SCIENCE · INVESTIGATE AND EXPLAIN

Separate an emission clock from photon arrival timing

A receding inertial source emits successive light pulses separated by proper period T0. The laboratory observer is at rest to the source’s left, so the returning photons travel opposite the source motion. This geometry is part of the problem; an approaching or transverse arrangement has a different arrival comparison.

Learning outcome: Construct the two emission events and their different travel distances before taking a frequency ratio. Compare the fixed-clock and received-signal statements without assigning either to a cosmological model.

Starting recap

Name event pairs, frame signs and c=1 units; retain simultaneity, worldline integration, four-momentum and unused evidence boundaries.

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

Try

For β=0.6 and T0=2, the laboratory emission interval is 2.5 and the extra travel delay is 1.5, giving arrival interval 4. The frequency ratio is 0.5, whereas pure clock-rate ratio is 0.8. The wavelength ratio is 2.

Open the experiment

Predict

Why does multiplying by the time-dilation factor alone fail to predict the receding source’s arrival period?

Your prediction and reason

Experiment

Construct the two emission events and their different travel distances before taking a frequency ratio. Compare the fixed-clock and received-signal statements without assigning either to a cosmological model.

Separate emission-clock and arrival intervals

Worked teaching model · synthetic values · Original inertial source recedes along+x from a laboratory observer at rest to its left. Photons travel back toward observer. Proper period T0; laboratory emission intervalγT0, then an additional path-delay factor1+β. No cosmological or gravitational redshift.

Receding source speed: 0.6 c Proper emission period: 2 reference time

Reset keeps your prediction, captures and practice history.

Longitudinal Doppler shift combines the emission-clock comparison and changing travel distance; it is not pure time dilation.

Original inertial source recedes along+x from a laboratory observer at rest to its left. Photons travel back toward observer. Proper period T0; laboratory emission intervalγT0, then an additional path-delay factor1+β. No cosmological or gravitational redshift.

Original conditional ledger; reference units retain their distinct meanings
Quantity	Value	Unit
Proper emission period	2	reference time
Lab emission-event interval	2.500000	reference time
Additional travel delay	1.500000	reference time
Lab arrival interval	4	reference time
Received to emitted frequency ratio	0.5000000	ratio
Pure clock-rate ratio	0.8000000	ratio
Wavelength ratio	2	ratio

These original virtual events and collision records are not an actual clock, accelerator, photon-source or practical experiment. No physical apparatus operation is assigned.

Longitudinal Doppler shift combines the emission-clock comparison and changing travel distance; it is not pure time dilation.

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 events, frames and conserved quantities

Time dilation makes the laboratory interval between emission events γT0. During that interval the source moves farther away by βγT0 in c=1 units. The second photon therefore has an extra travel delay βγT0, giving arrival period γT0(1+β).

Received frequency divided by source proper frequency is 1/[γ(1+β)]=sqrt[(1−β)/(1+β)]. The pure emission-clock rate ratio is only 1/γ. Both effects involve relativity, but the longitudinal Doppler comparison includes changing propagation distance as well as the clock relation.

The original output also reports the reciprocal wavelength ratio for light in the same vacuum frame. This special-relativistic inertial derivation does not model cosmological expansion or gravitational redshift. A measured spectrum would additionally require a source-rest-frequency identification and calibration; this packet supplies no actual spectral observation.

2. Reconstruct the original case

3. Predict and investigate

Why does multiplying by the time-dilation factor alone fail to predict the receding source’s arrival period?

Transfer the event construction

Set β=0.8 and T0=1. Find the arrival period, frequency ratio and pure clock-rate ratio.

Retain the chosen events, frame convention and intermediate reasoning before opening public feedback.

Compare a worked response

γ=5/3 gives emission interval 5/3 and additional delay 4/3, so arrival period is 3. Frequency ratio is 1/3, while pure clock-rate ratio is 0.6.

Primary mechanism context. Checked 31 October 2026. Original derivations, records and diagrams; no physical apparatus operation or actual independent clock/particle measurement is claimed. Retain first reasoning and public-feedback exposure in the course evidence workspace when registered.

Apply

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

Set β=0.8 and T0=1. Find the arrival period, frequency ratio and pure clock-rate ratio.

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: Derive photon energy with the emitter recoil retained Next: Fit a boost from one record and test unused event differences

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.