mass increases.
Nereid said:
IIRC, MM answered this before, either in this thread or another ... basically, you use the same equations, to get the same answers ... but you go through some hand waving first to convince yourself that you've come at these equations from a different direction than classic SR (a la Einstein).
Other critics of SR (and GR) either don't propose to account for the experimental and observational results at all, or (sometimes) say they'll be the same, or (very rare, but there are some) do propose situations where the differences can be brought to light (so to speak). Examples of members of this last, very exclusive club include Garth (his SCC alternative to GR predicts a distinctly different result from GPB than GR), wisp (he proposed a simple one-way test of the speed of light), and some folk who yogi mentions. Andrew Grey may also be a member of this club (it's been a while since I visited that thread).
Let's see what MM has to say ...
Very interesting, but I cannot see a reasonable ratio of math/physics in the explanation or the discussion.
MM's statement that he wasn't too concerned about the cause of mass incease and was content to conclude that mass increases was somhow due to the "nature of space that somehow causes" [the mass increase]. This sounds like complaceny to me. I cannot deny the gamma correlation between mass increase and acelerated electrons, for example, but even here to look at m/(1 - v^2)^1/2 expression that does not evoke many physical intuitions. I can see that the gamma can be used effectivley as a measure of the apparent velocity limitation, or velocity state of the electron, but to slide into relativisitc convenience here seems like such a dreadful waste of effort
The mass of a particle can increase without an increase in mass, not to contradict myself, once you grasp the concept of "effective mass". Wave your finger back and forth a few cm side to side at 1hz. Notice how the mass of your finger spends a certain dt in measurable volumes, dvols, as the finger moves. Increase the frequency of the finger to 2hz and notice how the m[(dvols/dt)(2hz)] increases as the frequency increases. Now oscillate your finger at 500hz and notice the
m[(dvols/dt)(500hz)] increases.
Of course you can't move your finger to 500hz because the finger is frequency limited to absorbing, storing and using energy that inceases the frequency of the finger. You will never get your finger to move at 500hz so we could use this number as the corrollary to gamma, except we intuitively know that the true limit is much less than 500hz. You can most certainly, however, train your finger to go faster than its intrinsic limitations at this moment.
The moral of the story is that electrons become massive because they spend an ever increasing amount of time within any dvols/dt. If someone were to see what your 500hz finger felt like and actually touched the finger, they would proabbly lose theirs, or at least suffere some serious physical damage. The moving finger could punch holes in walls similar to rocks thrown against the wall, or bullets.
The effective mass I am suggesting is simply an increase in velocity and frequency of the accelerated particle. As the frequency reaches a certain constraining velocity, the efficiency of the energy exchange between the accelerating energy and the electron decreases. More energy is needed to simply onload and store the accelerating energy and less to actually increasing velocity. Velocity is increasing tremendously, to a point ~ c, but the slack is seen in frequency and M(f) increases.
One must eventually begin to look at the processes in all this physical stuff that is going on around us, but unfortunately the QM police always nab those who dast to peek behind the interference amplitude curtains, or even just a quick discreet glance under Mother Nature's hem.
Theerfore the effective mass is, Meff = M0 + M(dx/dt) + M(f), or the effective mass is the sum of the rest mass plus the mass as a function of velocity plus the mass as a function of frequency, brought about during the application of the force, d(mv)/dt = m(dv/dt) + v(dm/dt).
Gamma merely tells us the limited velocity state. Of course other inferences can be made form gamma, but the expression is essectially physics free.
Think abiut energy exchanges with the modulated frequency of the accelerating field and the frequency of the electron. Brute force .999c velocity is a measure of having exceeded a reasobnable return on the energy investment. You have to get off the mgamma curve if you are ever going to exceed the speed of light, and as a reminder, all that space out there? well we ain't going to get there from here the way we are going.
"The moving finger writes and having writ moves on, nor with all your piety nor wit shall ye lure it back to cancel even half a line."
Omar K.