iSoul In the beginning is reality

# Distance, duration, and angles

Let’s follow the orbit of a particle or the route of a vehicle as a curvilinear function with associated directions at every point. Measurement produces travel distance r, travel time t, with directions θ and φ. The directions may be considered as functions of either travel distance or travel time: θr, φr, θt, or φt. There are accordingly four possibilities:

(r, t, θr, φr), (r, t, θt, φt), or (t, r, θr, φt), or (t, r, θt, φr).

The latter two may be made equal by a change of convention for measuring the angle. These may be represented rectilinearly as:

(t, rx, ry, rz), (r, tx, ty, tz), (rw, rx, ty, tz), or (tw, tx, ry, rz).

The latter two may be made equal by a change of convention for the axes.

Three possibilities remain: (3D space + 1D time), (1D space + 3D time), or (2D space + 2D time).

An example of the third possibility would be a traveler who measured their horizontal angle relative to magnetic north and their vertical angle relative to the sun. Since magnetic north is (approximately) fixed, it serves to measure the horizontal angle spatially. Since the sun’s position continually changes, it serves to measure the vertical angle temporally. The result is (2+2) with (r, θr) and (t, φt).

Or one could do the opposite and measure the horizontal angle temporally, as with a sundial, and the vertical angle spatially, as with a theodolite. The result is (2+2) with (t, θt) and (r, φr).

If both angles are measured relative to a fixed point, then the result is (3+1) or (t, r, θr, φr). If both angles are measured relative to a moving point, then the result is (r, t, θt, φt). The moving point should be moving at a constant rate, or at least a constant acceleration.

If three coordinates are measured relative to a fixed axis, then the result is (1+3) or (t, rx, ry, rz). If three coordinates are measured relative to a rotating axis, then the result is (r, tx, ty, tz). The moving axis should be moving at a constant rate, or at least a constant acceleration.

The potential reality of (r, t, θr, φr, θt, φt) collapses to one of the possibilities above in the act of measurement. The potential reality of (rx, ry, rz, tx, ty, tz) collapses to one of the rectilinear possibilities above in the act of measurement.

# Anisotropy and reality

This follows posts on synchrony conventions such as here.

Astronomers say things like this: “it takes sunlight an average of 8 minutes and 20 seconds to travel from the Sun to the Earth.”

The statement above assumes the Einstein convention that the one-way speed of light is isotropic and so equal to one-half of the two-way speed of light. However, it is possible that the one-way speed of light could be anywhere in the range of c/2 to infinity as long as the two-way speed of light equals c. So the speed of light could be c/2 one direction and infinity in the opposite direction.

The possibility seems strange until we consider how we ordinarily speak. We see the sun in the sky and its position now is taken as the position where it appears to be. It turns out there is nothing wrong with that manner of thinking and speaking. It is the same as saying the incoming speed of light is infinite, which is perfectly acceptable as long as the outgoing speed of light is c/2.

And so it is with all the comets, moons, planets, and stars: where they appear to be now is where we ordinarily speak of them as being. If there were something wrong with this manner of speaking, we should correct it, but there is nothing wrong with it.

There is something similar happening down on Earth with measurements of the travel time of commuters. The time and location of multiple travelers may be compiled by a traffic data office from electronic communications or from recordings made at the time of measurement. Travel times are then presented with tables and maps such as this isochrone map:

The travel times are taken as they were at one instant, as if vehicles all arrived at the isochrone lines simultaneously. That is how we think and speak about it, whether or not it is exactly true.

Effectively this says that the speed of each commuter or signal they transmit is infinite in one direction – the direction to the traffic data office – and a finite measured value in the travel direction. In this case the round-trip speed is finite but irrelevant.

Anisotropy is more common than we realize.

# Conventions of here and now

This follows a post on synchrony conventions here. The question is, What is the meaning of here and now for what is observed? Is everything than an observer observes part of their here and now? Some things observed may be a long distance away. Some things observed may be from signals sent in the past, such as distant starlight.

There is no one correct answer. A convention is needed to define here and now. The usual convention is that here and now only apply to what is within a minimal distance and a minimal span of time, or what is at the same point in space and time as the observer.

But consider how we speak about what we observe. We don’t say, Look, there’s the sun as it was 8 minutes and 20 seconds ago. Nor do we say, Look, there’s the north star as it was 433.8 years ago. Instead, we speak of where the sun and stars are now, even though they are a long distance away.

It’s similar concerning distance. Go into the countryside, away from lights at night and observe the stars. There are so many of them – and they are so close. People say things such as: The stars are close here. Or: I’m closer to the stars here. So the stars can be here, even though they are a long distance away.

If we accept that everything observed here and now is here and now, then the incoming light is instantaneous, and its speed is infinite. For the round-trip speed of light to equal c, that means the outgoing speed of light equals c/2. This looks strange, but it is consistent with the way we speak.

