Thought experiment: I am starting to walk on a corridor. From the corridor's perspective I have a certain increase of kinetic energy. From my perspective the whole universe is gaining kinetic energy because it has a speed relative to me. The kinetic energy increase from the corridor's point of view is definitely not equal to the kinetic energy increase of the universe from my perspective. What am I doing wrong?
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There are two distinct points to make, and both are related to the implicit assumption of Galilean invariance that you're making. Galilean invariance is the idea that all inertial frames are equally valid so, for example, you might stand by a train track watching the train and regard yourself as stationary and the train as moving, but a passenger on the train would be equally justified in regarding themselves as stationary and you as moving. In this case the choice is between you moving and the corridor stationary and the corridor moving and you stationary.
The first point is that kinetic energy is not an invariant under Galilean transformations. This is obviously so since if a fly is moving towards an elephant the total kinetic energy measured in the rest frame of the fly is (far) higher than the total kinetic energy measured in the rest frame of the elephant. However this does not violate conservation of energy, it just moves the reference point that we define as zero energy. No energy is appearing or disappearing.
The second point is that Galilean invariance applies only between inertial frames, i.e. frames moving at constant velocity, and introducing acceleration breaks the invariance. Velocity is relative, and you can't say what your velocity is or what the corridor's velocity is because it depends on the observer. However you can always say what your acceleration is because you can measure it using an accelerometer (like the one in your smartphone) without referring to any other object.
This matters because with acceleration you do have to worry about conservation of energy. When you begin walking you experience some force, and the work done on you is equal to force times distance moved. This work is equal to the increase in your kinetic energy. Likewise the corridor (and presumably the planet Earth) feels an equal and opposite force and it's kinetic energy must increase by the force times the distance the corridor moves.
You can choose any inertial frame to watch your progress down the corridor, but in all frames the force on you and the force on the corridor will be the same. It's straightforward to demonstrate the the work done is equal to the total kinetic energy change in all frames, but I won't do it here since this is dicussed in detail in the question Perspective and changes in kinetic energy.
John Rennie
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Let us assume as you move (velocity $v$) you will see the relative kinetic energy of the Universe increases, therefore energy of $KE_0$ we measure is different to the kinetic energy in perspective of the Universe of us $KE_1$, and since the mass of universe is greater than you we can assume the kinetic energy will also be greater, therefore we will model this situation mathematically and say: $KE_0 > KE_1$ therefore observer will assume the energy conversations are broken. However now, each object in the universe will move away from other objects relatively at velocity $v$ as well therefore the relative kinetic energy between any 2 given coordinates will always remain $0$ in any & all frames of reference as the distance between them will never change but remain constant, so the 2 objects can never collide.
Using the above statement of
so the 2 objects can never collide
We can deduce that the $KE_0$ is not kinetic energy but should be considered more of a potential energy and since we must release this potential energy to break conservation of energy as we would create more energy and since using the statement of the 2 objects never colliding we can safely say the relative potential energy may never be harnessed by an means.
In other words, rather than looking at the relative kinetic energy we should consider it "relative potential kinetic energy". Finally, we can deduce that since we cannot directly create any energy using this "relative potential kinetic energy" the observer observers , we cannot have broken any laws of physics as no energy is created in any frames of reference.