Part of me wonders if this is a parody thread. In case it’s not, maybe this will help.
Imagine you have a sphere, one light-year in diameter. In the middle of that sphere, you put a lamp. Hold up a coin up on one side of the lamp, so that it now casts a shadow onto that side of the sphere. It takes half a year for the shadow to reach the side of the sphere, but you do end up with a shadow on the side of the sphere eventually. The “shadow” in this case does move at c, because what you are really timing is how long it takes for the last of the light emitted from the map to reach the sphere. After that last bit of light has hit the sphere, there is no more light following it, so the “shadow” appears at the sphere.
Now rotate the coin around the outside of the lamp, so that it takes you 5 seconds to go halfway around the light, which is pretty easy to do since your hand is next to the lamp. Your shadow will now also go halfway around the sphere, and it will only take the shadow 5 seconds to do so. The shadow on the sphere won’t start to move until half a year after you start moving the coin, but the shadow will go halfway around the sphere in exactly 5 seconds after that.
The light moves at c. That’s why it takes half a year from the time you put the coin up in front of the light for the shadow to reach the side of the sphere. All of the light that was already emitted from the lamp still has to get to the side of the sphere. But the shadow moves 1.57 (pi multiplied by the diameter divided by 2 to get half of the circumference of the sphere) light years in 5 seconds, which is dramatically faster than c.
In other words, when you start moving the coin, one second later you are 1/5th the distance around the side of the lamp. The last of the light that came from the lamp before you blocked it with the coin now takes half a year to reach the sphere. After that, there’s a shadow at that spot on the sphere. So the time for the shadow to move 1/5th the distance around the sphere is half a year plus 1 second. Similarly, 2 seconds after you move the coin, the last of the light from the lamp before you blocked it with the coin starts moving towards the sphere. That light takes half a year to reach the sphere, which is half a year plus 2 seconds from the time you first started moving the coin.
If that doesn’t make sense, then I don’t know how to explain it to you.
Nitpick: If I understand your analogy correctly, and the observer is at the center of the sphere, then it might be more accurate to say that it takes a full year for the observer to see the shadow begin to change, because of the half-year transit time of the photons from the center source plus the half-year transit time of the information at the sphere back to to the central observer. An observer at the sphere would see the central light change after six months, while for the central observer moving the coin, the change in light will indeed appear to travel around the sphere in five seconds once it begins, but the observation from the central point won’t be possible until a year has passed. Yes?
To be honest, I cannot see what you are getting at. Moving shadows could potentially stretch far across the universe, if the light source were bright enough; here they stretch more than a light year and (sometimes) move at superluminal speeds.
Yes, exactly. The shadow actually begins to move at a half year after the coin has moved, and completes its move in 5 seconds. But the observer doesn’t see the shadow move until one year after the coin has started its movement, and the shadow completes its movement five seconds after that.
I don’t know how you’ve talked yourself into a philosophical position about something you cannot calculate and therefore demonstrably do not understand. But your philosophical reasoning is factually incorrect and the various calculations prove it.
The perception of the “movement” of the shadow, or of the light beam for the other thought experiments, will lag in time versus its “reality” out at the edge. But that’s a mere artifact of the non-zero transit time of the photons carrying information about the shadow’s / beam’s position from the source to the background, then back to you.
Effectively, there’s no difference between the water sprinkler analogy, where for a strong enough stream, the circumferential speed of the stream’s impact point exceeds the radial speed of the stream itself. Resulting in a simple and readily calculable lag between the azimuth of the stream’s impact point and the azimuth of the sprinkler at that moment.
Cranking the whole thing up in scale and speed to c doesn’t change anything, except needing to account for the lag in perception which is still fully present with the water sprinkler, but is measured in handfuls of nanoseconds and therefore negligible both percentagewise and in human terms. But is fully present in reality.
It appears to be a failure to understand the disconnect between:
The propagation of a shadow from the light source to the screen, which will never exceed c
The apparent transverse movement of the shadow on the screen, which is not constrained by speed limits, since its movement is a geometric illusion, with approximately the same physical substance as the phenomenon of parallax, to which it is related. Nothing is actually moving on the screen. It’s just areas being illuminated, or not.
Wikipedia, the s font of unimpeachable accuracy /s, agrees with me
To move the goalposts clarify, I define a shadow as a coherent projection of a physical object on a surface due to the physical object occulting a light source. It is a broad definition that does not specify the parallax (distances between the light source, physical object and shaded surface). The key point is that there is at least one measurable boundary on the target surface that defines the shadow edge.
As to being an illusion, the shadow is indeed not the physical object that creates it. But a shadow has a cause and effects and is observable, so it is not an abstraction.
