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In addition to the revision notes for Classical Principle of Relativity on this page, you can also access the following Relativity learning resources for Classical Principle of Relativity
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 18.2 | Classical Principle of Relativity |
In these revision notes for Classical Principle of Relativity, we cover the following key points:
The equation of position of a point P when it is considered in two inertial systems of reference: a system S at rest and another inertial system S' in uniform motion relative to S, is
where V⃗ is the velocity of the system S' relative to the system S.
The parametric equations of a point P for the two above inertial systems of reference, are
Since the motion of S' is linear (one-dimensional), the three components of velocity vector V⃗ are (V, 0, 0). This is why only the x-component of parametric equations contains a V-element.
When adding the time t as the fourth parameter and giving that t' = t in all inertial frames of reference, we obtain
The above equations are nothing else but the known equations of Galilean Transformations of Coordinates.
Dividing side by side all the above equations by Δt, we obtain:
The limit of the above equations for Δt → 0 give the corresponding velocities. Thus, we obtain
These formulae represent the three Galilean Transformations for Velocity. They mean not only the position is relative; the velocity can be relative as well. Velocity depends on where do we make the observation (in S or S').
Giving that the relative velocity V between the two reference systems is constant, we obtain for the acceleration after dividing the above equations by the time interval Δt and taking the limit when ∆t → 0:
Therefore, we have
From the above equation, we conclude that the acceleration remains constant; no matter how the motion is made. Thus, we say that "acceleration (unlike position and velocity) is an absolute quantity (just like the time t) in all inertial systems of reference." In other words, acceleration in independent from the system it is measured for the same particle's motion.
All mechanical phenomena have the same features in all inertial frames (systems) of reference because the laws of mechanics have the same form for all of them.
The speed of light in terms of electric and magnetic constants (vacuum permittivity ε0 and permittivity of free space μ0) is
We can extend the relativistic reasoning used in mechanical-related phenomena in electromagnetic-related ones and in all the other fields of physics as well.
Scientists once believed that a material medium is necessary for the propagation of light waves, just like occurs in other types of waves (mechanical waves). They tried to explain this drawback by "inventing" the concept of "cosmic ether" - a medium extending at infinity, odorless, massless, transparent and non-observable in normal conditions. In this way, they believed that all objects flow through this cosmic ether without any mechanical resistance.
The two constants ε0 and μ0 were thought to be the electric and magnetic constants that characterize the cosmic ether, while ε and μ the corresponding electric and magnetic constants characterizing the space inside material objects. The speed of light in vacuum (about 300 000 km/s) was considered as the speed of light relative to the cosmic ether. However, it resulted that there is no cosmic ether in the universe, so the above theory is wrong.
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