iSoul In the beginning is reality

Tag Archives: Transportation

Observers and travelers

Let us distinguish between observer-receivers and traveler-transmitters. Although observers can travel and travelers can observe, insofar as one is observing, one is not traveling, and insofar as one is traveling, one is not observing. The main difference is this: traveler-transmitters have a destination but observer-receivers do not (or at least not as observers).

Compare the roles of the driver and the passengers in a vehicle: the driver is focused on the road and traveling to the destination, whereas the passengers are looking out the window and observing things in the landscape. These are two different roles.

Observer-receivers of motion naturally compare the motion observed with the elapsed time. But traveler-transmitters have a destination and naturally compare the travel motion with the elapsed distance, which measures progress toward the destination. Because of this, the frame of mind for observer-receivers is 3D space + 1D time, whereas it is 1D space + 3D time for traveler-transmitters.

Observers of the sky naturally think of celestial bodies as appearing when they are observed, as with celestial navigation. That is, they act as though the light observed arrives in their sight instantaneously.

Transmitters of light naturally expect that the light reaches its destination as they transmit it, as with visual communication. That is, they act as though the light transmitted arrives at its destination instantaneously.

This is consistent with having two conventions of the one-way speed of light (previously discussed here). To be consistent with the round-trip speed of light equaling the value, c, for all observers, that implies the following:

For observers: observed light is instantaneous but transmitted light travels at the speed c/2.

For transmitters: transmitted light is instantaneous but observed light travels at the speed c/2.

Although relativity theory is the scientific approach, for everyday life the above speeds make things simpler, and are fully legitimate.

From 1D to 3D in two ways

Among the instruments on a vehicle there may be a speedometer, an odometer, a clock, and a compass, which provide scalar (1D) readings of the vehicle’s location. But what is the location of the vehicle in a larger framework? The compass shows two dimensions must exist on a map of this framework, but of what are they dimensions?

The identity of the two dimensions depends on whether the dimensions are associated with the odometer reading (the travel distance) or the clock reading (the travel time). Let’s represent the travel distance by s, the travel time by t, the speed by v, and the travel direction by angle α clockwise from North.

Consider a simple example in which the vehicle is traveling at a constant speed and not changing direction. Then the ratio of the travel distance to the travel time is a constant, which equals the reading on the speedometer: v = s / t.

The vehicle location may be envisioned in two different kinds of maps: (1) In the first kind of map, which is the familiar one, the travel direction is associated with the travel distance. Then the odometer and compass determine the vehicle location, which may be specified by the polar coordinates (s, α) = s. This ordered pair represents a spatial position vector, s. A velocity vector may be constructed from it as v = s / t.

(2) However, we could just as well associate the travel time with the travel direction. So for the second kind of map, the clock and compass determine the vehicle location, which may be specified by the polar coordinates (t, α) = t. This ordered pair represents a temporal position vector, t. A celerity vector, u, may be constructed from it as u = t / s.

Let’s look at another simple example. Consider a vehicle on a curve that turns for an angle θ at a constant angular velocity of ω with a turning radius of r. The travel distance on the curve is s = = ωt. The travel time is t = /ω = s/ω. In the first case the spatial vector is s = (r cos(ωt), r sin(ωt)). In the second case the temporal vector is t = (r cos(s), r sin(s)), which is found by reparameterizing by the arc length.

Note that in the first kind of map the travel time remains a scalar, which is not associated with any particular position on the spatial map and so is a universal time. Note that in the second kind of map the travel distance remains a scalar, which is not associated with any particular position on the temporal map and so is a universal distance.

The question, “What time is it?” refers to scalar time, which is associated with all points of 3D space. Similarly, one could ask, “what space is it?” referring to the scalar distance, a 1D space, which is associated with all points of 3D time.

Time and space as scalars or vectors

We need to distinguish between scalar (1D) and vector (3D) versions of both time and space. Motion in scalar (1D) time and scalar (1D) space is measured by clocks and odologes, respectively, and apply throughout the associated vector space or vector time (in Newtonian mechanics).

Scalar space is like scalar time. They are proportional if an odologe with constant pace is used. If celestial bodies are used, they may be not quite proportional.

Motion in vector (3D) time and vector (3D) space is measured as points on a curve (trajectory), which may be decomposed into components. The position vector to each point is its distimement or displacement, respectively.

Each instance of vector space is associated with one point of scalar time, and each instance of vector time is associated with one point of scalar space. A value of scalar time is called the time. A value of scalar space may be called the space because it answers the question, ‘which instance of space is it?’

