SCIENCE FAQ
The universe of Problem Sleuth is just lousy with science! This phrase could serve to suggest either it is "chock full of science", or that it is "terribly inaccurate with science", depending on your perspective!
Usually the laws of physics in this universe cause readers to shrug and say, "Ok, if you say so!" and click the next page. But sometimes people will say, "Hey wait a minute! That's not quite how things work!" Or they will shout, "Hey I don't quite understand this! Can we talk about this for a while!"
The answer to that last enthusiastically-posed question is yes!
I will explore some of the major technical issues here. While we should all be aware that the most fundamental answer to these questions is, "It's just a cartoon, guys! Relax!" I think it is also fun at times to strap on our science mortarboards and pretend all these concepts SIMPLY MUST hold up to the rigors of scrutiny.
The Fan Cord: Does electricity travel faster than light?
What's the deal with all the particles/PART-PICKLES?
If PI divided himself into all the matter in the universe, wouldn't it constantly be increasing in mass over time?
Is any of this black hole stuff accurate?
Time dilation doesn't work that way!!!
When electricity finally traveled through the cord to turn on the fan, wouldn't PI and everything else around have aged by 36 billion years as well?
"Across the relativistically shortened span of the universe in the blink of a relativistically accelerated eye." This is a mysterious statement!
The Fan Cord: Does electricity travel faster than light?
This was probably one of the most controversial subjects in the story.
When GPI elongated the fan's power cord to sew the universe together, it stretched across the the entire universe, a span of about 18 billion light-years. Thus when power was finally supplied to the outlet, the electricity had to travel all the way across the universe, and back, to reach the fan for a total of 36 billion light-years. Consequently, we were told the fan would not receive power until AT LEAST 36 billion years had passed.
There were some who didn't think the flow of electricity worked this way. There were many varying accounts, but the crux of most of the objections had to do with a few assumptions some people had, that A) flow of electricity has nothing to do with the speed of light, or B) electricity should reach its destination "instantaneously", and there should be no delay.
Without getting too bogged down in the science of electric current, I will just state one fact that should clear this up.
Nothing can travel faster than light! Ever. Not space ships, not electricity, not even prayers whispered to your guardian angel. So no matter what, 36 billion years is the minimum duration for that trip.
But the trip could take longer. I think also some people thought I was implying it would take exactly that long, suggesting electricity travels at the speed of light. This isn't really what I was implying. I was just glossing over the concept of electrical propagation speed for the sake of salvaging some simplicity. More realistically I would guess current would travel through the cord somewhere between 70% and 90% of the speed of light, making the total trip more like 45 billion years.
Thinking about it intuitively, this is how the flow electric current works. Electrons themselves are not traveling through the cord that fast. In fact, they remain relatively still. But they "bump" into their neighbors in response to the voltage introduced when the switch is flipped. This "bump" is communicated by the electromagnetic force each electron emits. This force travels at the speed of light. In fact, it is light! (light is the visible frequencies of electromagnetic radiation) So the current can only reach the other end once all these little "electron bumps" have been chained together, like a row of dominoes, which can happen no faster than the rate at which electrons communicate with each other, which is the speed of light.
But that doesn't mean that what is happening is actually realistic! In truth, a cord that long would have such a high electrical resistance, this would diminish the current to virtually nothing. (Current = Voltage / Resistance) The current in fact is never even getting out the front door. You would get the same result by plugging in a tree stump or something.
This is an instance where the "It's just a cartoon!" answer comes into play.
What's the deal with all the particles/PART-PICKLES?
This is in reference mostly to PFPI's attack, TEMPORAL REPLICOLLISION, wherein he used the giant ship portholes / traffic lights as a particle accelerator, and he and FFPI played the roles of the particles and smashed into each other.
I'll keep this short. If you haven't already, you should read about the Large Hadron Collider, and maybe brush up on the Standard Model of particle physics. They are looking for the Higgs Bonehead. I mean Higgs Boson. They haven't found it yet.
If PI divided himself into all the matter in the universe, wouldn't it constantly be increasing in mass over time?
When the deceased PPI, FPI, PFPI, and FFPI used TEMPORAL REPLICSIMILE AD INFINITUM, each one split into two, a smaller past version and future version. They all kept doing this recursively, until they were subatomic in size, and plentiful enough to stock every moment in time with every particle in the universe.
