So it's here you are :)
Glad you found me, yor_on. With the anti-evangelizing rule, you have to click on my profile and go down the list of my posts to find the discussion of my "pet theory". I just now added some biography to my profile to make it a bit easier.
Okay, if you don't mind, let's start from the beginning, because I'm stuck on your definition of a Euclidean space and photons?
Named for Euclid, it's the kind of space that you learned about in high school geometry class. It's the only kind of space most people know about, and the only kind there was until Minkowski came along. The "party line" is that Minkowski "discovered" the only real kind of space-time, and Euclidean space is as outmoded as the flat Earth. The truth is that Euclidean space is still valid, and the two kinds of mathematical space coexist as analogies of physical space.
How do you find that Euclidean space allows photons to have mass?
Make it as simple as you can please :)
Let's move that a little farther down, shall we?
Even thought you are right in that you can see the path taken in SpaceTime as a 'straight line' it is from the energy view this reasoning holds best to me. The photon will always take the path of least energy expenditure no matter how that space is defined. If you consider the path taken by placing detectors between you and the source and measure the light 'propagating' you should get a image of how that 'space' is distorted.
The "path of least energy expenditure" is actually the "principle of least action (http://en.wikipedia.org/wiki/Principle_of_least_action)". Action is energy times time; it has the same units as angular momentum, except the latter has one of its length vectors perpendicular to the motion instead of parallel. I believe this principle is valid in both kinds of space.
If your detectors are aligned on a Euclidean grid, they will see the light bending around a star; if they are aligned on a Minkowski grid, they will see the light following a straight line.
Could I assume that if 'straightened out' that space would resemble your idea of an Euclidean? But applying that reasoning it seems to me that the photon in a 'straightened space' would curve outwards from a sun seen, not inward?
Think of the two kinds of space as different kinds of graph paper. Suppose you draw a curve on lin-lin paper, trace it onto log-log paper and then stretch the log-log paper until it looks like lin-lin. You get a distortion of the original curve. If you trace that curve onto the inverse of log-log paper and stretch it to look like lin-lin paper your curve returns to its original shape. This can be done mathematically using the inverse of the log function (exponentiation). As far as I know, no mathematician has ever attempted the math to create an inverse function that converts Minkowski space-time back to Euclidean space. Do so successfully, and you might be nominated for a Nobel prize.
My ADD is kicking in, here. I need to pause to watch a movie, or something. I'll come back later and edit in the rest of my answer.
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Okay, I'm back.
As I see it, a gravity well turns the photon 'inward' towards the gravity well, for us 'being still' relative it as I think. But applied on a flat plane that same space fabric will get a greater area as it no longer acts in three dimensions plus time? Or am i thinking wrong here?
As I said, I'm stuck on your Euclidean Space :)
Are you imagining a gravity well as a bowling ball on a trampoline? It’s not that great of an analogy, and it doesn’t mean what people think it means. In truth, the vertical dimension, there, represents gravitational potential. The horizontal dimensions are a 2D slice of 4D space-time; they represent two spacial dimensions, with time and the other spacial dimension being constant. The normal force on the tennis ball is the gradient of gravitational potential, i.e. force of gravity on the tennis ball. When the tennis ball nears the bowling ball it trades gravitational potential (vertical height) for kinetic energy. The tennis ball can’t represent a photon; a photon in Minkowski space-time would come out the other side on the same 4D line it started on, but not on the same 3D line (with time being constant). It ain’t easy to explain, and it’s impossible to illustrate in pictures or models. The trampoline analogy illustrates gravity in Euclidean space, not Minkowski space-time.
And also, even if I 'straightened out' the path to fit, it doesn't give the photon a mass, only a complementary motion as described on a flat surface? Am I wrong, if so, where do I need to start to see it your way? ?
The photon’s path is straight (by definition) in Minkowski space-time. Converting that straight 4D line in warped space-time to the bent path in 3D Euclidean space takes the warp out of the space-time. It’s much easier for me to envision the conversion to Minkowski space-time than it is converting back the other way.
