# Light Direction in Different Frames: Resnick & Halliday

• Gireesh
In summary, the conversation discusses the behavior of light in different frames of reference, particularly in the context of a moving train with a laser and mirror. It is explained that the angle of the light beam is dependent on the frame of reference and not just the direction of the laser. The concept of inertia is also brought up, with the understanding that it affects the trajectory of objects but not necessarily light. The conversation ultimately concludes that the behavior of light is governed by the laws of electricity and magnetism and is frame-dependent.
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 ?

#### Attachments

• Relative_Motion.png
63.8 KB · Views: 496
Gireesh said:
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.

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).

Gireesh said:
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.

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 ?

Gireesh said:
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.

## 1. What is "light direction" in the context of Resnick & Halliday?

In Resnick & Halliday, "light direction" refers to the direction in which light rays are traveling or being emitted in a given frame of reference. This can be affected by factors such as the motion and orientation of the frame, and can impact the observed properties of light such as its frequency and wavelength.

## 2. How does light direction change in different frames according to Resnick & Halliday?

According to Resnick & Halliday, light direction can change in different frames due to the principle of relativity. This means that the observed direction of light can vary depending on the relative motion and orientation of the observer and the light source. In other words, the direction of light is not absolute and can be affected by the frame of reference.

## 3. Why is understanding light direction important in physics?

Understanding light direction is important in physics because it allows us to accurately describe and predict the behavior of light in different situations. This is crucial in fields such as optics and relativity, where the direction of light can have a significant impact on the observed phenomena. Additionally, understanding light direction is fundamental to our understanding of the nature of light and its properties.

## 4. How is light direction related to the speed of light?

The speed of light is a fundamental constant in physics and is related to the direction of light. According to Einstein's theory of relativity, the speed of light is constant in all frames of reference, regardless of their motion or orientation. This means that the direction of light can affect its speed, but the speed of light itself does not depend on the observer's frame of reference.

## 5. Can the direction of light be changed?

Yes, the direction of light can be changed through various phenomena such as reflection, refraction, and diffraction. These processes involve the interaction of light with different materials or surfaces, causing it to change direction. Additionally, the direction of light can also be affected by the motion and orientation of the observer or the light source, as explained by the principle of relativity.

• Special and General Relativity
Replies
51
Views
3K
• Special and General Relativity
Replies
15
Views
624
• Special and General Relativity
Replies
28
Views
2K
• Special and General Relativity
Replies
20
Views
856
• Special and General Relativity
Replies
2
Views
632
• Special and General Relativity
Replies
45
Views
3K
• Special and General Relativity
Replies
11
Views
1K
• Special and General Relativity
Replies
14
Views
2K
• Special and General Relativity
Replies
35
Views
366
• Special and General Relativity
Replies
26
Views
644