stedwards said:
Using older terminology than Peter, you're talking about relativistic mass (a concept that has largely fallen out of favour, by the way), not rest mass.stedwards said:
My $0.02 is that one should consider the dynamical group for the entire system. E.g., in a rocket, matter is ejected in one direction to change the rocket's velocity in the opposite direction. The rocket thus feels acceleration, so one must be cautious about naively applying the Poincare group to the rocket in isolation, and hence should also be cautious about the "invariant mass" Casimir of the Poincare group. Rather, one should probably decompose into com and relative coordinates, and find the full dynamical group applicable to the system with com dofs factored out. Then look at the Casimirs of that group applicable to the relative motion...ChrisVer said:
PeterDonis said:
- The energy of a tree is just as little affected by your change of choice of reference system as the amount of gasoline in a car is affected by your choice of using gallons or liters. Changing the observation (assuming no interaction) can not affect what is observed.stedwards said:
What's your problem, mate? Peter is not the one who made an incorrect statement. You did, in post #6, i.e.,stedwards said:
That's just plain wrong. The word "no" is entirely appropriate in an answer to correct an error.stedwards said:
If by "P" you mean 4-momentum, then,... PeterD said essentially the same thing. But that's different from your incorrect statement that "rest mass is synonymous with energy".
strangerep said:
Uh oh. To answer that properly needs a lot more than a mere "$0.02 worth", but I don't have much spare time at the moment. Sorry.ChrisVer said:
Rest mass time dependent refers to the concept that the rest mass of an object can change over time due to factors such as motion, acceleration, and interactions with other objects.
Rest mass time dependent can affect an object's properties such as its momentum, energy, and gravitational force. As an object's rest mass changes, these properties can also change.
Rest mass can change over time due to factors such as an object's velocity, acceleration, and interactions with other objects. For example, as an object approaches the speed of light, its rest mass will increase.
Yes, rest mass time dependent is a concept that arises from Einstein's theory of relativity. It is based on the principle that an object's mass and energy are equivalent, and that the rest mass of an object is not constant but can change depending on its state of motion.
Rest mass time dependent is related to time dilation in that as an object's velocity increases, its rest mass increases and time appears to pass slower for the object compared to an observer at rest. This is due to the fact that time and mass are interconnected in relativity, and as an object's rest mass increases, it experiences time dilation.