Cosmic adventure 5.4 Moving Objects in Visonics

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OBJECTS IN MOTION IN VISONICS

Cosmic Adventure 5.4


Two Observers

The relativity theory uses more than two observers so that a transformation of the coordinate systems can take place.

0’ P0’’

Systems 0’ Systems 0’’


A Single Coordinate System

The visonic theory does not involve coordinate system changes because it is a direct study of the effects of light on observed objects. So a single system is employed. It involves only an observer and an object. This object is preferably a clock that can move around in case motion is involved.

0 P


Observer and Runaway Object

To start with, we have two atomic clock perfectly and locally synchronized. One is used by the observer and the other acts as the runaway object.

Clock A[Observer]

Clock B[Object]


𝑥 = 0 𝑡 = 0 𝑠𝑒𝑐

Observer and object are staying at the same spot O to start with at time 𝑡 = 0. Actually, we can start off anywhere, from 𝑠 = 0 to 𝑠 = ∞.

Observer

Object

Starting Point


Synchronized Clocks

Clock A stays with the observer and clock B begins to move away at a velocity of 𝑣 at time 𝑡 = 0. It is expected that both clock keeps on telling time at the same rate wherever even when they are separated. The physical laws are the same for all inertial systems.

𝑣


Clock Images

As clock B move along, it keeps on sending a stream of images back to the observer. What the observer sees is therefore the image of the clock, not the actual clock itself. We select only one or two images for our discussion.

𝑣𝑐

Image carried by light


𝑣

So there are three objects involved. The two clocks are real material bodies; the light image are made up of photons. All these bodies are ‘physically real’. No abstract mathematical bodies are present.

3. Image carried by light

1. Clock A 2. Clock B

𝑐

Real Material body Real material bodyImage composed of photons


The distance covered by clock B after a period of ∆𝑡1 is:

𝑠 = 𝑣∆𝑡1. For example, we assume ∆𝑡1to be three seconds. We take this moment of time as the starting point of our investigation.

𝑠 = 𝑣∆𝑡1

𝑣

❶


𝑣

Clock A

At this moment ∆𝑡1, clock B sends an image of clock B to A at velocity 𝑐 while keeps on moving to the right at velocity 𝑣.

𝑠 = 𝑣∆𝑡1

Object Clock B at time = ∆𝑡1

❷

Image of B carried by light at speed c

Clock B carried on moving to the right

Clock A remains stationary

𝑐


𝑣

A B

By the time the image reaches A after time 𝑡2, clock B would have moved to C within time 𝑡2. Let’s say it takes light one second to reach A. Both the real clock would have advanced by 𝑡2 as well.

𝑥1 = 𝑣∆𝑡1 = 𝑐∆𝑡2

❸

Image

∆𝑥 = 𝑣∆𝑡2

C

𝑐

Real clock A Real clock B

𝑥3 Actual position of B


𝑣

A B

𝑥1 = 𝑣∆𝑡1

𝑥1 = 𝑐∆𝑡2

Image of B at B

∆𝑥 = 𝑣∆𝑡2

C

𝑐

Real clock A

Real clock B

Observation 1: Apparent Position of B

Since what the observer intercepted is the image of clock B at B, the apparent position of B is:

𝑥1 = 𝑣∆𝑡1

This position is called ‘apparent’ because clock B is already not there.

𝑥3

Apparent position


𝑣

A B

𝑥1 = 𝑣∆𝑡1

𝑥1 = 𝑐∆𝑡2

Image of B at B

∆𝑥 = 𝑣∆𝑡2

C

𝑐

Real clock A

Real clock B

Observation 2: Current Time

The time taken for the image to reach A is 𝑡2 at speed c. Since it covers the same distant 𝑥1initially taken by the clock:

𝑥1 = 𝑐∆𝑡2 = 𝑣∆𝑡1

∆𝑡2 =𝑣∆𝑡1𝑐

The clocks A and B has now advanced by a time = ∆𝑡2. The current time ∆𝑡3 is therefore:

