Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: yor_on on 14/02/2011 05:20:01
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I better start with a answer :)
"You're making an issue of something that can be seen in everyday life.
Someone in a car driving past you will say they waved to you at (x1',y1', z1', t1') and crashed at (x1',y1', z1', t2') using their space and time coordinates, whereas you claim these events occured at (x1, y1, z1, t1 = t1') and (x2, y2, z2, t2 = t2') in your frame.
Can you see the difference?
There is a difference in the space interval you both measure between these two events, and so you could view it as a space contraction of some sort. Special relativity takes it a stage further with the introduction of a time contraction between events, between different frames."
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Do you agree to this answer, or is there something you would like to add to it, or subtract, or, well?
In one way this make perfect sense. In another it makes me look at everything with new suspicion :) Also it, to me naturally, lifts up the question of 'speed' and how to define one?
Are we all Lorentz contracted?
If so, are we then differently Lorentz contracted as defined from different speeds?
Simultaneously, with it all being a real effect?
And who/what defines the speed?
Does the universe have a gold standard for 'motion' or not?
It seem to need it for this to be true? And if so, where and, can we use it?
Or am I just bicycling in the great younder :)
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If Einstein was right,then let's see your very fast travel to Sun.We see your reduced length and travel.However you do not see your travel.You see only contraction of distance from Earth until Sun until length of your body. [:D]
Length of your body = distance from Earth until Sun [:o]
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Yes, and it works too :) The only thing I want to understand, and I guess you too :) is how it 'works'. We have too much evidence for it working to ignore it. and any real 'time dilation/Lorentz contraction won't be seen until you speed up like a muon. And at those speed the hard radiation should punch holes in any ship. For me it's the question of how to see the universe and my place in it that makes me pursue this question. Pompous to a fault, huh :)
Anyway, as I think of it now it seems to me that we're constantly Lorentz contracted, as well as time dilated :) Okay, saying that we are constantly 'time dilated' might seem a little to much, but if we consider a 'time dilation' as something that takes place between frames of reference, then we should be doing it :). That we won't be able to confirm that 'dilation', as we could with the twin experiment, doesn't change the facts. What you might want to argue is that as most everything in our universe is moving uniformly it isn't before 'something' accelerates this 'time dilation' takes place. But as far as I understand uniformly moving frames are 'time dilated' too and so, as soon they are moving relative us, there have to be a theoretic 'time dilation' taking place.
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My reasoning builds on me looking at it as a relation. In the twin experiment none of the twins at any time will find their own 'time arrow' to differ, which to me makes it a relation. Any relation is defined by needing at least two components that are in 'communication' if you like. The rest becoming a question about how you define 'communication'. Me, I do it by assuming that all objects 'communicate' distance and size being no hindrance to that, just as I assume gravity to be 'everywhere'. The thing defining a meaningful communication to us is light-speed, as expected in 'gravity waves' and lights 'propagation'. To the universe I'm not sure, I can't speak for that one, but we have entanglements and tunneling proved, and used, by nature.
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If you understand it differently I would like to know how you see it.
And as a Lorentz contraction is one thing that only seems to express itself at those other 'frames of reference' you observe we definitely should have a awful lot of different 'contractions' taking place simultaneously from any of those frames 'observing' us. You might want to argue that this is only a 'conceptual idea' and that in 'reality' there are no such thing as what I describe, but then again, that argument I as easily can use too, and about the exact same. Proving time dilations and Lorentz contractions by comparing 'frames of reference'. and that's the only way proving one that I know?
Does this mean that I doubt those two? Nope, it just mean I don't see how it works, and using math doesn't help me here. If you have a final definition why I only should consider them at some times, and not at other I'm all ears, well, eyes at least :)
The question I come back to in all of this is how 'real' they are. We definitely expect a time dilation to be real, how about the Lorentz contraction? I expect it to be real too. But where exactly does this 'reality' exist? Only in the eye of the beholder? What is a mirage then, if this is 'real'?
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To affirm a 'time dilation' only when leaving the same place of origin, and only proved as when arriving back at that same origin, is to me just a way of conceptualize something that should happen between all frames of reference. To assume otherwise makes 'time dilation' a magic thing, only applicable under certain circumstances, and also extremely 'local', if defined that way? Why would the universe only time dilate you relative your origin, and only when leaving the same, coming back? That doesn't make sense to me?
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So how do we define it. In the muon example the time dilation is what we as observers will see, whilst from the pilot seat of the muon no time dilation takes place, only a Lorentz contraction. As you can see you need both effects to make sense of it, looked at this way. The Lorentz contraction because of that, from your frame of reference as the 'muon pilot', your own 'time' can't differ. And that's perfectly logical as long as we define the time dilation as taking place 'everywhere' you can be in that moving frame, relative the Earth. Then you won't notice it, but you will notice the Lorentz contraction doing the same work as the 'time dilation' will do for the Earthly observers.
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Illusion is not science.If we see your length contraction,then you see our lengthening.
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You are thinking of two uniformly moving objects meeting right? And that they both are expected to see the other ones clock going slower and their ship being 'Lorentz contracted'?
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Using that we should expect that if placing two clocks, one on Earth and one in our 'muon ship' we both would see the others clock go slower than ours. But here we have defined one of the frames as 'inertial' when we make that example, namely Earth. But I agree, in any uniformly moving frame relative any other uniformly moving frame, it seems to me that it is up to you to define who is moving and who is 'inertial' relative who. As long as the universe doesn't have a gold standard for defining who is moving relative who. If we would find such a gold standard though? What would it tell us, that all objects move relative each other? Can you see how murky such a argument becomes if used?
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There is one more argument you can make to differ it, that the 'muon ship' is accelerating relative Earth as it 'falls'. That one I find suspicious as I see it as the 'muon ship' following a geodesic, and looked at that way there is no difference between it falling to a planet or 'falling' in deep space. In fact Einstein himself defined gravity's potential to exist even when not measurable, which some didn't like at all. But I like that way of looking at it, as I see gravity as something permeating all there is.
"...what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the G^1ik, not the non-vanishing of the [curvature]. If one does not think intuitively in such a way, one cannot grasp why something like a curvature should have anything at all to do with gravitation. In any case, no reasonable person would have hit upon such a thing. The key for the understanding of the equality of inertial and gravitational mass is missing."
And
"as Einstein later recalled, the thought occurred to him while writing this paper that a person in gravitational free-fall doesn’t feel their own weight. It’s as if the gravitational field does not exist. This is remarkably similar to Galileo’s realization (three centuries earlier) that, for a person in uniform motion, it is as if the motion does not exist. Interestingly, Galileo is also closely associated with the fact that a (homogeneous) gravitational field can be “transformed away” by a state of motion, because he was among the first to explicitly recognize the equality of inertial and gravitational mass. As a consequence of this equality, the free-fall path of a small test particle in a gravitational field is independent of the particle's composition. If we consider two coordinate systems S1 and S2, the first accelerating (in empty space) at a rate g in the x direction, and the second at rest in a homogeneous gravitational field that imparts to all objects an acceleration of –g in the x direction, then Einstein observed that
…as far as we know, the physical laws with respect to the S1 system do not differ from those with respect to the S2 system… we shall therefore assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system...
This was the beginning of Einstein’s search for an extension of the principle of relativity to arbitrary coordinate systems, and for a satisfactory relativistic theory of gravity, a search which ultimately led him to reject special relativity as a suitable framework in which to formulate the most fundamental physical laws."
"Here's the modern physicist's list (again, not sweating the fine points):
Spacetime Structure; Spacetime is a 4-dimensional riemannian manifold. If you want to study it with coordinates, you may use any smooth set of local coordinate systems (also called "charts"). (This free choice is what has become of the General Principle of Relativity.)
Principle of Equivalence; The metric of spacetime induces a Minkowski metric on the tangent spaces. In other words, to a first-order approximation, a small patch of spacetime looks like a small patch of Minkowski spacetime. Freely falling bodies follow geodesics.
Gravitation = Curvature
A gravitational field due to matter exhibits itself as curvature in spacetime. In other words, once we subtract off the first-order effects by using a freely falling frame of reference, the remaining second-order effects betray the presence of a true gravitational field.
The third feature finds its precise mathematical expression in the Einstein field equations. This feature looms so large in the final formulation of GR that most physicists reserve the term "gravitational field" for the fields produced by matter.
The phrases "flat portion of spacetime", and "spacetime without gravitational fields" are synonymous in modern parlance. "SR" and "flat spacetime" are also synonymous, or nearly so; one can quibble over whether flat spacetime with a non-trivial topology (for example, cylindrical spacetime) counts as SR. Incidentally, the modern usage appeared quite early. Eddington's book The Mathematical Theory of Relativity (1922) defines Special Relativity as the theory of flat spacetime.
