# Inertia and Time Dilation

## Main Question or Discussion Point

First....I am not a physicist, and while I do have an engineering degree, advanced math was along time ago for me. However, I am very fascinated with Quantum Physics, the standard model, and cosmology and I've read several "layman" level books including Oerter,
Feynman, and Smolin. If anyone can point to similar books I would appreciate it....

My general question is whether there is anything that points to mass or inertia as really being a resistance to a change in the rate of time??? (I understand mass and inertia are different)

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but if traveling along in a spaceship at .5c, and I fire my handgun,
the velocity I percieve the bullet to have will be the same in any frame
of reference I'm in.....the powder charge behind the bullet is the same,
so the energy imparted to the bullet is the same.....so I'm missing something
with respect to relativity and mass or inertia.

JesseM
but if traveling along in a spaceship at .5c, and I fire my handgun,
the velocity I percieve the bullet to have will be the same in any frame
of reference I'm in.....the powder charge behind the bullet is the same,
so the energy imparted to the bullet is the same.....so I'm missing something
with respect to relativity and mass or inertia.
The bullet will always have the same speed in the frame where the gun is at rest, regardless of how fast the gun is moving relative to the Earth or any other landmark. If that's what you were saying, why do you think you're missing something here?

I think I'm missing something because at relativistic speeds it takes more energy
to achieve a delta-v, the chemical energy imparted to the bullet is the same...
but then I suppose the time dilation effect offsets the increased energy for acceleration effect such that my measurement of the velocity in the spaceship would seem the same
as the measured reference in the earth frame. But if I looked at the bullet in the spaceship from the frame of reference on earth, the velocity would look slower than the one I fired on the earth reference frame........right??

JesseM
I think I'm missing something because at relativistic speeds it takes more energy
to achieve a delta-v, the chemical energy imparted to the bullet is the same...
Well, the delta-v is always the same in the frame where the gun is at rest. In a frame where the gun is moving, the delta-v can be smaller or larger than in the gun's rest frame, depending on whether the bullet was traveling with the gun's direction of motion or against it (see relativistic velocity addition), and the energy imparted by the chemical explosion would also be different in this frame (since the molecules send outward by the explosion can have a higher velocity in this frame, they have greater kinetic energy to impart to the bullet).

Thanks........

Dale
Mentor
It is important to note that energy is a frame-variant quantity. Specifically, energy and momentum have the same relationship to each other that time and space do via the Lorentz transform. If you want more details look up "four momentum".