∆𝑡3 = ∆𝑡1 + ∆𝑡2

It takes the image time ∆𝑡2to reach A,

say 1 second

∆𝑡3 ∆𝑡3


𝑣

A B

𝑥1 = 𝑣∆𝑡1

𝑥1 = 𝑐∆𝑡2

Image of B at B

∆𝑥 = 𝑣∆𝑡2

C

𝑐

Real clock A

Real clock B

Observation 3: Apparent Time

The observed or apparent time shown on the image of B is that of a time ∆𝑡2 earlier. So the apparent time on the clock image appears to be slower than clock A by ∆𝑡2:

∆𝑡3= ∆𝑡1 + ∆𝑡2∆𝑡3> ∆𝑡1

𝑥3

It takes the image time ∆𝑡2to reach A,

say 1 second

𝑡3 𝑡3


𝑣

A B

𝑥1 = 𝑣∆𝑡1

𝑥1 = 𝑐∆𝑡2

𝑐∆𝑡2 = 𝑣∆𝑡1∆𝑡2 = 𝑣∆𝑡1/𝑐

Image of B at B

∆𝑥 = 𝑣∆𝑡2

C

𝑐

Real clock A

Real clock B

Observation 4: Actual Position of B

The actual position of B is C when A sees the image:

𝑥3 = 𝑥1 + ∆𝑥= 𝑣∆𝑡1 + 𝑣∆𝑡2= 𝑣(∆𝑡1 + ∆𝑡2)

Now ∆𝑡2 = 𝑣∆𝑡1/c, so:𝑥3 = 𝑣(∆𝑡1 + 𝑣∆𝑡1/c)= (1 + 𝑣/𝑐)𝑣∆𝑡1

= 1 +𝑣

𝑐𝑥1

𝑥3


𝑣

A B

𝑥1 = 𝑣∆𝑡1

𝑥1 = 𝑐∆𝑡2

Image of B at B

∆𝑥 = 𝑣∆𝑡2

C

𝑐

Real clock A

Real clock B

Observation 5: Actual Timing

The actual time of clock A and clock B are the same, both registering the current time at 4 seconds:

∆𝑡3 = ∆𝑡1 + ∆𝑡2

∆𝑡3

∆𝑡3

∆𝑡1


𝑣

Image

𝑐


Actual time Actual timeApparent time

Overall Configuration


𝑣

A B

𝑥1 = 𝑣∆𝑡1 = 𝑐∆𝑡2

Image

∆𝑥 = 𝑣∆𝑡2

C

𝑐


Actual position of B 𝑥3

Apparent position of B

Actual time Actual timeApparent time

General Measurements


Summary of Observations

The apparent position of B is:

𝑥1 = 𝑣∆𝑡1

The apparent time of B is (Slower than what is now on A & B):

∆𝑡1

The actual position of B is farther than apparent position:

𝑥3 = 1 +𝑣

𝑐𝑥1

The actual time of B is the same as A but longer than apparent time:

∆𝑡3 = ∆𝑡1 + ∆𝑡2

= ∆𝑡1 +𝑣

𝑐∆𝑡1

= 1 +𝑣

𝑐∆𝑡1


Conclusions

The actual position of B is farther away than its apparent position:

𝑥3 = 1 +𝑣

𝑐𝑥1 > 𝑥1

The actual time of A & B is longer than apparent time (apparent time is slower):

∆𝑡3 = 1 +𝑣

𝑐∆𝑡1 > ∆𝑡1

A B

𝑥1 = 𝑣∆𝑡1 = 𝑐∆𝑡2 ∆𝑥 = 𝑣∆𝑡2

C

Actual position of B 𝑥3

Apparent position of B

Actual time ∆𝑡3 Actual time ∆𝑡3Apparent time ∆𝑡1


They are all physically real quantities. Even the apparent time and position are made up of real photons of light.

They are all physically real quantities. Even the apparent time and position are made up of real photons of light.

The equations are derived through classical approaches, so the study of visonics is in essence a branch of classical physics dedicated to the study of light speed.

These are the basic equations from visonics. It does not need the Lorentz transformations of coordinates so that no complicated mathematics is involved.


RELATIVISTIC LENGTHCONTRACTION

To be continued in

Cosmic Adventure 5.5

Science

Cosmic adventure 5.4 Moving Objects in Visonics