# Understanding Sideways Momentum in Heisenberg's Thought Experiment

• FeDeX_LaTeX
In summary, The book describes Werner Heisenberg's thought experiment about a particle scattering electromagnetic radiation with a specific wavelength. To enter the microscope lens, the scattered photons must have a 'sideways momentum' between - h/lambda * sin alpha and + h/lambda * sin alpha. This refers to the component of total momentum in the sideways direction and is different from ordinary momentum. An analogy to something more familiar would be helpful. Additionally, the uncertainty of a particle is represented by the equation delta x = lambda/sin alpha. Is there a geometrical reason for this?
FeDeX_LaTeX
Gold Member
Hello;

I was reading a book that described Werner Heisenberg's thought experiment. It said that, when a particle scatters electromagnetic radiation with wavelength $$\lambda$$, for the scattered photons to enter the lens of the microscope, they must have a 'sideways momentum' between $$-\frac{h}{\lambda}\sin\alpha$$ and $$+\frac{h}{\lambda}\sin\alpha$$. My question is, what is meant by 'sideways momentum' and how is it any different to ordinary momentum? Can anyone give an analogy to something that I might be more familiar with?

Also, is there a geometrical reason why, for the uncertainty of a particle;

$$\delta x = \frac{\lambda}{\sin\alpha}$$

Thanks.

Hello FeDeX_LaTeX!

It just means the component of the total momentum in the sideways direction.

## 1. How does Heisenberg's thought experiment explain the concept of sideways momentum?

Heisenberg's thought experiment, also known as the uncertainty principle, states that it is impossible to know both the position and momentum of a particle with absolute certainty. This means that if we know the position of a particle with high accuracy, its momentum becomes highly uncertain. This uncertainty in momentum can manifest as sideways momentum, as the particle can potentially move in any direction with varying velocities.

## 2. What is the significance of sideways momentum in Heisenberg's thought experiment?

Sideways momentum is significant because it demonstrates the limitations of our ability to measure and predict the behavior of particles at a quantum level. It also highlights the fundamental uncertainty and randomness that exists in the behavior of particles, challenging our traditional understanding of cause and effect.

## 3. How does this thought experiment relate to the broader concept of quantum mechanics?

Heisenberg's thought experiment is a cornerstone of quantum mechanics, which studies the behavior of particles at a subatomic level. It highlights the fundamental principles of uncertainty and probability that govern the behavior of particles, and has been crucial in developing our understanding of the quantum world.

## 4. Can sideways momentum be observed in real-world experiments?

Yes, sideways momentum has been observed in various experiments, such as the double-slit experiment, where particles exhibit wave-like behavior and can be observed to have sideways momentum as they pass through the slits. This phenomenon has also been observed in particle accelerators, where particles can collide at different angles due to their sideways momentum.

## 5. How does the concept of sideways momentum impact our understanding of the universe?

Sideways momentum, along with other principles of quantum mechanics, has revolutionized our understanding of the universe and has led to significant technological advancements. It challenges our traditional, deterministic view of the world and has opened up new possibilities for technology, such as quantum computing, that utilize the principles of uncertainty and probability.

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