The question certainly has merit, since the way they divide, this would seem to put an exceptional density of PIs toward the middle of the lifespan of the universe, while the PIs gradually thin out toward the endpoints of history. At the beginning and end of the universe, there would only be one instance of each PI.
So the answer is, yes, the universe is increasing in mass, until it reaches the midpoint, and then it starts decreasing symmetrically.
This is apparently one respect in which the PS universe differs from ours!
Is any of this black hole stuff accurate?
Only in the loosest sense. MK's gravity brassier raises his mass and reduces his volume, actions which are critical to the formation of any black hole.
Originally I had the numbers way off by foolishly misusing exponents. Earlier on I had his mass multiplied by 10^100, or one googol, which would be heavier than the entire universe! People pointed that out and I went back and changed them to more reasonable values. I saved the big ones for later, 10^100 for a super massive black hole, and 10^googol (one googolplex) for an ultra massive black hole. (Which might not even be a real term...)
Whenever any mass is compressed to fit within its Schwarzschild radius, it becomes a black hole. Probably the only thing about this that's somewhat realistic is that I did some calculations on what MK's approximate Schwarzschild radius was for a given mass, and used that to determine at what point he'd become a black hole.
And by "did some calculations" of course I mean "googled the Schwarzschild radius for Earth (which is only 9 mm), set MK's mass to be about the same as Earth (6*10^24 kg, i.e. a whole lot of zeroes), and then brought his volume within that radius". BHMK was born.
That was a much better way of doing it, cause really, who wants to sit around doing a lot of math??
That covers the creation of a black hole. The time dilation mechanics are another can of worms...
Time dilation doesn't work that way!!!
That wasn't a question! But yeah, you're right.
To briefly recap, when HD and NB got close to the event horizon, they began to witness events in the rest of the universe speed up. Until finally, they saw all the events in history happen at once.
This is a rough approximation of how gravitational time dilation works. I bent the rules a bit for dramatic effect. Here's a decent, somewhat intuitive primer on how gravitational time dilation works. But the bottom line is this: near the event horizon, clocks run slow compared to clocks further away. Of course, it is a bit more complicated than this in reality. For instance, a clock near the event horizon would not actually "see" the other clock running faster. It's only when you finally bring the two clocks together would you be able to measure the difference.
But in the PS universe, someone near an event horizon will see time speed up in the rest of the universe. That's just how it works in this story. It's more fun that way!
When electricity finally traveled through the cord to turn on the fan, wouldn't PI and everything else around have aged by 36 billion years as well?
Now we're getting into a complicated subject!
Quick recap: When PS finished his final SEPULCHRITUDE attack, he fell near the event horizon of the ultra massive black hole. He, like NB before, saw every event in the future unfold in the blink of an eye, which included the electricity finally reaching the fan. When this happened, the fan turned on, it blew the bust off the mecha legs, and it fell into the sudocube maze. PI then guided it through the maze by flipping the universe around a lot with the ship's wheel.
It all sounds perfectly reasonable, right? Well, no, not if you consider PI probably died 36 billion years ago!!!
This is a very logical objection, and certainly could be considered a weird plot hole, if it is indeed true that 36 billion years passed equally for everyone and everything not near the event horizon. But this isn't really what I was intending.
By this point, the black hole is now ridiculously "ultra massive". It's time dilation effects spread far beyond its event horizon, modifying the passing of time for locally surrounding objects, such as the fan, the bust, the cube, the ship, and PI. The time distortion (slow-down) just isn't nearly as severe as it is on the event horizon.
Also keep in mind that I'd imagined the fan cord stitching the universe to be very far away in the background. Think of the background as a long arc, like the interior of a half-sphere, which is 18 billion light-years in diameter. That means the fan cord is 9 billion light-years away, well out of reach of the time dilation effects.
So imagine three frames of reference, occupied by:
PS : PI : Fan cord
The following approximate times passing in those frames would be equivalent to each other:
nanoseconds = minutes = 36 billion years
Or, looking at this diagram of the universe when seen from above:
You can see there are strata of time distortions radiating from the black hole, with time becoming progressively less slowed down going outward. Or at least that is the way I say it is! Should I have explained all this in the story when it was happening? I guess it would have made it more clear exactly what was going on, if you were one of those who thought "Hey, wouldn't PI have been long dead by then??" But I don't know, I think explaining all that might have been a bit of a wet blanket. After all, by that point the reader has already slogged through 1500 pages of my BS! Best to let it slide, and explain it here.
