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The second law of thermodynamics states that entropy, Δs ≥ 0.

So, suppose we have a closed universe where Ω0,R = Ω0,Λ = 0 and Ω0,M > 1. If you then solve the Friedmann Equation with these parameters, you can get a plot of the radius of the universe, r, against time, t, which looks like this. As expected, the universe collapses in on itself.

Now, the Bekenstein bound places a limit on the entropy within a sphere of space according to s ≤ 2πkrM/ħc, where k is the Boltzmann Constant, r is the radius of the universe and M is the total mass-energy of the universe. After substituting some values into the inequality, you can find that, for a closed universe that contains only mass, s≤αr, where α is some constant and s is the entropy of the entire universe.

Therefore, as the radius of the universe begins to decrease, the maximum entropy of the universe will also begin to decrease. This means that there is no way for the entropy of the universe to increase without exceeding the maximum value of entropy allowed.

So, does this mean that a closed, mass-only universe is impossible because it violates the second law of thermodynamics?


I shower in the evening and my hair is still wet the next day


I found it pretty commonsensical that looking at bright shiny things can hurt your eyes, but when I get to ask myself deeper why, I can't help but handwave it simply as "too much light hurts you". I'm thinking either the light energy becomes heat energy that literally burns something sensitive in our eyes, or maybe the photoreceptor sends an information-overload signal to the brain, and that maybe translates to pain. Can someone please shed light on this? Thank you.


I'm a HS science teacher, and about to try to fold some geology into one of my biology classes. Reconstructions of where the modern continents were part of Pangaea, and the subsequent breakups to Laurasia and Gondwanaland, are pretty easy to find. But, it seems logical that we should be able to at least speculate about what landforms looked like (or where they were located) even earlier than that.

And, I'm considering folding something like this into a requirement for a project I'll be assigning - but when my preliminary efforts to try to find something were fruitless, I figured I should check here for whether any such things actually existed and pointers on where to find them.


Just something that crossed my mind recently, since the horizon isn't made up of anything. What is the rotating. Or is it just a way to allow for the conservation of angular momentum without having to go inside the BH with our current understanding?


Since visible light is in between radio and X-rays on the EM spectrum, what makes it different? Is there a specific cutoff point where certain frequencies go through and then after that they are blocked (and then after a point they are unblocked again)? Is there a 2-slit experiment for radio waves?


How did they find the exact nanosecond to place the second pulse? Is it set exactly to the split second from solar mean time? Or did they just find an arbitrary moment approximately about mean solar noon? Why isn't the time 0,5 second ahead, or a half minute?


I have a dim memory, that my math teacher once said, he can "easily" find such a polynom. Doing that with value pairs (x,y) where they have a form of (x,0) is trivial, so I think it could be possible to do manually. Do you know of any viable method, or did my memory play a trick on me?


Some stars seem brighter than others. At first thought, I would think that we see more photons from it. But then I think about how wide of an angle a star is shooting photons in all direction... and how far we are away, and the very very pricise angle needed to hit our eyes. I think the number of photons being released by a star has to be astronomical even if just 1 or more hit our eyes.

I bet the math is beautiful on how we estimate how many photons that a star releases over a time period.


I read about fava beans and see they've historically been a staple-food for mediterranean and north african peoples, and then I read about favism and see that mediterranean and north african peoples are more genetically predisposed to G6PDD.

And I wonder...why?

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