I decide to start a separate thread because I know the kind of exploration I like isn't everyone's cup of tea.
Most, maybe all, EI'ers are science fiction fans. We've read a lot of [fictional] theories of time travel, and we each have our favorites. It's a lot of fun to explain the various fictional SF universes we visit in terms of our own favored theories, in what seems (to us) like a selfconsistent way. Heck, if we dare, we may even venture to explain the occasional factual observational datum through whatever view of spacetime that supports our worldview and favorite theories of time travel.
Wait. "Spacetime"? I'm getting way ahead of myself. You see, I'd like to put aside my decades of Sf, before I knew the nittygritty of Real Science/Math, and take a fresher look at the subject. Maybe I'll believe something different when I'm finished. Science only advances when we *prove* ourselves wrong (Data that seems to confirm our beliefs won't advance us far, except in distant hindsight, after we've been proven wrong!).
I'd like to start with what was known when I was born say from Einstein's Special Relativity (1905) to mankind reaching space (Yuri Gargarin, 1961)  a period when you still needed to explain that things ALMOST made sense in classical Newtonian mechanics (after some minor tweak) OR show that some easily observed phenomenon proved Newton was completely off his rocker in that one particular area.
I won't say we have to limit ourselves to that. We've all heard a lot of more modern science words, It would be silly to pretend we had never heard of quark theory or Cosmic Background Radiation (aka "3K microwaves") or superconductors. I'm just thinking that I (for one) would like to go back to my beginnings, and see if I would find a new favorite Theory of Time Travel (and The Universe).
For example: here's an idea (which I'll explain in my next post): a well established principle before I was born was "CPT conservation" (ChargeParityTime). In really crude terms, you could say that this means that "our universe, running forward in time, would look exactly the same as an antiuniverse. made of antimatter, running backwards in time". There's a lot more to it than that, but take a moment to imagine what that universe would look like to its inhabitants!
Now just take my word for this: there is only one known kind of interaction that doesn't obey CPT conservation. What does that mean for the prospects of time travel? On one hand, there's a pretty solidlooking "physical law", and on the other hand, there's a known exception.
The cool part (to me) is that you don't really have to know a lot of fancy physics to start thinking about this (and even be right). See ya next post!
0
Orph revisits time travel (via SHIELD/Fitz)
Started by
Orpheus
, Apr 12 2016 11:13 PM
SHIELD S.H.I.E.L.D. Quantum Time Travel Particle Physics
6 replies to this topic
#1
Posted 12 April 2016  11:13 PM
#2
Posted 13 April 2016  05:37 PM
Yeah, I think there's only one variety of subatomic decay that violates CPT Conservation. That's what I meant in the other thread when I said that the arrow of time has barely been proven.
This should be fun. I don't really believe that time travel can exist, in any meaningful way, but I'm very interested in the possibilities of doing something innovative with it in fiction. That's where my idea of changes in the timeline propagating along at the usual rate, while the time traveler jumps back and forth in confusion, creating additional changes, each overwriting the other. Imagine what that kind of time travel might look like.
This should be fun. I don't really believe that time travel can exist, in any meaningful way, but I'm very interested in the possibilities of doing something innovative with it in fiction. That's where my idea of changes in the timeline propagating along at the usual rate, while the time traveler jumps back and forth in confusion, creating additional changes, each overwriting the other. Imagine what that kind of time travel might look like.
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#3
Posted 16 April 2016  08:42 PM
Sorry I took so long to start. I got caught up in some of the math and thoroughly confused myself.
Maybe I should just stick to tossing out principles.
I mentioned CPT conservation. That's as good a good place to start as any.
CPT means "Charge Parity Time". Now, as it turns out, Charge, by itself, is conserved (within certain quite reasonable constraints). We learn this quite early in school: positive and negative charges can cancel each other, and you can often separate neutralized charges to "create" both positive and negative charges (e.g. a child rubbing a balloon on their hair), but never just positive or negative charges alone. That's pretty simple.
Charge and time are familiar terms. "Parity" is, if anything, even simpler but perhaps less familiar. In general, "parity" is used to refer to many different phenomena that have two mutually exclusive states, especially if they interconvert easily  or don't interconvert at all. Some math puzzles, for example, fall apart into an easy solution if you label some states as "odd" and others as "even" (even if they aren't "odd/even" in the arithmetic sense). Another common type of parity is called "chirality" or "right handed" vs "left handed".
A righthand glove won't fit a left hand, even though they are otherwise identical in all their properties. We say they are mirror images  but did you ever really stop to think what a mirror does? We say it reverses right and left, but if you lie down with your head to the left and you feet tothe right, it won't reverse your head and feet, it'll exchange the (now) top half of your body and the bottom half!
Is this a human perceptual artifact? Do we only perceive a left/right reversal because we evolved with left and right eyes? No, sketch the way light goes from your face, reflects in the mirror, and returns to your eye, you'll see that it is physically independent of how your body (or the mirror) is turned.
However, it IS a psychological illusion in one sense. When we look in the mirror, we perceive the reflection as if it was a doorway to part of our world, full of objects which can (only) be manipulated as the real objects in the world around us. We know this isn't true (fun house mirrors can cause distortions that we never see with real objects, like "flowing around a doughnut hole"), but casually we trust the image to be "real" enough to trust it for a big date or a big scientific experiment.
