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Re: 4/3 problem resolution/Action-reaction paradox in pdf format

On Tue, 19 Jun 2001 16:48:04 -0400, Bob Sciamanda <trebor@VELOCITY.NET>

wrote:

----- Original Message -----
From: "David Rutherford" <drutherford@SOFTCOM.NET>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, June 19, 2001 01:02 PM
Subject: Re: 4/3 problem resolution/Action-reaction paradox in pdf format


I said:
3.) Therefore, an observer travelling with this CM is viewing the world
from a non-inertial frame.

You objected:
No, he's viewing the world from an inertial frame. Maybe it would be
easier if you explain to me why you think his frame is non-inertial.

In the Newtonian world, there is a simple criterion which applies here:
(also true in the world of special relativity). The CM
of your electron system is accelerating as viewed in the lab . . . Ergo .
. . -->

Right, I agree with that. The CM frame is accelerating 'as viewed in the
lab frame'. I also agree that any frame which is accelerating (as viewed
from an inertial frame) _should_be_ a non-inertial frame, but the CM frame
is _not_ accelerating when viewed from the CM frame. To illustrate this,
let's forget about the lab frame, for a moment. If we start by analyzing the
forces only in the CM frame, then the forces are _always_ equal and
opposite, so the center of mass is _always_ inertial (stationary as viewed
from the CM frame).

(1) Do you agree with that?

(2) A frame which is inertial must appear to be inertial when viewed from
any other inertial frame. Do you agree with that?

(3) The lab frame is an inertial frame. Do you agree with that?

If you agree with (1), (2), and (3) then you must agree that the CM frame
should be inertial when viewed from the lab frame. How do you explain the
discrepancy between the two methods of analysis (lab frame -> CM frame, and
CM frame -> lab frame)? Both should be equally valid and should yield the
same results.

I said:
He will see objects accelerate with no forces
acting on them;

You replied:
All sorts of weird things will happen because the Lorentz force
equations give conflicting results, in this situation. That's my point.

I don't know what this means. (The Lorentz transformations connect only
inertial frames.)

You don't need to use the Lorentz transformations to see that there is
an inconsistency with the Lorentz force description of the situation.
You can analyze the forces in the two frames separately as if the
observers have no knowledge of each other. If their results lead to a
paradox, as in this case, there's a problem with physics. My equations
lead to consistent results in both frames, at all times (CM is inertial
in all frames), the Lorentz force equations lead to a mess.

I said:
he will of course see objects at rest relative to him NOT
accelerate even though there is a net force on them

You asked:
From where?

If they are at rest in an accelerating frame, there must be a net force on
them.

They are at rest in an inertial frame.

When I somersault, the coins in my pocket would be an example of
such objects.

So don't sumersault while carring coins :-).

I added:
(as there must be on him).

You replied:
The observers are assumed not to interact with the particles.

He must be experiencing a net force from something (probably not the
particles), because he must accelerate in order to stay with the
accelerating CM.

There is only the particles, nothing else (except the observers). Where are
these phantom forces coming from?

How else does he become a "CM observer"?

It doesn't matter how he got to the pool room? Once you're there you're
standing still in the pool room frame while you watch the balls collide.

I said:
He cannot apply Newton's laws to his observations without adding
corrections which take into account his own acceleration.

You articulated:
As I said, he's inertial according to himself.
I haven't a clue as to what this means!

It means that he is not accelerating from his viewpoint.

We went on - I speculated:
4.) I think that by your phrase "then the center of mass is inertial"
you are asserting something other than the (false)statement that an
observer travelling with the CM is at rest in an inertial frame. What
is it that you really mean?

You repied:
By definition, if two particles start out with equal and opposite (or
zero) velocities, as in this case, and the net forces on the particles
sum to zero (which they do in the CM frame), then the velocity of the
center of mass
of the particles is constant (or zero). That means that the reference
frame
of the center of mass (CM frame) is inertial from the point of view of an
observer at rest in the CM frame.

The accelerations sum to zero in the CM frame; the forces do not.

How can you have identical particles which undergo equal
and opposite accelerations without them experiencing equal and opposite
forces?

In fact
in the (v<<c) Newtonian scheme forces are invariant - the same to all
observers - and acceleration is only a valid measure of force in inertial
(non-accelerating) frames. The last sentence is inscrutable. To be an
inertial frame it is not sufficient for the CM to be at rest in its own
frame (all frames are!) - it must be at rest in some inertial frame - and
have a constant velocity in all other inertial frames (eg: your lab
frame).

In a universe where there are only the two electrons which are initially
travelling at constant equal speeds in opposite directions toward each
other, the center of mass of the two particles is inertial. Do you agree
with that? If you do, then why all of a sudden do you think it's
non-inertial when viewed from a different inertial frame (lab frame)?

Imagine two identical pool balls travelling with equal and opposite
velocities (CM frame view). They collide elastically then move away from
each other with equal and opposite velocities. The center of mass of the
two balls is stationary throughout the interaction, therefore it's
inertial.
If there was a very short observer standing at the center of mass, he
would
say that he is inertial, too.

Now just insert pool balls=electrons and you've got the situation in the
CM frame.

If the pool balls constitute an isolated system and their forces of
interaction obey the third law, then their CM will not accelerate and will
be at rest in an inertial frame. The Maxwellian forces between two
electrons do not obey Newton's third law. In order to preserve our very
useful Conservation of Momentum calculational tool, we assert that neither
are they isolated - there are other momentum/energy sharing entities
involved (the fields).

I showed you that your "useful Conservation of Momentum calculational tool"
is fundamentally flawed, since the Poynting vector term ExB/4pi doesn't
completely describe the momentum density of the field. But when confronted
with inconsistencies in your dogma, you choose to act like a glassy eyed
fanatical cult member, quoting Bible phrases and hearing nothing.

If you have a better (or even equivalent) model,
it is welcome - but you should still be bound by logic,

It's conventional physics that's logically flawed. That's what I've been
showing you.

consistency

My theory is perfectly consistent, which is more than I can say for
conventional theory, as I've shown.

and lucid terminolgy.

What about my terminology has been illucid?

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555