It is also consistent with other modes. If we measure our commuting speed and send this information to someone else, the communication time is ignored, that is, the communication is considered instantaneous. One may say that relativistic effects are ignored, but that is equivalent to saying that the communication is effectively at an infinite speed.

# Space and time standards

The value of an independent variable may be selected first, and so is arbitrary, even subjective. One may select anything or everything within its range. A graph normally covers a whole range of the independent variable.

Given an independent time interval, different travel rates result in different travel distances or, the other way around, different travel distances have different average rates. Similarly, given an independent space interval, different travel rates result in different travel times or different travel times have different average rates. These are shown on an event map, which is either events projected on a geographic map or shown graphically with a consistent time-scale.

Boston T Map with Time-Scale

Time is measured by a clock, which moves at a standard rate: the hour hand at one revolution per hour, the minute hand at one revolution per minute. A monthly calendar is updated at a rate of once per month, with the day updated once per day.

In space-time, time is measured by rotating or oscillating motion, which is independent of the surrounding space; space is measured by linear motion. In time-space, space is measured by rotating or oscillating motion, which is independent of the surrounding time; time is measured by linear motion.

If the travel rate is the speed of light, then distances and durations are proportional. Distance can be defined in terms of duration or vice versa. The difference between time and space then is only how they are measured. Light is the standard mode for modern physics.

For transportation the expected rate of travel in each mode is the standard, the modal rate. This is either determined by management, as with scheduled transport services, or empirically, as with measurement or experience. For physics, the modal rate is measured or determined from theory.

The modal rate is a standard for the mode; it reflects the mode rather than any particular travel in the mode (although a set of travel data may be used to estimate it). It is used to understand the past or to set expectations for the future. In transportation, trip planning and system management are the main applications. There are many applications in physics.

# Time and circular motion

Consider two circular motions, one a wheel and the other a clock (click for animations):

The wheel is the target motion to be measured. The clock is the reference motion, which maintains a constant angular velocity.

Comparison can be made of either the motion of a radius (e.g., a spoke of the wheel or hand of the clock) or the motion of a point along the circumference (which equals the motion of the wheel along the ground). If the length of the radius or circumference is known, it doesn’t matter which is used because there is a known proportionality between the motion of the two (C = 2πR).

If the length of the radius or circumference are not known or not specified, then there is a choice of whether to use a radius or circumferential point. For the clock, the length of the radius or circumference are not specified, so only the angular velocity is known. For the wheel, it depends on whether the wheel is moving along the ground or not. If it is moving along the ground, a circumferential point is used (case 1), otherwise the motion of a radius would be simpler since it has the same units as the clock (case 2).

The motion of the clock corresponds to time (duration). The motion of the wheel corresponds to space (distance) in case 1 and time (duration) in case 2. The rate of motion is the ratio of a measure of the wheel to a measure of the clock. The rate of motion in case 1 is the ratio of the distance traversed by a point on the circumference to the angle traversed by a hand of the clock (e.g., kilometers per hour). The rate of motion in case 2 is the ratio of the angle traversed by a spoke on the wheel to the angle traversed by a hand of the clock (e.g., revolutions per minute).

What does this tell us about space and time? It shows how time is an angular measure and space is a linear (circumferential) measure. A body (e.g., vehicle) with an internal clock has its own measure of time by the motion of the clock at hand and its own measure of space by the wheel(s) traversing the ground (e.g., odometer). A body with an external clock (e.g., the motion of the sun) depends on external observation for knowledge of time (duration). A body that moves without wheels (e.g., a boat) depends on external observation for knowledge of space (distance).

Is it possible that the clock could be traversing the ground and so its movement measured by the travel distance? That would be an unusual clock but it is possible. Would such a clock be measuring time or space? It would measure space in that its units would be units of distance but time in that it would be a measure of the reference motion or independent flow. Is time any measure of the reference motion or is time duration?

time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration (Isaac Newton)

Time for Newton, and to this day, is considered both flow and duration but these are different concepts, and should be distinguished.

# Inverse terminology

I’ve written about the inverse perspectives of travelers and shippers versus observers and scientists here. This post focuses on the language used, primarily the expectation of what motions larger or smaller values of measures correspond to.

For an observer we’re accustomed to larger values corresponding to faster, more powerful motions. But travelers are usually trying to minimize something such as the time or energy expended. So smaller values correspond to faster, more powerful movements.

Terms should follow these expectations. Speed is faster as its magnitude increases and slower as its magnitude decreases. Pace is the opposite of this. Pace is faster as its magnitude decreases and slower as its magnitude increases.

The term for pace with direction should be similar: it is a measure of motion that decreases with faster movements and increases with slower movements. This is counter-intuitive at first but fits the pattern of an inverse perspective.

