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Joined: 8/13/2011
Posts: 272
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So it's inevitable whenever you're reading about science fiction that people'll start complaining about it not being accurate, but it's not just realistic physics that's the problem. there's often fundemental issues that technobabble and science myths that can often get in the way of actually telling a believable story. So what is science? And how do you get it right?
I've got a Physics degree I'm not really using so I'm throwing out to my fellows. What do you want to know? I'm going to start with a couple of topics, areas that are often misrepresented, but feel free to chip in with questions. I'll try and answer to the best of my abilities.
Coming up: Space, surprisingly hot.
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Joined: 2/27/2011
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What an awesome offer, sir! Bumping this so others can see it. I'll be curious what our members want to ask you.
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Joined: 6/28/2011
Posts: 188
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Great thread topic. I don't have any specific science questions, but I'll say a couple of things about what I do and don't want to know as I'm reading a science fiction story.
I do want to know that the author has done some homework about the scientific plot drivers. If the story involves a rogue planet wandering into a solar system and threatening to destroy civilization on an inhabited planet, I need to get a sense that the author understands the speed at which such a rogue planet would be approaching, how much advance notice the inhabitants would have, and what the actual effects of proximity between two planets would be. If it becomes clear to me that the author does not even know what the Roche limit is, I'm going to be unimpressed with the story.
On the other hand, I don't need a bunch of numbers and factoids bogging down the story. Don't give me the numerical figures for the velocity and mass of the rogue planet, then describe the calculation of its kinetic energy in joules, and then convert that figure to kilotons of TNT and tell me how much greater it would be than all the bombs ever exploded by man. That's going to turn me off just as quickly as ignorance of the Roche limit.
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Joined: 2/9/2012
Posts: 427
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Time travel, please!
It's a fascinating yet frustrating concept.
For example, I believe that the TV series HEROES ultimately failed because the writers weren't able to define and contain what "time travel" meant for the show. Because of the unlimited possibilities for "time travel," the present could be changed unrelentingly. Any defeat of the bad guys could be reversed, and the causal sequence of events was made inconsequential.
So, what is in your opinion a well-done version of time travel in sci-fi? And what should writers know about the "physics" of time travel in order to preempt future ridiculousness?
Thanks!
Nevena
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Joined: 8/13/2011
Posts: 272
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I'll be honest and say that any discussion of time-travel immediately becomes insanely confusing very quickly, so with that proviso, let's see. There's a number of suggested ways of time travel, most of which rely on applications of relativity that I don't understand very well, so I'll just discuss a few of the more sane ideas.
Firstly, as long as you only want to go forwards in time, the easiest solution is to go really, really fast and abuse relativity. If you go fast enough, the passage of time from the perspective of a stationary observor would slow considerably. So you could travel for 1 year and come back to find 100 years have passed. The challenge here? Hitting close to light speed velocities. No one's really worked out how to do that yet.
A similar thing can of course be done with hibernation of any form.
Going backwards is a lot harder. One proposed solution relies on FTL travel/ communication. Let's take two observers, A and B, with B moving relative to A with a speed V. Now if we assume that they can send a message via some kind of faster than light communicator (I'll call it an 'ansible' for now) then we can set up a situation where messages can go backwards in time. For some values of V, it's possible for a signal sent by A to B to arrive before it was sent.
This'll hopefully make it make more sense (a little):
http://en.wikipedia.org/wiki/Tachyonic_antitelephone
Most other options revolve around distorted spacetime which makes things a little interesting. One option is to use a wormhole. Let's assume that you manage to build a small wormhole in your garage, with both ends there. You then put a synchronised pair of clocks at either end. Now, finally, you expose one end to a high gravitational field (due to relativity, this slows the passage of time at this end). Now, if you travel from the unslowed end to the slowed end, you'll arrive before you left. The restriction here is that this won't work past the time of creation of the wormhole.
A lot of these solutions rely predominantly on loophole abuse with the laws of relativity and some assumption of FTL travel or oddball distortions of the universe's physical constants (for example wormholes are currently believed to only be constructable if we can produce negative energy. No, I have no idea how to do that), so this isn't very easy.
Okay, now good uses of time travel. The central challenge with time travel is how you handle destiny and paradoxes. Is what happened fixed, or can it be changed? If you do change something, how do you know how to change it if it never existed in your history? It's how well the inevitable questions are handled that makes a good time travel story.
Oddly enough, my favourite time travel story I've read is actually a fanfic. It's only a small part of Harry Potter and the Methods of Rationality, a take on the HP universe where Harry's learnt a lot about rationalism before the series begins. The fun begins when he's given a Time Turner, allowing him to go back up to 24 hours. He immediately decides to set up a time loop and see what happens. The result? A short message in his own handwriting: 'DO NOT MESS WITH TIME TRAVEL'. Through out the rest of the series, it's generally accepted that while time-travel is available, care should be taken not to induce paradoxes (ie waiting to act until after an event has happened).
What should writers consider when writing time travel? Well the basics of the grandfather paradox is pretty much a must. The actual behaviour of time and its relationship with paradoxical events is up in the air (as we haven't tested it yet) so they can have fun with it from there. As for the actual time machine itself? Well that's more complex. I quite like the Looper approach where it's just not touched on, but in general, talking about wormholes, distorted spacetime geometries and the like is probably the best answer.
