Question

In a television picture tube, a beam of electrons is sent from the back to the front (screen) by an electron gun. When an electron strikes the screen, it causes a phosphor to glow briefly. To produce an image across the entire screen. the beam is electrically deflected up and down and left and right. The beam may sweep from left to right at a speed greater than \(c\). Why is this not a violation of the claim that no information may travel faster than the speed of light?

Short answer

In this case, the universal speed limit is not violated because it refers to the transfer of information, not the physical movement of objects. Even though the electron beam moves across the screen at a speed greater than c, the image displayed - which is the actual information transferred - does so at or below the speed of light.

Step-by-step solution

Understand the function of an electron gun

An electron gun in a television screen emits a beam of electrons. These high-speed electrons hit a phosphor coated screen causing portions of the screen phosphor to illuminate, creating an image.

Understand the motion of the electron beam

The electron beam moves across the screen, being deflected up and down, and left and right. It creates an image as it moves quickly enough to cover the entire screen before the phosphors stop glowing from its previous pass.

Understand the speed of the electron beam

In theory, the electron beam moves at a speed faster than the speed of light (\(c\)). However, this speed doesn’t refer to the movement of a singular electron, but the movement of the next point on screen that the beam hits, which is driven by electrical deflections.

Realize the speed restriction does not apply to the electron beam

The claim that “no information may travel faster than the speed of light” does not apply to the motion of electron beams in this context. The reason is that the phosphors glow when they are excited by electrons and emit light, and the whole picture appears on the screen because electrons have excited different phosphors at different points on screen. But light from those phosphors reach our eyes at the speed of light or less. Therefore, the true information transfer – the image created by glowing phosphors - obeys the universal speed limit.

Key concepts

Television Picture Tube

The television picture tube, often known as a cathode-ray tube (CRT), is a fascinating piece of technology that functions thanks to complex electron beam dynamics. The process begins with an electron gun at the back of the tube, emitting a stream of electrons, which are tiny negatively charged particles. These electrons are accelerated towards the screen, which is coated with a phosphorescent material. The purpose of moving the electrons rapidly is to form images on the screen.

To successfully create an image, the electron beam needs to be highly controlled. This control is achieved through magnetic or electrical means that deflect the beam. Deflection is necessary because the beam must be able to traverse the entire screen quickly. By doing this, it interacts with every pixel to produce the full picture display. The technique utilizes a sweeping motion from left to right and top to bottom in a rapid sequence. This speed is so fast that it may seem like the beam travels faster than the speed of light; however, it's important to distinguish the beam's rapid deflection from the speed of individual electrons.

Phosphor Excitation

Phosphor excitation is the key to creating visible images on a CRT screen. When the electron beam hits the screen, it excites the phosphor particles coating it. These phosphors are special chemical compounds that emit light when energized.

The process works like this: electrons collide with the phosphor on the screen, transferring energy. This energy excites the phosphor's atoms, and as these excited atoms return to their lower energy state, they release light. This emitted light is what forms the visible image.

• Different phosphors emit different colors, which is how a color CRT can display colorful images.
• The longevity of the glow is short, so the electron beam must continually refresh the phosphor for sustained image display.

The refreshing happens fast enough that your eye does not notice the flickering, offering a seamless viewing experience.

Speed of Light

The speed of light, denoted as \( c \), is a fundamental constant in physics, precisely 299,792,458 meters per second in a vacuum. It's crucial to understand this because it sets the ultimate speed limit for information transfer across the universe.

In the context of a television picture tube, the electron beam's traversal across the screen might exceed this speed, not in terms of physical motion, but in terms of how quickly the electron impacts are sweeping across. This can be confusing because light from excited phosphors is the ultimate source of information reaching our eyes.

The key to this seeming paradox is recognizing that while the electron sweep appears fast, no individual electron is moving faster than light. Each electron travels at a high speed, but the perceived briskness results from successive electrons hitting new target areas on screen. Thus, no actual information or physical matter moves between two points faster than the speed of light.