A transformation is a change. Dr. Jekyll turns into Mr. Hyde. Ice turns into water. Cinderella's coach turns into a pumpkin.
In some transformations a thing turns into something else. But transformations can describe any kind of change.
The Lorentz Transformation tells how the time and distance between two events change when the velocity of the observer changes.
Before the time of Lorentz and Einstein this was not thought to be an issue.
It was thought that two events, the beginning and the end of a sprinter's dash of 100 yards in 9 seconds, will just always, unconditionally, be 100 yards of distance and 9 seconds of time, apart.
Regardless.
Period.
If two people observe the runner, one observer sitting still and the other observer chasing the runner, it had been assumed that they would each find that d = 100 yards and that t = 9 seconds.
In algebra, this equality would be described by the two equations:
d' = d and
t' = t.
Transformations are often best described using an equation or several equations. This should not be frightening. Especially if the equations are as simple as d' = d and t' = t !
It just happens not to be unconditionally true that d' = d and t' = t.
It is not true when one observer is at rest and another is moving rapidly.
Lorentz thought this was an illusion, that these equalities do hold, but give the appearance that they do not hold true in some situations. Lorentz believed that the time and distance between two events are absolute quantities, but seem at times to be different from what they really are.
Einstein proposed that time is not "absolute," and that in fact the difference in what a stationary and a moving observer measure is not just an appearance, but is actually there.
Why Einstein thought this is a very interesting story, which is told in the book,
"A serious but not ponderous book about Relativity."
This is a simple example of a transformation, that has nothing to do with relativity or the time and distance between events.
It is just an example to help you see what "transformation" means and how transformations can sometimes be described.
You look at an object, and some dimension of it has a length of d. Then you look at the same object through a black tube and find that it looks twice as big. You give the name d' to the same dimension as you see it now.
You may know nothing about lenses or telescopes. All you know is that every dimension is doubled by looking through the box.
The transformation equation is: d' = 2d. You don't have to know why in order to describe it.
An example of a transformation based on a change of point of view is the one in which two points P and Q are observed with graph paper on a glass plate.
The diagram at the left is a reminder if you've forgotten. To review it click "Space-time interval"
The point of view is changed by rotating the glass plate containing the x and y axes.
What is totally new in relativity is the interdependence of time and space.
This means that the velocity of the observer may change both the time and the distance between two events.
As with the telescope there is a distance d and time t between the events in the initial observation and then the new distance d' and time t' after the observer has changed his velocity.
And why do we want to study this particular transformation?
Because this is the transformation that the mathematicians had found that would describe what "appeared" to happen.
Einstein found that if this were what "really happens", it would permit keeping both Galilean Relativity and Maxwell's Laws, which otherwise would be in conflict.
It was the price of keeping both principles.
That price and what it bought is what Einstein's relativity is all about.
In the end, of course, we had no choice. Nature had already decided for us that Galilean Relativity and Maxwell's Laws should both hold fast, and that time and space were not absolute and independent of each other but transformed in just the way the mathematicians had found!
That's often how science works. Someone proposes a solution to a knotty problem posed by some observations. Then everyone gets busy with the math trying to see what the consequences are of solving this knotty problem in this way. In the process you discover whether that solution is the correct one.
Back for more questions and answers.
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