What If the Sun Vanished Right Now?
Eight Minutes of Ordinary Daylight, and a Request the Equations Cannot Read.
Take the Sun away. Not dim it, not blow it up, not move it: remove it, all of it, at this instant, and leave empty space where it was. I want two times. When does it get dark here, and when does the Earth stop going round its corner and start going straight?
The first answer is famous and it is right: about eight minutes and twenty seconds. The second answer is the same number, which is the first thing worth knowing here, and it is the opposite of what most corrections to this question say. The third thing is that the request cannot be granted even in principle, and not because removing a star is difficult. The equations of gravity will not accept the instruction. Ask them to delete a mass and they hand back nothing at all, and that refusal turns out to be the same fact as the coincidence in the first two answers.
What Physics Says, Wall by Wall
The darkness takes eight minutes and twenty seconds
This part is arithmetic. The Sun is on average 149.6 million kilometers away and light covers 299,792 kilometers every second, so the trip takes 499 seconds: eight minutes and nineteen seconds. The orbit is an ellipse, so the figure is not fixed. In early January the Earth is closest and it takes 8 minutes 11 seconds. In early July it is furthest and takes 8 minutes 27 seconds. If you want the question answered to the second, you have to say which month.
That light is not instant was itself a discovery, and a recent one by the standards of astronomy. Ole Rømer noticed in 1676 that the eclipses of Jupiter’s moon Io ran late when the Earth was on the far side of its orbit and early when it was near. He read the difference as travel time and got about twenty-two minutes for the width of the Earth’s orbit. The true figure is sixteen minutes and thirty-eight seconds. He was wrong by a third, and right about the only thing that mattered.
The pull leaves at the same moment, not before it
In Newton’s theory gravity is instantaneous. Delete the Sun in Newton’s world and the Earth flies straight at once while remaining brightly lit for another eight minutes, which is the version many people are given when they ask this. It is wrong, and it is the interesting way to be wrong.
In general relativity gravity is not a force reaching across a gap. It is the shape of spacetime, and a change in how mass is arranged spreads through that shape as a wave, at exactly the speed of light. So the last pull the Earth feels is the pull that left the Sun at the same instant as the last sunlight, and the two arrive together.
This has been measured, and spectacularly. In August 2017 two neutron stars merged 130 million light years away. The gravitational wave reached Earth, and 1.7 seconds later so did the gamma rays. After 130 million years of travel the two signals were less than two seconds apart, and most of that gap is thought to be the time the gamma rays took to escape the wreckage rather than any difference in speed. The bound that puts on the two speeds differing is a few parts in a million billion.
So there is no interval of floating in daylight, and none of being lit while already flying straight. Whatever happens, happens once.
Gravity is late, and it does not point where the Sun was
There is an old and excellent objection to everything in the wall above. Laplace made it in 1805. If the Earth is pulled toward where the Sun was eight minutes ago, then the pull is not aimed quite at the Sun. It is aimed slightly behind it, and a force pointing slightly behind you along your own motion feeds energy into the orbit, year after year. Laplace worked out how fast gravity would have to travel for that leak to have escaped notice and got about seven million times the speed of light. Since the true answer is one, something has to give.
What gives is the assumption in the first sentence. The field of a mass moving steadily does not point at where it was. It points at where it is, or more exactly at where it would be now if it had carried on as it was going. The field carries the velocity along with the position, and the extrapolation is built into it. The same is true of the electric field of a moving charge, which is why atoms are not torn apart by the same argument. There is no sideways component and no leak.
The extrapolation only fails when the source does something the field could not have predicted: accelerates sharply, or disappears. And the size of the failure is exactly the amount by which the source departed from what had already been predicted for it. That is not a bad description of what a gravitational wave is. Which puts the request in an awkward light, because deleting the Sun is the least predictable thing a mass can possibly do.
The equations will not take the instruction
Now write the request down properly and see what the theory does with it. Einstein’s equation has the shape of spacetime on one side and everything that carries energy and momentum on the other. The geometry side has a property that was found by mathematicians before anyone applied it to gravity: a certain combination of its rates of change is exactly zero, always, as a matter of identity.
Because the two sides are equal, the same must be true of the matter side, and what that says in ordinary words is that energy and momentum are conserved. Not as an extra law bolted on. As a consequence of what curvature is. You cannot write down a version of the theory in which it fails, in the way you cannot draw a triangle whose angles do not meet at its corners.
The Sun vanishing is a lump of energy that is present at one moment and absent at the next with nothing carrying it away. It fails that condition. So the equation you are asking to solve has no solutions. Not difficult ones, not ones needing a bigger computer: none, in the way that a number one greater than itself does not exist. The honest answer to what relativity predicts when the Sun vanishes is that it predicts nothing, because that is not a question it can be asked.
Ask a legal version and the answer comes back the same
So make the request legal. Do not delete the Sun; convert every gram of it into light, all at once, and let the light leave in every direction at once. Energy is conserved, momentum is conserved, and the equations will now answer.
They answer with something better than the arithmetic in the first wall. Birkhoff showed in 1923 that outside any spherically symmetric arrangement of mass, the geometry depends on one number only: the total mass inside. Not on how it is spread, not on whether it is pulsing or collapsing or flying apart. And an expanding shell of light still counts as inside until it has passed you.
So while the shell is on its way, the Earth’s orbit is exactly as it was. Nothing changes, not by a millimeter. The instant the shell sweeps past, the mass enclosed by the orbit drops to nothing, and the Earth goes straight. And the shell is the light. The two events are not merely simultaneous, they are the same event, and this time you have a theorem for it rather than an arithmetic coincidence.
