# Do different reference frames agree with total energy?

• BomboshMan
In summary, total energy is not agreed upon by different frames of reference in both relativistic and non-relativistic physics. While energy is conserved in any inertial reference frame, it is not invariant between frames.
BomboshMan
I know total energy is conserved, but does this mean that different frames agree on the total energy of a particle?

I'm assuming they don't agree on energy, because if I measured the total energy of a particle moving relative to me (which would equal the rest energy plus its kinetic energy) surely this can't be the same as the total energy of the particle measured by someone in a frame where the particle's at rest (where the total energy would just be its rest energy). Or am I going wrong somewhere?

Thanks :)

Indeed not: if you measure the energy of a massive particle at rest relative to you and then boost to the frame of an observer who has a non - vanishing relative velocity in say the +x direction then under a lorentz transformation the energy is mapped as $m_{0}c^{2} \rightarrow \gamma m_{0}c^{2}$.

BomboshMan said:
I know total energy is conserved, but does this mean that different frames agree on the total energy of a particle?

No. This is true both in relativistic and non-relativistic physics, by the way. Energy is conserved in any inertial reference frame, but is it not invariant between inertial reference frames.

Thanks guys :D

I can confirm that different reference frames do not necessarily agree on the total energy of a particle. This is because total energy is a relative concept and can depend on the observer's frame of reference. In other words, the total energy of a particle can be measured differently by different observers depending on their relative motion.

For example, if we take the scenario described, where one observer measures the total energy of a moving particle and another measures the total energy of the same particle at rest, they will get different values. This is because the moving observer will also take into account the particle's kinetic energy, while the observer at rest will only measure the particle's rest energy.

However, it is important to note that while the values of total energy may differ, the principle of conservation of energy still holds true in all reference frames. This means that the sum of all energies in a closed system remains constant, even if the individual values may vary.

In summary, different reference frames may not agree on the total energy of a particle, but the concept of conservation of energy remains consistent in all frames.

## 1. What is a reference frame?

A reference frame is a set of coordinates used to describe the position and motion of objects. It serves as a point of reference for measuring physical quantities such as distance, time, and energy.

## 2. How do different reference frames affect the measurement of total energy?

Different reference frames can affect the measurement of total energy because energy is relative to the observer's frame of reference. This means that the total energy measured by one observer may differ from the total energy measured by another observer in a different reference frame.

## 3. Is total energy conserved in all reference frames?

Yes, total energy is conserved in all reference frames. This is known as the principle of energy conservation, which states that energy cannot be created or destroyed, only transformed from one form to another.

## 4. How does the theory of relativity relate to reference frames and total energy?

The theory of relativity explains how different observers in different reference frames may measure different values for total energy. It also shows that time and space are relative to the observer's frame of reference.

## 5. Can reference frames be transformed to agree on total energy?

Yes, reference frames can be transformed to agree on total energy. This can be done using mathematical equations, such as the Lorentz transformation, which allows for the conversion of measurements between reference frames.

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