Special relativity and rest mass

In summary, the conversation discusses the formula for the relativistic energy of a particle and the consequences of a particle traveling at the speed of light. It is noted that while the equation E = (m²c⁴ + p²c²)^(1/2) correctly gives infinite energy for a particle at the speed of light, the method used to reach this result is incorrect. It is also questioned whether it is physically possible for a particle to have infinite energy.
  • #1
Qyzren
44
0
What is the rest mass m of a particle traveling with the speed of light in the laboratory frame?

i believe m = (E² - (pc)²)^.5 / c² is the correct equation to use?
as velocity goes up, so does energy and momentum? so when velocity is at speed of light, E = infinity and momentum = infinity? so we have infinity - infinity on the numerator? so this gives mass = 0? is any of this correct? thanks for help.
 
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  • #2
The answer turns out to be correct, but the method is not. For one thing, you can not simply subtract off infinities in the manner that you just did.

What is the formula for the relativistic energy of a particle of rest mass, m? Write this down. Now if v=c, this gives you the result you (incompletely) stated above, namely that E = infinity, unless _______ (fill this in).

Ask yourself: Is it physical for a particle to be given an infinite amount of energy?
 

1. What is special relativity and how does it relate to rest mass?

Special relativity is a theory developed by Albert Einstein that describes the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, and that the speed of light is constant regardless of the observer's frame of reference. Rest mass is the measure of an object's mass when it is at rest, and it plays a crucial role in special relativity as it is used to calculate an object's energy and momentum.

2. How does special relativity explain the concept of mass-energy equivalence?

Special relativity explains mass-energy equivalence through its famous equation E=mc², where E represents energy, m represents rest mass, and c represents the speed of light. This equation shows that mass and energy are two forms of the same thing and can be converted into each other. This concept was first proposed by Einstein and has been proven through experiments such as nuclear reactions and particle accelerators.

3. Can an object with rest mass travel at the speed of light?

No, according to special relativity, an object with rest mass cannot travel at the speed of light. As an object approaches the speed of light, its mass increases and requires an infinite amount of energy to reach the speed of light. Therefore, it is impossible for an object with rest mass to travel at the speed of light.

4. How does special relativity affect time dilation and length contraction?

Special relativity predicts that time and space are relative and can be affected by an object's velocity. This means that time can appear to pass slower for a moving object compared to a stationary one, a phenomenon known as time dilation. Similarly, the length of an object can appear shorter in the direction of its motion, a phenomenon known as length contraction.

5. What are some real-world applications of special relativity and rest mass?

Special relativity and rest mass have many real-world applications, including GPS systems, nuclear power plants, and medical imaging devices. GPS systems use special relativity to account for the time dilation of satellites in orbit, while nuclear power plants use mass-energy equivalence to generate energy through nuclear reactions. Medical imaging devices such as PET scans and MRI machines also utilize special relativity to accurately measure an object's mass and energy.

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