Is the Light Cone a Valid Representation of Light's Behavior?

[zarmewa]

As smatter in the subject therefore I have the following confused questions about the light-cone.

As we all know that when a flash of light is released from source, light-rays spread out isotropically in space, tracing out a cone on a space-time diagram. As "light-cone" is expanded at the speed of light, and light emitted at the apex and moves on the surface of the cone, therefore, at any instant “t” say one light second, the radius, edge and the vertical axis of cone represent a right angle triangle in which

Vertical axis is the perpendicular of triangle; x = time

Radius of cone is the base of triangle; y = speed of light in one second

Edge of the cone is the hypotenuse of triangle; z = space-time diagram of a pulse in one second

Thus x² + y² = z², where z > c, so is this possible?

The space-time interval is always zero between two events connected by a light speed path BUT the slant edge of cone which is GREATER than the speed of light "c" represents the true motion of a pulse [world line] in both space and time, therefore, isn’t time dilating even in a stationary light clock due to extra distance covered by a pulse in its world-line?

 

[Drakkith]

I don't think the Light Cone in a spacetime diagram is the same as a light cone from an object emitting light.

 

[zhermes]

Vertical axis is the perpendicular of triangle; x = time

Radius of cone is the base of triangle; y = speed of light in one second

Edge of the cone is the hypotenuse of triangle; z = space-time diagram of a pulse in one second

Thus x² + y² = z², where z > c, so is this possible?

The hypotenuse you're describing doesn't represent the path of any particle or signal---its just some line that you're drawing. The length of that line is 'z', which is not a velocity (like the speed of light 'c').

The space-time interval is always zero between two events connected by a light speed path BUT the slant edge of cone which is GREATER than the speed of light "c" represents the true motion of a pulse [world line] in both space and time

The spacetime interval (ds) is zero along a null-like trajectory (i.e. light path); a 'pulse' would follow the same time of (45deg) null-trajectory----not a world-line (horizontal or vertical depending on how you're drawing your diagram).