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time-dilation-calculator

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broadfield-dev commited on 6 days ago

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c463819

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1 Parent(s): c1f3e16

Update app.py

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app.py +101 -24

app.py CHANGED Viewed

@@ -15,12 +15,10 @@ def gravitational_time_dilation(mass, radius, t0):
     Returns: Dilated time (seconds)
     """
     try:
-        # Schwarzschild radius factor
         rs = (2 * G * mass) / (C ** 2)
-        # Time dilation factor sqrt(1 - rs/r)
         factor = math.sqrt(1 - rs / radius)
         if factor <= 0 or math.isnan(factor):
-            return None  # Invalid due to event horizon or negative sqrt
         return t0 / factor
     except Exception:
         return None
@@ -35,8 +33,7 @@ def relativistic_time_dilation(velocity, t0):
     try:
         beta = velocity / C
         if beta >= 1:
-            return None  # Cannot exceed speed of light
-        # Lorentz factor
         factor = math.sqrt(1 - beta ** 2)
         return t0 / factor
     except Exception:
@@ -51,11 +48,37 @@ def home():
             <style>
                 body { font-family: Arial, sans-serif; margin: 20px; }
                 .container { max-width: 800px; margin: auto; }
-                .input-group { margin: 10px 0; }
-                label { display: inline-block; width: 200px; }
-                input { padding: 5px; width: 200px; }
-                button { padding: 10px 20px; margin: 10px 0; }
-                #result { margin-top: 20px; }
             </style>
         </head>
         <body>
@@ -64,23 +87,84 @@ def home():
                 <p>Calculate gravitational and relativistic time dilation for two observers.</p>
                 <div class='input-group'>
                     <h3>Observer 1</h3>
-                    <label>Mass (kg):</label><input type='number' id='mass1' value='5.972e24'><br>
-                    <label>Radius (m):</label><input type='number' id='radius1' value='6.371e6'><br>
-                    <label>Velocity (m/s):</label><input type='number' id='velocity1' value='0'><br>
                 </div>
                 <div class='input-group'>
                     <h3>Observer 2</h3>
-                    <label>Mass (kg):</label><input type='number' id='mass2' value='5.972e26'><br>
-                    <label>Radius (m):</label><input type='number' id='radius2' value='6.371e6'><br>
-                    <label>Velocity (m/s):</label><input type='number' id='velocity2' value='0'><br>
                 </div>
                 <div class='input-group'>
-                    <label>Proper Time (s):</label><input type='number' id='proper_time' value='86400'><br>
                 </div>
                 <button onclick='calculate()'>Calculate</button>
                 <div id='result'></div>
             </div>
             <script>
                 async function calculate() {
                     const data = {
                         mass1: parseFloat(document.getElementById('mass1').value),
@@ -116,32 +200,26 @@ def calculate():
         velocity2 = data.get('velocity2', 0)
         t0 = data.get('proper_time')
-        # Input validation
         if not all([mass1, radius1, mass2, radius2, t0]) or any(x <= 0 for x in [mass1, radius1, mass2, radius2, t0]):
             return jsonify({"message": "Invalid input: All values must be positive numbers."}), 400
-        # Calculate gravitational time dilation
         t1_grav = gravitational_time_dilation(mass1, radius1, t0)
         t2_grav = gravitational_time_dilation(mass2, radius2, t0)
         if t1_grav is None or t2_grav is None:
             return jsonify({"message": "Error: Invalid gravitational parameters (e.g., within event horizon)."}), 400
-        # Calculate relativistic time dilation
         t1_rel = relativistic_time_dilation(velocity1, t0) if velocity1 > 0 else t0
         t2_rel = relativistic_time_dilation(velocity2, t0) if velocity2 > 0 else t0
         if (velocity1 > 0 and t1_rel is None) or (velocity2 > 0 and t2_rel is None):
             return jsonify({"message": "Error: Velocity exceeds speed of light."}), 400
-        # Combine effects (approximate by multiplying factors)
         t1_total = t1_grav if velocity1 == 0 else t1_grav * (t1_rel / t0)
         t2_total = t2_grav if velocity2 == 0 else t2_grav * (t2_rel / t0)
-        # Calculate relative time difference
         time_diff = abs(t1_total - t2_total)
-        # Prepare response
         message = (
             f"Results for proper time {t0:.2f} seconds:\n"
             f"Observer 1:\n"
@@ -159,6 +237,5 @@ def calculate():
         return jsonify({"message": f"Error: {str(e)}"}), 500
 if __name__ == '__main__':
-    # For Hugging Face Spaces, use the PORT environment variable
     port = int(os.environ.get("PORT", 7860))
     app.run(host='0.0.0.0', port=port)

