# Energy as a non relativistic scalar and Galilean invariance

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## Summary:

Why is there no contradiction between energy as a non relativistic scalar and Galilean invariance?

## Main Question or Discussion Point

Summary: Why is there no contradiction between energy as a non relativistic scalar and Galilean invariance?

If energy is a non relativistic scalar, doesn't it mean that there is a contradiction with Galilean invariance?
What i mean is that if i try to accelerate an object within the Galilean ship that has no windows and if it takes more energy to accelerate the object inside the ship, than the energy it took to do so on the wharf/platform, then i presumably know the ship is at constant movement in relation to the platform and not standing near the platform, without looking out of the ship windows, or isn't that so? I bet it isn't so, but why?
Please explain with words, no math, i can't read math.

## Answers and Replies

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PeterDonis
Mentor
2019 Award
Moderator's note: Thread moved to Classical Physics since it is asking about non-relativistic physics.

PeterDonis
Mentor
2019 Award
If energy is a non relativistic scalar
Why do you think energy is a non-relativistic scalar? Energy is frame-dependent in non-relativistic physics.

PeterDonis
Mentor
2019 Award
if it takes more energy to accelerate the object inside the ship, than the energy it took to do so on the wharf/platform
It doesn't take more energy relative to the ship. It does relative to the platform. Which illustrates that, as I said in my last post, energy is frame-dependent.

Heikki Tuuri
But if i push the object inside the ship, couldn't now the inside of the ship be considered a new platform and so, since as i get closer to the speed of light, there is a need to invest more energy, in order to accelerate an object, now inside the ship, if i see that i need more energy than was needed on the platform, i know the ship is moving, without looking out of the ship windows, which contradicts Galilean principle of relativity, which states that the only way to know if the ship is moving at constant speed in relation to the platform, is to look outside and observe the platform moving? I guess i am not articulating what bugs me here well enough..Say both on the platform and inside the ship trying to accelerate the same object by +1 m/s, the ship of course is either moving at constant speed or not at all, if it is moving, the value of constant speed does not matter and when doing this experiment inside the ship, i have to find out if the ship is moving or not, by pushing that same object to +1 m/s and measuring the energy needed for this action, without looking outside at the platform and comparing results of energy investment to the same experiment, when made on the platform.

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Ibix
I am not certain whether you are talking about Newtonian physics (your references to Galilean relativity suggest so) or relativistic physics (as your references to the speed of light suggest). Either way the answer is the same.

The whole point of the principle of relativity is that you can always regard yourself as stationary. Accelerating something from stationary with respect to you to 1m/s with respect to you will always take the same amount of energy whatever your state of motion. Other observers may disagree on how much energy it took, but they will always have a consistent explanation for where the energy came from.

You specified no maths so I cannot prove this to you, but it's easy enough to do.

Dale
Spaceship
-----|===>
100 m/s --->

Weight 1 kg O -> 1 m/s

If you are standing inside a spaceship, which moves at a constant speed, it always takes you 0.5 joules of muscle chemical energy to accelerate a 1 kg weight to the speed 1 m/s, to the direction of the spaceship.

An outside observer sees the kinetic energy of the weight to increase much more, say, 100 joules. From where did this extra 99.5 joules of energy come from? It did not come from your muscles. They spent just that 0.5 joules of chemical energy.

The extra 99.5 joules comes from the kinetic energy of the spaceship. The outside observer sees the spaceship slow down a little bit and the weight to start moving at 1 m/s relative to the spaceship.

https://en.wikipedia.org/wiki/Oberth_effect

The Oberth effect, which is discussed in another thread today, utilizes the above math. If you fire your rocket when the spaceship moves at a high speed relative to a planet, you will gain more kinetic energy in the frame of the planet. The secret is that you rob kinetic energy from the jet exhaust gas.

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PeterDonis
Mentor
2019 Award
i know the ship is moving, without looking out of the ship windows
How do you know? The amount of energy relative to the ship that is needed to push the object to a given speed relative to the ship never changes.