"andreas" wrote in message ...
hi,
In the formula F=GM1M2/R^2 there is the multiplier G.
Why is there no one in the formula E=MC^2 ?
I presume that the units of E,M and C already existed before the formula was
known.
Maybe this is a stupid question but i like to know the answer.
Thanks for any response

You address here a very profound topic, even if it has the appareance
of a simple one. The very nature of physical magnitudes and their
relationships are involved. Yes, the unit system used plays a role
here...but the problem is that ALL unit systems are completely
arbitrary with no essential physical content.
Going to history we found the Astronomic Unit System. In that system G
was made equal to dimentionless 1. Then, in that system, Newton's
gravitation equation has the form F=M1M2/R^2, without any
"multiplier". The equation E=Mc^2 is also unit system dependent. The
equation would be E=M if you put the relativistic system with c equal
to dimentionless 1.
About the right of physicists to put any thing they want equal to
dimentionless 1 I have a lot to say, but I think this is sufficient
for the moment to start a talking about this topic with interested
readers.

RVHG

andreas:
thanks to all for the responses but my question is in more detail :
why not f.e. e= 0.1574864...mc^2
where 0.1574864... is a constant that is mesured

First forget that `c' is the speed of light and let's just call it an
arbitrary velocity. Now we can dispense with your constant `f' and take
`c' to be an arbitrart number between 0 and infinity. From the first
postulate in special relativity, i.e., the equivalence of inertial frames,
one can derive the relation E = mc^2, where `c' is the velocity of a
_massless_ particle. Then you can ask if light propagates at that velocity
and why it might propagate at that velocity. There are many ways to
determine this, one of which is to perform experiments to determine
whether or not the speed of light is _constant_, i.e., independent of any
observer or source velocity. Only something propagating at `c' will have a
velocity which is observer independent. Experiments have so far been
unable to measure any deviation in the speed of light, so apar from
theoretical considerations, the speed of light is constant and therefore
we assume that `c' = the speed of light.

Why woud the speed of light be constant? Einstein postulated it because
maxwell's equations were known to be nominally the correct equations
of E&M. Since maxwell's equations require the speed of light to be constant
and from the first postulate in special relativity one obtains the
constant `c' from the geometric structure of spacetime, einstein postulated
that `c' = the speed of light as a geometric origin of maxwell's equations.

But we can do better than that today. We know that a constant speed
of light is necessary for electric charge to be conserved. From the
standard model, we also find that charge conservation is a good thing.
It's not absolutely necessary, but the model becomes more complicated
without it and we have never observed any of the consequences the
standard model would require if charge wasn't conserved. The standard
model has so far been able to explain every phenomena other than gravity,
without exception, so we have good reason to believe it represents the
correct low energy theory of all particle interactions. The bottom line,
however, is that if you look deep enough, we do not have a fundamental
reason that the speed of light should be the constant `c' in special
relativity.

RVHG wrote:

...but the problem is that ALL unit systems are completely
arbitrary with no essential physical content.

The units km/hr have physical content when I say I am
riding my bicycle at 28 km/hr. Don't you think so?

Going to history we found the Astronomic Unit System. In that system G
was made equal to dimentionless 1. Then, in that system, Newton's
gravitation equation has the form F=M1M2/R^2, without any
"multiplier". The equation E=Mc^2 is also unit system dependent. The
equation would be E=M if you put the relativistic system with c equal
to dimentionless 1.
About the right of physicists to put any thing they want equal to
dimentionless 1 I have a lot to say, but I think this is sufficient
for the moment to start a talking about this topic with interested
readers.

I'm interested in the topic. Please consider the link below
and explain exactly where the problems lie.

http://math.ucr.edu/home/baez/constants.html


---Tim Shuba---

shuba wrote in message news:tim.shuba-D470CD.13101409092004@cp...
RVHG wrote:

...but the problem is that ALL unit systems are completely
arbitrary with no essential physical content.

The units km/hr have physical content when I say I am
riding my bicycle at 28 km/hr. Don't you think so?