What a mirror actually does is "reverse the frontback axis" (anteroposterior dimension). This is not something that physical objects generally do, because their front would actually have to pass through their back and come out the other side (and vice versa). Even a T2000 (liquid metal Terminator) couldn't pull that off stunt, because at the instant when its front and back side met, it's volume would be zero! In the physical world, we rotate objects. Rotation preserves chirality (you can't turn a left hand glove around to make it a right hand glove), but reflection inverts chirality because it changes only one dimension, while leaving the other dimensions unchanged.
Of course, if you reflect something through two mirrors, the image uninverts giving a "real image".
The third element of CPT is Time. Now, as I'll explain, it's not exactly clear WHAT time is (to a physicist, it's not exactly clear what charge, mass or energy is, either, but we understand how they seem to behave (Physicists consistently dismiss "what it really IS" as "more philosophy" unless/until they work on a problem that makes them confront their definitions  a change of mental frame that any field of physics tends to only be able to tolerate once every several generations).
One principle we have decided to use in evaluating/constructing physical laws is "reversibility", meaning that timereversible. We have very solid reasons for that choice, but just because the physical laws are reversible doesn't mean that larger (epi)phenomena are completely and easily reversible. We all know this: a watermelon can go splat but is unlikely to spontaneously reassemble; a cooked egg could, in theory, uncook, but it is highly unlikely to do this spontaneously. This is largely a statistical process, aka "thermodynamics".
CPT parity means that Charge, Parity, and Time are conserved *together*. In other words, if you change the Charge of an isolated particle you have to *also* change its Parity or reverse Time to make up for it. Well, actually, you can't change the charge of an isolated particle at all, because Charge is conserved all by itself. So what does CPT conservation give us? That's where it gets interesting.
To be continued...
Maybe I should just stick to tossing out principles.
I mentioned CPT conservation. That's as good a good place to start as any.
CPT means "Charge Parity Time". Now, as it turns out, Charge, by itself, is conserved (within certain quite reasonable constraints). We learn this quite early in school: positive and negative charges can cancel each other, and you can often separate neutralized charges to "create" both positive and negative charges (e.g. a child rubbing a balloon on their hair), but never just positive or negative charges alone. That's pretty simple.
Charge and time are familiar terms. "Parity" is, if anything, even simpler but perhaps less familiar. In general, "parity" is used to refer to many different phenomena that have two mutually exclusive states, especially if they interconvert easily  or don't interconvert at all. Some math puzzles, for example, fall apart into an easy solution if you label some states as "odd" and others as "even" (even if they aren't "odd/even" in the arithmetic sense). Another common type of parity is called "chirality" or "right handed" vs "left handed".
A righthand glove won't fit a left hand, even though they are otherwise identical in all their properties. We say they are mirror images  but did you ever really stop to think what a mirror does? We say it reverses right and left, but if you lie down with your head to the left and you feet tothe right, it won't reverse your head and feet, it'll exchange the (now) top half of your body and the bottom half!
Is this a human perceptual artifact? Do we only perceive a left/right reversal because we evolved with left and right eyes? No, sketch the way light goes from your face, reflects in the mirror, and returns to your eye, you'll see that it is physically independent of how your body (or the mirror) is turned.
However, it IS a psychological illusion in one sense. When we look in the mirror, we perceive the reflection as if it was a doorway to part of our world, full of objects which can (only) be manipulated as the real objects in the world around us. We know this isn't true (fun house mirrors can cause distortions that we never see with real objects, like "flowing around a doughnut hole"), but casually we trust the image to be "real" enough to trust it for a big date or a big scientific experiment.
What a mirror actually does is "reverse the frontback axis" (anteroposterior dimension). This is not something that physical objects generally do, because their front would actually have to pass through their back and come out the other side (and vice versa). Even a T2000 (liquid metal Terminator) couldn't pull that off stunt, because at the instant when its front and back side met, it's volume would be zero! In the physical world, we rotate objects. Rotation preserves chirality (you can't turn a left hand glove around to make it a right hand glove), but reflection inverts chirality because it changes only one dimension, while leaving the other dimensions unchanged.
Of course, if you reflect something through two mirrors, the image uninverts giving a "real image".
The third element of CPT is Time. Now, as I'll explain, it's not exactly clear WHAT time is (to a physicist, it's not exactly clear what charge, mass or energy is, either, but we understand how they seem to behave (Physicists consistently dismiss "what it really IS" as "more philosophy" unless/until they work on a problem that makes them confront their definitions  a change of mental frame that any field of physics tends to only be able to tolerate once every several generations).
One principle we have decided to use in evaluating/constructing physical laws is "reversibility", meaning that timereversible. We have very solid reasons for that choice, but just because the physical laws are reversible doesn't mean that larger (epi)phenomena are completely and easily reversible. We all know this: a watermelon can go splat but is unlikely to spontaneously reassemble; a cooked egg could, in theory, uncook, but it is highly unlikely to do this spontaneously. This is largely a statistical process, aka "thermodynamics".
