I hate it when otherwise sane-seeming physicists start spouting trash about the Big Bang. You can tell they're doing it by rote, that they're parroting some propaganda they've been indoctrinated with. Something they've never examined to see whether it makes a lick of sense.
NO EVIDENCE
First of all, there is no evidence for a Big Bang. There cannot ever be any evidence for it since the whole point of inventing Inflation Theory was to erase every last trace of the big bang to remedy the defects of the theory. The reason the Ekpyrotic model is viable at all is because of this total erasure of all traces of any big bang. But inflation? Oh you can't erase that! Even the Ekpyrotic model generally tries to replicate it. So what is today called "evidence for" the big bang is invariably evidence for hot inflation. Cosmic microwave background? Hot inflation. Expansion of the universe? Inflation.
MATHEMATICALLY IMPOSSIBLE
Secondly, you have to realize that there can be no distinction between inflation and eternal chaotic inflation. If inflation happens then eternal chaotic inflation is the best possible model for it. You get eternity for free. Read my lips, no extra charges! Add quantum mechanics to inflation theory and you get chaotic inflation. And with chaotic inflation you have eternal inflation. It's FREE!
Worse than that, our living in a finite universe is mathematically impossible. If the probability of a universe arising out of nothing (assuming the whole notion isn't absurd which it is, more on that later) is finite then the probability of our living in an infinite universe is infinite. Infinity trumps finity!
If there were only one single eternal universe, and a billion billion billion finite universes, we could never tell the difference between them from any scientific experiments, but pure mathematics says that the probability of us coming from the eternal universe is 1 and the probability of us coming from any of the billion billion billion finite universes is ZERO.
It's statistically impossible.
ABSURDITY
The whole notion of something arising out of nothing is absurd. It's incoherent. It literally doesn't mean anything. The only way to ascribe any meaning to it is to say that the universe as-is is equivalent to nothing.
Which is very likely since a flat universe (as ours seems to be) has net zero energy. But to say that it's equivalent to nothing is to say that 'nothing' is subject to physical laws. or at least to mathematical laws. So it's not a true 'nothing' is it? It's something, it's laws of mathematics.
In order to say that what's beyond the universe is true nothing, you can't appeal to any sort of equivalence, you can't say that the universe came out of nothing at all. You can only say that the universe created itself. And what can you appeal to when making such a statement?
Well actually you can say that the universe created itself because it was self-consistent. But if you're going to say that then there are tons of other self-consistent universes possible. And every single one of them must have created itself.
Bravo, you've got the Mathematical (Multi)verse Hypothesis. Which is the exact kind of thing the Big Bang believers are trying to avoid. In trying to provide any kind of rigorous meaning to "the universe came out of nothing" you inevitably run into the fact that our universe can't be the only thing.
You get the same result when you try to define "non-determinism". It literally doesn't mean anything. And when you try to give it some meaning, it always turns out to be inconsistent with the vague notion of "non-determinism".
REVERSION TO RELIGIOUS DOCTRINE
So if the Big Bang is unprovable, mathematically impossible and it's not even coherent then why do these big headed logical types believe in this utter crap? Well first of all, physicists lack big picture thinking. Also known as judgement, which relies on synthesis. And synthesis is a cognitive trait physicists uniformly lack. But that only explains why it's possible for physicists to believe this crap.
Why they actually believe in it is because it's a religious notion. It's a belief in Creation. It's something that people used to believe in until science became atheistic. Until four young scientists made a manifesto and signed it with their own blood. That's why Einstein was so adamantly opposed to the Big Bang. Because it's a religious notion which science had gotten rid of!
And really, that explains it all. When cosmologists were confronted with the fact of an expanding universe, they couldn't handle the notion that ours isn't the only universe out there. So they reverted to religion. They reinvented the "Big Bang" - the Moment of Creation.
The same thing happened in the 1920s with the so-called Copenhagen "interpretation" of quantum mechanics. Which is no interpretation at all - it's the physical theory behind a bunch of useless math. Physicists like Richard Feynman who dismiss the physical meaning of math as unimportant are lackwits. So anyways, Copenhagen would be the physical meaning of QM if it weren't completely absurd and incoherent.
So believers in the Copenhagen doctrine revived vitalism because they couldn't handle the idea of a non-singular timeline. They invented all kinds of crap about "duality" and "uncertainty" because they couldn't handle that Platonism is wrong, that the universe really isn't made up of mathematical points. Even though mathematical points are physically incoherent.