Besides, it wouldn't be much fun if PS just watched PI died of old age, and that was it! (Ok, I guess that might have been kind of funny, in a way.)
Oh, there's even more stuff to think about:
When PS got near the event horizon, the story seems to suggest this by itself "triggered" these events, sending electricity through the cord and such. I.e. him witnessing it from his frame of reference is sort of what "made it happen".
That's a way of looking at it I guess. But when NB fell into the black hole earlier, and the same thing happened, her witnessing all future events did not trigger the same consequence! She certainly must have seen the fan turn on and all that, because it happened in the future. Yet her seeing it did not "make it happen". Why?
The answer is two-fold: 1) Problem Sleuth is the hero of the story! And 2) maybe more importantly, when NB went in, the black hole was much smaller then! There were no radiating layers of time distortion as in the above diagram. Those are the layers of slowed time which "hold in place" those moments, allowing them to respond to the consequences of the electricity reaching the fan. With NB, the black hole was not that big yet, so all that stuff couldn't "happen" yet!
You know you're dealing with an abstract topic when you find yourself putting the word "happen" in quotation marks. Really, this is hard stuff to think about.
And it gets harder.
What may be the biggest paradox is yet to come. As PS watches all future events unfold, it is logically true that this is because for the entire duration of the universe, that black hole will be there, and so will PS, stuck on its event horizon in a perma-slowed state watching it all happen in superfast-motion. But when the black hole is finally destroyed (IF it is destroyed!) then this too will be an event that takes place in the future. This is something that PS should have witnessed, and in fact it should cause him to stop experiencing the time distortion altogether. The same is true for NB and HD! In fact, none of them should ever even cross through the event horizon. They should all get stuck there for a little while, watching future events, until the black hole is destroyed (IF it is!).
But this is just one of those paradoxes we will ignore and chalk up to the Cartoon Gods of Whimsy and Horseplay. It's a lot more fun when we all just sit back and chill the fuck out!
"Across the relativistically shortened span of the universe in the blink of a relativistically accelerated eye." This is a mysterious statement!
Again, not a question! But that's ok, because no one ever asked me about this. I just thought it would be worthwhile to discuss, because for me it is an interesting window into the subject of relativity.
It refers to this.
It makes it seem as though the stars in the backdrop are all getting scrunched together by the gravitational pull of the black hole. This is logical, and is a fine interpretation. But I feel what's going on is a little more abstract than that. For one thing, as I established above, those stars are awfully far away! Maybe too far to be pulled together like that.
By "relativistically shortened span" I guess I'm in a way referring to the concept of length contraction in Special Relativity. That is, the faster you go, the more squashed you appear to observers in the direction of the motion. This is because the speed of light is always constant, no matter where you are, or how fast you or anyone else is going. So if it takes a beam of light 1 second to travel from the back of a box to the front of a box, then if that box is moving, then that box has to be a little narrower for that same beam of light to reach the front of the box in one second!
Same with time, regarding the "relativistically accelerated eye". If you are using light pulses with mirrors in that box to measure, say, 1 second, and the light pulses are taking longer and longer to mark the second the faster the box goes, then I guess time itself for the box is slowing down! It can't be the speed of light slowing down, because we know that never changes!
So that's closer to what I meant by that. From the perspective of the event horizon, the dimensions and pace of the universe itself have reconfigured themselves (squashed, hastened) to accommodate the speed of light so it may still appear to move at a constant rate through the cord to all observers. The speed of light is the one unchanging meter stick in the universe, and everything else, time, space, are highly variable and will always bend so that the meter stick reads true.
Actually if I were being totally literal with this, I would have squashed the backdrop universe to the thickness of a hair. But I didn't want to get that carried away with it. Furthermore, I'm not suggesting this is literally what one observes near a black hole. Again, we keep in mind that we are discussing science, juxtaposed with a tale about detectives armed with key-guns who turn into candy monsters. As I said to someone, I'm sort of functioning like an expressionist painter who uses the laws of physics rather than colors.