So modern usage demotes the uniform "gravitational" field back to its old status as a pseudo-field. And the hallmark of a truly GR problem (i.e. not SR) is that spacetime is not flat. By contrast, the free choice of charts---the modern form of the General Principle of Relativity---doesn't pack much of a punch. You can use curvilinear coordinates in flat spacetime. (If you use polar coordinates in plane geometry, you certainly have not suddenly departed the kingdom of Euclid.)"
I find Einsteins picture easier to relate too.
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In fact I didn't know this when I started to wonder about gravity, neither did I realize that modern physics treat gravity as a 'localized' phenomena. To me gravity has to be everywhere, in some weird way it's 'space' to me. And one simple reason for treating it that way is Inertia. If you want to treat it as a local effect you will need to free inertia from gravity, alternatively expect it to be non-existent in 'a flat portion of SpaceTime' without any measurable gravity. Or you do as Einstein.
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Excuse me ,dear! If you are very fast traveler relatively of Earth and Sun,then you are traveling in gravitation field of solar system.Gravitation field of solar system slows down your time.Your gravitation field does not slow down time of Earth and Sun,because it is tiny.
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And who/what defines the speed?
Does the universe have a gold standard for 'motion' or not?
There is no "standard" for motion, observers define speed. It is only possible to define relative motion. That is, you must choose an origin and describe the motion relative to it. The origin can be moving with respect to another origin, that is how Lorentz formulas work. One of the fundamental principles for our universe is that there is no preferred perspective, all laws of physics hold in inertial frames. (Inertial frames are non-accelerating) Thus, a speed is different for every observer and each speed is equally acceptable if the point of view is taken into account.
Illusion is not science.If we see your length contraction,then you see our lengthening.
This is not true at all. Two frames moving with respect to each other experience a length contraction and a time dilation of the others frame. Suppose you were in the first frame, you would see the length contracted for the other frame because it is moving at v. Now, if you are in the other frame, the first frame is traveling at -v, where the minus sign only indicates direction. The direction is irrelevant and thus you also see a contraction of the other frame.
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Yes Bardman, that's how we define it. But do the universe do so too? When I think of a universe with 'motion' I can't help presuming a principle defining it. It might be 'relative motion' that does it, and if so I feel both length contraction and time dilation being real phenomena, with our whole idea of 'fixed or not fixed distances' becoming a sort of cosmic joke being put upon us.
And if that is true then light being a static phenomena, although a constant 'c' to us, also becomes possible to me, and that puts me in a very weird universe, does it not?
The other way to see it is that motion have a 'gold standard', although none that we can measure directly. In that case we introduce a way of defining who is moving relative who for the universe, although not necessarily for us. You might view it as a question of ' how do a universe 'expand' ' too, if you like. I do :)
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You might also look at it this way. If there is no 'zero movement' unless defined relative something else, then all uniform motion is a true 'zero motion', unless defined relative something else. And so all uniform motion should be exempt from time dilation and Lorentz contraction, unless you can prove it to 'move' by comparing. And in a black box scenario you can't. That will then mean that as soon as you stop accelerating the universe's 'skewed room time geometry' will instantly become the one you see from any inertial 'unmoving' frame, aka Earth.
You still have the possibility of 'skewing' it by invariant mass of course, but not by 'potential/momentum/relative' mass as I see that as non-existent in any uniformly moving 'frame of reference', until 'interacting' like colliding. All uniformly moving objects has an infinite amount of potential 'relative mass/momentum', simultaneously. Same as 'potential energy' do, as defined by invariant mass and the interaction they create, when colliding for example.
Am I right?
If you accept this statement you will need to accept that 'speed' also becomes a meaningless attribute for uniform motion, as it does not exist in our black box, no matter if we, when observing, find something to change 'position' relative us. The only time you will be able to define a speed will then be relative a non-uniform, non-constant, acceleration. That as all constant acceleration then is equivalent to a 'gravity', which then in our black box will mean that you can't differ it from a heavenly object (planet:).
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So which of those two ways are truest?
Both I would say. To me it's a question of 'relations'. Without any relations speed does not exist, and the black box scenario is one where there exist no outside relation that you can 'use'. So does it mean that speed exist if alone in a universe? That question seems meaningless as it assume something existing there, if that is so you have already introduced 'distance' and to observe it you've introduced 'times arrow'. Those two combined will give you the possibility of speed, even though that there is nothing to compare it against. So does that mean that 'speed' exist by itself? Well, as I don't think such a universe is possible to make sense from I find it difficult to imagine.
The really interesting question to me is why we never find our 'measurements' to change, no matter our 'speed' or 'mass'. The universe may 'contract' but our measurements and durations stay the same.
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Does this make it easier to understand though? I have to agree with Sim there, it doesn't. Myself I think and expect that it should be no difference between a uniform motion and a acceleration, I've made arguments for that elsewhere here on TNS. But for arguments sake, let's assume that it actually matter if it's a acceleration or not. What would it make time? A 'field' that when 'compressed' slows the 'compressed' travelers time? And a Lorentz contraction would then include? A whole universe? But only mine??
Mine universe?
What about 'yours' then? As I 'compressed' mine, actually compressing my whole universe, but yours never noticed? And what would it make of three 'travelers' 'compressing' their universe's relative each other?
What kind of existence does that make?
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Add to that, that in this case it will only be an acceleration that can do it. If I use the arguments presented above. That really would make 'speed' a very weird thing, wouldn't it? And an 'acceleration' even weirder as we would have two kinds, the constant and the non-constant. Speed as such can't have a meaning except 'locally' inside the same ''inertial' frame of reference' if so? Earth I was thinking of there :)
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And to that you can add that I'm not sure where/if cut offs for 'frames of reference' are? Where do I draw the line? And how? We say that Earth is a inertial frame of reference, don't we? What about the molecules, atoms? They may all 'speed away' at the approximate same 'speed' as our Earth, and solar system, and galaxy etc. but they do have 'speeds' of their own too, don't they? Shouldn't that make them into 'frames of reference' too? it becomes a very 'flowing' concept to me, all depending on where I define my 'system'.
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One simple solution is to redefine the idea of 'speed' so that it works. To do that you need to redefine what a distance is, or time, or both. We don't really know what this universe is, we thought we did, and up to Einstein it all made 'sort of sense', as from our Earth-bound perspective. But with Einstein came a revolution in the way we saw light and time. And with it 'time dilation' and 'Lorentz contraction'. So those days we live in a 'split reality', one in where we although accepting Einsteins ideas still cling to what we know from our own history on Earth, using descriptions we know to be true, like speed and distance. And we still try to make them fit those new ideas.
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So what is uniquely unchanging in your new universe?
Your own 'frame of reference' I would say.
Does that include mine too?
Well, let's test it. If I make the same experiment as you in a constantly accelerating frame having a same 'gravitational potential' (Earth), will I observe the same as you? How about all uniformly moving frames? If I do, is that a proof for our individual 'frames of reference' originally being the same? Or is it so that we all should be defined different 'frames of reference' individually, but get them 'equalized' by joining this 'greater' frame of reference, as we might consider Earth for this question?
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Do you find it a philosophical question only. Then I guess your point of view is that by defining a 'system' you lift up a 'part of reality' for inspection, and by using different 'cut offs' you create different 'systems', all valid from your 'systems' point of view. Looked at that way string theory has to be real, and loop quantum theory, as well as any other system that will give you a consistent and mathematically valid view. The problem with that reasoning that you can have several 'systems' simultaneously, inconsistent when compared, but valid in themselves.
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Does this make it easier to understand though? I have to agree with Sim there, it doesn't. Myself I think and expect that it should be no difference between a uniform motion and a acceleration, I've made arguments for that elsewhere here on TNS. But for arguments sake, let's assume that it actually matter if it's a acceleration or not. What would it make time? A 'field' that when 'compressed' slows the 'compressed' travelers time? And a Lorentz contraction would then include? A whole universe? But only mine??
Mine universe?
What about 'yours' then? As I 'compressed' mine, actually compressing my whole universe, but yours never noticed? And what would it make of three 'travelers' 'compressing' their universe's relative each other?
What kind of existence does that make?
