Dr. Aaron Titus | Department of Physics, High Point University
PHY1050      Astronomy of Stars, Galaxies, and the Cosmos
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spacetime

You have learned so far about inertial reference frames. In an inertial reference frame, if there is no force on an object, then it will remain at rest or move at a constant speed in a straight line. According to special relativity, in all inertial reference frames, the laws of physics are the same and the speed of light is the same.

As you will see, special relativity has far-reaching consequences. It requires that you completely change your notions of space and time!

Suppose that an observer is in a rocket ship traveling to the right at a constant speed (relative to another observer who is in the lab "at rest"). We will call them the lab observer and the rocket observer, respectively. The rocket observer emits a laser beam which travels across the rocket, reflects off the other side, and returns to a detector. An animation of the situation is shown below.

Click the link "Rocket observer" to view the path of the beam of light, in slow motion. If the rocket's width is 3 meters, then the light travels a total roundtrip distance of 6 meters. The time for this to occur is what I will call 6 lightmeters. (That's just the time required for light to travel a distance of 6 meters.)

The start of the beam and the detection of the beam are called events. The rocket observer will say that the distance between events is zero (because the beam stars and ends at the same place) and the time between events is 6 lightmeters. You will notice in the animation, that t=6 lightmeters between the initiation and detection of the beam.

Now click the link for "Lab observer" to see the path taken by the light beam, as seen by a person at rest relative to the rocket. Note that the speed of the light is exactly the same as for the rocket observer, in accordance with special relativity.

You will notice that the two events, (1) start and (2) detection, of the beam are now seen to occur 8 meters apart. Also, the total distance traveled by the beam is 10 meters which is greater than that measured by the rocket observer.

Also, the total time of travel for the light is now 10 lightmeters, as measured by the lab observer. This again is greater than the 6 lightmeters of time measured by the rocket observer.

For the two events of (1) start of beam and (2) detection of beam, the rocket observer and the lab observer report a difference in the measured distance between events and time between events.

Before Einstein, physicists would have said that observers in different reference frames will, of course, disagree about distance between events but WILL agree on time between events.

However, Einstein's special relativity predicts that BOTH distance between events and time between events depends on the observer's inertial reference frame.

So, the observers disagree about distance and time between events. Then, what will they agree on?

The observers will agree on the quantity:

Check this out! The rocket observer measures:

And the lab observer measures:

They agree when they about the result when they do this calculation! This quantity is called spacetime interval, and it shows us that space (made up of 3 dimensions) and time (the fourth dimension) are the dimensions of the 4-dimensional coordinate system of the universe called spacetime.

In an inertial reference frame, when no force acts on an object, the object will move in a straight line at constant speed. Spacetime for these objects is said to be flat.

A two-dimensional illustration of flat spacetime is shown below.

 

 

 

 

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