An “analytical-metaphysical” take on Special Relativity!

[AnssiH]

i think hofstadter disagrees and has space and object as a simultaneity. neither figure or ground is "first". this following source is just a review of GEB mind you, but it goes to the facts of the matter. whether this nuance is of any consequence to your larger discussion is for you to decide of course, but your comment struck a chord and i have a weakness for turtles. :Alien: :)

 

No, good thing you made a comment as I see I have a very unfortunate choice on words there. By "before there exists any notion of space there must exist definitions for persistent objects" I just meant to say "definitions of objects are what give meaning to the notion of "space"", i.e. that they are the flipsides of the same coin, not that one needs to pre-exist before the other

 

And I take it that is exactly the assertion of Mr. Hofstadter.

 

At any rate, the point I was trying to make with that comment is that as far as our world model building capabilities go, there is no reason to take the stance of a preferred frame one way or another, as any sort of "space" is an epistemological construct as much as the "defined entities" that give the meaning of that space.

 

Since you say that comment "struck a chord", I take it you understand that issue between defined space and defined entities, and I am very tempted to expand on that... And I hope there are more people who could try and understand the following:

 

First, understand that the perception of any object, is a case of some sort of definition on some sorts of unknown data patterns. A specific pattern is taken to simply MEAN that there is such and such object there, and conciously we have a perception of a tennis ball. We have this idea in our mind that it is a single, time-wise persistent object that is moving. Even when on the data patterns there is no explicit information of such an object ever existing.

 

Please at this point read another post I just made at:

http://hypography.com/forums/philosophy-of-science/3650-what-is-time-63.html#post276222

 

I.e. any persistent object is an immaterial reference to a pattern; something we have defined to "be" that object in our worldview.

 

I would understand if people say at this point "well I've never really thought about it that way" and then perhaps spend some time thinking about how they can never really tell what is the ontological nature of anything they perceive or see, as all they are "thinking about" are "patterns defined to mean something".

 

But quite many people fight back at this point, and defend their "Seeing just happens, no explanation necessary, and we know what exists by looking at it" stance to the last man.

 

Now if you do actually understand that whatever you think to exist is more properly an immaterial reference to a specific pattern (=persistence of anything is an epistemological tool, not ontological fact), and you do understand that self-coherence is the important bit for prediction ability (as oppose to absolute ontological correctness), then you should start to see where DD's work is coming from.

 

It is an investigation of the consequences of the need for self-coherence, and it leads to surprisingly specific constraints. It doesn't lead to specific definitions, it leads to very specific relationships between definitions (whatever things we define, they are related to each others in specific ways).

 

It leads to quantum mechanical relationships, which means that quantum mechanics is not valid because world is ontologically made of the entities it works on (quantum mechanically behaving photons, electrons, etc). It is just that that set of definitions, is one example of a self-coherent set of defined objects, that ultimately obey the relationships exposed by DD's work. I.e. "the standard model" is only one possibility out of an infinite number of possibilities. (And the strange quantum mechanical behaviour is a result of requirement of self-coherence, and it is not occurring between real things, but between self-defined objects that are IMMATERIAL REFERENCES TO THE DATA PATTERNS.

 

Now once again this issue of "self-coherence" is visible in our ability to interpret quantum mechanics in multitude of valid ways, and also another important point to make here is that, since our worldview is simply "a self-coherent set", all the arguments to defend any particular ontological stance are circular in their logic. Under careful analysis of any physical model, you will find it is just a very large circle of beliefs, where one definition supports another definition that eventually comes back to support the first definition.

 

Also, when self-coherence alone is shown to lead to such specific constraints, it also explains how a useful world model can come to start off at all (how to build generic learning mechanism for an AI, for one); how it is possible to have a mechanism that does not know anything about reality, but still can start ordering the raw data in meaningful ways; how to make any definitions that are useful for predictions.

 

The fact that that mechanism leads exactly to definitions of relativity and quantum mechanics is very telling, don't you think?

 

 

Now, having already thought of this problem of "anything we define is just an immaterial reference to some patterns, and many valid self-coherent possibilities always exist, and having walked through the steps to Schrödinger's Equation and Special Relativity, it is clear to me that DD is quite correct in his argument.

 

The counter arguments I have seen so far have essentially been saying that he is incorrect because "world is actually made of such and such entities" or "such and such model tells otherwise" (insert an entity or concept defined by modern physics). Or given enough time to work out the equivalence between his constraints and relativity/QM, the argument is "that's just another way of modeling reality". Completely ignoring the fact that no hypothetical existence of anything was ever postulated! Oops.

 

Many people have the idea stuck in their head that the ontological entities of modern physics are ontologically correct simply because the way they have been defined yield correct predictions. I.e. people are completely unaware of the logical reasons for why the definitions are valid (when taken together), and why they are just one arbitrary "valid set" out of incredibly many possibilities.

 

You don't need to look far to see people essentially just defending their specific definitions, informing us that the patterns that have been defined in their worldview are also ontologically correct entities ("how world really is").

 

The latest post (#622) in "What is Time" is informing us that "sounds" are "air that is compressed". Few posts before that, we are told what rainbows "really are". Few posts before that, Modest explains how few things are defined in terms of relativity. Quite valid for all we know, but only one of many valid possibilities, so what does its validity tell us about ontological reality? (If you look at the post he is responding, perhaps you can make out that I am trying to point out that there are completely immaterial reasons for relativistic definitions being valid, i.e. it doesn't tell us about the existence of static spacetime ontology in any way, much like your avoidance of an accident doesn't tell us anything about the existence of God, even if you really would like to explain your experience with "God did it".

 

Interestingly, Little Bang is talking about an idea that would model "time" and "magnetic fields" and "photons" etc little bit differently, which is another example of us being able to model the same thing in different ways (and if he can show his definitions are valid predictionwise, does that tell us something about how reality ontologically is? Not without faith it won't, and remember when Kant said "...groping among mere concepts"?)

 

And in the end, since people wonder what's the point of such analysis; "why wouldn't we just take all physical models as exactly that; immaterial models?" Well, it does give you a pretty good idea about what parts of our physical models are actually the reasonable logical parts, and what are extraneous baggage that leads to all those strange "mysteries" and apparent conflicts between valid views. If you are screaming for unification, then look no further, eh?

 

Well, in the end, I just hope whoever reads that would think about it little bit, and try to see the analysis for what it's worth. Now if you excuse me, I think I'll concentrate mostly on walking through the logical steps to Dirac's equation and then to general relativity.

 

Thank you for listening.

-Anssi

[AnssiH]

If no one sees any improvement in this post over my previous posts let me know or if no one replies I’ll take that the same way and plan on rereading most all of the thread if not all of it, instead of just what seems to be of most importance, before posting again and see if I can pick up anything from doing that.

 

Don't have time to write a proper reply (just about to go to bed), but I got the impression that you are closer to the mark now.

 

Actually I think I have been misdirecting my attention away from why you defined an object. I have been under the impression that the reason for defining an object was because you knew that you could define an object so that it would obey the relation [imath] r=v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2} [/imath] and I have been overlooking the fact that you defined an object so that you could simply construct a vary useful object called a clock.

 

Yes, if you look at my earlier posts directed to you, I tried to point that out; the point is to show how an object commonly known as "a clock" behaves under self-coherent transformations.

 

[imath] r=v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2} [/imath] is a requirement arrived at via a lot of algebraic work from the self-coherence requirements. Defined elements obey it, if they are part of a self-coherent set (or rather "that's how things are defined" or rather "that's one way to express a necessary relationship").

 

If there are defined "higher-order (macroscopic) objects", they are collections of those "elemental objects".

 

After some thought on the matter I have to wonder if considering an object to be any collection of elements that obey the relation [imath] r=v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2} [/imath] is an entirely rational stance as there are defiantly collections of elements that could be considered an object under this definition that would not be considered an object for any other reason then that they satisfy this relation. You could for instance consider completely unrelated things to be part of the same object.

 

Like I commented in earlier posts, one could in theory just pick up some set of muons from different parts of the universe and call that an object. But it would be quite useless view; those elemental entities are not staying together at all.

 

That is what my comment "any collection that stays together long enough for us to point our finger at it at label it with a name" meant.

 

None of that means reality is made of x,y,z,tau space with elemental entities flying around. This is a way of expressing some necessary relationships. Completely immaterial, but completely valid.

 

Hope that helps a bit, have to hit the sack... :)

 

-Anssi

[Bombadil]

Hi AnssiH I didn’t entirely mean to take so long but I wanted to take a look at some of the earlier posts in this thread before posting, not to mention I’ve been a littlie busier then normal lately. Anyhow, I know that you have other threads that I’m sure are keeping you busy but if you are willing to help me with this I would like to still try and understand it.

 

Yes, if you look at my earlier posts directed to you, I tried to point that out; the point is to show how an object commonly known as "a clock" behaves under self-coherent transformations.

 

[imath] r=v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2} [/imath] is a requirement arrived at via a lot of algebraic work from the self-coherence requirements. Defined elements obey it, if they are part of a self-coherent set (or rather "that's how things are defined" or rather "that's one way to express a necessary relationship").

