Aberration of Starlight - Revision history

Washcarso at 02:12, 29 August 2026

2026-08-29T02:12:17Z

← Older revision		Revision as of 22:12, 28 August 2026
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	* [[AetherCosPlay_Aberration_or_Starlight]]		* [[AetherCosPlay_Aberration_or_Starlight]]

	[[Category:Globe ~~Evidence~~]]		[[Category:Globe evidence]]

Martin: Category:Globe Evidence added

2026-08-28T16:57:28Z

Category:Globe Evidence added

← Older revision		Revision as of 12:57, 28 August 2026
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	* [[AetherCosPlay_Aberration_or_Starlight]]		* [[AetherCosPlay_Aberration_or_Starlight]]

			[[Category:Globe Evidence]]

Graugnarz: /* Special Relativity Mathematics */

2026-07-26T21:48:31Z

Special Relativity Mathematics

← Older revision		Revision as of 17:48, 26 July 2026
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	The relativistic aberration formula is:		The relativistic aberration formula is:

	~~Test:~~ <math>\sqrt{\frac{1-v/c}{1+v/c}}</math>		<math>\tan\frac{\phi}{2} = \sqrt{\frac{1-v/c}{1+v/c}}\tan\frac{\theta}{2}</math>

	<math>\tan\frac{\phi}{2} = \frac{\sqrt{1-v/c}}{\sqrt{1+v/c}}\tan\frac{\theta}{2}</math>		<!--<math>\tan\frac{\phi}{2} = \frac{\sqrt{1-v/c}}{\sqrt{1+v/c}}\tan\frac{\theta}{2}</math>-->

	The classical aberration formula, by James Bradley, 1727, is:		The classical aberration formula, by James Bradley, 1727, is:

Graugnarz: /* Special Relativity Mathematics */

2026-07-26T21:44:47Z

Special Relativity Mathematics

← Older revision		Revision as of 17:44, 26 July 2026
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	The relativistic aberration formula is:		The relativistic aberration formula is:

			Test: <math>\sqrt{\frac{1-v/c}{1+v/c}}</math>

	<math>\tan\frac{\phi}{2} = \frac{\sqrt{1-v/c}}{\sqrt{1+v/c}}\tan\frac{\theta}{2}</math>		<math>\tan\frac{\phi}{2} = \frac{\sqrt{1-v/c}}{\sqrt{1+v/c}}\tan\frac{\theta}{2}</math>

Nerd Alert: formatting fixes (cursive)

2026-07-26T21:18:18Z

formatting fixes (cursive)

Nerd Alert: Explain effect, history and special relativity mathematics

2026-07-26T21:15:02Z

Explain effect, history and special relativity mathematics

← Older revision		Revision as of 17:15, 26 July 2026
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	~~Flerfs cannot explain~~ the Aberration of ~~Starlight~~. ~~They invent all sorts~~ of ~~cope~~.		{{Brandolini}}
	See: [[AetherCosPlay_Aberration_or_Starlight]]
			== Introduction ==

			Stellar aberration is a change in the direction of incoming star light caused by lateral movement of the observer relative to the star. In some obsolete rsp. fringe theories, it is caused by the absolute motion of one or the other.

			Stellar aberration should not be confused with stellar parallax, which is a change in the angle of incident light from nearby stars due to a change in the orbital position of Earth. It is a distinct effect and the light of a star can be affected by either or both. Important differences are:

			* Stellar aberration is maximal when the Earth is moving laterally to the star's position on its orbit, and decreases to zero when the Earth is moving straight towards or away from the star. In contrast, stellar parallax of a star in the ecliptic plane is most easily measured between the points at which Earth is moving towards or away from the star.
			* Stellar aberration does not depend on the distance to the star. In contrast, stellar parallax is only observed for "nearby" stars, which, depending on the available measurement precision, is at most in the hundreds of light years.

			To summarize the difference in one sentence: Aberration is a velocity effect whereas parallax is a position effect.

			Stellar aberration is also subject to a minor diurnal effect due to the tangential velocity of an observer on the rotating Earth, at less than polar latitudes.

			Also, aberration affects sunlight and the light reflected off of planets, though the effect is usually discussed in the context of distant stars. (It is also tiny in comparison to the angular size of Sun and Moon as seen from Earth.)

