physics

Geometrized unit system

Geometrized unit system 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 Geometrized unit system rather than just read about it. In short: A geometrized unit system or geometrodynamic unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum (c), and the gravitational constant (G), are used as defining constants. The geometrized unit system is not a completely defined system.

Key takeaways

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

Reference excerpt

A geometrized unit system or geometrodynamic unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum (c), and the gravitational constant (G), are used as defining constants. The geometrized unit system is not a completely defined system. Some systems are geometrized unit systems in the sense that they set these two constants, in addition to other constants, to unity, for example Stoney units and Planck units. This system is used in physics, especially in the special and general theories of relativity, which focus on physical quantities that are identified with dynamic quantities such as time, length, mass, dimensionless quantities, area, energy, momentum, path curvatures and sectional curvatures. Many equations in relativistic physics appear simpler when expressed in geometrized units, because all occurrences of G and of c "drop out". For example, the Schwarzschild radius of a nonrotating uncharged black hole with mass m becomes rs = 2m. For this reason, many books and papers on relativistic physics use geometrized units. An alternative "rationalized" system of geometrized units is often used in particle physics and cosmology, in which 4πG or 8πG are used instead. This makes equations such as the Einstein field equations, the Einstein–Hilbert action, the Friedmann equations and the Newtonian Poisson equation seem simpler and more natural.

Definition Geometrized units were defined in the book Gravitation by Misner, Thorne, and Wheeler such that the speed of light c, the gravitational constant G, and Boltzmann constant kB are all "set to 1". Some authors refer to these units as geometrodynamic units. In geometrized units, every time interval is interpreted as the distance travelled by light during that given time interval. That is, one second is interpreted as one light-second, so time has the geometrized units of length. This is dimensionally consistent with the notion that, according to the kinematical laws of special relativity, time and distance are on an equal footing. Energy and momentum are interpreted as components of the four-momentum vector, and invariant mass is the magnitude of this vector, so in geometrized units these must all have the dimension of length. We can convert a mass expressed in kilograms to the equivalent mass expressed in metres by multiplying by the conversion factor G/c2. For example, the Sun's mass of 2.0×1030 kg in SI units is equivalent to 1.5 km. This is half the Schwarzschild radius of a one solar mass black hole. All other conversion factors can be worked out by combining these two. The small numerical size of the few conversion factors reflects the fact that relativistic effects are only noticeable when large masses or high speeds are considered.

Conversions Listed below are all conversion factors that are useful to convert between combinations of the SI base units, based on the constants c, G, ε0 (vacuum permittivity) and kB (Boltzmann constant).

References

Wald, Robert M. (1984). General Relativity. Chicago: University of Chicago Press. ISBN 0-226-87033-2. See Appendix F

External links Conversion factors for energy equivalents

Worked examples

Example 1 — a first encounter with Geometrized unit system

Start with the simplest possible case. Write down what Geometrized unit system 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 Geometrized unit system 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 Geometrized unit system 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 Geometrized unit system

In research: Geometrized unit system 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 Geometrized unit system 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: Geometrized unit system is common in secondary-school and first-year university syllabi. It links to neighbouring topics General relativity, Natural units, Systems of units, so understanding it makes those chapters shorter.
In everyday life: Look for Geometrized unit system 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 Geometrized unit system in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Geometrized unit system 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 Geometrized unit system out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Geometrized unit system in simple terms?

Why does Geometrized unit system 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 Geometrized unit system?

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 Geometrized unit system.