1. From a Newtonian perspective:

    • F = ma
    • F dx = ma dx
    • E = m (dv/dt) dx
    • m = (E dt) / (dv dx)

Mass is directly proportional to time, if time slows down then mass goes down or decreases.

  1. From a Relativistic perspective:

    • Approaching c, time slows down and mass goes up or increases. Mass is inversely proportional to time.

Irrespective of what speed you are travelling, the fundamental relationship between mass and time should remain. So is mass directly or inversely proportional to time?

  • 3
    $\begingroup$ My mass seems to increase with time (sigh)... But, you can perform math manipulations on any equation, but that doesn't mean that they are physically meaningful. $\endgroup$
    – Jon Custer
    Jan 18, 2016 at 15:30
  • $\begingroup$ Interesting application, since mass increases with increased velocity then it stands to reason that you can lose weight by sitting on the couch watching the big bang theory... I should submit that theory to weight watchers magazine. $\endgroup$ Jan 18, 2016 at 21:34
  • $\begingroup$ Well actually, from your rearranging, shouldn't mass proportional to $dt$ rather than time? I don't see time appearing anywhere $\endgroup$
    – Steeven
    Jan 18, 2016 at 22:33

3 Answers 3


Mass doesn't depend on time. As in your equation, if the difference in time increases or decreases, the difference in velocity will increase or decrease, so the mass will be constant. As velocity is a variable you cannot come to a conclusion like that. To get a proportional relationship all the other factors should be constant on the equation.

  • $\begingroup$ The equation m = (E dt) / (dv dx) is correct, but that doesn't mean m is proportional to dt. For that all the other factors should be constant. $\endgroup$ Jan 18, 2016 at 17:53

Please bare in mind that although your relations are mathematically correct, this is not the case conceptually. Mass is a concept which in Newton's framework, is intrinsic to bodies and independent of its motion or time, or any other conditions. Whereas in Einstein framework, mass as the inertial property, does depend on the state of motion, but the mass as origin of gravity does not.


Thanks, that helped me work it out, both the mathematics and the concept hold. I thought about "all the other factors should be constant on the equation".

So, say with constant energy E=1, travel 1 metre at 1 metre/second and this takes 1 second and you weigh 1 kilogram. If time slows down then on this journey you would actually experience more seconds. Relativistically 10 seconds would pass, time would conceptually pass slower but mathematically, the value of t would have a greater value and increase. If distance, velocity and energy are held constant then mass must increase.

Mass is directly proportional to time, but cramming more time into "t" is actually "slowing down time" and therefore slowing down time creates mass.


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