## Friday, April 27, 2018

### Unizor - Physics - Mechanics - Kinematics - Galileo's Relativity Principle

Notes to a video lecture on http://www.unizor.com

Galileo's Relativity Principle

Galileo's Relativity Principle is experimentally obtained result that states that

the same mechanical experiment conducted in two different inertial frames produces the same results.

We accept this as an axiom, which has very deep meanings. Some of them are specified implicitly by omission, some are explicitly stated.

Galileo's Relativity Principle implies the possibility of space and time
separation between two equivalently organized experiments, since it
does not require any location coincidence or simultaneousness of
conducting these experiments.

By omitting any time requirements, the Principle implies that the flow of time does not change the results of experiment. Today's 10 seconds of time are equivalent to yesterday's or tomorrow's 10 second.
Time is completely symmetrical towards past or future at any moment.

In other words, time is invariant relative to any moment (or uniform, or isomorphic).

Now let's analyze the space. Here, again, the Relativity Principle does not specify any dependency of the results of an experiment from the location. So, space is invariant relative to location, in other words, space is uniform (or isomorphic).

Similarly, the results of experiment are independent of orientation of
an apparatus used to conduct this experiment in space. Any direction is
no different than any other. So, the Relativity Principle implies that space is invariant relative to any direction, that is space is isotropic.

All the above implications are quite fundamental and intuitively
obvious, but the most interesting meaning of the Relativity Principle is
explicitly specified. It states that there is no experiment that would
allow to differentiate one inertial system from another. In other words,
the motion of an inertial system cannot be detected from inside.

Consider two people in different inertial systems. For example, one is
on the ground and another is on a train without windows going along a
straight line with the same speed. Let's ignore the curvature of the
Earth and its gravitation directed perpendicularly down and balanced by
the reaction of the ground for a person on the ground and the reaction
of the train's floor for a person on a train. The Relativity Principle
states that there is no experiment that the person on a train can
conduct that would tell him that he is moving relative to the ground,
his results would be identical to those that a person on the ground has.

For instance, if both of them take balls of the same weight and size and
roll it with the same effort, the balls will roll with the same speed,
one - relative to the ground, another - relative to the train's floor.

The water in the pot standing still on the floor of the train will look
exactly like a similar pot with water on the ground - no waves, the
level is strictly horizontal.

The weight of an object on the ground will be the same as on the train.

A bullet on the train will cover the same distance in certain amount of
time relative to the train as in case of a bullet shut by a person on
the ground.

We can come up with many experiments, and all of them will show identical results.

Here we have to bring attention to the words "relative to" used in all
the above cases. They signify the connection of results of any
experiment to the frame of reference. All these results are
"relative". Speed of the rolling ball in the above example is the same,
if we measure it separately in two different inertial frames -
one connected to the ground, another - to the train. Similarly, the
speed and distance covered in certain time by a bullet were measured
separately with identical results.

While such important characteristics like distance and speed are obviously relative to a frame of reference, one physical characteristic is considered absolute in classical Physics. It's time.
We always assume that the clocks in the hands of a person on the ground
are identical to clocks on the train. If two people synchronized their
ideal clocks, one boarded our train, while another remains on the
ground, their clocks will remain synchronized, no matter how far and how
long the train goes.

So, time is absolute in classical Physics, while such physical characteristics as distance and speed are relative to the frame of reference. This Galileo's Relativity Principle predates Einstein's Theory of Relativity that developed this principle much further.