RVHG wrote:

You take a phrase again out of context. I said that "alpha does not
have a value" only to immediately say that "alpha is a value", a
distinction necessary to show you why your logic deduction were not
valid.

So now you think that \alpha is a value which can have at least
two values? Or have you yet again decided to disagree with
yourself, this time about premise one? The more contradictory
nonsense you write, the clearer it becomes that you have no
tenable position about \alpha being a velocity.

As I said already many posts ago, you do not understand that a
velocity (or any other physical magnitude) continue being a velocity
(or an angle in another example), no matter if it is measured with a
dimensionless unit or not.

I do understand that, and I also understand that a fundamentally
dimensionless constant cannot become a dimensionful constant in
any unit system, unlike a velocity expressed as a dimensionless
number. You do not understand that, or you wouldn't continue to
state the obvious falsehood about \alpha being a velocity, while
pretending to agree with references that contradict you. Until
you decide to approach the issue honestly, there is no hope of
having a useful discussion about units. The Baez article in
particular states the difference between a dimensionless constant
and a constant that isn't dimensionless, and uses \alpha and c as
examples. Your continuing efforts to lie about the agreement of
the Baez and NIST article with your claim are getting rather old,
which is why I'm not much interested in broadening the discussion.

The natural constant c (or any other one) does not lost its physical
meaning, being a velocity in this case, after a "=1 dimensionless
assignment". I am really avid to discuss this in all detail with you.

The basics are sketched out in the Baez reference. The units of
length and/or time can be defined so that c=1. Since it's easy
enough to double the time unit (or halve the length unit), we can
also find a system where c=2 dimensionless. Any velocity can be
expressed by any positive dimensionless number by choosing the
units for length and time appropriately. Again, \alpha does not
depend on the units we use and therefore cannot possibly be a
velocity, unless you disagree with the Baez reference.


---Tim Shuba---

shuba wrote in message ...
RVHG wrote:

You take a phrase again out of context. I said that "alpha does not
have a value" only to immediately say that "alpha is a value", a
distinction necessary to show you why your logic deduction were not
valid.

So now you think that \alpha is a value which can have at least
two values? Or have you yet again decided to disagree with
yourself, this time about premise one? The more contradictory
nonsense you write, the clearer it becomes that you have no
tenable position about \alpha being a velocity.

From where do you take the idea that I said that alpha is a value that
can have "at least two values"? I wrote very clearly in my last post
"A value for ANY constant quantity of ANY physical magnitude measured
in ANY unit system has only one number associated with it, being that
physical magnitude dimensionless or not in that unit system". I
consider alpha THE (unique) value for the constant quantity v1 (a
velocity, the first orbit electron one in Bohr's model stated in the
NIST reference) measured in a unit system were the c=1 dimensionless
assignment is done. I wrote also to you sufficiently clear that " v1
is not simply \alpha, \alpha is only one of the many values of v1,
its dimensionless value in a unit system where the c=1 dimensionless
assignment is done". V1 is the entity (a velocity) that can have two
values (indeed, infinite ones). I will repeat to you once more, alpha
is not an entity that can have a value (or two ones), it is the unique
value for v1 in some kind of unit systems, the ones where the c=1
dimensionless assignment is done.

Premise one:
If v1 (or xyz) is a velocity, then v1 (or xyz) can have at least two
values.

I have not problem at all with premise one. V1 (a velocity) is the
entity that can have more than one value. Alpha cannot have a single
value (with more reason cannot have two values!), alpha IS a unique
value, the one for v1 in a specific unit system.

I explained to you already sufficiently clear the relationship between
alpha (one of the many values the velocity v1 can have) and v1 (a
velocity). I will repeat here my words.
"Yes, alpha is not simply a velocity, it is a dimensionless value for
a velocity in some particular unit system. Your conclusion that alpha
is not a velocity can be supported only if you accept that a value for
some quantity of a physical magnitude (using some particular unit
system) is something different from the physical quantity in itself.
This is not common practice among physicists. You find constantly an
equation sign (=) between a physical quantity and some of its value in
some unit system. In rigor, alpha does not has a value (unique or not,
putting down your premise two), it is a value (the dimensionless
~1/137), that corresponds to the v1 velocity measured in c=1
dimensionless units".

