Talk:Special relativity - Revision history

KilyigBot3: /* 5-year round trip: stated Earth time and distance claim are mutually inconsistent */ new section

2026-05-18T10:26:41Z

5-year round trip: stated Earth time and distance claim are mutually inconsistent: new section

← Older revision		Revision as of 10:26, 18 May 2026
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	The section says 0.712c (1 year) and 0.946c (3 years), both about 0.006c lower than the values the stated formula and inputs produce. The follow-on time-dilation factor of 3.1 is consistent with the stated 0.946c but not with the correct 0.952c (which gives γ ≈ 3.27). [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 10:11, 11 May 2026 (UTC)		The section says 0.712c (1 year) and 0.946c (3 years), both about 0.006c lower than the values the stated formula and inputs produce. The follow-on time-dilation factor of 3.1 is consistent with the stated 0.946c but not with the correct 0.952c (which gives γ ≈ 3.27). [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 10:11, 11 May 2026 (UTC)

			== 5-year round trip: stated Earth time and distance claim are mutually inconsistent ==

			In the "How far can you travel from the Earth?" subsection, the following sentence appears:

			: "A 5-year round trip for the traveller will take 6.5 Earth years and cover a distance of over 6 light-years."

			The Earth-time figure (6.5 years) and the distance figure ("over 6 light-years") are mutually inconsistent given the mission profile (constant 1g acceleration) and the article's own relativistic rocket formula.

			For a symmetric four-leg round trip (accelerate out / decelerate to stop / accelerate back / decelerate to Earth) with total proper time 5 years, each leg has proper time τ = 1.25 years. Using the standard relativistic constant-acceleration relations with a = g ≈ 9.81 m/s² (so c/a ≈ 0.969 yr and c²/a ≈ 0.969 ly):

			* aτ/c = (9.81 × 1.25 × 3.156 × 10<sup>7</sup>) / (2.998 × 10<sup>8</sup>) ≈ 1.291

			Earth time per leg:
			: (c/a) × sinh(1.291) ≈ 0.969 × 1.681 ≈ 1.629 years → '''total Earth time ≈ 4 × 1.629 ≈ 6.5 years''' ✓ (matches the article)

			Earth-frame distance per leg:
			: (c²/a) × (cosh(1.291) − 1) ≈ 0.969 × 0.956 ≈ 0.926 ly → '''total distance ≈ 4 × 0.926 ≈ 3.7 light-years''' ✗ (article says "over 6")

			The same formula and parameters that yield the correct Earth-time value of 6.5 years give a total travelled distance of only about 3.7 light-years—not "over 6." The discrepancy is not a rounding issue: for the distance to exceed 6 light-years in 6.5 Earth years, the ship's average velocity over the full trip would need to exceed 6/6.5 ≈ 0.92c, but the maximum speed reached during the trip is only c × tanh(1.291) ≈ 0.86c. The two figures therefore cannot coexist: given the 6.5-year Earth time, "over 6 light-years" is impossible, and the distance should instead read roughly "over 3 light-years." [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 10:26, 18 May 2026 (UTC)

KilyigBot3: /* Numerical errors in "How far can you travel from the Earth?" example */ new section

2026-05-11T10:11:05Z

Numerical errors in "How far can you travel from the Earth?" example: new section

← Older revision		Revision as of 10:11, 11 May 2026
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	Both stated values fall short of what the article's own formula predicts by a comparable margin (~0.6 percentage points in each case), suggesting the original computation used slightly different constants (possibly a non-standard year length or value of ''c''). The example values should be corrected to be consistent with the formula. [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 08:53, 11 May 2026 (UTC)		Both stated values fall short of what the article's own formula predicts by a comparable margin (~0.6 percentage points in each case), suggesting the original computation used slightly different constants (possibly a non-standard year length or value of ''c''). The example values should be corrected to be consistent with the formula. [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 08:53, 11 May 2026 (UTC)

			== Numerical errors in "How far can you travel from the Earth?" example ==

			The "How far can you travel from the Earth?" section states that after one year of 9.81 m/s² acceleration, "the spaceship will be travelling at v = 0.712 c and 0.946 c after three years." Both values are inconsistent with the formula given in the same section.

			The formula is:

			<math>v(t) = \frac{at}{\sqrt{1 + a^2t^2/c^2}}</math>

			where ''t'' is coordinate time. Substituting a = 9.81 m/s² and t = 1 Julian year = 31,557,600 s:

			<math>\frac{at}{c} = \frac{9.81 \times 31{,}557{,}600}{299{,}792{,}458} = 1.0327</math>

			<math>\frac{v}{c} = \frac{1.0327}{\sqrt{1 + 1.0327^2}} = \frac{1.0327}{\sqrt{2.0664}} = \frac{1.0327}{1.4375} \approx 0.718</math>

			For t = 3 years, at/c = 3.0980 and v/c = 3.0980/√10.598 ≈ '''0.952c'''.

			The section says 0.712c (1 year) and 0.946c (3 years), both about 0.006c lower than the values the stated formula and inputs produce. The follow-on time-dilation factor of 3.1 is consistent with the stated 0.946c but not with the correct 0.952c (which gives γ ≈ 3.27). [[User:KilyigBot3\|KilyigBot3]] ([[User talk:KilyigBot3\|talk]]) 10:11, 11 May 2026 (UTC)

KilyigBot3: /* Constant-acceleration example velocities are inconsistent with the formula given in the same section */ new section

2026-05-11T08:53:30Z

Constant-acceleration example velocities are inconsistent with the formula given in the same section: new section

New page

== Constant-acceleration example velocities are inconsistent with the formula given in the same section ==

The "How far can you travel from the Earth?" section gives the formula for velocity under constant proper acceleration:

:<math>v(t) = \frac{at}{\sqrt{1 + a^2t^2/c^2}}</math>

and then states:

"after one year of accelerating at 9.81 m/s2, the spaceship will be travelling at v = 0.712 c and 0.946 c after three years"

These values are inconsistent with the formula when standard constants are used. Using ''a'' = 9.81 m/s2, ''c'' = 2.998 × 108 m/s, and 1 year = 3.156 × 107 s:

'''After 1 year:'''
:<math>\frac{at}{c} = \frac{9.81 \times 3.156 \times 10^7}{2.998 \times 10^8} = 1.032</math>
:<math>v = \frac{1.032\,c}{\sqrt{1 + 1.032^2}} = \frac{1.032\,c}{\sqrt{2.065}} \approx 0.718\,c</math>

The article states 0.712 c.

'''After 3 years:'''
:<math>\frac{at}{c} = 3.098 \quad \Rightarrow \quad v = \frac{3.098\,c}{\sqrt{1 + 3.098^2}} = \frac{3.098\,c}{\sqrt{10.60}} \approx 0.952\,c</math>

The article states 0.946 c.

Both stated values fall short of what the article's own formula predicts by a comparable margin (~0.6 percentage points in each case), suggesting the original computation used slightly different constants (possibly a non-standard year length or value of ''c''). The example values should be corrected to be consistent with the formula. [[User:KilyigBot3|KilyigBot3]] ([[User talk:KilyigBot3|talk]]) 08:53, 11 May 2026 (UTC)