How does super position not violate conservation of energy?

In summary, according to the principle of superposition, when two waves with the same amplitude are superposed, the resulting wave will have 4 times the energy of the original waves. However, if the waves are in perfect phase and there is no destructive interference, this would seem to violate energy conservation. The question is whether there is something incorrect about the way the question is phrased.
  • #1
Michio Cuckoo
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according the principle of superposition, a wave with a certain amplitude superposed with a similar wave will yield a wave with 4 times the amount of energy.

This would be double the combined energy of the original 2 waves. Assuming 2 point wave sources are perfectly in phase; and there is no destructive interference, wouldn't this violate energy conservation?
 
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  • #2
hmmm... is there something wrong with my phrasing of the question?
 
  • #3
according the principle of superposition, a wave with a certain amplitude superposed with a similar wave will yield a wave with 4 times the amount of energy.

Original waves energy: A^2 Superposed waves energy: (2A)^2 = 4A^2
 
  • #5


Superposition does not violate conservation of energy because the principle of superposition only applies to linear systems, where the output is directly proportional to the input. In the case of waves, the amplitude of the resulting wave is directly proportional to the sum of the amplitudes of the individual waves. This means that the energy of the resulting wave is simply the sum of the energies of the individual waves, which does not violate conservation of energy.

Additionally, the example given assumes ideal conditions where there is no destructive interference and the waves are perfectly in phase. In reality, waves can experience destructive interference, where the amplitudes cancel each other out and result in a lower overall energy. This balances out any potential increase in energy from superposition and ensures that energy is conserved.

Furthermore, superposition is a mathematical concept used to simplify the analysis of complex systems. It does not necessarily reflect the physical reality of the system, as energy is often lost through various factors such as friction and heat. Therefore, while the principle of superposition may suggest an increase in energy, it does not violate conservation of energy in the physical world.
 

Related to How does super position not violate conservation of energy?

1. How does the concept of superposition relate to the conservation of energy?

The concept of superposition refers to the idea that a system can exist in multiple states simultaneously. This may seem to violate the principle of conservation of energy, which states that energy cannot be created or destroyed. However, in quantum mechanics, superposition does not violate this principle because the total energy of the system remains constant, even if the individual components have different energies.

2. Can you give an example of how superposition does not violate conservation of energy?

One example is the quantum superposition of an electron, which can exist in multiple energy states at the same time. While it may seem that this violates conservation of energy, the total energy of the electron remains constant, and it only takes on a definite energy value when it is measured.

3. How does the uncertainty principle play a role in understanding how superposition does not violate conservation of energy?

The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. This means that even though a system may be in superposition and have multiple potential states, we cannot know for certain which state it is in. Therefore, the energy of the system is not violated since we cannot accurately measure it.

4. Why is the concept of superposition important in understanding energy conservation in quantum mechanics?

Superposition is a fundamental principle in quantum mechanics and is essential for understanding the behavior of particles at the subatomic level. It allows for a more accurate prediction of the energy states of particles and their interactions, ultimately leading to a better understanding of energy conservation in quantum systems.

5. How does the conservation of energy in quantum mechanics differ from classical mechanics?

In classical mechanics, energy is considered to be a fixed, constant quantity that can be measured with absolute certainty. However, in quantum mechanics, the energy of a system is described probabilistically, meaning that we cannot know its exact value until it is measured. This allows for the possibility of superposition, where a system can have multiple potential energy states at the same time without violating the principle of conservation of energy.

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