physics

Hidden momentum

Hidden momentum is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hidden momentum rather than just read about it. In short: In special relativity, hidden momentum or hidden mechanical momentum is the mechanical momentum (mass times velocity) that is unaccounted for by Newtonian mechanics. The concept of "hidden momentum" has been used in answering "paradoxes" in electromagnetism and other problems, including the Shockley–James paradox, the Mansuripur paradox, and the Aharonov–Casher effect.

Key takeaways

Hidden momentum belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hidden momentum to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hidden momentum from memory before moving on to harder problems.

Reference excerpt

In special relativity, hidden momentum or hidden mechanical momentum is the mechanical momentum (mass times velocity) that is unaccounted for by Newtonian mechanics. The concept of "hidden momentum" has been used in answering "paradoxes" in electromagnetism and other problems, including the Shockley–James paradox, the Mansuripur paradox, and the Aharonov–Casher effect. However, these paradoxes have resolution without introducing hidden momentum.

Hidden Momentum Several mechanisms for hidden momentum are proposed in Resource Letter EM-1: Electromagnetic Momentum. However, none of these mechanisms have rigorous derivations or are effective in replacing the electromagnetic momentum of charge-current distributions.. There is no evidence that Hidden Momentum actually exists.

References

External links On the Definition of "Hidden" Momentum - Princeton Physics Archived 2019-08-02 at the Wayback Machine

Worked examples

Example 1 — a first encounter with Hidden momentum

Start with the simplest possible case. Write down what Hidden momentum claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hidden momentum before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hidden momentum ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hidden momentum

In research: Hidden momentum appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hidden momentum in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hidden momentum is common in secondary-school and first-year university syllabi. It links to neighbouring topics Relativity stubs, Special relativity, so understanding it makes those chapters shorter.
In everyday life: Look for Hidden momentum outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hidden momentum in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hidden momentum means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hidden momentum out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hidden momentum in simple terms?

Why does Hidden momentum matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hidden momentum?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hidden momentum.