SCIENCE · INVESTIGATE AND EXPLAIN

Separate a spectral shift from an additive calibration error

A line’s observed wavelength can differ from a reference because of motion, gravity, cosmic expansion or measurement calibration. Before assigning a physical cause, identify the transition, wavelength convention and observer reference frame. Air and vacuum wavelengths are not interchangeable reference lists; a shared convention is part of the evidence.

Learning outcome: Compare both observed lines at changed shift and offset, reconstruct slope/intercept and retain the naive single-line error. Explain the evidence needed before interpreting the result as velocity rather than another shift mechanism.

Starting recap

Keep photon energy/count, density convention, propagation, collection/resolution, calibration and source-quality assumptions distinct.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

At z=0.01 and additive offset 1 nm, observed positions are 506 and 607 nm. Their difference 101 nm recovers z=0.01; the intercept is 1 nm. Using only the first line as if offset were zero gives 506/500−1=0.012, a biased result.

Open the experiment

Predict

Could one shifted line distinguish an additive wavelength zero-point error from a true fractional shift?

Your prediction and reason

Experiment

Compare both observed lines at changed shift and offset, reconstruct slope/intercept and retain the naive single-line error. Explain the evidence needed before interpreting the result as velocity rather than another shift mechanism.

Separate a common fractional shift from an additive wavelength error

Worked teaching model · synthetic values · Two original exact rest wavelengths500 and600 nm share observed=(1+z)rest+offset. Difference identifies multiplicative factor; intercept identifies additive error. If solely radial special-relativistic Doppler, beta=[(1+z)²−1]/[(1+z)²+1]; not a cosmological-redshift velocity conversion.

Original fractional wavelength shift: 0.01 ratio Additive calibration offset: 1 nm

Reset keeps your prediction, captures and practice history.

A common additive wavelength error and a common fractional shift have different signatures across two lines.

Both rest wavelengths share the same vacuum convention. Two exact lines identify these two parameters only because line identities and the affine error model are supplied. Cosmological or gravitational shifts require different physical interpretation; the actual QSO pipeline redshift is not a peculiar-speed measurement.

Explicit physical or source units
Quantity	Value	Unit
First observed line	506	nm
Second observed line	607	nm
Recovered fractional shift	0.01000000	ratio
Recovered additive offset	1	nm
Naive first-line fractional shift	0.01200000	ratio
Pure radial Doppler equivalent beta	0.009950002	v/c under special assumptions
Small-speed cz approximation	2997.925	km/s under special assumptions

Actual SDSS records are explicitly labeled; all other packets are original models. No direct solar viewing, radiation experiment or instrument operation is requested.

A common additive wavelength error and a common fractional shift have different signatures across two lines.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Define the light and measurement

2. Connect physical and instrumental mechanisms

The original exact pair has rest wavelengths 500 and 600 nm and observed relation λobs=(1+z)λrest+b, where b is an additive calibration offset. Subtracting the two observed positions removes b and identifies 1+z from their separation. The intercept then recovers b. A single line alone would leave fractional shift and additive error confounded.

If the recovered shift is exclusively due to radial special-relativistic motion of an isolated source, β=v/c=[(1+z)²−1]/[(1+z)²+1]. The approximation v≈cz is useful only when its assumptions and small-shift limit apply. The actual high-redshift quasar source in the next lesson has a cosmological interpretation, so neither this isolated-source formula nor cz should be applied as its peculiar velocity.

Two exact lines identify two parameters only because the transition identities and affine error form are supplied. Blends, unequal shifts, nonlinear calibration or uncertain rest references can break that inference. Additional independent features and residuals test the assumptions; more decimal places in a fit do not supply missing physical evidence.

3. Work the evidence

4. Predict and investigate

Could one shifted line distinguish an additive wavelength zero-point error from a true fractional shift?

Apply the evidence to a changed case

Use z=0 and additive offset 2 nm. What do one-line and two-line inferences report?

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Observed positions are 502 and 602 nm. The two-line separation stays 100 nm, recovering z=0 and offset 2 nm. Ignoring offset in the first line would falsely give z=0.004. A calibration displacement need not represent motion.

Source and boundaries

Primary source. Checked 30 October 2026. Original teaching and fictional numerical models are separate from the explicitly labeled actual SDSS archive; no direct observing, radiation experiment or instrument operation is requested.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Use z=0 and additive offset 2 nm. What do one-line and two-line inferences report?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Distinguish an absorption line’s depth from its integrated deficit Next: Audit an actual spectrum before treating a curve as an inference

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.