yuiop
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RandallB said:...
Way to many inconsistencies in the definitions I’ve seen such as: If this form of mass is “invariant” how does invariant mass of a particle change over time; except by acquiring additional invariant mass to change into a new and different particle; such as an electron that converts into a heavier electron able to maintain a higher energy level.
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As far as I know, an invariant quantity in the context of relativity is defined as not changing under a Lorentz transformation, but does not imply the quantity can not change over time. An example of an invariant quantity is transverse length. A vibrating spring in the rest frame has its length continually changing but the length of the vibrating spring at any instant is invariant under transformation to a reference frame that has motion orthogonal to the length of the spring.
The (invariant mass)^2 is simply the quantity that is left when the (momentum mass)^2 is subtracted from the (inertial mass)^2. Inertial and gravitational propeties are related to the inertial mass which is why a photon has those properties, despite have zero rest (invariant) mass. As far as I can tell the only physical property related to rest mass is that non zero mass precludes a particle from moving at the speed of lightand the converse (a particle with zero rest mass can not move at less than the local speed of light). It is also worth noting that the inertial mass of a photon can change under transformation to a different reference frame, because the frequency changes.