 

 

Yes, I am defiantly getting the impression that the idea of a object has very little to do with whether or not the Lorenz transformation has to be part of a transformation to a new reference frame. What the Lorenz transformation does have to do with is if there exists other reference frames in which the fundamental equation is still valid in. If they exist then the Lorenz transformation must be used to transform measurements to a new reference frame, however this will require that we can make the measurements in the first place which does not seem to be an entirely trivial issue, because a means of making measurements has not previously been defined.

 

The Lorenz transformation is in fact necessary to maintain a constant speed of all elements given by the relation [imath] r=v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2} [/imath] the idea of alternative reference frames is then used to show that there exists reference frames moving with respect to the rest observer for which the fundamental equation must still be valid. The first condition must hold, the second one seems to be more of a case of much interest as it seems to match our experiences and the field of science would be more or less useless without multiple reference frames in which the fundamental equation is valid in.

 

Now in order to make measurements we must construct either a clock or a way of measuring length, this is what a object was defined for. The thing here is that since all elements must move the same distance in our four dimensional space (defined in the derivation of the fundamental equation) for any change in our evolution parameter t. When we define distance in any direction it is also defined in the remaining three. Furthermore due to the uncertainty in the [imath] \tau [/imath] direction we can’t construct a measuring rod (think ruler) in the [imath] \tau [/imath] direction. However the clock has been shown to measure distance moved in the [imath] \tau [/imath] direction.

 

It actually seems to me that we could use an object to make our measurements that is constantly changing and that it would have the same effect on the fundamental equation as changing the type of coordinates used in the fundamental equation and have no effect on possible explanations. So we really can use any object to make our measurements. If this doesn’t make since to you just ignore it, as it is may be a little off topic.

 

Now using a clock and a measure of length (the clock that Doctordick has defined seems to be doing both) we can define velocity in a way very much equivalent to the way that it is defined in Newtonian physics which allows us to define the speed of our oscillator. However this is a vary circular definition of the speed of our oscillator as the clock was defined by using the fact that the oscillator moves only in the x,y,z directions. So that when we try and measure the speed of the oscillator we are in fact comparing its speed to that of another oscillator. The point is that this definition requires that we can only measure one possible speed of the oscillator but that we are free to label that speed whatever we want as we are completely uninterested in the idea of units.

 

Whatever we choose to use for units we should probably not use the idea of units to hide the fact that distance in the [imath] \tau [/imath] direction is measured the same as in any other direction even though the [imath] \tau [/imath] direction was only a consequence of maintaining self consistence in any possible explanation and not a dimension like one of length. Ill hold off on getting into the issue of if length is just a construct of our mind for the time being.

[AnssiH]

Hi AnssiH I didn’t entirely mean to take so long but I wanted to take a look at some of the earlier posts in this thread before posting, not to mention I’ve been a littlie busier then normal lately. Anyhow, I know that you have other threads that I’m sure are keeping you busy but if you are willing to help me with this I would like to still try and understand it.

 

Great! I was meaning to give you a better reply from your previous post too, but when I started it, I decided perhaps best let you respond first :)

 

Yes, I am defiantly getting the impression that the idea of a object has very little to do with whether or not the Lorenz transformation has to be part of a transformation to a new reference frame. What the Lorenz transformation does have to do with is if there exists other reference frames in which the fundamental equation is still valid in. If they exist then the Lorenz transformation must be used to transform measurements to a new reference frame,

 

Hold on.... Just to be sure that we are on the same page, it's not a question of what sorts of frames exist in reality, but a question of mapping the data correctly over different reference frames, while preserving a specific constant velocity. That is entirely a data mapping issue, nothing to do with what exists in reality.

 

So as long as you are thinking about data mapping, then yes; The fundamental equation requires that each element is moving at a constant velocity, and a newtonian transformation from one frame to another would not preserve their velocity. Lorentz transformation is the well known transformation that does.

 

Btw, I think you might find it helpful to look at the various visualizations of Lorentz transformation, unless you are already familiar with the subject anyway...?

 

The only reason the concept of "objects" was mentioned already at that stage was to point out that it is possible to conceive universe in clear portions that have dynamics only within themselves (are fairly separated from the rest of the universe); we often think about the dynamics of some systems in their own rest frame. If you think about a juggler inside a train, you don't need to think about it in the rest frame of the embankment. (This had to be pointed out because the fundamental equation is valid by itself only in the rest frame of all the known data)

 

From the point of view of the epistemological analysis, that juggler is a case of "collection of elements that is separated from the rest of the universe". Now the question is, how do you transform the [imath]x,y,z,\tau[/imath] description from the embankment, to the description from inside the train, while preserving the constant velocity of the elements. (Of course the analysis itself goes about this with something far simpler than the juggler, thank god :D)

 

however this will require that we can make the measurements in the first place which does not seem to be an entirely trivial issue, because a means of making measurements has not previously been defined.

 

Yes, now the thing that helps here is that the definition of mass, energy and momentum has been arrived at (At schrödinger's...). They come into play in our ability to say, what would a massive object such as "a mirror" look like in [imath]x,y,z,\tau[/imath] representation

 

The Lorenz transformation is in fact necessary to maintain a constant speed of all elements given by the relation [imath] r=v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2} [/imath] the idea of alternative reference frames is then used to show that there exists reference frames moving with respect to the rest observer for which the fundamental equation must still be valid. The first condition must hold, the second one seems to be more of a case of much interest as it seems to match our experiences and the field of science would be more or less useless without multiple reference frames in which the fundamental equation is valid in.

 

Here I am still a bit troubled by the phrase "that there exists reference frames", as the issue is rather "that it is possible to map the data to different reference frame while preserving that relationship of constant velocity". But yes, you can think of this issue as something that is certainly very useful ability, and epistemologically it makes sense to be able to do it.

 

So, you do want your worldview to allow for that transformation, but it is still not immediately obvious at all, why it is a relativistic transformation that is valid. Normally that is conceived as an effect of geometry of spacetime, but the analysis connects it to the underlying definitions (incl. mass, momentum etc), which were arrived at via symmetry constraints.

 

Now in order to make measurements we must construct either a clock or a way of measuring length, this is what a object was defined for. The thing here is that since all elements must move the same distance in our four dimensional space (defined in the derivation of the fundamental equation) for any change in our evolution parameter t. When we define distance in any direction it is also defined in the remaining three. Furthermore due to the uncertainty in the [imath] \tau [/imath] direction we can’t construct a measuring rod (think ruler) in the [imath] \tau [/imath] direction. However the clock has been shown to measure distance moved in the [imath] \tau [/imath] direction.

 

Yes and remember how the length measurements between moving observers become complicated via their different definition of simultaneity (if they choose to use simultaneity defined by their personal reference frame). That issue is entirely analogous to the "length contraction" circumstance in relativity.

 

It actually seems to me that we could use an object to make our measurements that is constantly changing and that it would have the same effect on the fundamental equation as changing the type of coordinates used in the fundamental equation and have no effect on possible explanations. So we really can use any object to make our measurements. If this doesn’t make since to you just ignore it, as it is may be a little off topic.

 

I shall ignore it :)

 

Now using a clock and a measure of length (the clock that Doctordick has defined seems to be doing both) we can define velocity in a way very much equivalent to the way that it is defined in Newtonian physics which allows us to define the speed of our oscillator.

 

That's incorrect; the speed of the oscillator was arrived at via the definition of mass. It was purposely chosen to be a massless oscillator, i.e. a photon bouncing between mirrors. A massless entity (that btw ends up behaving exactly like light) is a defined element that is moving entirely in x,y,z directions, but not in tau direction at all.

 

That is because momentum along tau is conceived as mass (this is due to how it relates to everything else in this picture). That is also why the "clock that is at rest" means more accurately that the mirrors are at rest in x,y,z directions. They do have mass, i.e. their momentum is along "tau".

 

However this is a vary circular definition of the speed of our oscillator as the clock was defined by using the fact that the oscillator moves only in the x,y,z directions.

 

It sort of is circular, but not quite the way you describe it.

 

Without putting much expectations as to what we will find in the end, the OP goes through to show what does this dynamic look like like in rest frame of the mirrors (how does the oscillator make a 2-way trip between mirrors in terms of [imath]x,y,z,\tau[/imath] and "t"), and that is exactly what you see in the first video I made. Very simple by itself.

 

Then, in order to see what does that look like from a different frame, first the Lorentz transformation is employed to transform the same plotted data self-coherently to a new frame, while preserving the constant velocity of the elements. That yields a transformation to the distance between the mirrors.

 

Then you can use trigonometry or computer simulations or whatever you want to find out how does the massless oscillator make the 2-way trip in terms of this frame. That is what you see in the second video clip I made.

