Einstein gave us these neat thought experiments. I already dealt with one, but here’s another train example.
You’re standing on the ground watching a train pass by. A man on the train comes parallel to you, and as he comes even with you, he drops a pebble from his hand. Einstein says the pebble will fall straight down from the point of view of the man on the train, but will describe a curved shape, a parabola, to you who are walking or standing on the ground, watching the train pass by.
Einstein asks, which is the “true” trajectory?
Actually, there is only one trajectory, and that is the pebble falling straight down. It moves in accord with the inertial frame of the moving train.
How do we know? By simply reversing the conditions. Suppose you are on a moving platform, The train, unmoving, sits on that platform. As you and the man on the train come parallel, the man drops a pebble. If the speed is the same, and if the pebble is dropped at the same instant between the train man and the stationary man, the pebble will fall straight down from the train and strike the platform at the same place it struck the ground before.
In either case, the pebble will fall according to the inertial frame of the train, not the platform or ground. There is only ONE true trajectory for the pebble.
The only way to create a parabola is to draw a graph, with the vertical side representing the downward fall of the pebble, and a horizontal side, reflecting the movement of the train “sideways” on the ground. Only by combining movement with non-movement on the graph, can a parabola be detected, and that is done by drawing a connecting line from each point on the trajectory of the pebble until it hits the ground.
Even though the pebble had an accelerating rate of fall(gravity), it still falls straight down from the inertial reference of the train.
Let’s suppose the train is now a small toy held in the hand of a giant being in one hand, and the ground is held by the same giant being in another hand. The train, in one hand, is waved over the ground in a uniform motion, which is held rigidly in the other hand.
A little man on the train releases a pebble, and it begins falling down. Suppose the giant now takes both his hands and waves them abruptly back and forth after the pebble is released. Once it is released, it will still fall straight down according to the rate of gravity toward the ground, even if the ground moves. If the giant switches hands and suddenly puts the ground above the train, the pebble will fall on the top of the train, assuming the giant hasn’t moved the actual earth and suddenly reversed positions of train and earth.
Take another example using light. Place two tracks in deep space parallel. Two object sit side by side, each with a beam of light extending from it. The object of one track is connected at midpoint by a wire capable of carrying messages at light speed. The wire runs at a ninety degree angle between the two tracks.
Suddenly one object begins hurtling down the track at near light speed. What is the speed of light as measured from that moving object? In “American standard version”, 186,000mps.
What does the speed of light measure from the object that hasn’t moved at all? Same speed.
However, the light from the moving object will be altered in relation to the stationary object. It will move in exact proportion to the speed of the moving object, so that the relationship between the two lights can be measured in terms of the speed at which the moving object is traveling. Even though light is measured the same for both moving and non-moving object, the relationship between the two lights can be determined by the change created in the movement of one object.
If it moves at 180,000mps, the rate of change between the two will be 180,000mps. While both speeds are measured the same, the rate of change between the two will be 6,000mps, in accordance with the inertial frames between the moving and non-moving object.
So, we’re not talking about a speed which is absolute in all frames, but a speed which is measured according to different inertial frames, and will measure 186,000mps from all such frames.
If light beams from an object moving at 180,000mps, the light itself will still measure at 186,000mps from that object. The only measurable difference between the two would be in terms of the inertial frame of each body. The speed of light, therefore, is subject to every inertial frame of reference for its position in relation to each frame.
In other words, the movement of light in relation to an inertial frame would function just as the pebble dropped from a moving train onto the ground, only the difference is negligible due to the “absolute” speed of light in relation to all inertial frames.
So, back to the example of two objects on parallel tracks in deep space. Einstein pointed out that light is “bent” in a gravitational field. If the moving object were moving at a constantly accelerating pace this would be the same as a gravitational field, and would affect light according to rate of force created by the acceleration.
The moving object slides down the track, and crosses the line connecting the two tracks at a ninety degree angle. When it hits that line, it automatically turns on a powerful light that is aimed at the parallel track at a ninety degree angle . At the same instant the light is turned on, a stopwatch signals the instant the light is turned on, and the message is sent at he speed of light to the parallel track, where you are waiting.
At the instant your sensor receives the message, it also clicks a stopwatch registering the time received. Obviously there will be a delay between the time sent and the time received, limited by light speed itself.
But if the constantly accelerating object created a gravitational field, that light sent at the instant the light was turned on would be “bent’ by the field of gravity, which would indicate a discrepancy between the time the light turned on,m the time the message was received, and the perceived position of the light to our senses.
If the light is “bent” by the gravitational field, we would see it at the same place as the time registered by the reception of the message, but not at the time the message was sent. Our sight would register a delay corresponding to the time the message was received, not the time the message was sent, and the position of the light we see would be behind the actual position from the source according to what we see.
The amount that the light is “bent” by the gravitational field would correspond to an adjustment of light between the two tracks, in which the speed of light from one is stationary in relation to the one that is moving. Is light “bent”, or is it “slowed” to accommodate the force of gravity?