- #1
Pushoam
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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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