• snoopies622
In summary, the conversation discusses the relationship between the premises p = \gamma m v, F = \frac {dp}{dt}, and W= \int F dx, and how they lead to dW = mc^2 d \gamma and W = \gamma mc^2 + k, where m is the rest mass and k is a constant of integration. The conversation also addresses the question of why k=0 and concludes that k does not equal 0, but rather represents the negative "rest energy" of the object.
snoopies622
I see how the premises

$$p = \gamma m v$$

$$F = \frac {dp}{dt}$$

and

$$W= \int F dx$$

$$dW = mc^2 d \gamma$$

and therefore

$$W = \gamma mc^2 + k$$

where m is the rest mass and k is a constant of integration. But why do we conclude that k=0?

That constant won't equal 0. (The work done equals the KE, not the total energy.) Assume you start from rest and integrate to speed v.

I get

$$W = \gamma mc^2 - mc ^2 = ( \gamma - 1 ) mc^2$$

so

$$k = -mc^2 \neq 0$$

Since W(v=0) = 0 this is indeed the kinetic energy and not the total energy. Thanks, Doc Al.

Follow-up: Am I to conclude that the constant of integration here represents the (negative) "rest energy" of the object, or is there a better way to arrive at that relationship?

What is the mass-energy relation?

The mass-energy relation, also known as the famous equation E=mc^2, is a fundamental principle in physics that describes the relationship between mass and energy. It states that mass and energy are interchangeable and can be converted into one another.

Who discovered the mass-energy relation?

The mass-energy relation was first proposed by Albert Einstein in 1905 as part of his theory of special relativity. However, it was later refined and fully understood in the context of general relativity.

What is the significance of the mass-energy relation?

The mass-energy relation is significant because it revolutionized our understanding of the universe and paved the way for many groundbreaking discoveries in physics. It also has practical applications, such as in nuclear energy and the development of nuclear weapons.

How is the mass-energy relation used in everyday life?

The mass-energy relation has many practical applications in everyday life, such as in medical imaging technologies like PET scans and MRI machines. It is also used in nuclear power plants to generate electricity.

Is the mass-energy relation proven?

Yes, the mass-energy relation has been extensively tested and proven through various experiments and observations. It is a cornerstone of modern physics and is widely accepted by the scientific community.

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