# Same Link Between Momentum, Energy & Mass

• Islam Hassan
In summary, energy and mass are distinct concepts, with energy being able to be converted to mass and vice versa according to Einstein's formula. However, this does not mean that mass is a condensed form of energy. Similarly, energy and momentum are also distinct concepts, and while they are related in relativity, energy cannot be considered a condensed form of momentum. The concept of intrinsic mass and relative mass also adds to the complexity of this idea.
Islam Hassan
If mass is a condensed form of energy, can we likewise consider that energy is a condensed form (or store) of momentum at the molecular/atomic/particle physics level?

IH

It's not correct to think of mass as a "condensed form of energy." By Einstein's formula, $E=mc^2$, energy can be converted to mass and vice versa. Or, in other words, all mass is associated with some energy. Thus, objects with mass m, have an associated "rest energy" of mc^2. However, this is not the same as saying that mass is a "condensed form of energy."

It is also not correct to say that energy is a "condensed form of momentum." Even at the atomic level, energy and momentum are distinct concepts.

In relativity, energy and momentum are related, both being part of the energy momentum 4-vector, but, this does not mean that energy is "condensed momentum." That statement is nonsensical.

Condensed is a strange way of putting it. it refers to a lot of stuff in a small volume, but what is a lot and what is small?

I think the OP means to refer to intrinsic mass as being entirely a relativistic correction of some sort. In the case of a photon it turns out that the mass is only due to relative motion and the "rest" mass is zero. So the photon has mass, but it is really just energy. This is why physicists are careful to distinguish rest (or intrinsic) mass and relative mass.

So of course it is a common question to ask "Could the rest mass of particles like electrons really just be some hidden motion or aspect of space we don't understand."

## What is the link between momentum, energy, and mass?

The link between momentum, energy, and mass is known as the mass-energy-momentum relationship, which is a fundamental principle in physics. It states that energy and momentum are conserved quantities and that mass is a form of energy. This means that any change in the energy or momentum of a system will result in a corresponding change in its mass.

## How are momentum, energy, and mass related mathematically?

The mathematical relationship between momentum, energy, and mass is expressed through the famous equation E = mc², also known as the mass-energy equivalence equation. This equation was first proposed by Albert Einstein and shows that mass and energy are two forms of the same physical quantity. It states that the energy (E) of an object is equal to its mass (m) multiplied by the speed of light (c) squared.

## What is the significance of the mass-energy-momentum relationship?

The mass-energy-momentum relationship has major implications in the fields of physics, including mechanics, relativity, and quantum mechanics. It helps explain the behavior of particles at high speeds and in extreme conditions, such as those found in nuclear reactions and black holes. It also provides a deeper understanding of the fundamental nature of matter and energy.

## How does the mass-energy-momentum relationship affect everyday life?

The mass-energy-momentum relationship may seem like a concept that only applies to the world of physics, but it actually has real-life applications that impact our daily lives. For example, nuclear power plants rely on the conversion of mass into energy to generate electricity. The relationship also plays a role in medical imaging technologies, such as PET scans, which use the conversion of mass into energy to create images of the body.

## Is the mass-energy-momentum relationship proven to be true?

Yes, the mass-energy-momentum relationship has been extensively tested and has been proven to be accurate. It has been supported by numerous experiments, including the famous atomic bomb tests during World War II. The relationship is also consistent with the principles of conservation of energy and momentum, which have been verified through countless experiments and observations.

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