Anyway, I think this is a pretty good way of understanding relativity, for me at least.
Usually the laws of physics in this universe cause readers to shrug and say, "Ok, if you say so!" and click the next page. But sometimes people will say, "Hey wait a minute! That's not quite how things work!" Or they will shout, "Hey I don't quite understand this! Can we talk about this for a while!"
The answer to that last enthusiastically-posed question is yes!
I will explore some of the major technical issues here. While we should all be aware that the most fundamental answer to these questions is, "It's just a cartoon, guys! Relax!" I think it is also fun at times to strap on our science mortarboards and pretend all these concepts SIMPLY MUST hold up to the rigors of scrutiny.
The Fan Cord: Does electricity travel faster than light?
What's the deal with all the particles/PART-PICKLES?
If PI divided himself into all the matter in the universe, wouldn't it constantly be increasing in mass over time?
Is any of this black hole stuff accurate?
Time dilation doesn't work that way!!!
When electricity finally traveled through the cord to turn on the fan, wouldn't PI and everything else around have aged by 36 billion years as well?
"Across the relativistically shortened span of the universe in the blink of a relativistically accelerated eye." This is a mysterious statement!
The Fan Cord: Does electricity travel faster than light?
This was probably one of the most controversial subjects in the story.
When GPI elongated the fan's power cord to sew the universe together, it stretched across the the entire universe, a span of about 18 billion light-years. Thus when power was finally supplied to the outlet, the electricity had to travel all the way across the universe, and back, to reach the fan for a total of 36 billion light-years. Consequently, we were told the fan would not receive power until AT LEAST 36 billion years had passed.
There were some who didn't think the flow of electricity worked this way. There were many varying accounts, but the crux of most of the objections had to do with a few assumptions some people had, that A) flow of electricity has nothing to do with the speed of light, or B) electricity should reach its destination "instantaneously", and there should be no delay.
Without getting too bogged down in the science of electric current, I will just state one fact that should clear this up.
Nothing can travel faster than light! Ever. Not space ships, not electricity, not even prayers whispered to your guardian angel. So no matter what, 36 billion years is the minimum duration for that trip.
But the trip could take longer. I think also some people thought I was implying it would take exactly that long, suggesting electricity travels at the speed of light. This isn't really what I was implying. I was just glossing over the concept of electrical propagation speed for the sake of salvaging some simplicity. More realistically I would guess current would travel through the cord somewhere between 70% and 90% of the speed of light, making the total trip more like 45 billion years.
Thinking about it intuitively, this is how the flow electric current works. Electrons themselves are not traveling through the cord that fast. In fact, they remain relatively still. But they "bump" into their neighbors in response to the voltage introduced when the switch is flipped. This "bump" is communicated by the electromagnetic force each electron emits. This force travels at the speed of light. In fact, it is light! (light is the visible frequencies of electromagnetic radiation) So the current can only reach the other end once all these little "electron bumps" have been chained together, like a row of dominoes, which can happen no faster than the rate at which electrons communicate with each other, which is the speed of light.
But that doesn't mean that what is happening is actually realistic! In truth, a cord that long would have such a high electrical resistance, this would diminish the current to virtually nothing. (Current = Voltage / Resistance) The current in fact is never even getting out the front door. You would get the same result by plugging in a tree stump or something.
This is an instance where the "It's just a cartoon!" answer comes into play.
What's the deal with all the particles/PART-PICKLES?
This is in reference mostly to PFPI's attack, TEMPORAL REPLICOLLISION, wherein he used the giant ship portholes / traffic lights as a particle accelerator, and he and FFPI played the roles of the particles and smashed into each other.
I'll keep this short. If you haven't already, you should read about the Large Hadron Collider, and maybe brush up on the Standard Model of particle physics. They are looking for the Higgs Bonehead. I mean Higgs Boson. They haven't found it yet.
If PI divided himself into all the matter in the universe, wouldn't it constantly be increasing in mass over time?
When the deceased PPI, FPI, PFPI, and FFPI used TEMPORAL REPLICSIMILE AD INFINITUM, each one split into two, a smaller past version and future version. They all kept doing this recursively, until they were subatomic in size, and plentiful enough to stock every moment in time with every particle in the universe.
