Description
Return only the weak-field received-minus-emitted frequency fraction -deltaPhi/c²; validity requires a small potential ratio.
Relativistic quantities depend on the frame, units, and approximation being used. Rapidity supports collinear velocity composition, four-momentum has a signed invariant, and weak-field frequency shifts are approximations. A numerical term should be interpreted within its own model rather than combined indiscriminately with classical formulas.
Return only the weak-field received-minus-emitted frequency fraction -deltaPhi/c²; validity requires a small potential ratio.
When to use this tool
Use Gravitational Redshift Weak Field Term when you need this collinear composition, invariant residual, or weak-field approximation with compatible physical units.
How to use the tool and how it works
- Enter potentialDifference, lightSpeed. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read fractionalFrequencyShift. Use the output convention below.
For positive lightSpeed return fractionalFrequencyShift=-potentialDifference/lightSpeed^2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| potentialDifference | Receiver minus emitter gravitational potential, in units of speed squared. | Required. Finite number. |
| lightSpeed | Positive propagation speed in compatible length per time units. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| fractionalFrequencyShift | Fractional Frequency Shift | Required. Finite number. |
{
"input": {
"potentialDifference": 100,
"lightSpeed": 299792458
},
"output": {
"fractionalFrequencyShift": -1.1126500560536184e-15
}
}Limitations and assumptions
- PotentialDifference must mean receiver minus emitter gravitational potential, in energy per mass units matching speed squared. This is a first-order weak-field shift; the code does not enforce abs(deltaPotential)/c^2 being small or model motion.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete frame transformation or spacetime model when collinear or weak-field assumptions do not apply. Check invariant units and approximation size before interpreting a residual or shift.
References
Similar or alternative tools
- Gravitational Potential Datum Energy Term
For nonnegative mass return energyShift=mass*potentialShift.
- Relativistic Four Momentum Norm Residual
Signed +--- four-momentum norm residual in consistent caller-supplied units.