They reinvented the notion that humans and other living things (so-called "observers") are Special, that they have this fundamental Living Force that makes them different from the rest of physical reality. How absurd is that!? But it's something that humans believe intuitively. It's an anthropomorphic notion. And that's why it got reinvented.
Same thing with Creation, or the Big Bang, whatever you want to call it. It's an intuitive anthropomorphic ('we are special') notion that just got reinvented when scientists were challenged to shatter it utterly. They were challenged and they failed. Because they're morons who can't grasp the big picture. Who can't grasp that maybe "creation" is something that needs to be defined before it means anything. Before it can ever be used to explain anything.
Kinda like God. For God to explain anything, it first needs to be defined. Which defeats the whole purpose of it since God is supposed to be this mysterious incomprehensible ball of crap and handwavy bullshit. And bullshit can't explain jack.
Same with Creation. /shakes head/
Previously, the disease process in physics.
Monday, April 12, 2010
Dodging Asteroids at Lightspeed? You Fail Physics Forever
Okay, this rant is inspired by a story (which I won't recommend) that tried to one-up the standard "dodging asteroids" scene by having the spaceship (a small two-man fighter) do it at light speed. Seriously, for the love of all that's good, WHY? Apparently, because light speed is KEWL.
I think anyone reading this blog probably knows all of this but what the hell, I put several hours into this rant so I might as well put it in a convenient place. Who knows, maybe someone will find it useful to smash some ignoramus over the head.
VISIBILITY
First issue, visibility of destinations and obstacles. In the story, this carrier ship is supposed to be 8 kilometers long. If the fighter is traveling at lightspeed then one second away from the carrier, it's 1 light-second away. Well,
arctan((8 km) / (1 light-second)) in degrees = 0.00152894519 degrees
Do you know what that is? From http://en.wikipedia.org/wiki/Naked_eye
> Angular resolution: 1-2' (about 0.02°-0.03°), which corresponds to 30–60 cm at a 1 km distance
0.02 / 0.00152894519 = 13.
In other words, 1 second away from the carrier at lightspeed is still thirteen times too small to see with the naked eye.
Even assuming that Talking Is A Free Action and the protagonist was able to point out and describe the carrier to his passenger instantaneously, the passenger would still have been unable to see it.
In fact, since the human eye sees at about 18 frames per second, the passenger would just barely be able to see a tiny speck of white if he stared at the exact spot the carrier was going to pop up at in advance.
So first he would see nothing, then immediately after he would see a speck, then immediately after that he would see the entire ship.
KINETIC ENERGY
Going on, the author doesn't seem to have heard of this thing called "kinetic energy", whether the relativistic or the newtonian kind. Behold,
(((1 / 2) * ((0.9 * c)^2)) * 1 gram) / (1180 (kilojoules per gram)) = 30.8471057 tonnes
The top half of the left hand side of that equation is the kinetic energy of 1 gram of matter (say, space dust) travelling at a velocity of 90% the speed of light. The bottom half of the left hand side of the equation is the heat necessary to fuse lead starting from 0 degrees Kelvin (absolute zero). The right hand side is how much of your ship is going to melt away from a collision with 1 gram of space dust. Assuming nothing heats up that doesn't melt and blah blah blah.
(((1 / 2) * ((0.9 * c)^2)) * 1 gram) / (4637 (kilojoules per gram)) = 7.8498134 tonnes
This is the same equation but including heating from 0 degrees kelvin to fusion, past fusion to boiling, past boiling to ionization. In other words, this is how much of your starship is going to turn into pure plasma from a collision with 1 gram of space dust. It's straightforward to come up with similar equations for iron (steel) and uranium, but unnecessary.
The fact that air going at 90% of the speed of light has the oomph of a thermonuclear explosion is really useful when designing real starships because it means an air shield misted in front of your starship in its direction of travel can reduce asteroids down to free nuclei and anything smaller than that into subatomic particles.
Starship design hint: you can make your starship as long as you want without increasing its cross-section. So it can store any finite amount of air you might possibly need on your interstellar and/or intergalactic trip to vaporize everything in its way. Once vaporized (well, ionized actually) it's easy to sweep the debris out of the way with your magshield. Particle accelerators do that every day.
And lest you think that I'm exaggerating when talking about thermonuclear explosions,
(((1 / 2) * ((0.9 * c)^2)) * 1 kilogram) / (4.2 petajoules) = 8.66656779
a 1 kilogram mass going at 90% lightspeed has a yield of a cool 8.67 megatons.
(((1 / 2) * ((0.99 * c)^2)) * 1 kilogram) / (4.2 petajoules) = 10.486547
at 99% lightspeed, it clocks 10 megatons.
