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In the late 19th century, some “minor” cracks started to appear in our knowledge of physics. The first one might have been because of Maxwell’s equations. They, together with the Lorentz force law (that is a combination of the laws for magnetic and electric forces acting on a point charge), will describe all electromagnetic phenomena very well, including the behaviour of light. There was just one problem. One can use the equations to find the speed of light – Woo Hoo – but that would not include relative motion – D’oh! It was like the speed of light was independent of the motion of the source and the observer.
Then came the Michelson–Morley experiment, where they failed to detect the linear motion of the Earth using light. It was as if the speed of light were independent of the motion of the Earth.
Enter Einstein. To solve these problems, he came up with the theory of relativity.
By the way, the word theory means something different in science than in everyday language. A scientific theory is a well-substantiated explanation of some aspect of the natural world that is based on a body of evidence and has stood up to repeated testing and scrutiny. Laws, experimental results and observations are parts of a scientific theory, so theories are not promoted to laws; laws are parts of a theory.
First, some general terms
Frame of reference: The set of coordinates used in a physics problem. We usually use a fixed coordinate system in the classroom as our frame of reference.
Inertial frames of reference: A frame of reference with no acceleration. All things not moving relative to each other are then said to be in the same frame of reference.
The classroom is technically not an inertial frame of reference because the Earth rotates around its axis and also around the sun.
Some exercises – and the key to them.
- The Earth’s surface moves due to its rotation at about 465 m/s at the equator, and the Earth has an equatorial radius of 6378000 m.
- What will the corresponding centripetal acceleration be?
- How much is this relative to the free-fall acceleration?
- If you are experimenting at some point away from the equator, the corresponding centripetal acceleration will be even smaller. Do you need to consider this acceleration when experimenting in the classroom?
- The Earth rotates one turn around the sun every 365.24 days, and the distance to the sun is 1 AU. What will the centripetal acceleration be due to this motion?
The Postulates of Special Relativity
- The laws of physics are invariant – the same – in all inertial frames of reference. This is known as the principle of relativity.
- The speed of light in a vacuum is the same for all observers. The motion of the light source or the observer does not matter. We call this the principle of the light speed invariance.
The first one is especially borrowed from classical physics, and the second one is to cover the cases mentioned above.
Some terminology
Worldline: A thought line tracing an object in space/time. A worldline is time-like if it follows an object moving slower than the speed of light, i.e. a real object.
Proper time: Proper time along a (time-like) world line is defined as the time as measured by a clock following that line. I.e. the time measured by the clock itself, not the time measured by some other observer.
If you hold on to a clock and move around, your proper time is the time as measured by your clock. Someone else, moving relative to you, will possibly observe your time changing at some other pace than what you observe.
Proper time is often denoted t0.
Proper length: This is the length of an object in the object’s rest frame. I.e., if you measure the length of an object that is at rest relative to you, then you have measured its proper length.
Proper length is often denoted L0.
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