If you use the relativistic unit system (where c is put equal to
dimensionless 1), the velocity of your bicycle becomes some tiny
dimensionless number and the physical dimensions of length and time
become equal. Which is then the "physical content" of something that
you can change arbitrarily? Which is then the "physical content" of
the "physical dimensions" that we find in ALL unit systems?
Going to history we found the Astronomic Unit System. In that system G
was made equal to dimentionless 1. Then, in that system, Newton's
gravitation equation has the form F=M1M2/R^2, without any
"multiplier". The equation E=Mc^2 is also unit system dependent. The
equation would be E=M if you put the relativistic system with c equal
to dimentionless 1.
About the right of physicists to put any thing they want equal to
dimentionless 1 I have a lot to say, but I think this is sufficient
for the moment to start a talking about this topic with interested
readers.

I'm interested in the topic. Please consider the link below
and explain exactly where the problems lie.

http://math.ucr.edu/home/baez/constants.html


---Tim Shuba---
The article you refer is an excellent one, but do not address the
topic I am considering. It assumes that the "physical dimension"
concept is completely clear. Something has or not "physical
dimensions", something is dimensionless or not, there exist
dimensionless constants and others with physical dimensions. All seems
to be clear. You will see immediately that this is not the case.
Let us consider the famous "fine structure constant" alpha. To begin
with, the expression showed for it is unit system dependent (it
changes from one system to another). It is equal to the electron
velocity in the first orbit of the Bohr 1913 H atom model (assuming c
equal to dimensionless 1, it has the value 1/137). And what occur if
we decided to make alpha equal to dimensionless one? Then it will be
1, not 1/137, and c will be 137. Or you can use your km/hour unit to
express the electron velocity in the first orbit, obtaining another
arbitrary number for alpha, in this case with "physical dimensions".
In the CGS unit system the electrical permitivity of vacuum is make
arbitrarily equal to dimensionless 1 (the alpha=[e2/hbar c] is valid
under that assumption), in many other unit systems (including the
actual SI) it has physical dimensions. In the Astronomic System (G=1)
we find only two basic physical magnitudes (length and time), and mass
is a derived one with a unit with physical dimension 3 respect length
and –2 respect time. Mass is a "basic" physical magnitude in many unit
systems, thanks to an arbitrary decision. I think this is sufficient
for the moment, but if you are not yet convinced that ALL unit systems
are completely arbitrary without any physical content, I can continue
showing you many others examples. The number and the selection of
basic physical magnitudes in any unit system are completely arbitrary!
Only the continue use of some of them (like mass, length and time) had
created in our minds the idea that they are "basic" in a physical
sense. The actual SI has 7 basic physical magnitudes with their
corresponding basic units, and it is no less arbitrary than any other
one.
The problem must exist before any solution for it. If you recognize
already that some problem exist here, I am ready to show you my
proposed solution.

RVHG

RVHG wrote:

The units km/hr have physical content when I say I am
riding my bicycle at 28 km/hr. Don't you think so?

If you use the relativistic unit system (where c is put equal to
dimensionless 1), the velocity of your bicycle becomes some tiny
dimensionless number and the physical dimensions of length and time
become equal. Which is then the "physical content" of something that
you can change arbitrarily? Which is then the "physical content" of
the "physical dimensions" that we find in ALL unit systems?

You seem to understand exactly the physical content of my bicycle
travelling at 28 km/hr. How did that happen? Though probably
not practical, we can certainly use units where c=1 to describe
the same velocity. In that case, we find

v_bike = v_bike/c = 2.5943874 x 10^-8.

That number in that particular system of units has the same
physical content. If you think that systems of units are devoid
of physical content, then tell me about the speed of my bike
without using one.

http://math.ucr.edu/home/baez/constants.html

The article you refer is an excellent one, but do not address the
topic I am considering. It assumes that the "physical dimension"
concept is completely clear. Something has or not "physical
dimensions", something is dimensionless or not, there exist
dimensionless constants and others with physical dimensions. All seems
to be clear. You will see immediately that this is not the case.
Let us consider the famous "fine structure constant" alpha. To begin
with, the expression showed for it is unit system dependent (it
changes from one system to another).

The fine structure constant is not dependent on choices of units.
The official definition of the fine structure constant (\alpha)
is given at http://physics.nist.gov/cuu/Constants/alpha.html

\alpha = e^2/(4*\pi*\epsilon0*\hbar*c)

It just so happens that in cgs units, 1/(4*\pi*\epsilon0) = 1.

