Interesting Coincidence with Classical/Modern View of Mass and Energy

[Cadaei]

Has anyone ever noticed that, even in classical physics, energy is shown as a scalar multiple of mass?

For example, consider the joule;

1 J = 1 kg*(m/s)^2

If you consider the units of motion (m/s) to be a vector quantity, then squaring such a vector would be interpreted as a dot product that produces a scalar.

1 J (energy) = [mass in kg]*[scalar speed]

Which is eerily similar to E=MC^2. Thus, whether anyone in the past realized it or not, did they inadvertently stumble on the mass-energy equivalence just by dealing with these units?

 

[A.T.]

The units in a physical formula actually do work out? What a coincidence!

 

[Doc Al]

Creepy!

 

[mfb]

If you set the speed of light to 1, mass and energy have the same units. This is not a coincidence, and shows that the concepts are related in relativity.

If, for some strange reason, nonrelativistic kinetic energy would be something like mv^3, the rest energy of objects should be something like mc^3. But I do not think this would give meaningful physics.

 

[PJC01]

This is a fascinating observation and it does seem to suggest a connection between classical physics and the famous equation E=MC^2. However, it is important to note that the concept of energy has evolved significantly over time and was not always understood or measured in the same way. So while there may be a coincidence in the units of energy and mass, it is not necessarily evidence of a deeper connection between the two concepts.

In classical physics, energy was primarily thought of as the ability to do work, and was measured in units such as joules or foot-pounds. It wasn't until Albert Einstein's theory of special relativity that the concept of energy was expanded to include mass and the famous equation E=MC^2 was derived.

Furthermore, the units of energy and mass in classical physics were not always consistent. For example, in the early 19th century, energy was often measured in units of "calories," which were defined as the amount of energy needed to raise the temperature of one gram of water by one degree Celsius. This unit does not have a direct relationship with mass and speed, as seen in the joule equation.

So while it is interesting to note the similarity in units between energy and mass in classical physics, it is likely just a coincidence and not evidence of a deeper connection. It was only through Einstein's groundbreaking work that we now understand the true relationship between mass and energy.