On Sunday, September 29, 2019 at 9:51:25 PM UTC+1, Jos Bergervoet wrote:

On 19/09/29 12:58 AM, larry harson wrote:

On Saturday, September 28, 2019 at 6:04:52 PM UTC+1, Jos Bergervoet wrote:

On 19/09/23 1:40 AM, larry harson wrote:

On Friday, September 20, 2019 at 8:18:56 AM UTC+1, Jos Bergervoet wrote: >>>> On 19/09/20 1:26 AM, larry harson wrote:

...>>> ... Yet "massa gravitazionale" translates as this. On the >> other hand, pesante can translate as difficult, hard, weighty etc. I had >> high hopes that I might come up with something of the same high quality
as another Fermi translation:

https://en.wikisource.org/wiki/Translation:Electrodynamic_and_Relativistic_Theory_of_Electromagnetic_Mass

I don't see the name of the translator being mentioned there.. Who would >>>> actually do those translations "by Wikisource"?

Wikisources own policy states that the translator should be "credited as >>>> such in the header":
<https://en.wikisource.org/wiki/Wikisource:Translations#Translator_as_author>

But realistically, it's going to take far more time than I originally thought.

While you're here, Jos, can I ask your opinion on the following question which is related to this paper?

Suppose I have N point masses m all stationary in the center of momentum frame and equally distributed along the x-axis between +l and -l. This system will have a rest mass Nm with the COM frame travelling at velocity v in some other frame. Now let

there be a constant force +F_x along the x-axis in the initial COM frame between +L and -L where L >> l, hence accelerating each point mass m inside this region. If +F_x is 'small', then:

work done = 1/2L F_x = total change in KE = 1/2 Nm v^2, where v is the velocity of the COM frame.

You mean 2 L F_x, surely? The force works over a length 2L, over -L..L
and in fact this is true regardless whether F_x is 'small' or large.

Yes.

You mean no! (Below you say L F_x, while I wrote 2 L F_x).

I wanted to avoid the complication of the initial transition, and so assumed the continuous force was applied as an initial condition in the COM frame.

I see. Your starting condition has the point masses all inside the acceleration region, while I assumed that time started before they
enter it (so then each of them traverses the same acceleration region
and all of them end up with the same speed).
Clearly I misunderstood the description.

Hence the distance travelled by every point in the rigid mass system is approx 0 -> +L for L >> 2l, so I can define L as the distance travelled by the center of mass point for the system. I therefore meant work done = L F_x

Correct, and still valid for any value of F_x, either 'small' or large.

My question is: as +F_x increases, does this lead to an increase in the rest mass of the system?

I would have thought so because although the masses are equally accelerated initially in the COM frame, not so in the new COM frame a time dtau later leading to the masses having different velocities.

After all masses have traversed the region -L..L they have all acquired
the same new velocity (whatever it is). They then travel as one single
system again which has a rest frame with that velocity. So in that
frame they are again stationary.

They will have different velocities only as long as at least one of the
masses is still in transition. And indeed, during that time span they
form a total system with a larger rest mass. But afterwards it's back
to the old rest mass.

I believe they will also have different velocities in the COM frame while every mass is being hyperbolically accelerated by the same constant proper force F_x.

That will only be the case after they leave the acceleration region.

Initially they are accelerated all the same and their velocities
increase all at the same rate. But the leading one leaves the region
after a shorter time (and has traversed a smaller part of it) than
the trailing one. So of course the leading one comes out with the
lowest speed.

This means that the particles will all overtake each other (or collide, whatever they prefer) after leaving the region!

New question: will all N of them collide at the same time?

...

This problem was also written down by prof Kirk MacDonald in April 2019: http://www.physics.princeton.edu/~mcdonald/examples/rel_accel.pdf

"1 Problem
Acceleration is not often considered in special relativity, but it can be, as in the following problem.

A set of point like objects, each with initial velocity v_0 = (u, 0, 0), initially moving according to x_i(t)=(iL + ut, 0, 0) in one inertial frame, begin accelerating at a constant value a = (a, 0, 0) in the first frame at time t'_(i,0) = 0 in a second
inertial frame that has velocity v = (v, 0, 0) with respect to the first. Both a and v are positive. What are the subsequent histories of these objects according to observers in these two frames? Can these objects collide with one another for any values
of a, L, u and v?"

That's one hell of a problem, and an interesting coincidence! Yet hardly surprising since the acceleration of an extended charge by a constant E field is an interesting example related to this.

[snipped]

Larry Harson

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