Converting back to Euclidean doesn't "give the photon mass"; it changes the meaning of the word "mass" to something which the photon has.
…not that I'm sure how that transformation from one type of geometry to the other would look as 'paths'. I have problems imagine it as it seems as 'bubbly' to me. Very hard to get a perfect fit imagining it, maybe there exist some tool for translating paths between them?
It's not that hard to do from your Euclidean Space to our Einsteinian SpaceTime. A perfect triangle would 'bulge' if bent to a sphere for example and its angles would no longer give the correct result for a euclidean space but doing the opposite applying this perfect triangle in some arbitrarily chosen place in SpaceTime to then 'straighten it out' seems to hang on the gravitational potential at that place where I 'draw it' in SpaceTime, giving me different results depending on from where I 'lift' it.
There seems no 'simple' way to do it geometrically?
Or maybe I will see it later?
Like I said, solve this mathematically and accept your Nobel prize.
So it's here you are :)
Glad you found me, yor_on. With the anti-evangelizing rule, you have to click on my profile and go down the list of my posts to find the discussion of my "pet theory". I just now added some biography to my profile to make it a bit easier.
Okay, if you don't mind, let's start from the beginning, because I'm stuck on your definition of a Euclidean space and photons?
Named for Euclid, it's the kind of space that you learned about in high school geometry class. It's the only kind of space most people know about, and the only kind there was until Minkowski came along. The "party line" is that Minkowski "discovered" the only real kind of space-time, and Euclidean space is as outmoded as the flat Earth. The truth is that Euclidean space is still valid, and the two kinds of mathematical space coexist as analogies of physical space.
[EDIT: Minkowski invented a new mathematical analogy for physical space; he didn't discover something that already had a physical existence.]
How do you find that Euclidean space allows photons to have mass?
Make it as simple as you can please :)
Let's move that a little farther down, shall we?
Even thought you are right in that you can see the path taken in SpaceTime as a 'straight line' it is from the energy view this reasoning holds best to me. The photon will always take the path of least energy expenditure no matter how that space is defined. If you consider the path taken by placing detectors between you and the source and measure the light 'propagating' you should get a image of how that 'space' is distorted.
The "path of least energy expenditure" is actually the "principle of least action (http://en.wikipedia.org/wiki/Principle_of_least_action)". Action is energy times time; it has the same units as angular momentum, except the latter has one of its length vectors perpendicular to the motion instead of parallel. I believe this principle is valid in both kinds of space.
If your detectors are aligned on a Euclidean grid, they will see the light bending around a star; if they are aligned on a Minkowski grid, they will see the light following a straight line.
Could I assume that if 'straightened out' that space would resemble your idea of an Euclidean? But applying that reasoning it seems to me that the photon in a 'straightened space' would curve outwards from a sun seen, not inward?
Think of the two kinds of space as different kinds of graph paper. Suppose you draw a curve on lin-lin paper, trace it onto log-log paper and then stretch the log-log paper until it looks like lin-lin. You get a distortion of the original curve. If you trace that curve onto the inverse of log-log paper and stretch it to look like lin-lin paper your curve returns to its original shape. This can be done mathematically using the inverse of the log function (exponentiation). As far as I know, no mathematician has ever attempted the math to create an inverse function that converts Minkowski space-time back to Euclidean space. Do so successfully, and you might be nominated for a Nobel prize.
My ADD is kicking in, here. I need to pause to watch a movie, or something. I'll come back later and edit in the rest of my answer.
____________________________________________________________
Okay, I'm back.
As I see it, a gravity well turns the photon 'inward' towards the gravity well, for us 'being still' relative it as I think. But applied on a flat plane that same space fabric will get a greater area as it no longer acts in three dimensions plus time? Or am i thinking wrong here?