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Joined: 8/13/2011
Posts: 272
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So, we've discussed Time travel already, but let's get a little deeper. Let's talk about the process of Science itself, the Scientific Method. In fiction, it's common for scientists to make discoveries and immediately proceed to various inventions, but how does this really work?
The Scientific Method is a thousand year old system for discovering how the universe really works and it's at the core of how a scientist works. It can be divided into five sections:
Question: (What controls the rate of descent of a falling object?). The central part of any piece of science is a question to which the scientist has no answer. By formulating this question, the scientist defines the size and shape of the problem. Here, it's common for a scientist to look at other scientists' work to see if someone has asked this question and what answers they've gathered.
Hypothesis: (the earth pulls the object towards it with an equal force regardless of size). The Hypothesis is a theory that answers the question using knowledge that the scientist already has or extrapolates from existing knowledge. An important component is that the hypothesis must contain the possibility of being wrong, this is called falsifiability.
Prediction: (If I drop a number of different sized objects, they should all fall to the ground with similar speeds). The prediction is a logical extention of the hypothesis and most importantly, can be tested. Larger hypothesis often have multiple testable predictions and much of science revolves around finding ways to test these predictions. For example, several predictions of relativity have only been recently confirmed using satellites designed specifically for the process.
Test: (I'm going to drop a number of objects and I'm going to see what happens). This is the fun bit. The scientist directly tests the hypothesis by seeing what the universe does in this situation. Preferably, these should be repeated, so that the scientist can make sure it's not a one-off or that other factors interfere.
Analysis (the heavier objects fell at the same speed as the lighter ones, but a few of the very light objects fell slower). This is the really hard bit. The scientist has to take the results of the experiment and see what they say about his prediction and as a result his hypothesis. As you can see from the example, the prediction doesn't match with the results. This is a relatively common problem for researchers and the challenge is to find out whether the experiment has additional factors that get in the way of the prediction or if the hypothesis is wrong. This can be especially problematic if the theory is highly regarded or a personal project of the scientist.
That's the basics of the scientific method and science is done in a constant cycle of developing accurate hypothese (scientific theories) and developing them out into further predictions that can be tested.
One important element of science is replication. It should be possible for someone else to reproduce your experiment and get the same result (so in our example above, another scientist should be able to drop the same objects and get the same puzzling results). If the results can't be replicated, then the experiment isn't valid and any results are suspect.
As you can see, the two central components of good science are replication and falsibility. If you can't reproduce an experiment, it's useless and if you can't find a way to try and wreck a hypothesis and test it, the hypothesis isn't useful.
So what's good science in fiction? Well one of my favourite examples is Inherit The Stars by James P Hogan. The entire book revolves around figuring out how a ancient human body in a spacesuit ended up on the moon, with the cast trying to pull together a whole load of very odd evidence into one coherent conclusion. One of the characters point-blank refuses to accept any theory that doesn't cover every single piece of evidence they have on him.
What's bad science in fiction? The short answer is anecdotal science: basing theories and research on single events or stories. Without the option to repeat an experiment, its conclusions are next to useless. The other one is disconnected theories. There's a common solution to the light speed limit to proclaim relativity to be 'wrong', but it's not. There's conclusive proof of most of the Theory or Relativity so the universe runs on it. Claiming it to be wrong means you have to explain where it's wrong while it still applies to most of the universe.
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Joined: 2/9/2012
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I don't know what to say, I'm in awe.
Thank you so much for taking the time to explain all of this, Timothy.
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Joined: 3/13/2011
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I have a question about string theory, actually!
My understanding is that the quantum strings which most theories (I know there are a few different forms) describe are small vibrating, basically lines. these "line particles" have a certain small length, that, if I understood correctly, change as part of their vibration. My mental model saw something similar to such a changing length.
There's a classic thought experiment in regards to a flatworm on a pond, seeing just the surface of the water in 2 dimensions, and how a finger and hand entering the water looks in that case. The vibrating strings, to me, looks like a 3 dimensionsal wave form (perhaps a spiral?) moving through a fourth spatial dimension, and being the "slice" we can see in three dimensions at a time. It seems to me that if there is an additional spatial dimension involved, then perhaps the force/particle pairing hasn't been seen not because the particles are too massive, but because they exist in a direction we simply aren't capable of seeing?
Probably total sci fi bunk, most of the math is still beyond me to evaluate the idea, but I'd love your input. Thank you! (now to read the time travel post here that everyone's talking about)
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Joined: 3/13/2011
Posts: 412
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On the scientific method in books, the problem is that so many people don't understand the difference between scientists, inventors, and engineers. I think Heinlein really handled the differences between them a lot better than most.
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Joined: 5/25/2011
Posts: 121
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Hello Timothy,
I think I agree with you as far as time travel stories are concerned - don't worry about how it's done. I often point to the example of a story about someone driving a cart along a road. You don't find the author going off on a tangent about how an internal combustion engine works. The story might center on what the character does with the car (has he/she stolen it? just going for a Sunday ride?). So I approach Scifi the same way. Assume the technology works and concentrate ont he story. Of course I agree with you that you cannot violate known science.
Back to time travel. My story A Streak of Silver in the Sky is a time travel story. If you get a chance I'd appreciate your thoughts on it.
P.S. Read Hogan's book years ago. I know I enjoyed it, but all I remember is the cover (which attracted me to it - two astronauts finding a skeleton in a space suit), and the ending when an anthropology team finds the watch and throws it away assuming it's someone's idea of a joke.