CPT parity means that Charge, Parity, and Time are conserved *together*. In other words, if you change the Charge of an isolated particle you have to *also* change its Parity or reverse Time to make up for it. Well, actually, you can't change the charge of an isolated particle at all, because Charge is conserved all by itself. So what does CPT conservation give us? That's where it gets interesting.
To be continued...
#4
Posted 16 April 2016  11:46 PM
I'll come back to CPT in a bit, but first let me cover "Determinism".
There are a lot of variant views of Determinism, so I'm going to make up my own terms to define specific situations.
No matter how smart or scientific you are (the two are very different things that only sometimes overlap), you've probably bumped your head on some of the weirder aspects of modern physics and asked yourself "do we really need that?" and even after/[/i]if[/i] you've decided we do, you'll keep asking yourself for much longer "WHEN do we need that?" (Do I have to drag out the fancy math EVERY time I cross the street or my SO asks if these pants makes them look fat, or can I usually trust Newton's Laws?)
Let's get one thing straight: Newton's Laws are great, but they fall completely flat at the level of "existence as we know it". Do you believe in atoms? Chemistry? Atoms can't exist under for long (microseconds) under Newtonian physics. The slightest bump would send an electron spiraling into the nucleus or wobbling out in increasingly eccentric ellipses until it breaks free of the nucleus. Quantum physics is necessary to hold electrons in anything like a stable orbit. No quantum physics = no stable atoms = no chemistry as we know it.
Yet quantum deniers abound, who think they can apply some clever tweak to Newton's Laws to avoid the spookier bits of quantum physics that they find distasteful. I don't blame them. It's a phase we all have to grow through. I've been there many times, at many stages, long after I learned quantum mechanics. One of my personal bugaboos has been Heisenburg Uncertainly (which I'll discuss later). It's easy to imagine some "hidden states": i.e. if we knew every detail with enough precision (even details we can't measure), we'd live in a Cartesian universe. Descartes famously said that if he knew the exact position and momentum of every particle in the universe, he could predicts the entire future and see the entire past as well.
There's a lot of very good evidence that "hidden states" don't exist, but physicists keep testing theories where they might.
Heisenberg's uncertainly principle stated that we can't know the exact position AND the exact momentum of ANY particle: the more precisely you know one, the less precisely you can know the other. This wasn't a slap at Descartes. He wasn't even thinking of Descartes. He was looking at physics data. He even put a number on the limits: the uncertainty of position times the uncertainty of momentum = hbar/2 [hbar is Planck's constant divided by 2*pi; Planck's constant is a tiny number on the human scale but huge for subatomic particle, so position and velocity seem pretty clear to us, but an electron can't tell if a housefly or a bowling ball just landed on its nose  and may react as if either were true!)
As much as Heisenberg Uncertainty annoys me, it may save us all, especially when we think about time travel  in much the way the weirdness of quantum physics make good old sensible atoms (and matter itself) possible.
For the purposes of this thread, let me define a term, "StrictDet" [Strict Determinism] as the following: in a StrictDet universe, you can run any physical even back and forth as many times as you want, and it will always replay exactly the same  no Chaos Theory, no Butterfly Effect, no nothing. Just the same video played forwards and backwards ad infinitum. This is impossible with Heisenberg's uncertainty, and may not even be possible with Newton's Laws, unless we posit "hidden" (unseen or unknowably precise] states/variables. In other words, it's a very strict criterion, much stricter than a purely Newtonian universe  but it's what most of us probably intuitively assume.
We've all heard the question "Would it be ethical to go back and kill Hitler as a baby to prevent the Nazi horrors?" Forget the ethics, I doubt it would even be possible in a StrictDet universe: if you killed Baby Hitler, you'd have no reason to kill Baby Hitler (unless you turned into a random infanticidal time traveler). It's like the grandfather paradox: if you killed Grandpa, you wouldn't even exist to kill Grandpa  so what happens if you even try? Heisenberg and Schroedinger and all their pals at least offer some hope of resolution to that: a cosmic furball, a complex waveform of all possibilties that ultimately collapses into some stable outcome that makes sense. Maybe your time machine blows up if you try to travel to the past or maybe you spawn a parallel Hitler/Grandpa free universe. Either way: it works out.
Now here's another question: can you see the future, and if you can, can you change it? Well, if you can't change it, foresight is a pretty pisspoor superpower to have (unless your future is all immutable hugs and kittens) and if you CAN change it, it's not seeing the future, is it? It's just seeing a possible future and we ALL can do that every day. Okay, maybe you'll see the consequences of some factors you have no way of knowing at present, but that's just some weird form of ESP, not time travel/perception. It might happen to us all the time, but the effects are so muddied by all of us independently having hunches (which others of us cancel out) that it doesn't end up being significant.
How could we tell? Think about it. It's not a dumb question.
More later.
There are a lot of variant views of Determinism, so I'm going to make up my own terms to define specific situations.
No matter how smart or scientific you are (the two are very different things that only sometimes overlap), you've probably bumped your head on some of the weirder aspects of modern physics and asked yourself "do we really need that?" and even after/[/i]if[/i] you've decided we do, you'll keep asking yourself for much longer "WHEN do we need that?" (Do I have to drag out the fancy math EVERY time I cross the street or my SO asks if these pants makes them look fat, or can I usually trust Newton's Laws?)
