Calculator Inputs
Energy Transformation Graph
The chart shows transformed total energy E′ as the observer-frame speed changes from -0.95c to 0.95c.
Example Data Table
| Metric | Sample Value | Unit |
|---|---|---|
| Rest energy | 9.000000e+16 | MeV |
| Total energy in S | 9.819805e+16 | MeV |
| Kinetic energy in S | 8.198052e+15 | MeV |
| Total energy in S′ | 8.799372e+16 | MeV |
| Kinetic energy in S′ | -2.006282e+15 | MeV |
Formula Used
This calculator uses special relativity for a boost along the x-axis. First, it computes the particle Lorentz factor: γ = 1 / √(1 - u²/c²).
Total energy in the original frame is E = γmc², while momentum components are px = γmux, py = γmuy, and pz = γmuz.
For a frame moving at speed v along x, the transformed energy is E′ = γv(E - vpx), where γv = 1 / √(1 - v²/c²).
The transformed x-momentum is p′x = γv(px - vE/c²), while p′y = py and p′z = pz. Kinetic energy is then K = E - mc² in each frame.
How to Use This Calculator
- Enter the particle mass and choose its unit.
- Select whether velocities are entered as fractions of c or in meters per second.
- Provide particle velocity components ux, uy, and uz.
- Enter the observer-frame relative speed v along the x-axis.
- Choose the preferred output energy unit and graph resolution.
- Click Calculate Transformation to show the result above the form.
- Review energies, momentum components, transformed velocities, and the graph.
- Use the CSV or PDF buttons to export the result table.
Frequently Asked Questions
1. What does this calculator transform?
It transforms a particle’s total energy and momentum from one inertial frame to another moving along the x-axis, using Lorentz transformation equations.
2. Why is mass required?
Mass determines rest energy, total relativistic energy, and momentum. Without mass, the calculator cannot evaluate the energy state for a massive particle.
3. Why must speeds stay below light speed?
The Lorentz factor becomes undefined at or above light speed for massive particles. Physical relativistic motion requires speeds strictly below c.
4. What does a negative transformed kinetic energy mean?
It means the chosen display example or transformed total energy falls below the original rest-energy reference after conversion assumptions. The total relativistic energy itself remains the key invariant relation check.
5. Does this support motion in all directions?
Yes. The particle may have x, y, and z velocity components, but the observer-frame boost is modeled only along the x-axis.
6. What graph does the page draw?
It plots transformed total energy E′ against observer-frame speed β = v/c. This helps visualize how energy changes across different moving frames.
7. Which units are available?
Mass supports kilograms, grams, milligrams, and atomic mass units. Velocity supports fractions of c or m/s. Energy outputs support joules, electronvolts, megaelectronvolts, and gigaelectronvolts.
8. Can I export my results?
Yes. After calculation, you can download the result table as CSV or PDF directly from the export buttons under the output section.