# A question about speed of light and sunrise time

I would like to propose a school task, that may lead to some paradox (to my mind):

It is known that light travels from Sun to Earth for about 8 minutes. If light propagates instantaneously will we observe sunrise 8 minutes earlier?

DaveC426913
Gold Member
I would like to propose a school task, that may lead to some paradox (to my mind):

It is known that light travels from Sun to Earth for about 8 minutes. If light propagates instantaneously will we observe sunrise 8 minutes earlier?
No. Sunrise is due to the rotation of the Earth, not due to the sun turning on and off.

Setting aside the strange question of "what would the world be like if the world weren't the way it was?"...think of this:

Regardless of whether any particular photons of light coming from the sun took 8 milliseconds, 8 minutes or 8 days to reach Earth, the photons making up the sun's rays are continuously streaming from the sun - essentially a solid line. The Earth turns and, when the spot where you are standing has a clear line of sight with the Sun, that's sunrise.

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But let’s consider another point of view. Suppose I’m standing, looking to East and waiting for sunrise. When I see an edge of solar disk I conclude that my eye were hit by photons emitted by Sun 8 minutes before. But since light propagates along straight line, 8 minutes ago the edge of solar disk, edge of Earth and my eye were on a straight line. If light propagates instantaneously, I could see the sunrise earlier. Where I’m wrong?

russ_watters
Mentor
Where you went wrong is that the sun isn't moving, the earth is rotating.

Don't sweat it, I wiffed on this exact question a few months ago.

Where you went wrong is that the sun isn't moving, the earth is rotating.

It depends on choice of frame of reference. Within Earth-based frame the Earth isn't moving, but the Sun is rotating.

DaveC426913
Gold Member
It depends on choice of frame of reference. Within Earth-based frame the Earth isn't moving, but the Sun is rotating.
It doesn't matter which frame of reference. You can consider the speed of light to be infinite or zero or anything you want. It is a continuous beam, and the speed of the particles within the beam is irrelevant. The only thing that affects the time of sunrise is the angle of the beam related to your position on the Earth and the horizon.

Drakkith
Staff Emeritus
If you are somewhere you can see the horizon, and you see the sun just start rising, you are viewing light that has already travelled 8 minutes to get to us. Right before the sun starts to come up the light is simply blocked by the Earth. The moment there is a clear LOS to the Sun you see it because there is already light there to see.

mathman
The difference between instantaneous and 8 minutes is about when the photons you see left the sun. Since photons are continuously leaving the sun it doesn't matter.

As others have indicated the time is set by the earth's rotation.

It doesn't matter which frame of reference. You can consider the speed of light to be infinite or zero or anything you want. It is a continuous beam, and the speed of the particles within the beam is irrelevant. The only thing that affects the time of sunrise is the angle of the beam related to your position on the Earth and the horizon.

To maybe expand a bit on this. The time a photon of light takes to travel from the sun to the earth ≈ 8mins 19 secs.

However because photons are emitted continuously they is no time delay between the sun being inline with your position and photons reaching the earth, because 8 mins and 19 seconds ago photons where already zipping across space towards the earth.

Think of it like a line of traffic passing a window in a traffic jam. Each car moves very slowly but because cars are constantly entering the stream of traffic the stream of cars passing the window is constant.

phinds
Gold Member
It depends on choice of frame of reference. Within Earth-based frame the Earth isn't moving, but the Sun is rotating.

You are missing the point. Your question has been correctly answered and you just don't seem to like the answer.

Rob D
Gold Member
Imagining for the sake of virtual experiment that the earth is a smooth orb and we are all 2m in height, then the photons exciting our eye cells at the proclaimed moment of sunrise - previously stated as the moment line of sight is established with the sun - are all 8mins 19secs old. But oh if it were so simple.

Our problem is that our planet has an atmosphere and that atmosphere, at the moments nearing line of sight but slightly before, refract the sunlight and bend it in an arc toward the sunrise observer so that he perceives the sunrise without actually achieving line of sight with any portion of the solar disk. I like to imagine the earth coated with a twenty mile thick lens of varying density that refracts all light near the visible horizon.

This of course has nothing to do with the fact that any photons emitted by the sun are 8mins 19secs "old' when we see them whether refracted or not. I just thought that we were leaving it out.

RobD

AlephZero
Homework Helper
There is no problem understanding the analogous problem where the distance to the object changes. As soon as the telescope was invented, people discovered that the moons of jupiter appear to speed up and slow down in their orbits as seen from earth, as the distance between earth and jupiter changed.

I'm certainly missing something about to why the OPs thought experiment is fundamentally different.

Suppose the sun is already well above the horizon, and the speed of light suddenly becomes instantaneous. I would say that for 8 minutes we would see two images of the sun at different points in the sky, at one from the light arriving at finite speed, and one from the instantaneous light. This is the same situation as observing a fast moving plane, travelling across your field of view, and noticing that the sound appears to come from a position behind where you see the plane.

