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

Each repeated cycle is a bundle of quarks

And the total number of quarks in the bundle is a finite positive integer. Depending on the level of objectification, this bundle might be thought of as a set of sensations or maybe a seed aggregate or perhaps some kind of spatial trajectory. But for any interpretation we can make a *mathematical* description of P just by counting bundles.

The chain connects an indefinite number of cycles, there may be two or two-billion repetitions. But we can specify a definite quantity, written as by making the description relative to seeing the Sun.

Let be the number of bundles that are experienced during one solar day. Or in other words, determine by using the Sun as a clock while counting how often P is observed. This quantity is called the **number of daily occurrences**. The units of are bundles-per-day or cycles-per-day. The Sun is presumably always available for this purpose because it is a reference sensation for EthnoPhysics.

Solar clocks are historically important, but not much used anymore. So consider evaluating for 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. So is number established by convention. It is called the **time units conversion factor**.

Sensory interpretation: 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.

## Frequency

A temporal *frequency* is usually defined as some quantity of events happening per unit of time. But EthnoPhysics begins with the premise that time is known from sensory experience. So we have explicitly employed a solar clock to specify as the number of daily occurrences for some event. This tally is used to define the **frequency** as

This frequency describes a flux of quarks because allows for the number of quarks in a bundle. So the frequency has units like quarks-per-second. Formally, frequency units are called hertz and abbreviated as (Hz).

Sensory interpretation: The frequency describes 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 a particle is directly proportional to its frequency in a fixed ratio that is now 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 some particle P as a repetitive bundle of quarks written as

Let P be characterized by its mechanical energy. Then we can define a number called the **action** of P by

To expound on the action recall that is a constant, and that is the number of bundles observed during one day. So if is dispersed over all these bundles, then is directly proportional to the daily-average energy of one bundle. Roughly speaking, the action is like the energy of a *typical* bundle. is also used to define the action of an average individual quark as

So in terms of the frequency the action due to this *typical* quark is

Thus describes the action of a *typical* quark in a *typical* bundle. And

Consider evaluating for a special case where P is the Earth. The number is presumably a constant because the Earth is so large and permanent. Quark distributions are at least as stable as rock formations that change on geological time scales. This number is called Planck’s constant. It is traditionally noted by so we write

Now let P be some other big terrestrial particle. That is, let be large enough so that the statistical law of large numbers takes effect. This implies that a measurement of is close to and that they tend to get closer as rises. So if P is large enough, we may say it satisfies the **large particle condition** written as

Thus for large particles we can combine the last three equations to obtain

This is the conventional statement of Planck’s postulate. It is an experimental fact that 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.

## Time of Occurrence

Titus Lucretius Carus was a Roman poet best known for proclaiming the ideas of Epicurus a Greek philosopher who founded one of the most famous and influential 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 **orbital period** as

This expression can be simplified using the modern notion of mechanical energy. Recall that So the period can always be written as

Furthermore, for particles containing many quarks, we can use Planck’s postulate which states that where is the frequency. So for large particles the period can be put simply as

To relate this orbital period to time, let some particle P be characterized by a repetitive chain of events written as where each orbit is described by its period The **time of occurrence** of event is then defined by

where notes the direction of time. Let be historically ordered then and the time-of-occurrence is given by a straightforward sum of periods. The value of the original event is arbitrary. In general, the time-of-occurrence may also be referred to as **the time** or a **time coordinate**.

The time is an important parameter for describing repetitive sensations. But recall that each repetition is a set of quarks written as

where is a finite integer. So the most detailed description of sensation could expand into an account of individual quarks. Then the smallest change in would be due to the effect of a single quark. This little step is called an **increment of time**. It is written as and defined by

Finally, we remark that the time-of-occurrence is a relative characteristic. The orbital period depends on a particle’s momentum, which in-turn depends on whatever frame of reference is used to describe a particle’s motion. So the time coordinate is frame-dependent too. If then is called the **proper time**.

### Elapsed Time

Let P be represented by a historically ordered chain-of-events written as

And let each event be described by its time-of-occurrence . Then consider an arbitrary pair of events and where . Since is in historical order we call them initial and final events. The **elapsed time** between these two events is defined by

If P is isolated and the frame of reference is inertial then the mass 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

Sensory interpretation: The elapsed time while experiencing one bundle of sensation , is the period . This period is some fraction of a day. So the elapsed-time is based on the reference sensation of seeing the Sun. However, the direction of time is defined by thermal similarity to the Earth. And thermal descriptions are ultimately referred to touching steam and touching ice.

