## Larsons units

This forum is dedicated to the student just starting out with the concepts of the Reciprocal System, or RS2. Questions and clarifications for the RS/RS2 concepts go here; please place new ideas and commentary in the appropriate RS2 fora.
rossum
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### Larsons units

Larson somehow (through long series of inductions) arrived to conclusion, that mass is m=t3/s3. I would like to know if there is some way to deduce it from experience, like any other physical laws in the deductive science.

Metric system (not just SI but also cgs and other conventional systems) can be reduced to min. four independend irreducible units of space, time, mass and current (or their combinations). RS reduces the metric system by two more units - mass and current. Current can be got rid of by similarity between voltage and force:

F=dp/dt U=dP/dt

where F is force, dp is change of momentum, dt change of time, U is voltage, dP chage of magnetic flux. In order to have the same units, in the second relation current must be speed times some constant. However for mass I didn't find any such similarity (and I doubt there is one - the playground with relations containing only time and space is quite small).

I wonder - can the relation between space, time and mass be somehow shown without "theory contamination"? (E.g. the relations above describe only the experience, they don't represent any particular theory. On the other hand 'electron' is a result of a theory used to explain certain experience. 'An electron was accelerated by 5V' is a "theory contamined" description. It is not necessarily right or wrong, but you have to use some theory to understand the statement.)

Jan

bperet
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### mass = dp/dv

Not sure if this is what you are looking for...

From Gustav LeBon, circa 1907, mass is dp/dv, where dp is the change in momentum (called "weight" in those days) and dv is change in velocity.

In electronics, inductance replaces mass with the same units.
Every dogma has its day...

Horace
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### From Gustav LeBon, circa 1907

From Gustav LeBon, circa 1907, mass is dp/dv, where dp is the change in momentum (called "weight" in those days) and dv is change in velocity.
But the cubed exponents s^3/t^3 are not evident from this relation and cannot be gathered from mere observation. His point is how to arrive at that empirically without making theoretical assumptions.

silvio.caggia
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### m=t3/s3 from E=mc2

If I have well understood your problem, you can derive m=t3/s3 from Einstein formula E=mc2.

m=E/c2

[m]=(t/s) / (s2/t2)=t3/s3

Hope it helps

bperet
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### Only space is observable; time changes space

But the cubed exponents s^3/t^3 are not evident from this relation and cannot be gathered from mere observation. His point is how to arrive at that empirically without making theoretical assumptions.
Jan gave dp as empirical; velocity is also empirical. Mass is just defining the relationship between the two. (You have your ratio inverted.)

$Mass \left( \frac{t^3}{s^3} \right) = \frac{dp \left( \frac{t^2}{s^2} \right)}{dv \left( \frac{s}{t} \right)}$

In my opinion, mass isn't an empirical quantity, it is one that was invented by scientists as a device to explain equivalent space, a rotational space (imaginary numbers) that cannot be described with linear mathematics, but is still there in observation. Space is linear, time (as a clock) is linear, current (speed, the ratio of space to time) is linear--the only non-linear component is mass, which is why it was considered an irreducible unit. In space, you start with 0 dimensions and work up to 3, which is why linear space (1D, first step) is predominant in our thought. It is the baseline from which geometry is built.

Rotation, however, occurs in time, which is the reciprocal of space. That means it works backwards--you start with 3 dimensions (everything, the inverse of nothing), and work down to 0. In the equivalent space represented by time, 3D is analogous to the spatial 0D--unmanifest. Therefore, the first manifestation we see with rotational spaces is a 2D rotation, momentum (Larson's magnetic rotation), the most predominant. Then you get a 1D rotation (electric) as the next step. These two rotations occur separately in time, but because we only observe the net effect here in space, we see it as a single, 3D rotation that is called "mass."

Observation and experience are based solely on changes in space. Mass is in time, therefore inherently unobservable with no direct experience. The only thing "observable" is how time changes space. None of the rotational systems (mass, magnetic, electric) can therefore be empirical from a linear, spatial perspective.
Every dogma has its day...

Gopi
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### Units of mass

Mass units can be derived in a different way from Larson's:

Consider movement - s/t. In the RS where "1" is the datum, the only expression that can oppose or resist a motion is t/s, because (s/t)*(t/s) = 1. Hence, t/s is geometrically polar to s/t, rotational instead of linear, temporal instead of spatial, indirectly observable instead of directly empirical. Since the resistance is independent of spatial direction, it can hold in all three dimensions, giving (t/s)3 or t3/s3. Hence, it can be considered a sort of "friction" to the movement, that casts a shadow for the light.