 

In the end, you can compare these two plotted clocks. If you plot both a moving clock and a rest clock in a single frame (or just run the two videos side by side), you can see the rate that the clocks count cycles are different. They are different exactly by what is the prediction of special relativity. The must be different due to what is meant by "a clock". If they weren't, different reference frames would yield different predictions (as to how things interact; how dynamics evolve). Anyone who understand special relativity, understands also why the clocks can run at different rate when plotted to different frames, and still yield a self-coherent picture.

 

The [imath]x,y,z,\tau[/imath] space itself is just a good way to represent this situation (a way to prove in relatively simple manner that the given definitions do actually yield the expectations of relativistic time measurements by macroscopic clocks), so don't take any of this as an attempt to show that reality is in some sense [imath]x,y,z,\tau[/imath] space. Rather keep a close eye at the definitions that are used, where they came from (the initial symmetry arguments), and how they are shown to lead to the idea of "relativity".

 

So that when we try and measure the speed of the oscillator we are in fact comparing its speed to that of another oscillator.

 

We compare their "cycle count" actually (very important to keep in mind)

 

I hope this is helpful.

 

-Anssi

[Doctordick]

Actually, Bombadil, the thing is quite simple. I have proved that my equation constrains the fundamental ontological elements underlying any and all explanations of anything.

[math]\left\{\sum_i \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\Psi} = K\frac{\partial}{\partial t}\vec{\Psi}.[/math]

 

From that equation, within my derivation of Schrödinger's equation, I define “momentum”, “energy”, and “mass”. What is significant is that the equation is only valid in a universe where the sum of the momentum of the universe is zero (what is commonly called the rest frame of the universe). It follows that, if you cannot prove the rest frame of the universe is different from the frame you are using, you have but no choice but to assume you are in that rest frame (otherwise, you could prove you are not in that frame).

 

The nugget of that realization is that, if you have two inertial frames (neither of which can be proved not to be in the rest frame of the universe) the fact that the form of that equation must be the same in both frames requires special relativity to be valid. This is true because the special theory of relativity is the solution to the conundrum of something having a fixed velocity. As my equation is no more than a simple wave equation (containing point interactions of little significance) with a wave velocity given by the inverse of K, it is exactly such a constraint. You cannot have two different values of K because the equation is valid only if the whole universe is included.

QED

 

We are dealing with a "fact"!

 

Have fun -- Dick

[Bombadil]

Hold on.... Just to be sure that we are on the same page, it's not a question of what sorts of frames exist in reality, but a question of mapping the data correctly over different reference frames, while preserving a specific constant velocity. That is entirely a data mapping issue, nothing to do with what exists in reality.

 

I am talking about mapping the data that our explanation is based on in such a way that we can map it into multiple reference frames and still have a valid explanation. That is, whatever information our explanation explains, we can map that information from one reference frame to another reference frame.

 

Yes and remember how the length measurements between moving observers become complicated via their different definition of simultaneity (if they choose to use simultaneity defined by their personal reference frame). That issue is entirely analogous to the "length contraction" circumstance in relativity.

 

In fact our definition of simultaneity is equivalent to that of length contraction, that is if an observer in one reference frame used the definition of simultaneity in a different reference frame to decide when to measure the ends of a moving object he would arrive at the same measurements that would be arrived at in the reference frame that would consider his measurements to be simultaneous.

 

Now it seems that one important point of this is that simultaneity has been defined by assuming that the speed of the oscillator or that of light is the same in both directions which can not be proven. This means that our definition of simultaneity is a consequence of all elements moving at a constant speed which is a requirement of the fundamental equation and so no two reference frames can agree on what events are simultaneous.

 

This shows that the length of our measurements being Lorenz contracted is not a consequence of our definition of simultaneity, likewise our definition of simultaneity is not a consequence of our measurements being Lorenz contracted, but both are a consequence of the requirement that all elements must have a constant speed when transformed between reference frames. This is derived form the fundamental equation.

 

Further more the Lorenz transformation is the only transformation that will allow all elements to have the same speed when transformed from one reference frame to another.

 

 

That's incorrect; the speed of the oscillator was arrived at via the definition of mass. It was purposely chosen to be a massless oscillator, i.e. a photon bouncing between mirrors. A massless entity (that btw ends up behaving exactly like light) is a defined element that is moving entirely in x,y,z directions, but not in tau direction at all.

 

So we use the fact that by choosing a mass less element for our oscillator we define its speed in the x,y,z space to be [imath] v_? [/imath] by the relation [imath] v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2} [/imath] because the movement in the [imath] \tau [/imath] direction will vanish for a mass less element. All that we have to do to measure this speed is to say that the value of [imath] \tau [/imath] is the same as the value of t in the rest frame which requires that [imath] v_? [/imath] is the speed of the oscillator. But is the relation [imath] t=\tau [/imath] in the rest frame a definition or is it algebraically arrived at, at some earlier point?

 

Another important point of this is that any observer will use his frame as though he is in the rest frame and so will use the value of [imath] \tau [/imath] in place of t.

 

It looks like the only reason that the value of v in the Lorenz transformation was defined was to give a method of calculating the location that would be considered the origin in another reference frame. It seems that this definition if not derived from is equivalent to that of velocity used in Newtonian physics but was defined for a different reason.

 

The point being that this definition doesn’t require the definition of our measurements but we can only consider the speed of an object after we have defined our measurements of length and [imath] \tau [/imath]. The value of t is impossible to be measurable and so will be considered to be equal to [imath] \tau [/imath] in the rest frame but seeing that we don‘t know what the rest frame is anyone is free to use their reference frame as though it is a rest frame and use the relation [imath] \tau=t[/imath] as long as they keep all measurements in there reference frame. The conclusion is that an observer in any reference frame will use his clock as the value of t (the evolution parameter) and use this to define the value of v. This can be done as long as we have no way to find the rest frame.

[AnssiH]

Just a really quick reply...

 

I am talking about mapping the data that our explanation is based on in such a way that we can map it into multiple reference frames and still have a valid explanation. That is, whatever information our explanation explains, we can map that information from one reference frame to another reference frame.

 

Great :)

 

In fact our definition of simultaneity is equivalent to that of length contraction,

 

"...is related to length contraction", just to be accurate.

 

that is if an observer in one reference frame (A) used the definition of simultaneity in a different reference frame (B) to decide when to measure the ends of a moving object he would arrive at the same measurements that would be arrived at in the reference frame that would consider his measurements to be simultaneous.

 

(took the liberty to name the reference frames as "A" and "B")

 

Well not quite correct; you have to also factor in the fact that the reference frame "B" is moving in reference frame "A". I mean, first consider an object that is at rest in A. Since it is at rest, it's length would not change no matter when you marked down the positions of its ends, i.e. no matter whose notion of simultaneity you used.

 

And when that object is moving very slowly, you can understand intuitively that you would still get wrong results. You would get wrong results across the spectrum actually. The point is that from the perspective of reference frame B, not only is the measurement done according to different simultaneity, the object is also "moving" differently.

 

Or another way to put it: 'you need to factor in the fact that the reference frame "B" is moving in reference frame "A"' :)

 

Nevertheless, I think you understand that the definition of simultaneity must affect your notion of lengths.

 

Now it seems that one important point of this is that simultaneity has been defined by assuming that the speed of the oscillator or that of light is the same in both directions which can not be proven. This means that our definition of simultaneity is a consequence of all elements moving at a constant speed which is a requirement of the fundamental equation and so no two reference frames can agree on what events are simultaneous.

 

Well, they "can" agree, but they cannot prove one to be more correct than another. The important bit is how simultaneity is to be determined, and why as a consequence of that, they both can use their personal notion of simultaneity without arriving at different predictions about reality.

 

This shows that the length of our measurements being Lorenz contracted is not a consequence of our definition of simultaneity, likewise our definition of simultaneity is not a consequence of our measurements being Lorenz contracted, but both are a consequence of the requirement that all elements must have a constant speed when transformed between reference frames. This is derived form the fundamental equation.

 

Not really sure what to respond to that paragraph, it seems maybe you were being a bit sloppy when writing it. The length contraction is consequential to a relativistic definition of simultaneity, and the analysis with constant velocity to the elements explores the epistemological roots of our ability to describe reality in that manner (setting the simultaneity to be a function of velocity of the observer)

 

So we use the fact that by choosing a mass less element for our oscillator we define its speed in the x,y,z space to be [imath] v_? [/imath] by the relation [imath] v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2} [/imath] because the movement in the [imath] \tau [/imath] direction will vanish for a mass less element. All that we have to do to measure this speed is to say that the value of [imath] \tau [/imath] is the same as the value of t in the rest frame which requires that [imath] v_? [/imath] is the speed of the oscillator. But is the relation [imath] t=\tau [/imath] in the rest frame a definition or is it algebraically arrived at, at some earlier point?

 

Well the relation [imath]v_?t=\sqrt{x'^2+y'^2+z'^2+\tau'^2}[/imath] is algebraically arrived at, and the rest kind of follows from that. When you say [imath]t=\tau[/imath], I suppose you mean that the [imath]\tau[/imath] of an element "at rest" (in x,y,z) is essentially the same as "t".