The question certainly has merit, since the way they divide, this would seem to put an exceptional density of PIs toward the middle of the lifespan of the universe, while the PIs gradually thin out toward the endpoints of history. At the beginning and end of the universe, there would only be one instance of each PI.
So the answer is, yes, the universe is increasing in mass, until it reaches the midpoint, and then it starts decreasing symmetrically.
This is apparently one respect in which the PS universe differs from ours!
Is any of this black hole stuff accurate?
Only in the loosest sense. MK's gravity brassier raises his mass and reduces his volume, actions which are critical to the formation of any black hole.
Originally I had the numbers way off by foolishly misusing exponents. Earlier on I had his mass multiplied by 10^100, or one googol, which would be heavier than the entire universe! People pointed that out and I went back and changed them to more reasonable values. I saved the big ones for later, 10^100 for a super massive black hole, and 10^googol (one googolplex) for an ultra massive black hole. (Which might not even be a real term...)
Whenever any mass is compressed to fit within its Schwarzschild radius, it becomes a black hole. Probably the only thing about this that's somewhat realistic is that I did some calculations on what MK's approximate Schwarzschild radius was for a given mass, and used that to determine at what point he'd become a black hole.
And by "did some calculations" of course I mean "googled the Schwarzschild radius for Earth (which is only 9 mm), set MK's mass to be about the same as Earth (6*10^24 kg, i.e. a whole lot of zeroes), and then brought his volume within that radius". BHMK was born.
That was a much better way of doing it, cause really, who wants to sit around doing a lot of math??
That covers the creation of a black hole. The time dilation mechanics are another can of worms...
Time dilation doesn't work that way!!!
That wasn't a question! But yeah, you're right.
To briefly recap, when HD and NB got close to the event horizon, they began to witness events in the rest of the universe speed up. Until finally, they saw all the events in history happen at once.
This is a rough approximation of how gravitational time dilation works. I bent the rules a bit for dramatic effect. Here's a decent, somewhat intuitive primer on how gravitational time dilation works. But the bottom line is this: near the event horizon, clocks run slow compared to clocks further away. Of course, it is a bit more complicated than this in reality. For instance, a clock near the event horizon would not actually "see" the other clock running faster. It's only when you finally bring the two clocks together would you be able to measure the difference.
But in the PS universe, someone near an event horizon will see time speed up in the rest of the universe. That's just how it works in this story. It's more fun that way!
When electricity finally traveled through the cord to turn on the fan, wouldn't PI and everything else around have aged by 36 billion years as well?
Now we're getting into a complicated subject!
Quick recap: When PS finished his final SEPULCHRITUDE attack, he fell near the event horizon of the ultra massive black hole. He, like NB before, saw every event in the future unfold in the blink of an eye, which included the electricity finally reaching the fan. When this happened, the fan turned on, it blew the bust off the mecha legs, and it fell into the sudocube maze. PI then guided it through the maze by flipping the universe around a lot with the ship's wheel.
It all sounds perfectly reasonable, right? Well, no, not if you consider PI probably died 36 billion years ago!!!
This is a very logical objection, and certainly could be considered a weird plot hole, if it is indeed true that 36 billion years passed equally for everyone and everything not near the event horizon. But this isn't really what I was intending.
By this point, the black hole is now ridiculously "ultra massive". It's time dilation effects spread far beyond its event horizon, modifying the passing of time for locally surrounding objects, such as the fan, the bust, the cube, the ship, and PI. The time distortion (slow-down) just isn't nearly as severe as it is on the event horizon.
Also keep in mind that I'd imagined the fan cord stitching the universe to be very far away in the background. Think of the background as a long arc, like the interior of a half-sphere, which is 18 billion light-years in diameter. That means the fan cord is 9 billion light-years away, well out of reach of the time dilation effects.
So imagine three frames of reference, occupied by:
PS : PI : Fan cord
The following approximate times passing in those frames would be equivalent to each other:
nanoseconds = minutes = 36 billion years
Or, looking at this diagram of the universe when seen from above:
You can see there are strata of time distortions radiating from the black hole, with time becoming progressively less slowed down going outward. Or at least that is the way I say it is! Should I have explained all this in the story when it was happening? I guess it would have made it more clear exactly what was going on, if you were one of those who thought "Hey, wouldn't PI have been long dead by then??" But I don't know, I think explaining all that might have been a bit of a wet blanket. After all, by that point the reader has already slogged through 1500 pages of my BS! Best to let it slide, and explain it here.