It is equal to the electron
velocity in the first orbit of the Bohr 1913 H atom model (assuming c
equal to dimensionless 1, it has the value 1/137).

This is much different than the velocity of my bike. \alpha is
equal to ~1/137 no matter whether c=1 or not. It is independent
on the system of units chosen.

And what occur if
we decided to make alpha equal to dimensionless one?

We cannot do that and have a consistent system of units. That is
the reason such constants are *fundametally* dimensionless. They
cannot be changed without also changing the underlying physics.

Then it will be
1, not 1/137, and c will be 137. Or you can use your km/hour unit to
express the electron velocity in the first orbit, obtaining another
arbitrary number for alpha, in this case with "physical dimensions".

That is nonsense. Sorry if the first link I provided threw you
off by not mentioning the factor of (4*\pi*\epsilon0)^(-1). The
author was quite explicit in saying that "certain constants don't
depend on the units we use", and gave the fine structure constant
as an example.

In the CGS unit system the electrical permitivity of vacuum is make
arbitrarily equal to dimensionless 1 (the alpha=[e2/hbar c] is valid
under that assumption), in many other unit systems (including the
actual SI) it has physical dimensions.

I've given the official definition, and you are incorrect. In
the mks (SI) system, \epsilon0 has units of Farad/Meter, giving
the value of \alpha equal again to a dimensionless ~1/137.

The number and the selection of
basic physical magnitudes in any unit system are completely arbitrary!

Not completely. They have to be consistent. But yes, units are
arbitrary. So what? You understood perfectly the physical
content of my bicycle going at 28 km/hr. I eagerly await your
description of the physical content of my bicycle's velocity that
is independent of any system of units.


---Tim Shuba---

Tim Shuba wrote:

RVHG wrote:

In the CGS unit system the electrical permitivity of vacuum is make
arbitrarily equal to dimensionless 1 (the alpha=[e2/hbar c] is valid
under that assumption), in many other unit systems (including the
actual SI) it has physical dimensions.

I've given the official definition, and you are incorrect. In
the mks (SI) system, \epsilon0 has units of Farad/Meter, giving
the value of \alpha equal again to a dimensionless ~1/137.

Apologies to RVHG, your statement above is correct. I
erroneously thought you were referring to \alpha when you
were referring to \epsilon0.


---Tim Shuba---

shuba wrote in message news:tim.shuba-2E9CB2.18584116092004@cp...
RVHG wrote:

The units km/hr have physical content when I say I am
riding my bicycle at 28 km/hr. Don't you think so?

If you use the relativistic unit system (where c is put equal to
dimensionless 1), the velocity of your bicycle becomes some tiny
dimensionless number and the physical dimensions of length and time
become equal. Which is then the "physical content" of something that
you can change arbitrarily? Which is then the "physical content" of
the "physical dimensions" that we find in ALL unit systems?

You seem to understand exactly the physical content of my bicycle
travelling at 28 km/hr. How did that happen? Though probably
not practical, we can certainly use units where c=1 to describe
the same velocity. In that case, we find

v_bike = v_bike/c = 2.5943874 x 10^-8.

That number in that particular system of units has the same
physical content. If you think that systems of units are devoid
of physical content, then tell me about the speed of my bike
without using one.

Not only your bicycle velocity, but ANY quantity of ANY physical
magnitude has a physical content that is totally independent of ANY
arbitrary unit system men made. I do not know if we share the same
philosophical ideas, but for me that physical content is also totally
independent of the knowledge that any man can have about it; more
ever, it is independent of the existence or not of the whole humanity.
You had seen how your bicycle speed could be expressed with a
dimensionless number, what implies that the use of an arbitrary unit
like km/hr (with physical dimension 1 respect length and physical
dimension –1 respect time) is NOT what gives physical content to your
bicycle speed. I identify "physical content" with "natural existence",
something that it is not arbitrarily depending of a man decision. More
later we will talk about a unit system that I consider not arbitrary.
I can advance you that the dimensionless number that you found for
your bicycle speed is using it.
http://math.ucr.edu/home/baez/constants.html

The article you refer is an excellent one, but do not address the
topic I am considering. It assumes that the "physical dimension"
concept is completely clear. Something has or not "physical
dimensions", something is dimensionless or not, there exist
dimensionless constants and others with physical dimensions. All seems
to be clear. You will see immediately that this is not the case.
Let us consider the famous "fine structure constant" alpha. To begin
with, the expression showed for it is unit system dependent (it
changes from one system to another).