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Add to that, that in this case it will only be an acceleration that can do it. If I use the arguments presented above. That really would make 'speed' a very weird thing, wouldn't it? And an 'acceleration' even weirder as we would have two kinds, the constant and the non-constant. Speed as such can't have a meaning except 'locally' inside the same ''inertial' frame of reference' if so? Earth I was thinking of there :)
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And to that you can add that I'm not sure where/if cut offs for 'frames of reference' are? Where do I draw the line? And how? We say that Earth is a inertial frame of reference, don't we? What about the molecules, atoms? They may all 'speed away' at the approximate same 'speed' as our Earth, and solar system, and galaxy etc. but they do have 'speeds' of their own too, don't they? Shouldn't that make them into 'frames of reference' too? it becomes a very 'flowing' concept to me, all depending on where I define my 'system'.
That is right. Motionless gravitation field does not slow my time if I stand without motion on Earth.And such field does not exist.Because electrons and kernels of atoms create moving gravitation field relatively of me.It slows my time. [:)]
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This is not true at all. Two frames moving with respect to each other experience a length contraction and a time dilation of the others frame. Suppose you were in the first frame, you would see the length contracted for the other frame because it is moving at v. Now, if you are in the other frame, the first frame is traveling at -v, where the minus sign only indicates direction. The direction is irrelevant and thus you also see a contraction of the other frame.
[/quote]I don't need Einstein's truth.I need my benefit. [:D]
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Yes Sim, you want to define it from invariant mass, right? Or do you include motion? If we look at the muons? they must be time dilated, and if you define it from their mass only, that mass is all to small without including motion. Also you will need an explanation why nobody ever notices their own personal time 'slowing down', as it then will be the only effect existing, if I got you right. That is, if you find the Lorentz contraction to strange to be possible?
On the other hand, shouldn't we all be 'time dilated' constantly, relative all other 'frames of reference'? If we should, where is the Lorentz contractions? Against that one might argue, as I did before, that it's only a acceleration that creates it? possibly also that in the twin experiment neither twin notice any time dilation, and only the moving twin noticing the Lorentz contraction. but then we come to the question of how 'time' differ between uniformly moving frames, knowing who should age slower? If we argue time dilation only from acceleration, surely there have to be some few objects in SpaceTime accelerating as I write, and as I understand 'frames of reference' this should 'influence' us, although we won't notice it.
Or am I wrong in looking at it as a relation between frames? Should I define it as something (a relation) only existing in its own 'frame' moving? That we then find the twins age differ is not a result of a relation between those frames, but two different relations versus motion and/or invariant mass inside each frame of reference? and with the universe using no 'gold standard' for it other than what happens inside them, frame by frame? That actually makes a certain sense.
I think I'll use that one.
It make sense in that we do seem to have a unique 'unchanging' relation to SpaceTime, from our own perspective. We have our expiration date set, sort of :) no matter where we spend our 'time'. but then the universe uses some guidelines that it has to keep count off it seems, if I stop looking at it as relations between frames. But I still like the idea :)
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I like this definition as it gives gravity its full importance. But it will need 'constants' defined for it to work. If I ignore invariant mass (for the moment:) and assume that gravity exist everywhere, then maybe that could be one? And then I will use invariant mass for defining 'gravity's potential' but not 'gravity' per se.
He :)
I do like it, it's a weird weird idea, and I'm partial to those :)
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If you look at it from that point of view there is no need for the universe to differ between uniformly moving frames as each frame defines itself, in its relation to gravity and motion. The problem still being motion or 'speed'? But with each frame defining it there will be needed a constant. And we have it already, the speed of light in a vacuum. I like this one better and better. Probably my downfall waits just around the corner, but, so far so good :)
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There is one big thing that needs to be explained though, and that is how it all 'binds together' into a seamless universe, including us all as we observe each other, still being unique for each one of us. But that one needs to explained in my older version of 'frames of reference' too. It's one of the weirdest things I know in fact. That we all find it the universe so seamless, when it infact seem to consist only of 'fragmented frames of reference' from the microscopic to the macroscopic, and all flowing into each other, creating 'reality'.
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On the other hand, shouldn't we all be 'time dilated' constantly, relative all other 'frames of reference'? If we should, where is the Lorentz contractions? Against that one might argue, as I did before, that it's only a acceleration that creates it? possibly also that in the twin experiment neither twin notice any time dilation, and only the moving twin noticing the Lorentz contraction. but then we come to the question of how 'time' differ between uniformly moving frames, knowing who should age slower?
If we have two relatively moving frames (constant and one being 0 or not), then as I understand it, the time is always being dilated for both and both are being length contracted. Here is what I understand of the twin paradox.
If you end up with two equally aged people moving relative to each other, accelerating to the relative motion is a problem but suppose we ended up with equally aged people with motion relative each other, and they both die at the same age (their life is the same amount of time in their respective frames of reference after the position and time coordinates are synced) Each will have appeared to died after the other in the frame they are in. To a person who also synced up the time and position of the twins and had them moving at equal speed in opposite directions relative to that person, they appeared to die simultaneously, but after the time they did in their frames.
The problem with saying who actually aged more is that relative to each other, they both aged more and the only way to compare clocks is at the proper time, which means you read the clocks at the same point in space. This is impossible unless they turn (or one person turns) around and come back. Then acceleration takes effect. This destroys the formulas for constant motion. When the clocks are brought back to the same point in space, the times read the same and so the twins must have died at the same time.
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If you look at it from that point of view there is no need for the universe to differ between uniformly moving frames as each frame defines itself, in its relation to gravity and motion. The problem still being motion or 'speed'? But with each frame defining it there will be needed a constant. And we have it already, the speed of light in a vacuum. I like this one better and better.
The Lorentz transformations were first developed to explain the fact that light moves constantly in a vacuum no matter the frame of motion. It couldn't be disproved no matter how hard they tried. Einstein later used it in special relativity. So yes, the constant of motion in all frames is light we use that as a standard.
Personally, the calculations are there, so for me light is the only necessary constant of motion. I don't need a standstill frame if I can just convert all other frames into my space-time coordinates.
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Quite pleased to meet you Bardman :)
And yes, you're right. And that's troubling me, sort of :). The description you give actually define each 'frame of reference' as unique. But, let us now look at those frames.
1. where is the 'smallest' defined 'frame of reference' you can imagine?
I don't know, but, as I think of it, its limit should be above Planck size. It's not a planet, it's not a car moving relative a man. 'Frames' can be used all the way down to atoms as I see it. And to me they all will be 'time dilated' and 'Lorentz contracted' relative each other. In a way they are very similar to the idea of a 'system', and you have no limits there, except possibly Planck.
2. Your definition seems to put all 'time dilation' on acceleration? Or am I reading you wrong?
If we assume that, then it seems to me that all Lorentz contraction should disappear in a uniform motion. So then your 'speed' won't contract your SpaceTime, as long as you don't assume Doppler to be a contraction too? If you do, are there any experiments testing that idea?
3. As I read you you support my view of all frames getting time dilated relative each other, even in a definition of that happening only in a acceleration? If we now assume that we share this SpaceTime, which we seem to be doing :) then comes the question of 'time'. One explanation is that 'time' is an illusion, defined through some sort of entropy.
Against that you can point out that all 'frames', when 'joined', seems to become the exact same, which to me seems to hang on two definitions. And here's a funny part, it's not 'acceleration', but 'motion' that seems to define it? And invariant mass (stress/tension of space). If 'entropy' adapts this way, what does that say? That we have a 'same entropy'? That can't be right if we look at the twin experiment, or can it?
I could presume that there is a 'gold standard' for 'entropy', as defined from your measurements inside your own frame of reference, as well as defined by the way anyone sharing that same 'frame of reference' will be able to do the exact same experiment, getting the same exact results. and the best 'thing' about such a definition is that it actually seems valid for all kind of motion, accelerating or not, as well as for any other definition for how gravity can come to be, as invariant mass.
I have some more argument but I need to wake up first :)
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And it's the fact that we have two contra dictionary statements that made me think of it as defined by relations inside those unique frames. It makes it easier for me to define what a time dilation is.
It's not something defined between 'frames', and we do not need to give it some unique name like 'entropy' if we use my idea. It will just be a 'same' arrow of time, defined as a 'gold standard' in each 'frame of reference' you make.
That it will differ, as when we look at the twin experiment, just confirm SpaceTimes game rules. But it will still, as proved by you joining my frame, be the exact same 'frame of reference' for us both.
But when we try to join those frames, that's when I find the problem. But, that problem exist any which way you look at SpaceTime. You will always need a explanation how 'disjoint frames of reference' can give you this 'whole seamless SpaceTime'. And that one is described by 'c' always being 'c' as I think of it. That's also the limit of 'meaningful communication' as we know it, also defined by the way each frame will be unique, although 'the same' when we 'join up'.
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Inside each frame there is one thing we can change as I see it, loosely defining a frame as for example the rocket you might be riding, or Earth. We can 'expend energy' transforming one state to another. And that's it, whatever you do is 'expending energy'.
