Create Relativity.java

src/main/java/com/thealgorithms/physics/Relativity.java

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+package com.thealgorithms.physics;
+
+/**
+ * Implements relativity theory formulae.
+ * Provides simple static methods to calculate length contraction and time dilation
+ * in the laboratory frame with respect to the object's own frame, and velocity
+ * with respect to the moving frame.
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/List_of_relativistic_equations">Wikipedia</a>
+ */
+public final class Relativity {
+
+    /* Speed of light in m s^-1 */
+    public static final double SPEED_OF_LIGHT = 299792458.0;
+
+    /**
+     * Private constructor to prevent instantiation of this utility class.
+     */
+    private Relativity() {
+    }
+
+    /**
+     * Calculates the gamma parameter that is of paramount importance in relativity
+     * theory. It is a dimensionless parameter that is equal to 1 for zero velocity
+     * but tends to infinity when velocity approaches the speed of light.
+     *
+     * @param v The velocity (m/s).
+     * @return The value of gamma parameter.
+     */
+    public static double gamma(double v) {
+        if (Math.abs(v) >= SPEED_OF_LIGHT) {
+            throw new IllegalArgumentException("Speed must be lower than the speed of light");
+        }
+        return 1.0 / Math.sqrt(1 - v * v / (SPEED_OF_LIGHT * SPEED_OF_LIGHT));
+    }
+
+    /**
+     * Calculates the length of an object in the moving frame.
+     *
+     * @param length The length of an object in its own frame (m).
+     * @param v The velocity of the object (m/s).
+     * @return The length of an object in the laboratory frame (m).
+     */
+    public static double lengthContraction(double length, double v) {
+        if (length < 0) {
+            throw new IllegalArgumentException("Length must be non-negative");
+        }
+        return length / gamma(v);
+    }
+
+    /**
+     * Calculates the time that has passed in the moving frame.
+     *
+     * @param length The time that has passed in the object's own frame (s).
+     * @param v The velocity of the object (m/s).
+     * @return The time that has passed in the laboratory frame (s).
+     */
+    public static double timeDilation(double time, double v) {
+        if (time < 0) {
+            throw new IllegalArgumentException("Time must be non-negative");
+        }
+        return time * gamma(v);
+    }
+
+    /**
+     * Calculates the velocity with respect to the moving frame.
+     *
+     * @param v1 The velocity of the object with respect to laboratory frame (m/s).
+     * @param v The velocity of the moving frame (m/s).
+     * @return The velocity with respect to the moving frame (m/s).
+     */
+    public static double velocityAddition(double v1, double v) {
+        if (Math.abs(v1) > SPEED_OF_LIGHT) {
+            throw new IllegalArgumentException("Speed must not exceed the speed of light");
+        }
+        if (Math.abs(v) >= SPEED_OF_LIGHT) {
+            throw new IllegalArgumentException("Frame speed must be lower than the speed of light");
+        }
+        return (v1 - v) / (1 - v1 * v / (SPEED_OF_LIGHT * SPEED_OF_LIGHT));
+    }
+}

src/test/java/com/thealgorithms/physics/RelativityTest.java

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+package com.thealgorithms.physics;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for the Relativity utility class.
+ */
+final class RelativityTest {
+
+    // A small tolerance (delta) for comparing floating-point numbers
+    private static final double DELTA = 1e-6;
+    private static final double C = Relativity.SPEED_OF_LIGHT;
+
+    @Test
+    @DisplayName("Test the gamma parameter")
+    void testGamma() {
+        double myGamma = Relativity.gamma(0.6 * C);
+        assertEquals(1.25, myGamma, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test the length contraction")
+    void testLengthContraction() {
+        double myLength = Relativity.lengthContraction(5.0, 0.8 * C);
+        assertEquals(3.0, myLength, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test the time dilation")
+    void testTimeDilation() {
+        double myTime = Relativity.timeDilation(4.0, 0.6 * C);
+        assertEquals(5.0, myTime, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test the velocity addition in the same direction")
+    void testVelocityAdditionSameDirection() {
+        double myVelocity = Relativity.velocityAddition(0.8 * C, 0.75 * C);
+        assertEquals(0.125 * C, myVelocity, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test the velocity addition in different directions")
+    void testVelocityAdditionDifferentDirections() {
+        double myVelocity = Relativity.velocityAddition(0.8 * C, -0.75 * C);
+        assertEquals(0.96875 * C, myVelocity, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test the velocity addition with the speed of light")
+    void testVelocityAdditionWithSpeedOfLight() {
+        double myVelocity = Relativity.velocityAddition(C, 0.7 * C);
+        assertEquals(C, myVelocity, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test invalid inputs throw exception")
+    void testInvalidOrbitalVelocityInputs() {
+        assertThrows(IllegalArgumentException.class, () -> Relativity.gamma(1.2 * C));
+        assertThrows(IllegalArgumentException.class, () -> Relativity.gamma(-C));
+        assertThrows(IllegalArgumentException.class, () -> Relativity.lengthContraction(-1.0, 0.6 * C));
+        assertThrows(IllegalArgumentException.class, () -> Relativity.lengthContraction(1.0, 1.5 * C));
+        assertThrows(IllegalArgumentException.class, () -> Relativity.timeDilation(-5.0, -0.8 * C));
+        assertThrows(IllegalArgumentException.class, () -> Relativity.timeDilation(5.0, C));
+        assertThrows(IllegalArgumentException.class, () -> Relativity.velocityAddition(0.3 * C, -C));
+        assertThrows(IllegalArgumentException.class, () -> Relativity.velocityAddition(1.4 * C, 0.2 * C));
+        assertThrows(IllegalArgumentException.class, () -> Relativity.velocityAddition(-0.4 * C, 1.2 * C));
+    }
+}