When I wrote "alpha is a velocity" I was following the common practice
among physicists that identify a physical quantity with one of its
possible values. Don't you compute "my bicycle velocity is (some tiny
dimensionless number)"? This was before your distinction between a
velocity and some of its values, that you used in your Aristotelian
logic derivation with the intention to show that "alpha is not a
velocity". Yes, alpha is not a velocity (following your distinction),
it is a dimensionless value for the velocity v1 in some unit system
with the c=1 dimensionless assignment. But I know you are not
satisfied with this, you reject completely the alpha-v1 relationship,
even after reading that alpha=v1/c (NIST reference) and saying that I
am the one in contradiction with that reference.

As I said already many posts ago, you do not understand that a
velocity (or any other physical magnitude) continue being a velocity
(or an angle in another example), no matter if it is measured with a
dimensionless unit or not.

I do understand that, and I also understand that a fundamentally
dimensionless constant cannot become a dimensionful constant in
any unit system, unlike a velocity expressed as a dimensionless
number. You do not understand that, or you wouldn't continue to
state the obvious falsehood about \alpha being a velocity, while
pretending to agree with references that contradict you. Until
you decide to approach the issue honestly, there is no hope of
having a useful discussion about units. The Baez article in
particular states the difference between a dimensionless constant
and a constant that isn't dimensionless, and uses \alpha and c as
examples. Your continuing efforts to lie about the agreement of
the Baez and NIST article with your claim are getting rather old,
which is why I'm not much interested in broadening the discussion.

Then why do you reject my view of alpha as a dimensionless value for a
velocity? I am not converting alpha in a dimensionful constant by
saying that it is a dimensionless value for a velocity. You seem to
interpret that any velocity is always dimensionful, being this the
cause of your resistance to admit the alpha-v1 relationship, even
after reading in the NIST reference that alpha=v1/c. V1 is the one
that can be dimensionful in many unit systems, alpha is only one of
the possible values for v1 (a dimensionless value). I do not identify
alpha with v1, even if we can write alpha=v1 in some unit systems
where is valid the phrase "alpha is a velocity", without any
contradiction at all with the dimensionless character of alpha,
because in that kind of unit systems ALL velocities are dimensionless.

I consider me having an honest discussion with you, but both of us
have the right to stop it in any moment for any reason valid or not.
In any case I will continue considering you an honest opponent, even
if you stop our talking that perhaps are boring you.

In my view does not exist any "fundamentally dimensionless
constant" different from the dimensionless 1 (like alpha). I claim
that all dimensions (in the context of unit systems) are totally
arbitrary and without physical meaning. I also reject any
"fundamentally dimensionful constant" (sharing that opinion with one
of the physicists in the Mel reference). ANY physical quantity of ANY
physical magnitude can be expressed as a dimensionless number in my
approach, including here your bicycle velocity (with the tiny number y
that you compute) or the v1 velocity in Bohr's model (that has
precisely the alpha value).
The natural constant c (or any other one) does not lost its physical
meaning, being a velocity in this case, after a "=1 dimensionless
assignment". I am really avid to discuss this in all detail with you.

The basics are sketched out in the Baez reference. The units of
length and/or time can be defined so that c=1. Since it's easy
enough to double the time unit (or halve the length unit), we can
also find a system where c=2 dimensionless. Any velocity can be
expressed by any positive dimensionless number by choosing the
units for length and time appropriately. Again, \alpha does not
depend on the units we use and therefore cannot possibly be a
velocity, unless you disagree with the Baez reference.


You seem to think that velocity=length/time in a "fundamentally" way.
As strange it can appear to you in a first look, this apply only to
unit systems where length and time are considered (arbitrarily) as
basic entities, and velocity a derived one (take a look to the
Planck's unit system where velocity, action and gravitation are the
basic entities, being length, time and mass among the derived ones).
Yes, you can conceive a unit system where c can have any dimensionless
value (put v1=1 dimensionless per example and you will obtain
c=1/alpha=137). But why do you say that alpha cannot be a velocity?
(well, in rigor a value for a velocity, are you starting to consider
that alpha can be a velocity in some case?). In this case we can write
c*alpha=1 dimensionless. Alpha remains being a dimensionless value for
a velocity. Notice here how can you multiply two dimensionless
velocity values obtaining 1 dimensionless.
By the way, I have yet a lot to say about the "=1 dimensionless
assignment" practice, much more than you can read in Baez's (without
implying that there exist anything wrong in that reference).
---Tim Shuba---

RVHG

RVHG wrote:

From where do you take the idea that I said that alpha is a value that
can have "at least two values"?