Unless the answers to the OP's question are considering time measurement in terms of solar time, i.e. the sun's apparent position in the sky. In other words, when the speed of light becomes instantaneous, all clocks showing solar time will have an error of 8 minutes, and when you reset the clocks sunrise is at the same time as before???

DaveC426913
Gold Member
No Aleph, we are not talking about the motion of objects against the background stars, or relative to other objects, that's what you're describing.

We are talking about the movement of the Earth that we are standing on. Sunrise is determined by the angle of the horizon and the angle of the sun to us. And that does not change regardless of how fst or slow the particles within the sunbeam are moving.

I could set up a clear acrylic pillar 93 million miles long, attach one end to the Sun and the other end to the Earth. When the Earth rotates so that the pillar comes into view, that's sunrise. It makes no difference whether any particles in the pillar are moving at c or zero.

I would like to propose a school task, that may lead to some paradox (to my mind):

It is known that light travels from Sun to Earth for about 8 minutes. If light propagates instantaneously will we observe sunrise 8 minutes earlier?

The light from the sun is already at the earth. At night, it is simply blocked from your eyes by the horizon. When the earth rotates so that the horizon is no longer blocking this light, the light only has to jump the remaining distance from the horizon to your eyes...NOT from the sun to your eyes. That's like, what? 5km? There is still some delay, but not 8 minutes.

It's akin to opening the blinds in your room during the day. You don't open the blinds and wait 8 minutes for the light to fill the room, because the light is already there, at the blinds, at the window. As soon as you open the blinds, it then takes just a nanosecond for it to jump from the window to your room.

AlephZero
Homework Helper
We are talking about the movement of the Earth that we are standing on. Sunrise is determined by the angle of the horizon and the angle of the sun to us. And that does not change regardless of how fst or slow the particles within the sunbeam are moving.

OK, I think I understand your agument now, but I still think it's wrong.

This is what I think you are saying. The sun is emitting a continuous stream of photons in all directions. At any instant in time, these are striking half the surface of the earth and the other half is in shadow. This is independent of the speed of the photons, therefore the speed makes no difference, and the time of sunrise and sunset is determined only by the rotation of the earth about its axis.

I disagree, because you are ignoring the rotation of the earth about the sun. The speed around the orbit is about 30 km/s or about 10^-4 times the speed of light. The apparent direction of the light as seen from the earth is given by a triangle of velocities. Ignoring relativity (because it's so long since I studied SR I have forgotten the details!) the angular change of apparent direction will be 10^-4 radians. The earth rotates once / 24 hours = 2 pi / 86400 = 7.3 x 10^-5 rad/sec, so a rotation of 10^-4 rad takes about 1.4 seconds.

That certainly isn't the same as 8 minutes, but it's big enough to measure!

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Dear Lsos, Dave, phinds et al

I don’t argue with you, your reasoning seems to be clear enough. But could you not tell that I’m wrong, but point out where I’m wrong.

I prefer consider the situation from point of view of reference frame where the Earth is still (no movement, no rotation). May I do it? Within this framework the Sun revolves around motionless Earth. Since light propagation is straightforward, I can not see the Sun beyond the horizon. Since it takes 8 min for light travelling to my eye, I see not the present position of the Sun but its position 8 min ago. When I see the Sun at the horizon it means for me that it was there 8 min ago. Where is my mistake?

Dear Lsos, Dave, phinds et al

I don’t argue with you, your reasoning seems to be clear enough. But could you not tell that I’m wrong, but point out where I’m wrong.

I prefer consider the situation from point of view of reference frame where the Earth is still (no movement, no rotation). May I do it? Within this framework the Sun revolves around motionless Earth. Since light propagation is straightforward, I can not see the Sun beyond the horizon.

If you really want to use such a reference frame, you have to account for the fact that light won't travel in a straight line, so it is possible to see the sun when it's behind the horizon.

Dear Lsos, Dave, phinds et al

I don’t argue with you, your reasoning seems to be clear enough. But could you not tell that I’m wrong, but point out where I’m wrong.

I prefer consider the situation from point of view of reference frame where the Earth is still (no movement, no rotation). May I do it? Within this framework the Sun revolves around motionless Earth. Since light propagation is straightforward, I can not see the Sun beyond the horizon. Since it takes 8 min for light travelling to my eye, I see not the present position of the Sun but its position 8 min ago. When I see the Sun at the horizon it means for me that it was there 8 min ago. Where is my mistake?

But a reference frame where the Earth is still with no orbit and rotation is not what happens in reality so there is nothing to be gained by using this frame. Also making the sun orbit the "still" earth != earth orbiting the "still" sun.

