Question

Particles of light have no mass. Does the Sun's mass change as a result of all the light it emits? Explain.

Short answer

Yes, the Sun's mass decreases over time due to the emission of light. Although the light particles (photons) themselves are massless, they carry away energy, which is equivalent to mass according to Einstein's theory of relativity.

Step-by-step solution

Understand the Chief Concepts

We must first understand the basics - light is composed of particles called photons, which are massless; however, they do carry energy. This is vital because, according to Einstein's theory of relativity, energy has mass in a manner of speaking. Einstein's equation \(E = mc^2\) articulates this relationship, where E is the energy, m is the mass and c is the speed of light.

Apply the Concepts to the Sun

We should then apply this knowledge to the sun. The sun emits countless photons every moment, and every photon carries away a bit of energy. Because energy 'has mass', this translates to a loss of mass for the sun.

Conclusion

In answering the original question, we can deduce that even though the photons themselves are massless, the energy they carry away still results in a decrease in the sun's mass over time.

Key concepts

Physics of Light

The physics of light, often referred to as optics, is a fundamental branch of physics that deals with the properties and behavior of light. Light travels at an enormous speed of approximately 299,792 kilometers per second, which is the constant denoted by 'c' in various physics equations. When we discuss light in a particle context, we refer to photons, which are the basic units of light.

Photons have several unique properties: they are massless, carry energy, and travel at the speed of light in a vacuum. Despite their lack of mass, the energy a photon carries can exert pressure (known as radiation pressure) and can have significant effects when absorbed or emitted by objects, such as the Sun emitting light and emitting energy in the process.

Photons

Photons are the quantum mechanical packets of light, pivotal to understanding modern physics. They are always in motion and, as mentioned, lack rest mass. Despite this, photons have momentum and are key carriers of electromagnetic force. This is particularly important because when we talk about light energy, we are essentially discussing the energy of photons.

Under the quantum theory framework, photons are absorbed or emitted by electrons in atoms, leading to various phenomena including the emission of light from stars like our Sun. A photon's energy is directly proportional to its frequency and is given by the formula: \( E = h u \), where 'E' is energy, \( u \) is frequency, and 'h' is Planck's constant. This relationship underscores the dual wave-particle nature of light.

Einstein's Theory of Relativity

Einstein's theory of relativity revolutionized our understanding of physics, particularly with the mass-energy equivalence principle embodied in the famous equation \( E=mc^2 \). This equation suggests that mass and energy are two sides of the same coin and can be converted into each other.

This notion defies classical mechanics and implies that even massless particles, such as photons, can have an equivalent mass based on the energy they carry. Thus, when we say photons are 'massless', we are referring to rest mass—they still contribute to the total energy, and therefore 'mass', of a system from a relativistic viewpoint. Relativity thus allows us to comprehend how emitting light, which carries energy, can affect the mass of celestial bodies like the Sun.

Conservation of Mass-Energy

The conservation of mass-energy is a principle stating that within a closed system, the total amount of mass and energy remains constant over time. Mass can be converted into energy and vice versa, but the total conserved quantity doesn't change. This conservation law is foundational in all of physics and allows us to predict and understand complex systems.

Regarding our celestial example, as the Sun emits photons, it is effectively emitting energy. Since energy is equivalent to mass, this emission results in a reduction of the Sun's mass over time. Yet, in the grand scheme of the cosmos, the total mass-energy of the system remains conserved, which is a profound insight for astrophysics and cosmology alike. These conservation principles remind us that the Universe is a finely balanced space, where everything from the tiniest particle to the largest star is interconnected.