Calculator Inputs
Example Data Table
| Case | Δt | Δx | βx | Expected class | Use case |
|---|---|---|---|---|---|
| Lab pulse | 1 s | 100,000,000 m | 0.20 | Timelike | Check causal separation |
| Light signal | 1 s | 299,792,458 m | 0.50 | Lightlike | Photon path test |
| Wide separation | 1 s | 500,000,000 m | 0.10 | Spacelike | Relativity exercise |
Formula Used
The calculator uses the Minkowski interval and a three-dimensional Lorentz boost.
γ = 1 / √(1 - β²)
Δt′ = γ(Δt - β · Δr / c)
Δr′ = Δr + [((γ - 1)(β · Δr) / β²) - γcΔt]β
s² = c²Δt² - Δx² - Δy² - Δz²
If s² is positive, the interval is timelike. If s² is zero, the interval is lightlike. If s² is negative, the interval is spacelike.
How to Use This Calculator
- Enter the coordinates for Event A.
- Enter the coordinates for Event B.
- Select matching time and distance units.
- Enter velocity components as beta fractions.
- Choose the boost direction.
- Press the calculate button.
- Review the transformed coordinates and interval class.
- Use the export buttons to save results.
Spacetime Coordinate Analysis
Why Spacetime Coordinates Matter
Spacetime coordinates describe where and when an event occurs. In ordinary geometry, distance is measured only through position. In relativity, time and position are joined. This makes event comparison more precise. It also shows whether events can influence each other.
Understanding Frames
A frame is a point of view moving at a steady speed. Two observers can measure different times and distances for the same event pair. This does not mean either observer is wrong. Their measurements are connected by Lorentz transformations. The calculator applies that transformation in three spatial directions.
Interval Classification
The spacetime interval is the key result. It stays the same for all inertial observers. A timelike interval means one event can causally follow the other. A lightlike interval means only light can connect the two events. A spacelike interval means no signal can connect them without exceeding light speed.
Advanced Output Meaning
The Lorentz factor shows how strongly motion changes time and distance measurements. Rapidity gives another way to describe relativistic speed. Proper time is shown for timelike intervals. Proper distance is shown for spacelike intervals. These outputs are useful in physics classes, astronomy examples, accelerator problems, and simulation checks.
Practical Notes
Use consistent units for each coordinate group. Enter beta components carefully. Their combined magnitude must stay below one. Very large astronomical values may produce scientific notation. That is normal. Compare the original interval with the boosted interval. Small differences can occur because computers round decimal numbers during calculation.
FAQs
1. What does this calculator measure?
It measures coordinate differences between two events. It also transforms them into a moving frame and classifies their spacetime interval.
2. What is beta?
Beta is speed divided by light speed. A beta of 0.5 means the frame moves at half the selected light speed.
3. Why must beta stay below one?
Special relativity does not allow massive observers to move at or above light speed. The Lorentz factor becomes undefined there.
4. What is a timelike interval?
A timelike interval means a slower-than-light object could travel between the events. Proper time can be calculated for that separation.
5. What is a spacelike interval?
A spacelike interval means the events are too far apart for causal contact. No light-speed or slower signal can connect them.
6. What is a lightlike interval?
A lightlike interval means light can connect the events. The interval is zero, within the calculator tolerance.
7. Why do original and boosted intervals match?
The spacetime interval is invariant. Different inertial observers measure different coordinates, but the interval remains the same.
8. Can I use custom light speed?
Yes. The default value is physical light speed. A custom value can help classroom models, simulations, or scaled examples.