Let's get one thing straight: Newton's Laws are great, but they fall completely flat at the level of "existence as we know it". Do you believe in atoms? Chemistry? Atoms can't exist under for long (microseconds) under Newtonian physics. The slightest bump would send an electron spiraling into the nucleus or wobbling out in increasingly eccentric ellipses until it breaks free of the nucleus. Quantum physics is necessary to hold electrons in anything like a stable orbit. No quantum physics = no stable atoms = no chemistry as we know it.
Yet quantum deniers abound, who think they can apply some clever tweak to Newton's Laws to avoid the spookier bits of quantum physics that they find distasteful. I don't blame them. It's a phase we all have to grow through. I've been there many times, at many stages, long after I learned quantum mechanics. One of my personal bugaboos has been Heisenburg Uncertainly (which I'll discuss later). It's easy to imagine some "hidden states": i.e. if we knew every detail with enough precision (even details we can't measure), we'd live in a Cartesian universe. Descartes famously said that if he knew the exact position and momentum of every particle in the universe, he could predicts the entire future and see the entire past as well.
There's a lot of very good evidence that "hidden states" don't exist, but physicists keep testing theories where they might.
Heisenberg's uncertainly principle stated that we can't know the exact position AND the exact momentum of ANY particle: the more precisely you know one, the less precisely you can know the other. This wasn't a slap at Descartes. He wasn't even thinking of Descartes. He was looking at physics data. He even put a number on the limits: the uncertainty of position times the uncertainty of momentum = hbar/2 [hbar is Planck's constant divided by 2*pi; Planck's constant is a tiny number on the human scale but huge for subatomic particle, so position and velocity seem pretty clear to us, but an electron can't tell if a housefly or a bowling ball just landed on its nose  and may react as if either were true!)
As much as Heisenberg Uncertainty annoys me, it may save us all, especially when we think about time travel  in much the way the weirdness of quantum physics make good old sensible atoms (and matter itself) possible.
For the purposes of this thread, let me define a term, "StrictDet" [Strict Determinism] as the following: in a StrictDet universe, you can run any physical even back and forth as many times as you want, and it will always replay exactly the same  no Chaos Theory, no Butterfly Effect, no nothing. Just the same video played forwards and backwards ad infinitum. This is impossible with Heisenberg's uncertainty, and may not even be possible with Newton's Laws, unless we posit "hidden" (unseen or unknowably precise] states/variables. In other words, it's a very strict criterion, much stricter than a purely Newtonian universe  but it's what most of us probably intuitively assume.
We've all heard the question "Would it be ethical to go back and kill Hitler as a baby to prevent the Nazi horrors?" Forget the ethics, I doubt it would even be possible in a StrictDet universe: if you killed Baby Hitler, you'd have no reason to kill Baby Hitler (unless you turned into a random infanticidal time traveler). It's like the grandfather paradox: if you killed Grandpa, you wouldn't even exist to kill Grandpa  so what happens if you even try? Heisenberg and Schroedinger and all their pals at least offer some hope of resolution to that: a cosmic furball, a complex waveform of all possibilties that ultimately collapses into some stable outcome that makes sense. Maybe your time machine blows up if you try to travel to the past or maybe you spawn a parallel Hitler/Grandpa free universe. Either way: it works out.
Now here's another question: can you see the future, and if you can, can you change it? Well, if you can't change it, foresight is a pretty pisspoor superpower to have (unless your future is all immutable hugs and kittens) and if you CAN change it, it's not seeing the future, is it? It's just seeing a possible future and we ALL can do that every day. Okay, maybe you'll see the consequences of some factors you have no way of knowing at present, but that's just some weird form of ESP, not time travel/perception. It might happen to us all the time, but the effects are so muddied by all of us independently having hunches (which others of us cancel out) that it doesn't end up being significant.
How could we tell? Think about it. It's not a dumb question.
More later.
#5
Posted 19 April 2016  11:59 PM
I'll try to keep my comments nuggetsized to encourage ideas/discussion
You've mentioned (and I agree) that we don't have any sense of WHAT time is. We don't even know if it exists or is a delusion.
We've all heard that Time is the Fourth Dimension, like the X, Y and Z directions. Well, it definitely isn't. At least that's not the thing we usually call "Time".
So why do scientists keep saying it? They don't. At least Experts don't, in serious discussions with each other. They may say time is *like* a fourth dimension, and they definitely speak of "timelike" and "spacelike" directions, but they aren't speaking in the normal English sense of those words (not that "timelike" even has a "normal" meaning; it just sounds like it might)
So let's start with: what is a dimension? If I asked you to point in the direction of the X dimension you couldn't do it. Well, you could, and you'd be right by definition, but no more right than a gorilla pointing in a completely different direction. I try to be more right than a pointing gorilla. In my experience, when a gorilla points, it never means anything good.
We seem to exist in a 3space, but it's uniform in ALL directions. You can pick any direction and call it X. You can then pick any direction "at right angles" to that X and call that direction Y. By picking an X direction you've severely constrained the range of possible Ys, but there's still an infinite number of candidates. However, once you've picked an X and a Y, there's only one possible Z direction that is at right angles to X and Y. We often call these directions "axes" (sing. "axis") and imagine they have distances marked off on them, as they did in algebra class.