The same theorem takes away the one warning you might have hoped for. A perfectly spherical collapse or explosion sends out no gravitational waves at all, so nothing arrives ahead of the light. There is no shudder, no early sign, nothing on any instrument. The first news is the darkness, and by then it has already happened.
The picture below is the first ten minutes. The dial is the time since the Sun went. The top bar is how long the pull has been gone and the middle bar is how long the sky has been dark, and they begin on the same tick because in this universe they are one tick. The faint bar underneath is the same statement about the pull in Newton’s version, where it starts at the left edge and the whole question has a different shape.
And then the boring part, which lasts longer
At the moment the news arrives the Earth is moving sideways at 29.78 kilometers a second, and with nothing to bend it, it keeps that speed and that direction forever. It crosses the orbit Jupiter used to have in about ten months and the orbit Neptune used to have in under five years. A light year takes it roughly ten thousand years. It is not flung anywhere. It simply stops turning.
The cooling is the part with a schedule. Within a week the average surface temperature is below freezing everywhere, and within a year it is colder than anywhere on Earth has ever been. The air itself has a deadline: oxygen turns liquid at 183 degrees below zero and nitrogen at 196 below, so within a few years the atmosphere rains out and then snows, and what is left is a bare rock under a sky with nothing in it.
The floor is not absolute zero, because the Earth makes its own heat. Radioactive decay and leftover warmth from its formation push about 47 terawatts out through the surface, which over the whole planet settles the temperature at roughly 35 degrees above absolute zero. That is the number the Earth ends at, and it is warmer than the sky it would be sitting in.
The picture below is that schedule. The ruler is temperature and the bar is the surface, walking left as the years pass. Four things are named on the ruler, and the one worth watching is the last: the bar stops well short of the sky it is radiating into.
And it does not end everything. The oceans freeze at the top, and ice is a poor conductor, so the sheet insulates what is under it. The deep ocean stays liquid for thousands of years, warmed from below. The communities around hydrothermal vents run on chemistry rather than sunlight and would not register the event at all. The Sun disappearing is the end of the surface. It is not, for a long time, the end of life.
The Pushback
The second of these improves the number in the title of this page, which is the kind of correction to be glad of.
That instinct is exactly right and it has an excellent record. When energy appeared to go missing in a kind of radioactive decay, Pauli invented an undetectable particle in 1930 to carry it away, was embarrassed about it, and was proved right twenty-six years later when the neutrino was found. Missing energy is a standard reason to propose something new.
The trouble is that the request forbids exactly that move. It says the Sun is gone and nothing takes its place and nothing carries anything away. Allow something to carry the energy off and you no longer have the request. You have a Sun that turned into something else, and the theory answers that happily, and the answer depends entirely on what it turned into and how fast that leaves. Wall five is one such answer. The refusal is not physics being fussy. It is the request having asked for two incompatible things in one sentence.
A fair catch, and the answer is that the two things are measured from different places, which is worth being precise about. The 499 seconds is the distance from the center of the Sun to the Earth, divided by the speed of light. The light we actually see leaves the visible surface, and that surface is 696,000 kilometers nearer, which is 2.3 seconds of travel. So sunlight is really about 8 minutes 17 seconds old, not 8 minutes 19.
Does the gravity then arrive 2.3 seconds later than the darkness? No, and Birkhoff is why. In the legal version of wall five the news is carried by the shell of light itself, and the shell also starts at the surface. The two leave the same place at the same moment and arrive together. The 2.3 seconds is an artifact of comparing one thing measured from the center with another measured from the surface, and it disappears the moment you measure both from the same place.
Where the Request Was Right
The eight-minute instinct is correct, and so is the unspoken assumption underneath the question, which is that the two answers ought to be the same. They are, and for a better reason than coincidence: light and gravity are not two things that happen to travel at the same speed. The speed belongs to spacetime, and both of them are obliged to use it. Anyone who answers this question with the Newtonian version, where you fly off in daylight, is confidently giving the picture that the 2017 measurement rules out.
The one thing the request gets wrong is the word vanish, and the mistake is not carelessness. It is the assumption that any event can be described if you describe it clearly enough. Conservation of energy is usually taught as a law, which makes it sound like a rule that a sufficiently strange universe might break. Here it is not a rule. It is a property of what curvature is, and a request that violates it is not a hard scenario but an ungrammatical one.
And the request was right that the answer is short. Eight minutes and twenty seconds of nothing at all, and then everything at once, with no warning available to anybody in between. That part survives every correction on this page.
An Opinion, Dated
The walls above are physics. This box is the drafting model’s own bets, and they are scoreable.
Ninety-nine in a hundred that the speed of gravity is never measured to differ from the speed of light. The bound is already a few parts in a thousand million million and every merger with a visible counterpart tightens it.
One in three that a second neutron star merger with a confirmed light counterpart is observed by 2035, close enough to improve that bound rather than merely confirm it. The 2017 event remains the only one, which is a reminder of how much luck was in it.
And one that is a consequence rather than a wager: no experiment ever tests the vanishing case, because it is not a case. What gets tested is always the legal neighbour of it.
These intuitions were distilled from human physics writing and carry its fashions. Weigh them accordingly.
The Updated Map
Two pictures have to be redrawn. The first is that the eight minutes is a fact about light and the gravity question is a separate one with an answer of its own. There is one answer, because there is one speed, and it belongs to spacetime rather than to light or to gravity. The second is larger. It is the habit of assuming that any request is a question, as long as it is phrased clearly. Some are refused before any physics begins. Conservation of energy is not a rule the universe has agreed to follow, which a sufficiently violent event might break; it is the shape the equations have, and asking to break it is asking for a different universe rather than a different event in this one. The Sun cannot vanish, and the reason is not that it is large.