The fine structure constant is not dependent on choices of units.
The official definition of the fine structure constant (\alpha)
is given at http://physics.nist.gov/cuu/Constants/alpha.html

\alpha = e^2/(4*\pi*\epsilon0*\hbar*c)

It just so happens that in cgs units, 1/(4*\pi*\epsilon0) = 1.

Then you suggest that the Baez definition alpha=e^2/hbar c is not
correct? At least it is not the "official" one. How can anyone say
that alpha is not dependent on choices of units if we need a different
definition expression for it in every different unit system? Don't you
see that the definition expression is selected in every unit system in
order to obtain the same 1/137 dimensionless value? Why it was
necessary to introduce the epsilon0 constant in the definition
expression for alpha in the SI unit system? Which is the relationship
between an electrical permitivity and a velocity?

It is equal to the electron
velocity in the first orbit of the Bohr 1913 H atom model (assuming c
equal to dimensionless 1, it has the value 1/137).

This is much different than the velocity of my bike. \alpha is
equal to ~1/137 no matter whether c=1 or not. It is independent
on the system of units chosen.

Put c=1 in the "official" definition expression (without any other
change) and you will see that the alpha value is no more 1/137.
And what occur if
we decided to make alpha equal to dimensionless one?

We cannot do that and have a consistent system of units. That is
the reason such constants are *fundametally* dimensionless. They
cannot be changed without also changing the underlying physics.

You can create a unit system choosing arbitrarily the quantity you
want for the unit of any physical magnitude. You can obtain a
completely consistent unit system declaring the velocity of the first
orbit electron in the Bohr's 1913 model the unit for velocity. Why you
can select c as the unit and not alpha? Which is the cause for this
discrimination? Is arbitrary or not the equal to dimensionless one
declarations that physicists had made many times in all epochs? Which
is the rule to decide if something can be declared or not equal to
dimensionless one? How can you decide if a constant is *fundamentally*
dimensionless or not?
Then it will be
1, not 1/137, and c will be 137. Or you can use your km/hour unit to
express the electron velocity in the first orbit, obtaining another
arbitrary number for alpha, in this case with "physical dimensions".

That is nonsense. Sorry if the first link I provided threw you
off by not mentioning the factor of (4*\pi*\epsilon0)^(-1). The
author was quite explicit in saying that "certain constants don't
depend on the units we use", and gave the fine structure constant
as an example.

Yes, I know it, I read it many times in many different places. But
why?
In the CGS unit system the electrical permitivity of vacuum is make
arbitrarily equal to dimensionless 1 (the alpha=[e2/hbar c] is valid
under that assumption), in many other unit systems (including the
actual SI) it has physical dimensions.

I've given the official definition, and you are incorrect. In
the mks (SI) system, \epsilon0 has units of Farad/Meter, giving
the value of \alpha equal again to a dimensionless ~1/137.

The number and the selection of
basic physical magnitudes in any unit system are completely arbitrary!

Not completely. They have to be consistent. But yes, units are
arbitrary. So what? You understood perfectly the physical
content of my bicycle going at 28 km/hr. I eagerly await your
description of the physical content of my bicycle's velocity that
is independent of any system of units.

I think the answer to this is covered in my previous writing.

---Tim Shuba---

RVHG

Rafael Valls Hidalgo-Gato:
shuba wrote in message news:
RVHG wrote:

...but the problem is that ALL unit systems are completely
arbitrary with no essential physical content.

The units km/hr have physical content when I say I am
riding my bicycle at 28 km/hr. Don't you think so?

If you use the relativistic unit system (where c is put equal to
dimensionless 1), the velocity of your bicycle becomes some tiny
dimensionless number and the physical dimensions of length and time
become equal.

OK, that means someone designing a bicycle doesn't need to worry
about relativity.

Which is then the "physical content" of something that you can change
arbitrarily?