So, discussing relativity, the only thing I know you can manipulate is this 'energy'. And the 'energy' you find will be the direct result of the interactions made. Those interaction can either be seen as 'something' manipulating on a object like 'forces', or as 'relations', then also defining that object. Even though this sounds like I might imagine everything being a illusion, I do not.
I'm just trying to find a description that will work with what we observe. And there 'relations' allows for a greater span of effects than what defining it as 'objects' does. That way I can define a 'spin' as a relation, a super positioned electron will also be the result of your observation of relations. But then we come to the way it 'join up' into matter, if we from a QM perspective could be described as the result of 'relations', how can we be 'solids'? To make that jump I'm lending from Chaos theory and their 'emergences'. Also it has to do with 'time' I believe. the 'arrow' we see have a relation to our macroscopic reality, Einstein called it SpaceTime, meaning that you should not expect it to be 'split' into 'quantum's'. QM does just that, although accepting Einsteins Relativity they try to prove that it all is 'quantum's', and a lot of it seems to make sense. Now you can choose either one, or both, but if you choose both you need a explanation for how one 'flows' into the other. And that I will define as 'emergences'. also I think 'constants' is what defines 'SpaceTime' and that they, just like Plank scale, exist 'on their own', as observed from inside our SpaceTime. I'm not sure we ever will be able to know what's outside 'SpaceTime'. We don't live there, we're in here, trying to look out. But I'm sure that the more 'constants' we succeed to find the better we will define where 'here' is.
Pompous to a fault :)
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To see it my way we need to use the constants. One is lights speed in a vacuum, the other , possibly, gravity as being something existing on its own, permeating' SpaceTime. A constant is not defined by any relations, although it will have a connection to all relations you will find, expressing itself through them. To me they seem like 'borders' for SpaceTime, telling us where its 'limits' are. and if gravity and light are two 'limits' then all frames will 'interact' through and inside those. This is just an idea I have, no theory although I like it :)
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Then what we see as a 'time dilation' will be whatever frame we are in, relative any other 'frame of reference', as defined by your frames relations to light and gravity. In a way you might look at those as the canvas upon which SpaceTime paints, but as they are a part of what becomes us, we are a part of that canvas too. and now I'm sounding like a mystic..
Da*n.
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The feeling is mutual, yor_on.
I need to examine what you are saying more thoroughly before I decide what parts I agree with but there are couple of statements I would like to address before I delve in deeper.
1. where is the 'smallest' defined 'frame of reference' you can imagine?
As I understand it, frames of reference are all infinitely big. The concept of frame of reference is a space-time 4-coordinate system that extends through the whole of space-time. If you are talking about what size scale is the smallest in which the rules apply, I think that it applies on the quantum level and is useful up until uncertainty takes over.
2. Your definition seems to put all 'time dilation' on acceleration? Or am I reading you wrong?
If we assume that, then it seems to me that all Lorentz contraction should disappear in a uniform motion. So then your 'speed' won't contract your SpaceTime, as long as you don't assume Doppler to be a contraction too? If you do, are there any experiments testing that idea?
I may have misspoken at some point or not made myself clear enough but I did not mean to put dilation or contraction on acceleration.
Suppose you have the origin of two frames of reference moving relative to each other at a constant rate (think of two axes passing each other) and at the point the origins meet, you reset your two clocks from what they are to zero. Then you may start measuring distances and time intervals, observing the contraction and dilation respectively. This is how the Lorentz transforms are set up. You never need introduce acceleration to produce the effect, and in fact lose the effect (unless proper adjustments are made, but this is complicated) if either frame accelerates.
Thus, you don't lose length contractions in uniform motion, they only appear there. Thus, the combined contraction of space and stretching of time leaves velocity untouched (which is the whole point of Lorentz).
I thought more about it and doppler is not a contraction. Doppler is the idea that where a wave is propagating from is changing, thus each peak of the wave is either closer or farther away from where the last one was, making the frequency appear different than the source is emitting. Think of a light moving away and emitting each photon of light at a point farther away than the last, thus the wavelength appears to be longer than it is.
I have never heard of time defined as a type of entropy, but I will continue to read through this. My perception of time was always a fourth, abstract axis on which our "time-momentum" carries us in the direction which entropy is increased, as well as other time related properties of space hold. I have dealt with some aspects of time-reversal in particle physics. But, I'm not sure about how to actually go about the actual physical performance of this.
Against that you can point out that all 'frames', when 'joined', seems to become the exact same, which to me seems to hang on two definitions. And here's a funny part, it's not 'acceleration', but 'motion' that seems to define it? And invariant mass (stress/tension of space).
All frames, when joined in one rest frame together, are only exactly the same if the space and time coordinates were defined in the following way:
All the frames were together at rest and the space and time coordinates were chosen to be the same.
Then, you could take those frames, accelerate them in some directions move them around at constant velocity, decelerate them, bring them back and line their origins up at rest. At this point, all the measurements are synced once again. However, while those frames were moving (accelerating or not) the measurements were not synced up properly.
This syncing of moving frames can only be accomplished if previously moving frames sync up their measurements at some point in time and space. Then, while they continue to move as they were, they continue to have comparable spacetime coordinates.
As far as invariant mass goes, all I know is that the rest mass is invariant in all inertial frames (nonaccelerating). So, I guess this too can be a standard for all motion, but I don't know it's usefulness other than to determine total mass in a frame.
Let me read some more and get back to you.
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And it's the fact that we have two contra dictionary statements that made me think of it as defined by relations inside those unique frames. It makes it easier for me to define ...
I'm going to take this whole comment at once. First, hopefully I've removed the contradiction. If not, present it to me again. As for the definition of time dilation, let me try and take a crack at it.
Time dilation is the effect of a moving frame (if we consider the other to be a rest frame for our two frame system, Also remember that the frames extend through all space and time, they are just like moving axes. If you have dealt with Lin Alg, then the frames are two different basis for the same vector space, thus they are just different measurements of the same thing). Dilation corrections account for discrepancies in measurements due to motion. This is necessary for the the movement away an event (which changes when the observed light or other signal can reach the observer). If you examine the ladder paradox, this becomes more clear. A person running (relativistically) with a ladder longer than a barn appears to a stationary observer to be completely in the barn at one point in time (even though the ladder won't fit and the runner doesn't see this odd effect) the reason is that the light from the ladder leaving the barn does not arrive until after the light from the ladder finishing entering the barn arrives (because the light moves finitely and is on the same order of magnitude as the velocity of the runner). This is a result of time dilation and the phenomenon is called length contraction (they are a pair). If the proper corrections are made, the time dilation is removed and the order of the events fixes itself. The ladder is then realized to protruded from the barn before the whole thing was inside. However, time dilation would cause an observer to say otherwise.
Also, so I am absolutely clear; you can sync up coordinates of moving frames in order to properly observe Lorentz transforms and when you bring them to rest together, those coordinates will no longer be in sync. It is necessary to maintain inertia for the frames to properly measure coordinates. Also, if you sync moving frames, let them move for a while, then bring them back in the other direction, and then set up the original velocities, the values will sync up again at the same point in space you synced them originally.
As far as seamlessness of space goes, I see no issue. Time dilation and length contraction (it never gets enough recognition) were the corrections Lorentz made in order to explain why a relativistically moving object reports time and space coordinates for an event that is seemingly incorrect.
If you forget these corrections, picture a star exploding and someone on earth observes it, as well as someone in a rocket moving away from earth. The rocket reports the time of the explosion and the point in space incorrectly according to the person on earth. This is because the light reaches the rocket at a different time and point in space, which is only measurable at relativistic speeds. Then, we realize we must correct for this change in coordinates of space and time, that is why we dilate time and contract space.
In essence, time and space do not change in the frames of motion, our ability to interpret them does.
Lets me see if there is anything else to cover.
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All frames, when joined in one rest frame together, are only exactly the same if the space and time coordinates were defined in the following way:
All the frames were together at rest and the space and time coordinates were chosen to be the same.
Then, you could take those frames, accelerate them in some directions move them around at constant velocity, decelerate them, bring them back and line their origins up at rest. At this point, all the measurements are synced once again. However, while those frames were moving (accelerating or not) the measurements were not synced up properly.
This syncing of moving frames can only be accomplished if previously moving frames sync up their measurements at some point in time and space. Then, while they continue to move as they were, they continue to have comparable spacetime coordinates.