 

That is so simply because an element that is "at rest" must use all its velocity in [imath]\tau[/imath] direction. That's not a matter of measuring anything, it's just a matter of underlying definitions. I guess the best answer to your question is, "it is algebraically arrived at, from specific underlying definitions" :)

 

Another important point of this is that any observer will use his frame as though he is in the rest frame and so will use the value of [imath] \tau [/imath] in place of t.

 

It looks like the only reason that the value of v in the Lorenz transformation was defined was to give a method of calculating the location that would be considered the origin in another reference frame. It seems that this definition if not derived from is equivalent to that of velocity used in Newtonian physics but was defined for a different reason.

 

The point being that this definition doesn’t require the definition of our measurements but we can only consider the speed of an object after we have defined our measurements of length and [imath] \tau [/imath]. The value of t is impossible to be measurable and so will be considered to be equal to [imath] \tau [/imath] in the rest frame but seeing that we don‘t know what the rest frame is anyone is free to use their reference frame as though it is a rest frame and use the relation [imath] \tau=t[/imath] as long as they keep all measurements in there reference frame. The conclusion is that an observer in any reference frame will use his clock as the value of t (the evolution parameter) and use this to define the value of v. This can be done as long as we have no way to find the rest frame.

 

Hmm, not entirely sure if I'm reading you right, but that looks valid to me... The value of "v", meaning the relative speed between 2 coordinate systems, is something that both coordinate systems agree on after all these definitions. The thing to pick up is also, that while you cannot measure "v", "t", or "length", you can arrive at self-coherent definitions via how they are related to each others. Allowing you to put numbers to those parameters in self-coherent manner.

 

-Anssi

[Bombadil]

Well not quite correct; you have to also factor in the fact that the reference frame "B" is moving in reference frame "A". I mean, first consider an object that is at rest in A. Since it is at rest, it's length would not change no matter when you marked down the positions of its ends, i.e. no matter whose notion of simultaneity you used.

 

Actually now that I look at it again I’m not quite sure how I came up with simultaneity and length contraction being equivalent. Somehow it made sense at the time but looking at it again I can’t see how it could have.

 

Not really sure what to respond to that paragraph, it seems maybe you were being a bit sloppy when writing it. The length contraction is consequential to a relativistic definition of simultaneity, and the analysis with constant velocity to the elements explores the epistemological roots of our ability to describe reality in that manner (setting the simultaneity to be a function of velocity of the observer)

 

I’m not sure that I follow what you are saying, isn’t simultaneity really a question of when we make our measurements. And it is a fact that our measurements must be Lorenz contracted due to a constant speed of all elements. Hence if we chose to make our measurements at times that weren’t simultaneous then we could only use those measurements if they where Lorenz contracted. Hence it makes since to define simultaneity by when we make our measurements so that they are Lorenz contracted.

 

I’m not sure but it looks like defining simultaneity as when we must make our measurements so that they are Lorenz contracted will define a unique definition of simultaneity which will be equivalent to any other definition of simultaneity.

 

Or we could take the opposite approach and say that we want to make our measurements at the same reading of a clock in which case we have to calculate when the clock will give a particular reading and decide to make our measurements when it gives a particular reading. In which case in order to calculate when a clock will give a particular reading we will have to calculate the speed that a signal travels from our clock to where we will make our measurements. if we use a mass less element to do this we will have to use the value [imath]v_?[/imath] for the speed of our signal. There are other options but they all seem to be equivalent.

 

Either way I can’t see how length contraction is due to a relativistic definition of simultaneity (actually I’m not even sure what you mean by relativistic definition of simultaneity). As length contraction is due to all elements being required to have a constant speed in our explanation and simultaneity can be defined as a consequence of this.

 

That is so simply because an element that is "at rest" must use all its velocity in [imath]\tau[/imath] direction. That's not a matter of measuring anything, it's just a matter of underlying definitions. I guess the best answer to your question is, "it is algebraically arrived at, from specific underlying definitions" :)

 

I still have to wonder if [imath]v_?[/imath] is the speed that all elements must move at, or if [imath]v_?t[/imath] just has to be the total distance that a element must move. Either way I can’t see it as having any effect on the fact that all elements must have a constant speed in the [imath]\tau,x,y,z,[/imath] space, so for the time being I’m going to agree that [imath]v_?[/imath] is the speed of the elements as I see no effect that any other value of a elements speed might have.

 

Any how, this results in the length of the diagonal S in the second diagram being the same as the reading given by a clock in the rest frame or in whatever frame the diagram represents their measurements in. This is ultimately what results in triangles A and B, and triangles a and b being shown to be the same. This results in showing that all clocks will measure distance moved in the [imath]\tau[/imath] direction.

[AnssiH]

Actually now that I look at it again I’m not quite sure how I came up with simultaneity and length contraction being equivalent. Somehow it made sense at the time but looking at it again I can’t see how it could have.

 

Well you may have been on the right track.

 

When you have an object that is moving in your coordinate system, and you measure its length, you obviously would like to make sure you mark its front and rear ends "simultaneously".

 

In a newtonian worldview, the motion of the chosen coordinate system does not affect its definition of simultaneity. So by that definition, the length is always the same no matter which way the coordinate system moves (=no matter how the object moves in relation to the observer)

 

But if you establish simultaneity in relativistic manner; according to a signal speed that you suppose to be constant across all coordinate systems, you also change your idea of where the front and the rear end are "simultaneously".

 

So in that sense, length contraction is indeed a consequence of relativistic definition of simultaneity.

 

Not really sure what to respond to that paragraph, it seems maybe you were being a bit sloppy when writing it. The length contraction is consequential to a relativistic definition of simultaneity, and the analysis with constant velocity to the elements explores the epistemological roots of our ability to describe reality in that manner (setting the simultaneity to be a function of velocity of the observer)

I’m not sure that I follow what you are saying, isn’t simultaneity really a question of when we make our measurements.

 

First, I think I may have been quite sloppy when writing my own post, so let me re-phrase my quote above a bit, just to be sure:

 

The length contraction is consequential to a relativistic definition of simultaneity, and the analysis with constant velocity to the elements explores the epistemological roots of our ability to describe reality in that manner (in the manner of setting the simultaneity to be a function of velocity of the observer/coordinate system)

 

It is certainly not immediately obvious for intuitive thought, why should we expect it to be valid, that we suppose a different simultaneity for different coordinate systems. The common approach to explain its validity is to come up with an ontological fantasy that gives you an intuitive idea of how it all works (i.e. relativistic spacetime), but whose validity over all the other logically equivalent fantasies cannot be defended.

 

This analysis shows where its validity comes from, from an epistemological standpoint. Remember, the fact that the defined elements move at constant speed is not tied to ontological knowledge at all. It is tied to the fact that the elements are defined in shift symmetrical manner.

 

And it is a fact that our measurements must be Lorenz contracted due to a constant speed of all elements. Hence if we chose to make our measurements at times that weren’t simultaneous then we could only use those measurements if they where Lorenz contracted. Hence it makes since to define simultaneity by when we make our measurements so that they are Lorenz contracted.

 

Um.... I can't figure out what you might mean by that :(

 

I’m not sure but it looks like defining simultaneity as when we must make our measurements so that they are Lorenz contracted will define a unique definition of simultaneity which will be equivalent to any other definition of simultaneity.

 

Or we could take the opposite approach and say that we want to make our measurements at the same reading of a clock in which case we have to calculate when the clock will give a particular reading and decide to make our measurements when it gives a particular reading. In which case in order to calculate when a clock will give a particular reading we will have to calculate the speed that a signal travels from our clock to where we will make our measurements.

 

Hmmm, yes... That "opposite approach" is the approach of standard relativity, and in terms of this analysis, it is exactly the result you get when you can (and choose to) suppose that the elements always move at constant speed across all coordinate systems (i.e. everybody thinks they are at rest).

 

If you look at my post #48:

http://hypography.com/forums/philosophy-of-science/18861-an-analytical-metaphysical-take-special-relativity-5.html#post271521

 

From the "one-way speed of information" onwards, you can see me commenting on that standard approach. It is well known fact that one-way speed of information cannot be measured, without first knowing what that one-way speed is (doh), or supposing that clocks as physical constructions are unaffected by motion (shown to be false by relativistic relationships, and explained via epistemological consequences by this analysis)

 

if we use a mass less element to do this we will have to use the value [imath]v_?[/imath] for the speed of our signal. There are other options but they all seem to be equivalent.

 

Either way I can’t see how length contraction is due to a relativistic definition of simultaneity (actually I’m not even sure what you mean by relativistic definition of simultaneity).

 

Relativistic definition of simultaneity is the definition you get when you suppose that the speed of light is the same for all coordinate systems. I.e. each observer establishes which events are simultaneous by supposing the signal about the events approached them at exactly the speed C in relation to themself.

 

As length contraction is due to all elements being required to have a constant speed in our explanation and simultaneity can be defined as a consequence of this.