However, I'd like you to consider what else "axis" might mean. You can rotate around an axis. In fact, the most interesting thing about 3space may just be "the set of symmetries" it implies. For the sake of simplicity/sanity, I'm going to start by talking about the kind of "flat" 3space you study in Geometry class. If we assume it is a "uniform" 3space (no special locations or directions), it will have some very familiar symmetries: translation (moving in a straight line), rotation (around a line), reflection, spherical symmetry (rotating in arbitrary directions around a single point vs the more constrained rotation around a line) etc. Interesting, some of the physical laws seem to fall right out of this geometry.
Let's take the "inverse square laws". The simplest one is "radiation", like light shining from a star. If you move twice as far from a star, the light will be 1/4th as bright; at 3x the distance, the light is 1/9th as bright; and so on. This makes perfect sense, because the star produces a fixed amount of photons (or energy) in any given instant, which radiates out in every direction in an ever expanding spherical shell of light. in case you've forgotten (and any sensible human surely has better things to remember) the surface of a sphere is 4·pi·r², so the same energy from the sphere of light at r will have to spread out top cover 4x as much area at a distance of 2r [(2r)² = 4r²] and 9x as much area at a distance of 3r [(3r)² = 9r²]
The way light dims with distance is not some inscrutable mystery of physics. It's simple geometry: the same amount of "stuff" (photons) spreads out over time in a growing sphere, and spheres in 3space grow with the square of the radius. 1/bigger = dimmer. Now consider how many OTHER physical forces follow inverse square laws: charge, magnetism, gravity... hmm... we just might be glimpsing the navel of the universe's mysteries here.
Let's contrast that with a 2space like Flatland. If it is REALLY a 2D universe, then light from a Flatland star would be stretching out in everincreasing CIRCLES (not spheres) and the outer edge of that circle is given by 2·pi·r. The circumference grows linearly, so starlight dims linearly in 2space. All the other laws that are inversesquare for us would be linear for Flatlanders.
This has a LOT of implications for Flatlander physics. For example, you may remember that in 3space, the force of gravity decreases by the inverse square, but the energy of gravity follows a linear inverse (the potential energy is proportional to 1/r). If you've studied calculus, you probably never gave it a second thought in physics because it's a math rule in calculus that's so common that you learn to do it without thinking. But think about it now: in 3space we integrate an inversesquare and get an inverselinear potential energy. In 2space, they'd be integrating an inverse linear and getting a ...
Well, I just want to point out the principle, not go over the math. The lesson here is: the math changes  not just the strength of gravity, but the WAY gravity [charge, magnetism, etc.) changes with distance. ALMOST EVERYTHING in our universe where one kind of force balances against another WOULDN'T WORK: satellites wouldn't orbit planets; electrons wouldn't be stable in atoms  even energy wouldn't be conserved! In fact, they've done the math and 2space universes can't physically exist (nor most other nspaces) with any physical laws we can imagine.
What about the actual Flatland of the books  a 2space embedded in our 3space universe? Well, you can pretty much forget conservation of energy; energy and mass would appear from or disappear into the larger 3D context seemingly at random. It would be hard for them to NOT notice. (the book points that out, but doesn't harp on the implications) The same applies to our 3D universe being embedded in a larger 4D universe. You get a choice: either we can't interact with the other dimensions AT ALL (to the point that they don't exist to us) or the effects from outside our 3space would be very noticeable. Indeed we'd expect *some* life to have evolved to perceive the effects, in order to avoid lethal dangers or exploit possible benefits.
I'm not saying that it's impossible to formulate an elaborate system of math/physics where 4D works. I'm just saying that adding another dimension is not as simple as "throw another shrimp on the barbie". The very existence of the other dimension changes the fundamental geometry  and the way things work is an amazingly good fit for exactly 3 dimensions.
But I've gone afield. Remind me to talk about relativity and how this misleading "timespace" talk became so common.
You've mentioned (and I agree) that we don't have any sense of WHAT time is. We don't even know if it exists or is a delusion.
We've all heard that Time is the Fourth Dimension, like the X, Y and Z directions. Well, it definitely isn't. At least that's not the thing we usually call "Time".
So why do scientists keep saying it? They don't. At least Experts don't, in serious discussions with each other. They may say time is *like* a fourth dimension, and they definitely speak of "timelike" and "spacelike" directions, but they aren't speaking in the normal English sense of those words (not that "timelike" even has a "normal" meaning; it just sounds like it might)
So let's start with: what is a dimension? If I asked you to point in the direction of the X dimension you couldn't do it. Well, you could, and you'd be right by definition, but no more right than a gorilla pointing in a completely different direction. I try to be more right than a pointing gorilla. In my experience, when a gorilla points, it never means anything good.
We seem to exist in a 3space, but it's uniform in ALL directions. You can pick any direction and call it X. You can then pick any direction "at right angles" to that X and call that direction Y. By picking an X direction you've severely constrained the range of possible Ys, but there's still an infinite number of candidates. However, once you've picked an X and a Y, there's only one possible Z direction that is at right angles to X and Y. We often call these directions "axes" (sing. "axis") and imagine they have distances marked off on them, as they did in algebra class.
