Additions:

Additions:

""""In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Meanwhile vectors on Earth are contracted because of the expansion of the Universe. Let the classical momentum of Pioneer be ""p"" at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth, classical energy is given by (note that ""t_{0"" is now the earlier time)}

Deletions:

""""In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Meanwhile vectors on Earth are contracted because of the expansion of the Universe. Let the classical momentum of Pioneer be ""p"" at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth, classical energy is given by (note that ""t_{0"" is now the earlier time)}

Additions:

""""In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Meanwhile vectors on Earth are contracted because of the expansion of the Universe. Let the classical momentum of Pioneer be ""p"" at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth, classical energy is given by (note that ""t_{0"" is now the earlier time)}

Deletions:

""""In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Meanwhile vectors on Earth are contracted because of the expansion of the Universe. Let the classical momentum of Pioneer be ""p"" at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth classical energy is given by (note that ""t_{0"" is now the earlier time)}

Additions:

""""In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Meanwhile vectors on Earth are contracted because of the expansion of the Universe. Let the classical momentum of Pioneer be ""p"" at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth classical energy is given by (note that ""t_{0"" is now the earlier time)}

Deletions:

In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Let the classical momentum of Pioneer be ""p"" at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth classical energy is given by (note that ""t_{0"" is now the earlier time)}

Additions:

In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Let the classical momentum of Pioneer be ""p"" at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth classical energy is given by (note that ""t_{0"" is now the earlier time)}

Deletions:

In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Let the classical momentum of Pioneer ""p""at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth classical energy is given by (note that ""t_{0"" is now the earlier time)}

Additions:

In the absence of calibration between clocks on a distant body and clocks on the earth, the energy-momentum of a distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Let the classical momentum of Pioneer ""p""at the time, ""t₀"", of loss of radar lock. Ignoring radiation pressure and local gravitational effects such as the gravity of the Sun (set ""k = 1"" in the metric), for a signal emitted at time ""t"" and detected on Earth classical energy is given by (note that ""t_{0"" is now the earlier time)}

Deletions:

In the absence of calibration between clocks on a distant body and clocks on the earth, the momentum of the distant body is constant in ""τ-ρ"" coordinates with non-physical metric """". Ignoring local gravitational effects (set ""k = 1"" in the metric), as determined in signals detected on Earth classical energy is given by (note that ""t_{0"" is now the earlier time)}

Additions:

These coordinates are defined such that the speed of light is unity, but, due to the variability of ""k : ρ → k(ρ)"" , lines of constant ""ρ"" are not geodesic (as is the case for a standard Friedmann cosmology). Quantum theory was formulated with the non-physical metric, """", given by

Deletions:

These coordinates are defined such that the speed of light is unity, but, due to the variability of the of ""k : ρ → k(ρ)"" , lines of constant ""ρ"" are not geodesic (as is the case for a standard Friedmann cosmology). Quantum theory was formulated with the non-physical metric, """", given by

Additions:

""""

Deletions:

"""".