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1st postulate of relativity has emerged from the fact that there is no distinction/difference between state of rest and moving with a constant velocity. Thus, they are part of single frame, inertial frame!

But I have a thought experiment which shows how this assumption/law violates the law of conservation of energy. Kindly comment your views on this thought experiment and tell me where I am wrong....

Assume the universe has total energy equivalent to 10 units. Now the law of conservation of energy states that the number "10" would be constant until the end of time-as energy can't be created nor be destroyed.

Now imagine two sections of this universe 'A'and 'B'. One is full of frame of references like planets, starts, humans, etc. But another section of the universe, which is completely empty with no stars or planets around there. Now imagine a ball being shot across the sky. So some energy used to make that ball move hence some energy reduced from 10 units. Let us assume 2 units of energy has been used and that 2 units of energy is carried/possessed by the ball in form of kinetic energy thus, the total energy of unuverse is still constant i.e. 8+2.

Now imagine the ball travelled from 'A'to'B' where no stars or planets around to provide a reference frame. In that area, moving vs non moving is equivalent. Velocity is derivative of position with respect to the time. But, how would we know that the ball is moving of there is "NOTHING" to compare hence it would be in state of rest-by the defination that velocity is relative.

But! if the ball is at rest the kinetic enrgy is 0. Therefore, the total energy of the universe is reduced by 2 units i.e. 10-2=8. And thus, the law violates!

Dale
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Swayam Jha
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2 Answers2

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The principle of relativity says that the laws of physics are the same in all inertial frames. The laws of physics are usually written in terms of an action principle, or in other words in terms of a Lagrangian or a Hamiltonian. So what this means is that you can use the same action principle in any frame.

Now, locally the action principles of physics are the same today as they were yesterday, which is called time translation symmetry. This symmetry leads inevitably to the conservation of energy as proven in Noether’s theorem. So the conservation of energy holds in every reference frame.

However, the amount of energy in the universe is not a consequence of the laws of physics. There is no way to derive the energy from first principles. So there is no requirement that the amount of energy be the same.

Thus energy is a quantity that is conserved in every frame but which is different in different frames. Conservation and invariance are distinct concepts. The principle of relativity (together with the local form of the laws of physics) requires energy conservation to hold locally in all frames. But it does not require that the amount of energy be the same in all frames.

So your observation that there is a different amount of energy is correct, but your conclusion that the principle of relativity forbids that is not correct.

Dale
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The answer to the question in the title is: No.

@Dale's answer does a better job addressing details of your thought experiment.

However, regardless of the details,
the conservation of energy-momentum of two particles can be described by a quadrilateral,
the sum of the 4-momentum before is equal to the sum of the 4-momentum after.
The sum before [added tip-to-tail] makes a triangle with the total 4-momentum, and similarly for the sum after. (In the totally-inelastic case, the quadrilateral degenerates into a triangle.)

Just as a Euclidean rotation is a linear transformation that will transform that quadrilateral to another quadrilateral, a Lorentz transformation and Galilean transformation [which are associated with the principle of relativity] are linear transformations that will transform a quadrilateral into another quadrilateral, and thus conservation of total energy-momentum in one inertial frame implies its conservation holds all inertial frames... again, regardless of the details.

By the way, the principle of relativity is about inertial frames---
being "at rest" is not enough....
it must be "inertially at rest".... which excludes accelerated frames.

In addition, technically, special relativity is a vacuum spacetime... no matter sources. However, we always assume that there are observers that can make measurements anywhere in spacetime... even empty ones.

robphy
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