how can we make time inapplicable? prove it?
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Answer:
There are many experimental proofs for this. I can give you two of them to support time dilation which ultimately proofs that time is relative.
• Decay of μ-meson : A muon or μ- meson is an elementary particle, whose mean life is 2.2 × 10^-6 sec in a frame in which it is at rest. When cosmic rays fall on the upper part of the of the atmosphere, π-meson are produced which decay with a very short life to μ- meson. The velocity of μ- mesons should be less than speed of light, so the expected distance, travelled by them, is less than 2.2 × 10^-6 c which is equal to 0.66km ( c= speed of light). Thus, in the absence of any time dilation effect, the μ- mesons should not travel a distance greater than 0.66 km and so there is no possibility for these μ- mesons created at the top of atmosphere, to reach Earth's surface but experimentally, we found on the earth's surface an appreciable number of them. This can only be possible when time dilation is real and that causes life time of fast μ- meson to be much longer than the measured life time.
• Clocks on GPS satellites : The location finding method requires that a satellite transmit a time signal to a GPS receiver which can then determine its distance from the satellite by measuring the time that the signal took to reach the receiver. The satellites contain accurate atomic clocks and it has been noticed that these clocks in orbit run at a different rate than clocks on Earth. This could be a big problem for GPS because it means that errors in calculated positions would grow steadily larger each day. This is due to time dilation as GPS satellites are high above the earth in low Gravitational field and clocks in low Gravitational fields run faster than the clocks in high Gravitational fields.