Hm :)
Enjoyed reading you. Imagine a constantly accelerating rocket. If I now happen to get that 'absolutely synced' to another rocket, could I then say that they share the same frame of reference. One might want to argue that they can't be the exact same invariant mass, but we can still imagine a point where both from the perspective of stressing 'SpaceTime' by motion/invariant mass will create the same effect 'time dilation/Lorentz contraction relative some arbitrarily chosen point of reference, like Earth. Or assume them to be identical in all aspects. Then that would place them in the exact same 'frame of reference' to me. do you agree?
And the same seem to work for all kind of acceleration. And if you accept the idea of combinations of 'invariant mass/motion' being able to create the same effects, including when in uniform motion, it to me seem like we already are 'synced up' into a whole lot of common 'frames of reference', most of them out of reach and knowledge, assuming a universe large enough :). To me it goes back to how to see the universe. Assuming that Lorentz contraction is real, from my perspective in that space-ship the universe actually have 'shrunk' proving that this 'frame of reference' actually is my own unique one, but then, we have those frames 'synced' to mine as outlined above? What would it make of Rindler observers, unknowingly sharing the same 'frame of reference'? Could I assume that they too could be defined as being at rest relative each other, sharing the 'exact same universe'?
If I trust in that all uniform motions can be defined as being 'at rest relative each other' no matter their speed, what would this situation make of it? Nothing, as long as we're talking about a 'black box scenario' I presume? But if they were observing our surroundings, would that make those 'shared frames of reference' more 'real'? I don't know there, the easiest way out of that one is to assume that all uniform motion will share the same exact 'frame of reference' (black box) and this Rindler situation I was speculating about only will be valid for accelerations.
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"A person running (relativistically) with a ladder longer than a barn appears to a stationary observer to be completely in the barn at one point in time (even though the ladder won't fit and the runner doesn't see this odd effect) the reason is that the light from the ladder leaving the barn does not arrive until after the light from the ladder finishing entering the barn arrives (because the light moves finitely and is on the same order of magnitude as the velocity of the runner). This is a result of time dilation and the phenomenon is called length contraction (they are a pair). If the proper corrections are made, the time dilation is removed and the order of the events fixes itself. The ladder is then realized to protruded from the barn before the whole thing was inside. However, time dilation would cause an observer to say otherwise."
Now, there is the crux for me :)
Either it is a illusion, then you must be right, or it is not a illusion, then there come to be a moment where the pole in fact, as defined from the stationary observer, is inside the barn without 'sticking out'. If the later is true my idea makes sense. With it only being geometrics, as described by light propagating described differently from two different positional systems in SpaceTime, the observer and then from the 'event' itself, I will have to change my reasoning. Myself I see it as there actually is a moment, from the stationary observer point of view, where the pole will 'fit' inside the barn. Not looking at it that way seem to make a Lorentz contraction into a illusionary event?
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If I assume it would be a matter of geometrics, presented to us by light, then we would have to assume that the muon would be 'time dilated', from its own view as well as from our observer on Earth. that one becomes tricky as we then can't have two uniformly moving observers both observing the other clock ticking slower than its own, as I think of it?
Alternatively you might then want to blame it all on lights 'geometrics' assuming your arrow to be the illusion. But we have the example with two 'light clocks' placed 90 degrees to each other |_ they will not be synchronized from the far observers frame, but will from the observer 'at rest' relative them. And the reason that they still are able to have the same 'time dilation' is, as far as I remember, the vertical light clocks Lorentz contraction, correcting its photons 'distance' as it bounces.
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What I mean by that is that if you assume a 'time dilation' to be real, as defined by the twin experiment' but assume a Lorentz contraction to be a 'geometric effect' due to lights unvarying propagation, as seen from and in all frames of reference, then there is only one effect left for the muon, or for anything under the influence of motion, relative some other frame of reference? And to then assume that this effect still would be non-existing inside his frame, maybe? It's a possibility. As I said I'm not sure of how to see that, but why would the universe bother with giving us two definitions for one thing?
If we use light clocks for defining a time dilation the assumption is that as seen from any moving frame, the clock will tick 'as always'. If using the argument that the 'photon' bounces through more 'space' the faster you move is correct, then that bouncing should be slowed down inside the moving frame too. As I said, it's a possibility, assuming everything ultimately being 'light', we too then could be assumed to 'jiggle' to the same drummer as our 'bouncing photon' does. That as we too are 'passing' that same 'stretch of space' in our motion :) But doing so, and still accepting an 'expansion' outside matter (galaxies), the reason that they don't expand being defined as them being of a higher gravity, seems to clash a little? Then, if that would be correct, you should expect yourself to 'expand' too, as soon as you leave the galaxy it seems?
As we then can't expect our body's invariant mass to present any problem for 'space' to permeate us, as both concepts discuss 'distance'? On the other hand, the light clock example is not perfect I think, even though it has to be near truth.
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Maybe one can consider it conceptually, finding no definition of 'times arrow' in any positional system more true than any other? But to do so I first will have to invalidate the arrow that brought me to this point from where I consider the question it seems :) As I then are questioning my own arrow too? I can do that, but doing so there will be no time dilation, as I understand the concept, and no Lorentz contraction either. The twin experiment will then be purely illusionary, no matter the biological difference between our twins, which leaves me a even weirder universe :)
Alternatively look at it as a sliding system, but then you still will have to ask yourself why we don't notice our 'arrow of time' slowing down when in motion? That it doesn't either way you look at it points to there being a 'gold standard' it seems to me? Can you see what I mean? That even though using 'distance' as a argument for 'times arrow' slowing down your measurements will be the exact same inside your black box, except in a acceleration which should create a gravitational blue-shift as observed from the 'gravity well' (Aft wall of your black box relative its acceleration), watching 'in falling' light.
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The problem really is about defining what an illusion is. I understand why you see it as an illusion, it appears to be one. But you need to ask this question:
Should we accept the observer's recording of the two events or the runner's record?
It would seem we should accept the runner's, after all he is recording in the same frame as the ladder is moving.
But the barn is moving in the observer's frame.
And can we say that anyone observation is better than another?
According to physicists, and I'm inclined to agree, we should not make it a matter of preference. What we should do is realize what the motions are and take them into account. This is what the Lorentz is, and why we have defined dilations and contractions.
We take observations, describe the events, and if desired; we can change to another frame and describe the events in that frame.
This is exactly what we do with muon. We observe a very short lifetime and everything that stems from that works with the other observations we can make. If desirable, we can adjust the lifetime into that of the muons frame. In this case, the lifetime is longer and other observations made in that frame are adjusted too.
However, the laws of physics are the same in every frame. The measurements change, but the laws remain the same.
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It should also be noted that the clock is not actually ticking slower, the point in space where the tick takes place is farther away than the last one, thus it takes longer for us to realize it ticked, causing us to record more than one tick for every tick in the movers frame
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Even using a sliding system you find yourself ending up in a universe where, alternatively.
1. Time dilation & Lorentz contraction is 'real'.
2. Time dilation is 'real'. Lorentz contraction is not.
3. Lorentz contraction is 'real'. Time dilation is not.
4. Neither is real, including your own arrow.
5. Neither are real, only our common Newtonian 'arrow of time' is
6.'Time dilation' is real, but your own arrow is an illusion? That one, as it starts from defining a 'time dilation' relative that same illusionary arrow :) Well, let's just say it begs for my imagination. Contradiction of terms that need some real brain gymnastics
7. Only your own arrow of time is 'real'. All other definitions are made from comparisons with other frames, containing their own unique 'arrows' relative you, when comparing.
What more possibility's?
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We'll need to dissect this Bardman :)
But as for arguing that no positional SpaceTime system, or 'frame of reference' are more 'true' than any other? Conceptually I agree, but looked at from my reality I find it very easy to define what 'system' that 'ticks' for me.
That I also can compare it to a Black hole, or a speeding rocket, and see a sliding correlation between them does not invalidate that. A easy argument is how we define a experiment to be true. We need to be in the same frame of reference for finding it true, as for example Einstein did with a constantly uniformly accelerating rocket at one G. Proving all experiments to deliver the same results, ignoring tidal forces, as for a planet of the same gravity.
I believe that definition to hold for all uniformly moving frames too, that you will get the same results from a experiment in that black box, their speed relative each other making no difference.
But it all comes back to how we define it. I believe the arrow I know to be real, and to me it will be the same no matter what I do. That when comparing different 'frames' introduce a difference is no hindrance to that concept. Neither is the returning twin being younger that the one staying at home. As long as we define 'the arrow' you perceive as 'the same' as any other arrow, the difference being how it will express itself relative lights speed, distance defined, and gravity.
Doing so I can isolate the changes to the frame involved, in it expending energy adjusting 'distance' and/or gravity, as it had to do so at some time of its existence to change those relations, presenting you the same 'Time/Lorentz sliding relation' to other frames as we normally expect, but being restricted by its own energy expenditure and gravity.