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Joined: 8/13/2011
Posts: 272
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Right, string theory. I'm going to be honest and say this is a little out of my expertise, being heavy duty theoretical physics.
The general 'goal' of physics is to develop a theory of everything, a model that predicts the behaviour of the entire universe, from the smallest particle to the largest galaxy. There are currently two main theories that cover almost everything: Relativity and Quantum Mechanics. The problem is that they both have scale issues. Relativity falls apart hideously at very small distances, while Quantum Mechanics goes the opposite way and disintegrates at long ranges.
String theory is an attempt to get the two to work. The central concept is that fundamental particles (photons, quarks, leptons etc) aren't actually 0-dimensional points (ie having not any actual volume) but rather 1 dimensional strings (having length, but neither width or height). Depending on the version of the theory, these strings are either closed loops or capable of splitting and reconnecting. What the theory predicts is that the string's oscillation makes it appear to act as a particle at any non-trivial distance (more than the Planck length, which is about 1.6 X 10 ^ -35 m, which is quite small) and the nature of the apparent particle is dependent on the oscillation of the string.
(Alex: to the best of my understanding the strings exist in more than one dimension, it's the structure that can only be defined in one dimension. Yeah, it's confusing. It's particle physics, it's like having Cthullu explain the plot of Lost).
The general output of string theory are pretty mindmelting. It predicts that the universe really has between 10 and 26 dimensions with the additional ones above the 4 we're used to being compactified to the point where they don't appear to our observations. The strings however oscillate in these additional dimensions. The alternate explanation is that we exist in a 'brane', a four-dimensional subspace of a larger universe with more dimensions, known as the 'bulk' (akin to how different a crease in a piece of paper is different to the paper itself while being a part of it).
String theory's main major contribution is an explanation of quantum gravity. Simply put, when you drill down to the Planck scale where quantum mechanics happens, gravity simply doesn't work. By making particles strings, their interaction isn't instantaneous, but rather occurring over a short period of time which sorts the problem out (mostly).
Overall, string theory is a good contender for the theory of everything as it holds the potential to explain every physical phenomena. Currently, there are two problems. One, it's hard to make testable predictions (one particular prediction requires 100,000,000,000,000 more power than CERN can generate, so yeah that's not happening any time soon), the second is that string theory generates an amazingly diverse set of theoretical models of the universe, many of which make near opposite predictions about reality.
How does string theory interact with SF? Well, firstly, it's worth pointing out that a theory of everything points to an end to scientific research. How that would affect the world is interesting. Secondly, the implications are interesting. If every fundamental particle is just a string vibrating a specific way, could you find a way to control that? Convert matter to light or electrons and back again? Finally, the brane-world model suggests interesting options. Could you resonate out of our brane, up into the 'bulk' and back down again? What's out there in the bulk?
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Joined: 8/13/2011
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One thing I forgot to mention in my discussion of the Scientific Method is what I tend to call the inherent 'true for a given value of 'true'' nature of scientific theories.
It's a fundamental part of the teaching of science that we have to begin with baby steps in our understanding. We can't really expect a child to begin with Relativity and Quantum Mechanics, yet these are at the core of our current understanding of Physics. Instead we begin with simpler, easier to grasp concepts that apply to more every day experiences. It's only as we examine these concepts that we can find deeper truths.
Let's go back to our earlier example of measuring the speed of an object falling. After a lot of experimentation and theorising, we've come to the conclusion that, assuming no air-resistance, all objects are accelerated downwards at the same rate and that is provably true.
So long as we don't look up at night.
If we do we see the Moon. Which is above us, but isn't falling. Which we know isn't true. So we go back and we do some more theorising and some more experiments until we come up with: assuming no air resistance, objects accelerate downwards at a constant rate, unless they are orbiting the planet. And again, this is true, but it is true for a different value of true.
So every scientific theory is true over a spectrum of truths, not in totality. Relativity and Quantum Mechanics represent theories that are the closest to a totality of 'true', but they still have holes (scale issues and some wall banging around event horizons predominantly). A theory of everything is, almost by definition, true for every definition of true.
Finally, it's worth pointing out that every theory is only an approximation of reality. If we throw a ball, no part of the universe breaks out the calculator, mutters 'okay, so he applied X amount of force in Y direction, so Z will happen'. The direction of the ball's travel naturally falls out of the interaction of all the physical phenomena that affect everything else. The maths we use is so that we can predict what will happen next, before we press the big shiny button and stand back.
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Joined: 8/13/2011
Posts: 272
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Well, I've neglected this for a while, so I'll go into one of my more favourite bits of weird physics: heat and space.
This really easy, right? Space is just really, really, cold?
Yes and, of course, No.
On average, the temperature of an area of space is approximately 4 degrees Kelvin. The important point there was 'on average'. Any area of space close to a planet or star is of course going to be hotter than that.
(Okay, quick note on nomenclature. I'm going to use Kelvin as it's the most scientific measurement of temperature(having 0 K as absolute zero). If you want to use Celsius, subtract 273.15. If you're using Fahrenheit then subtract 273.15, multiply by 12 and add 32.)
Understandably, stars give off a lot of heat. In addition, any planetoid emits a certain amount of heat, either via reflecting the incoming radiation or by emitting its own heat due to various chemical processes. This heat emission affects the temperature at any close point nearby.
