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If photons potentially take millions/billions of years to find their way to the surface of the Sun from the core, bouncing off billions of other atoms on their way. Is it theoretically possible to have a period of time of any length, where no photons make it to the surface? I realise that given the sheer amount of photons created and moving at the speed of light, any such event would be undetectable but is it possible that at some brief moment in time the Sun essentially blinks?

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    $\begingroup$ Sun has somewhat constant energy production and the same power crosses every layer. Where do you intend to store a second worth of solar luminosity? $\endgroup$
    – fraxinus
    Commented Jun 8 at 21:00
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    $\begingroup$ @fraxinus having read three good answers this question has generated, including Prof. Rob's interesting, educational and somewhat qualified "yes", I think your comment is more snark than science. voting to leave open. $\endgroup$
    – uhoh
    Commented Jun 10 at 3:53
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    $\begingroup$ The Q is good enough as is, my comment was intended to hint the author of an important aspect of his idea $\endgroup$
    – fraxinus
    Commented Jun 10 at 5:23
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    $\begingroup$ I have to point out that in about 20 billion years sun will be a black dwarf, and will only emit infrared. It will then not emit any visible light until falling onto another body. Whether that counts as a blink is a rhetorical question. $\endgroup$
    – Basilevs
    Commented Jun 10 at 13:02
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    $\begingroup$ Would that be the same as the "opaque plasma" stage of the big bang? $\endgroup$ Commented Jun 10 at 18:46

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Is it theoretically possible for a statue to wave at you? After all the atoms in a statue are moving randomly, so they could (by chance) all move in the same direction.

This doesn't happen.

It is the same with the Sun. Photons are emitted from its surface randomly at a rate of about $10^{45}$ photons per second. Since it is random you can ask for the probability of no photons being released in a second, and the number is so very small that it would make you wince (of the order $\exp(-10^{45})$).

At this level of improbability, we can't reasonably say, "It's a theoretical possibility" and settle on "This is impossible", because it won't happen.

The fact that photons take a long time to reach the surface is irrelevant to this. Moreover, it would be very detectable, by virtue of the Sun going dark for a second.

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    $\begingroup$ It will not go completely dark, it will dim for 3-4s. After all, its radius is ~2.5s. A nice black ring is to be expected, expanding from the visible center. Of course, we could calculate the probability of an Earth-directed time-synchronous blackout and this is many, many orders of magnitude higher and still deep into the 'impossible' realm. $\endgroup$
    – fraxinus
    Commented Jun 8 at 20:55
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    $\begingroup$ It's impossible either way $\endgroup$
    – James K
    Commented Jun 8 at 21:23
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    $\begingroup$ The probability of an Earth directed time-synchronous blackout is exactly the same as a blackout in a given second. $\endgroup$
    – Pere
    Commented Jun 9 at 9:52
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    $\begingroup$ (Nitpick: the atoms in a statue aren't moving randomly: AIUI, they're vibrating around (roughly) fixed positions in a rigid lattice, with amplitude depending on the temperature, so it would take more than just random motion to make the statue wave.  But I think a gaseous model (whose molecules do move randomly) would work.) $\endgroup$
    – gidds
    Commented Jun 10 at 13:11
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    $\begingroup$ A plank time is about 5.4e-44 seconds long, so the sun emits about 54 photons per plank time. How big is the chance that there is a plank time where no photon is emitted? But then i guess you have to deal with relativity (there is no such thing as simultaneity), quantum properties (can you detect the exact location of a photon?) and the fact that the sun hasn't a exactly defined surface. $\endgroup$ Commented Jun 11 at 10:41
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This is spontaneous reversal of entropy. It happens at Planck times and Planck lengths, but for macroscopic events, the likelihood is the product (not sum) of the particle event probabilities, all of which are tiny.

Electrons tunnel. Word on the street is that small molecules can. Cats and chairs don't. The sun, being even more massive, certainly doesn't reverse entropy.