It's the way I look at it for the moment :) from a unchanging internal 'arrow of time' :) But with distance and so also 'speed' becoming questionable as I expect the Lorentz contraction to be a real thing. And the 'time dilation' being defined as a relation to that distance, as expressed in lights invariant speed in a vacuum and gravity.
So three things I trust in :)
Lights speed in a vacuum.
Gravity permeating all of SpaceTime, measurable or not, as defined by Inertia.
Your own 'unchanging' arrow of time.
For the moment, that is:)
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It's not that I can't see your point. But one can alternatively see it as more of a conceptual exercise, describing how different positional systems, as defined from lights invariant speed in a vacuum, versus 'relative motion' & gravity introduces differences when comparing 'frames of reference'. To me it's about 'reality', and the question, if this is real, what does it say about our universe?
And I'm sure you agree that if it is real we have a very interesting universe :) In it you will be able to shrink the length of a distance by speeding up, as defined relative your place of origin. In it there are no defined speeds as all uniformly moving objects can be defined as inertial frames, actually stating that your speed relative A can be any speed, no matter what you define it as relative A. Yes, I think one can use the CBR as a speedometer? Or lights blue-shift, but both of those involves outside 'relations' which you won't have in a black box scenario.
Somehow reality seems to come down to 'relations'.
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On the other hand, shouldn't we all be 'time dilated' constantly, relative all other 'frames of reference'? If we should, where is the Lorentz contractions? Against that one might argue, as I did before, that it's only a acceleration that creates it? possibly also that in the twin experiment neither twin notice any time dilation, and only the moving twin noticing the Lorentz contraction. but then we come to the question of how 'time' differ between uniformly moving frames, knowing who should age slower?
If we have two relatively moving frames (constant and one being 0 or not), then as I understand it, the time is always being dilated for both and both are being length contracted. Here is what I understand of the twin paradox.
If you end up with two equally aged people moving relative to each other, accelerating to the relative motion is a problem but suppose we ended up with equally aged people with motion relative each other, and they both die at the same age (their life is the same amount of time in their respective frames of reference after the position and time coordinates are synced) Each will have appeared to died after the other in the frame they are in. To a person who also synced up the time and position of the twins and had them moving at equal speed in opposite directions relative to that person, they appeared to die simultaneously, but after the time they did in their frames.
The problem with saying who actually aged more is that relative to each other, they both aged more and the only way to compare clocks is at the proper time, which means you read the clocks at the same point in space. This is impossible unless they turn (or one person turns) around and come back. Then acceleration takes effect. This destroys the formulas for constant motion. When the clocks are brought back to the same point in space, the times read the same and so the twins must have died at the same time.
Speed = 259627884 m/s. Their lives move to the future with one speed.They have grown old for twenty years. Then the first has visited the second. The visitor is younger than the owner for ten years.And so acceleration of the first is process of rejuvenation then, and in general you have opened travel to the past.BillS was asking about it. [;)]
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I think we agree and disagree on somethings yor_on.
I understand and agree that your time (and space coordinates) are the golden measure for you, as well as the indisputable speed of light.
However, I think were we part paths is on the reality of the dilation and/or contractions. I simply state it as the variance in the 4-coordinates for different observers. I think that in certain parts of your arguments you try to present it as an actual change in the evolution of time. But, other times I feel like you're agreeing with what I'm saying, just in a roundabout way.
But as for arguing that no positional SpaceTime system, or 'frame of reference' are more 'true' than any other? Conceptually I agree, but looked at from my reality I find it very easy to define what 'system' that 'ticks' for me.
That I also can compare it to a Black hole, or a speeding rocket, and see a sliding correlation between them does not invalidate that. A easy argument is how we define a experiment to be true. We need to be in the same frame of reference for finding it true, as for example Einstein did with a constantly uniformly accelerating rocket at one G. Proving all experiments to deliver the same results, ignoring tidal forces, as for a planet of the same gravity.
I believe that definition to hold for all uniformly moving frames too, that you will get the same results from a experiment in that black box, their speed relative each other making no difference.
Somehow reality seems to come down to 'relations'.
You should define things in they the system "ticks" for you, I agree. So, when you measure different values than a uniformly moving frame, your results work for you. But, you have to realize those values work for the other frame too, realizing based on the Lorentz formulas, the values hold in that frame too.
The second paragraph there has no change in reference as far as I see (although if the non-rocket observer is on earth, they have no acceleration from g because the normal force balances the equation). But if two observers are accelerating with the same g, their frames are identical, the coordinates they measure will be the same if they choose the same zero coordinates (this is not the case in uniformly moving frames with nonzero relative motion, even if they zero their coordinates, they get different values). I said that all experiments must yield the same result.
The Lorentz transforms were created to maintain the laws of physics in moving frames. If you do an experiment on a single event in two relativistically moving frames, then the results will not provide the same laws of physics unless the Lorentz transformed distances and times are applied. Just for clarity: the same classical laws apply for each inertial frame, in that frame. If you step outside a relativistic inertial frame, you then must go relativistic.
I agree that reality is relations in regard to the fact that you must apply a transformation to understand why two people experience different things. But I hold that the reality is the same no matter what frame you are in. Our clocks might tick differently, but they tick differently in the same way for both of us. The rate at which my clock ticks faster than yours is the same rate faster your clock ticks than mine. And I realize that if I had the same perspective, they would be ticking the same, thus they are the same clock, just in different frames of reference. Its all a matter of perspective.
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Would the second paragraph be the one about 1G at Earth being identical to a uniform (constant) acceleration at the same G? When it comes to Earth some like to turn it around and say that Earth is 'accelerating' at one G. Although if we look at it from a time dilation it won't be true, it will still be impossible to differ it, inside a black box, tidal forces ignored that is.
"the coordinates they measure will be the same if they choose the same zero coordinates (this is not the case in uniformly moving frames with nonzero relative motion, even if they zero their coordinates, they get different values)"
What coordinates are we speaking of here, and how would you measure them inside a black box? I think we are thinking of two different definitions here. you are using positional systems, meaning that you expect them to have a way of defining those, whereas I'm talking about what you experience locked inside that 'black box'. Do you agree?
The Lorentz transformations, as I see it, is a way to define how two frames of reference differ from each other, translating them into each others frame. It's a extremely smart mathematical device, but also a mathematical 'tool', as I see it, You use it to define those frames in time and space relative each other to get a conceptual overview.
As I understand it Lorentz used them first to explain the Michelson-Morley experiment "In order to explain this absence of any effect of the Earth's translation, I have ventured the hypothesis, that the dimensions of a solid body undergo slight change, of the order of v2/c2, when it moves through the ether.
From this point of view it is natural to suppose that, just like the electromagnetic forces, the molecular attractions and repulsions are somewhat modified by a translation imparted to the body, and this may very well result in a change of dimensions. The electrons themselves become flattened ellipsoids.
This would enable us to predict that no experiment made with a terrestrial source of light will ever show us an influence of the Earth's motion."
But to apply them you will need to have a defined 'position' relative something else, or a 'origin' common to both as a reference point, and that's not what I was referring too. I discussed it from a 'black box scenario' when i called them 'equal'.
And no, it's not really true, although in fact it is one of the major headaches you lift up when you write "But I hold that the reality is the same no matter what frame you are in. Our clocks might tick differently, but they tick differently in the same way for both of us. The rate at which my clock ticks faster than yours is the same rate faster your clock ticks than mine. "
That you know that the 'time dilation' will belong to one twin, not both, is why there have been a recent proposition where they offer valid proofs for how you can solve that problem relative very far so called 'fixed stars'. It is in fact so that you in two moving frames of reference, like Earth versus a uniformly moving rocket near light speed, are free to define either Earth or the rocket as being a 'inertial frame' having a 'zero motion' relative the other, although some might want to differ here.
But as it turns out, in the twin experiment only one of our twins can be said to be 'time dilated' relative the other, if we accept that they otherwise originally should show the same biological age (Earth). And it's to get around that fact this proposal has been lifted up as a answer (Fixed stars) as I understands it.
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This is in fact one of my main reasons for wondering if the universe have a 'gold standard' defining motion, hidden or not. It may seem a solution, but it's ad hoc to me. On the other hand there might be no definite 'truths' when it comes to motion? It may be us having given it a definition that is wrong, using 'distance' and 'time' as our 'yard stick'. If relativity is right those two are plastic and ultimately reduces all matter to point particles, although always 'existing' (taking up 'place' in a prolonged manner, time wise.) as a proof for invariant mass/fermions relative the opposite, bosons/light.