 

They are all tied together; what's important from the point of view of the epistemological analysis is that the elements are defined in a manner where they move at constant speed in [imath]x,y,z,\tau[/imath] (for symmetry reasons; a specific pattern "here" must mean the same thing when it occurs "there"... And if that last sentence doesn't make sense to you, don't worry about it now, but take a look at it later, in the derivation of the fundamental equation).

 

I have to apologize at this point for jumping carelessly between explaining some things about standard relativity, and then explaining things about the epistemological analysis... It occurs to me that if you are not at all familiar with relativity, it may not be very obvious to you when I'm commenting which... :I

 

I still have to wonder if [imath]v_?[/imath] is the speed that all elements must move at, or if [imath]v_?t[/imath] just has to be the total distance that a element must move.

 

Like you commented yourself, that is completely inconsequential question. [imath]v_?[/imath] doesn't mean anything without [imath]t[/imath] and distance. You could look at these things simply as concepts that are defined by how they are related to each others. They are just handy algebraic definitions.

 

Either way I can’t see it as having any effect on the fact that all elements must have a constant speed in the [imath]\tau,x,y,z,[/imath] space, so for the time being I’m going to agree that [imath]v_?[/imath] is the speed of the elements as I see no effect that any other value of a elements speed might have.

 

Any how, this results in the length of the diagonal S in the second diagram being the same as the reading given by a clock in the rest frame or in whatever frame the diagram represents their measurements in.

 

Well, you should perhaps look closely at the animation that I did about the moving clock. I quote it:

 

S is the total displacement of the mirrors [over one clock cycle], thus the evolution parameter T has the relationship:

 

[math]T = \frac{S}{V_?}[/math]

 

When a clock is at rest in x,y,z directions, its S is exactly [imath]2L_0[/imath], thus T over its clock cycle is:

 

[math]

T = \frac{2L_0}{V_?}

[/math]

 

But for a moving clock, S is longer than [imath]2L_0[/imath] by the factor:

 

[math]\frac{1}{\sqrt{1-\sin^2(\theta )}}[/math]

 

So think about what the [imath]\Delta T[/imath] is over one clock cycle of the rest clock, versus what it is over one clock cycle of the moving clock. That's right, the moving clock completes its first clock cycle much later than the rest clock. I.e. it is running slower.

 

In other words, in terms of some chosen coordinate system, by the time the clock that is "at rest" has completed 1000 clock cycles, the clock that is in motion has completed [imath]1000\sqrt{1-\sin^2(\theta )}[/imath] clock cycles, as a consequence of how the dynamic behavior of that clock must be plotted. And that is, quite exactly, the relativistic prediction.

 

This is ultimately what results in triangles A and B, and triangles a and b being shown to be the same.

 

The triangles are mentioned there because they offer a nice route to finding out the length of "S" (i.e. finding out where the mirrors are when one clock cycle has been completed).

 

This results in showing that all clocks will measure distance moved in the [imath]\tau[/imath] direction.

 

Yes, or that is at least nice way to interpret the situation in "intuitive terms".

 

-Anssi

[Bombadil]

When you have an object that is moving in your coordinate system, and you measure its length, you obviously would like to make sure you mark its front and rear ends "simultaneously".

 

The reason for making measurements simultaneously is that since we find the location of a moving object by use of the change in [imath] \tau [/imath]. By making sure that we agree on the reading of a clock when we make our measurements every one in any particular reference frame will be forced to agree on the location of the object when the measurements are made.

 

It might be worth pointing out at this point that if we did have a reference frame that everyone agreed to use its definition of simultaneity when making all measurements then everyone not in that frame would say that the object moved between when the beginning and end of the object was measured. And we could no longer expect everyone to agree on the speed of an object in the x,y,z,[imath] \tau [/imath] space due to agreement on a rest frame to use to find the value of t but not using all of the measurements that would be made in the rest frame. As a result the Lorenz contraction would no longer be the correct transformation to use as all of the observers in different frames would not agree on the speed of all elements.

 

Actually it seems that there may be some details that could be quite confusing to make sense of, but the whole thing seems quite useless to figure out as we have agreed not to use a particular reference frames definition of simultaneity.

 

 

And it is a fact that our measurements must be Lorenz contracted due to a constant speed of all elements. Hence if we chose to make our measurements at times that weren’t simultaneous then we could only use those measurements if they where Lorenz contracted. Hence it makes since to define simultaneity by when we make our measurements so that they are Lorenz contracted.

 

Um.... I can't figure out what you might mean by that :(

 

Well I think without realizing it, I may have been thinking that v could be used without defining a way of knowing when events are simultaneous or knowing how far an object has moved in the [imath] \tau [/imath] direction. Something that we can’t do.

 

In particular what I suggested is that if you know the value of v and the rest length L of an object then we can call the time (I use the word loosely here) that one end of a object is at the origin of a ruler simultaneous with the time when the other end of the object is at [imath] L\sqrt{1-\sin^2(\theta )} [/imath]. The problem is of course that in order to do this we must measure the speed of the object that we are measuring.

 

The problem then becomes in order for us to know how fast an object is moving we must receive two signals, one to tell us when it passed one point and the other one to tell us when it passed some other point that we have defined to be a particular distance away from it. This will of course require that we know how fast our signals are traveling back to us. So we are back to having to assume that the signal speed is constant in order to find the value of v.

 

I have to apologize at this point for jumping carelessly between explaining some things about standard relativity, and then explaining things about the epistemological analysis... It occurs to me that if you are not at all familiar with relativity, it may not be very obvious to you when I'm commenting which... :I

 

I’m really not having any problem following you although I can’t be sure that I haven’t confused the two issues at least a little as any attempts that I have made at relativity have resulted in more confusion then anything else. Just try reading some of my earlier posts on this topic to DoctorDick for an example. Actually physics in general seems more like something that’s just made to work with little or no concern for why it works and at times seems confusing in how and what they come up with things or maybe a little confused or maybe its just me. This is actually one reason why I am finding DoctorDick’s work so interesting.

 

In other words, in terms of some chosen coordinate system, by the time the clock that is "at rest" has completed 1000 clock cycles, the clock that is in motion has completed [imath]1000\sqrt{1-\sin^2(\theta )}[/imath] clock cycles, as a consequence of how the dynamic behavior of that clock must be plotted. And that is, quite exactly, the relativistic prediction.

 

The point is that multiplication of the rest clocks number of cycles by [imath] \sqrt{1-\left(\frac{v}{v_?}\right)^2} [/imath] will give the number of cycles of a clock moving at speed v. While multiplication of the number of cycles of a moving clock by [imath] \frac{1}{\sqrt{1-\left(\frac{v}{v_?}\right)^2}} [/imath] will give the number of cycles of a rest clock. the same goes for the length of an object in the direction of movement instead of the number of cycles of a clock.

 

The triangles are mentioned there because they offer a nice route to finding out the length of "S" (i.e. finding out where the mirrors are when one clock cycle has been completed).

 

Yes there in fact seems to be several ways of finding the length of S and at the same time showing that a clock moves the same distance in the [imath] \tau [/imath] direction no matter its speed, one of which is the geometric approach that is used. Also we could use an approach based only on the Lorenz transformation or I suspect that we could approach it from the behavior of the differentials. No matter how we do it though we will come to the same conclusion, at least if we don’t make any mistakes. However the geometric approach seems to be a quite useful visual approach to what is going on.

 

The geometric approach also seems to make it clear that the Lorenz transformation is nothing more then a rotation in the [imath] \tau [/imath] direction. Which seems interesting when it is considered that the mass operator is defined as [imath] -i\frac{\hbar}{c}\frac{\partial}{\partial \tau} [/imath] so I have to wonder if this is not the cause of the so called mass dilation of an object that is not at rest. Or maybe a change in mass has more to do with the idea of accelerating an object and so is still outside of our interest.

[AnssiH]

The reason for making measurements simultaneously is that since we find the location of a moving object by use of the change in [imath] \tau [/imath]. By making sure that we agree on the reading of a clock when we make our measurements every one in any particular reference frame will be forced to agree on the location of the object when the measurements are made.

 

That, I think is quite confusing way to put it :)

 

I'm guessing you are referring to a circumstance where each observer, all in the same inertial frame, are using the same notion of simultaneity. That is, a simultaneity defined via supposing a uniform information speed "c" to all directions.

 

I.e. they all agree on the reading of some clock (also in their frame) upon the moment of measurement.

 

And, they could litter their frame full of clocks all around, and synchronize them in terms of that uniform "c". I.e. they would say all the clocks hit noon at exactly the same moment. And following that definition, they of course all then agree on the length of any moving object.

 

It might be worth pointing out at this point that if we did have a reference frame that everyone agreed to use its definition of simultaneity when making all measurements then everyone not in that frame would say that the object moved between when the beginning and end of the object was measured.

 

You could say that. On the other hand, if they had "agreed to use a specific simultaneity", I think they would not be too prone to say that the object moved during measurement... This stuff just goes knee-deep into semantics very quickly, when your simultaneity can be very much whatever you want it to be (as long as the simultaneous events are "space-like" separated) :I

 

And we could no longer expect everyone to agree on the speed of an object in the x,y,z,[imath] \tau [/imath] space due to agreement on a rest frame to use to find the value of t but not using all of the measurements that would be made in the rest frame. As a result the Lorenz contraction would no longer be the correct transformation to use as all of the observers in different frames would not agree on the speed of all elements.