DaveC426913
Gold Member
That certainly isn't the same as 8 minutes, but it's big enough to measure!

That may be so, but it has nothing to do with the OP's question; it merely obfuscates the answer.

DaveC426913
Gold Member
If you really want to use such a reference frame, you have to account for the fact that light won't travel in a straight line, so it is possible to see the sun when it's behind the horizon.

willem is correct (though it took me a while to visualize it). If you look at the frame in which Earth is rotationless and the sun is moving around the Earth, you would observe curving paths of light. A photon would appear to curve over the horizon toward you.

Imagine a photon were instead a tracer bullet, fired from the vicinity of the sun. Someone in the right position could watch it approach. No matter when they looked at it over the 8 minutes (or 8 hours), it would appear as a dot directly in front of the sun (since it's always in line with the sun) - but - the sun is moving across the sky over that time. Your tracer bullet would appear to be following a curved path through space toward them.

If light can reach you from behind the horizon (which means "sunrise" will occur before "dawn"), then it is obvious that this setup is going to mess with your time measurements. You must choose a frame of reference that gives you accurate readings.

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AlephZero
Homework Helper
That may be so, but it has nothing to do with the OP's question; it merely obfuscates the answer.

The OP asked "will the sun rise 8 minutes earlier". You claimed "It makes no difference". I claim it does make a difference, but not 8 minutes difference (and you haven't attempted to refute my argument).

In what way is that "obfuscation?"

AlephZero
Homework Helper
willem is correct (though it took me a while to visualize it).

Willem's point that you can see the sun when it is behiind the horizon is exactly the same as my "triangle of velocities" argument. Either you can work in a coordiate system where the path of the photons is curved, or you can work in a system where the path is straight but the horizon moves. Two different ways of looking at the same thing.

DaveC426913
Gold Member
The OP asked "will the sun rise 8 minutes earlier". You claimed "It makes no difference". I claim it does make a difference, but not 8 minutes difference (and you haven't attempted to refute my argument).

In what way is that "obfuscation?"

Uh well, because it is a red herring as far as the OP's understanding goes. It doesn't help the OP understand where he's going wrong in thinking that the 8 minute delay will cause the sun to appear where it was 8 minutes ago (which is what he's asking). That's the crux of the issue.

We could also point out that blue light will refract more than red as it passes through the atmosphere, causing an additional delay - or that the rarefied interplanetary gas and dust acting as a non-vacuum medium would cause a delay. Would you say pursuing these are going to help - or hinder - the OP's understanding the 8 minute delay of light?

phinds
Gold Member
Dear Lsos, Dave, phinds et al

I don’t argue with you, your reasoning seems to be clear enough. But could you not tell that I’m wrong, but point out where I’m wrong.

I prefer consider the situation from point of view of reference frame where the Earth is still (no movement, no rotation). May I do it? Within this framework the Sun revolves around motionless Earth. Since light propagation is straightforward, I can not see the Sun beyond the horizon. Since it takes 8 min for light travelling to my eye, I see not the present position of the Sun but its position 8 min ago. When I see the Sun at the horizon it means for me that it was there 8 min ago. Where is my mistake?

You are asking two entirely different questions and getting confusted by conflating the two.

The first issue you raise is whether or not you would see sunrise earlier if the speed of light were infinite. The answer is no and this has been explaned in a couple of ways and I don't think I can, or need to, add anything to that.

The second issue, that got brought in AFTER your original post, was whether or not you see the sun (with the current speed limit of c) 8 minutes off from where it "actually" is when the photons hit your eye, and the answer the this is yes. The photons are traveling on a straight line from where the sun was 8 minutes before they hit your eye. In fact, had the sun magically disappeared 7 minutes and 59 seconds ago, you would not even KNOW about it for another second. Everything you "see" about the sun is 8 minutes behind.

I think you had a correct understanding of the second issue and let that get in the way of your understanding of the first issue.

I would like to propose a school task, that may lead to some paradox (to my mind):

It is known that light travels from Sun to Earth for about 8 minutes. If light propagates instantaneously will we observe sunrise 8 minutes earlier?

The further we look, the more we see into the past. That is a consequence of the finite time it takes light to reach our eyes. You mention that it takes 8 minutes for light to travel from the sun to our eyes. For that reason, the apparent position of the sun is not the 'real' position of the sun. The apparent position is where the sun was 8 minutes ago. If light would travel instantaneously, the sun would be at the same position when it emitted the photon as when the photon reached your eye. That means that you would then see the sun where it 'actually' is. To see the sunrise means that photons have traveled from the sun to your eyes. The moment at which you see the sunrise therefore happens 8 minutes later than the moment at which the sun was positioned such to allow emitted photons to reach your eyes without earth being in the way. If light would travel instantaneously, you would see the sun without delay as soon as it reached this position. Therefore, the sunrise would be visible 8 minutes earlier.