Re: .Re: Why all the fascination with E = mc^2 ??

From: Leonard Pardin (leoppard_at_MailAndNews.com)
Date: 06/03/04 

Date: 3 Jun 2004 10:23:04 -0700

D.McAnally@i'm_a_gnu.uq.net.au (David McAnally) wrote in message news:<c9muid$qk4$1@bunyip.cc.uq.edu.au>...
> leoppard@MailAndNews.com (Leonard Pardin) writes:
>
> <snip>
>
> > Einstein seems to be saying just what you said: mass/energy in one
> >frame appears to be reduced in another frame.
>
> No. Einstein took the classical Conservation of Energy is both frames.
>He
> had already calculated how the energy of radiation transforms between
> frames, so he could use Conservation of Energy in both frames, and
> calculate how the energy of the body in question changes as a consequence
> of the radiation.
>
> Einstein starts off with a body of a certain mass (M, say).

    Where are you getting that from? Einstein doesn't even mention
mass until the conclusion.

>He uses the
> frame in which the body is stationary. He then allows, in the frame in
> which the body is stationary, the body to radiate radiation of energy L/2
> in one direction, and radiation of energy L/2 in the opposite direction.
> This allows the body to remain stationary after the radiation (the
> momentum of one lot of radiation cancels the momentum from the other lot
> of radiation, so that the momentum of the body remains unchanged, i.e. at
> zero).

    Okay. Total mass of the stationary body in the STATIONARY SYSTEM
is L (1/2 L one way, and 1/2 L the other). Fine so far.

>Einstein then investigates the same set-up in another frame which
> is moving relative to the original frame (at velocity -v). In this frame,
> the body has mass M and is moving at velocity v, and then it radiates a
> certain amount of energy in two directions

    HOLD IT!! Are we reading the same Einstein? That passage I
posted is a quote from Einstein's 1905b paper. He says nothing about
a second body in another frame.

    Instead, Einstein says that the energy radiated by the body in the
STATIONARY SYSTEM is measured from the MOVING SYSTEM with different
results. There is only one body, and it is located in the STATIONARY
SYSTEM. So we are going to get two measurements: one set as measured
from the STATIONARY SYSTEM and one set as measured from the MOVING
SYSTEM.

>(with the energies being
> calculated using the formula that Einstein had already derived), and then,
> after radiation, the body continues to move with velocity v.

   WAIT A MINUTE! The body doesn't move at all in the STATIONARY
SYSTEM. It just sits there radiating light. The motion of the body as
measured from the MOVING SYSTEM is due only to the motion of the
MOVING SYSTEM.

> Later in
> Einstein's working, he additionally assumes that |v| is much smaller than
> c (this is so that he can use Newton's approximation for the formula for
> the kinetic energy).

Lucky for Einstein Newton provided a classical formula for kinetic
energy.

>
> In the second frame of reference, the kinetic energy of the body before
> radiation is 1/2 M v^2 (plus a series of terms too small to worry about).
> The total energy content of the body in the second frame of reference is
> equal to the total energy content of the body in the first frame of
> reference plus the kinetic energy.

     Einstein mentions no body in the "second frame" (the MOVING
SYSTEM); there is only one body, and it's in the STATIONARY SYSTEM.
Are you getting your facts from a differenc source?

> We know how the total energy content
> of the body changes in the first frame of reference: the total energy
> content reduces by L. Einstein used his transformation formulae for
> radiated energy to show that the total energy content of the body reduces
> by L + L v^2/(2 c^2) plus terms too small to worry about.

   The measurement in the STATIONARY SYSTEM shows that the energy
content of the body is reduced by L. Nothing unusual happens in the
STATIONARY SYSTEM. Only the MOVING SYSTEM perceives a measurement that
is less than the measurement taken in the STATIONARY SYSTEM.

> Since the total
> energy content of the body in the second frame after radiation is the
> total energy content of the body in the first frame after radiation plus
> the kinetic energy of the body in the second frame after radiation, then
> the kinetic energy of the body after radiation drops by Lv^2/(2c^2) plus
> terms too small to worry about.

    There is no second body in the second frame; the MOVING SYSTEM
contains no body. Energy measurements by the MOVING SYSTEM are
converted to Kinetic energy for the body in the STATIONARY SYSTEM.
Kinetic energy as measured from the MOVING SYSTEM is less than the
kinetic energy as measured from the STATIONARY SYSTEM containing the
body. Measurements in the STATONARY SYSTEM where the body is located
would show no loss of kinetic energy.

>The kinetic energy in the second frame
> after the radiation is 1/2 M v^2 - 1/2 L/c^2 v^2 plus terms too small to
> worry about, so that the mass of the body after radiation is M - L/c^2,
> and the body has lost a nett mass of L/c^2.

      Only as measured from the MOVING SYSTEM. The kinetic energy
measurements taken by the MOVING SYSTEM are smaller than the same
kinetic energy measurements taken by the STATIONARY SYSTEM.

   There are only three variables in the formula for kinetic energy
(KE = 1/2 mv^2). The speed of light must remain constant, so v
becomes c and must stay the same. Therefore, as measured from the
MOVING SYSTEM, if KE is less, then m must be reduced--BUT ONLY FOR THE
MOVING SYSTEM. There is an only an apparent reduction of mass and
only as viewed from the MOVING SYSTEM.

>
> The decrease of the mass of the body takes place in BOTH frames.

    What a jump! The MOVING SYSTEM sees a reduction in mass in a body
located in the STATIONARY SYSTEM. Those in the STATIONARY SYSTEM
can't see it, can't measure it. It is happening right under their eyes
but they can't measure it. To know what is happening, they have to
contact the MOVING SYSTEM and get the measurements. But it must be
happening because Einstein says that the reduced measurements taken in
a different frame must apply to all frames.

    This is the famous Einstein derivation of E = mc^2 ?? You are
joking, aren't you?

Relevant Pages

  • Re: .Re: Why all the fascination with E = mc^2 ??
    ... >out radiation on only two sides? ... stationary in its initial rest frame after radiation. ... radiates radiation of energy L_1/2 in the opposite direction. ... of reference, Einstein's transformation law yields that the nett radiated ...
    (sci.physics)
  • Re: .Re: Why all the fascination with E = mc^2 ??
    ... >out radiation on only two sides? ... stationary in its initial rest frame after radiation. ... radiates radiation of energy L_1/2 in the opposite direction. ... of reference, Einstein's transformation law yields that the nett radiated ...
    (sci.physics.relativity)
  • Re: .Re: Why all the fascination with E = mc^2 ??
    ... >>No. Einstein took the classical Conservation of Energy is both frames. ... >>frame in which the body is stationary. ... Total mass of the stationary body in the STATIONARY SYSTEM ... Measurements in the STATONARY SYSTEM where the body is located ...
    (sci.physics)
  • Re: .Re: Why all the fascination with E = mc^2 ??
    ... >>No. Einstein took the classical Conservation of Energy is both frames. ... >>frame in which the body is stationary. ... Total mass of the stationary body in the STATIONARY SYSTEM ... Measurements in the STATONARY SYSTEM where the body is located ...
    (sci.physics.relativity)
  • Re: .Re: Why all the fascination with E = mc^2 ??
    ... >frame appears to be reduced in another frame. ... No. Einstein took the classical Conservation of Energy is both frames. ... had already calculated how the energy of radiation transforms between ... Einstein starts off with a body of a certain mass ...
    (sci.physics)