Un-Minkowski Diagram -- Constant Velocity

plus Screen Shots and Commentary

(Try the static version if you can't see the QuickTime animation below.)

Overview

Constant Velocity

Hyperbolic View

Graph of 3-Second Event

(1 Meg download--will take a minute or two if you are on dial-up.)

This graph is animated by varying the observer velocity V. In the interactive version, the user can pause the animation,
click on the triangle, and see instantaneous values for Δτ, ΔT, ΔX, and V.

Screen Shots and Commentary

V=0.00

V=0.00

The blue line represents the passage of time from zero to three seconds.

The horizontal line would represent movement through space, but in this instance, we and the event are at rest.

Here, we are moving relative to the event (or the event is moving relative to us) at one-tenth the speed of light. The length of the green line shows the duration in time we will now measure for the event. Because of relativistic effects, we will measure slightly more than 3 seconds. How much more, we can see directly by comparing the lengths of the green and the blue lines.

V=0.10

V=0.10

In this case, we passed by the exact position of the event at the instant the 3-second event began. The turquoise line (at the bottom of the triangle) represents the distance--as we measure it--that we traveled during the three seconds of the event. We could also say that this is the distance the event traveled relative to us--that is, that this is the duration of the event in space.

v=0.50

V=0.50

As we repeat our experiment at faster speeds and then plot our results, we can see that both the green and the turquoise lines eventually get quite long.

If we were using the interactive version, we would see that the lengths of time we measure actually don't change very much until we get up to about half the speed of light.

When we get close to the speed of light, say between 0.90, as at right, and 0.99, as below, the lengths of time and space that we measure for the 3-second event become very huge, very fast . . .

v=0.90

V=0.90

V=0.99

V=0.99

. . . and the angle between the green and turquoise lines approaches zero.

If we could reach the speed of light, we would measure an infinitely long time for any event. It would seem to us as if time were passing as normal for us, but that it had stopped for all things not moving along with us. The universe would appear frozen.

Of course, it would take an infinite amount of energy to accelerate us to lightspeed. Only if we had zero mass could we get there.

V=1.00

V=1.00 (Lightspeed)

QUESTIONS:

Entities that exist at lightspeed have no rest mass and exhibit zero proper time.

If we could slow such entities down to less than lightspeed, what would be their duration in time and space?
How much energy would it take to slow such an entity down?
How do you explain the results of experiments in which physicists say they have slowed light down "to a crawl"? *

* (See 1999 New York Times article and 2001 BBC Online update on the research of Lene Vestergaard Hau.)