iSoul In the beginning is reality.

# 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 may seem 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 free flow rate of travel in each mode is the characteristic rate, 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 characteristic of 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 adjust 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.

# 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:

legerity – pace with direction; values closer to zero indicate faster pace. [was lenticity, tempocity, progressity, allegrity]

fulmentum – allegrity divided by mass (or times elaphrence); values closer to zero indicate faster motion or smaller mass [was prolentum, celentum]

release – lentation divided by the mass (or times the elaphrence); smaller values indicate larger force [was retardation, gorce, elaphrence, mollence, egeirence or visity]

lentation – space rate of legerity; positive values indicate pace becoming closer to zero [was relentation, duralation, retardation, expedience, prestination, or modulation]

elaphrence – inverse of mass [was etherance, vass]

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. 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.

Lentation means the change in pace or legerity, which means motion will go slower. Delentation is the negative of lentation; it means the change in pace or legerity such that motion will go faster. Lentate means to raise the pace or legerity and go slower. Delentate means to lower the pace or legerity and go faster. Unlentated means the lentation is zero.

# 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 legerity, lentation, 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.

# Glossary of time-space terms

I’ve compiled a glossary of new terms on the top menu of this blog, or see here. These terms were coined for the study of 1D space + 3D time. It will be updated as needed.

A parallel comparison of space-time and time-space terms was added here.

# Modes and measures

What is the “distance” between two point events? That would include the length in both space and time. The measurement of the length of time between events depends on the mode of travel between them. For example, the time between leaving one’s residence and arriving at work depends on how one commutes. If the trip is by a slower mode such as walking, it will take longer than the same trip by a faster mode such as rapid transit. Another factor is the route that will vary by mode.

The situation is similar with space. What is the distance between two points? It depends on how the measurement is taken. The coastline paradox is the best-known example of this. Rigid measuring rods of different lengths will take different measurements. The length of a coastline depends on the unit of measure. The diagonal paradox shows another way the method of measurement makes a difference. In the commuting example, the distance of the commute depends on the route taken.

In order to have consistent measurement of space or time there must be a standard of measurement. For distance this is the shortest path using the fastest mode: light. Laser technology has made this method convenient and reliable. Can the light standard be applied to time, too? No. A laser would not help to measure a commute because a ray of light would simply go faster than any commute and arrive early.

The observation of an event is just-in-time so there’s no waiting time involved. So the motion from one event to another must meet it just as it happens. That means the shortest distance velocity is less than the speed of light in most cases.

Consider the 1+1 dimensions of time (t) and space (r) with the speed of light set to one, as above. The “distance” between two point events is the space-time distance between them. This depends on whether equal distances make circles or hyperbolas. For space and time, distance is hyperbolic since the speed of light is a barrier. So d² = Δt² – Δr².

# Direction in three-dimensional time, part 3

This is a continuation of a series of posts, see here.

V

Temporal direction is direction in a 1D space + 3D time geometry. So to understand direction in 3D time, one must understand a certain context. This is like understanding a map because direction is something that appears on a map but not a route per se. Compare a “triptik” produced by the American Automobile Association:

This shows the one-dimensional route within a strip map. Since it focuses on the route, not much of the 2D map is needed.

One can show a map with units of space (distances) or units of time (durations). As distances may represent travel distances or straight-line distances (displacements) so durations may represent travel durations or straight-line durations (distimes).

A turn in space is a turn toward a place that is farther away toward which one is moving. A turn in time is a turn toward a time in the future toward which one is moving. That future time may be a a scheduled appointment or a stop of a train or bus, for example. So a train schedule is an example of a 2D time map:

What then is the difference between turning toward say “Dr. Brown’s office” and turning toward “my 9:00 appointment” if it’s the same turn? There’s only a difference in how the turn is conceived: whether as toward a place or a time. We can choose whether to portray it as a turn in space or a turn in time. It’s really both.

A turn toward a place says little about the purpose of the trip. Is someone going to Dr. Brown’s office as a patient going to an appointment, as an employee to work there, as a delivery person or what? Giving the time usually goes with something about the purpose: an appointment at 9:00, a job that starts at 9:00, a delivery due by a 9:00, etc. Time brings up final causes, whereas efficient causes are sufficient for space.