What is the Difference Between Lorentz Transformation and Galilean Transformation?

The main difference between Lorentz and Galilean transformations lies in their applicability and the nature of time in each transformation. Here are the key differences:

1. Applicability:

• Galilean transformations are approximations of Lorentz transformations for speeds far less than the speed of light. They are valid only for small velocities compared to the speed of light and are not relevant in the realms of special relativity and quantum mechanics.
• Lorentz transformations are applicable for any speed, including those close to the speed of light, and are used in special relativity.

1. Time:

• In Galilean transformations, time is constant or universal, and it does not depend on the observer. This means that all inertial frames share a common time.
• In Lorentz transformations, time is relative, and it depends on the observer. This leads to the concept of time dilation, which is a consequence of special relativity.

In summary, Galilean transformations are crude approximations of motion for small velocities and are based on the idea of constant, universal time, while Lorentz transformations are more accurate and applicable for any speed, including those close to the speed of light. The latter also accounts for the relativity of time, which is a key concept in special relativity.

Comparative Table: Lorentz Transformation vs Galilean Transformation

The main differences between the Lorentz Transformation and the Galilean Transformation are:

• Scope: Lorentz transformations are valid for any speed, while Galilean transformations are not valid for speeds approaching the speed of light.

• Time: According to Galilean transformations, time is the same for all observers, while in Lorentz transformations, time is relative and depends on the observer's frame of reference.

• Velocity and Acceleration: Galilean transformations provide a crude approximation of the motion of particles, while Lorentz transformations are more accurate and consistent with special relativity.

Here is a comparison table:

In summary, the Galilean Transformation is a simpler and less accurate description of the relationship between space and time coordinates of events, while the Lorentz Transformation is a more complex and accurate description that takes into account the effects of special relativity.