## Wave-Particle Duality

Waves can exhibit particle-like characteristics and particles can exhibit wave-like characteristics. Is it possible that waves alone could behave as particles? What if the universe is composed of a single medium capable of supporting vibrations?...

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### How to Draw Four Dimensional Figures

In this article we will see how to draw a 2- dimensional representation of 4- dimensional objects. Fig. 1 The Number Line 1-D Space Fig. 1 shows the x-axis or number line. This is a single dimension. Any...

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### The x,y Minkowski diagram

The Minkowski diagram is a 4-diamentional diagram made up of six 2-D planes. The x,y Minkowski diagram is one of these planes. Normally when we show a single plane of the Minkowski diagam it is the x,t plane, which...

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### Hyperbolic Functions

Hyperbolic functions are related to the rectangular hyperbola, like the trigonometric functions are related to a circle. The equation for a hyperbola is x2/a2 - y2/b2 = 1. Hyperbolic functions are based on a hyperbola,...

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### The Twin Paradox

The twin paradox is an example used in relativity. In the story there are twin brothers. One of the brothers takes a long trip, in a spacecraft, moving at a speed close the speed of light, both going and returning,...

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### Using the Minkowski Diagram

How both the observer and the object see a linear contraction of the other How the observer and the object measure time dilation in other system The speed of light as measured in both systems Each coordinate...

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### Minkowski Diagram

The special theory of relativity is a theory by Albert Einstein, which can be based on the two postulates Postulate 1: The laws of physics are the same (invariant) for all inertial (non-accelerating) observers.* ...

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### What could cause the effects of Relativity

Uses a standing electromagnetic wave moving past an observer. The observer sees that the effects of relativity on the standing wave are caused by the Doppler Effect on the two waves creating the standing wave