Is this explanation of E=mc^2 correct or incorrect and why?

In summary, the explanation of E=mc^2 on pbs.org is that when converting matter to pure energy, the resulting energy moves at the speed of light, which is why the mass is multiplied by c^2. This is due to the concept of time as a dimension, where matter that is not stationary moves in both space and time directions. However, this explanation may be oversimplified and not entirely accurate.
  • #1
jason392
1
0
Hello,

I came across the following explanation of E-mc^2 on pbs.org:

"So why would you have to multiply the mass of that walnut by the speed of light to determine how much energy is bound up inside it? The reason is that whenever you convert part of a walnut or any other piece of matter to pure energy, the resulting energy is by definition moving at the speed of light. Pure energy is electromagnetic radiation—whether light or X-rays or whatever—and electromagnetic radiation travels at a constant speed of roughly 670,000,000 miles per hour."

Link: http://www.pbs.org/wgbh/nova/einstein/legacy.html" [Broken]

I've never heard this explanation before and it seems suspicious to me. It's as if the author is implying that the Newtonian equation for kinetic energy, E=mv^2/2, applies to something that is moving at the speed of light, and substitutes c for v, but doesn't divide by 2. So does the given explanation constitute one of the correct ways of looking at the meaning of E=mc^2, or is it only partially correct, or incorrect entirely?
 
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  • #2
It's a bit of a hand wavy explanation but its not totally wrong. If you think of time as a dimension then you could explain it as follows. Imagine that all matter and energy moves at a speed c but in different directions in space and in time. E=m c^2 applies only when the mass is stationary hence its only moving in the time direction at a speed c. A photon on the other hand moves only in the space direction and hence moves at c in space. To check this makes sense you can note that for a photon the time doesn't change due to time dilation. Matter that is not stationary will move in a direction that is partly spacelike and partly timelike(think of it at an angle to the time and space axes).
 
  • #3



The explanation provided on pbs.org is partially correct but also somewhat misleading. While it is true that converting matter into energy results in energy that is moving at the speed of light, the equation E=mc^2 is not derived from the Newtonian equation for kinetic energy.

E=mc^2 is a fundamental equation in Einstein's theory of special relativity, and it relates the amount of energy (E) to the mass (m) of an object and the speed of light (c). It is not simply a substitution of c for v in the kinetic energy equation.

Another issue with the given explanation is that it states that "pure energy is electromagnetic radiation." While electromagnetic radiation is one form of energy, there are other forms as well, such as nuclear energy or thermal energy. So, the statement that all energy is electromagnetic radiation is not entirely accurate.

In conclusion, while the explanation on pbs.org does touch on some aspects of E=mc^2, it is not a complete or entirely accurate explanation of the equation. It is important to understand the underlying principles of special relativity and the context in which the equation was derived in order to fully grasp its meaning.
 

1. Is E=mc^2 a correct explanation?

Yes, E=mc^2 is a correct explanation. It is a fundamental equation in physics that relates mass and energy.

2. How was E=mc^2 derived?

E=mc^2 was derived by Albert Einstein in his theory of special relativity. He proposed that mass and energy are equivalent and can be converted into one another.

3. What is the significance of E=mc^2?

E=mc^2 is significant because it revolutionized our understanding of the relationship between mass and energy. It also plays a crucial role in modern physics and has been verified through numerous experiments.

4. Can E=mc^2 be applied to all objects?

Yes, E=mc^2 can be applied to all objects with mass. However, it is most noticeable in objects with a large mass or traveling at high speeds.

5. Is E=mc^2 the complete equation for mass-energy equivalence?

No, E=mc^2 is not the complete equation for mass-energy equivalence. It is a simplified version that only applies to objects at rest. The complete equation, which takes into account objects in motion, is E^2 = (mc^2)^2 + (pc)^2, where p is momentum.

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