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You see that as a result of the fact that the speed of light is constant, we find inexorably that Kimball Kinnison and John Star disagree about the timing of the bombs. One of them says they both went off at the same time. The other says bomb A went off before bomb C. Time has gone awry. In the jargon of relativity, we speak of Kimball Kinnison being in one reference frame, while John Star is in another reference frame.

The two frames are moving relative to each other. One of the chief functions of relativity is to see how things happening in one frame appear to the people in the other frame. What we have just shown is that two events that are simultaneous in one frame are not necessarily simultaneous in another, moving frame.

For the events to appear simultaneous in both frames, the two events would have to be located at the same point in space. Another distortion of time is demonstrated by a different experiment. Suppose Kimball Kinnison sets up a light source, a detector, and a mirror, as shown in Fig. He flashes the light and measures the time it takes for a short pulse to go from the source to the mirror and back. What does John Star see? The drawing shows, not three different ships, but the same ship as seen at three different times while it moves past the Earth.

Now the path of the light flash as it goes from source to mirror to detector is much longer than it appeared to K.

Remember that the light travels with the same speed, regardless of the observer. So if John Star sees it traveling over a longer path, it must be taking a longer time. But John Star and Kimball Kinnison are measuring the time interval between the same pair of events: emission of the light flash from the source, and arrival at the detector. We see, then, that the time between these two events depends on the motion of the observer relative to the events. John Star says K. This effect is the famous time dilation—the slowing down of time in a moving reference frame.

You see that the time dilation is a necessary consequence of the fact that the speed of light is a constant. The formula for the time dilation can be derived from Fig. See any good book on relativity. Now we are in a position to ask some interesting questions.

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Take our friend Kimball Kinnison scooting along at half the speed of light, engaging in a conversation with headquarters back on Earth, using the instantaneous communication powers of his lens. First of all, what does instantaneous communication mean? It means the signal is transmitted and received at the same instant of time. This means transmission and reception is simultaneous. But we just showed that simultaneous is all in the eye of the beholder.

What is simultaneous to K. Communication that looks instantaneous in one frame will not be instantaneous in another. There is a set of equations that allows us to find out what is happening in one reference frame if we know what is happening in another. In other words, if we know the position and time of an event in K. These equations are known as the Lorentz transformations.

Hendrik Antoon Lorentz was a Dutch physicist—one of the giants of 19th century physics.

Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 2]

He discovered the equations that bear his name by considering the properties of electromagnetic Waves. These are the same equations that Einstein derived in developing the theory of relativity. The equations are named after Lorentz because he did them first. The irony of the situation is that Lorentz never completely understood the equations.

Physicists continue work to abolish time as fourth dimension of space

If he had, he would have been the inventor of relativity. But Lorentz never believed what the equations told him—that time could be different in two reference frames. He was stuck to classical ways of thinking, in which time is the same to all observers. In other words, instead of describing the universe by three dimensions of space and a completely separate dimension of time, we now deal with a four-dimensional spacetime. Time is now one of the four dimensions, on an equal footing with the three spatial dimensions. We merely mean that time is treated the same as space mathematically.

Incidentally, there are new theories which postulate three time-like dimensions to match the three space-like dimensions. To show where events are located in this four-dimensional space, we use a spacetime diagram, such as in Fig. The horizontal axis shows the distance in light-years away from the starting point, which in this case is Earth. The vertical axis is a time scale in years. There can also be y and z axes, but these are left out in a two-dimensional drawing.

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Any point on this diagram represents the location of an event: where it is relative to Earth, and at what time. In Fig. As time passes, the position of Earth advances upward on the time axis. Its position is shown after 10 years Earth time has elapsed, and it has traveled 5 light-years through space.


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In this article I am going to stick to ships traveling with constant speed, and will leave accelerating ships for another article. A ship traveling faster than light would go along a trajectory lying below the light path.

The Next Chapter in Story Development

In this article we are not going to consider FTL spaceships, but whatever we say about signals going faster than light would also apply to any kind of object, spaceship or otherwise. The diagram of Fig. You must understand, of course, that the people in the ship think that they are standing still, and that the rest of the universe is moving. However, when the people on Earth look across to the moving ship, they see its spacetime grid altered.

Its x-axis is leaning up, and its t-axis is leaning to the right. The two axes are no longer perpendicular to each other. Remember that the x-axis represents all the places where time is zero in the Earth frame. We can calculate what the Earth time is by using the Lorentz transformation equations. But, as Kinnison sees it, the explosion is only 8. And, as the Earth people see it, the explosion takes place 5 years after the starting time, rather than at time zero.

Notice that both space and time are transformed. Kimball Kinnison finds that the distance to the Klingon ship is less than the 10 light-years measured by the Earth-bound observers. This difference demonstrates the famous Lorentz-Fitzgerald contraction of space. This story also illustrates what we were saying previously about simultaneity. And these are a different set of events. So the people on Earth and the people in the ship disagree about what is meant by the word simultaneous.

To the people in the ship the blowing-up of the Klingon ship is simultaneous with the instant their clock hits zero.