The only thing arbitrary about `c' is it's value in meters/second,
which is strictly a result of human definition using units of measurement
which are convenient for humans to describe objects about the same
size as humans that don't go too fast. In other words, meters/second
has no physical content. On the other hand, the value 1 has a lot of
physical content. It's the slope of a line in the x-t plane when you
treat the x and t axes the same way you treat the x and y axes. How
much physical content is there in rescaling the y axis to be measured
in units that differ from the x axis by 10^8, i.e., y = 10^8 x?
None.

Which is then the "physical content" of the "physical dimensions"
that we find in ALL unit systems?

Which unit systems did nature create as opposed to humans?

[...]
I'm interested in the topic. Please consider the link below
and explain exactly where the problems lie.

http://math.ucr.edu/home/baez/constants.html



---Tim Shuba---
The article you refer is an excellent one, but do not address the
topic I am considering. It assumes that the "physical dimension"
concept is completely clear. Something has or not "physical
dimensions", something is dimensionless or not, there exist
dimensionless constants and others with physical dimensions.

The only constants which are physically meaningful are the
ones which are dimensionless.

All seems
to be clear. You will see immediately that this is not the case.
Let us consider the famous "fine structure constant" alpha. To begin
with, the expression showed for it is unit system dependent (it
changes from one system to another). It is equal to the electron
velocity in the first orbit of the Bohr 1913 H atom model (assuming c
equal to dimensionless 1, it has the value 1/137). And what occur if
we decided to make alpha equal to dimensionless one?

Since \alpha is dimensionless it can't be made equal to 1. It already
has the value 1/137.02... By setting c = 1 and \hbar = 1, the electric
charge on the electron is given by,

e = sqrt(4\pi\alpha)

Then it will be
1, not 1/137, and c will be 137. Or you can use your km/hour unit to
express the electron velocity in the first orbit, obtaining another
arbitrary number for alpha, in this case with "physical dimensions".
In the CGS unit system the electrical permitivity of vacuum is make
arbitrarily equal to dimensionless 1 (the alpha=[e2/hbar c] is valid
under that assumption), in many other unit systems (including the
actual SI) it has physical dimensions.

The permittivity and permeability are artifacts that exist from choosing
the wrong units for charges and fields in the first place.

In the Astronomic System (G=1)
we find only two basic physical magnitudes (length and time), and mass
is a derived one with a unit with physical dimension 3 respect length
and –2 respect time. Mass is a "basic" physical magnitude in many unit
systems, thanks to an arbitrary decision.

It's not an arbitrary. It happens to be convenient in general relativity
and have physical meaning. The length as defined for a mass is the radius
that mass would have if it were a black hole. The sun, for example has a
mass of 1.6 km. The earth has a mass of 0.8 cm. That's not very useful
for studying bicycles, but then neither is general relativity.

shuba wrote in message news:tim.shuba-8A9BC5.09184518092004@cp...
RVHG wrote:

More
later we will talk about a unit system that I consider not arbitrary.
I can advance you that the dimensionless number that you found for
your bicycle speed is using it.

Why not just state what 28 km/hr becomes in your system?

Do not refer it as "my" system. It belongs to Nature.
Sorry, English is not my native language and maybe I did not use the
right English words. The dimensionless number that you found is just
the answer to your last question. In the Natural Unit System (NUS) we
have not "physical dimensions", all physical magnitudes are
dimensionless, as strange it can appears to you for the first time.
There does not exist "basic" units or "derived" ones. The NUS has only
one unit, that I have denoted as THE Natural Unit (NU). Which is it?
The natural number 1 (one), an old-known in Mathematics (and also in
Philosophy), the "dimensionless" 1 that physicists of all epochs like
so much to assign to everything they wanted "to make things simpler".
We are now in a point where Mathematics, Physics and Philosophy
converges in a single concept.
Don't worry too much if you do not understand a bit about all I just
wrote! It is just a little advance!
The fine structure constant is not dependent on choices of units.
The official definition of the fine structure constant (\alpha)
is given at http://physics.nist.gov/cuu/Constants/alpha.html

\alpha = e^2/(4*\pi*\epsilon0*\hbar*c)

It just so happens that in cgs units, 1/(4*\pi*\epsilon0) = 1.

Then you suggest that the Baez definition alpha=e^2/hbar c is not
correct? At least it is not the "official" one.

This is a tricky issue.