I will revise the terms I have used to be consistent with this understanding. New terms:

celerity – pace with direction; values closer to zero indicate faster pace. [was lenticity]

celentum – celerity divided by mass (or times vass); values closer to zero indicate faster motion or smaller mass [was prolentum]

gorce – prestination divided by the mass (or times the vass); smaller values indicate larger force [was elaphrence, mollence or visity]

prestination – rate of celerity; positive values indicate pace becoming closer to zero [was relentation or retardation]

vass – inverse of mass

See the Time-Space Glossary above.

# Passenger kinematics

This post builds on the post Physics for travelers. Passengers are travelers or riders with a specific destination.

In a way passengers are passive; they just sit as a vehicle takes them where they want to go. But that comes after they entered the vehicle, which comes after they accepted a ride or bought a ticket, which comes after they decided to go on a trip, which comes after they chose a destination. There’s much activity before (and after) a passenger sits.

A passenger may decide to operate a vehicle themselves as the biker, the driver, the pilot. Even then they are passengers first and operators second, unless they are in the transportation business.

The passenger perspective may be explained by the four causal factors: (1) the passenger determines the destination of their trip; (2) the passenger decides on the mode and manner of their trip; (3) the passenger decides on the means of their trip, such as which route and vehicle; (4) the passenger decides the who and when and what of the trip.

The destination is a place that is different from the place where the passenger begins. Children who sit in a car and pretend they are going somewhere are not passengers. Passengers first need is a destination.

The physics of most interest to passengers is not the physics of an engine or of someone else’s transport but of their own transport to their own destination. That is, the physics of most interest is the physics of closing the gap between them and their destination. Passengers begin with a positive distance between them and their destination, which they want reduced to nothing.

Consequently, the independent variable for passengers is a distance, not a time interval. Time is always a dependent variable for passengers. This differs from the physics of scientists and engineers for whom time is the independent variable as they observe and design things in motion.

This leads to the rate of motion for passengers being measured in the amount of time taken (duration) per unit of length traversed (distance). This is called the pace in racing, in which the travel time is minimized. Passengers may be in a race, or may simply have a deadline for reaching their destination. A slower pace means a larger amount of time passing per unit distance. A faster pace means a smaller amount of time passing per unit distance.

What about the increase or decrease in the rate of motion? For passengers this is a change in the pace toward either a faster or slower pace. A slow pace getting slower means an increasingly large amount of time passing per unit distance. A fast pace getting faster means a decreasingly small amount of time passing per unit distance. That is, rate of change of the rate of change is the change of pace distance over which the change is measured.

Consider a passenger on a trip with several signposts that are equally spaced (to make it simple). One can measure the time it takes to pass each signpost and determine whether the time is getting larger or smaller. The independent variable is again the travel distance but it covers the distance of the two paces. The faster the change in pace, the smaller the amount of time per unit distance. The slower the change in pace, the larger the amount of time per unit distance.

The background to these measures is that the passenger would like arrive instantly at their destination, so any time passing until their arrival is viewed adversely. Larger numbers mean slower movements. Smaller numbers mean faster movements. This is the opposite to thinking that larger numbers mean faster movements.

Prestination means the pace value is declining, which means motion will go faster (cf. acceleration). Deprestination is the negative of prestination; it means the pace value is increasing so motion will go slower (cf. deceleration). Prestinate means to lower the pace value (cf. Italian presto).

# Physics for travelers

People have purpose and goals but natural science excludes final causes. People plan and design but natural science excludes formal causes. In that case call the science of formal and final (be)causes “hypernatural science”. These higher causes are not against nature (unlike supernatural) but are not inherent to nature (and so hypernatural).

A physics for people includes formal and final causes. People engage in motion with a purpose, an origin, a route, and a destination. Such movement is usually from place to place over a route, so that the spatial characteristics are chosen first. People are travelers. People also send (ship) objects for travel; such objects are called freight and the people are called shippers.

Once the destination is chosen, what remains is the temporal aspect which depends on the means and conditions of movement. Timed movement, as for exercise, is motion without a destination, which is less common. Even much exercise and game-playing has a place or target as a goal. Racing has a place goal par excellence.

Direction in space-time is measured from an origin, whereas direction in time-space is measured toward a destination. Extent of motion in space-time is measured spatially given the length of time, whereas extent of movement in time-space is measured temporally given the length of space. The difference is between the people-oriented view of movement given routes and destinations vs. the object-oriented view of motion given time and capability.

Given an origin, a route, and a destination the rate of progress is the pace, the elapsed time per unit distance. A zero rate is instantaneous, which is impossible. An infinite rate is motionless, which is no movement. Actual rates are finite. The pace of light is apparently the minimum pace. The other variables of celerity, prestination, and so on are defined from here.

As the physics of space-time works best for natural motion, so the physics of time-space works for hypernatural movement.