So what sort of temperature does a satellite around Earth experience? Well this where things get a little complicated. There's effectively two major types of temperature drivers (for this conversation at least) thermal radiation and convection. Thermal radiation is of course the infra-red radiation thrown off by any hot object. Now the important thing here is that it doesn't 'bend'. It travels in a straight line from the source until it strikes an object. Convection is the tendency for hot gasses to rise above cooler ones.
With the (near) total lack of an atmosphere in space, only thermal radiation drives an object's temperature. Now an object at 1 AU (ie near earth) is subject to 1,360 Watts per metre squared of incipient radiation (for perspective, the atmosphere lets between 1120-1000 Watts per square metre, depending on weather and season, while Mercury experiences between 14,446 and 6,272 Watts per square metre). This barrage of photons is then either absorbed by the object or radiated back out into space. Now of course, the ratio of how much it absorbs to how much it radiates is different for every material, as is the amount of energy required to make the material increase in temperature by one degree.
Where this gets either complicated or unfun (depending on how much you're trying to get your space-going thingy to work) is that it's hard to get rid of this energy. Normally, when an object gets hot on Earth, it sheds its heat into the nearby atmosphere. In space, there's no such useful object. That's a little bit of a problem. Instead, the object will eventually reach a point where it is radiating as much thermal radiation as it is absorbing, hopefully without melting.
(Note: At almost any orbit around Earth, there is 'some' atmosphere which will absorb some of the heat via convection. I'm just skipping over it as it's generally relatively negligible unless you're in a fairly low orbit)
There are two results from this. Firstly, the side of a satellite facing the Sun will get a lot hotter than the side facing the Earth. Secondly, these temperatures will be both higher and lower than we're used to down here on Earth. Just for example, the sunward side of the ISS will hit ~394 K, while its shadowed side will hit ~116 K.
This causes quite a few problems. Let's start with something simple. Pick up/ turn round your computer monitor and have a look on the back. There should be a sticker telling you what its operating temperatures are. You'll quickly note that those temperatures will be no where near the temperatures above. So yes, your computer monitor wouldn't work in orbit.
This is one of the fun parts of satellite design: building something that doesn't mind being at either temperature, doesn't mind having different parts being at those two temperatures and still works! This is handled via a number of methods, beginning with the careful selection of materials that will either reflect away the majority of the radiation or reach relatively low temperatures under the bombardment (thus keeping the temperature down. There is a reason satellites are so shiny) and ending with various mechanisms to move the heat away from the important bits and out to various radiators. Making things worse, many observation tools (and of course, the many processors on board) only work in very specific temperature bands, which you of course have to keep them at. To make all this more fun, depending on the satellite's orbit, the thermal environment will change. It is not entirely unknown for a satellite's planned orbit to be changed entirely during the design process, making everything you've done entirely useless.
Things actually get worse when you send an enclosed atmosphere up as well (to keep your 'volunteers' alive). Remember how I mentioned that you have no convection in space? Well, remember the fun rule of micro-gravity? There is no up.
What this means is that any hot gasses created just sit there, rather than heading up towards the ceiling like normal. So, left to their own devices, any heat-generating object will quickly create a ball of hot air around itself and overheat. As a result, everything either needs to reach thermal equilibrium at its own operating temperature or the air needs to circulate. Yep, you really need the air conditioning in space.
(note: this also applies to the CO2 the human body creates. the AC is a big deal)
So what does this all mean for your SF novel? Depends. Presumably, any craft you've got floating around was designed by someone competent enough to prevent it from overheating, but it's really worth bearing in mind that when things start to go wrong, it's not just the air you need to worry about. Just for example, the reason you always saw the Shuttle floating around with its doors open is that those had most of its radiators on it. If the doors didn't open, they would have quickly begun to overheat.
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Joined: 8/13/2011
Posts: 272
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Right so I've neglected this for a while (hint: ask me questions!), so let's get on to something at once simple and profoundly confusing:
Energy
Here's a phrase to make Tim roll his eyes at your Sci-Fi:
'It's made of some kind of unknown energy'
Yeah, no.
Energy is like pornography and art: you know it when you see it, but it's hard to define. So what is energy?
Energy is a catch-all term we use to define a particle's ability to affect its surroundings. In short, there is no such thing as 'energy'. There is just a number of definable phenomenon that can all be treated under the paradigm we call 'energy'.
So what kinds of energy are there? Here's a list of the most common forms of energy:
Kinetic Energy
Thermal Energy
Chemical Energy
Electric Energy
Radiant Energy
Nuclear Energy
Magnetic Energy
Elastic Energy
Sound Energy
Mechanical Energy
Luminous Energy
Mass (e=mc^2, remember?)
The central rule with energy is that while it can be transferred or transformed, it cannot be destroyed (conservation of energy). Interestingly, this is a lot more relevant than almost anything else. Mass, momentum and a few other things are actually symptoms of energy, not actually entirely discreet objects in and of themselves.
So what's wrong with 'unidentified energy'? The answer is simple: there is no such thing as 'energy'. There can be unidentified particles, unidentified fields and unidentified molecules, but mysteriousness of these elements is what creates the confusion, not their inherent energy.
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Joined: 5/25/2011
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Hmmm...., reminds me of a line from an old scifi movie (Can;t remember the name, but it was a 50's B movie):
Wise old scientist, "This is the source!"
Young hero, "The source of what?"