As I said, I'm stuck on your Euclidean Space :)
Are you imagining a gravity well as a bowling ball on a trampoline? It’s not that great of an analogy, and it doesn’t mean what people think it means. In truth, the vertical dimension, there, represents gravitational potential. The horizontal dimensions are a 2D slice of 4D space-time; they represent two spacial dimensions, with time and the other spacial dimension being constant. The normal force on the tennis ball is the gradient of gravitational potential, i.e. force of gravity on the tennis ball. When the tennis ball nears the bowling ball it trades gravitational potential (vertical height) for kinetic energy. The tennis ball can’t represent a photon; a photon in Minkowski space-time would come out the other side on the same 4D line it started on, but not on the same 3D line (with time being constant). It ain’t easy to explain, and it’s impossible to illustrate in pictures or models. The trampoline analogy illustrates gravity in Euclidean space, not Minkowski space-time.
And also, even if I 'straightened out' the path to fit, it doesn't give the photon a mass, only a complementary motion as described on a flat surface? Am I wrong, if so, where do I need to start to see it your way? ?
The photon’s path is straight (by definition) in Minkowski space-time. Converting that straight 4D line in warped space-time to the bent path in 3D Euclidean space takes the warp out of the space-time. It’s much easier for me to envision the conversion to Minkowski space-time than it is converting back the other way.
Converting back to Euclidean doesn't "give the photon mass"; it changes the meaning of the word "mass" to something which the photon has.
…not that I'm sure how that transformation from one type of geometry to the other would look as 'paths'. I have problems imagine it as it seems as 'bubbly' to me. Very hard to get a perfect fit imagining it, maybe there exist some tool for translating paths between them?
It's not that hard to do from your Euclidean Space to our Einsteinian SpaceTime. A perfect triangle would 'bulge' if bent to a sphere for example and its angles would no longer give the correct result for a euclidean space but doing the opposite applying this perfect triangle in some arbitrarily chosen place in SpaceTime to then 'straighten it out' seems to hang on the gravitational potential at that place where I 'draw it' in SpaceTime, giving me different results depending on from where I 'lift' it.
There seems no 'simple' way to do it geometrically?
Or maybe I will see it later?
Like I said, solve this mathematically and accept your Nobel prize.
I don't think you're bicycling that much :) . But I better put in a slight declaimer too. That is that there is a clear difference between matter and 'energy/photons'. We can't just satisfy the difference by defining matter as 'photons' or even 'energy'. If they were 'the absolute same' then there is no reason for the difference at all as it seems to me. To me there has to be something that defines the 'transitions' that exist between matter and 'space' and light, allowing for the boundaries they get and the way motion can exist.
I don't get the bicyling reference. Actually, when I live in Phoenix, I biked quite a lot. Living in the rainy northwest,now, my bike hasn't been used for years, but I have been hiking 5 miles round trip to the post orifice more frequently of late. Gotta be in good shape to outrun the big tsunami when it wipes this area off the map.
Until very recently, I also thought there had to be a clear distinction between free photons and the orbiting shear waves that comprise fundamental particles. Photons must fit the formula, E = hc/λ, which makes a particle much smaller than the equivalent photons. I only started calling them "photons" when I saw HOW the Higgs mechanism packs them into such a small space−−by means of blueshifting as they fall into the Higgs potential well.
So, now, I see no need at all to distinguish the two. A particle's rest mass is nothing but the combined masses of its constitutent orbiting photons.
I like the idea of a particle as a 'gravity well' sort of :)...
Where the Higgs mechanism is concerned, it is a potential well. I works very much like a gravity well, but on a far smaller scale. You could even modify Minkowski space-time to include warping of space-time in the vicinity of a fundamental particle. As long as the path of light is the definition of a straight line, anything that bends the path of a photon in Euclidean space causes Minkowski space-time to warp. The warp caused by the Higgs field would be many orders of magnitude more intense than warping due to gravity. It is so intense, in fact, that photons falling into it become blueshifted by a factor of perhaps a million or even a trillion to one. (I'm struggling with the math to try and narrow that down a bit.)
...If you made our universe into a sum of points, then some of those points would get one number defining them as space and other another number defining them as particles, just playing a little here okay. Imagine that we exchange the numbers for gravitational potentials instead, ignoring the Higgs mechanism for now, just let there be bumps :) those bumps will then need to be differentiated somehow to create particles and space and light. And maybe, when those 'bumps' organize themselves they create a three dimensional space? But to do it we also need a arrow of time, or causality chain, that makes it all come true. The bumps themselves are not enough for this. The chain, and as I see it, the observer of the chain is a must for it to 'exist'. Then we need a principle for 'growth' and there both you and me seem to think the same, I think? It has to be a fractal principle, don't you agree?
