# Musings on energy

[From Bill Powers (2010.02.17.0920 MST)]
In high-school physics I got fascinated by all the simple equations
relating mass, energy, force, distance, velocity, and acceleration. As I
played with them I realize that they were all related to each other. But
when I asked the physics teacher about that, he just said that the actual
mathematics was much more complicated, and that I was wasting my time. So
I went on to other things.
But there’s still that same fascination. Look at this:
Velocity V is equal to acceleration A times elapsed time t:
(1)V = AtSquare both sides (^2 means an exponent of 2):
(2) V^2 = (A^2)(t^2)
Divide both sides by A:
(3) V^2/A = At^2
Now introduce the relationship between distance traveled X and
acceleration A:
(4) X = (1/2)At^2From equation 3, substitute V^2/A for At^2 in equation 4:
(5) X = (1/2)v^2/A
Multiply both sides of (5) by F for force:
(6) FX = (1/2)Fv^2/A
DEFINE energy E as the product of force F times distance X (distance
means the distance through which a force applied to an object moves
it).
(7) E = FXSubstitute E for FX in (6):
(8) E = (1/2)Fv^2/A
DEFINE mass M as Force divided by acceleration A:
(9) M = F/ASubstitute M for F/A in (8):
(10) E = (1/2)Mv^2
That is the equation for kinetic energy.
We can now combine (7) and (10) to eliminate E:
(11) FX = (1/2)MV^2
We have now shown that the product of force times distance is equal to
(1/2)MV^2, without energy appearing in the equation at all. We have
derived the equality of kinetic energy to potential energy or energy of
position without any observations of nature, simply by using two
fundamental equations:
(1)V = At(4) X = (1/2)At^2… and introducing two definitions:
(7) E = FX(9) M = F/AEquations 1 and 4 are basic factual observations, properties of space
and time at velocities that are low compared with the velocity of light.
The quantities called mass and energy are defined in terms of measurable
variables F, M, and A; neither mass nor energy is directly measurable. To
measure energy you apply a force to a constrained object and measure the
distance through which it moves. To measure mass you apply a force to an
free-moving object and observe how it accelerates.

I don’t recall how I worked all this out in high school far enough to ask
the physics teacher if we couldn’t just eliminate energy and mass from
all equations. He definitely didn’t like that idea. But as I return to
these ideas 67 years later, I can’t help feeling the same doubts about
the reality of energy and mass. They’re inventions, not
discoveries.

Much of physics has been built up this way, accumulating an ever-growing
superstructure made from mathematical manipulations of basic observable
quantities. How much of physics has simply been invented and defined into
existence? That’s what I wanted to know in 1943 or so; I still
wonder.

Best,

Bill P.

[From Bruce Gregory (2010.02.17.2243 UT)]

[From Bill Powers (2010.02.17.0920 MST)]

Much of physics has been built up this way, accumulating an ever-growing
superstructure made from mathematical manipulations of basic observable
quantities. How much of physics has simply been invented and defined into
existence? That’s what I wanted to know in 1943 or so; I still
wonder.

It is indeed impressive what you can do with dimensional analysis. If you haven’t read Frank Wilczek’s book, Fantastic Realities: 49 Mind Journeys and a Trip to Stockholm, I think you would enjoy it.

Bruce

[From Bill Powers (2010.02.17.1655 MST)]

Bruce Gregory (2010.02.17.2243 UT) --

It is indeed impressive what you can do with dimensional analysis. If you haven't read Frank Wilczek's book, _Fantastic Realities: 49 Mind Journeys and a Trip to Stockholm_, I think you would enjoy it.

I'll have a look for it, thanks. So far, the local public library doesn't have it, and it doesn't seem there is a reciprocal arrangement with the Boulder public library, which does. Interlibrary loan is probably possible. I'll see.

Do you have any opinions about the question I raised?

Best,

Bill P.

(Gavin Ritz 2010.02.18.17.53NZT)

[From Bruce Gregory (2010.02.17.2243 UT)]

[From
Bill Powers (2010.02.17.0920 MST)]

Much of physics has been built up this way, accumulating an ever-growing superstructure
made from mathematical manipulations of basic observable quantities. How much
of physics has simply been invented and defined into existence? That’s what I
wanted to know in 1943 or so; I still wonder.

It is indeed impressive
what you can do with dimensional analysis. If you haven’t read Frank
Wilczek’s book, Fantastic Realities: 49 Mind Journeys and a Trip to
Stockholm
, I think you would enjoy it.

Try stomach these two papers on musings of
energy; they have a great deal of relevance to PCT. You will be excited to see
that PCT and Cellular signaling have a common idea. A control System.

I don’t want to spend too much time on this though; I seem
to get myself into trouble too easily on this list.

···

I dont want to spend too much time on this though; I seem to get myself
into trouble too easily on this list.

[From Bill Powers (2010.02.18.0822 MST)]

Gavin Ritz 2010.02.18.17.53NZT –

Try stomach
these two papers on musings of energy; they have a great deal of
relevance to PCT. You will be excited to see that PCT and Cellular
signaling have a common idea. A control System.

Is this (from the cellular signaling paper) what you’re referring to as a
control system?

PdPC stands for Phosporylation-dePhosphorylation Cycle. The last
sentence in the legend says the dashed line is a positive feedback
connection, and the text says that this makes the change of state from A
to A* into a switch (that is, no stable state between A and A*).

The text says,

I confess that I got lost in the equations that led up to this, so
I’m not sure what [I] stands for, and I don’t see how the positive
feedback comes out of this. Aside from the problem that positive feedback
doesn’t produce control in the PCT sense, I don’t see how equation 4
leads to positive feedback. Can you explain that to me? What was it that
indicated a resemblance to PCT?

Best,

Bill P.

[From Rick Marken (2010.02.19.0730)]

Bill Powers (2010.02.18.0822 MST) to Gavin Ritz 2010.02.18.17.53NZT –

Is this (from the cellular signaling paper) what you’re referring to as a
control system?

Best

Rick

···

Richard S. Marken PhD
rsmarken@gmail.com

(Gavin Ritz 2010.02.20.10.13NZT)

[From Bill Powers
(2010.02.18.0822 MST)]

Gavin Ritz 2010.02.18.17.53NZT –

Sorry a bit snowed under at work.

Looks like I sent the wrong paper, I will
look for the one I wanted to send about feedback systems and signaling. There’s
been quite a bit of work done in this area of signaling, small systems, far-from
equilibrium systems, non linear dynamics and the energy relations. That can
support PCT.

I’m out of town on business for at least
a week. I will endeavor to find the paper and post it.

In the meanwhile I will be thinking about
reference levels and my proposal that reference signals at the highest level
can never be zero.

Regards

Gavin

Try stomach these two papers on musings of
energy; they have a great deal of relevance to PCT. You will be excited to see
that PCT and Cellular signaling have a common idea. A control System.

I don’t want to spend too much time on this though; I seem to get myself
into trouble too easily on this list.

Is this (from the cellular signaling paper) what you’re referring to as a
control system?

PdPC stands for Phosporylation-dePhosphorylation Cycle. The last
sentence in the legend says the dashed line is a positive feedback connection,
and the text says that this makes the change of state from A to A* into a
switch (that is, no stable state between A and A*).

The text says,

I confess that I got lost in the equations that led up to this, so
I’m not sure what [I] stands for, and I don’t see how the positive feedback
comes out of this. Aside from the problem that positive feedback doesn’t
produce control in the PCT sense, I don’t see how equation 4 leads to positive
feedback. Can you explain that to me? What was it that indicated a resemblance
to PCT?

Best,

Bill P.