How? The total energy of a single particle is given by
E^2=p^2c^2 + m^4c^4
...Woah, hold on a minute. Are you trying to claim that because E is a function of m, that m is a function of E? If so, that is just simply wrong.
The fact a set of numbers A can be expressed as function of a second...
Yes, of course, or rather it is isolated once the hands release the balls. 'Same with the vessel filled with gas. It is not a closed system while the heat is being added. OF course that is not really relevant to the discussion at hand. The point is, it is not the total energy of a system...
There is something else? What? We have point particles, we have binding energies between them, and we have massless partciles whose momenta sum to zero. What else is there?
No, because mass is not fundamentally a function of energy. It is only a function of rest energy. That said, the...
Check me if I am wrong, but that is only true if the photons produced by the the fission have momenta that all add to zero.
Doesn't that assume no gamma photon is emitted? Nonetheless, your point is taken. Any net momentum imparted to the two particles will have to be offset by the momentum...
Apparently you missed the very first sentence in the thread:
The fact is the number of physics classes I took was more than 20. My major was physics.
That's an odd statement. I don't recall any Newtonian references to a mass associated with a compressed spring, or one associated with...
Absolutely. No force is required to separate them, and consequently no additional energy. Detach the spring at that instant, and they will continue to move apart. Now, whether we decide it is inappropriate to consider a bound state to have a magnitude (it is certainly not valid for QM, but...
The kinetic energy of each ball changes, of course. How does the kinetic energy of the system WRT an external observer change? Whatever its mass, its position in space remains fixed relative to the external observer. The Lorentz transform for the center of mass of the system thus collapses to...
Because it isn't a bound state, at least not when the balls pass the zero crossing point of the force function. At that point the spring has no effect whatsoever on the motion of the balls. At that point the potential energy of the system is zero, of course, but the point is the mass of the...
Quite. I would definitely enjoy seeing a rocket being ripped apart relativistically - as long as no one was aboard.
It is relevant to note, I think, that reproducing the experiment at 1G would be impossible in practical terms. It just would not be possible to attach a rope frail enough to...
Who says it is moving at Relativistic speeds? And relative to what? This scenario does not require the ships to be moving at anything more than a vanishingly small velocity WRT the initial external reference frame.
Yes, but the effect is instantaneous. The elapsed time from when the force...
I don't see why you seem to be saying it is unimportant. Precisely the same fundamental principles apply to both situations. Understanding how and why those principles result in vastly different results under nearly - but not quite - identical circumstances is crucial to a proper understanding...
To my mind, that is a trivial aspect of the illustration. That almost nothing is the same in Newtonian physics as in Relativity is patently obvious. To my way of thinking, the important thing to understanding the issue is the fact there is a difference to the universe along the direction of...
Your interpretation of my scenario is correct. Of course, the other scenario is also interesting. I am pedestrian enough to enjoy seeing things ripped apart. :smile:
That has been discussed in the other threads, but to my mind stating it that way obscures what is going on. A simple simultaneity issue (yes, I know there isn't really such a thing) makes it sound as if in fact there are two values of t1 and t2 that will allow the two ships to remain at a fixed...