Wise old scientist, "We don't know!"
Right up there with another movie where they determined that the killer was from the future. Why? Because they radio-carbon dated the blunt instrument (a small statue) used as the murder weapon, and found out it was from 5,000 years in the future! I watched CSI quite a bit and oddly, they never bothered radio-carbon dating a murder weapon (let's not even get started on how radio-carbon dating tells you something's from the future!).
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Joined: 6/7/2011
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This is great stuff Timothy! It's almost enough to make me give up my usual method of just making stuff up based on half remembered episodes of Star Trek.
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Joined: 8/13/2011
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Tom: Yeah, radio-carbon dating won't tell you that, though at least they're in the right ball park for it (carbon 13 has a half life of about 6000 years). All radio carbon dating can do is how long it is since the organic material in question (leather/ papyrus/ bone) died. Though there are a number of dating techniques that could theoretically tell you that an object's from the future (dating soil samples from known nuclear test sites against the dates of the tests would be one way).
Atthys: I know I was taking 'unknown energy' from an unnamed book on this site, but I'm very sure it's from at least one Star Trek episode (though I suspect it's more like from at least one episode per series).
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Time travel may be best as the fiction in the story instead of the "science," being a movement of clock hands or numbers, a dimension of mathematics, a mere human convenience. Anyone travelling through time to say, a year of their childhood, would discover that the earth is no longer where it was when they were a child. Oops!
Sorry for the heresy  but this is what I have long thought. Dr. Michio Kaku expressed a similar opinion on his radio show the other night. He could be wrong of course and I certainly could have misunderstood him. But I'm throwing this thought out for critique because I would like to be corrected if possible. I want to go home again.
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Joined: 6/7/2011
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Yes, indeed. Like the good politically correct franchise it was, Star Trek believed in recycling.
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Joined: 8/13/2011
Posts: 272
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GD: I'd forgotten to mention that actually. Though, to be honest, if you can lob yourself backwards to a specific date and time, you should be able to specify your location as well. One's definitely easier than the other. Though of course any time machine fixed to a single location makes a lot less sense all of a sudden.
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Joined: 8/13/2011
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Well, I've just realised that this thread is now on the featured list, which is only a little terrifying. So I'd better do something new. So without further ado: the four fundamental forces (at the moment).
I touched on this a little in my discussion of string theory a while back, but one of the fundamental tenets of physics at the moment is that there are four forces that 'manage' the universe as best we understand it. These are (organised by increasing strength):
1) Gravity
2) The Weak Nuclear Force
3) Electromagnetism
4) The Strong Nuclear Force
Every physical interaction in the universe can be eventually devolved downwards into a combination of these four forces.
Gravity is the simplest of these forces to define: stuff tends to clump up. Gravity is at once the strongest and the weakest of the four forces. Gravity is the prime determinate of the universe's structure, yet on the scale of individual particles, the other three are significantly stronger.
The Weak Nuclear Force is the second force and is generally irrelevant to our day to day lives. The only major effect is causing beta decay in radioactive materials. Weak is however hugely relevant to the Standard Model (which I'll hopefully get into at a later date).
(The Weak Nuclear Force and Electromagnetism, at very high energies (e.g. during the Big Bang) combine to form the Electroweak force)
Electromagnetism is the force that governs the behaviour of any particles with a charge. Relative to the universe, this isn't hugely important, as the total charge (as far as we can tell) is effectively zero.
The Strong Nuclear Force is the force that holds Protons to Neutrons as well as binding quarks together within them. The Strong nuclear force is the most powerful of the four forces, but only has an effective range of about 0.8 femtometres.
How is all this relevant? Well that depends. On the grand scale of things, the weak and strong force are largely irrelevant to the process of your novel (unless you've somehow shrunk down to the quantum scale), but the important point is how they interact. A unified theory has to explain how these things go together, but why can't we figure one out now? How do they tie together and what have we missed?
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Joined: 8/13/2011
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So I read a fairly enraging article today and, aside from 'improving' my blood pressure, it reminded me of how interesting explaining physics can be. So, without further ado, new topic: E=mc^2!
There's probably no better known scientific equation than E=mc^2, but what does it actually mean.
Well, let's begin with the basics. E stands for energy, m for mass and c is the speed of light travelling through a vacuum (it's worth pointing out that light actually slows down in a material, so it's a lot more variable than you'd think, but when a physicist says 'speed of light', it almost always means 'in a vacuum'). So the implications are pretty clear: the ratio between energy and mass is the square of the speed of light, but what energy and what mass?
Let's rewrite this equation. A more accurate way of phrasing it would be:
E = (m(original)-m(current))c^2
That clears everything up!
Right, so what we've got here is that the energy of a change in mass is proportional to the square of the speed of light (a more common way to write this is as delta-m. Delta (the greek symbol that looks like a triangle) is the scientific notation denoting 'change in'. You can often see it as 'delta-v' when people are talking about acceleration or deceleration. What do I mean by this?
Well, this is one of the few times that antimatter makes things simpler. Let's take one proton and one anti-proton. Now when these two collide, they mutually annihilate each other, turning into nothing more than a lot of photons (gamma-rays). Problem is, photons don't have any mass.
So we're down the mass of two protons (about the only thing the same between a particle and its anti-particle is its mass) and we've got a load of energy coming out, but how much energy?
