# Conservation of energy and measurement problem

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• entropy1
In summary, the law of conservation of energy states that the total energy of a system remains the same no matter what state the system is in. If we have a two dimensional measurement basis, then we have two possible outcomes of the measurement. If we measure only one outcome, then the law of conservation of energy is violated. However, if we measure both outcomes simultaneously, the law of conservation of energy is still upheld.
entropy1
If we have a two dimensional measurementbasis, then we have two possible outcomes of the measurement. Now I figured: considering the law of conservation of energy, if one particle goes in, one and only one can come out. So outcome "both results simultaneously" cannot happen, for that would violate the law of conservation of energy. So would "neither outcome". So, that leaves us with one outcome or the other.

So I am wondering if the law of conservation of energy could account for measuring only single outcomes? (Measurement problem)

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entropy1 said:
I am wondering if the law of conservation of energy could account for measuring only single outcomes?

No, it can't. In the many worlds interpretation, the measured system becomes entangled with the measuring device, and the whole entangled state is still an eigenstate of total energy with the same eigenvalue. In the case of measuring a single particle, each "branch" of the entangled wave function only has one particle in it, so one particle goes in and one particle comes out. But because there are multiple branches, you can't attribute the total energy to each branch separately; you can only attribute it to the entire entangled wave function as a whole. Neither branch has a well-defined energy by itself, because neither branch is a well-defined state by itself; only the full entangled wave function is a well-defined state.

entropy1 said:
If we have a two dimensional measurementbasis, then we have two possible outcomes of the measurement. Now I figured: considering the law of conservation of energy, if one particle goes in, one and only one can come out. So outcome "both results simultaneously" cannot happen, for that would violate the law of conservation of energy. So would "neither outcome". So, that leaves us with one outcome or the other.

So I am wondering if the law of conservation of energy could account for measuring only single outcomes? (Measurement problem)
In the statistical interpretation of QM, only the expectations of the energy is conserved.

Thanks. I have to study that some.

I vaguely recall that I have asked this very question before. The search function is inadequate for searching threads.

## 1. What is the conservation of energy?

The conservation of energy is a fundamental law of physics that states that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another.

## 2. Why is the conservation of energy important?

The conservation of energy is important because it helps us understand and predict the behavior of physical systems. It also allows us to make efficient use of energy resources and develop technologies that use energy in sustainable ways.

## 3. What is the measurement problem in conservation of energy?

The measurement problem in conservation of energy refers to the difficulty in accurately measuring and quantifying all forms of energy within a system. This is because energy can exist in many different forms, such as kinetic, potential, thermal, and electromagnetic, and it can also be transferred between these forms.

## 4. How do scientists measure energy?

Scientists use a variety of methods to measure energy, depending on the type of energy being measured. For example, kinetic energy can be measured using equations that take into account an object's mass and velocity, while potential energy can be measured using equations that consider an object's height and mass. Other forms of energy, such as thermal and electromagnetic energy, can be measured using specialized instruments.

## 5. How does the conservation of energy relate to other laws of physics?

The conservation of energy is closely related to other fundamental laws of physics, such as the laws of thermodynamics and the law of conservation of momentum. These laws all describe different aspects of how energy and matter behave in the physical world and are interconnected in various ways.

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