What is the purpose to require that the laws of physics be the same in all so-called inertial frames? On one hand it is natural to suppose that the basic laws, such as laws of mechanics and electrodynamics, are equally valid in every part of the Universe. It seems that almost all scientists believe in the unity of the Universe. But on the other hand such a belief is not very useful unless we have the power to confirm or deny its validity. For example, we can't test the validity of fluid mechanics on a planet 100 ly far from the Earth. Can we? All we can say is that the electromagnetic waves coming from far planet to us are pretty much the same as the EM waves we produce and use in our Earth-bound laboratories. That's all we can.
Imagine two identical copies of a system--laboratories--where we test mechanical waves. The systems are isolated, as much as possible, one from another, but are moving relative to each other with constant velocity v. In each system we would test a wave equation--in one system the equation is expressed with (x,t) coordinates, and in the other system with coordinates (x',t') (spatial and temporal coordinates). It is a simple math to show that the wave equations have the same form, but if we relate the coordinates as x'=x-vt & t'=t, the wave equation changes its form. The same will happen if we use Lorentz transformation, simply because the speeds of mechanical waves are different from the speed of light in vacuum. But, why we need to do that--to express our equations in the coordinates from some other system? Is it not enough to state that the laws governing the mechanical wave are the same? We already have two equal equations. It is true that we can find linear transformation, which is neither Galilean nor Lorentz, preserving the form of the equations in two systems, but for what purpose we should do that?
The bottom line is this--we don't need any theory of relativity. Any theory of relativity is useless and brings only confusion into physics.
Of course the universe will not simply cease to function without inertial reference frames, but the point is that clever use of reference frames can simplify problems quite a bit. How can you expect to analyze the projectile motion of a basketball on earth without using the earth as your frame of reference? There are many scenarios where using a non-inertial frame of reference is useful or even essential, but a massive amount of understanding can be derived from being able to simplify problems - where appropriate.
Jory Seguin
First, the Earth is not an inertial system. It is only approximatelly an inertial system. One cannot find ideal inertial system in reality.
Second, I didn't suggest to abandon use of reference frames. Of course it is true that anything physical must be described in some reference frame. I've suggested that the imposition of linear connexion between coordinates of two systems as something that must be respected per se, is unnatural and unnecessary. In other words, one can use coordinates as he likes, but that does not mean that the equations should preserve their form.
Third, it is true that transformation of coordinates in some cases can simplify the problem at hand, but that kind of mathematical manipulations do not say anything physical about physical space and time. It's only a math. No more, no less.
I suppose that this issue relies on fundamental role of the hystorical Galilean invariance issue, that is that laws and solutions must be the same in any inertial reference system. After GR theory this assumption can be relaxed but in classical mechanics it is still useful. However, also in the GR an assumption of "inertial frame" is somehow implied by the Lorentz transformation.
Why are you stating that any theory of relativity introduces confusion?
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