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And yes I agree. That is if you ask if I see both the time dilation and Lorentz contraction as being very real, like that the pole actually being inside the barn? I'm afraid I do, and it makes it a very weird universe doing so? But so interesting to me :)
To invalidate the effects, we will need to invalidate the twin experiment first I think.
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In a way I'm contradicting my former statement here, that I see us all as time dilated and Lorentz contracted, referring to how only one twin can be said to be time dilated. But it's a way to conceptualize the fact that we have all those 'frames' moving at different 'speeds' relative us, even though we don't share the same origin.
The shared origin is the ultimate proof for a 'time dilation' and that's why the twin needs to be back on Earth comparing their 'biological age'. When I call it a 'time dilation' relative a frame not originating from Earth, I can't really prove that, not without first bringing it to a same 'origin' finding a way to define the 'clock ticks' valid for both , then sending it of and returning to see if they now differ.
But if the twin experiment is correct, then I can extrapolate it to those other 'unknown' frames too, as they should experience the exact same, if I did the experiment. And then there must be a constant 'time dilation taking place between both accelerating objects, as well as all uniformly moving. and the Lorentz contraction will be there if compared against moving 'frames', and then placing one self at rest with what one first compared to see the difference.
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"The problem really is about defining what an illusion is."
I totally agree there.
It's a factor of the utmost importance. We are so incredibly clever in creating our tools that we sometimes forget the pre/assumptions making us construct them. So what I'm also wondering about is where the limit goes for defining what is real. In relativity we have two definitions, they are not the same but we act as if they are. One is 'my black box' in where we absolutely goes only from what one observer can and will observe in his own 'frame of reference', and then act on what we expect him to observe. Even though this too is a conceptual exercise in that we're not 'there' it's as close as we can get to that 'reality'.
The other is the purely conceptual. In that realm we use Lorentz transformations and juggle with all kinds of concepts, mathematical or not, comparing them and drawing conclusions that, to their nature, is very hard to experimentally verify. As long as we want our ideas to be experimentally testable we need to be as close as possible, as I see it, to what a 'black box' will tell us. That is, going from what we believe us to be able to prove from a minimalistic viewpoint. But they constantly go into each other, don't they :)
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Would the second paragraph be the one about 1G at Earth being identical to a uniform (constant) acceleration at the same G?
I'm sorry, that got bound up. In order for us to talk about this, the frames need have the same acceleration, therefore there is a zero acceleration between the two.
As I understand it Lorentz used them first to explain the Michelson-Morley experiment "In order to explain this absence of any effect of the Earth's translation, I have ventured the hypothesis, that the dimensions of a solid body undergo slight change, of the order of v2/c2, when it moves through the ether.
From this point of view it is natural to suppose that, just like the electromagnetic forces, the molecular attractions and repulsions are somewhat modified by a translation imparted to the body, and this may very well result in a change of dimensions. The electrons themselves become flattened ellipsoids.
This would enable us to predict that no experiment made with a terrestrial source of light will ever show us an influence of the Earth's motion."
Yes, this is correct. They decided ether isn't a real medium of motion though. Also, the dimensions do change (in the direction of motion) for the observer. However, were you to be in frame of reference of the moving object, you would experience no change in dimensionality. You would see the earth change in the same way it saw you change. It is mutual.
But to apply them you will need to have a defined 'position' relative something else, or a 'origin' common to both as a reference point, and that's not what I was referring too. I discussed it from a 'black box scenario' when i called them 'equal'.
If I am understanding correctly, the origin you reference would be the 2, 4-coordinate axes of space-time (one for each observer) that at some point in space-time were aligned (synced or zeroed as I called it before) and as time passed, the time and a number of the space axes (the ones that are in relative motion) become dilated (time) and contracted (space).
And no, it's not really true, although in fact it is one of the major headaches you lift up when you write "But I hold that the reality is the same no matter what frame you are in. Our clocks might tick differently, but they tick differently in the same way for both of us. The rate at which my clock ticks faster than yours is the same rate faster your clock ticks than mine. "
That you know that the 'time dilation' will belong to one twin, not both, is why there have been a recent proposition where they offer valid proofs for how you can solve that problem relative very far so called 'fixed stars'. It is in fact so that you in two moving frames of reference, like Earth versus a uniformly moving rocket near light speed, are free to define either Earth or the rocket as being a 'inertial frame' having a 'zero motion' relative the other, although some might want to differ here.
But as it turns out, in the twin experiment only one of our twins can be said to be 'time dilated' relative the other, if we accept that they otherwise originally should show the same biological age (Earth). And it's to get around that fact this proposal has been lifted up as a answer (Fixed stars) as I understands it.
I think this is where we really diverge and we need to converge in order to make progress. Unfortunately, I read about the twin paradox in a textbook and I don't have it right here to reference specifically at the present time.
However, this is what I know to make sense. You say that the person on Earth is the person at rest. For the time being, in order to remove any bias as to what "rest" is, let us say instead that we have two people floating through space, in different directions, person 1 and person 2. Now let us reexamine the twin paradox. Suppose they are "twins" in our sense and their motion relative can be 100% uniform (I say this now because I will introduce acceleration later).
Let us assume that we observe from person 1's perspective, that is person 1 is our rest frame. Person 2 moves uniformly through space relativistically for some time. During this time, person 2's clock appears to read that person 2 is getting progressively younger than person 1 (not aging as fast-time dilation). Suppose person 2 instantaneously turns around, not losing any factor of this time dilation, thus as person 2 returns relativistically, it still appears that they are aging more slowly. Thus, person 2 is younger when they return to person 1.
Thus far you agree with me, it would seem person 2, being that they traveled, is younger. Now I think we diverge.
Suppose we reverse the roles now, we observe from person 2's perspective. This is an equally valid perspective, all perspectives MUST be otherwise physicists wouldn't bother proving anything. According to these observations, the space-time coordinate axes are at rest throughout this whole process. The motion of person 1 appears to be the same to person 2 as the motion of person 2 appeared to be to person 1 (except directionally). Thus, person 2 sees the identical effect. Person 1 must be younger than person 2.
This is why we call it the twin paradox. Both persons observe identical effects, meaning that each appears younger to the other. If you disagree with me here, I don't know how we can continue this discussion. The reason being, you must see that both perspectives are valid, the picking of which one to use is arbitrary because physics says the laws must hold for all perspectives.
So, this is how the paradox is resolved. The paradox is acceptable, time is allowed to appear dilated if we synced the clocks at one point in space and then try to measure them both from one point in space after the clocks have distanced themselves. The amount of dilation depends on distance and speed traveled to that point. However, they should not be dilated when we bring the clocks back to the same point to measure them. This measurement is called the proper time interval. Meaning synchronized clocks should read the same when measured at the same point in space. The flaw is in the fact that we tried to do an instantaneous reversal of velocity.
The deceleration and re-acceleration, no matter how large, affect the clocks. The deceleration performed a sort of "de-synchronization", if you will. Then the acceleration "re-synchronized" the clocks, by this I mean that it changed them in a way such that the dilation of the return trip made it so that the clocks read the same when read at the same point in space.
Hopefully you see that this is a resolution to the paradox.
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You're quite right, we diverge there :)
If your interpretation is right all clocks 'ticks' the same, and there we converge :) but your definition of why & how they 'tick the same' seem to differ from mine. In your twin experiment it seems as if both twins when meeting should be the same age, as you can interchange their frames. Assume that you have a position A<-0->B where 0 is a 'origin' for both A and B. Then assume both A and B accelerate as depicted in opposite directions from their 'origin' to then continue in a uniform motion.
Here we have three objects. 0=origin (Earth) and A&B are our rockets.
Assume identical trinns for this, not twins but three persons. One on Earth, one in A, and one in B. Also assume them making a circle in space meeting each other on their way back so that they can measure each other ships. They both measure each other as they move, each finding the other clocks to go equally slower and also their ships being equally Lorentz contracted. Assume that they both had a equal speed as measured against Earth. That should mean that they, according to how I understands it, both will be equally 'time dilated' relative Earth when returning, having done identical journeys, but starting in different directions relative each other.
Will the the sibling on Earth find the other two younger than him in your definition, after returning to 0 (Earth)?
Will the two travelers find each others age to be the same when compared?
Now assume that their journeys wasn't equal. A accelerated double the amount of B before 'coasting', moving uniformly. They meet up and measure each other again, both finding the others clock going 'slow', and the other ship being shorter than their own. But, will the others clock, as observed from either one 'tick' equally slow in the other ship, and will both clocks be equally slower than in our first example, as A accelerated double than B this time? And will their respective 'contraction' be equally larger, than measured the first time?
When they return to Earth (0) will the travelers age be the same, or will A now be biologically younger than B in your definition. How would you grade them in form of 'age', meeting up on Earth this time, after traveling?