1 dimensional "resistance": t/s (ENERGY)

2 dimensional "resistance": t2/s2 (MOMENTUM)

3 dimensional "resistance": t3/s3 (MASS)

Conventional physics does not have unit datum, but only zero datum. So once they had speed s/t, the only "resistance" they could consider was "change in speed magnitude/direction" i.e. ds/dt or acceleration. This means they also opened the door to an unlimited series of possible motions:

s/t, s/t2, s/t3, s/t4... s/tn

or: v, a, a', a'' ... a(n)

So this lead to an infinite series, which Newton and his followers used as wiggle room to apply to all of mechanics, instead of tackling rotation directly. It also led to an undigestible precipitate, mass, and thereby to F=ma. That is why the force ideas are so vague and non-intuitive, and leaves several paths untouched. One can ask for example, why does no one consider all the possible motions:

mv, ma, ma', ma'', ma''', ... ma(n)

Why stop with just P = mv and F = ma? What about the rest? No answer is given. Besides, what about the opposite series, why isn't the following series popular:

s/t, s2/t, s3/t... etc.?

Because the wiggle room is limited to three dimensions. Besides, no one measures area or volume directly, so you have limited application. But Larson spotted this, and s3/t especially, is nothing but his expanding balloon. Voila! We have the first hint of Scalar motion:

s/t, s/t2, s/t3 -> Vectorial Motion

s/t, s2/t, s3/t -> Scalar Motion

This helped him get at the reciprocity of space and time, and their consequences.

Hope that helps.

rossum
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### Relations as description

The beauty of the descriptive approach is in the fact, that you don't have to "believe" in mass, momentum, pressure etc., you only have to define them proprely: if it gets to e.g. calculating the heat needed to push a piston, you still use the same equation. It is only a meas to describe your experience through mathematics, so whether they are "real" or not doesn't make a difference.

Horace is right, I would like to arrive to the dimensions of mass, energy, momentum, moment of inertia, action or any other quantity that has time with positive exponent without theoretical assumptions. All the other relations are based on the definition of concept in question. If we didn't give this concepts names, we could write them down systematically (as Gopi showed). The problem is, if I would argue that mass is some other combination of space and time (e.g. t2/s), there is no way to experimentally disprove that. The only difference between science and pseudoscience is that a scientific theory can be disproven by an experiment. (Note that e.g. string theory is in fact pseudoscience)
Observation and experience are based solely on changes in space. Mass is in time, therefore inherently unobservablewith no direct experience. The only thing "observable" is how time changes space. None of the rotational systems (mass, magnetic, electric) can therefore be empirical from a linear, spatial perspective.
Perhaps not for masses and properties of physical objects, but rotations of real physical objects should have the same properties as rotations that make up matter. There are some experiments with forced precession that clearly show loss of weight. I guess the answer could be somewhere there. So there might be a way to show it without theoretical assumptions after all...

Jan

rossum
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### Summarizing...

Considering how much time I spent thinking about the units problem I wrote a short article on this - the units of measurement. I.e. what do they actually mean and how can one get from regular units to the ones used in RS. Someone might find it helpful... Anyway, is there a review process here? I'll post it right here. If someone has any comment (how to change it, to be more informative) please let me know. If someone wants to add, change, modify or use some part of it I can send the original TEX file...

Jan
Attachments
shortnote_units.pdf
Short note on units of measurement

bperet
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### Corrections / suggestions

Typeo on page 3: "mapping is quite indirect as, as we saw merging two units"

Page 3: "Consequently, the charge must be equivalent to the distance." Larson, in Basic Properties of Matter, points out that conventional physics use of "charge" has two different units associated with it, the energy of charge (t/s) and the quantity of charge (s). This arises because they do not have an uncharged version of the electron, as the RS does. The uncharged electron has units of space, and therefore appears as a quantity (number of electrons), versus the charged electron (t/s), where one is using the magnitude of the charge, not the quantity of electrons.

Page 4: typeo: "only “displacemes” from the unit level."; "originates from Philip Porter’s speach)", Phillip has 2 "L"s.

What is "Appendix A" for? Perhaps you should include the corresponding natural units there?

If you haven't already, read Larson's paper: The Dimensions of Motion. Larson goes over the derivation of many of his natural units there.
Every dogma has its day...

rossum
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### Thanks and next version

Thanks for comments and corrections. Here is the corrected version.

The appendix is there to show how are the same concepts differently complex different mappings.

Jan
Attachments
shortnote_dimensions.pdf