From your claim that \alpha is a velocity. I gave you two values
for my bicycle velocity. I will gladly give you another value
for the ficticious electron velocity v1 in the units m/s if you
want, but I'm quite sure you can do it yourself. We can do that
for any velocity. If \alpha were a velocity, it would also have
a value in units m/s, different from ~1/137. So tell me: what
is the value of \alpha in a unit system where a velocity has
dimensions m/s, and what units does \alpha have in that system?


---Tim Shuba---

shuba wrote in message ...
RVHG wrote:

You wrote in a previous post "It is true that \alpha can be a value
for a velocity (any nonzero velocity), but this gives no more
information than saying that \alpha is a positive number"
We share the conviction since many posts ago that alpha has a unique
number associated with it, the ~1/137 one. We had been discussing
about its meaning, if this number is a velocity or not, if it is a
value for a velocity in some kind of unit system or in any unit
system, etc. How can now you write that "\alpha can be a value for ANY
nonzero velocity"? Well, perhaps it is my fault about the meaning of
some English word (it is not my native language).

I don't think the problem is with your understanding of the
English language, which appears to be quite good. I have had
many experiences communicating with non-native users of English,
and I try to choose my words carefully. I have no desire to use
words in a confusing manner, but I will not "dumb down" my words
either.

I didn't think that you use words in a confusing manner, I thought
that I had an English interpretation problem. I see now from your very
well detailed answer that you are really claiming that alpha can be
the value for any nonzero velocity.
I claim that:
1) \alpha is a unique number ~1/137.
I accept that alpha has associated with it the unique pure number
~1/137, but not that alpha IS only that pure number.
2) \alpha is not a velocity.
Alpha is not a velocity because it is the unique value for the
specific velocity v1 in some very special kind of unit system.
3) \alpha is the ratio of v1/c in any unit system.
I accept the alpha=v1/c present in the NIST reference, but demand more
explanation about what is the ratio of two physical quantities that
can have dimensions in some unit systems and not in other ones. The
treatment of dimensions like pure numbers is not for me an evident
valid behavior.
I see some kind of contradiction between your claims 1) and 3). If
alpha is the unique number ~1/137, how can be it also "the ratio of
v1/c in any unit system"? Alpha is a number or it is a "ratio" of two
things that in some cases are not numbers? I can accept that the ratio
of two pure numbers is a unique pure number, but the "ratio" of two
dimensionful physical quantities is a completely different thing that
you must start defining what is it, no matters how evident, trivial or
obvious it looks to you.
4) \alpha is the ratio of (v1*k)/(c*k) in any unit system (k is a
constant nonzero real number). [#4 is actually redundant with #3]

Yes, you do not add anything new introducing the k. The problem
remains being how can you divide two things (v1 and c) in the case
they are not pure numbers, but dimensionful physical quantities.
I'll leave out my claim that a bound electron velocity is
ficticious, and I only mention it here so to leave no doubt that
#3 or #4 on my list should not be considered good definitions of
\alpha. A good definition of \alpha will be based on the
probability of an electron to emit or absorb a photon, but I'm
willing to be convinced that a better definition is possible.

Fine! You seem starting to understand that alpha is a concept (as
anyone!) that can pass from a "worse" definition to a "better" one,
without losing its history. Can you understand that "v1" has already
a "quantum" character (look at the ‘1', an integer number), even if
expressed as a "classical" velocity?
How can \alpha be a value for any nonzero velocity? Quite
simply. Here's just one way. Let's use my original bicycle
velocity 28 km/hr. I define a new length unit shubameter (sm),
1 sm = ~137*28 km. Now my bicycle has velocity \alpha sm/hr.

Why do you restrict your explanation to velocities? You can do the
same reasoning with ANY other physical magnitude. For example, define
sg (shubagram) as a unit for mass, being 1 sg=~137*28 kg (supposing
your bicycle's mass is 28 kg). Now your bicycle has a mass of \alpha
sg!
Would you rather see the value of my bicycle velocity equal to
\alpha dimensionless? Okay, I'll define a velocity s=1
dimensionless, such that s = ~28/(1/137) km/hr.