### Telling Time

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 rudimentary method for determining using a clock. Consider some particle P that is represented by a chain of events written as

The elapsed time between some pair of events and depends on the frame-of-reference F used to determine P’s momentum. Let this frame include a clock And let F be represented by a chain-of-events written as

Since F is employed as a reference frame, presumably every measurement of P is accompanied by an observation of F. That is, we assume that events of F and P can be closely associated in pairs such as

To make a generic measurement of elapsed time, first calibrate the frame’s clock so that its period is a known quantity. Then observe events to determine the numbers and by counting clock cycles. Report the result as

This approach is good enough for the large slow particles of everyday experience. But if P is very small or fast then the assumption of being “closely associated” with F may require further elaboration.

### Time Dilation

Let be a material clock that might be moving. The clock’s rest mass is written as And its mechanical energy is noted by

We now evaluate how the elapsed time, as told by is affected by motion. An earlier discussion of the Lorentz factor related mass and energy by So the clock’s period may be expressed as

Then the elapsed time between some arbitrary initial and final events is given by

For comparison, set to define the elapsed time that would be indicated if was at rest. This number is noted by and called the *proper* elapsed time

The two quantities are related as But the Lorentz factor of a moving particle is always greater than one. So a moving particle always experiences less elapsed time than a stationary particle. Thus and this effect is called **time dilation**.

## Cause and Effect

Consider some particle P that is described by its mean life its orbital period and a historically ordered chain of events written as

where and are the initial and final events in a history of P. They represent P’s formation and decay. So the difference in their occurrence times is P’s lifetime

Furthermore let P be isolated. Then for an inertial frame of reference, the period of P is a constant, and the elapsed time between initial and final events is just

But by definition So for P, eliminating the time coordinates and rearranging gives

If is a long chain containing very many events we write Then substitution implies that for long chains, P’s mean-life is much longer than its orbital period

For long chains it is probable that P will *not* decay during any specific cycle. One orbit will almost invariably follow another with dependable regularity. So a period that is negligible compared to the lifetime implies permanence, steadiness or *stability*.

Stability and predictability are very useful, so we give particles like P a special name. When the orbital period is much smaller than the mean life then P satisfies the **stability condition** that and we say that P is a **stable** particle. The initial event is called the **cause**. And the final event is called an **effect** of the cause.

The stability condition is easily satisfied for particles that have a temperature near or below zero (K) because by definition their mean-life will be at least as long as the lifetime of a proton. Measurements of the proton’s mean-life have determined^{5}K.A. Olive et al. Particle Data Group *Review of Particle Physics*, Chin. Phys. C, **38**, 090001 (2014). that it is more than ~10^{36} seconds. So for these cold particles is exceedingly large.

The orbital period of a proton is given by where The mass of a proton is well known and used to find as ~10^{-24} seconds. That is, the lifetime of a proton is at least 10^{60} times larger than its period. And for electrons, the lifetime-to-period ratio is at least ~10^{54}. So both the proton and the electron are exceptionally stable particles. This gives them starring roles in narratives connecting cause and effect.

## Phase Angle

Consider some particle P, that is characterized by a repetitive chain of events written as

where each repeated cycle is a bundle of quarks noted by

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 only if P is large. So we also discuss events using a **phase angle** defined by

where is arbitrary. The units of are called radians and abbreviated by (rad). This definition associates radians with each repetition of That is, one complete spatial rotation of radians for each phase-component of P.

The phase angle is an important parameter for describing repetitive sensations. But remember that each repetition is a set of quarks. So the most detailed description of sensation could possibly expand into an account of individual quarks. Then the smallest change in would be due to the effect of a single quark. This little step is called the **phase angle increment**. It is written as and defined by

The phase-angle increment may be combined with the increment of time to define the **angular speed** as

EthnoPhysics uses a finite categorical scheme of binary distinctions to describe sensation. So the number of quarks 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 regardless of quark type.

Next

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. |

5 | K.A. Olive et al. Particle Data Group Review of Particle Physics, Chin. Phys. C, 38, 090001 (2014). |