It took until 1954 for the United States to have a nuclear device with a yield more powerful than that.
The most powerful thermonuclear weapon ever tested in human history was the Tsar Bomba, which clocks at the equivalent of 5 kilograms of mass at 99% lightspeed.
Are you starting to get the picture? Hitting anything at lightspeed results in a big boom.
REACTION TIME - NAIVE
From http://pseudoastro.wordpress.com/2008/10/26/asteroid-belts-proximity-of-rocks-and-why-navigation-is-not-dangerous-sorry-han-solo/
> Even if we cut the size of asteroids in half again, and were interested in all asteroids larger than half a meter (1.5 ft) in size, then we have 8 times as many asteroids, but each one still has over 500 km2 all to itself, and even more space if we consider the vertical component.
Using the formula for the volume of a sphere, and given that half of (half a meter) diameter gives a radius of 1/4 meter, we have
(4 / 3) * pi * ((1 / 4)^3) = 0.0654498469 cc's.
Assuming it has the density of water, that's 0.686342898 megatons or 686 kilotons. More than 30 times the explosion at Nagasaki. In other words, that's some dangerous fucking asteroids. And they're an average of
sqrt(500 (km^2)) = 7.45871992 × 10-5 light-seconds apart.
In other words, the hotshot pilot protagonist has one ten thousandth of a second to dodge them.
The speed of nerve impulses in the human body is "up to 100 meters / second". In other words, the nerve impulses in the pilot's body have the time to travel a whole
((100 (meters per second)) / 7) * (10E-5 seconds) = 1.42857143 millimeters
yeah, one millimeter in the time he has to dodge an asteroid. Brilliant, are you feeling the gritty realism yet? I know I am!
DISTRIBUTION OF ASTEROIDS
Now you may have noticed that the sqrt(500 km^2) neglects the vertical dimension. But 65 cc's is still an enormously dangerous asteroid, and if you go down to 1 cc then you still have to worry about explosions on the scale of 10 kilotonnes. For comparison, the Hiroshima explosion was 15 kiloton. Now, 65 cc's is conveniently close to 64 cc's
64* 1 cc = 2^6 * 1 cc
which means that asteroids of that size are
8^6 = 262 144 times as numerous,
given that it's a power law of degree 3 (every time you 1/2 the size, you increase numbers by 2^3 = 8). And
(8^6) * sqrt(500 (km^2)) = 5 861 718.04 kilometers
That's the height of the asteroid belt that's compensated for by the fact we're neglecting any asteroids less than 65 cc's.
(8^2) * (8^6) * sqrt(500 (km^2)) = 375 149 954 kilometers
That's the height of the asteroid belt that's compensated for by the fact we're neglecting any asteroids with yields of less than about 1 kiloton when travelling at 99% the speed of light.
And we can stop there because 375 million kilometers is almost the RADIUS of the asteroid belt. And of course, explosions of less than 1 kiloton aren't a danger at all to a tiny two-man fighter.
CHANCE OF COLLISION
So yeah, anyway. Now that we've established we can use the 500 km^2 number as a simplifying assumption, this is the proportion of the area swept by a 2 meter wide spaceship going through 500 km^2
(2 m) / sqrt(500 (km^2)) = 8.94427191 × 10^-5
which is the same as the chance of hitting that speck of rock somewhere inside it. And this,
(1 million km) / sqrt(500 (km^2)) = 44 721.3595
is the number of such areas you travel through when going 1 million km (less than 1% of the radius of the asteroid belt) inside the asteroid belt. So logically, this
(1 - (8.94427191 × 10E-5))^44721 = 4.17433136 × 10^-18
is the probability that you will cross 44721 such areas without hitting anything. In three seconds going at light-speed.
Do you understand what 10^-18 is? It's one tenth of one millionth of one billionth of one percent. It's one billion billion to 1 odds against. I think your chances of surviving a point blank gunshot to the forehead are higher. How do you like them apples?
REACTION TIME - REVISITED
Now that we have a probability of a collision, some playing around with google shows that,
(1 - (8.94427191 × (10^(-5))))^7 749 = 0.500012276
and of course,
7749 * sqrt(500 (km^2)) = 0.577976206 light seconds
So every half-second, there's a 50/50 chance that you'll have to dodge something. If you can convert this to a Mean Time Between Failures (or tell me how to) then you'll know the average reaction time you have between any two dodge-or-die events. Whatever that number actually is, it's going to be close to half a second. And of course, your reaction time had better be much better than this if you want to live through a breezy five minute jaunt.
So yeah anyways. Dodging asteroids at lightspeed? You fail physics forever.