Well the mass of a proton is 1.007 u (u is a easier to use measure of particle mass, being a twelfth the mass of a carbon-12 atom. Working in 10^-27 kgs is a pain) and we've just lost two. So we're down 2.014 u, therefore:
E= 2.014 X 3X10^8
While we'd need to do some tweaking to get this out as joules (while u is useful, it needs to be converted back to kg if we want the answer in joules), we can see how this works.
This also occurs in nuclear fission and fusion, as well as in ordinary chemical reaction, albeit at much lower levels. One of the weirdest parts of atomic theory is that the mass of an atom isn't equivalent to the mass of its constituent protons and neutrons (the mass of electrons is basically negligible). Yeah, I know. This is called the mass defect, and it's due to the energy needed to bind the protons and neutrons together.
Again, this means that you can calculate the energy of these reactions by the change of mass. So the energy of a helium fusion reaction is based on the difference in mass between a helium atom and four hydrogen atoms (ignoring the complications of the electrons, etcetera. Fusions reactions are complicated), while the reaction between hydrogen and oxygen to create water creates an amount of energy based on the difference between the mass of the elements and the mass of water.
This change in mass is the primary relevance of E=mc^2, but it also goes the other way. When doing high-energy reactions (i.e. turning on CERN and watching what happens), it actually runs in reverse. The matter - anti-matter annihilation, when done at relativistic velocities, actually turns energy back into mass. In fact, this is the only way to get the rarer, unstable quarks and leptons (just for reference, the muon is 21 times heavier than the electron).
So, how is this relevant to your writing? Again, I'm going to go with an 'I have no idea'. The actual mechanics of E=mc^2 are probably largely irrelevant to any story, but the central conceits are useful. Any mass to energy conversion is shockingly powerful, giving a lot of energy for very little mass, and power plants like this can be very helpful while writing.
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Joined: 8/13/2011
Posts: 272
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Right, so let's do something different. What's in a constant?
Any time you see any physics equation, you're going to see some sort of physical constant, either implicit in the equation or as a part of it, but what are these things?
I've mentioned before that any physics equation is at best an approximation of the physical reality it's describing and this definitely applies to the constants in use. Let's head back to what we were looking at last time: E=mc^2
Now, the constant here is c, the speed of light in a vacuum. This is (approximately) 3 X 10^8 ms^(-1). In other words, a photon will travel 300,000,000 metres in one second. Which means we really have three constants here: the speed of light, the length of a metre and the duration of a second. Our speed here is only defined in the context of how far and how quickly it happens. If we were to measure the speed of light in feet and minutes, it's be different.
This is the first kind of constant, a multiplier that converts one measure into another. In this equation, the square of c, converts mass into energy, but what if we change the definition of energy?
The standard measure of energy is the joule, which in this context is measured in kgm^2s^(-2) (for those who haven't already worked it out, I haven't found a way to more elegantly write out a power than this). So 1 joule is 1 kilogram per metre squared per root second squared, which is useful, but what if we define energy as kilogram per the speed of light squared? Call it a BCJ (Book Country Joule). Then the equation looks like this:
E=m
It might look like we've cheated here, effectively making a new equation, but all we've really done is make our constant equal to one by changing the output value of our equation. One BCJ isn't equal to one joule, so nothing's really changed here, it just looks different.
This can be done with any physical constant (like the gravitational constant, the electron volt, the Planck constant etc), but why isn't done more often? Well, the only use of an equation is in how it helps us understand what's going on. The use of a BCJ is basically none. How much use is the energy release of the annihilation of a kilogram of matter in a daily calculation? Not a lot. A single joule is a far more relevant value to our daily calculations than the BCJ.
A good example of this is the electron volt (eV). This is the energy of a single electron moved across an electric potential difference of one volt. It's about 1.6X10^(-19) joules. The use of the electron volt is that it's a very small measure of energy. As such, when we get into particle scales, it starts to get useful when defining energies. The total energy of a particle (its rest energy (mass) plus its kinetic energy) in a particle accelerator is often express in electron volts as it makes things a lot more obvious. For example, the rest energy of a proton is 938 MeV/c^2, while the rest energy of a Higgs Boson is between 125 and 127 GeV/c^2. This makes it a bit easier to see the difference of scale between the two masses than it would if we were to talk in kilograms.
So basically, the physical constant's job is to help us translate the information we have into what we're looking for, but what about non-physical constants?
We're all familiar with Pi (yeah, I also don't know how to put greek symbols into these text boxes), the value that lets us work out the values of a circle. Pi is the ratio between a circle's diameter and its circumference (ie C=PiXd), but what is Pi?
Unlike our previous example of c, Pi is impossible to remove from the equation. Why? Because it isn't defined in terms of another constant. c is defined by both the measure of distance and time, but Pi isn't defined by any of that. It's dimensionless, utterly independent from whatever you're measuring. Pi remains as useful in relativity as it is in quantum mechanics.
The interesting thing about dimensionless constants is that they are mathematical constructs and they only remain as useful as jobs can be found for them. For example, there's a movement to replace pi with tau, a value twice its size. Why? Because 2XPi is far more useful to a mathematician than Pi itself (you would not believe how often I wrote 2XPi over the course of my degree).
Again, so how is this helpful? Well, if you ever want to invent your own units, its worth bearing in mind that their primary role is to translate what's happening into a useful scale. We use metres, seconds and kilograms not because of an inherent 'rightness', but because they are concrete values we can grasp with ease. As for dimensionless constants, let's just put it this way: if pi suddenly equals 3, your characters should start running very quickly.
