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Chapter 5: Problem 21

Given the fact that light travels at \(c,\) can it have mass? Explain.

Short Answer

Expert verified
In conclusion, light does not have a rest mass (invariant mass) but has energy and momentum, which can be thought of as having a relativistic mass (\(m_r\)). Light can travel at speed c because its particles (photons) are massless. If light were to have mass, it couldn't travel at the speed of light due to the principles of special relativity, and it would require infinite energy to reach the speed of light, which is impossible.

Step by step solution

01

Understanding Special Relativity

According to Einstein's theory of special relativity, there is a cosmic speed limit for particles with mass; they can never reach the speed of light in a vacuum (denoted as c). As an object with mass accelerates closer to the speed of light, its mass increases and the energy required to continue accelerating also increases. As a result, an infinite amount of energy would be needed to accelerate an object with mass to the speed of light, which is not possible.
02

Analyzing Photons

Light is made up of particles called photons, which have no rest mass. They are massless particles because they always travel at the speed of light, c. Photons are unique in this aspect because they are the only known massless particles that carry energy and momentum.
03

Mass-energy Equivalence

According to Einstein's famous mass-energy equivalence formula \(E=mc^2\), energy and mass are related. If an object has energy, it can be thought of having an equivalent mass given by the formula. For light (photons), the energy is given by the formula \(E=hf\), where h is the Planck constant, and f is the frequency of light. Although photons are massless, they have energy and momentum. So, they still "behave" as if they have a relativistic mass (\(m_r\)) given by the formula: \(m_r = \frac{E}{c^2}\)
04

Conclusion

In conclusion, light itself does not have a rest mass (invariant mass), but it does have energy and momentum, which can be thought of as having a relativistic mass (\(m_r\)). The reason why light can travel at speed c is that its particles (photons) are massless. If light were to have mass, it could not travel at the speed of light as per the principles of special relativity, and it would require an infinite amount of energy to accelerate it to the speed of light, which is not possible.

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Most popular questions from this chapter

(a) What is \(\gamma\) if \(v=0.100 c ?\) (b) If \(v=0.900 c ?\)

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Which of Einstein's postulates of special relativity includes a concept that does not fit with the ideas of classical physics? Explain.

A spacecraft starts from being at rest at the origin and accelerates at a constant rate \(g\), as seen from Earth, taken to be an inertial frame, until it reaches a speed of \(c / 2\). (a) Show that the increment of proper time is related to the elapsed time in Earth's frame by: \(d \tau=\sqrt{1-v^{2} / c^{2}} d t\) (b) Find an expression for the elapsed time to reach speed C/2 as seen in Earth's frame. (c) Use the relationship in (a) to obtain a similar expression for the elapsed proper time to reach \(c / 2\) as seen in the spacecraft, and determine the ratio of the time seen from Earth with that on the spacecraft to reach the final speed.

Suppose an astronaut is moving relative to Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his clocks to have slowed? (b) What change in the rate of earthbound clocks does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between two stars that lie in the direction of his motion? (e) Do he and an earthbound observer agree on his velocity relative to Earth?
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