Yes, this is indeed a very tricky issue. That's all what I want to
hear from you. I will suppose that you are now starting to realize
that all this topic about unit systems and arbitrary 1 dimensionless
assigments to anything is a very cumbersome and obscure one.

The short answer is that charge and
current are defined completely differently in cgs and SI, and the
"e" in the equation refers to quantities of different dimension
in each system. More information can be found here.

http://www.ee.surrey.ac.uk/Workshop/.../unit_systems/

But you know perfectly what is "e", the electric charge of the
electron. Don't you see now clearly that no matter how many "physical
dimensions" you assigned to "e" you do not add a bit of "physical
content" to it, only more and more confusion?

How can anyone say
that alpha is not dependent on choices of units if we need a different
definition expression for it in every different unit system? Don't you
see that the definition expression is selected in every unit system in
order to obtain the same 1/137 dimensionless value?

It is only because of way charge and current are defined that
there appears to be a problem here. The simplest (though perhaps
not the best) way to reconcile them for the above equation is to
include \epsilon0 in Baez' definition and note that it is equal
to 1/(4*\pi) in cgs as I've done above.

Well, I see you are now trying to resolve the problems that arise in
the creation of unit systems. I will make more explicit soon the
solutions I propose.
But why to expend more time and effort putting into accord two
"definition expressions" for alpha if we have many others different
ones for many others arbitrary unit systems? As all "physical
dimensions" to not add a bit of physical content, all the definition
expressions for alpha do not help us to understand what is alpha, to
know which is its physical meaning.
Why it was
necessary to introduce the epsilon0 constant in the definition
expression for alpha in the SI unit system?

Because, as explained in the link above, the Ampere was defined
as a base unit of SI, and was done in such a way as to be
compatible with the definition historically in use at that time.
The use of dimensionful units for vacuum permitivity is an
artifacts of using a particular system of units. The "official"
SI system is often not the best for theoretical physics,
electromagnetism in particular.

What is an "artifact" and what does not, what has a physical meaning
and what does not, this is the crucial point here.

Put c=1 in the "official" definition expression (without any other
change) and you will see that the alpha value is no more 1/137.

Look at it this way. To avoid the issue of SI versus cgs, I'll
write the equation as \alpha = [stuff]/c. Before we make the
substitution c=1, c has units of m/s. Neccesarily then, [stuff]
has units of s/m.

The point is not only the issue of SI versus cgs. The real important
point is that we have NOT a clear definition about what alpha is. I
mentioned it already before. If you have to change the "definition
expression" every time you change from one unit system to another, you
have no idea about what alpha really is. Which are the rules to follow
for obtaining a "definition expression" in some unit system? I do not
know what rules are you following when you put \alpha = [stuff]/c
trying to avoid the unit systems ambiguities. Why must c remains and
not epsilon0 per example?
The simple existence or more than one "definition expression" for an
entity is a clear signal that something is going wrong, very wrong.
When we say c=1, we are really redefining the
units of length and time so that 1 s = 3*10^8 m. We need also to
apply that same redefinition to [stuff], which introduces a
numerical term which precisely cancels how we changed the
numerical value of c when we switched systems.

You have discovered by yourself what is for me a very fundamental
point (and the basis to understand what the Natural Unit System NUS is
all about!), 1 second equals 3*10^8 meter! Some definite quantity of
some physical magnitude being equal to a definite quantity of another
different physical magnitude. If time and length are two different
physical magnitudes, with what right you declare that definite
proportion between them? Why not 137 s = 3*10^8 m, per example? (the
result obtained if you put alpha=1).
Yes, I can accept that could exist some NATURAL equivalence between
time and length, but not that men can fix it arbitrarily!
How can you decide if a constant is *fundamentally*
dimensionless or not?

As explained in Baez' article, *fundamentally* dimensionless
constants are those which don't depend on the units we use.

And how can you know when some entity is unit-system independent? Do
not answer that they are the *fundamentally* dimensionless constants!
The
author was quite explicit in saying that "certain constants don't
depend on the units we use", and gave the fine structure constant
as an example.

Yes, I know it, I read it many times in many different places. But
why?

Why indeed? No one knows, and a good answer would definitely be
Nobel material. Feynman wrote something to the effect that all
good theoretical physicists put the number 137 on their wall and
worry about it. Not coincidentally, the director's housing at
Fermilab has an address of 137 Eola Road. It is a great mystery.