     Returns: Dilated time (seconds)
     """
     try:
         rs = (2 * G * mass) / (C ** 2)
         factor = math.sqrt(1 - rs / radius)
         if factor <= 0 or math.isnan(factor):
+            return None
         return t0 / factor
     except Exception:
         return None
     try:
         beta = velocity / C
         if beta >= 1:
+            return None
         factor = math.sqrt(1 - beta ** 2)
         return t0 / factor
     except Exception:
             <style>
                 body { font-family: Arial, sans-serif; margin: 20px; }
                 .container { max-width: 800px; margin: auto; }
+                .input-group { margin: 20px 0; }
+                label {
+                    display: inline-block;
+                    width: 200px;
+                    cursor: pointer;
+                    color: #007bff;
+                    text-decoration: underline;
+                }
+                label:hover { color: #0056b3; }
+                input { padding: 5px; width: 200px; margin-left: 10px; }
+                button {
+                    padding: 10px 20px;
+                    margin: 20px 0;
+                    background-color: #007bff;
+                    color: white;
+                    border: none;
+                    cursor: pointer;
+                }
+                button:hover { background-color: #0056b3; }
+                #result { margin-top: 20px; padding: 10px; border: 1px solid #ddd; }
+                .popdown {
+                    display: none;
+                    margin-top: 5px;
+                    padding: 10px;
+                    background-color: #f8f9fa;
+                    border: 1px solid #ddd;
+                    border-radius: 4px;
+                    max-width: 400px;
+                    font-size: 14px;
+                }
+                .popdown.show { display: block; }
             </style>
         </head>
         <body>
                 <p>Calculate gravitational and relativistic time dilation for two observers.</p>
                 <div class='input-group'>
                     <h3>Observer 1</h3>
+                    <div>
+                        <label onclick="togglePopdown('mass1-info')">Mass (kg):</label>
+                        <input type='number' id='mass1' value='5.972e24'>
+                        <div id='mass1-info' class='popdown'>
+                            The mass of the object (e.g., planet or star) affecting Observer 1, in kilograms.
+                            This determines the strength of the gravitational field. For example, Earth's mass is approximately 5.972 × 10²⁴ kg.
+                            Larger masses cause greater gravitational time dilation, slowing time for the observer.
+                        </div>
+                    </div>
+                    <div>
+                        <label onclick="togglePopdown('radius1-info')">Radius (m):</label>
+                        <input type='number' id='radius1' value='6.371e6'>
+                        <div id='radius1-info' class='popdown'>
+                            The distance from the center of the massive object to Observer 1, in meters.
+                            This is typically the radius of the planet or star. For example, Earth's radius is about 6.371 × 10⁶ m.
+                            Smaller radii (closer to the mass) increase gravitational time dilation.
+                        </div>
+                    </div>
+                    <div>
+                        <label onclick="togglePopdown('velocity1-info')">Velocity (m/s):</label>
+                        <input type='number' id='velocity1' value='0'>
+                        <div id='velocity1-info' class='popdown'>
+                            The speed of Observer 1 relative to a stationary reference frame, in meters per second.
+                            This affects relativistic time dilation. For example, a velocity of 0 m/s means no relativistic effects,
+                            while high speeds (e.g., 0.5 × speed of light) significantly slow time. Must be less than 299,792,458 m/s.
+                        </div>
+                    </div>
                 </div>
                 <div class='input-group'>
                     <h3>Observer 2</h3>
+                    <div>
+                        <label onclick="togglePopdown('mass2-info')">Mass (kg):</label>
+                        <input type='number' id='mass2' value='5.972e26'>
