Light Direction in Different Frames: Resnick & Halliday

[Gireesh]

I am posting a diagram directly from textbook of Resnick and Halliday. In second part of the diagram the assumption is that the light will travel with an angle in the direction of the velocity of the moving reference frame. Is that a valid assumption? Won't they have to direct the light beam such that the light will catch up to the mirror which is already moving ?

 

[Nugatory]

I am posting a diagram directly from textbook of Resnick and Halliday. In second part of the diagram the assumption is that the light will travel with an angle in the direction of the velocity of the moving reference frame. Is that a valid assumption? Won't they have to direct the light beam such that the light will catch up to the mirror which is already moving ?

The light does indeed make a different angle in different frames.

The easiest way of seeing this is to imagine that I am standing on the deck of a ship, bouncing a ball straight up and down, while you are standing on the land watching the ship move by. We will both agree that the ball leaves leaves my hand, then bounces off the deck and back into my hand. However, we will see the path of the ball making a different angle with the deck: I will see it as straightup and down while you will see the ball following a zigzag path. It's the same thing with the light signal in the light clock.

If we actually go through the (somewhat non-trivial) problem of calculating what the bounce angle of the ball should be... We'll realize that we're solving different problems so it's not surprising that we get different answers. I'm calculating the angle the ball makes when it hits a stationary deck; you're calculating the angle it makes when it hits a moving deck.

 

[PAllen]

If you are on a train and bounce a ball, to you, the ball goes up and down perpendicular to the floor. Someone watching from the tracks sees the ball moving at an angle so as keep up with you and the train. The same is true for light - if, for one observer, it passes from one mirror to another, it will do so for any other observer.

Another way to look at this is to think about a laser pointer. If I am stationary with respect to a laser pointer, its beam moves parallel to its length. If the laser pointer is moving relative to me (e.g. orthogonally to its length), the beam is not parallel to its length, as observed by me (e.g. made visible by mist that is stationary with respect to me).

 

[ghwellsjr]

I am posting a diagram directly from textbook of Resnick and Halliday. In second part of the diagram the assumption is that the light will travel with an angle in the direction of the velocity of the moving reference frame. Is that a valid assumption? Won't they have to direct the light beam such that the light will catch up to the mirror which is already moving ?

Something is causing the beam in the first diagram to go straight up such as a laser. In the second diagram, as the light is moving upwards through the laser, the laser itself is moving so it is traveling on a diagonal path before it leaves the laser and it just continues in a straight line along the same path.

 

[Gireesh]

Thanks for the explanations .

To Nugatory: Isn't that the ball is behaving like that because of the inertia. And my understanding was that inertia is a property of objects with mass. Light which does not have any mass should not have inertia right?

To Pallen : thanks for the LASER example. Let us imagine I am in a train which has a breadth of c (3x 10 ^8m), which has glass windows except for a laser w source on my side and a mirror (tiny) exactly on my opposite side . Now I am sending a small pulse of LASER towards mirror lasting 10 nanosecond (length of the laser pulse will be 10^-9 x10x 3x10^8 = 3 meters). Now if my train is moving at a speed of 100 m/s . In that case the light pulse that I sent will miss the mirror by the time it reach the other end of the train .. right? Am I doing anything wrong ?

 

[Nugatory]

To Nugatory: Isn't that the ball is behaving like that because of the inertia. And my understanding was that inertia is a property of objects with mass. Light which does not have any mass should not have inertia right?

Inertia (and conservation of energy, and conservation momentum, and the elasticity of the ball, and probably some other stuff too) explains the trajectory of the ball as calculated in either frame. When you do that calculation you find that the angles are frame-dependent.

The laser pulse that PAllen describes isn't governed by inertia of course; but it is governed by the laws of electricity and magnetism, and if you're willing to grovel through the calculations using them, you will get a result analogous to the result with the ball. The angle at which the light pulse leaves the laser and the angle at which is reflected back from the mirror are different in a frame in which the laser and mirror are moving and a frame in which the laser and mirror are at rest. Again, the angles are frame-dependent.