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One-way speed of light

One-way speed of light 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 One-way speed of light rather than just read about it. In short: When using the term "the speed of light" it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector.

One-way speed of light — main illustration
One-way speed of light — illustration

Key takeaways

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

Reference excerpt

When using the term "the speed of light" it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed (or "two-way" speed of light) from the source to a mirror (or other method of reflection) and back again to the detector. Albert Einstein chose a synchronization convention (see Einstein synchronization) that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame is the basis of his special theory of relativity, although all experimentally verifiable predictions of this theory do not depend on that convention. Experiments that attempt to directly probe the one-way speed of light independent of synchronization have been proposed, but none have succeeded in doing so. Those experiments directly establish that synchronization with slow clock-transport is equivalent to Einstein synchronization, which is an important feature of special relativity. However, those experiments cannot directly establish the isotropy of the one-way speed of light since it has been shown that slow clock-transport, the laws of motion, and the way inertial reference frames are defined already involve the assumption of isotropic one-way speeds and thus, are equally conventional. In general, it was shown that these experiments are consistent with anisotropic one-way light speed as long as the two-way light speed is isotropic. The "speed of light" in this article refers to the speed of all electromagnetic radiation in vacuum.

The two-way speed

The two-way speed of light is the average speed of light from one point, such as a source, to a mirror and back again. Because the light starts and finishes in the same place, only one clock is needed to measure the total time; thus, this speed can be experimentally determined independently of any clock synchronization scheme. Any measurement in which the light follows a closed path is considered a two-way speed measurement. Many tests of special relativity such as the Michelson–Morley experiment and the Kennedy–Thorndike experiment have shown within tight limits that in an inertial frame the two-way speed of light is isotropic and independent of the closed path considered. Isotropy experiments of the Michelson–Morley type do not use an external clock to directly measure the speed of light, but rather compare two internal frequencies or clocks. Therefore, such experiments are sometimes called "clock anisotropy experiments", since every arm of a Michelson interferometer can be seen as a light clock having a specific rate, whose relative orientation dependences can be tested. Since 1983 the metre has been defined as the distance traveled by light in vacuum in 1⁄299,792,458 second. This means that the speed of light can no longer be experimentally measured in SI units, but the length of a meter can be compared experimentally against some other standard of length.

The one-way speed

Although the average speed over a two-way path can be measured, the one-way speed in one direction or the other is undefined (and not simply unknown), unless one can define what "the same time" is in two different locations. To measure the time that the light has taken to travel from one place to another it is necessary to know the start and finish times as measured on the same time scale. This requires either two synchronized clocks, one at the start and one at the finish, or some means of sending a signal instantaneously from the start to the finish. No instantaneous means of transmitting information is known. Thus, the measured value of the average one-way speed is dependent on the method used to synchronize the start and finish clocks. This is a matter of convention. The Lorentz transformation is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen. Some authors such as Mansouri and Sexl (1977) as well as Will (1992) argued that this problem doesn't affect measurements of the isotropy of the one-way speed of light, for instance, due to direction-dependent changes relative to a "preferred" (aether) frame Σ. They based their analysis on a specific interpretation of the RMS test theory in relation to experiments in which light follows a unidirectional path and to slow clock-transport experiments. Will agreed that it is impossible to measure the one-way speed between two clocks using a time-of-flight method without a synchronization scheme, though he argued: "...a test of the isotropy of the speed between the same two clocks as the orientation of the propagation path varies relative to Σ should not depend on how they were synchronized...". He added that aether theories can only be made consistent with relativity by introducing ad hoc hypotheses. In more recent papers (2005, 2006) Will referred to those experiments as measuring the "isotropy of light speed using one-way propagation". However, others such as Zhang (1995, 1997) and Anderson et al. (1998) showed this interpretation to be incorrect. For instance, Anderson et al. pointed out that the conventionality of simultaneity must already be considered in the preferred frame, so all assumptions concerning the isotropy of the one-way speed of light and other velocities in this frame are conventional as well. Therefore, RMS remains a useful test theory to analyze tests of Lorentz invariance and the two-way speed of light, though not of the one-way speed of light. They concluded: "...one cannot hope even to test the isotropy of the speed of light without, in the course of the same experiment, deriving a one-way numerical value at least in principle, which then would contradict the conventionality of synchrony." Using generalizations of Lorentz transformations with anisotropic one-way speeds, Zhang and Anderson pointed out that all events and experimental results compatible with the Lorentz transformation and the isotropic one-way speed of light must also be compatible with transformations preserving two-way light speed constancy and isotropy, while allowing anisotropic one-way speeds.

… excerpt ends here. Continue reading the full article.

Illustrations

One-way speed of light: Unidirectional light path in the aberration of light
Unidirectional light path in the aberration of light
One-way speed of light: List of eclipses of the Jupiter moon Io that formed the basis of Ole Rømer's discovery of the finite speed of light.
List of eclipses of the Jupiter moon Io that formed the basis of Ole Rømer's discovery of the finite speed of light.
One-way speed of light: Artist's illustration of a bright gamma-ray burst. Measurements on light from such objects were used to show that the one-way speed of light does not vary with frequency.
Artist's illustration of a bright gamma-ray burst. Measurements on light from such objects were used to show that the one-way speed of light does not vary with frequency.
One-way speed of light: Hendrik Antoon Lorentz
Hendrik Antoon Lorentz

Worked examples

Example 1 — a first encounter with One-way speed of light

Start with the simplest possible case. Write down what One-way speed of light 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 One-way speed of light 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 One-way speed of light 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 One-way speed of light

In research
One-way speed of light 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 One-way speed of light 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
One-way speed of light is common in secondary-school and first-year university syllabi. It links to neighbouring topics Special relativity, Velocity, so understanding it makes those chapters shorter.
In everyday life
Look for One-way speed of light 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 One-way speed of light in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what One-way speed of light means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain One-way speed of light out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is One-way speed of light in simple terms?

When using the term "the speed of light" it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source a…

Why does One-way speed of light 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 One-way speed of light?

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 One-way speed of light.

Tags

  • Special relativity
  • Velocity

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