The Light Cone

The observer's light cone is represented here in a classical spacetime diagram, called the Minkowski diagram, named for one of Einstein's former teachers who realized that space and time could be integrated mathematically into a single four-dimensional manifold.

In order to represent the fourth dimension of time in our three-dimensional objective space, one of the space dimensions must be dropped from the picture. In this way, all of three-dimensional space is represented by a two-dimensional plane, and the passage of time is represented by the movement of that plane through what used to be the other space dimension.

This plane of three-dimensional space is called a hypersurface. More specifically, it is called a spacelike hypersurface. It represents all of space at a given moment in universal time, a universal simultaneity. This is not the simultaneity experienced by an individual observer in that space at that time. Since light takes time to travel through space, and everything we see is light coming to us, our experience of simultaneity is our light cone, and since it is always relative to the observer, Einstein suggested that the notion of absolute time is meaningless. No universal simultaneity can ever be realized.

What we see in space at any instant in time is entirely contained on the surface of our past light cone, which becomes a mere singularity at the hypersurface of the present. Even our bodies lie on our past light cone, inside and out! Different observers are represented by different singularities on the hypersurface of the present, each with a distinct light cone and a unique perspective on the field of spacetime.

As we look into space, we are observing our past light cone slicing concentric rings through the hypersurfaces of the past. Each ring on the past light cone represents a spherical plane in 3-D space centered on the observer. The largest ring at the base of the past light cone is called the particle horizon, the farthest spherical plane of observation, representing what we see as the blackness of infinity itself.

The future light cone represents the region of spacetime that the observer can influence through normal causality. Movement of the physical body is limited to the region of wherewhens within the cone, and to reach any spacetime position on the surface of the future light cone would require movement at the speed of light. Individuals who do not have overlapping light cones will never come in contact or influence each other through physical means. Obviously everyone on Earth has overlapping future light cones.

 

"A human being is a part of a whole, called by us "universe", a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest... a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty." -- Albert Einstein