Why does E=MC^2 require the speed of light and why is it squared?

In summary, The equation E=MC^2 is a fundamental relationship in physics that explains the relationship between energy and mass. It is derived from the concept that all physical reality is made up of the electromagnetic field. The speed of light, being the only absolute velocity in the universe, plays a crucial role in this equation. Without it, energy and mass would not have consistent units, making the equation nonsensical. The squared term in the equation is due to energy being equivalent to mass times a squared velocity. While there are still unanswered questions about this concept, it has been proven to hold true through various experiments.
  • #1
KingNothing
881
4
Hi. I understand the equation, but I don't understand logically in my head why it is that way. Maxwell's equations, etc show it mathematically but I'm looking for a logical explanation of why it is this way. Like for instance, the logical connection for F=MA would be "more force is needed to move a bigger object, or to move it faster."...now, as far as E=MC^2...

What I know so far is this:
energy should be directly proportional to mass, because something of more mass should release more energy. The speed of light fits in because it's sort of a measure of pure energy that's already been converted into mass completely.

However, I don't understand:
Why the speed? How does speed fit in?
Why squared?

Now, I know you all could prove it with maxwell's equations and such, but I'm not asking for proof, I'm asking for a logical explanation so I can see in my head why it works this way.
 
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  • #2
All physical equations must have consistent units. The equation "E = m" does not have consistent units, because energy and mass are not the same quantity. To make this equation sensible, you must provide some kind of conversion factor.

You are no doubt aware that the Newton, the SI unit of force, is defined as

[tex]\textrm{force (N)} = \frac{kg \cdot m}{s^2}[/tex]

Energy can also be found by integrating a force over a distance:

[tex]\textrm{energy (J)} = F \cdot d = \frac{kg \cdot m^2}{s^2}[/tex]

As you can see, energy has the same units as mass times a squared velocity. So why is that velocity the speed of light? It's the only absolute velocity in the universe, measured the same by all observers, no matter how they are moving.

- Warren
 
  • #4
There's a 100 year old proposition that explains why E=mcc; that proposition has never been put to rest. It is:

The final irreducible constituent of all physical reality is the electromagnetic field.

Understand that and you will understand all of the "WHY" questions we can't answer with our present day assumptions.
 
  • #5
Vern said:
The final irreducible constituent of all physical reality is the electromagnetic field.
.

I'm interested in this. Can you provide a reference which discusses this concept? Guess I felt there was no irreducible constituent so I'd like to know about it.
Thanks
Salty
 
  • #6
That is a quote from Einstein; I found it in one of Einstein's articles in "The World of Physics", Weaver. I can look it up if there is any question about its accuracy.

Einstein was explaining how the theories of Maxwell, (Not Maxwell's EM theory) Lorentz, etc had basic flaws. He couldn't find a basic flaw in "final irreducible ..." concept but never used it in his work as far as I can understand.
 

Related to Why does E=MC^2 require the speed of light and why is it squared?

1. What is the meaning of E=MC^2?

E=MC^2 is a famous equation developed by Albert Einstein that relates mass (M) to energy (E) and the speed of light (C). It states that energy and mass are equivalent, and that a small amount of mass can be converted into a large amount of energy.

2. How is E=MC^2 logically connected?

E=MC^2 is logically connected because it is derived from the principles of special relativity, which states that the laws of physics are the same for all observers in uniform motion. This principle leads to the conclusion that the speed of light is constant for all observers, and from there, Einstein was able to develop the equation.

3. What is the significance of E=MC^2 in modern science?

E=MC^2 is significant in modern science because it revolutionized our understanding of energy and mass. It also paved the way for advancements in nuclear energy, nuclear weapons, and our understanding of the universe.

4. How is E=MC^2 applied in everyday life?

E=MC^2 has practical applications in everyday life, such as in medical imaging techniques like PET scans, which use the equation to convert the energy emitted from radioactive isotopes into images of the body. It is also used in nuclear power plants to generate electricity.

5. Are there any limitations to E=MC^2?

While E=MC^2 is a foundational equation in modern physics, it does have its limitations. It only applies to objects moving at constant speeds and does not account for factors such as gravity and quantum mechanics. Additionally, it only applies to situations where mass is converted to energy, and not vice versa.

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