			== History ==

			The discovery of stellar aberration in the late 17th century came as a surprise. Scientists were mainly looking for stellar parallax, potentially allowing for a triangulation of the distance of some stars and also confirming the still relatively young heliocentric model.

			One of the first noteworthy measurements was that of [Eltanin\|https://en.wikipedia.org/wiki/Gamma_Draconis] by Robert Hooke in 1674. At first, the measured deviation was not understood to be a separate phenomenon from parallax. Also, the propagation of light was neither well understood nor the focus of scientific inquiry at the time. Even after Ole Rømer measured the speed of light in 1676, and, in particular, demonstrated that it was not instantaneous, it took decades for scientists to draw a definitive connection between the angles at which stars appeared to be and the way that light propagates in a vacuum.

			Once the significance of stellar aberration, and its distinctness from parallax, were understood, there were however a number of astronomical experiments that attempted to use the effect to distinguish between different theories of light propagation, namely emission theory, which treated light as a stream of particles inheriting momentum from the emitting object, and the undulatory theory of light (better known as aether theory), which treated light as a wave in a ubiquitous but "non-tangible" medium.

			== Modern Scientific Explanation ==

			In modern science, stellar aberration is understood to be consistent with, and quantitatively predicted by, the theory of special relativity. When a lateral Lorentz boost, i.e. a velocity addition, is performed to transform a ray of light from the inertial reference frame of a star to the inertial reference frame of an observer, the angle of propagation changes depending on said lateral speed. (The existence of "instantaneous" inertial frames is enough.)

			However, one should be careful when citing stellar aberration alone as evidence for special relativity because aberration experiments are not precise enough to be specific towards testing relativity. In particular, while there is a relativistic formula that makes distinct predictions, the "classical" math, e.g. derivable from emission theory or from an aether in which the light source is stationary, still works extremely well in practice.

			== Special Relativity Mathematics ==

			{{Note\|text=So, is light a stream of particles or a wave? You have probably heard that it is a bit of both, as a rough summary of quantum mechanics. However, it is probably better described as a quantized wave usually, and in this context can be treated simply as a wave (individual photons are not relevant here). The direction in which a ray of light propagates as a wave is perpendicular to its wavefront, which is what matters here.}}

			In this subsection, a closer look is taken at the mathematics of stellar aberration in special relativity.

			The derivation of stellar aberration uses a standard relativistic coordinate transformation, namely a so-called Lorentz boost. (However, while the simplest type of boost is colinear, this boost occurs at an angle.)

			{{Note\|text=Lorentz transformations in general are used to transform spacetime coordinates from one inertial reference frame to another and can apply a velocity boost in any spatial direction, rotate the coordinate axes or move the coordinate origin. Usually origin and coordinate axes are kept fixed for simplicity, and we only apply velocity changes. This specific class of Lorentz transformations are called the Lorentz boosts.}}

			In the following, v is the speed of the observer relative to the light source, θ is the angle of relative motion (90° for perpendicular motion) and ɸ is the light's angle of incidence. Note that the actual aberration is θ - ɸ. c is the speed of light in a vacuum.

			The relativistic aberration formula is:

			<math>\tan\frac{\phi}{2} = \frac{\sqrt{1-v/c}}{\sqrt{1+v/c}}\tan\frac{\theta}{2}</math>

			The classical aberration formula, by James Bradley, 1727, is:

			<math>\tan\phi = \frac{\sin\theta}{v/c + \cos\theta}</math>

			And here it is crucial to note that, while both formulas make different predictions, the classical formula as derived using emission theory or, alternatively, an aether in which the light source is stationary and the observer is moving, is not practically distinguishable from the relativistic version. This is because the classical formula is essentially an approximation of the relativistic formula for "non-relativistic speeds", which includes Earth's orbital speed.

			Anyway, for θ=90°, this further simplifies to

			<math>\sin(\theta - \phi) = v/c</math>

			And for <math>v\ll c</math>, the small angle approximation for the sine applies, so:

			<math>\theta-\phi \approx v/c</math>

			{{Note\|text=The small angle approximation gives an angle ''in radians''. Remember to translate the result to a different unit (conventionally arcseconds when it comes to stellar aberration) as necessary.}}

			=== Example values ===

			The following table shows the predicted aberration angle <math>\theta-\phi</math> in arcseconds, i.e. 1/3,600th of a degree, using the exact SR formula, the classical formula, rsp. the small angle approximation <math>v/c</math> for <math>\theta=90^\circ</math> and the minimum and maximum orbital speeds of Earth around the Sun. Results are rounded to 6 decimals.