 

Actually it seems that there may be some details that could be quite confusing to make sense of, but the whole thing seems quite useless to figure out as we have agreed not to use a particular reference frames definition of simultaneity.

 

Yeah that can get confusing and goes little bit off-topic, which was about the validity of relativistic transformations.

 

Well I think without realizing it, I may have been thinking that v could be used without defining a way of knowing when events are simultaneous or knowing how far an object has moved in the [imath] \tau [/imath] direction. Something that we can’t do.

 

In particular what I suggested is that if you know the value of v and the rest length L of an object then we can call the time (I use the word loosely here) that one end of a object is at the origin of a ruler simultaneous with the time when the other end of the object is at [imath] L\sqrt{1-\sin^2(\theta )} [/imath]. The problem is of course that in order to do this we must measure the speed of the object that we are measuring.

 

The problem then becomes in order for us to know how fast an object is moving we must receive two signals, one to tell us when it passed one point and the other one to tell us when it passed some other point that we have defined to be a particular distance away from it. This will of course require that we know how fast our signals are traveling back to us. So we are back to having to assume that the signal speed is constant in order to find the value of v.

 

I can't be sure if I understand what you are suggesting, but at any rate I think you can pick up from all of this that definitions of lengths and simultaneity are related to each others.

 

I’m really not having any problem following you although I can’t be sure that I haven’t confused the two issues at least a little as any attempts that I have made at relativity have resulted in more confusion then anything else. Just try reading some of my earlier posts on this topic to DoctorDick for an example. Actually physics in general seems more like something that’s just made to work with little or no concern for why it works and at times seems confusing in how and what they come up with things or maybe a little confused or maybe its just me.

 

Right I see... Well yeah these things can certainly become confusing, at least I find most presentations of relativity to be so dumbed down that they are just almost useless for anyone who actually wants to understand why something is thought to be so. They tend to give you a hand-waving argument about some premise, then state the relativistic solution to that, and give the impression that relativity is thus proved to be an ontological fact.

 

The point is that multiplication of the rest clocks number of cycles by [imath] \sqrt{1-\left(\frac{v}{v_?}\right)^2} [/imath] will give the number of cycles of a clock moving at speed v. While multiplication of the number of cycles of a moving clock by [imath] \frac{1}{\sqrt{1-\left(\frac{v}{v_?}\right)^2}} [/imath] will give the number of cycles of a rest clock. the same goes for the length of an object in the direction of movement instead of the number of cycles of a clock.

 

Yes that's correct.

 

Yes there in fact seems to be several ways of finding the length of S and at the same time showing that a clock moves the same distance in the [imath] \tau [/imath] direction no matter its speed, one of which is the geometric approach that is used. Also we could use an approach based only on the Lorenz transformation or I suspect that we could approach it from the behavior of the differentials. No matter how we do it though we will come to the same conclusion, at least if we don’t make any mistakes. However the geometric approach seems to be a quite useful visual approach to what is going on.

 

I'm not sure what you are referring to when you say "approach based only on the lorentz transformation", but otherwise "Yes".

 

The geometric approach also seems to make it clear that the Lorenz transformation is nothing more then a rotation in the [imath] \tau [/imath] direction.

 

Hmm, I guess not quite accurate way to put it, but I think I know what you mean by that.

 

Which seems interesting when it is considered that the mass operator is defined as [imath] -i\frac{\hbar}{c}\frac{\partial}{\partial \tau} [/imath] so I have to wonder if this is not the cause of the so called mass dilation of an object that is not at rest. Or maybe a change in mass has more to do with the idea of accelerating an object and so is still outside of our interest.

 

Well it all boils down to algebraic relationships. It appears there are few slightly different definitions when it comes to mass in conventional physics, but each definition and consequence (how you would say "mass" behaves in dynamic conditions) should be relatively easy to derive from this point on.

 

-Anssi

[Bombadil]

I'm guessing you are referring to a circumstance where each observer, all in the same inertial frame, are using the same notion of simultaneity. That is, a simultaneity defined via supposing a uniform information speed "c" to all directions.

 

I may be, but if so it is not entirely intentional. What I am trying to say is that we want to make a measurement when two observers at the ends of the object being measured will agree on the location of the object being measured. That is the object has a uniquely defined location in their reference frame. How else can we define the location of an object other then to use the reading of a clock to describe how it moves and agree to make our measurements at a particular reading. Of course this brings into question how we come to the reading given by a clock.

 

You could say that. On the other hand, if they had "agreed to use a specific simultaneity", I think they would not be too prone to say that the object moved during measurement... This stuff just goes knee-deep into semantics very quickly, when your simultaneity can be very much whatever you want it to be (as long as the simultaneous events are "space-like" separated) :I

 

But would the idea of using another frames definition of simultaneity even make sense. Simultaneity really does seem to be a question of where we think an object is located. As all observers must agree on where an object has been but they need not agree on when an object is at any particular location. So the point is that we need to define a way of knowing when an object is at a particular location. This is further complicated by the fact that our measurements must obey the Lorenz transformation so that we measure a constant speed of an oscillator.

 

The point seems to be that the idea of simultaneity is really a question of how we define an origin in the [imath] \tau [/imath] direction. That is, we want a point from which every one in a reference frame will agree on to measure their movement in the [imath] \tau [/imath] direction from. But this is kind of overlooking the fact that we are defining a coordinate system so that the speed of a mass less element which will have zero movement in the [imath] \tau [/imath] direction will be measured to have a constant speed.

 

So can we really justify calling the speed of the oscillator constant when defining how we know when events are simultaneous? In order to try and make sense of this let us consider that the two way speed of an oscillator is all that we can measure but we are using the two way speed of an oscillator for our clock. This will certainly result in a constant speed of the oscillator. If we agree, as I think that we must, that any other idea of something that we can measure and use as a evolution parameter must be equivalent to our basic clock. That is, that it must measure distance moved in the [imath] \tau [/imath] direction.

 

What I am trying to get at is that using a different definition of simultaneity will require that we use a coordinate system in which we no longer use a constant speed of the oscillator. Could this be done, it seems that if this were all that we were interested in then we could use a particular reference frame for all of the measurements and then use our reference frame as though it where a moving frame in a Newtonian space. It seems that it could be made to work. However it totally over looks why we chose a coordinate system in which the oscillator has a constant speed, we did this because we want to maintain self consistency. We are doing this by using the fundamental equation and so we must set up a coordinate system where it is valid (or we must find a way to find the rest frame). In order to do this we must choose a coordinate system so that all elements have a constant speed in the rest frame. This leads to the problem that we can’t find the rest frame so that the fundamental equation must be valid for all observers.

 

This leads to the Lorenz transformation being the necessary transformation from one coordinate system to another. And it appears to be the reason that such a point of the speed of light not being assumed constant in this model has been made.

 

Well it all boils down to algebraic relationships. It appears there are few slightly different definitions when it comes to mass in conventional physics, but each definition and consequence (how you would say "mass" behaves in dynamic conditions) should be relatively easy to derive from this point on.

 

Yes, I think that we have all of the tools to derive it in what would be the standard way I think that normally Newtonian mechanics and the Lorenz transformation are all that is needed. But my point is that it seems that we shouldn’t have to, we should be able to derive these relations directly from the fundamental equation. Maybe I’m just trying to get ahead of myself again or not fully understanding the issue.

 

At this point I think I should explain the reason for some of my questions, I keep getting the impression that there is far more to this then what has even been hinted at so far and that is considerably more then what has been said. And every now and then I have to wonder if one of these things that seems to be suggested is where we are headed as the next step. In all actuality I don’t expect much for a answer at this point. Actually I don’t expect you to know much more then me about these questions I’m just putting them out there to see if I’m on the right track as to what we are talking about or to make sure that something hasn’t been overlooked that we need to go back and look at.

[AnssiH]

Hi, I've been incredibly busy lately, but thought I'd give a quick reply here... :I

 

I may be, but if so it is not entirely intentional. What I am trying to say is that we want to make a measurement when two observers at the ends of the object being measured will agree on the location of the object being measured. That is the object has a uniquely defined location in their reference frame. How else can we define the location of an object other then to use the reading of a clock to describe how it moves and agree to make our measurements at a particular reading. Of course this brings into question how we come to the reading given by a clock.

 

It is incredibly hard for me to interpret that, because people assign very different meanings to these words... I really had to guess a lot in my previous reply, and now also I am supposing that you mean a circumstance where 2 observers are in the same reference frame with each others, observing an object in a different frame. Then yes, if the 2 observers have established a definition of simultaneity that they both agree on, i.e. they agree on the simultaneity of events, then you can imagine a situation where the moving object just happens to be right in between 2 poles. Saying that the observers agree on simultaneity means they agree on the simultaneity of the events "front-end is passing the pole 1" and "rear-end is passing the pole 2".

