# Quantized Kinetic Energy of Relativistic Objects

• jrvinayak
In summary, the kinetic energy of an object is quantized, but the energy of a moving object depends on the boundary conditions.
jrvinayak
Hello,

I want to know if energy added to moving objects is quantized. Kinetic energy of an moving object is given as KE = (γ - 1) mc2 , where γ is 1/√(1-v2/c2).

And quantum theory talks about any energy always being quantized. So can the KE in moving objects be quantized?

Hi jrvinayak, welcome to PF!
jrvinayak said:
And quantum theory talks about any energy always being quantized.
This is a very common misconception. Even in quantum mechanics there are some systems where energy is quantized and other systems where the energy is not quantized. One very interesting and simple system is the so-called finite potential well

https://en.wikipedia.org/wiki/Finite_potential_well

This system includes both bound states which are quantized and free states which are not quantized.

vanhees71 and PeroK
I agree with DaleSpam's response. I'd just add that less formally, the "potential well" problem is known as a "particle in a box". You might google for this term. The particle in a box has quantized momentum and energy, but the details depends on the size of the box. Formally, we'd describe this dependence by saying "it depends on the boundary conditions". The free particle that's not confined to a box doesn't have quantized momentum or energy levels. The best forum to ask for further details would be the quantum mechanics forum, it's not really within the scope of GR.

Be, however, warned that "particle in a box" often means the only apparently simpler problem of an infinitely high potential well. However, this is a particularly difficult case, if done mathematically correctly, because for this problem no proper momentum observable exists anymore, but that's a topic belonging more to the quantum-theory forum. The finite-potential well is only a bit more work but has the advantage of having a well-defined realization of the Heisenberg algebra in terms of the wave-mechanics formulation.

## What is quantized kinetic energy?

Quantized kinetic energy refers to the concept that the energy of a moving object is not continuous, but is instead made up of individual packets or "quanta" of energy. This concept is derived from quantum mechanics and is particularly applicable to objects moving at relativistic speeds.

## How is the quantized kinetic energy of relativistic objects different from that of non-relativistic objects?

The quantized kinetic energy of relativistic objects is different from that of non-relativistic objects in that it takes into account the effects of special relativity on the mass and energy of the object. At extremely high speeds, the mass of an object increases and its energy becomes quantized, meaning that it can only exist at specific energy levels.

## What is the formula for calculating the quantized kinetic energy of a relativistic object?

The formula for calculating the quantized kinetic energy of a relativistic object is E = mc^2 / √(1 - v^2/c^2) - mc^2, where E is the energy, m is the mass, c is the speed of light, and v is the speed of the object.

## Can the quantized kinetic energy of a relativistic object ever be zero?

No, the quantized kinetic energy of a relativistic object can never be zero. This is because even at rest, an object still has a mass and therefore has a minimum energy level. Additionally, according to the theory of relativity, an object can never truly be at rest as it is always moving through time.

## What are some real-world applications of understanding quantized kinetic energy of relativistic objects?

Understanding the quantized kinetic energy of relativistic objects is important in many fields, including particle physics, astrophysics, and engineering. It allows us to accurately predict the behavior of particles at high speeds and design technologies that take into account the effects of special relativity, such as particle accelerators and space travel.

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