In units s=1 dimensionless, my bicycle has velocity \alpha
dimensionless. This works, in case it's not obvious, because s
was chosen so that v_bike/s = \alpha. In this unit system,
v_bike, c, s, and v1 are all dimensionless, but only
v_bike is equal to \alpha.

Yes, I see that you can make almost ANYTHING equal to alpha, with
dimension or without it! This is a result owed to your 1) claim,
considering that alpha IS only the unique pure number ~1/137. Doing
that you cut the alpha relationship with its own history! This is what
you cannot do with any concept, running the risk to open the door to
all kind of absurdities. How can you conciliate an alpha being the
probability of an electron to emit or absorb a photon with your view
of an alpha being anything? It is not evident for you yet that you
cannot forget the v1 and c present in the alpha history? Velocity (not
mass or any other physical magnitude) is related with alpha (until now
at least). This is the historic fact that you cannot forget. The past
is not simply "wrong" things that you can take out. The "false" past
is the root of our present " true".
Alpha is the dimensionless value for the velocity v1 in unit systems
with the c=1 dimensionless assignment, as I derived many times already
from the alpha=v1/c present in the NIST reference (and always without
any comment for your part!).

In on
15 October I did comment and agree, and it trivially follows from
my claim #3 in this post. I have consistently agreed with the
NIST reference.

I will repeat here your Octuber 15 reference.
[ Yesterday alpha was a
velocity

\alpha was NEVER a velocity.

"The quantity alpha, which is equal to the ratio v1/c where v1 is the
velocity of the electron in the first circular Bohr orbit" (from your
NIST reference).
Putting c=1 dimensionless (any objection?), alpha=v1.

No objection. And putting c= 3*10^8 m/s, \alpha != v1, because
\alpha is not a velocity.]

When you put c=1 dimensionless, the ratio v1/c corresponds to the one
for two numbers that can be considered equal to the number ~1/137
without any problem. But when you put c= 3*10^8 m/s, v1/c corresponds
to the "ratio" of two things that are not pure numbers. This is why I
insist in the c=1 dimensionless assignment as a crucial point in our
discussion. Try to explain me what is the "ratio" of two non-numbers!
I can advance you that a measure for v1 using some unit related with c
is involved here. This is not a simple algebraic operation, this is a
completely different thing full of physical meaning!
You do not understand yet that only making a c=1 dimensionless
assignment (characterizing some kind of unit system) can you obtain a
dimensionless alpha associated with the number ~1/137. Using 1
einstein= 3*10^8 m/s as the unit for velocity give you a dimensionful
value ~1/137 einstein for v1. Of course that alpha is not equal to v1
in that case, alpha is only the dimensionless value for v1 under the
c=1 dimensionless assignment.

---Tim Shuba---

RVHG

RVHG wrote:

Try to explain me what is the "ratio" of two non-numbers!

Farmer A has x cows. Farmer B has y cows. We say that the ratio
of their cows is x/y. This is a definition. Many physical units
are defined this way. As long as we stick to linear units and
use care to define zero consistently, there is no problem using
these definitions. You have certainly never once presented any.
As you have said, we have to recognize a problem before needing a
solution. There is no problem here other than your attempt to
deny that mathematics can be applied to the physical realm. I
suppose you are equally baffled that we can add 2 cows + 3 cows.

I can advance you that a measure for v1 using some unit related with c
is involved here. This is not a simple algebraic operation, this is a
completely different thing full of physical meaning!

A bound electron velocity has no physical meaning. It is a
fiction in both classical and quantum mechanics.

You do not understand yet that only making a c=1 dimensionless
assignment (characterizing some kind of unit system) can you obtain a
dimensionless alpha associated with the number ~1/137.

Nonsense. I already suggested that you read Feynman, but I guess
you are not interested in physics past the Bohr atom. Your loss.


---Tim Shuba---

shuba wrote in message ...
RVHG wrote:

Try to explain me what is the "ratio" of two non-numbers!

