Infinite Starlight: A Thought ExperimentPosted on May 5th, 2011 2 comments
Albert Einstein, a patent clerk in Bern, performed what are now called “Thought Experiments”. He was born in 1879 and received the Nobel Price in Physics in 1922. So, he was just 42. What makes Einstein’s story so unique is that he wasn’t classically trained in physics.
Like Einstein, I’m also not an astrophysicist, but the topic of stars, space and astronomy has always intrigued me. I’ve always thought it would be interesting to come up with my own thought experiment, and I think I finally have one.
Most of us with even a basic science or astronomy class know what a star is: a gigantic ball of burning hydrogen in the void of space. Carl Sagan described the universe most simply and profoundly: 100 billion galaxies each with 100 billion stars. That’s an incredibly large number of stars to be sure, but it’s not infinite, I think we could all agree on that.
My theory is that the amount of energy a star has is infinite, and it gives off an infinite amount of energy at all times. I know that sounds crazy. Impossible. There must be a limit, although very large. But nothing is truly infinite, right? So this brings about a paradox then, and I would love to understand it fully.
For this thought experiment, though, let’s talk about just one star, any star. Look up in the night sky and pick a star, and gaze at it. Which star you pick is irrelevant.
How about Betelgeuse, a red supergiant, Orian’s shoulder in the constellation of Orion. You see that bright star, one of the brightest in the heavens? Good. Walk around your back yard (be careful in the dark) and pause and look up again. Still see the Orion’s shoulder? Yep. Go down the street a ways. Yep, you can still see Betelgeuse. No matter where you walk, and look up, you can still see that star. Go to the other side of the world (stick to the same hemisphere, consult a star map, etc.) — somewhere and sometime that Orion is visible. Arizona in the spring, for example.
The point is, no matter where you look, there’s Orion and Betelgeuse. No matter where you go, light from that star is hitting your retina. If the moon ever goes in front of Orion, the light that would’ve hit your retina is instead going to hit the dark side of the moon. Technically, Betelgeuse casts a shadow on earth when the moon passes in front of it (when the moon casts a shadow on earth from our own star, it’s an eclipse.) Still, had the moon not been in the way, you could’ve seen the light that was destined for your retina.
Theoretically, you could travel to another star in a different constellation, and assuming you could keep track of where you are in relation to Betelgeuse, you could land on an earth-like planet orbiting around a different star, and look up, and see Betelgeuse from that vantage point, too.
The point of all of this is to visualize more clearly the way that light expands outward from a star.
Time divides infitely. How many moments are in between the start of the big bang and now? How many nanoseconds are inside of a second? We use the term nanosecond today because that’s the thinnest sliver of time we can measure with modern technology. But any mathematical scholar will tell you that you can always take half of something, or a quarter, or an eighth or sixteenth – we can increase the denominator all the way to ∞. So how many 1/∞ths of a second are in a minute? ∞. How many 1/∞ths of a nanosecond are in a billion years? ∞ of them.
Angles divide infinitely, too. How many angles are in between 0° and 90°? For example, an arcsecond is 1/3600th of a degree. But how many photons fit into an arcsecond? The farther away you go from the origin of the angle, the easier that is to measure, right, because the angle is getting wider. But how can it work that way? If you think about it for a moment, you’ll have to realize that there are ∞ angles which are each 1/∞th of one degree in size, in between any two other vectors that converge at a point.
We can describe this expansion of light from a star as an ever-enlarging spherical volume. You can think of a sun as a huge beachball factory releasing an ∞ number of beachballs every 1/∞th of a moment. The edge of each beachball is a photon ready to hit any eyeball that might be gazing upward to see it.
We proffered before that angles are infinitely divisible. To think about this some more, lets say you had a Sharpie marker and a beach ball, and you started drawing black dots on the beach ball and counting up how many dots it took to color the beach ball 100% black, at some point way in the future, the ball would be totally black and you would have a number of dots recorded which represented how many sharpie marker dots fit on the surface of the sphere. Now switch to a razor fine-point pen. Obviously it would take a lot more fine-point dots to cover the ball than the larger dots made by the sharpie marker, but it should still be possible to turn the ball black and record the number of fine-point razor dots it took to color the ball completely black.
How does that apply to starlight? Well, we described before the way light expands out from the source star as being an expanding sphere. If we imagine the light expansion edge-horizon as a huge beachball, then we can imagine that for every photon-width point on the edge of the light-sphere, as as well as for every place inside the volume of the light sphere, at any moment in time there has to be at least one photon there, had our eye been in that exact spot to observe it. In other words, if you could have ∞ eyeballs from ∞ imaginary people all forming a circle (sphere) around Betelgeuse, then every single one of the ∞ eyeballs would get hit by a photon.
That brings us to the width of a photon. If a photon has a width, which I’m fairly sure it does, then there should be a finite number of photons required to draw the light sphere. Or, if the width and height of a photon is 0, then it would take ∞ photons to cover the edge of an arbitrary light sphere some time/distance from the star. So let’s call the width of a photon, ƒ. I’m not sure what the equation would be, but I think we would all agree that if ƒ is > 0 then some finite quantity of photons would be required to ensure that any eyeball pointed towards the source would receive a photon.
The farther away you go from the star, the wider the ∞ angles become. In other words, if you go 1 billion light years away from the source, then you’re on the edge of a light sphere whose radius is 1 billion light years. We can focus on two arbitrary photons next together at this distance. If a photon has a width, ƒ, and we choose two photons π and ∂ which are next together, their combined width is 2ƒ.
What happens if we go another 1 billion light years farther away to 2 billion light years away from the source, parallel to π’s original trajectory. At twice the distance, isn’t the number of ƒ-width photons needed to cover the light-sphere equal to twice the number of photons required to cover the light sphere at 1 billion light years? If photons have a width ƒ > 0 then would it be correct or incorrect to assume that only a finite number of photos could fit around the edge of the star, during every 1/∞th moment in time since the star started burning?
So, either stars have an infinite amount of energy, or something special about the speed of light (faster than light communication?) enables photons to be a wave (no energy required?) until they are observed (photon created at moment of observation). Since I think any sane person would argue that there is no possible way for a star to possess infinite energy, then there are clearly some things I am missing.
Think for a moment why it is that it hurts to stare directly at the sun but not at Sirius. Also, time does not divide infinitely.
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