# Conservation of energy

If velocity is reference frame dependent then kinetic energy should also be.
Considering this we will have different energies in different frames.
Doesn't it violate conservation of energy?

No it doesn't. Being frame dependent and conserved are different things. Conserved means it is constant in time, but it can be different constants in different frames.

So it means conservation of energy is limited to a single frame

No, it means that energy is constant in every frame, but in principle this constant may have different (but constant in time) values in different frames.

So we can have a zero energy frame also?

ZapperZ
Staff Emeritus
So we can have a zero energy frame also?

When a mass m is at rest in your reference frame, what is its kinetic energy?

Zz.

Zero!

ZapperZ
Staff Emeritus
Zero!

Zz.

That I know but what about the original question..
How to explain conservation?

PeroK
Homework Helper
Gold Member
2021 Award
So we can have a zero energy frame also?
For a system of particles there is no zero kinetic energy frame as there is a zero momentum frame. That should be obvious, as kinetic energy is non negative.

ZapperZ
Staff Emeritus
That I know but what about the original question..
How to explain conservation?

Again, as has been stated by other responses, there is no issue with energy conservation.

If you are in one reference frame, and the object is moving at speed v, the object has KE = ½ mv2.

On the other hand, an observer moving with the object will measure zero KE.

There is no issue with conservation of energy here. Each observer is in a different frame, as has already been mentioned.

If you are in one reference frame and wish to go to another reference frame, you have to BOOST yourself to that frame, and thus, require external energy input. This is now no longer an isolated system and energy should not be conserved for the original system.

Zz.

• vanhees71
If velocity is reference frame dependent then kinetic energy should also be.
Considering this we will have different energies in different frames.
Doesn't it violate conservation of energy?
The fact a quantity doesn't vary changing the frame of reference is not called "conservation" in physics, it's (usually) called "invariance". They are both important, but completely different concepts.

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lightarrow

Dale
Mentor
2021 Award
If velocity is reference frame dependent then kinetic energy should also be.
Considering this we will have different energies in different frames.
Yes, this is correct.

Doesn't it violate conservation of energy?
No, it does not. Let’s consider a specific toy example. Suppose we have two 1 kg masses joined by a compressed spring containing 1 J of elastic energy.

In the frame where they are initially at rest the initial KE is 0 J and the initial PE is 1 J. If the spring is released then one mass will move at 1 m/s and the other mass will at -1 m/s. So the final KE is 1 J (evenly divided between the masses) and the final PE is 0 J. Energy is conserved.

In the frame where they are initially moving at 2 m/s the initial PE is 1 J and the initial KE is 4 J. After release one mass will move at 3 m/s and the other will move at 1 m/s. So the final KE is 5 J (4.5 J in one mass and 0.5 J in the other) and the final PE is 0 J. Energy is also conserved.