Outline

EthnoPhysics begins with the premise that we can understand time by describing sensory experience. Mysteries of the universe aside, we start by simply counting heartbeats and days. Then we assess Planck’s postulate as a feature of life on Earth. Time dilation is discussed. And the relations between cause and effect are linked to the notion of stability. Finally, the phase angle is introduced for describing small particles.

## Counting Bundles

To extend an earlier discussion about counting quarks, consider some particle P, that is characterized by a repetitive chain of events written as

where each repeated cycle is a bundle of quarks written as

Depending on the level of objectification, each bundle may be thought of as a set of sensations, or an orbit, or an aggregation of seeds, or perhaps a compound quark. But for any interpretation we can make a *mathematical* description of P just by counting bundles.

The chain is a sequence of an indefinite number of bundles, there may be two or two-billion of them. But we can specify a definite quantity by making the description relative to a reference sensation provided by seeing the Sun. Let be the number of P’s bundles observed during one solar day. This quantity has units of bundles-per-day or cycles-per-day.

Solar clocks are historically important, but not much used anymore. So consider evaluating where P is an ordinary clock noted by . If this clock is calibrated so that its cycles are in seconds, then

86,400 (seconds per day)

This number comes to us from the Sumerian and Babylonian peoples of ancient Mesopotamia^{1}George Sarton, *A History of Science*, page 74. Harvard University Press, Cambridge 1952.. About four thousand years ago their astronomical observations and sexagesimal mathematics established what we mean by a **second**. Namely that one day is parsed as twenty-four hours of sixty minutes, each of sixty seconds.

For EthnoPhysics, we also associate with the reference sensation of hearing a human heartbeat because the heart rate of human adults usually pulsates between forty and one hundred beats-per-minute when resting. So gives an order-of-magnitude account of the number of heartbeats-per-day for most people, thereby relating celestial and human-scale events.

The foregoing tallies of bundles are used to define the **angular frequency** of P as

This angular frequency has units like bundles-per-second. As descriptions are objectified, we associate radians with each bundle and speak more generally of radians-per-second. And since all physical particles are supposedly made of quarks, we can also define a very general expression of the **frequency** as

where is the number of quarks in . This generic frequency characterizes the flux of quarks associated with P. It has units like quarks-per-second, or more generally *hertz*, and is abbreviated by (Hz). This frequency describes the flow strength in a stream of consciousness. It is proportional to the quantity of Anaxagorean sensations experienced per second.

## Planck’s Postulate

In 1900 the German physicist Max Planck asserted that the energy of any particle P, is directly proportional to its frequency, in a fixed ratio called Planck’s constant.^{2}*The Theory of Heat Radiation* by Max Planck. Translated into English by Morton Masius and published by P. Blakiston’s Son & Co. in Philadelphia, 1914. Here is a plausibility argument for the postulate that is based on understanding P as a repetitive chain of events written as

Let P be characterized by its angular frequency and mechanical energy Then we can specify a number called the **action** of P as

Also let each repeated bundle be composed from quarks so that Then the action associated with a typical quark is

Recall that the generic frequency of any particle is given by . So the action for some average quark in P can be written in terms of the frequency as

For terrestrial particles made from lots of quarks, the statistical law of large numbers guarantees that has a definite value determined by the distribution of quarks on Earth. Moreover, this value is presumably constant because the quark distribution is at least as stable as rock formations that change on geological time scales. This constant is called Planck’s constant, and noted by . We can write

Then if is large enough, the foregoing result that implies that

This is the conventional statement of Planck’s postulate. It is an experimental fact that the ‘constant’ is well known to about one part in a billion, and apparently not much changed over the last century. So we make vigorous use of Planck’s postulate for particles that contain many quarks.

Sensory interpretation: The angular frequency is proportional to the number of sensory bundles observed per day. So if the mechanical energy of P is randomly spread out between these bundles, then the action represents the energy in a typical bundle. And is like the energy of a typical quark in a typical bundle.

## Time of Occurrence

Titus Lucretius Carus was a Roman poet best known for proclaiming the ideas of Epicurus who founded one of the most famous and influential philosophical schools of antiquity. His physics was taught at Athens around 300 BCE. According to Lucretius^{3}Titus Lucretius Carus, *De Rerum Natura*, translated by R. E. Latham, page 40. Penguin Books 1951.

... time by itself does not exist; but from things themselves there results a sense of what has already taken place, what is now going on and what is to ensue. It must not be claimed that anyone can sense time by itself apart from the movement of things or their restful immobility ...

The EthnoPhysics approach to understanding time follows this Epicurean recipe. First we consider “things themselves” by carefully defining particles. Then we characterize “the movement of things” from a particle’s momentum Next “their restful immobility” is represented by the rest mass And finally these numbers are combined to define the **period** as

Recall that is the mechanical energy, and that Planck’s postulate asserts that where is the frequency. So the foregoing definition implies that for large particles

Now let some particle P be characterized by a repetitive chain of events where each repetition is described by its period . The **time of occurrence** of event is defined as

where notes the direction of time. The value of the original event is arbitrary. Let be historically ordered, then and the time of occurrence is given by a simple sum of periods. The period depends on a particle’s momentum, which in-turn depends on whatever frame of reference is used to describe the particle’s motion. So the time of occurrence is frame-dependent too. If then is called the **proper time**. Please notice that this quantity has been entirely established by a systematic description of sensation.