One can envision a shadow of high parallax (the distance between the light source and the occulting physical object is much less than the distance between the light source and the shaded surface) and imagine that the transit of the shadow boundary along the surface should exceed c. But, the speed of the light itself delays the transit of the shadow boundary because it has to stop arriving at c.
But there is an additional complication. The shadow at a high parallax becomes incoherent, meaning it is no longer distinct enough to measure reliably. You can no longer tell where the boundary is. This is an inherent aspect to how a shadow is created in the first place.
The physical object that creates the shadow must have an edge where the occultation occurs. One thing that always happens to light at occultation edges is diffraction. The light is scattered somewhat. Obviously not enough at closer proximities to prevent a relatively clear image, but the farther away the shaded surface is, the greater the diffraction spread is. At a high parallax, the diffraction cone overtakes the occultation, scattering photos ahead of and behind the shadow boundary to effectively erase it into a vague dimming that does not fit with the definition of a coherent shadow: its rate of transit cannot be measured because its light/dark boundary cannot be established.
Thus, a shadow near enough to meaure is constrained in its boundary transit by the speed of the light failing to arrive as the occulting object moves. And a very distant shadow is not a shadow because diffraction has blurred it into incoherence.
The Wikipedia article is fine. It’s referring to the speed at which the loss of light goes from the source to the projection surface, which is of course limited to c. The speed of the shadow along that surface can still exceed c. And it notes that the movement is really just a new projection of the shadow in a different position.
The wiki article is talking about the interuption of the light source propegating along the path of the light; not the shadow appearing to move along a wall. So your cite is correct, but not relevant to the question at hand. I think you should try to read this thread more closely and try to understand what people are saying.
Yes, I did. Did you read what I wrote? Did you understand it?
Imagine the position where the Earth’s orbit aligns to the plane of the orbit of Jupiter, and imagine both planets being in that particular alignment position, so that the Earth is exactly between the Sun and Jupiter. Would you expect to see a shadow of the Earth on Jupiter?
My point is that high parallax fails to create an actual shadow, because diffraction around the edges of the occulting body erases the primary shadow. The diffraction overtakes the primary occultation, scattering photons ahead of and behind the shadow boundary lines. The shadow becomes an indistinct dimming that cannot reliably be observed/measured.
Your hypothetical assumes a pure occultation cylinder that is not at all bounded by diffraction cones. I am not talking about theoretical shadows, I am talking about shadows as they occur in reality. Go outside, stand under that oak and look at the shadows of the leaves on the driveway: do the shadows have sharp, crisp edges? If so, you are inhabiting a universe that is not like the one I live in.
The Moon-Earth parallax is relatively small – about 0.2% of the Earth-Sun distance – so the Moon can cast a fairly well-defined shadow on the Earth, and vice versa. When the parallax gets a lot higher, you lose your shadow in the diffraction.
Think about pulsars. Rapidly rotating neutron stars, emitting a tight beam of radiation that sweeps across space; a typical pulsar may rotate anywhere between once every couple of seconds, to thousand times a second. They have been observed hundreds of light years distant from us, so that’s a beam of radiation sweeping (at our range) a circle of hundreds of light years in radius, multiple times per second.
That projected spot of radiation is travelling many multiples of the speed of light. The spot is only being propagated out from the source at the speed of light, but the place the spot lands is a moving target, moving incredibly fast.
Sorry, but this is nonsense. If the Sun were occluded by a half-shell that blocked its light, no light whatever would reach one half of the universe. Maybe there would be a small region of penumbra at the edges of the shadow, but most of the shadow would be totally free of light.
Now imagine the Sun embedded in a nebula that reaches in all directions for at least a light year. If my hypothetical half-sphere were to orbit the Sun in a matter of days, then the shadow of this sphere would move considerably faster than light at the edge of this nebula.
Indeed, this is almost exactly what is happening in Hubble’s Variable Nebula; the star there (R Mon) is surrounded by a bank of intermittent clouds which are similar in size to itself, and on occasion these clouds block out the light of the star completely in certain directions. Diffraction and penumbral overlapping are not sufficient to allow these shadows to disappear before they cast superluminal shadows,
This is not a myth or a misperception - it is really happening in a star a few hundred light years away, and it shows that your hypothesis is incorrect.
None of the details you are bringing up now about parallax and diffraction are relevant. And your main thesis, that a moving shadow conveys information, is wrong so everything you’ve said is based on an incorrect assumption.
Shadows aren’t objects and therefore the edge of a shadow can appear to move at superluminal speeds. No information is being conveyed by the appearance of the edge of the shadow.
That is a horrifically bad hypothetical. If I were standing on Pluto, do you actually think I could see the terminator line of your half-shell pass across the surface of the planet? Seriously?
Something is happening at Monocerotis. Exactly what that is has not been established.