See also,
Atomic Rocket - http://www.projectrho.com/rocket/index.html -- includes technical info on everything up to and including time travel (more plausible than you might think, infinitely more plausible than FTL)
Bad Astronomy and Universe Today Forum - http://www.bautforum.com/ -- if there's any name in starship design I'd recommend it's Isaac Kuo - he does it with today's technology, not hypothetical future technology
Hint: starships don't travel through the solar system, let alone something as dirty as the asteroid belt. They avoid collisions because they're in space.
This review was sponsored by Google TM search engine and Google TM calculator.
I think anyone reading this blog probably knows all of this but what the hell, I put several hours into this rant so I might as well put it in a convenient place. Who knows, maybe someone will find it useful to smash some ignoramus over the head.
VISIBILITY
First issue, visibility of destinations and obstacles. In the story, this carrier ship is supposed to be 8 kilometers long. If the fighter is traveling at lightspeed then one second away from the carrier, it's 1 light-second away. Well,
arctan((8 km) / (1 light-second)) in degrees = 0.00152894519 degrees
Do you know what that is? From http://en.wikipedia.org/wiki/Naked_eye
> Angular resolution: 1-2' (about 0.02°-0.03°), which corresponds to 30–60 cm at a 1 km distance
0.02 / 0.00152894519 = 13.
In other words, 1 second away from the carrier at lightspeed is still thirteen times too small to see with the naked eye.
Even assuming that Talking Is A Free Action and the protagonist was able to point out and describe the carrier to his passenger instantaneously, the passenger would still have been unable to see it.
In fact, since the human eye sees at about 18 frames per second, the passenger would just barely be able to see a tiny speck of white if he stared at the exact spot the carrier was going to pop up at in advance.
So first he would see nothing, then immediately after he would see a speck, then immediately after that he would see the entire ship.
KINETIC ENERGY
Going on, the author doesn't seem to have heard of this thing called "kinetic energy", whether the relativistic or the newtonian kind. Behold,
(((1 / 2) * ((0.9 * c)^2)) * 1 gram) / (1180 (kilojoules per gram)) = 30.8471057 tonnes
The top half of the left hand side of that equation is the kinetic energy of 1 gram of matter (say, space dust) travelling at a velocity of 90% the speed of light. The bottom half of the left hand side of the equation is the heat necessary to fuse lead starting from 0 degrees Kelvin (absolute zero). The right hand side is how much of your ship is going to melt away from a collision with 1 gram of space dust. Assuming nothing heats up that doesn't melt and blah blah blah.
(((1 / 2) * ((0.9 * c)^2)) * 1 gram) / (4637 (kilojoules per gram)) = 7.8498134 tonnes
This is the same equation but including heating from 0 degrees kelvin to fusion, past fusion to boiling, past boiling to ionization. In other words, this is how much of your starship is going to turn into pure plasma from a collision with 1 gram of space dust. It's straightforward to come up with similar equations for iron (steel) and uranium, but unnecessary.
The fact that air going at 90% of the speed of light has the oomph of a thermonuclear explosion is really useful when designing real starships because it means an air shield misted in front of your starship in its direction of travel can reduce asteroids down to free nuclei and anything smaller than that into subatomic particles.
Starship design hint: you can make your starship as long as you want without increasing its cross-section. So it can store any finite amount of air you might possibly need on your interstellar and/or intergalactic trip to vaporize everything in its way. Once vaporized (well, ionized actually) it's easy to sweep the debris out of the way with your magshield. Particle accelerators do that every day.
And lest you think that I'm exaggerating when talking about thermonuclear explosions,
(((1 / 2) * ((0.9 * c)^2)) * 1 kilogram) / (4.2 petajoules) = 8.66656779
a 1 kilogram mass going at 90% lightspeed has a yield of a cool 8.67 megatons.
(((1 / 2) * ((0.99 * c)^2)) * 1 kilogram) / (4.2 petajoules) = 10.486547
at 99% lightspeed, it clocks 10 megatons.
It took until 1954 for the United States to have a nuclear device with a yield more powerful than that.
The most powerful thermonuclear weapon ever tested in human history was the Tsar Bomba, which clocks at the equivalent of 5 kilograms of mass at 99% lightspeed.
Are you starting to get the picture? Hitting anything at lightspeed results in a big boom.
REACTION TIME - NAIVE
From http://pseudoastro.wordpress.com/2008/10/26/asteroid-belts-proximity-of-rocks-and-why-navigation-is-not-dangerous-sorry-han-solo/
> Even if we cut the size of asteroids in half again, and were interested in all asteroids larger than half a meter (1.5 ft) in size, then we have 8 times as many asteroids, but each one still has over 500 km2 all to itself, and even more space if we consider the vertical component.
