Related to Connection between Quantum and Classical worlds

1. What is the difference between the Quantum and Classical worlds?

The main difference between the Quantum and Classical worlds is the scale at which they operate. The Classical world deals with objects that are large and can be observed directly, while the Quantum world deals with objects that are very small, such as atoms and subatomic particles, and can only be described through mathematical equations.

2. How are the Quantum and Classical worlds connected?

The Quantum and Classical worlds are connected through the process of measurement. In the Quantum world, particles exist in multiple states until they are observed or measured, causing them to "collapse" into a single state. This is known as the measurement problem. The Classical world, on the other hand, operates on a macroscopic level where objects have well-defined properties, and measurements do not cause any change in their state. Therefore, the connection between the two worlds lies in the measurement process and the way in which they are observed and interact with each other.

3. Can Classical mechanics explain Quantum phenomena?

No, Classical mechanics cannot fully explain Quantum phenomena. Classical mechanics is based on Newton's laws of motion and deals with macroscopic objects, while Quantum mechanics is based on principles such as uncertainty and superposition and deals with microscopic objects. The two theories have fundamentally different principles and cannot be used to explain each other's phenomena.

4. What is the role of probability in the Quantum and Classical worlds?

Probability plays a crucial role in both the Quantum and Classical worlds, but in different ways. In the Classical world, probability is used to predict the outcomes of events, based on known laws and initial conditions. In the Quantum world, probability is inherent in the nature of particles and their behavior, and it is not possible to make deterministic predictions about their exact behavior. This is due to the inherent uncertainty principle in Quantum mechanics.

5. How does the concept of entanglement connect the Quantum and Classical worlds?

Entanglement is a phenomenon in which two or more particles become connected in such a way that the state of one particle affects the state of the other, regardless of the distance between them. This concept connects the Quantum and Classical worlds as it allows for the transfer of quantum information to a macroscopic scale. This has potential applications in quantum computing and communication, bridging the gap between the two worlds and allowing for the use of quantum properties in everyday technology.

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