However, I'd like you to consider what else "axis" might mean. You can rotate around an axis. In fact, the most interesting thing about 3space may just be "the set of symmetries" it implies. For the sake of simplicity/sanity, I'm going to start by talking about the kind of "flat" 3space you study in Geometry class. If we assume it is a "uniform" 3space (no special locations or directions), it will have some very familiar symmetries: translation (moving in a straight line), rotation (around a line), reflection, spherical symmetry (rotating in arbitrary directions around a single point vs the more constrained rotation around a line) etc. Interesting, some of the physical laws seem to fall right out of this geometry.
Let's take the "inverse square laws". The simplest one is "radiation", like light shining from a star. If you move twice as far from a star, the light will be 1/4th as bright; at 3x the distance, the light is 1/9th as bright; and so on. This makes perfect sense, because the star produces a fixed amount of photons (or energy) in any given instant, which radiates out in every direction in an ever expanding spherical shell of light. in case you've forgotten (and any sensible human surely has better things to remember) the surface of a sphere is 4·pi·r², so the same energy from the sphere of light at r will have to spread out top cover 4x as much area at a distance of 2r [(2r)² = 4r²] and 9x as much area at a distance of 3r [(3r)² = 9r²]
The way light dims with distance is not some inscrutable mystery of physics. It's simple geometry: the same amount of "stuff" (photons) spreads out over time in a growing sphere, and spheres in 3space grow with the square of the radius. 1/bigger = dimmer. Now consider how many OTHER physical forces follow inverse square laws: charge, magnetism, gravity... hmm... we just might be glimpsing the navel of the universe's mysteries here.
Let's contrast that with a 2space like Flatland. If it is REALLY a 2D universe, then light from a Flatland star would be stretching out in everincreasing CIRCLES (not spheres) and the outer edge of that circle is given by 2·pi·r. The circumference grows linearly, so starlight dims linearly in 2space. All the other laws that are inversesquare for us would be linear for Flatlanders.
This has a LOT of implications for Flatlander physics. For example, you may remember that in 3space, the force of gravity decreases by the inverse square, but the energy of gravity follows a linear inverse (the potential energy is proportional to 1/r). If you've studied calculus, you probably never gave it a second thought in physics because it's a math rule in calculus that's so common that you learn to do it without thinking. But think about it now: in 3space we integrate an inversesquare and get an inverselinear potential energy. In 2space, they'd be integrating an inverse linear and getting a ...
Well, I just want to point out the principle, not go over the math. The lesson here is: the math changes  not just the strength of gravity, but the WAY gravity [charge, magnetism, etc.) changes with distance. ALMOST EVERYTHING in our universe where one kind of force balances against another WOULDN'T WORK: satellites wouldn't orbit planets; electrons wouldn't be stable in atoms  even energy wouldn't be conserved! In fact, they've done the math and 2space universes can't physically exist (nor most other nspaces) with any physical laws we can imagine.
What about the actual Flatland of the books  a 2space embedded in our 3space universe? Well, you can pretty much forget conservation of energy; energy and mass would appear from or disappear into the larger 3D context seemingly at random. It would be hard for them to NOT notice. (the book points that out, but doesn't harp on the implications) The same applies to our 3D universe being embedded in a larger 4D universe. You get a choice: either we can't interact with the other dimensions AT ALL (to the point that they don't exist to us) or the effects from outside our 3space would be very noticeable. Indeed we'd expect *some* life to have evolved to perceive the effects, in order to avoid lethal dangers or exploit possible benefits.
I'm not saying that it's impossible to formulate an elaborate system of math/physics where 4D works. I'm just saying that adding another dimension is not as simple as "throw another shrimp on the barbie". The very existence of the other dimension changes the fundamental geometry  and the way things work is an amazingly good fit for exactly 3 dimensions.
But I've gone afield. Remind me to talk about relativity and how this misleading "timespace" talk became so common.
#6
Posted 24 April 2016  08:58 PM
Let me make a little bit of an aside, before discussing the flip side "why do we call time the fourth dimension".
100 years ago, there was a renowned French philosopher Henri Bergson. It's really difficult to overstate his reputation, in that era, when philosophy was truly taken seriously  as it should be. Philosophy is the parent discipline of the sciences, not some random noodling off to the sides
Having said that, while I think modern science and scientists would benefit greatly from a solid grounding in fundamental philosophy, I'm as annoyed as the next guy by many fulltime "philosophers". To me, philosophy is a framework to keep in mind to keep us from falling prey to the many pitfalls of "obviousness", rather than a fulltime pursuit on its own (except for few rare and uniquely gifted philosophers that may emerge each century). I can understand pursuing a career in academic philosophy as a teacher, but too many "professional philosophers" seem to be pasta makers who got lost in their own spaghetti, and they give all of us a bad name. They're no different than the annoying folks whose first and often only approach to everything in life is to turn it into an equation  we all know people like that, but they are boggeddown in their limited world. Actual MATHEMATICIANS know that equations are just the start of a larger world of useful tools, and most don't actually deal in equations very much in their work.
