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## Main Question or Discussion Point

Consider a frame S' moving with speed u along +ve x direction with respect to another frame S. Consider a body moving with speed v along +ve x direction with respect to frame S . Both frame are inertials.

here,force acting in S frame on the body is $$ F\hat x=\frac {dp} {dt}\hat x,$$

$$F\hat x=v\frac {dm} {dt}\hat x+m\frac {dv} {dt}\hat x,$$

According to Galilean transformation,

force acting in S' frame on the body is $$ F'\hat x'=\frac {dp'} {dt'}\hat x',$$

where $$\hat x'=\hat x,$$

and $$t'=t,$$

$$F'\hat x={(v-u)}\frac {dm} {dt}\hat x+m\frac {dv} {dt}\hat x,$$

So, under Galilean transformation, Newton's 2nd law of motion is invariant only when mass of the system is constant with respect to time; otherwise it is not co-variant,too. Is this right?

Is it only Maxwell wave equation, which is not co-variant under Galilean transformation or all wave equations derived using laws of classical mechanics are not co-variant under Galilean transformation?

Even if Maxwell wave equation is not not co-variant under Galilean transformation,why should this lead to special relativity?

here,force acting in S frame on the body is $$ F\hat x=\frac {dp} {dt}\hat x,$$

$$F\hat x=v\frac {dm} {dt}\hat x+m\frac {dv} {dt}\hat x,$$

According to Galilean transformation,

force acting in S' frame on the body is $$ F'\hat x'=\frac {dp'} {dt'}\hat x',$$

where $$\hat x'=\hat x,$$

and $$t'=t,$$

$$F'\hat x={(v-u)}\frac {dm} {dt}\hat x+m\frac {dv} {dt}\hat x,$$

So, under Galilean transformation, Newton's 2nd law of motion is invariant only when mass of the system is constant with respect to time; otherwise it is not co-variant,too. Is this right?

Is it only Maxwell wave equation, which is not co-variant under Galilean transformation or all wave equations derived using laws of classical mechanics are not co-variant under Galilean transformation?

Even if Maxwell wave equation is not not co-variant under Galilean transformation,why should this lead to special relativity?

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