Understanding Lorentz Transformation
A Lorentz transformation converts space and time coordinates between two inertial frames. It is used when relative speed becomes large enough for relativity to matter. Ordinary motion formulas work well at low speed. They fail near light speed. This calculator helps compare both views of the same event. It accepts position, time, velocity, axis, and direction. It then returns transformed coordinates and supporting values.
Why Gamma Matters
The gamma factor controls the size of relativistic effects. When speed is small, gamma stays close to one. The transformed values then resemble classical results. As speed approaches light speed, gamma rises sharply. Time dilation becomes stronger. Length contraction also becomes stronger. The calculator reports beta, gamma, rapidity, and interval checks. These details make the result easier to audit.
Coordinate And Time Results
The selected axis is treated as the direction of motion. The coordinate on that axis changes with time and velocity. The other two coordinates remain unchanged. This matches the usual one dimensional Lorentz setup. The tool also supports inverse transformation. That option is useful when values are known in the moving frame. It converts them back to the original frame.
Interval Check
The spacetime interval is an important reliability check. It should remain the same in both frames. Small differences may appear from rounding only. A positive interval is time-like. A negative interval is space-like. A zero interval is light-like. The calculator labels the interval type. It also estimates proper time or proper distance.
Practical Uses
This page is useful for physics study, relativity examples, and classroom demonstrations. It also helps writers and developers test science based simulations. Export buttons let users save results quickly. The example table gives starting values. Try several velocities to see how gamma changes. Keep speed below light speed. That rule is required by special relativity. Use consistent units for meaningful answers.