In April 1922, Bergson and Einstein (both somewhat unwillingly) debated Relativity. My French isn't good enough that I can directly understand every nuance of their meaning (since they were both intimately familiar with the issues and problems, they didn't spell out every detail of their reasoning), and their exact context is forever lost to me (I can't separate myself from the nearcentury of subsequent discussion that formed my own intuitions), but the outcome was clear:
Later that year, Einstein won the Nobel Prize  for the photoelectric effect. The Nobel announcement itself acknowledged that “most discussion centers on his theory of relativity,” but explicitly stated the prize was not awarded for that. I'm sure the reasons were many and subtle, but one was explicitly stated by the Committee: “It will be no secret that the famous philosopher Bergson in Paris has challenged this theory.” [Einstein ignored the Committee and devoted his entire Nobel Speech to Relativity]
Many elements of relativity (and quantum physics) were and still are hotly debated on grounds that have traditionally been considered philosophy, such as epistemology ("how do we know what we know?") and ontology ("the nature of things, their relations and causality")
These are important questions, even to physicists. Though they aren't "what a physicist does", they are AT the core of WHY physicists perform their work: even if we "had the all equations", what do they mean? Closer to home: since we don't "have all the equations", epistemology and ontology can be key in choosing what areas a theoretical physicist explores. Without some sense of "the meaning of it all", a theoretician can only blindly jigger with equations and notions. Even a vague sense of the meaning of it all, however, offers guidance of potentially meaningful (or productive) topics to explore. (Experimental physicists, by some measure, have it easier; they are constrained to explore only whatever next step current technology makes possible)
When we talk about time travel, we're pretty heavily in those philosophical weeds. I want to make it clear that I don't think current math or scientific observations are the endall of the issue. They are a valuable guide perhaps the only guide to keep us from getting lost in the swamp, just as some sense of "what it all means" philosophically may keep a theoretical physicist from devoting their entire career to murky corners of the swamp where there is nothing to find.
Let me offer a concrete example:
Several years ago, I took a course on Special Relativity from Larry Lagerstrom of Stanford. I can't recommend his course enough. He is such a patient and clear speaker that any interested student who has absorbed the first half of Basic Algebra, even a junior high/middleschooler, should be able to understand Special Relativity better than many physics graduates I've known (You get his lectures through this bittorrent or contact me, and I'll see if I can get you a copy of the problem sets and videos)
Over the decades, I've taken many different views of "what Special Relativity means". I've treated it as "a correction factor" to classical physics, an inescapable optical illusion caused by the speed of light, an effect of a fourth dimension, and much more. Each view seemed to work well enough, but all are wrong. On one hand, there turned out to be more to Relativistic Effects than simply knowing how to apply the gamma factor (a simple algebraic factor, essentially identical to one form of the grade school Pythagorean formula for triangles) to calculate spatial distortions or time dilation; OTOH, Special Relativity turns out to be far simpler than I imagined.
Professor Lagerstrom used simple math and drawings to prove that Special Relativity is what we should EXPECT from a threespace where A) there is no privileged frame (i.e. the physical laws are identical in all places, times, velocities, etc.) and B) the speed of light is fixed. I think we all accept (A) as common sense, so the whole world of Relativity boils down to what we should have expected from the fixed speed of light in gradeschool 3D geometry
Let me say that again: if we had had better intuition when we studied geometry as kids, we should have expected Relativity to work as it does (I blame millennia of cultural myths, baked into our languages, for perverting children's minds with wrongheaded expectations)
Where does the fixed speed of light come from? Well, that's a bit epistemological/ontological/philosophical, but consider this:
1) There's a (measurable) fundamental physical constant (ε_{0}) for the strength of electric fields [electric permittivity]
2) There's a (measurable) fundamental physical constant (µ_{0}) for the strength of magnetic fields [magnetic permeability]
ε_{0} and µ_{0 are }properties of Space itself. Basically, they are "how much <a vacuum> permits (or resists) fields permeating through it"
3) Even in classical nonquantum electromagnetism, a light wave is expressed as an electric wave at right angles to a magnetic wave
4) The speed of light © equals 1/ ε_{0}µ_{0}
In other words, if light is an electromagnetic wave, the speed of light is the inverse of the limiting factors on electric and magnetic fields to permeate space.
A 70's middle schooler might say "the rate of progress of my love life is the inverse of how much mom and dad each allow me to get away with" [1]
[1] as middle schoolers have been proving since Time began ... albeit with various loopholes in the definition of "allow"
100 years ago, there was a renowned French philosopher Henri Bergson. It's really difficult to overstate his reputation, in that era, when philosophy was truly taken seriously  as it should be. Philosophy is the parent discipline of the sciences, not some random noodling off to the sides
Having said that, while I think modern science and scientists would benefit greatly from a solid grounding in fundamental philosophy, I'm as annoyed as the next guy by many fulltime "philosophers". To me, philosophy is a framework to keep in mind to keep us from falling prey to the many pitfalls of "obviousness", rather than a fulltime pursuit on its own (except for few rare and uniquely gifted philosophers that may emerge each century). I can understand pursuing a career in academic philosophy as a teacher, but too many "professional philosophers" seem to be pasta makers who got lost in their own spaghetti, and they give all of us a bad name. They're no different than the annoying folks whose first and often only approach to everything in life is to turn it into an equation  we all know people like that, but they are boggeddown in their limited world. Actual MATHEMATICIANS know that equations are just the start of a larger world of useful tools, and most don't actually deal in equations very much in their work.
