Hyper Objects Help

By — McGraw-Hill Professional
Updated on Oct 3, 2011

Introduction to Hyper Objects

Now that we’re no longer bound to 3D space, let’s put our newly empowered imaginations to work. What are 4D objects like? How about five dimensions (5D) and beyond?

Time As Displacement

When considering time as a dimension, it is convenient to have some universal standard that relates time to spatial displacement. How many kilometers are there in one second of time? At first this seems like a ridiculous question, akin to asking how many apples there are in a gallon of gasoline. But think of it like this: time and displacement can be related by speed in a sensible way, as long as the speed is known and is constant.

Suppose someone tells you, “Jimsville is an hour away from Joesville.” You’ve heard people talk like this, and you understand what they mean. A certain speed is assumed. How fast must you go to get from Jimsville to Joesville in an hour? If Jimsville and Joesville are 50 kilometers from each other, then you must travel 50 kilometers per hour in order to say that they are an hour apart. If they are only 20 kilometers apart, then you need only travel 20 kilometers per hour to make the same claim.

Perhaps you remember the following formula from elementary physics:

d = st

where d is the distance in kilometers, s is the speed of an object in kilometers per hour, and t is the number of hours elapsed. Using this formula, it is possible to define time in terms of displacement and vice versa.

Universal Speed

Is there any speed that is universal, and that can be used on that basis as an absolute relating factor between time and displacement? Yes, according to Albert Einstein’s famous relativity theory. The speed of light in a vacuum, commonly denoted c , is constant, and it is independent of the point of view of the observer (as long as the observer is not accelerating at an extreme rate or in a super-intense gravitational field). This constancy of the speed of light is a fundamental principle of the theory of special relativity. The value of c is very close to 299,792 kilometers per second; let’s round it off to 300,000 kilometers per second. If d is the distance in kilometers and t is the time in seconds, the following formula is absolute in a certain cosmic sense:

d = ct = 300,000 t

According to this model, the moon, which is about 400,000 kilometers from the earth, is 1.33 second-equivalents distant. The sun is about 8.3 minute-equivalents away. The Milky Way galaxy is 100,000 year-equivalents in diameter. (Astronomers call these units light-seconds, light-minutes , and light-years .) We can also say that any two points in time that are separated by one second, but that occupy the same xyz coordinates in Cartesian three-space, are separated by 300,000 kilometer-equivalents along the t axis.

At this instant yesterday, if you were in the same location as you are now, your location in time-space was 24 (hours per day) × 60 (minutes per hour) × 60 (seconds per minute) × 300,000 (kilometers per second), or 25,920,000,000 kilometer-equivalents away. This mode of thinking takes a bit of getting used to. But after a while, it starts to make sense, even if it’s a slightly perverse sort of sense. It is, for example, just about as difficult to jump 25,920,000,000 kilometers in a single bound, as it is to change what happened in your room at this time yesterday.

The above formula can be modified for smaller distances. If d is the distance in kilometers and t is the time in milliseconds (units of 0.001 of a second), then:

d = 300 t

This formula also holds for d in meters and t in microseconds (units of 0.000001, or 10 −6 , second), and for d in millimeters (units of 0.001 meter) and t in nanoseconds (units of 0.000000001, or 10 −9 , second). Thus we might speak of meter-equivalents, millimeter-equivalents, microsecond-equivalents , or nanosecond-equivalents .

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