+                        <div id='mass2-info' class='popdown'>
+                            The mass of the object affecting Observer 2, in kilograms.
+                            For example, a planet 100 times Earth's mass would be 5.972 × 10²⁶ kg.
+                            This influences gravitational time dilation, with larger masses causing greater time dilation.
+                        </div>
+                    </div>
+                    <div>
+                        <label onclick="togglePopdown('radius2-info')">Radius (m):</label>
+                        <input type='number' id='radius2' value='6.371e6'>
+                        <div id='radius2-info' class='popdown'>
+                            The distance from the center of the massive object to Observer 2, in meters.
+                            For example, using Earth's radius (6.371 × 10⁶ m) assumes Observer 2 is on the surface.
+                            Smaller distances amplify gravitational time dilation effects.
+                        </div>
+                    </div>
+                    <div>
+                        <label onclick="togglePopdown('velocity2-info')">Velocity (m/s):</label>
+                        <input type='number' id='velocity2' value='0'>
+                        <div id='velocity2-info' class='popdown'>
+                            The speed of Observer 2 relative to a stationary reference frame, in meters per second.
+                            High velocities cause relativistic time dilation, slowing time for the observer.
+                            Set to 0 for no relativistic effects. Must be less than the speed of light (299,792,458 m/s).
+                        </div>
+                    </div>
                 </div>
                 <div class='input-group'>
+                    <div>
+                        <label onclick="togglePopdown('proper_time-info')">Proper Time (s):</label>
+                        <input type='number' id='proper_time' value='86400'>
+                        <div id='proper_time-info' class='popdown'>
+                            The time experienced by a reference observer in a weak gravitational field and at rest, in seconds.
+                            For example, 86,400 seconds equals 1 day. This is the baseline time used to calculate how much
+                            time each observer experiences after dilation effects are applied.
+                        </div>
+                    </div>
                 </div>
                 <button onclick='calculate()'>Calculate</button>
                 <div id='result'></div>
             </div>
             <script>
+                function togglePopdown(id) {
+                    const popdown = document.getElementById(id);
+                    popdown.classList.toggle('show');
+                }
                 async function calculate() {
                     const data = {
                         mass1: parseFloat(document.getElementById('mass1').value),
         velocity2 = data.get('velocity2', 0)
         t0 = data.get('proper_time')
         if not all([mass1, radius1, mass2, radius2, t0]) or any(x <= 0 for x in [mass1, radius1, mass2, radius2, t0]):
             return jsonify({"message": "Invalid input: All values must be positive numbers."}), 400
         t1_grav = gravitational_time_dilation(mass1, radius1, t0)
         t2_grav = gravitational_time_dilation(mass2, radius2, t0)
         if t1_grav is None or t2_grav is None:
             return jsonify({"message": "Error: Invalid gravitational parameters (e.g., within event horizon)."}), 400
         t1_rel = relativistic_time_dilation(velocity1, t0) if velocity1 > 0 else t0
         t2_rel = relativistic_time_dilation(velocity2, t0) if velocity2 > 0 else t0
         if (velocity1 > 0 and t1_rel is None) or (velocity2 > 0 and t2_rel is None):
             return jsonify({"message": "Error: Velocity exceeds speed of light."}), 400
         t1_total = t1_grav if velocity1 == 0 else t1_grav * (t1_rel / t0)
         t2_total = t2_grav if velocity2 == 0 else t2_grav * (t2_rel / t0)
         time_diff = abs(t1_total - t2_total)
         message = (
             f"Results for proper time {t0:.2f} seconds:\n"
             f"Observer 1:\n"
         return jsonify({"message": f"Error: {str(e)}"}), 500
 if __name__ == '__main__':
     port = int(os.environ.get("PORT", 7860))
     app.run(host='0.0.0.0', port=port)