			{\| class="wikitable" style="margin:auto"
			\|+ Predicted Aberration Angles
			\|-
			! v [m/s] !! SR !! Classical !! Small Angle
			\|-
			\| 29290.0 \|\| 20.15226208 \|\| 20.15226199 \|\| 20.15226205
			\|-
			\| 30300.0 \|\| 20.84716768 \|\| 20.84716757 \|\| 20.84716764
			\|}

			Again, the point is to show that there is no meaningful difference in the predicted values. The predictions are less than one millionth of an arcsecond apart, which is far closer than common measurement accuracy for astronomical observations.

			== See Also ==

			* [[AetherCosPlay_Aberration_or_Starlight]]

MCToon: Replaced content with "Flerfs cannot explain the Aberration of Starlight. They invent all sorts of cope. See: AetherCosPlay_Aberration_or_Starlight"

2026-07-01T14:52:57Z

Replaced content with "Flerfs cannot explain the Aberration of Starlight. They invent all sorts of cope. See: AetherCosPlay_Aberration_or_Starlight"

← Older revision		Revision as of 10:52, 1 July 2026
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	~~Work in Progress:~~		Flerfs cannot explain the Aberration of Starlight. They invent all sorts of cope.
			See: [[AetherCosPlay_Aberration_or_Starlight]]
	~~On 2026-06-26 on the Earth Awakenings Discord server [[Piezo]] and [[MCToon]] had this conversation:~~

	~~Insert conversation here~~


	~~In the comments section of that video TruthNerds wrote this response:~~
	~~A flat Earther found a formula which he doesn't understand and put some numbers in it. When has that ever happened before! (Warning, long post … see Brandolini's Law)~~

	~~Anyway, Geo claims that Alan calculated the expected stellar aberration in Airy's failure experiment and that it doesn't match SR. By plugging in different light speeds, apparently. 😂~~

	~~Ok, insider joke? I'll elaborate.~~

	Let's first look at what Geo means by Bradley's formula. The classical formula is derived assuming that light propagates as a wave with a given speed in a stationary medium, aka aether, and the application of Newtonian mechanics.

	~~It is θ - arctan(sin θ / (v/c + cos θ)) where θ is the angle of movement relative to the viewing direction, v is speed and c is the speed of light.~~

	Then there's the relativistic formula, which is θ - 2 arctan(sqrt((1-v/c)/(1+v/c)) * tan(θ/2)). The relativistic formula reduces to the classical formula for v << c. Furthermore, for θ = 90° and v<<c, both reduce to v/c (in radians) as an approximation.

	Ok, first, let's do some calculations, plain 90° aberration with Earth's average orbital speed gives about 0.0996 mrad (about 20.5 arcseconds) both for the classical and for the relativistic formula. It really makes no difference at those speeds!

	Now, what did Alan presumably do to model Airy's experiment? Changing θ makes no sense, we want to keep that constant for comparability. Changing v makes no sense because Earth's speed wouldn't change. So he must've modified c. And that is hilarious!

	Why? Well, for how Bradley's formula was derived, it would make sense because it is originally based on the assumption of a wave propagating through the aether. Slower wave propagation would thus affect the aberration angle.

	But it doesn't make any sense to vary c in the relativistic formula! The relativistic formula is not derived from any assumption about a wave propagating through a fixed medium, it is based on the Lorentz transformation and the ~~postulates of Special Relativity:~~

	~~1. The laws~~ of ~~physics are the same in all inertial frames.~~
	~~2. The speed of light in a vacuum (denoted c) is the same for all observers.~~

	The speed of light to plug into the relativistic formula is always that same c, it has nothing to do with wave propagation in a medium. The formula follows from a coordinate transform in 4D spacetime. I.e. it is derived geometrically. It doesn't care about whether the light goes through a vacuum, air, water, glass or what have you.