### Time Dilation

Let P be represented by the historically-ordered chain-of-events

And let each event be described by its time of occurrence . Then consider a pair of events and where . Since is in historical order we call them the initial and final events of the pair.

The **elapsed time** between these initial and final events is . If P is isolated and the frame of reference is inertial then the energy and momentum do not change from event to event along the chain . For these conditions, the period is constant too. But the time coordinate is defined from a sum of periods, so the elapsed time can be written as .

We evaluate this quantity for a material particle that is considered to be a clock in motion. Let P be described by its mechanical energy and its mass. These are related by where is the Lorentz factor. Then the period is given by

So in terms of the mass

If P is a clock, this is the elapsed time that it would indicate between events. For comparison, set to define

This is the elapsed time that would be recorded if P was at rest, it is called the proper elapsed time. The two quantities are related as . The Lorentz factor for a particle in motion is always greater than one, . So a moving particle always experiences less elapsed time than a stationary particle, . This effect is called **time dilation**.

According to Albert Einstein time is what a clock tells.^{4}To be more precise, this quotation has been translated by Robert W. Lawson as “… we understand by the *time* of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially capable of observation.” From *Relativity, the Special and the General Theory*, page 24. Published by Methuen & Company, London 1936. So here is a generic description of how to determine using a clock.

The elapsed time between initial and final events depends on the frame of reference F which is represented by another chain of events

Since F is employed as a reference frame, we assume that every report about P is accompanied by an observation of F, so that events of F and P can be associated in pairs like

To make a laboratory measurement of elapsed time first select some clock that is presumably part of the frame of reference F. Let this clock be calibrated so that its period is a known quantity. Observe events to determine the numbers and by counting clock cycles. Report the result as

Sensory interpretation: The elapsed time while experiencing one bundle of sensation , is the period . This period is the reciprocal of the frequency, which is proportional to the number of bundles observed per solar day. So the period can be interpreted as some fraction of a day. And the elapsed-time is based mostly on the reference sensation of seeing the Sun. However the direction of time is defined from thermal sensations, that are ultimately referred to the sensations of touching steam and touching ice.

## Cause and Effect

Consider some particle P that is described by its lifetime , its orbital period and a chain of events that is written as

Let these events be historically ordered. Then and are called the initial and final events of . And if the particle is perfectly isolated then and are established by the formation and decay of P. With an inertial frame of reference, the period does not vary. Then the elapsed time between initial and final events is P’s lifetime, and all these quantities are related as

Let be a chain of very many events so that

For this case the lifetime must be much greater than the orbital period

and we say that P is **stable**. Then it is probable that P will *not* decay during any specific cycle. P is steady and consistent. One orbit will almost invariably follow another with dependable regularity. This predictability is useful, so we give the events of particles like this special names. If

then the initial event of is called the **cause**, and the final event is called the **effect** of the cause. We may say that P’s events are *causally* linked to each other. For example consider the proton in its ground-state. It has a period of about 10^{-24} seconds, so in principle we could assign a very precise time of occurrence to any events in the history of a proton.

For protons, the lifetime is more than 10^{36} seconds, so And for electrons, the period is about 10^{-20} seconds with a lifetime of more than 10^{34} seconds. So both the proton and electron are *extremely* stable particles. This gives them starring roles in narratives connecting cause and effect.

## Phase Angle

Let particle P be described by an ordered chain of events written as

that is repetitive so that may also be written as

where each orbital cycle is composed of sub-orbital events

If P contains just a few quarks then the time of occurrence may not be a useful parameter for describing these events because Planck’s postulate is plausibly justified on a statistical basis. So we also discuss the order of events using a **phase angle** defined by

where is arbitrary and is the helicity of P. The ground-states and many excited-states of atoms have spin-down orientations, then Also, the change in during one sub-orbital event is called the **phase angle increment**. It is defined by so usually

EthnoPhysics uses a finite categorical scheme of binary distinctions to describe sensation. So the number of sub-orbital events may be large but not infinite. This requirement can be relaxed later to make a continuous approximation, thereby allowing the use of calculus. But in principle is finite and accordingly changes in may be small but not infinitesimal. For isolated particles the increment in the phase angle does not vary and so there is an equipartition of between sub-atomic events regardless of their quark content.

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1 | George Sarton, A History of Science, page 74. Harvard University Press, Cambridge 1952. |
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2 | The Theory of Heat Radiation by Max Planck. Translated into English by Morton Masius and published by P. Blakiston’s Son & Co. in Philadelphia, 1914. |

3 | Titus Lucretius Carus, De Rerum Natura, translated by R. E. Latham, page 40. Penguin Books 1951. |

4 | To be more precise, this quotation has been translated by Robert W. Lawson as “… we understand by the time of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially capable of observation.” From Relativity, the Special and the General Theory, page 24. Published by Methuen & Company, London 1936. |