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

From: David McAnally (D.McAnally_at_i'm_a_gnu.uq.net.au)
Date: 06/09/04 

Date: 9 Jun 2004 15:05:49 GMT

leoppard@MailAndNews.com (Leonard Pardin) writes:

>D.McAnally@i'm_a_gnu.uq.net.au (David McAnally) wrote in message news:<ca5vv6$r58$1@bunyip.cc.uq.edu.au>...
>> leoppard@MailAndNews.com (Leonard Pardin) writes:
>
>> > Later Einstein informs us:
>>
>> >"H and E are energy values of the same body referred to two systems of
>> >co-ordinates which are in motion relatively to each other, the body
>> >being at rest in one of the two systems (system (x, y, z))."
>>
>> > Einstein must be referring to "light" energy, simply because that
>> >is the only energy that is measured anywhere in the article.
>>
>> That is an invalid conclusion. By what line of reasoning do you come
>> to the conclusion that Einstein was referring to "light" energy? I
>> have not seen you logically and rigourously work towards that conclusion.
>>
>> And what do you mean by the "light" energy of a body, anyway?

> Ask Einstein. Here's a quote from the paper:

>"Let this body send out, in a direction making an angle f with the
>axis of x, plane waves of light, of energy 1/2L measured relatively to
>(x, y, z), and simultaneously an equal quantity of light in the
>opposite direction."

Einstein did not say anything about the "light" energy of body here. Do
you have trouble with comprehension?

><snip>
>
>> >So Einstein says that (light energy from the body measured in the
>> >moving frame "H") less (the light energy from the body measured in the
>> >stationary frame "E") must equal some change in the kinetic (motion
>> >energy) of the body.
>>
>> Einstein said that the decrease in the energy of the body relative to
>> the second frame minus the decrease in the energy of the body relative
>> to the stationary frame is equal to the decrease in the kinetic energy
>> relative to the second frame. This comes from the definition of the
>> kinetic energy, as the difference between the energy of the body and
>> its energy relative to its rest frame.
>>
>> > That's very clever: Presto! Chango! light energy is converted to
>> >Kinetic energy.
>>
>> That is based on your loose interpretation of what Einstein wrote, and
>> your unproven assumption that he was discussing the "light" energy of
>> the body, whatever that is. Do you know anything about conservation
>> of energy? The radiation energy comes from the body. Where else
>> could it have come from? This means that some of the energy of the
>> body is converted into radiation energy, including part of the kinetic
>> energy when working in the frame with respect to which the body is moving
>> (which is the reverse of your claim above that radiation energy is
>> converted to kinetic energy, thus showing that you have not understood
>> anything).
>>

> Well, I understand that if you are going to allow loss of
>radiation energy to reduce kinetic energy,

That is actually a loss in kinetic energy due to an increase of radiation
energy. Again, that is because of conservation of energy.

>then it should work both
>ways: an increase of kinetic energy must result in an increase in
>radiation energy.

Even if you had worded this correctly, you would be wrong. There are
other forms of energy.

> So let's start from the beginning. The total energy of the body
>in the frame moving relative to the body must be many times more than
>the total energy of the body in the frame that is stationary relative
>to the body.

Not many more times. That is another of your fantasies.

>In other words, we have to add the kinetic energy
>relative to the moving frame.

> The kinetic energy in the frame stationary relative to the body
>must be zero. But the kinetic energy in the frame moving relative to
>the body is KE = 1/2 mv^2.

That is only the Newtonian approximation. Why do you insist on imposing
the Newtonian approximation to the kinetic energy of the relativistic
formula?

>So we start with body having many times
>more energy relative to the moving frame than relative to the
>stationary frame to begin with.

Not many more times. There is just an additional kinetic energy.

> As we proceed through the experiment, the kinetic energy in the
>moving frame is reduced by a small fraction represented by the emitted
>radiation energy

Not true. Try again.

>--but the total energy in the moving frame (H) is
>still much greater than the energy in the stationary frame (E).

H is greater than E. Where did you get "much greater" from? And why
do you persist in your nomenclature of "stationary frame" and "moving
frame"?

> Now we can subtract and get the difference in total energy between
>the frames and according to Einstein: "the difference H - E can
>differ from the kinetic energy K of the body, with respect to the
>other system (x, h, z), only by an additive constant C, which depends
>on the choice of the arbitrary additive constants of the energies H
>and E."

Where C is to account for the fact that the data for H and E may not
correspond.

> Conversely, the radiation energy relative to the stationary frame
>must also change relative to the total kinetic energy relative to the
>moving frame.

Which was Einstein's starting place. Einstein calculated the
transformation law for radiated energy in his first 1905 relativity paper.
It was due to the fact that Einstein had ALREADY calculated the
transformation law for radiated energy that Einstein was able to calculate
the exact reduction in the kinetic energy.

>So while there has been a slight decrease in the energy
>and therefore the mass of the moving frame, the energy relative to the
>stationary frame must have increased by converting the kinetic energy
>from the moving frame into radiation energy for the stationary frame,

You can't transfer energies between frames. In what you call the
"stationary frame", the body radiates energy, so its energy decreases, and
the balance of the energy radiates off. In what you call the "moving
frame", the body radiates energy, and both the intrinsic energy and the
kinetic energy decrease, and balance of the energy radiates off.

>and therefore the energy in the stationary frame must have increased
>dramatically.

How could it increase dramatically, when there is nowhere from where it
could have come?

David

        And all dared to brave unknown terrors, to do mighty deeds,
        to boldly split infinitives that no man had split before -
        and thus was the Empire forged.

-----

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