	Alan is once again debunking himself: If (classical) aether theory were correct, then Airy's experiment should have detected a change in aberration angle consistent with Bradley's formula (using different c).

	~~Airy did not detect such a change, which is entirely consistent with SR. Alan therefore must straw man SR and misapply the relativistic formula in order to try and discredit it.~~

	~~Reply~~

	~~2 replies~~
	2
	~~@TruthNerds~~
	~~@TruthNerds~~
	~~Member (5 years, 9 months)~~
	~~Received one of the highest number of hearts from you~~
	~~Publicly subscribed to you (6 years)~~
	~~• 3 days ago~~
	~~PS: The speed of light is actually the same in~~ all ~~media if you take the front velocity~~ of a light pulse. That might also be called the speed of causality. What changes in water is the phase velocity. While this is very important for some optical effects, namely refraction, it is irrelevant for the derivation of the relativistic aberration formula.

	~~PPS~~: Why do we still use the classical formula? It is simpler and a good approximation for non-relativistic speeds. However, we now know to also only use constant c in it. Then the formula's original derivation becomes invalid, but it remains valid as a numerical approximation. (It can be independently derived as an approximation of the SR formula.)

MCToon at 03:14, 30 June 2026

2026-06-30T03:14:17Z

← Older revision		Revision as of 23:14, 29 June 2026
Line 1:		Line 1:
	Work in Progress:		Work in Progress:

	On 2026-06-26 on the Earth Awakenings Discord server Piezo and MCToon had this conversation:		On 2026-06-26 on the Earth Awakenings Discord server [[Piezo]] and [[MCToon]] had this conversation:

	Insert conversation here		Insert conversation here

MCToon: Created page with "Work in Progress: On 2026-06-26 on the Earth Awakenings Discord server Piezo and MCToon had this conversation: Insert conversation here In the comments section of that video TruthNerds wrote this response: A flat Earther found a formula which he doesn't understand and put some numbers in it. When has that ever happened before! (Warning, long post … see Brandolini's Law) Anyway, Geo claims that Alan calculated the expected stellar aberration in Airy's failure exper..."

2026-06-30T02:50:30Z

Created page with "Work in Progress: On 2026-06-26 on the Earth Awakenings Discord server Piezo and MCToon had this conversation: Insert conversation here In the comments section of that video TruthNerds wrote this response: A flat Earther found a formula which he doesn't understand and put some numbers in it. When has that ever happened before! (Warning, long post … see Brandolini's Law) Anyway, Geo claims that Alan calculated the expected stellar aberration in Airy's failure exper..."

New page

Work in Progress:

On 2026-06-26 on the Earth Awakenings Discord server Piezo and MCToon had this conversation:

Insert conversation here

In the comments section of that video TruthNerds wrote this response:
A flat Earther found a formula which he doesn't understand and put some numbers in it. When has that ever happened before! (Warning, long post … see Brandolini's Law)

Anyway, Geo claims that Alan calculated the expected stellar aberration in Airy's failure experiment and that it doesn't match SR. By plugging in different light speeds, apparently. 😂

Ok, insider joke? I'll elaborate.

Let's first look at what Geo means by Bradley's formula. The classical formula is derived assuming that light propagates as a wave with a given speed in a stationary medium, aka aether, and the application of Newtonian mechanics.

It is θ - arctan(sin θ / (v/c + cos θ)) where θ is the angle of movement relative to the viewing direction, v is speed and c is the speed of light.

Then there's the relativistic formula, which is θ - 2 arctan(sqrt((1-v/c)/(1+v/c)) * tan(θ/2)). The relativistic formula reduces to the classical formula for v << c. Furthermore, for θ = 90° and v<<c, both reduce to v/c (in radians) as an approximation.

Ok, first, let's do some calculations, plain 90° aberration with Earth's average orbital speed gives about 0.0996 mrad (about 20.5 arcseconds) both for the classical and for the relativistic formula. It really makes no difference at those speeds!

Now, what did Alan presumably do to model Airy's experiment? Changing θ makes no sense, we want to keep that constant for comparability. Changing v makes no sense because Earth's speed wouldn't change. So he must've modified c. And that is hilarious!

