Why Did Einstein Use the Speed of Light in E=mc²?

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SUMMARY

Einstein's use of the speed of light in the equation E=mc² stems from his 1905 paper "Does the inertia of a body depend upon its energy content?" where he demonstrated that mass and energy are equivalent. The derivation involves analyzing the behavior of an object emitting light in different frames of reference, leading to the conclusion that a loss of energy results in a decrease in mass by E/c². While the constant c is associated with the speed of light, it can also be interpreted as the maximum speed of causality, allowing for derivations of E=mc² without direct reference to light.

PREREQUISITES
  • Understanding of Einstein's 1905 paper "Does the inertia of a body depend upon its energy content?"
  • Familiarity with the concept of frames of reference in physics.
  • Basic knowledge of mass-energy equivalence.
  • Awareness of Lorentz transformations and their implications.
NEXT STEPS
  • Read Einstein's original paper "Does the inertia of a body depend upon its energy content?" for foundational insights.
  • Study the Lorentz transformations to understand their role in special relativity.
  • Explore the concept of the mass-energy four-vector and its implications in modern physics.
  • Investigate the interpretation of the constant c as the maximum speed of causality in theoretical physics.
USEFUL FOR

Students of physics, educators, and anyone interested in the foundational concepts of relativity and mass-energy equivalence will benefit from this discussion.

alex.cordero
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I'm 3/4 of the way through David Bodani's, E=mc2: A Biography of the World's Most Famous Equation book and I'm really enjoying it. Thanks to this book, I finally understand that "e=m" and also understand why "C^2", but I still can't understand why Einstein used the speed of light to connect the two?

Is it just a constant? Did he use "c" because there is nothing faster?
 
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alex.cordero said:
Thank you. Can you enlighten me as to where I should have posted this?

Relativity
 
Frame Dragger said:
Relativity

Perfect, thank you.
 
alex.cordero said:
Perfect, thank you.

No sweat, enjoy PF!
 
FAQ: Where does E=mc2 come from?

Einstein found this result in a 1905 paper, titled "Does the inertia of a body depend upon its energy content?" This paper is very short and readable, and is available online. A summary of the argument is as follows. Define a frame of reference A, and let an object O, initially at rest in this frame, emit two flashes of light in opposite directions. Now define another frame of reference B, in motion relative to A along the same axis as the one along which the light was emitted. Then in order to preserve conservation of energy, we are forced to attribute a different inertial mass to O before and after it emits the light. The interpretation is that mass and energy are equivalent. By giving up a quantity of energy E, the object has reduced its mass by an amount E/c2.

Although Einstein's original derivation happens to involve the speed of light, E=mc2 can be derived without talking about light at all. One can derive the Lorentz transformations using a set of postulates that don't say anything about light (see, e.g., Rindler 1979). The constant c is then interpreted simply as the maximum speed of causality, not necessarily the speed of light. Constructing the mass-energy four-vector of a particle, we find that its norm, E2-p2c2, is frame-invariant, and can be interpreted as m2c4, where m is the particle's rest mass. In the case where the particle is at rest, p=0, and we recover E=mc2.

A. Einstein, Annalen der Physik. 18 (1905) 639, available online at http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51
 
bcrowell said:
FAQ: Where does E=mc2 come from?
Einstein found this result in a 1905 paper, titled "Does the inertia of a body depend upon its energy content?" This paper is very short and readable, and is available online. A summary of the argument is as follows.
Thank you for your summary. It's more clear now.
 

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