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- Under what circumstances are they different?
Under what circumstances are they different?
This, from the abstract, looks like a speculative paper from a questionable journal. It appears to be behind a paywall so I can't read the full paper.Hatch, R.R. (2007) "A New Theory of Gravity", Physics Essays 20:1
No such effect has ever been observed experimentally. The current limits are pretty tight:"Inertial and gravitational mass diverge in value as a function of velocity." So he is wrong?
I’m confused by this as I believe it was explained in a recent time dilation thread that the time dilation experienced by a particle has dependence on the length of its world line compared to the length of another particle’s world line, when the particles are separated and then brought back together.Also, since in relativity "velocity" has no invariant meaning, it's hard to see what "as a function of velocity" would mean physically.
This is true. Why does it make you confused about what I said about velocity?the time dilation experienced by a particle has dependence on the length of its world line compared to the length of another particle’s world line, when the particles are separated and then brought back together
No. Velocity is not an invariant, just as "at rest" is not an invariant.Isn’t the “age” of the particle a function of its velocity?
Although it can be expressed as a functional of the velocity, it is an invariant quantity. However, you have misunderstood what it means to have a short world-line. The length of your world-line is the amount that you have aged. Hence, the shorter the world-line, the younger the object. Now, geometry in spacetime does not work the same way as geometry works in a "normal" space so the object moving around actually has a shorter world-line.If 2 particles are at rest, one then moves around wildly and is then brought back to rest with respect to the other particle, isn’t it now younger than the other particle that had a shorter world line or in plain language younger than the particle that had “less velocity?” Isn’t the “age” of the particle a function of its velocity?
If, by "at rest", you actually mean "at rest in an inertial frame" then yes. Otherwise, maybe. It depends on what you mean by "at rest".If 2 particles are at rest, one then moves around wildly and is then brought back to rest with respect to the other particle, isn’t it now younger than the other particle
The length (more precisely, the interval) of the worldline is the key thing here, the invariant on which everyone will agree. Whether or not an object had "more" or "less" velocity is dependent on your choice of frame.isn’t it now younger than the other particle that had a shorter world line or in plain language younger than the particle that had “less velocity?”
If you pick a frame then you can express the length of the worldline as a function solely of the velocity of the particle with respect to the frame. The form of the expression depends on your choice of frame, however, which is how the result can be the same even if you choose to use a frame where the velocity of the "wildly moving" one is zero.Isn’t the “age” of the particle a function of its velocity?
The following comment is not relevant to the issue of inertial versus gravitational mass, but I would like to suggest that interpreting time dilation as "speed slowing aging" is a bad way to think about it.If 2 particles are at rest, one then moves around wildly and is then brought back to rest with respect to the other particle, isn’t it now younger than the other particle that had a shorter world line or in plain language younger than the particle that had “less velocity?” Isn’t the “age” of the particle a function of its velocity?
If I understand this correctly,"not accelerating" an unstable particle can "hasten" its loss of inertial mass.How much your t-coordinate changes depends on the t-component of your velocity
No, I wasn't saying that. What I was saying was that if you're traveling to a particular point in spacetime--say, the point "Seattle, July 1, 2019", you can get there quicker (according to your watch) if you have a larger 4-velocity.If I understand this correctly,"not accelerating" an unstable particle can "hasten" its loss of inertial mass.
Should that say "3-velocity"? 4-velocity is normalised to ##c##. Or am I missing your point?larger 4-velocity.
I assume that, as @Ibix suggested, you mean a larger 3-velocity. 4-velocity is a unit vector; all 4-velocities are "the same size".you can get there quicker (according to your watch) if you have a larger 4-velocity.
Yes, that's what I meant.Should that say "3-velocity"? 4-velocity is normalised to ##c##. Or am I missing your point?
Although you’ll also have to start later and closer.say, the point "Seattle, July 1, 2019", you can get there quicker (according to your watch) if you have a larger43-velocity.
If you want to keep a constant 4-velocity, yes. But you can zig-zag to Seattle, July 1, 2019 and get there in arbitrarily small amount of proper time.Although you’ll also have to start later and closer.