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One of the postulates special relativity is that "The laws of physics are the same in all inertial frames of reference." What is meaning of this statement?

If it is talking about physical laws I do not understand why because the laws of physics do not depend of the observer, for example , Maxwell equation is Maxwell equation in a accelerated frame or in a inertial frame.

If it talk about observation let us take the example of an source emitting light of frequency $\nu$ .Due to the doppler effect a static observer in relation to the source and one moving with velocity $v$ in relation to the source will see different frequencies and so different observation. So what is the meaning of this statement?

Qmechanic
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amilton moreira
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    Does this answer your question? What does the statement "the laws of physics are invariant" mean? – jng224 Apr 09 '21 at 18:10
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    In Newtonian physics, for an observer in an inertial frame the laws of physics take the form $\mathbf a = \mathbf F/m$, with $\mathbf F$ the net force on the particle. To an observer in a frame which is accelerating with acceleration $\mathbf a_0$, the laws of physics take the form $\mathbf a = \mathbf F/m - \mathbf a_0$. If you observed the latter, you would be able to experimentally determine that you were accelerating, which means that inertial frames and non-inertial frames are inequivalent in the context of Newtonian mechanics. – J. Murray Apr 09 '21 at 19:22
  • @ J. Murray That is because you are using a wrong formulation of Newtonian physics. Take a look at this lecture https://www.youtube.com/watch?v=IBlCu1zgD4Y&list=PLFeEvEPtX_0S6vxxiiNPrJbLu9aK1UVC_&index=9&t=4541s&ab_channel=TheWE-HeraeusInternationalWinterSchoolonGravityandLight – amilton moreira Apr 09 '21 at 19:33
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    @amiltonmoreira You are confused. In Newtonian physics, a (global) inertial frame is a cartesian coordinate system on spacetime in which Newton's laws hold. In such a frame, the laws of physics (i.e. Newton's 2nd law) take the form $\mathbf x''(t) = \mathbf F/m$. When we transform to another inertial frame via rotation, translation, or Galilean boost, each of the quantities in the 2nd law transform such that its form is preserved. If we move to a non-inertial frame, the non-zero Christoffel symbols change the form of the equation of motion. In this sense, inertial frames are special. – J. Murray Apr 10 '21 at 00:37

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I'm no expert on special relativity, but I believe the statement is based on the fact that all inertial (non accelerating) reference frames are considered equivalent, i.e., there is no preferred inertial reference frame. If physics laws were different in different inertial frames, then all inertial frames would not be equivalent.

the laws of physics are the same in all frame. Take for example a electron in electric field, what the trajectory of the electron has to do if the observer is accelerated or in inertial reference frame

If you are saying the trajectory (path) taken by the electron is the same for all observers, I believe that is incorrect.

Let's take a simpler example. Suppose there is an observer next to an open window on a train moving in a straight line at constant speed, i.e., constant velocity, with respect to the tracks. The observer is in an inertial frame of reference. The observer releases a ball out the window and watches it fall. To the observer on the train, its trajectory (path) is a straight line down until it impacts the ground. But to an observer on the tracks (a different inertial frame) the trajectory of the ball is a parabola. The trajectory (path) of the ball is not a physical law. It depends on the inertial frame of reference.

On the other hand, its acceleration is the same in both inertial frames. The observer on the train has a stop watch and determines the time it takes for the ball to impact the ground. The observer knows the vertical distance $d$ it has fallen and determines its acceleration from $d=1/2 at^2$. The observer on the tracks measures the same time to impact and comes up with the same acceleration.

Hope this helps.

Bob D
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  • the laws of physics are the same in all frame. Take for example a electron in electric field, what the trajectory of the electron has to do if the observer is accelerated or in inertial reference frame – amilton moreira Apr 09 '21 at 18:24
  • @amiltonmoreira Not clear what you're saying. Exactly what do you mean by "trajectory"? And then are you saying the trajectory of the electron is the same to an inertial observer as to an accelerating observer, or are you saying the observations would be different? Please clarify – Bob D Apr 09 '21 at 18:40
  • What i mean is that the trajectory(path in space) of the electron is independent of the observer – amilton moreira Apr 09 '21 at 18:50
  • You can record it in a cloud chamber – amilton moreira Apr 09 '21 at 18:56
  • See update to my answer – Bob D Apr 09 '21 at 21:44