Either you agree with me in that their age will differ. If you do so then we have the universe I expect. Or you have a different definition of 'time dilation' and 'Lorentz contraction'.
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(Sorry, I'm slow today. Think I overslept here :)
Phieew, this took some time, and I'm not sure it's understandable now either..
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(You might mean that a true 'time dilation' only comes to be in the acceleration though?
I see it as a effect from both acceleration and uniform motion.)
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This is not a perfect description in that ideally we would like 0 Earth being equally 'still' relative both. It's much simpler when comparing only two uniformly moving frames, as Earth moves a third way relative A and B, as I think of it. But for this one we can assume 0-Earth to be a really, really, still world :) Our gold standard for zero movement sort of :)
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We could alternatively let them go the exact same direction, but at different times (Greenwich Mean Time :) so that they would have to meet each other while journeying forth to some predefined position, and back. Not that this is perfect either, but slightly better maybe.
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Never mind, I hope my question is clear anyway :)
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Anyway, my view of those two situations is that, when measuring each other ships in space, both situations will show them equally contracted and their time ticking equally slow, although in the second version A and B will find each other clocks slower than the first time, also having a bigger contraction passing each other. And, finally back on Earth, in the first situation A & B will find themselves, assuming having the same time dilation relative Earth under their journeys, both to be younger than 0, but having the same age relative each other. In the second version I would expect A to be youngest, then B, with 0 becoming the biologically oldest.
If that is wrong I will get a headache :)
Not that I ever haven't had those before.
I have I mean ::))
This one might help define it, my point of view.
the relativity of simultaneity and time dilation, (http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction)
But I agree, the idea is certainly hard to 'melt' as we say in Sweden (as in stomach:), But I think it is true, even though weird. I can definitely see why you would prefer yours, it makes sense, whilst my view make for some real weird statements. It is also this effect of really, truly, desynchronizing clocks by motion, meaning that my and yours time actually differs, for real, that creates the statement that a 'event' can be happening before X for A but after X for B, and both be true. Lorentz transformations is not only a transformation between frames, but also a way of linking those frames to each other in SpaceTime, treating time and space as one whole 'unit', but differentiating with motion and gravity. That's also why I wonder if each SpaceTime observed won't have to be unique for this to be true.
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I think that Einsteins description of it being a 'whole SpaceTime' is to blame for this one. With motion and, as JP calls it, the stress–energy–momentum tensor defining gravity rebuilding that SpaceTime. To me it's very weird as it opens for so many questions.
1. How can we have a undifferentiated SpaceTime if both distance and time change, just by me moving?
2. How can we communicate?
3. Two Rindler observers synchronized without ever knowing it, do they have their own SpaceTime, I mean they should? Is then that SpaceTime the 'real one' for them, themselves unknowing.
4. And depending on what I compare myself against it seems I can get a 'new SpaceTime' just by changing my focus, or do I get that wrong?
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I think I can guess about 1 and 2.
I blame those on lights speed in a vacuum always being the same. At the same time as that is what seem to introduce those effects it is also what binds them together. I can't see any other answer to that one? It has to be light.
And what the he* is 'reality'.
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When it comes to the stress–energy–(momentum?) tensor i find that so much nicer as a description of gravity that the idea of it being invariant mass creating it. That we thought so earlier made sense as gravity is so strongly coupled to invariant mass but lately I've started to wonder about why it is. Before I just took it for granted that 'Gravity' must have invariant mass to exist. Now I'm not sure about that any more.
To see how I started to wonder let's assume that gravity is a expression, not a force. Also assume that SpaceTime is the only game in town, with its own set of gaming rules. Those rules only have to make sense to and in the 'game'. If you like, or don't like, the game will not matter as it is the only game you have. And the expression (gravity) will then express itself according to strict 'rules'. One of them seems to involve acceleration of your personal SpaceTime, another involves 'invariant mass'. I think this one is easier to stomach for those into RPG:s (Role playing games) :) and those used to see their 'screens' reality change with the site they get on :) And for us a little older more questionable as we remember such weird things as real trees, stretches of wet stuff that we called water, etc, etc :)
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The pole in the barn makes sense if we remember that from the position of the man at rest relative the barn, both the barn and him will be 'un-contracted' relative the speeding pole. you might see it as a spear thrown really fast, contracting relative us watching it, standing still relative that spear, at rest on the sideline so to say, just as the barn is. If we could get a gnome to sit on the spear he would find it as long as it was before being thrown, but that is a result of him adapting to that contraction too.
So when the spear gets inside the barn, we looking at it from the side will find it to 'fit' momentarily inside that barn, before moving out the back door. but what did the gnome see? I mean it's not the spear that have shrunk to him, it's everything that he sees that is contracted instead, including the barn and us looking at him. That is a direct effect from him moving so fast, all distances shrinking. So if we ask him he would tell us that at no point was the spear inside that same barn, the barn being, in his own words, 'Just too da*ed small for my big spear' Well, he was actually looking, very meaningfully, at our female reporter as he said that, but I still think it was the spear he was talking about?
Anyway, that is how I understands the pole in the barn, excluding gnomes and reporters that is :) The same way as the muon finds the distance to Earths surface being shorter than we do being 'at rest' with and on it, ah, Earth that is. And if that is the 'truth' then the gnome and I didn't share the same 'room time geometry' at that moment, according to how I see it, or 'frame of reference' as we also call it. And maybe not even the same 'SpaceTime' although that is a matter of definition. If we let 'communication' be the arbiter of that I expect us to have been able to 'communicate' as any radiation he sent out, like radio waves still would move relative both him and me at the speed of light in a vacuum, more or less :) Just being extremely blue-shifted for me. So, using light we share the same 'SpaceTime', but in all other manners we see two totally different 'reality's'.
In mine reality the spear was fitting inside the barn.
In his reality it never was.
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If we get rid of the idea of 'speed' then both the gnome and me was at rest, relative our own 'reality'. Meaning that the 'room time geometry' you have always will be 'at rest' relative you, just as the clock-ticks never will change for you, no matter how fast you go, or what 'stress tension' are acting on you in form of gravity.
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In the link I gave we can find this explanation to the pole experiment.
"Can we or can we not trap the rod inside the barn by closing the front door while the whole rod is inside according to a ground observer? When the front end of the rod hits the rear door, information about this impact will travel backwards along the rod in the form of a shock wave. The information cannot travel faster than c, so the rear end of the rod will continue to travel forward at its original speed until the wave reaches it. Even if the shock wave is traveling at the speed of light, it will not reach the rear end of the rod until after the rear end has passed through the front door even in the runner's frame. Therefore the whole rod (albeit quite scrunched up) will be inside the barn when the front door closes. If it is infinitely elastic, it will end up compressed and "spring loaded" against the inside of the closed barn."
This is one explanation but it does not explain how the whole of SpaceTime become contracted as you travel. And so it's not sufficient at all. Well, not as I can see at least? Space is not light, the only way I see to make sense of it, looking at space, would then be to assume that space do not contain 'distance' at all?
Headache time :)
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There are some other things too, that explanation builds on Lorentz first descriptions of how atoms gets 'squeezed' in the direction of motion. but if they did we could assume that the spear not only would get contracted but also thicker. If we assume that it doesn't and that it keep its 'normal' thickness as seen from all frames then there should be a state where the spear is so contracted/compressed in the direction of its motion that it could become a Black Hole. Also it assume that when you 'speed up' the contraction will have a 'starting point' on that spear the contraction traveling as a wave down, or possibly up, the shaft, as it seems to me? Now that might be right in rocket where I might assume that the force from the engine 'pushes' the contraction to greater and greater 'shrinkage' starting where the force is strongest, the engines to then spread through the ship, possibly? but with that spear?
Ah well, it's weird :)
I don't agree to that assumption, to me it's the whole of SpaceTime that gets contracted when you accelerate, not only a geometric illusion combined with 'atom squeezing'. That also seem to have been the way Einstein described it, as I understand it? If I would guess, reading that, I would say that we once more have tried to apply what we've seen working from our common frame of reference (Earth) and tried to apply that on Einsteins concept of SpaceTime? Hey, it's just a guess :) Stop throwing things..
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The answer in Einstein’s own words.
“Relativity The Special and General Theory” by Albert Einstein is great. Translated by Robert Lawson. It the 1920 translation. It’s a free book online.
XII. The Behaviour of Measuring-Rods and Clocks in Motion
http://www.bartleby.com/173/12.html
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Or in Lorentz's own words:
http://en.wikisource.org/wiki/The_Relative_Motion_of_the_Earth_and_the_Aether