Why? Well, for how Bradley's formula was derived, it would make sense because it is originally based on the assumption of a wave propagating through the aether. Slower wave propagation would thus affect the aberration angle.

But it doesn't make any sense to vary c in the relativistic formula! The relativistic formula is not derived from any assumption about a wave propagating through a fixed medium, it is based on the Lorentz transformation and the postulates of Special Relativity:

1. The laws of physics are the same in all inertial frames.
2. The speed of light in a vacuum (denoted c) is the same for all observers.

The speed of light to plug into the relativistic formula is always that same c, it has nothing to do with wave propagation in a medium. The formula follows from a coordinate transform in 4D spacetime. I.e. it is derived geometrically. It doesn't care about whether the light goes through a vacuum, air, water, glass or what have you.

Alan is once again debunking himself: If (classical) aether theory were correct, then Airy's experiment should have detected a change in aberration angle consistent with Bradley's formula (using different c).

Airy did not detect such a change, which is entirely consistent with SR. Alan therefore must straw man SR and misapply the relativistic formula in order to try and discredit it.

Reply

2 replies
2
@TruthNerds
@TruthNerds
Member (5 years, 9 months)
Received one of the highest number of hearts from you
Publicly subscribed to you (6 years)
• 3 days ago
PS: The speed of light is actually the same in all media if you take the front velocity of a light pulse. That might also be called the speed of causality. What changes in water is the phase velocity. While this is very important for some optical effects, namely refraction, it is irrelevant for the derivation of the relativistic aberration formula.

PPS: Why do we still use the classical formula? It is simpler and a good approximation for non-relativistic speeds. However, we now know to also only use constant c in it. Then the formula's original derivation becomes invalid, but it remains valid as a numerical approximation. (It can be independently derived as an approximation of the SR formula.)

← Older revision		Revision as of 17:18, 26 July 2026
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	* Stellar aberration does not depend on the distance to the star. In contrast, stellar parallax is only observed for "nearby" stars, which, depending on the available measurement precision, is at most in the hundreds of light years.		* Stellar aberration does not depend on the distance to the star. In contrast, stellar parallax is only observed for "nearby" stars, which, depending on the available measurement precision, is at most in the hundreds of light years.

	To summarize the difference in one sentence: Aberration is a velocity effect whereas parallax is a position effect.		To summarize the difference in one sentence: Aberration is a ''velocity'' effect whereas parallax is a ''position'' effect.

	Stellar aberration is also subject to a minor diurnal effect due to the tangential velocity of an observer on the rotating Earth, at less than polar latitudes.		Stellar aberration is also subject to a minor ''diurnal'' effect due to the tangential velocity of an observer on the rotating Earth, at less than polar latitudes.

	Also, aberration affects sunlight and the light reflected off of planets, though the effect is usually discussed in the context of distant stars. (It is also tiny in comparison to the angular size of Sun and Moon as seen from Earth.)		Also, aberration affects sunlight and the light reflected off of planets, though the effect is usually discussed in the context of distant stars. (It is also tiny in comparison to the angular size of Sun and Moon as seen from Earth.)
Line 20:		Line 20:
	The discovery of stellar aberration in the late 17th century came as a surprise. Scientists were mainly looking for stellar parallax, potentially allowing for a triangulation of the distance of some stars and also confirming the still relatively young heliocentric model.		The discovery of stellar aberration in the late 17th century came as a surprise. Scientists were mainly looking for stellar parallax, potentially allowing for a triangulation of the distance of some stars and also confirming the still relatively young heliocentric model.

	One of the first noteworthy measurements was that of [Eltanin\|https://en.wikipedia.org/wiki/Gamma_Draconis] by Robert Hooke in 1674. At first, the measured deviation was not understood to be a separate phenomenon from parallax. Also, the propagation of light was neither well understood nor the focus of scientific inquiry at the time. Even after Ole Rømer measured the speed of light in 1676, and, in particular, demonstrated that it was not instantaneous, it took decades for scientists to draw a definitive connection between the angles at which stars appeared to be and the way that light propagates in a vacuum.		One of the first noteworthy measurements was that of [Eltanin\|https://en.wikipedia.org/wiki/Gamma_Draconis] by Robert Hooke in 1674. At first, the measured deviation was not understood to be a separate phenomenon from parallax. Also, the propagation of light was neither well understood nor the focus of scientific inquiry at the time. Even after Ole Rømer measured the speed of light in 1676, and, in particular, demonstrated that it was ''not'' instantaneous, it took decades for scientists to draw a definitive connection between the angles at which stars appeared to be and the way that light propagates in a vacuum.