The travel time of a body between two points of vector time, A and B, may be measured with a stopwatch accompanying the body starting simultaneously with A and ending simultaneously with B. The travel distance of a body between two points in vector space, C and D, is measured with a measuring wheel (odometer) accompanying the body starting at location C and ending at location D.

The speed of a body is the travel distance per unit of travel time. The pace of a body is the travel time per unit of travel distance. The velocity and celerity include the vector travel direction of the body with the ratios given.

Since the travel time or travel distance may not be available to an observer not on the body, the velocity and celerity may make use of the scalar time or space in the denominator, respectively.

For the velocity one can substitute the vector travel distance per unit of scalar time. The speed uses the magnitude of the vector travel distance per unit of scalar time.

For the celerity one can substitute the vector of travel time per unit of scalar space. The pace uses the magnitude of the vector travel time per unit of scalar space.

Direction and time

The measurement of the length of a motion follows the course of motion at its own pace. It is a measurement of something passive, and the motion may be past when the measurement takes place.

Cartesian space lacks direction. The independent axes are just coordinates that describe a passive space. The origin is arbitrary and the direction hidden in the coordinates. There are three coordinates, three dimensions to this physical space.

Motion in space is relative to an origin, and so where the motion is coming from. The wind is coming from a certain direction; that is its direction.

Modern natural science excludes teleology. There are no natural goals, no directions. Nature is passive. If there is any goal-seeking, it must come from outside nature.

The measurement of the time of a motion follows the course of motion at its pace. It is a measurement of something active, in motion while the measurement takes place.

A direction is a command and a course. Go West, young man is a course to take and a direction to follow. Trains are distinguished by their destinations. Their direction is indicated by the last stop. The goal and the direction are the same.

Motion in transportation always has a goal, a direction. Motion is physical, but the goal is part of the motion. There’s always a destination.

The destination is some distance away. It takes time to reach the destination. It makes a difference which direction is taken. There are two directions and one distance, which makes three dimensions.

Time in transportation has three dimensions. It is oriented toward the where the vehicle is going, the destination. The train is going toward a certain direction; that is its direction.

Introduction to 3D time with 1D space

Since Newton, time has been the usual and ultimate independent variable for physics. This contrasts with problems in transportation, where time is often optimized. Whether transporting goods across the world, commuters across town, or athletes to the finish line, length is the independent variable against which time is measured and optimized. If length is taken as the independent variable for physics, a mechanics results that is different from Newton’s but equivalent to it. In what follows we explore the basic kinematics and dynamics with length as the independent variable, first in classical, then in relativistic mechanics.

To represent time on a map, one may use isochrones (time contours), as in this map of tsunami travel time in hours:

Or time may be used instead of length, as in this map of European rail travel times in hours:

Note that in this map it is time that is two dimensional, not space. It looks like a distortion of the spatial representation, but it is not a distortion. It is a time map with units of time rather than units of length. The multidimensionality of time will be a main feature of taking distance as the independent variable.

Length could be included as a distance from a particular place, represented by an iso-distance contour. That is, length is reduced to one dimension if time is the dependent variable.

Units such as natural units may be adopted to equalize the units for length and time, i.e., by adopting a constant modal speed dependent on the mode of travel. However, they are still different measurements. Such units allow constant speeds to be represented the same, whether in space or time, which minimizes the seeming distortion of a time map.

As I pointed out here, an independent variable is given to us and so not in our control, and so may seem to flow on independently. A clock is like that, and it gives us a sense that time flows. But a stopwatch starts and stops at our command. Time no longer flows.

Distance can seem to flow if we allow it to. Consider a hop-on, hop-off transit system with a fixed route. It cycles through its various destinations and then repeats the cycle. The distance between two stops may be read from an odometer by subtracting the earlier from the later distance. This is just like finding the time between two points with a clock. Only here it’s the transit system that flows on, accumulating distance indefinitely. Distance flows instead of time.

Posts on space and time chronologically, updated

I previously listed posts on space and time chronologically here. This is a chronological list that includes the posts since then, starting with the most recent (with hyperlinks):