I prefer to deal with concrete things rather than abstract points or numbers. To me, those points consist of sub-universe galaxies. They are perhaps very much like the galaxies of our universe except for their size. (I have to say "perhaps" because the sub-universe must be operating in reverse time, and the two universes could only have the same age for one instant in their existence. For all we know, the sub-universe could resemble the way our universe was 10 billion years ago or the way it will be 100 billion years in the future.)
Reducing particles to bumps on a potential map is a simplification. There will come a time when simplification from my model to something more utilitarian will be called for, and that will be the time to invoke Occams razor. For now, Occams razor is an obstacle to a deaper understanding. First you should analyze football as individual players with abilities and personalities; then you can reduce them to force fields influencing the movement of the ball in a program that places bets on games.
The observer is not part of my model, but that doesn't make him/her irrelevant. If anyone ever gets into a discussion of free will vs. predestination from the perspective of my model, I'm sure the observer will be central to the subject.
The chain is a sequence of strange attractors in the chaotic mix of waves and particles. Each time the scale increases by about 5 orders of magnitude, the particles of the previous level become strange attractors for the next level. So fundamental particle organize into quarks, nuclei, atoms, DNA, organisms, societies, planets, solar systems, galaxies, cosmic foam, and super-universe particles.
I have to break, now, to take my walk to the post orifice before it closes. I'll be back in a couple of hours.
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And then we come to 'forces' and 'energy'. Because as soon as you introduce a arrow there should become transformations, you might want to turn that around of course and define the transformations as 'times arrow' but, I don't know? It depends, both seems to build on a idea of there being something from where the 'arrow' comes, any which way you choose.
I think of time's arrow in terms of cause and effect; also it is the direction of increasing entropy in a "closed system", if there is such a thing. Also, time necessarily flows in the direction of expansing space.
In my model, it is evident that time in alternate scale-wise universes must run in opposite directions. This follows from the idea that bubbles can't un-pop in forward time, as that would violate causality and the flow of entropy. Expansion of space in one universe pops its cosmic-foam bubbles, which are the ether-foam bubbles of the next universe. When a bubble pops, that's one less bubble, and expanding space implies more bubbles, not less.
And photons, you seem to build it on the idea of photons propagating, right? And maybe also on that you see 'photons' as being the same under as over Planck time, so called 'virtual photons'. I do so at least, it's the arrow differing them to me, 'photons' don't care :)
I see photons as propagating like acoustic shear waves in a resilient foamy solid medium, i.e. the ether. Anything below the Planck scale belongs to the sub-universe. Shear waves at that scale would be like ripples within a single wall of galaxies in the cosmic foam of the sub-universe; from our point of view, they would propagate from effect toward cause.
I am guessing that the median bubble size in the ether foam is roughtly a Planck length, and photons emitted by electron transitions in atoms are many quintillions of Planck lengths long. Another wild guess is that the side to side motion of the ether as a photon passes is just a tiny fraction of a Planck length; the photons only seem energetic to us because the ether is incredibly dense and stiff.
The ultimate source of photons for our universe is a mystery. It can't come from electrons, because then where did the electrons come from? My only guess, so far, is the the ultimate source of our shear waves is the non-uniformity of the ether at a scale of a few Planck lengths. At that scale there must be regions where the median bubble size is significantly different from the large-scale average; I call those "blobs" for lack of a better word. When a dark energy pressure wave enters a blob, it changes speed; leaving the blob, it returns to normal speed. This shakes the blob, leaving it out of its equilibrium position, and shear forces pull it back to equilibrium, radiating shear waves perpendicular to the path of the pressure wave.
Those primal shear waves interact chaotically with the pressure waves to produce particles and forces among the particles. So the arrow of time follows the shear waves from the shaking of the blob (cause) to interaction with other shear waves (effect).