Oh! I didn't realize that this topic were so important! You are now
ready to understand the physical meaning of the Natural Unit System
(NUS) and the Natural Unit (NU).

Axiom RV. For each one of all physical magnitudes there exist a
determined natural constant that are all equivalent among them.

The Natural Unit System (NUS) is simply the unit system that selects
for unit the natural constant of every physical magnitude. We can put
all these constants equal to dimensionless 1, denoted as "the" Natural
Unit (NU).

What is alpha? The electron velocity of the first orbit in Bohr 1913 H
atom model, expressed in Natural Unit under the assumption that c is
the natural constant for velocity. Under axiom RV you must have a
unique natural constant for every physical magnitude. I refer to them
in the future speaking about "the" natural constant that correspond to
some physical magnitude, to emphasize its unique character.

Under axiom RV only one of c and alpha can be the natural constant for
velocity. I think that Nature selected c! From this we can derive the
value 1/137 for alpha, indeed a natural value not depending at all of
all men-made unit systems!

Can you guess which is the natural unit for the angle physical
magnitude? (Yes, angle is a physical magnitude, not less and not more
valid than length, time or mass).


---Tim Shuba---

RVHG

RVHG wrote:

Do not refer it as "my" system. It belongs to Nature.

As someone who thinks the fine structure constant is best defined
by a model incompatible with nature, you're hardly one to claim
to be some kind of prophet with the true understanding of nature.

Sorry, English is not my native language and maybe I did not use the
right English words.

Well, speaking in riddles is not my first language. I've given
links to information that backs up and clarifies my statements.
You keep on saying that you will make things explicit *soon*, but
you never do so. Whatever system *you* have defined most
certainly is *your* system.

The real important
point is that we have NOT a clear definition about what alpha is.

Speak for yourself.

Which are the rules to follow
for obtaining a "definition expression" in some unit system? I do not
know what rules are you following when you put \alpha = [stuff]/c

It's called algebra.

When we say c=1, we are really redefining the
units of length and time so that 1 s = 3*10^8 m. We need also to
apply that same redefinition to [stuff], which introduces a
numerical term which precisely cancels how we changed the
numerical value of c when we switched systems.

You have discovered by yourself what is for me a very fundamental
point (and the basis to understand what the Natural Unit System NUS is
all about!), 1 second equals 3*10^8 meter! Some definite quantity of
some physical magnitude being equal to a definite quantity of another
different physical magnitude. If time and length are two different
physical magnitudes, with what right you declare that definite
proportion between them? Why not 137 s = 3*10^8 m, per example? (the
result obtained if you put alpha=1).

You clearly didn't understand either the Baez article or my
explanation. There is no way that \alpha can be equal to 1. We
can define 137 s = 3*10^8 m, and we *still* get \alpha = ~1/137.

How can you decide if a constant is *fundamentally*
dimensionless or not?

As explained in Baez' article, *fundamentally* dimensionless
constants are those which don't depend on the units we use.

And how can you know when some entity is unit-system independent? Do
not answer that they are the *fundamentally* dimensionless constants!

I guess *you* can't know, since you disagree with Baez' article,
and claim that \alpha can be 1. The fact the it cannot means
that \alpha is a fundamentally dimensionless constant.

Axiom RV. For each one of all physical magnitudes there exist a
determined natural constant that are all equivalent among them.

The Natural Unit System (NUS) is simply the unit system that selects
for unit the natural constant of every physical magnitude. We can put
all these constants equal to dimensionless 1, denoted as "the" Natural
Unit (NU).

What is alpha? The electron velocity of the first orbit in Bohr 1913 H
atom model, expressed in Natural Unit under the assumption that c is
the natural constant for velocity.

I hate to break it to you, but the Bohr model is known to not
correctly model nature. There is no electron velocity around the
nucleus. \alpha is much more fundamental than is shown by your
poor definition of it. There already is a useful system that was
proposed by Planck in 1899, and it appears to be free from the
crackpottery of *your* system.

\alpha = ~1/137, independent of what unit system we use. That's
why it is fundamental. and c is not. Until you can understand
and accept this simple concept, you really have no business
pretending to have some special insight.


---Tim Shuba---