Farmer A has x cows. Farmer B has y cows. We say that the ratio
of their cows is x/y. This is a definition. Many physical units
are defined this way. As long as we stick to linear units and
use care to define zero consistently, there is no problem using
these definitions. You have certainly never once presented any.
As you have said, we have to recognize a problem before needing a
solution. There is no problem here other than your attempt to
deny that mathematics can be applied to the physical realm. I
suppose you are equally baffled that we can add 2 cows + 3 cows.

x and y are pure numbers, x cows and y cows are not. Of course we have
no problem with the ratio x/y, obtaining as a result another pure
number like x and y. The problem is with the "ratio" x cows/y cows,
that maybe you process in an "algebraic" form (that implies that "x
cows" is the "multiplication" of "x" by "cows") putting
x cows/y cows=(x/y)(cows/cows), as if "cows" were an algebraic entity,
perhaps supposing later that (cows/cows)=1, obtaining finally that x
cows/y cows=(x/y) (do not try to change the things now saying that
this is a "definition", we both know that this is the common
"dimension" handling in today Physics). I am making a comment here
compatible with the treatment of "cows" as a dimensionful unit for
some physical magnitude in some unit system, that it is our real
topic.
You perhaps did not notice that I am not rejecting that procedure, I
am only demanding an explanation to it from where we can extract a
physical meaning. That kind of ratios are normally used to describe
measurements. Suppose "y cows" is some quantity of cows that we want
to use as a unit to measure some another quantity of "x cows". Let us
put 1 ucow=y cows, reading ucow as "units of cows". The result is x
cows=(x/y) ucow.
Why we obtain in this case a dimensionful result (supposing ucow a
dimensionful unit) and not a dimensionless one, like the alpha=v1/c
case? Who decide when a unit is dimensionful or dimensionless? Let us
emphasize the following question:

Have the physicists the right to declare "=1 dimensionless" ANY
quantity of ANY physical magnitude?

You did already it in your free use of "alpha" making it equal to
anything, with dimensions or without it! As you consider that alpha is
only a pure number (claim 1), you used it to measure any physical
quantity adjusting the used unit, dimensionful or not. Perhaps
understanding that all those results are completely absurd, I see that
you now return again to Feynman to maintain some physical meaning for
alpha, even if rejecting its historic one, a dimensionless value for
v1.

It is time to make a clear declaration about this point. No,
physicists have not the right to do that. The 1 dimensionless
assignment is only a Nature right!
I think that it is not too difficult to understand why. If you make
two different "=1 dimensionless assignment" to two different
quantities of two different physical magnitudes, you are in a formal
way establishing an equivalence between them. It is absurd, per
example, that a physicist has the right to declare equivalent 1 Kg of
mass and 1 Joule of energy. And what about Nature? Thanks to Einstein
all we know now that exist a universal equivalence between mass and
energy, expressed in the formula E=Mc^2 that appears in the title of
this thread, the original question. To make explicit this equivalence
you only need…to do the c=1 dimensionless assignment! After this you
have a kind of unit system where mass and energy share the same
physical dimension with a unique unit (usually the electron-volt). All
velocities are now dimensionless! Well, not exactly, I am a little
fast writing. All velocities have now dimensionless values, including
of course v1 and c, THE NATURAL UNIT for velocity, having now v1 the
~1/137 dimensionless value! I hope you are now starting to understand
all our long talking. When I say that alpha is the dimensionless value
for v1 under the c=1 dimensionless assignment, this is not an
arbitrary decision from my part, it is only the expression of my
belief that Nature took that decision, choosing only that velocity as
a dimensionless entity.
Perhaps you are thinking now in a very natural question. If velocity
has the Natural Unit c, which is the situation with all the others
physical magnitudes? Have they also "Natural Units"? If you think some
minutes about this topic (perhaps only seconds) you will soon end with
the conclusion that we do not need any other Natural Unit, a single
dimensionless 1 is sufficient! We only need to discover which is the
quantity of every physical magnitude selected by Nature to be the "=1
dimensionless". To find them we only need to search in the Physics
history. Those quantities surely appear in all Physic's branches. For
action it is sure h-bar, for entropy k (Boltzmann constant), for
gravitation G, for electrical permittivity \epsilon, for magnetic
permeability \mu, etc. And for angle? Surely your vote is for the
radian. I made a big error about 10 years ago, voting for the cycle
(2\pi radian) as the Natural Unit for angle. M. Planck had a similar
error in 1900, he thought that h was the Natural Unit for action,
equal to 2\pi h-bar. Yes, men can have errors, but not Nature (by
"definition" if you want).