Outline of spacetime symmetry paper
Work and energy, exertion and verve
Circular orbits
Foundations of mechanics for time-space
Distance, duration, and angles
Center of vass
Equations of motion in space-time and time-space
Derivation of Newton’s second law
Clock race
Centripetal prestination
Motion equations revised
Gravitation and levitation theories
Simple harmonic motion
1D space + 3D time again
Measuring mass
Numbers large and small
Dynamic time-space
Four rates of motion
No motion as zero speed or pace
Simple motion in space and time
Observability of the rotation of the earth
Places in time
Conventions of here and now
Places and events
Four space and time dimensions
2D space + 2D time
Event-structure metaphors
Space and time standards
Space and time from the beginning
Dual differential physics
Time and linear motion
Time and circular motion
Gravity with dependent time
Sun clocks
Inverse terminology
Passenger kinematics
Physics for travelers
Non-uniform motion
Uniform motion
Two ways to symmetry
More equations of motion
Relating space and time
Parallel equations of motion
Corresponding equations of motion
Glossary of time-space terms
“Synchronizing” space
Characteristic limits
Minimum speeds
Modes and measures
Direction in three-dimensional time, part 3
Problems in mechanics, part 2
Measurement by motion
6D as two times 4D
Transformations for one or two directions
Travel time and temporal displacement
Galilei doesn’t lead to Lorentz
Transformations for time and space
Six dimensions of space-time
Time scale maps
A new geometry for space and time
Why time is three dimensional
Necessary and possible dimensions
Geometric and temporal unit systems
Time conventions
Direction in three-dimensional time, part 2
Dimensions of space and time
Terminology for time-space
Newtonian laws of motion in time-space
Phases of a 3D time theory
Problems in mechanics, part 1
Equations of motion in time-space
Conservation of prolentum
Dynamics for 3D time
Flow of independent variables
Switching space and time
Lorentz transformation for 3D time
Space and time expanded
Pace of light
Terminology for space and time, part 3
Synchrony conventions
Consciousness of space and time
Lorentz transformations and dimensions
Fixed sizes and rates in space and time
Lorentz and co-Lorentz transformations
Galilean and co-Galilean transformations
Relativity of time at any speed
Motion science basics
Flow of motion
3D time + 1D space, pace, and lenticity
Three dimensional clock
3D time in ancient culture
Relativity at any speed
1D space and 3D time
Characteristic speeds
6D space-time collapses into 4D
Direction in three-dimensional time, part 1
Terminology for space and time, part 2
Lorentz transformation in any direction
Superluminal Lorentz transformation again
The physics of a trip
Measuring movement
Total time
Dimensions of movement
Time on space and space on time
Dual Galilei and Lorentz transformations
Measurement of space and time
Invariant interval check
Six dimensional space-time
Two one-way standard speeds
Movement and dimensions
Insights on the complete Lorentz transformation
Subluminal and superluminal Lorentz transformations
Complete spatial and temporal Lorentz transformations
Limits of the Lorentz transformation
Lorentz for space & time both relative?
Absolute vs relative space, time, and dimension
Complete Lorentz group
Complete Lorentz transformation
Four perspectives on space and time
Change flows
Three arguments for 3D time
Variations on a clock
Conversion of space and time
Time and memory
Time in the Bible
Temporal and spatial references
Perspectives on space and time
Homogeneity and isotropy
Multidimensional time in physics
Multidimensional time in transportation
Angles in space and time
Basis for the symmetry of space and time
Lorentz without absolutes
Optimizing travel time routes
Different directions for different vectors
Claims about time, updated
Modes of travel
Lorentz for space and time
Galilei for space and time
The speed of spacetime
Representations of space and time
Travel in space and time
Proof of three time dimensions
Velocity with three-dimensional time
Dimensions of dimension
Space, time, and spacetime
Time and distance clocks
Actual and default speeds
Time at Mach 1
Centers of time measurement
Directional units
Cycles and orbits
Converting space and time
Actual and potential time and space
Defining space and time
Equality of space and time
Kinds of relativity
Symmetric laws of physics
Diachronic and synchronic physics
Measurement of space and time
Lorentz with 3D time
Time defined anew
Lorentz interpreted
Lorentz generalized
Transportation and physics
Average spacetime conversion
Galileo revised
Movement and measurement
Distance without time
Velocity puzzle
Bibliography of 3D time and space-time symmetry
Symmetries and relativities
Distance, duration and dimension
Coordinate lattices
Independent and dependent time
Claims about time
Reality and relativity
What is single-value time?
Parametric time and space
Speed and its inverse
Symmetry of space and time
An introduction to co-physics, part 2
An introduction to co-physics, part 1
Terminology for space and time, part 1
Direction and units of magnitude
Six dimensional spacetime
Duals for Galilean and Lorentz transformations
Geometric vectors in physics
Speeds and velocities
Direction and dimension
No change in time per distance
The flow of time and space
Is time three-dimensional?
Is space one-dimensional?
Time in spacetime
Space, time and causality
Mechanics in multidimensional time
Measures of speed and velocity
Homogeneity and isotropy of time
Multidimensionality of time
Space, time, and arrows
Arrow of tense
Duality of space and time

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.