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Joined: 4/24/2013
Posts: 18
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I can be an awful nitpicker in sci-fi or any genre that contains a science element such as forensic crime novels. I went to see the new Star Trek last week and was squirming in my seat at the howling error they made with Spock's 'cold fusion' device.
I actually have an idea for a sci-fi novel in my head which is a crime thriller with a space setting. I'm on fairly safe ground with the forensic science having done 3 years of forensic anthropology at university but to make it as accurate as I can I've spent the last 48 hours getting my head around the classification system for main sequence stars, which stars are in proximity to one another within the Milky Way and which ones already have confirmed exo-planets. Then I gave myself a real headache reading up on the Alcubierre propulsion system. I could probably write the story without all this reading and just make this stuff up but I think you have to start with a factual foundation even if you then head off into the realms of total fantasy.
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Joined: 8/13/2011
Posts: 272
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I can probably help you a little with the Alcubierre field system. Plus it gives me something to talk about here and I've neglected this for a while.
Right so the central issue. The Alcubierre field is best described as a very interesting piece of loophole abuse in Relativity. Basically, while relativity restricts any particle from going faster than the speed of light (in a vacuum), it doesn't say anything about space itself. So the basic theory is that you could accelerate a patch of space past the speed of light and hitch a lift as it goes.
(It's worth pointing out that Alcubierre was apparently inspired by the Enterprise's warp drive. Yeah, cutting edge research is a little odd somedays)
The general accepted system is to compress the space-time before the ship and stretch the space-time behind it, creating a wave that you can ride. What's kind of cool /insane about this is some of the side-effects of this. Firstly, there's no forces being applied on your actual ship, so it's in a constant free-fall state. Secondly, you're not actually moving, so there's no relativistic effects to worry about.
The obvious problem here is simple: how do you warp space like this? That's where things get a little interesting. Creating a field firstly relies on negative mass (made from negative energy) which while theoretically possible, really hasn't been made physically possible. Next, there's the problem of actually steering the bubble, as a few theories suggest that it might be impossible to actually send any control messages to the bubble during flight.
The central problem with the Alcubierre drive is that we honestly don't know enough about one to say what it can and can't do. Some theories reckon that to build one capable of crossing the galaxy you'd need more mass than there is in the universe. Others suggest that actually getting one up part the speed of light would irradiate the contents of the bubble. Yet others suggest that there are ways around these problems, that a mix of cunning design and subtle tweaks could reduce the load on it considerably.
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Joined: 4/24/2013
Posts: 18
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I was reading a paper yesterday that suggested that an Alcubierre engine could be tweaked to run on the same amount of fuel as a standard rocket engine.
The big problem I see, from what I've read, is that when the wave is allowed to collapse - because you've reached your destination - the energy released would be enough to blow up any planets in the vicinity. If someone could design some kind of feedback system that funnels that energy back to the engines to be stored for the next trip that would solve that problem as well as reducing the energy requirements of the engine. Just like the breaking system on a modern car.
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Joined: 8/13/2011
Posts: 272
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So I've left this alone for a while, so let's see what I've got now.
Orbits
So, orbits. Nice and simple. Little thing goes round big thing due
to gravity.
Of course, it's never that simple.
Let's start with the physics of an orbit. There are effectively
two different elements of any orbit, speed and gravity. The ratio
between the two of them determines the nature of the orbit. Now, why
is that?
Anyone who's ever driven a car round a corner will know that you
have to apply force inwards into the curve. The faster you go, the
more force you need to apply. This is why formula one cars can take
corners far faster than your minivan, as they're designed to apply
more force. This is known as centripetal acceleration.
Now of course, scientists being scientists, there's an equation to
calculate how large this force has to be to take the curve as planned
(if it's too low, the car won't finish the turn, if it's too high,
the car will take the turn to quickly). The formula for what this
force needs to be is simple:
F= m*(v^2)/r
Where:
F = force on the vehicle
m = mass of the vehicle
v = velocity of the vehicle
r = radius of the circle the vehicle is trying to inscribe
It's worth noting here that this is all measured from the
vehicle's centre of mass, not its nearest or closest edge. In
addition, the speed here is its speed tangential to the curve it's
taking. In simpler terms, it is the speed directly forwards at every
moment of its turn.
Now what's applying this force? Well in our example of the car,
this is the friction between the car and the road. If the friction is
too low, the car will slide outwards until the friction is equal to
the centripetal acceleration. If the friction is too high, the car
will slide inwards.
Now in an orbit, the centripetal force is provided by gravity
(unusually, this actually simplifies the math from the example). The
gravitational force between two objects can be calculated using the
following formula:
F = G*m(1)*m(2)/ r^2
Where:
F = force between the two objects
G = the gravitational constant
m (1) = mass of the first object
m (2)= mass of the second object
r= distance between the two objects
Again, this distance is measured between the centre of mass of
both objects. Now, when an object orbits a planet, these two forces
are equal. With a little calculus, we end up with:
v^2= gm/r
Where:
v = the speed of the orbiter
g = the gravitational constant
m = the mass of the object being orbited
r = the distance between the orbiter and the orbited
As the gravitational constant and the mass of the orbited body are
unlikely to change any time soon, the two variables here are the
speed of the orbiter and the distance between it and they have an
inverse square relationship. In short, the closer an orbiter gets to
what it orbits, the faster it needs to travel to maintain a stable
orbit.