Besides, it wouldn't be much fun if PS just watched PI died of old age, and that was it! (Ok, I guess that might have been kind of funny, in a way.)
Oh, there's even more stuff to think about:
When PS got near the event horizon, the story seems to suggest this by itself "triggered" these events, sending electricity through the cord and such. I.e. him witnessing it from his frame of reference is sort of what "made it happen".
That's a way of looking at it I guess. But when NB fell into the black hole earlier, and the same thing happened, her witnessing all future events did not trigger the same consequence! She certainly must have seen the fan turn on and all that, because it happened in the future. Yet her seeing it did not "make it happen". Why?
The answer is two-fold: 1) Problem Sleuth is the hero of the story! And 2) maybe more importantly, when NB went in, the black hole was much smaller then! There were no radiating layers of time distortion as in the above diagram. Those are the layers of slowed time which "hold in place" those moments, allowing them to respond to the consequences of the electricity reaching the fan. With NB, the black hole was not that big yet, so all that stuff couldn't "happen" yet!
You know you're dealing with an abstract topic when you find yourself putting the word "happen" in quotation marks. Really, this is hard stuff to think about.
And it gets harder.
What may be the biggest paradox is yet to come. As PS watches all future events unfold, it is logically true that this is because for the entire duration of the universe, that black hole will be there, and so will PS, stuck on its event horizon in a perma-slowed state watching it all happen in superfast-motion. But when the black hole is finally destroyed (IF it is destroyed!) then this too will be an event that takes place in the future. This is something that PS should have witnessed, and in fact it should cause him to stop experiencing the time distortion altogether. The same is true for NB and HD! In fact, none of them should ever even cross through the event horizon. They should all get stuck there for a little while, watching future events, until the black hole is destroyed (IF it is!).
But this is just one of those paradoxes we will ignore and chalk up to the Cartoon Gods of Whimsy and Horseplay. It's a lot more fun when we all just sit back and chill the fuck out!
"Across the relativistically shortened span of the universe in the blink of a relativistically accelerated eye." This is a mysterious statement!
Again, not a question! But that's ok, because no one ever asked me about this. I just thought it would be worthwhile to discuss, because for me it is an interesting window into the subject of relativity.
It refers to this.
It makes it seem as though the stars in the backdrop are all getting scrunched together by the gravitational pull of the black hole. This is logical, and is a fine interpretation. But I feel what's going on is a little more abstract than that. For one thing, as I established above, those stars are awfully far away! Maybe too far to be pulled together like that.
By "relativistically shortened span" I guess I'm in a way referring to the concept of length contraction in Special Relativity. That is, the faster you go, the more squashed you appear to observers in the direction of the motion. This is because the speed of light is always constant, no matter where you are, or how fast you or anyone else is going. So if it takes a beam of light 1 second to travel from the back of a box to the front of a box, then if that box is moving, then that box has to be a little narrower for that same beam of light to reach the front of the box in one second!
Same with time, regarding the "relativistically accelerated eye". If you are using light pulses with mirrors in that box to measure, say, 1 second, and the light pulses are taking longer and longer to mark the second the faster the box goes, then I guess time itself for the box is slowing down! It can't be the speed of light slowing down, because we know that never changes!
So that's closer to what I meant by that. From the perspective of the event horizon, the dimensions and pace of the universe itself have reconfigured themselves (squashed, hastened) to accommodate the speed of light so it may still appear to move at a constant rate through the cord to all observers. The speed of light is the one unchanging meter stick in the universe, and everything else, time, space, are highly variable and will always bend so that the meter stick reads true.
Actually if I were being totally literal with this, I would have squashed the backdrop universe to the thickness of a hair. But I didn't want to get that carried away with it. Furthermore, I'm not suggesting this is literally what one observes near a black hole. Again, we keep in mind that we are discussing science, juxtaposed with a tale about detectives armed with key-guns who turn into candy monsters. As I said to someone, I'm sort of functioning like an expressionist painter who uses the laws of physics rather than colors.
Anyway, I think this is a pretty good way of understanding relativity, for me at least.