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I look at life with detachment and distance, like a window shopper. Not only I study the window but also my own reflections in it.

Icecream Cone

Sunday, March 27, 2005 3 comments

Judging simultaineity of two spatially separated events is depended on exchange of information between the two events. This exchange can happen not faster than speed of light. Hence the two events can be judged for simultaineity only if they are at such time and space - where the two can communicate with each other. In jargon of Relativity the two events must be within the World-cone of a photon. It is like saying that icecream can be found only inside of icecream cone.

On a graph of distance on x-axis(horizontal) and Time on t-axis(vertical), when we draw two lines (one on left and the other on rightof t-axis) representing the movement of a photons from the originating event - these will be called the world-lines - the slope representing the speed of light. These two world-lines would enclose a triangle between them. In a two dimentional-distance this triangle would become a cone . This is called the world-cone(green in diagram above) of the photon. This world-cone represents those distances and times where the information from the original event can reach. Outside of this cone the events cannot have information about each other and hence cannot be judged for simultaineity. Thus simultaineity can be judged only by events within the world cone.
In a three dimentional world - the world-cone will be a similar cone in Four dimentions - sorry more difficult to be imagined physically.
An example would clarify this. Suppose a supernova at a distance of 20 light-years away from us - bursts today, while I write this. (In cosmology, Distances are measured in terms of distance light would travel in a year - light-years). So my writing and the supernova burst are simultanious to our common-sense. But this simultaineity cannot be physically judged, because I am outside the world-cone of the photons emanating from the burst. I am at same time but the place is outside the cone. I am on the x-axis itself 20 light-years distance from the event. There is no way for me to know of this supernova burst today.
Me, twenty years later in time, sitting in the same chair, at the age of 75 - would come within the world cone and would see the event as simultaneous then.
Thus simultaineity in relativity is different from common-sense perception of simultaineity.
As I hinted earlier, the lining up and simultaineity require, some a-priory estimation of distance or time (that it is zero between the lined up things). So there is some approximation in these measurements - How much?
Don't leave my world-cone, till the next post!

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3 comments: to “ Icecream Cone so far...

  • Jaspal March 27, 2005 12:01 PM
     

    Analogy with cone is not clear, even for two dimensions. Kindly explain a bit more. Thanks.

  • Girish March 27, 2005 8:25 PM
     

    Does the diagram clarify?

  • Jaspal March 29, 2005 12:11 AM
     

    Thanks for the diagram. Now I get what you are trying to explain. In your example, as you experience, supernova burst occurs when you are 75 (and for supernova burst you were 75 when it occured). It occuring now really doesn't convey much due to non-absolute or relative simultaneoty.

    I am not a physicist, nor have I read Theory of Relativity since my school days in the 60's. As I recall, if two objects (photons) are travelling towards each other at velocity of light, with common sense, they should see each other travelling at double the velocity of light (towards each other, or away from each other if they have passed). As per relativity, both see the other as travelling at velocity of light (and themselves as stationary in time). These relative symmetry put together in math equations results in famous relatively equations.

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