In April 1922, Bergson and Einstein (both somewhat unwillingly) debated Relativity. My French isn't good enough that I can directly understand every nuance of their meaning (since they were both intimately familiar with the issues and problems, they didn't spell out every detail of their reasoning), and their exact context is forever lost to me (I can't separate myself from the nearcentury of subsequent discussion that formed my own intuitions), but the outcome was clear:
Later that year, Einstein won the Nobel Prize  for the photoelectric effect. The Nobel announcement itself acknowledged that “most discussion centers on his theory of relativity,” but explicitly stated the prize was not awarded for that. I'm sure the reasons were many and subtle, but one was explicitly stated by the Committee: “It will be no secret that the famous philosopher Bergson in Paris has challenged this theory.” [Einstein ignored the Committee and devoted his entire Nobel Speech to Relativity]
Many elements of relativity (and quantum physics) were and still are hotly debated on grounds that have traditionally been considered philosophy, such as epistemology ("how do we know what we know?") and ontology ("the nature of things, their relations and causality")
These are important questions, even to physicists. Though they aren't "what a physicist does", they are AT the core of WHY physicists perform their work: even if we "had the all equations", what do they mean? Closer to home: since we don't "have all the equations", epistemology and ontology can be key in choosing what areas a theoretical physicist explores. Without some sense of "the meaning of it all", a theoretician can only blindly jigger with equations and notions. Even a vague sense of the meaning of it all, however, offers guidance of potentially meaningful (or productive) topics to explore. (Experimental physicists, by some measure, have it easier; they are constrained to explore only whatever next step current technology makes possible)
When we talk about time travel, we're pretty heavily in those philosophical weeds. I want to make it clear that I don't think current math or scientific observations are the endall of the issue. They are a valuable guide perhaps the only guide to keep us from getting lost in the swamp, just as some sense of "what it all means" philosophically may keep a theoretical physicist from devoting their entire career to murky corners of the swamp where there is nothing to find.
Let me offer a concrete example:
Several years ago, I took a course on Special Relativity from Larry Lagerstrom of Stanford. I can't recommend his course enough. He is such a patient and clear speaker that any interested student who has absorbed the first half of Basic Algebra, even a junior high/middleschooler, should be able to understand Special Relativity better than many physics graduates I've known (You get his lectures through this bittorrent or contact me, and I'll see if I can get you a copy of the problem sets and videos)
Over the decades, I've taken many different views of "what Special Relativity means". I've treated it as "a correction factor" to classical physics, an inescapable optical illusion caused by the speed of light, an effect of a fourth dimension, and much more. Each view seemed to work well enough, but all are wrong. On one hand, there turned out to be more to Relativistic Effects than simply knowing how to apply the gamma factor (a simple algebraic factor, essentially identical to one form of the grade school Pythagorean formula for triangles) to calculate spatial distortions or time dilation; OTOH, Special Relativity turns out to be far simpler than I imagined.
Professor Lagerstrom used simple math and drawings to prove that Special Relativity is what we should EXPECT from a threespace where A) there is no privileged frame (i.e. the physical laws are identical in all places, times, velocities, etc.) and B) the speed of light is fixed. I think we all accept (A) as common sense, so the whole world of Relativity boils down to what we should have expected from the fixed speed of light in gradeschool 3D geometry
Let me say that again: if we had had better intuition when we studied geometry as kids, we should have expected Relativity to work as it does (I blame millennia of cultural myths, baked into our languages, for perverting children's minds with wrongheaded expectations)
Where does the fixed speed of light come from? Well, that's a bit epistemological/ontological/philosophical, but consider this:
1) There's a (measurable) fundamental physical constant (ε_{0}) for the strength of electric fields [electric permittivity]
2) There's a (measurable) fundamental physical constant (µ_{0}) for the strength of magnetic fields [magnetic permeability]
ε_{0} and µ_{0 are }properties of Space itself. Basically, they are "how much <a vacuum> permits (or resists) fields permeating through it"
3) Even in classical nonquantum electromagnetism, a light wave is expressed as an electric wave at right angles to a magnetic wave
4) The speed of light © equals 1/ ε_{0}µ_{0}
In other words, if light is an electromagnetic wave, the speed of light is the inverse of the limiting factors on electric and magnetic fields to permeate space.
A 70's middle schooler might say "the rate of progress of my love life is the inverse of how much mom and dad each allow me to get away with" [1]
[1] as middle schoolers have been proving since Time began ... albeit with various loopholes in the definition of "allow"
#7
Posted 25 April 2016  05:57 PM
I think the biggest question in philosophy is "Who copyrighted the speed of light?" Once we figure that one out, all will fall into place.
I'd love to be a professional philosopher. I have all the qualifications I'm intelligent, well educated, imaginative, and exceedingly lazy but there are no listings on Monster.com.
Actually the one thing that makes me a philosopher instead of a scientist is my complete inability to understand math.
I'd love to be a professional philosopher. I have all the qualifications I'm intelligent, well educated, imaginative, and exceedingly lazy but there are no listings on Monster.com.
Actually the one thing that makes me a philosopher instead of a scientist is my complete inability to understand math.
Please visit The RJDiogenes Store. And my Gallery. And my YouTube Page. And read Trunkards. And then there's my Heroes Essays.
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