 

So yes I think you understand how the definition of simultaneity is related to definitions of lengths of objects when viewed from different frames.

 

And yes it does bring into question how we come to the reading given by a clock, i.e how do we synchronize clocks. The relativistic convention is to synchronize via the assumption that the speed of information is C in whatever frame you choose to synchronize the clocks in (in their rest frame basically)

 

But would the idea of using another frames definition of simultaneity even make sense. Simultaneity really does seem to be a question of where we think an object is located.

 

Well I would say it is a question of undefendable assumptions that allow us to assign some speed to the information... Which in turn allows us to say which events were simultaneous.

 

It does have to do with what do we mean by "space" (which has to do with what do we mean by "objects") as much as what do we mean by "time" (which has to do with how can we track "change" in our knowledge in orderly fashion).

 

As all observers must agree on where an object has been but they need not agree on when an object is at any particular location.

 

Yeah, or since "when" becomes such an ambiguous concept, they do not agree on the simultaneity of some clock readings and the moment the object was next to something else (or any definable "event"). And the ability to disagree on that point comes about via the transformation mechanisms discussed. It does not mean they must define simultaneity that way ->

 

So the point is that we need to define a way of knowing when an object is at a particular location. This is further complicated by the fact that our measurements must obey the Lorenz transformation so that we measure a constant speed of an oscillator.

 

Actually "measurement" is a bad word to use there, as measurement is very much what you interpret it to be. Different worldviews could allow different observers to "measure a different speed to the oscillator" just by choosing to use a specific reference frame (much like you suggest at the end of your post), and that is a change brought about simply by defining reality differently. Undefendable idea in ontological sense, but so is relativistic spacetime and relativistic simultaneity.

 

At any rate, the relativistic time relationships are a consequence of the symmetries to our definitions (of objects), and you could look at the existence of tau and the constant speed of elements in z,y,x,tau as an expression of those symmetries. There are be many different ways those symmetries could manifestate themselves in a worldview (just as an arbitrary example, I think you should be able to see fairly trivially that an idea of an aether can be worked on to yield all the same predictions as relativity, if you just define it appropriately. It would be a worldview that would have a very different idea about "simultaneity" than relativity, and things would be explained very differently, but the same observable predictions would be there), and the z,y,x,tau space and the fundamental equation are just a handy way to explore the necessary relationships.

 

The point seems to be that the idea of simultaneity is really a question of how we define an origin in the [imath] \tau [/imath] direction. That is, we want a point from which every one in a reference frame will agree on to measure their movement in the [imath] \tau [/imath] direction from. But this is kind of overlooking the fact that we are defining a coordinate system so that the speed of a mass less element which will have zero movement in the [imath] \tau [/imath] direction will be measured to have a constant speed.

 

So can we really justify calling the speed of the oscillator constant when defining how we know when events are simultaneous?

 

Ontologically, no. The interesting point is, why is it valid to define isotropic speed.

 

In order to try and make sense of this let us consider that the two way speed of an oscillator is all that we can measure but we are using the two way speed of an oscillator for our clock. This will certainly result in a constant speed of the oscillator. If we agree, as I think that we must, that any other idea of something that we can measure and use as a evolution parameter must be equivalent to our basic clock. That is, that it must measure distance moved in the [imath] \tau [/imath] direction.

 

What I am trying to get at is that using a different definition of simultaneity will require that we use a coordinate system in which we no longer use a constant speed of the oscillator. Could this be done, it seems that if this were all that we were interested in then we could use a particular reference frame for all of the measurements and then use our reference frame as though it where a moving frame in a Newtonian space. It seems that it could be made to work.

 

Yes.

 

However it totally over looks why we chose a coordinate system in which the oscillator has a constant speed, we did this because we want to maintain self consistency. We are doing this by using the fundamental equation and so we must set up a coordinate system where it is valid (or we must find a way to find the rest frame). In order to do this we must choose a coordinate system so that all elements have a constant speed in the rest frame. This leads to the problem that we can’t find the rest frame so that the fundamental equation must be valid for all observers.

 

This leads to the Lorenz transformation being the necessary transformation from one coordinate system to another. And it appears to be the reason that such a point of the speed of light not being assumed constant in this model has been made.

 

Well, as I said above, the fundamental equation is an expression of the necessary symmetries. The fact that they yields relativistic relationships means that the relativistic relationships are a consequence of self-coherent definitions of objects. I could discuss that part little bit more, but not right now (just about to head to sleep :).

 

Yes, I think that we have all of the tools to derive it in what would be the standard way I think that normally Newtonian mechanics and the Lorenz transformation are all that is needed. But my point is that it seems that we shouldn’t have to, we should be able to derive these relations directly from the fundamental equation. Maybe I’m just trying to get ahead of myself again or not fully understanding the issue.

 

At this point I think I should explain the reason for some of my questions, I keep getting the impression that there is far more to this then what has even been hinted at so far and that is considerably more then what has been said. And every now and then I have to wonder if one of these things that seems to be suggested is where we are headed as the next step. In all actuality I don’t expect much for a answer at this point. Actually I don’t expect you to know much more then me about these questions I’m just putting them out there to see if I’m on the right track as to what we are talking about or to make sure that something hasn’t been overlooked that we need to go back and look at.

 

What there is to it is that there's no reason to look at relativistic relationships as arising from such and such kind of "reality" (you know, spacetime and wormholes and what have you), but rather they are shown to arise from epistemological circumstances; from our definitions of what it means to have "an object" and what does it mean that they "move" in "space". The relativistic time relationships can be seen in many different ways; imagining that the speed of light actually is "c" for all observers is just one way to see it.

 

The problem that most people seem to have at grasping this is that they take reality as they see it far too seriously. It is easy to think that once you have defined an object, it really is exactly like that. And as a consequence, space is what we defined it to be. When you try to point that out, people think you are talking about idealism. I am just talking about meaningful ways to define data patterns into persistent objects. Very different issue.

 

And yes the presentation does say something quite significant about quantum mechanics, but not at this thread.

 

I'm sorry the above is so sloppy, if something sounds very strange it's probably because I'm stating it in very obfuscated manner. I just don't think I'd have time for a better reply in quite some time :(

 

-Anssi

[Rade]

.... However the clock has been shown to measure distance moved in the [imath] \tau [/imath] direction.....So we really can use any object to make our measurements....Now using a clock and a measure of length (the clock that Doctordick has defined seems to be doing both) we can define velocity in a way very much equivalent to the way that it is defined in Newtonian physics...

I have a question. Suppose an object A that moves a distance C-->D in the [imath] \tau [/imath] direction between two moments of time time X-Y. It seems to me, based on the above statements, that the 'clock' then measures two things simultaneously: (1) the distance A is moved in the [imath] \tau [/imath] direction and (2) that which is intermediate between the two moments, X and Y. Would this be correct understanding of what you said ? Seems to be so, for then this 'clock' of DD would not only measure the distance moved by A in the [imath] \tau [/imath] direction, it also would measure (2) when A is at rest.

[AnssiH]

I have a question. Suppose an object A that moves a distance C-->D in the [imath] \tau [/imath] direction between two moments of time time X-Y. It seems to me, based on the above statements, that the 'clock' then measures two things simultaneously: (1) the distance A is moved in the [imath] \tau [/imath] direction and (2) that which is intermediate between the two moments, X and Y. Would this be correct understanding of what you said ? Seems to be so, for then this 'clock' of DD would not only measure the distance moved by A in the [imath] \tau [/imath] direction, it also would measure (2) when A is at rest.

 

No, the whole discussion is about relationships between definitions. The statement that "clocks measure displacement along [imath]\tau[/imath] simply means that given the definitions, the situation can always be interpreted that way (and this ability can be handy).

 

There is no meaning to the idea of measuring "intermediate between moments" in this context, it would be like measuring the temperature of gravity; appropriate definitions have not been given.

 

-Anssi

[Bombadil]

It is incredibly hard for me to interpret that, because people assign very different meanings to these words... I really had to guess a lot in my previous reply, and now also I am supposing that you mean a circumstance where 2 observers are in the same reference frame with each others, observing an object in a different frame. Then yes, if the 2 observers have established a definition of simultaneity that they both agree on, i.e. they agree on the simultaneity of events, then you can imagine a situation where the moving object just happens to be right in between 2 poles. Saying that the observers agree on simultaneity means they agree on the simultaneity of the events "front-end is passing the pole 1" and "rear-end is passing the pole 2".

 

Yes I think that we are talking about the same thing the only difference seems to be where we put the emphasis. You seem to be putting the emphasis on the question of defining simultaneity of the two events where simultaneity is defined by use of two observers agreeing on the reading of a clock, while I am putting the emphasis on the question of where the observers will say that the object is at by use of some parameter to use to describe the movement of the object and then making measurements when they agree on the location of the object. It might be better to say they agree on the location of a particular point on the object as saying that they agree on the location of the object may imply that they agree on length which has not necessarily been found yet. Actually it seems that this may be a bad approach to the problem as one could easily confuse the reading of a clock with an evolution parameter which it is not. Either way I think we are arriving at the same conclusions.

