RS-105 - Reciprocity

Transcript

hello and welcome to the presentation on the reciprocal system of theory by Dewey B Larson a universe of motion this time we would be exploring the concept of reciprocity I am Gopi Krishna and I will be guiding you through this presentation so let's begin first of all what do we mean by the word reciprocal and where does it apply because in the postulates we have the phrase to reciprocal aspects so let us try to describe what this means first of all let us assume that motion can be represented by a disk of which one side is space and the other side is 10. we represent Space by the lighter color and time by the darker blue color and both of them are two sides of the same coin now space and time are reciprocally related to speed which is an increase in space is equivalent to a decrease in time and vice versa or in other words an increase in the numerator is equivalent to a decrease in the denominator and vice versa what do we mean by the word equivalent it is equivalent for our observation using the conventional reference system that is when we measure it we see it as having the same magnitudes this behavior of space and time are seen to be reciprocal of each other also we can now write the equivalence relation where space is equivalent to the reciprocal of time let's try to understand this let us assume that the number of space and time units which we have in the motion are equal now if we change the space units such that the magnitude decreases we get a different speed or a different ratio the same ratio can be obtained by increasing the number of units of time as you can see clearly in the figure even though the two sets of space and time are different in their sizes the ratio of the lighter circle to the darker circle is the same in both the cases this is what we mean by equivalence a ratio which is the ratio of space to time Remains the Same in both cases this is another example in this instance we are changing the number of space units in the bottom figure and changing the magnitude of time units in the upper figure once again both the ratios are the same notice how the two have the same effect on the ratio of space and time that is the two have the same effect on speed in the first example of the two the speed is decreased in the second example the speed is increased and in both the examples this is done in two separate reciprocal ways this is what we mean by the reciprocity between space and time now we will examine the relation between spatial and temporal coordinate reference systems up till now we were examining the reciprocity between space and time now we will examine how we measure the two reciprocally first let's recollect the two natural datum options first one was Zero space per indefinite time this was a usual origin of 3D spatial coordinate system and the second one of the temporal coordinate reference system we have the origin as indefinite space per zero time that is thickening imagine the origin of the conventional 3D spatial coordinate system the origin is a location of 0x10 hence space is equal to zero there is no clock time associated with the origin it has no definite value when we measure something the clock time is pretty much independent of what spatial value we are measuring hence time is indefinite the origin of measurements of space and time are hence zero and indefinite respectively now since the spatial origin is a specific location in this system it is localized in the system it is at a particular point in other words however the value of clock time Associated is of indefinite magnitude as we have already mentioned it can vary from 0 to Infinity so if we try to represent this in the 3D temporal system neither the magnitude nor the direction of time is fixed in other words there is no definite location hence the spatial origin is non-local in this reference system to rephrase since the value of clock time is indefinite the magnitude of time is indefinite and so is the direction of time and hence we have the non-locality of the spatial origin in the temporal system the same happens with the temporal origin so what this means is the spatial and temporal reference Origins are mutually non-local the origin of temporal coordinates is everywhere in special coordinates and the origin of spatial coordinates is every when in temporal coordinates to have another look at the reciprocal Origins on the left we have the 3D spatial coordinate system where the origin is a single point in other words it is local and that very same origin when we project it onto the 3D temporal coordinate reference system or in other words we measure the same point using this system we get a totally non-local distribution all these points every single point in the temporal coordinate reference system represents the origin of the spatial coordinate reference system now another look at the same thing we have a single point localized in coordinate space and it is totally delocalized in coordinate time so to summarize we have discussed two separate thing as the reciprocal properties first one was to show that the increase in magnitude of space or time is equivalent to a decrease in the magnitude of time or space this was where we saw the reciprocal nature of space and time as related to speed second one was to do with the reference systems origin of the spatial coordinate reference system is totally non-local in the temporal coordinate system and vice versa thank you this is the end of this presentation coming up next is math and euclidean geometry