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

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Discussion Overview

The discussion centers around the reasons why Einstein used the speed of light in the equation E=mc². Participants explore the implications of this choice, its derivation, and whether the speed of light is merely a constant or has deeper significance in the context of relativity and energy-mass equivalence.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about why Einstein used the speed of light in E=mc², questioning if it is simply a constant or if it relates to the idea that nothing can travel faster.
  • Another participant suggests that the connection follows from the derivation of the equation, implying a straightforward relationship without delving into quantum physics.
  • A later reply provides a historical context, mentioning Einstein's 1905 paper and explaining a derivation involving the conservation of energy and the emission of light, while noting that E=mc² can also be derived without reference to light.
  • It is mentioned that the constant c can be interpreted as the maximum speed of causality rather than strictly the speed of light.
  • One participant acknowledges the clarity gained from the summary of Einstein's argument provided in the discussion.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding and interpretation regarding the use of the speed of light in E=mc². There is no consensus on whether the speed of light is merely a constant or has a more profound significance in the derivation and implications of the equation.

Contextual Notes

The discussion reflects a range of interpretations and assumptions about the derivation of E=mc², including the role of light and the concept of causality. Some participants reference specific historical texts and derivations, which may not be universally agreed upon.

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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