Enter Calculator Inputs
Example Data Table
| Case | Mass (kg) | vx/c | vy/c | vz/c | u/c | px′ (kg·m/s) | E′ (J) |
|---|---|---|---|---|---|---|---|
| Electron sample | 9.11e-31 | 0.60 | 0.20 | 0.00 | 0.30 | 1.108828e-22 | 9.086096e-14 |
| Proton sample | 1.67e-27 | 0.40 | 0.10 | 0.05 | 0.25 | 8.526264e-20 | 1.533666e-10 |
| Muon sample | 1.8835e-28 | 0.70 | 0.00 | 0.10 | -0.20 | 7.335260e-20 | 2.785470e-11 |
Formula Used
This calculator transforms the four-momentum vector for a Lorentz boost along the x-axis.
The displayed 4×4 matrix multiplies the vector [E/c, px, py, pz]T. This keeps the invariant mass relation unchanged across inertial frames.
How to Use This Calculator
- Enter the particle rest mass in kilograms.
- Choose whether velocities are fractions of c or direct m/s values.
- Provide particle velocity components vx, vy, and vz.
- Enter the frame speed u along the x-axis.
- Keep c at the default value unless needed otherwise.
- Select the number of decimals or scientific precision.
- Click Calculate Transformation to show results above the form.
- Review the matrix, transformed momentum, energy, velocity, and invariant check.
- Use the CSV or PDF buttons to export your results.
Frequently Asked Questions
1. What does this calculator transform?
It transforms a particle’s relativistic momentum and energy from one inertial frame to another. The implementation uses a Lorentz boost along the x-axis and also reports transformed velocity components, gamma factors, and the invariant mass check.
2. Why is energy included with momentum?
Relativistic momentum and energy form one four-vector. They transform together under Lorentz boosts. Treating them together preserves spacetime symmetry and keeps the invariant quantity (E/c)² − |p|² constant between inertial frames.
3. Why do py and pz remain unchanged here?
Only the x-direction is boosted in this model. A pure x-axis Lorentz boost mixes E and px, while transverse momentum components py and pz stay unchanged. Their associated velocities still rescale through the transformed denominator.
4. Can I enter velocities as fractions of c?
Yes. Choose the fractions-of-c mode for quick physics work. Then values like 0.6 mean 0.6c. Choose m/s mode when you already have direct laboratory velocities and want exact unit-based inputs.
5. What does the invariant check confirm?
It confirms numerical consistency. In exact relativity, (E/c)² − |p|² equals (mc)² for every inertial observer. If the original and transformed invariant values closely match, the transformation has been applied correctly.
6. What happens if my speed reaches c?
The calculator blocks that case. Material particles must remain below the speed of light. If any entered speed magnitude equals or exceeds c, gamma becomes undefined and the transformation stops with a warning.
7. Can this handle arbitrary boost directions?
This version is specialized for boosts along the x-axis. For arbitrary directions, you would need a more general Lorentz transformation tensor or a coordinate rotation before and after the boost.
8. Why does the graph use E/c instead of E?
E/c has the same units as momentum. Plotting px, py, pz, and E/c together makes the comparison physically consistent and visually clearer because all bars then represent momentum-equivalent quantities.