Undergrad Integrate time dilation with derivative

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Integrating time dilation with derivatives requires a clear understanding of the specific problem being analyzed. The time dilation formula is a limited case of the broader Lorentz transformations, which may be more beneficial for complex scenarios. Abandoning the time dilation formula in favor of Lorentz transformations is often recommended for better applicability. Providing additional context about the intended application will yield more precise guidance. Clarifying the problem will enhance the quality of responses received.
Franyer
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I need to integrate time dilation with derivative, how could I do that?
 
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Franyer said:
I need to integrate time dilation with derivative, how could I do that?
Without knowing the problem you're trying to analyze it's hard to answer with any certainty... But the chances are very good that you will be better off abandoning the time dilation formula and working with the more general Lorentz transformations.
The time dilation formula is a special case of the Lorentz transformations, and applicable only under very limited circumstances.

But tell us more about what you're trying to do and you'll get better and more helpful answer.
 

Thread 'Am I understanding the concept of proper frame of reference?'

MOVING CLOCKS In this section, we show that clocks moving at high speeds run slowly. We construct a clock, called a light clock, using a stick of proper lenght ##L_0##, and two mirrors. The two mirrors face each other, and a pulse of light bounces back and forth betweem them. Each time the light pulse strikes one of the mirrors, say the lower mirror, the clock is said to tick. Between successive ticks the light pulse travels a distance ##2L_0## in the proper reference of frame of the clock...
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