 

I think one of the points of this is that the definition of simultaneity and how one performs measurements of length are not only closely related to each other but you can define one from the other under some conditions. Although in general this is not the case.

 

Well I would say it is a question of undefendable assumptions that allow us to assign some speed to the information... Which in turn allows us to say which events were simultaneous.

 

I can only assume that you are referring to the assumption of what frame to use as a rest frame as all other requirements seem to be not so much assumptions as much as definitions of length, speed and time. As isn’t any other information that we need supplied by how we use these definitions to define speed? And so not so much an assumption as a consequence of requiring certain symmetries to hold by use of the fundamental equation. This is of course assuming that these definition have been made in a consistent way which does not seem to be an entirely trivial question.

 

Yeah, or since "when" becomes such an ambiguous concept, they do not agree on the simultaneity of some clock readings and the moment the object was next to something else (or any definable "event"). And the ability to disagree on that point comes about via the transformation mechanisms discussed. It does not mean they must define simultaneity that way ->

 

I think that I understand what you are saying although I’m having a little trouble following what you are saying. I think that you are saying that two observers need not agree on the order or simultaneity of events that take place but that they must agree on the location that an event takes place at. Which makes sense from the prospective that all observers must agree on what events take place but need not agree on what events are simultaneous due to different definitions of simultaneity.

 

I am wondering though, what about the issue of cause and effect that is due to the observers need to agree on what events cause other events? My first impression is that different observers need not agree on the cause and effect of events but I’m not sure if this is the case. Also will cause always be considered to be before the effect?

 

What there is to it is that there's no reason to look at relativistic relationships as arising from such and such kind of "reality" (you know, spacetime and wormholes and what have you), but rather they are shown to arise from epistemological circumstances; from our definitions of what it means to have "an object" and what does it mean that they "move" in "space". The relativistic time relationships can be seen in many different ways; imagining that the speed of light actually is "c" for all observers is just one way to see it.

 

It also seems interesting to note that the idea of a clock telling what time it is at any particular location is entirely a question of what time is defined as. And the idea of a signal traveling backwards though time really doesn’t make sense with how we are defining time and [imath]\tau[/imath] even if we defined time as what clocks measure (something sure to cause confusion) a signal traveling backwards though time makes no sense as when we think that the signal arrives is entirely a question of what reference frame we are in and if we were to calculate when the signal arrives in comparison to when it was sent for any particular reference frame it will never arrive before it was sent.

 

And yes the presentation does say something quite significant about quantum mechanics, but not at this thread.

 

I'm sorry the above is so sloppy, if something sounds very strange it's probably because I'm stating it in very obfuscated manner. I just don't think I'd have time for a better reply in quite some time :(

 

Well parts of it seem a little sloppy but I think I can still get the idea of most of what you are trying to say all the same.

 

Also I have been starting to try and take a detailed look at the thread ‘Anybody interested in Dirac’s equation’ which seem to deal with the quantum mechanics of this presentation that you are talking about. This may be something that I should have done earlier instead of just glancing at the posts in it like I have done previously.

[AnssiH]

Yes I think that we are talking about the same thing the only difference seems to be where we put the emphasis. You seem to be putting the emphasis on the question of defining simultaneity of the two events where simultaneity is defined by use of two observers agreeing on the reading of a clock, while I am putting the emphasis on the question of where the observers will say that the object is at by use of some parameter to use to describe the movement of the object and then making measurements when they agree on the location of the object. It might be better to say they agree on the location of a particular point on the object as saying that they agree on the location of the object may imply that they agree on length which has not necessarily been found yet.

 

Well actually I thought you were talking about length, that's why I put up those 2 poles in my description.

 

And I must say I am not able to interpret what you are trying to say exactly... But since you comment that it would be better to say they agree on the location of a particular point rather than length, I take it you understood how the notion of simultaneity and notion of length are connected. The moments when some part of the "moving" ship is passing some "stationary" marking poles, are taken as events, and it's the assumptions regarding how the information about those events reached different observers, that give those observers their idea of "simultaneity", and consequently the notion of length of "moving objects".

 

That is all part of conventional relativity and just falls out from logical consequences of the idea that the speed of light is plotted as the same for each frame.

 

I think one of the points of this is that the definition of simultaneity and how one performs measurements of length are not only closely related to each other but you can define one from the other under some conditions. Although in general this is not the case.

 

Well depends on what you mean by "in general" :)

 

Simultaneity really does seem to be a question of where we think an object is located.

Well I would say it is a question of undefendable assumptions that allow us to assign some speed to the information... Which in turn allows us to say which events were simultaneous.

I can only assume that you are referring to the assumption of what frame to use as a rest frame as all other requirements seem to be not so much assumptions as much as definitions of length, speed and time. As isn’t any other information that we need supplied by how we use these definitions to define speed? And so not so much an assumption as a consequence of requiring certain symmetries to hold by use of the fundamental equation. This is of course assuming that these definition have been made in a consistent way which does not seem to be an entirely trivial question.

 

I guess you could say that.. I mean, there are many ways to look at the issue, but the fact remains that the same consequences can be modeled in many different ways, and the relativistic idea of simultaneity is kind of a case of taking the spacetime ontology way too seriously (ontologically isotropic C etc.)

 

I think that I understand what you are saying although I’m having a little trouble following what you are saying. I think that you are saying that two observers need not agree on the order or simultaneity of events that take place but that they must agree on the location that an event takes place at. Which makes sense from the prospective that all observers must agree on what events take place but need not agree on what events are simultaneous due to different definitions of simultaneity.

 

Well, I think here you should just look at Lorentz transformation closely.

Lorentz transformation - Wikipedia, the free encyclopedia

 

That animated gif in there is probably revealing to you. It's a 2D spacetime, marking events, and the scaling/skewing that is displayed is the transformation from changing the inertial frame.

 

It is the spatially separated events whose order is changed if you take a relativistic notion of simultaneity. (Imagine a horizontal line in the middle and that's simultaneity)

 

Now your idea of "agree on location" is what confuses me a lot, I don't know how two different inertial frames agree on the location of something; In terms of the two different inertial frames, "Eiffel Tower" of course is not found form the same coordinates. At least not all the time :)

 

You must be thinking about defining the locations in terms of some well-defined objects, like, all observers will agree that the warning light blinking on top of eiffel tower is really blinking on top of eiffel tower in terms of each coordinate system. Yes that is so and they will also agree on the order of those blinkings of course. It is the order of blinkings between the light on eiffel tower and the light on Sears tower that they might disagree on.

 

At any rate, this is all just absolutely conventional relativity, while the focuse of this thread is in displaying the epistemological roots of those ideas being valid.

 

I am wondering though, what about the issue of cause and effect that is due to the observers need to agree on what events cause other events? My first impression is that different observers need not agree on the cause and effect of events but I’m not sure if this is the case. Also will cause always be considered to be before the effect?

 

The conventional idea of cause and effect is completely preserved in relativity. If you think about the spacetime representation as a web of connections, one event leading to another, leading to another etc, then you can think of Lorentz transformation as a procedure of skewing the whole thing. All the connections are preserved, and nothing inside the spacetime can observe that skewing of course.

 

It also seems interesting to note that the idea of a clock telling what time it is at any particular location is entirely a question of what time is defined as. And the idea of a signal traveling backwards though time really doesn’t make sense with how we are defining time and [imath]\tau[/imath] even if we defined time as what clocks measure (something sure to cause confusion) a signal traveling backwards though time makes no sense as when we think that the signal arrives is entirely a question of what reference frame we are in and if we were to calculate when the signal arrives in comparison to when it was sent for any particular reference frame it will never arrive before it was sent.

 

Well there is the idea of "tachyons" in relativity, or another name for basically the same thing, "advanced waves" (as oppose to "retarded waves"), which arises as a QM interpretation, and it's basically like a photon traveling backwards along the same paths as ordinary photons are traveling forwards in time... ...only that in ontological sense, that whole subject is made possible by the idea of static reality (and, transactional interpretation is nothing but ontological interpretation; predictionwise it doesn't offer anything at all)

 

See:

Transactional interpretation - Wikipedia, the free encyclopedia

 

Isn't it funny how they talk about the whole thing in terms of dynamic processes. Waves are "sent" here and there. All the while the whole thing is a consequence of the idea that spacetime is a static construction where nothing ever moves. Sorry now I'm rambling...

 

Well parts of it seem a little sloppy but I think I can still get the idea of most of what you are trying to say all the same.

 

I think this post was even more sloppy, and it took me so long time to even attempt to give a reply because I was getting waaaay too confused about what you mean. There are too many possible meanings to the words you use, especially in the context of relativity. I think all your questions right now would be best answered by simply better understanding of the conventional view of relativity. This analysis is sort of an explanation of the conventional view :)

 

I'm very glad though that you are interested and have actually walked through the logic, which is what more people should do. :)

 

-Anssi