I can advance you that a measure for v1 using some unit related with c
is involved here. This is not a simple algebraic operation, this is a
completely different thing full of physical meaning!

A bound electron velocity has no physical meaning. It is a
fiction in both classical and quantum mechanics.

Yes, I know that you think that what Feynman says today is the "true"
(it will be "false" tomorrow). The fact is that alpha remains today
having the same associated ~1/137 dimensionless number! (and we have
not reason to think that it will change in the future!)
You do not understand yet that only making a c=1 dimensionless
assignment (characterizing some kind of unit system) can you obtain a
dimensionless alpha associated with the number ~1/137.

Nonsense. I already suggested that you read Feynman, but I guess
you are not interested in physics past the Bohr atom. Your loss.

You can understand now the meaning of my RV axiom. For every physical
magnitude exist a specific natural constant, all equivalent among
them.
The dimensionless 1 is the Natural Unit, the natural constants of
every physical magnitude are different faces for the same entity.
Every physical magnitude pass to be dimensionless when you use its
Natural Constant as the unit to measure it (vacuum value for
electrical permittivity, Boltzmann constant k for entropy, radian for
angle, etc.)You can measure with the Natural Unit any thing. You can
add a mass with an energy (remember the electron-volt, perhaps the
pioneer), an energy with an angular velocity (under the h-bar=1), a
length with a time (remember Lorentz's transform, using c=1), etc.
Read the Mel reference and you will have the opportunity to compare
what I had been saying to you with the today state-of-the-art in the
topic. You will understand then if I had been taking with you about
the past or about the future. I know that you feel only comfortable
with Feynman in the present. The trees do not permit you to see the
forest.Your loss.

---Tim Shuba---

RVHG

RVHG wrote:

You can understand now the meaning of my RV axiom.

Yes, it is the ranting of a crackpot.


---Tim Shuba---

shuba wrote in message ...
RVHG wrote:

You can understand now the meaning of my RV axiom.

Yes, it is the ranting of a crackpot.

I realize that you are now not able to continue this talking. I remain
open to continue it in the future when you want. Thank you for your
attention.
RVHG

---Tim Shuba---

RVHG wrote:

I realize that you are now not able to continue this talking. I remain
open to continue it in the future when you want. Thank you for your
attention.

You either do not understand what I have been saying, or more
likely you are simply lying about it. For example, reread our
exchanges if you care to see why the statement "alpha is
only a pure number (claim 1)" is falsely attributed to me.

The concept of (2 cows)*3 = (6 cows) can be used as a definition
for the ratio (6 cows)/(2 cows) as a dimensionless 3. I'm sorry
if your extensive research into units has never got you that far.

You say that physicists have "no right" to make a dimensionless
1 assignment to a physical magnitude. Your claim contradicts
the idea that units are arbitrary. Nature doesn't use any
units, dimensionless or not. The only physical magnitudes that
cannot be set to 1 are the fundamentally dimensionless ones
which are not 1, like \alpha, \pi or e. Any velocity can be set
to a dimensionless 1, as I've already shown, and your claim that
it leads to absurdity is specious.

Yes, given your level of condescension and crackpottery, I
believe it is unproductive to continue our discussion.


---Tim Shuba---

shuba wrote in message ...
RVHG wrote:

I realize that you are now not able to continue this talking. I remain
open to continue it in the future when you want. Thank you for your
attention.

You either do not understand what I have been saying, or more
likely you are simply lying about it. For example, reread our
exchanges if you care to see why the statement "alpha is
only a pure number (claim 1)" is falsely attributed to me.

From my 8-Nov-04 post:
[ I claim that:
1) \alpha is a unique number ~1/137.
I accept that alpha has associated with it the unique pure number
~1/137, but not that alpha IS only that pure number.]
You can see above your claim 1) with your own words and my direct
answer to it. From your claim 1) you derived later your complete
absurd statement about alpha been equal to ANY velocity (that I
generalized easily to ANY thing). I was the one who pointed you (a
little ahead in that same cited post):
[How can you conciliate an alpha being the probability of an electron
to emit or absorb a photon with your view of an alpha being anything?]

The concept of (2 cows)*3 = (6 cows) can be used as a definition
for the ratio (6 cows)/(2 cows) as a dimensionless 3. I'm sorry
if your extensive research into units has never got you that far.