Using the formula for the volume of a sphere, and given that half of (half a meter) diameter gives a radius of 1/4 meter, we have
(4 / 3) * pi * ((1 / 4)^3) = 0.0654498469 cc's.
Assuming it has the density of water, that's 0.686342898 megatons or 686 kilotons. More than 30 times the explosion at Nagasaki. In other words, that's some dangerous fucking asteroids. And they're an average of
sqrt(500 (km^2)) = 7.45871992 × 10-5 light-seconds apart.
In other words, the hotshot pilot protagonist has one ten thousandth of a second to dodge them.
The speed of nerve impulses in the human body is "up to 100 meters / second". In other words, the nerve impulses in the pilot's body have the time to travel a whole
((100 (meters per second)) / 7) * (10E-5 seconds) = 1.42857143 millimeters
yeah, one millimeter in the time he has to dodge an asteroid. Brilliant, are you feeling the gritty realism yet? I know I am!
DISTRIBUTION OF ASTEROIDS
Now you may have noticed that the sqrt(500 km^2) neglects the vertical dimension. But 65 cc's is still an enormously dangerous asteroid, and if you go down to 1 cc then you still have to worry about explosions on the scale of 10 kilotonnes. For comparison, the Hiroshima explosion was 15 kiloton. Now, 65 cc's is conveniently close to 64 cc's
64* 1 cc = 2^6 * 1 cc
which means that asteroids of that size are
8^6 = 262 144 times as numerous,
given that it's a power law of degree 3 (every time you 1/2 the size, you increase numbers by 2^3 = 8). And
(8^6) * sqrt(500 (km^2)) = 5 861 718.04 kilometers
That's the height of the asteroid belt that's compensated for by the fact we're neglecting any asteroids less than 65 cc's.
(8^2) * (8^6) * sqrt(500 (km^2)) = 375 149 954 kilometers
That's the height of the asteroid belt that's compensated for by the fact we're neglecting any asteroids with yields of less than about 1 kiloton when travelling at 99% the speed of light.
And we can stop there because 375 million kilometers is almost the RADIUS of the asteroid belt. And of course, explosions of less than 1 kiloton aren't a danger at all to a tiny two-man fighter.
CHANCE OF COLLISION
So yeah, anyway. Now that we've established we can use the 500 km^2 number as a simplifying assumption, this is the proportion of the area swept by a 2 meter wide spaceship going through 500 km^2
(2 m) / sqrt(500 (km^2)) = 8.94427191 × 10^-5
which is the same as the chance of hitting that speck of rock somewhere inside it. And this,
(1 million km) / sqrt(500 (km^2)) = 44 721.3595
is the number of such areas you travel through when going 1 million km (less than 1% of the radius of the asteroid belt) inside the asteroid belt. So logically, this
(1 - (8.94427191 × 10E-5))^44721 = 4.17433136 × 10^-18
is the probability that you will cross 44721 such areas without hitting anything. In three seconds going at light-speed.
Do you understand what 10^-18 is? It's one tenth of one millionth of one billionth of one percent. It's one billion billion to 1 odds against. I think your chances of surviving a point blank gunshot to the forehead are higher. How do you like them apples?
REACTION TIME - REVISITED
Now that we have a probability of a collision, some playing around with google shows that,
(1 - (8.94427191 × (10^(-5))))^7 749 = 0.500012276
and of course,
7749 * sqrt(500 (km^2)) = 0.577976206 light seconds
So every half-second, there's a 50/50 chance that you'll have to dodge something. If you can convert this to a Mean Time Between Failures (or tell me how to) then you'll know the average reaction time you have between any two dodge-or-die events. Whatever that number actually is, it's going to be close to half a second. And of course, your reaction time had better be much better than this if you want to live through a breezy five minute jaunt.
So yeah anyways. Dodging asteroids at lightspeed? You fail physics forever.
See also,
Atomic Rocket - http://www.projectrho.com/rocket/index.html -- includes technical info on everything up to and including time travel (more plausible than you might think, infinitely more plausible than FTL)
Bad Astronomy and Universe Today Forum - http://www.bautforum.com/ -- if there's any name in starship design I'd recommend it's Isaac Kuo - he does it with today's technology, not hypothetical future technology
Hint: starships don't travel through the solar system, let alone something as dirty as the asteroid belt. They avoid collisions because they're in space.
This review was sponsored by Google TM search engine and Google TM calculator.
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