What that means is that a satellite close to the earth will rotate
round it faster than one further away. What's important about this is
that it's non-negotiable. Closer must equal faster, further must
equal slower.
Now we can pull back this math back a bit and using our knowledge
of circles, we can work out that the time it takes an object to orbit
a body is:
t= 2 pi (r^3/gm)^0.5
Where:
t = the time taken to complete one entire orbit
r = the distance between the orbiter and the orbited
g= the gravitational constant
m = the mass of the orbited
Now that means that again, the time it takes an object to orbit a
body is determined by its distance from the body only. This means
that if you want an satellite with specific period (say 24 hours), it
can only orbit at one altitude, which of course fixes its speed.
For example, it's worth pointing out that a geosynchronous orbit
(a period of exactly 24 hours) has only one altitude: 42164 km.
Now all of this assumes we're talking about a simple, circular
orbit. Unfortunately, in the real world, almost every orbit is
slightly off circular, being elliptical, rather than circular. This
complicates matters.
In an elliptical orbit, the important term is the eccentricity of
the orbit. This is a value that's derived from the orbit's apoapsis
(the furthest the orbiter gets from its orbited body) and its
periapsis (the closest the orbiter gets to its orbited body) and it
given using this calculation:
e = 1 – 2/ ((r(a)/r(p))+1)
Where:
e = is the orbiter's eccentricity
r(a) = the distance between the two bodies at apoapsis
r(p) = the distance between the two bodies at periapsis
Now, we then define orbits as one of four types based on their
eccentricity:
circular orbit: e = 0
elliptic orbit: 0 < e < 1
parabolic orbit: e =1
hyperbolic orbit: e > 1
Now for our purposes, it's only important that we note that
parabolic and hyperbolic orbits trend to infinity, meaning that any
orbit with an eccentricity of 1 or greater is an escape orbit.
The important thing to bear in mind is that this still obeys
everything above. Speed and altitude are still linked, but they are
now variable, with the orbiter speeding up the closer it gets to the
orbited and slowing down as it moves away.
The really useful thing about an eccentric orbit is that the
velocity at periapsis (the lowest point) is faster than it would be
in a circular orbit at the same altitude and in addition the velocity
at apoapsis (the highest point) is lower than it would be in an
circular orbit at the same altitude. This let's you do something
clever.
As I mentioned earlier, an orbit is defined by the speed of an
orbiter and its altitude. If we take an object in a circular orbit
and speed it up, it's going to move outwards. This lets us do
something clever called a hohmann transfer orbit. This is a pair of
timed accelerations designed to let us move between two separate
circular orbits (extremely usefully, this can be done either way,
either to rise or drop in altitude.
This done by firing the engines on a craft in a circular orbit,
which kicks it into an elliptical orbit. Once it reaches apoapsis, it
then kicks its engines in again, accelerating it to a high enough
speed to enter a new circular orbit at its new higher altitude.
The useful thing about the Hohmann transfer orbit is that it's
relatively energy efficient, only requiring two uses of the engine.
It's the best way of transferring orbits when using rocketry.
So how is all of this useful to you guys? Well, firstly, if you're
writing about space travel, some grasp of how orbits work and
interact is important. Its worth noting that much of this is only
really relevant if you're using relatively low energy transportation
like rockets. If your setting includes far more powerful drive
mechanisms, then worrying about orbital velocities becomes less
important. It's only once your engine turns off that things get interesting.
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Joined: 6/7/2011
Posts: 467
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Timothy! Another fascinating installment. Once I glossed, glazed-eyed, through the math I had found some intriguing take-aways. If any of my characters ever leave orbit (and they really must, someday), I'll put this stuff to good use. Thanks.
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Joined: 10/11/2013
Posts: 7
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I'd like to jump in and ask about the physics of space colonies, in particular the "artificial gravity" provided by the centripetal (sp?) acceleration of a rotating cylinder or torus. I tried figuring out what happens if you are in a cylinder of radius 50 meters, spinning so as to create an Earthlike "gravity" at interior surface, meaning that the centripetal acceleration is 9.8 meters/sec. If you drop something, say, a superball just for fun, from radius 10 meters or 40 meters, it will not appear to drop as it would on earth. From radius 10 meters it will drift backwards (that is, if forwards is in the direction of rotation) and land about 3/4 of the way around the cyclinder. At radius 40 meters (which is 10 meters above the inside surface) the superball will still not fall directly "down," it will drift backwards a bit. Even with a radius of 500 meters (a diameter of one kilometer) the effect should be noticeable. I promise I did the math, and I'm willing to try to reproduce it anyone wants. The National Space Society website (http://www.nss.org/settlement/space/index.html) describes several designs, but most of them ar pretty vast, probably to minimize this effect, which they call a Coriolos force. Gerard O'Neill's design for a cylindrical colony is 4 miles or 6.4 kilometers in diameter.
For the story I have in mind, the space colonies would be the first effort to have a significant population in space, so I wonder what would be the minimum radius to have a reasonable facsimile of gravity? This is pretty subjective, but I think people should be able to run, ride a bike, and throw things short distances, though I don't suppose that space baseball is very likely. Any thoughts?
Richard
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Joined: 9/4/2014
Posts: 1
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Science is always a vital part.
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