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    $\begingroup$ Given how they can appear in the most random/unexpected ways, cats can definitely quantum tunnel... I'll give you chairs, though. $\endgroup$
    – TripeHound
    Commented Jun 9 at 6:41
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    $\begingroup$ See Clifford Simak's seminal paper on the subject, Catface. $\endgroup$ Commented Jun 10 at 10:29
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    $\begingroup$ Spontaneous reversal of entropy happens on scales much larger than Planck scales. On scales that are closer, in terms of orders of magnitude, to macroscopic scales than to Planck scales. In fact there are some things that can be considered to be reversal of entropy that happen at macroscopic scales. You might be confusing the first and second laws of thermodynamics and the second. The former can be violated at Planck scales. $\endgroup$ Commented Jun 11 at 3:03
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The answer is yes, for a small time interval $\tau$ seconds, there is a probability $\sim \exp(-10^{45}\tau)$ that no photons are emitted by the Sun.

Photons do not take millions of years to find their way to the surface of the Sun. They are absorbed and then remitted in different processes on short length scales and from that you can estimate timescales which looks like it effectively takes a million years to reach the surface.

In reality, the photons escaping the Sun are emitted/created from the photosphere, they do not come from the centre.

Having got that out of the way. The Sun emits $3.8\times 10^{26}$ W with a spectrum that peaks at $\sim 550$ nm. Crudely assuming all photons have that wavelength, the Sun emits $10^{45}$ photons per second.

If we assume that counting those photons obeys Poissonian statistics, then the probability of emitting zero photons in a time $\tau$, when $10^{45} \tau$ is the expectation value, is $\exp(-10^{45}\tau)$, where $\tau$ is in seconds. So set your probability threshold and work out $\tau$.

e.g. If you want a 1 in $n$ chance that in some time interval the Sun emits no photons $$\frac{1}{n} = \exp(-10^{45}\tau) \ . $$ Take natural log of both sides to get $$\tau = 10^{-45}\ln(n)\ .$$

Of course you can modify the problem to ask whether if you (don't do this) look at the Sun, or use a camera with an exposure time $\tau$ seconds to take a picture, what is the probability of the Sun emitting no photons in your direction. That is a similar problem, but you need to reduce the figure of $10^{45}$ to be appropriate for the fraction of the Sun's light intercepted by your detector.

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    $\begingroup$ I'm wondering whether there are fundamental restrictions preventing such a blackout for intervals above some threshold. Yes, if 10^30 or so photons from the Sun hit my eye per second randomly, there 10^-35s intervals without photons will occur -- but that's probably not what the OP meant. They probably meant, say, something like at least 1/1000 or 1/100 seconds. That's akin to ask whether a pebble can move 1/100 on my desk because the thermal movement of its atoms coincidentally was aligned for a moment. But that's not possible: The sum of all momentums is close to zero and cannot change. $\endgroup$ Commented Jun 10 at 5:42
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    $\begingroup$ Depending on the exact mechanism of radiation production in the photosphere (oscillations? collisions?), perhaps it would be necessary to align all movement (to direct radiation inwards) which is impossible like with the pebble. Or something else impossible (not improbable) must happen. Then there is the problem of energy storage fraxinus mentioned in a comment. There may not be a mechanism to store the energy flowing through the underlying layer at all. Even just 1/1000 of a second is tremendous energy. Perhaps the sun would explode from the resulting shock wave reverberating. $\endgroup$ Commented Jun 10 at 5:52
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    $\begingroup$ @Peter-ReinstateMonica $exp(-10^{42})$ is too small for my calculator. I think statements about what is impossible must consider the uncertainty principle. $\endgroup$
    – ProfRob
    Commented Jun 10 at 7:06
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    $\begingroup$ A good example of where "impossible" thermal movement does in fact happen would be the aLIGO mirrors - these 50 kg mirrors are displaced by thermal motions in the mirror coating by sufficient $\sim 10^{-18}$ m to provide a significant source of noise in detecting gravitational waves. $\endgroup$
    – ProfRob
    Commented Jun 10 at 17:14
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    $\begingroup$ Well, 10^-18 is 15 orders of magnitude smaller than the 10^-3 I was suggesting as what the OP meant (and wondered whether it is strictly impossible). I am not surprised that there is thermal movement in the range of a tiny fraction of atom size. -- As an aside, one may argue that the uncertainty principle you mentioned in a previous comment is "orthogonal" to macroscopic conservation laws (that's the whole point, in a way) so that 1/1000 is not principally impossible the same way 10^-40 is not either; 1/1000 is just exponentially more unlikely which is discussed in all the other answers. $\endgroup$ Commented Jun 10 at 17:26

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