Multiplying a non-number (2 cows) by a number (3) and obtaining a
non-number (6 cows) has the same problem as the division of a
non-number (6 cows) by a non-number (2 cows) obtaining a number (3).
You explain nothing declaring one of them as a fundamental definition
and deriving later the other. What is implied here is the treatment of
dimensions as if they were simple numbers (I am supposing that
dimensions are represented here by "cows", not implying that "cows" is
"anything", you generalized too much ). You cannot give me a possible
valid solution for that problem simply because you do not realize yet
that there exist here a problem that needs a solution. If you do not
believe me about the existence of this problem, read about what are
saying other physicists today (the Mel's reference is waiting for
you).
You say that physicists have "no right" to make a dimensionless
1 assignment to a physical magnitude. Your claim contradicts
the idea that units are arbitrary.
You must distinguish a dimensionful unit from a dimensionless one. I
accept the right of physicists to choose the dimensionful unit they
want for any physical magnitude. What I put in doubt is their right to
declare that unit "dimensionless", specially if they use that right
more than one time. I put you already the 1 Kg and 1 Joule case
(unfortunately without any comment from your part). Putting another
example, can you admit that 1 meter=1 second (supposing physicists
desire were to declare 1 meter=1 (dimensionless) and 1 second=1
(dimensionless)? Do you accept the possible equivalence between 1
meter and 1 second? I am sure that you do not (claiming perhaps that
length and time are two completely different physical magnitudes that
cannot be mixed!). But suppose I declare now that 1
light-second=3*10^8 meter= 1 second. All relativistic physicists feel
very comfortable with this, that is what you can derive from a c=1
dimensionless assignment. With this particular kind of unit system,
length and time share the same "physical dimension" and THE VALUES for
all velocities become dimensionless entities!(alpha among them). You
can name the unique unit "light-second" (the length face) or "second"
(the time face). With the same unique unit you can measure length or
time. Notice that this unit is yet a dimensionful one, owed to its
relationship with the second, and arbitrary time unit chose by men.
What can we deduce from all of this? Many years ago I arrived to the
conclusion that length and time are equivalent in some natural
proportion, fixed by Nature. The c=1 dimensionless assignment is not a
thing that men have the right to make, it is only a thing that men can
discover in Nature.
Nature doesn't use any
units, dimensionless or not.
I am not the first talking about natural units. See the work of George
J. Stoney (1881), the one who measured for first time the value of the
elementary electrical charge e and coined the name "electron". More
known is a similar step made by Max Planck in 1899 just when he
discovered the constant h. In the Mel's reference you can obtain more
precise information about these works.
The only physical magnitudes that
cannot be set to 1 are the fundamentally dimensionless ones
which are not 1, like \alpha, \pi or e. Any velocity can be set
to a dimensionless 1, as I've already shown, and your claim that
it leads to absurdity is specious.

Not only for velocity, but for any other physical magnitude physicists
have not the right to assign a dimensionless 1 to any physical
quantity that they want (with a dimensionful 1 I have not objection at
all, and I guess that this is what you really have in mind). I will
suppose that my previous examples with 1Kg=1Joule=1 and
1meter=1second=1 had been sufficient clear for you. Only Nature has
the right to assign a 1 dimensionless. And it is my most profound
belief that Nature made it for only one physical quantity of every
physical magnitude, relating among them in this way all physical
magnitudes (can you conceive two different physical quantities for the
same physical magnitude being both equal to 1 dimensionless?). It
seems to be c for velocity, and this was really my starting point on
all of this analysis about what it is the real meaning of "dimension"
in the context of unit systems.
We share the idea that \alpha cannot receive the 1 dimensionless
assignment, but perhaps for different reasons. Having I already
accepted the Nature c=1 dimensionless assignment, I cannot accept that
any other velocity like v1 could share that distinction. Remember that
for me \alpha is the unique dimensionless value ~1/137 for the
velocity v1, a velocity that appeared in Physics as the first
quantified one and maintains its value in today QED with the original
name "fine structure constant" (you can read the history in the NIST
reference).

Yes, given your level of condescension and crackpottery, I
believe it is unproductive to continue our discussion.

I thought your last post were the last (the same occurred to me in at
least another occasion, if I do not remember bad). As I said in my
last post that I remain open to continue our talking when you want, I
am sending this one taking into account that you continued the contact
making new statements.
---Tim Shuba---

RVHG