	Once the significance of stellar aberration, and its distinctness from parallax, were understood, there were however a number of astronomical experiments that attempted to use the effect to distinguish between different theories of light propagation, namely emission theory, which treated light as a stream of particles inheriting momentum from the emitting object, and the undulatory theory of light (better known as aether theory), which treated light as a wave in a ubiquitous but "non-tangible" medium.		Once the significance of stellar aberration, and its distinctness from parallax, were understood, there were however a number of astronomical experiments that attempted to use the effect to distinguish between different theories of light propagation, namely emission theory, which treated light as a stream of particles inheriting momentum from the emitting object, and the undulatory theory of light (better known as aether theory), which treated light as a wave in a ubiquitous but "non-tangible" medium.
Line 28:		Line 28:
	In modern science, stellar aberration is understood to be consistent with, and quantitatively predicted by, the theory of special relativity. When a lateral Lorentz boost, i.e. a velocity addition, is performed to transform a ray of light from the inertial reference frame of a star to the inertial reference frame of an observer, the angle of propagation changes depending on said lateral speed. (The existence of "instantaneous" inertial frames is enough.)		In modern science, stellar aberration is understood to be consistent with, and quantitatively predicted by, the theory of special relativity. When a lateral Lorentz boost, i.e. a velocity addition, is performed to transform a ray of light from the inertial reference frame of a star to the inertial reference frame of an observer, the angle of propagation changes depending on said lateral speed. (The existence of "instantaneous" inertial frames is enough.)

	However, one should be careful when citing stellar aberration alone as evidence for special relativity because aberration experiments are not precise enough to be specific towards testing relativity. In particular, while there is a relativistic formula that makes distinct predictions, the "classical" math, e.g. derivable from emission theory or from an aether in which the light source is stationary, still works extremely well in practice.		However, one should be careful when citing stellar aberration ''alone'' as evidence for special relativity because aberration experiments are not precise enough to be specific towards testing relativity. In particular, while there is a relativistic formula that makes distinct predictions, the "classical" math, e.g. derivable from emission theory or from an aether in which the light source is stationary, still works extremely well in practice.

	== Special Relativity Mathematics ==		== Special Relativity Mathematics ==
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	{{Note\|text=Lorentz transformations in general are used to transform spacetime coordinates from one inertial reference frame to another and can apply a velocity boost in any spatial direction, rotate the coordinate axes or move the coordinate origin. Usually origin and coordinate axes are kept fixed for simplicity, and we only apply velocity changes. This specific class of Lorentz transformations are called the Lorentz boosts.}}		{{Note\|text=Lorentz transformations in general are used to transform spacetime coordinates from one inertial reference frame to another and can apply a velocity boost in any spatial direction, rotate the coordinate axes or move the coordinate origin. Usually origin and coordinate axes are kept fixed for simplicity, and we only apply velocity changes. This specific class of Lorentz transformations are called the Lorentz boosts.}}

	In the following, v is the speed of the observer relative to the light source, θ is the angle of relative motion (90° for perpendicular motion) and ɸ is the light's angle of incidence. Note that the actual aberration is θ - ɸ. c is the speed of light in a vacuum.		In the following, ''v'' is the speed of the observer relative to the light source, θ is the angle of relative motion (90° for perpendicular motion) and ɸ is the light's angle of incidence. Note that the actual aberration is θ - ɸ. ''c'' is the speed of light in a vacuum.

	The relativistic aberration formula is:		The relativistic aberration formula is:
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	\|+ Predicted Aberration Angles		\|+ Predicted Aberration Angles
	\|-		\|-
	! v [m/s] !! SR !! Classical !! Small Angle		! ''v'' [m/s] !! SR !! Classical !! Small Angle
	\|-		\|-
	\| 29290.0 \|\| 20.15226208 \|\| 20.15226199 \|\| 20.15226205		\| 29290.0 \|\| 20.15226208 \|\| 20.15226199 \|\| 20.15226205