An “analytical-metaphysical” take on Special Relativity!

[Doctordick]

Originally Posted by AnssiH

Okay, I was able to follow that whole thing now. (And spotted a small typo, the last isn't squared there, but it was correct in the subsequent steps)

Fixed it! Thank you.

Originally Posted by AnssiH

Btw, I found a very handy LaTex editor

I have bookmarked it and will examine it later; thanks a lot I always liked WYSIWYG type editors.

Originally Posted by AnssiH

So, I guess I just don't know what you meant by "divide through by the coefficient of ...", as when I tried that (however I interpreted it), I wasn't finding my way to your result.

When you got to

Originally Posted by AnssiH

And [moved] everything but the to the right side, to arrive at:

You were dividing through (through the whole equation) by the coefficient of : i.e., the factor .

You just did the square root first instead of after. Perhaps I confused you by my comment, "divide through by the coefficient of ...", as I should have said "divide through by the coefficient of ...".

Originally Posted by AnssiH

Oop, looks like another typo there at the OP. I think that should be:

And once again I bow to your clarity of observation. I didn't realize just how sloppy my presentation was.

Originally Posted by AnssiH

Hmmm... Okay, this once again involves algebraic steps that I'm not familiar with

...

And I suppose that can then be written:

The process you performed was exactly the process I had in mind when I said, “use 'common denominators' to add the two terms above”.

Originally Posted by AnssiH

Hmmm, I remember , but I don't remember (nor spot from the OP) where did we establish ...

You just proved to yourself (by that common denominator move) that

which implies (multiplying both sides by that

but we have also just shown that

Those two equations taken together imply that . You're just not as familiar with seeing algebraic relationships as most physicists would be. We would notice immediately that both alpha and delta had exactly the same factor in common and differed only by the factor .

Originally Posted by AnssiH

Also could not figure out how you got the

If you look back at the OP I think you will find that is one of the original four equations we started with.

Originally Posted by AnssiH

Phew, the Lorentz-part almost done already!

Unless you have more questions, I think we are done. I appreciate the time you have put into this very much. I really didn't realize how bad my presentation was until you took the trouble to try and understand it. I hope I can do a better job of presenting the GR deductions. The math there is nowhere near as complex as Einstein's Rieman geometry but neither is it "easy". The calculus required includes use of the Euler–Lagrange equation which is rather advanced mathematics.

I hope I can drag you through it. I have googled it and found no presentation which shows the history of its development (which was the way it was introduced to me). I am sorry but it seems to me that some of the aspects of classical mechanics are just not taught any more. Everyone seems to take the position that the standard modern presentation is the only rational presentation and that makes the subject hard to comprehend (in my opinion ). Sometimes I think scientists just want to confuse people.

Originally Posted by AnssiH

I'd have a few things to say to lurkers, about what all this implies, but I'll save it for little bit later... I hope these explicit baby-steps make it easier for all the lurkers to follow the thing though, and perhaps think about the implications themselves.

I am looking forward to those comments and I would like to hear the “lurker's” comments also. I am always wondering what is going on in their heads.

Have fun -- Dick

[AnssiH]

Just a quick reply...
Oh btw, I started to comment on Dennet and Consciousness Explained, but it went totally off-topic so quickly that I decided to not post it here. Anyhow, have not read the book, but been meaning to many times.

Originally Posted by Doctordick

You were dividing through (through the whole equation) by the coefficient of : i.e., the factor .

You just did the square root first instead of after. Perhaps I confused you by my comment, "divide through by the coefficient of ...", as I should have said "divide through by the coefficient of ...".

Hehe, actually it was just another silly ambiguity that got me there. was also a coefficient by itself so I interpreted "divide through by the coefficient of " as "divide through by the coefficient ", i.e. I attempted to divide through with itself. That didn't get me anywhere!

You just proved to yourself (by that common denominator move) that

which implies (multiplying both sides by that

but we have also just shown that

Those two equations taken together imply that .

Ah, I see it now.

If you look back at the OP I think you will find that [] is one of the original four equations we started with.

Ah, spotted it now

Back to OP:

Originally Posted by Doctordick

Finally, since and , it is quite obvious that clearly implies .

So now I understand that bit.

At this point, we have solved the problem; from the above it is quite clear the only possible relationship which can exist between moving coordinate system (moving at constant velocity v) is given by;

Right, so transformation for x' is:


And



So clearly


I was struggling with t', and after looking at it for a while, it seems like it was due to an error earlier in the OP;

...it is fairly easy to show that the transformation from one coordinate system to the other can be no more complex than and

I think that should be in there. That's how it's used in the subsequent steps in the OP, including the final result (me thinks).

So, assuming I'm right:


And



Then


And to tidy it up:




Which is your result. Yup, looks valid.

Just for convenience, one can define as this makes the square root in the above equations equal to yielding a simpler representation. If that constant velocity v_? were to be c, those would become exactly the standard relativistic transformations.

Yup.

I did this derivation in detail for one very simple reason: most publications merely publish the results and imply that their truth is support for Einstein's theory of special relativity. I prefer to view it as nothing more than the result of requiring a very specific symmetry: namely that some specific velocity must be the same in any inertial coordinate system. These relations are exactly the standard Lorentz transformations Einstein's theory of special relativity was concocted to explain.

Yup, so we've drawn out - with explicit logical steps - that the transformation required to maintain a specific constant velocity between moving coordinate systems, must (unsurprisingly) affect the way that all the data is laid down in a given coordinate system. And that the transformation is, unsurprisingly, Lorentz transformation.

And from that I also know that if the data is plotted in a coordinate system where "t" is also expressed as an axis of its own, the transformation can be intuitively understood as a straightforward scale procedure.

And in this context the transformation is simply a requirement of the explanation to remain self-coherent when it's referring to the same data expressed, only expressed in different (moving) coordinate systems.

The fact that my model requires them for internal consistency implies that my model actually requires any conceivable universe to satisfy the relations associated with special relativity.

Yup, certainly looks that way.

Unless you have more questions, I think we are done.

I think I'll still walk through the bits about definition of simultaneity carefully, albeit the result there seems to me to be a very obvious consequence of everything we've talked thus far. But at least I might spot some more typos

Also I'll do those clarifying animations for all the lurkers, and have a stab at explaining what all this means as it appears there is quite a bit of confusion there still, and I think I know where that confusion is (people try to view this result as if it says something about the ontological reality of nature, as otherwise they don't understand how could any result be meaningful)

I appreciate the time you have put into this very much. I really didn't realize how bad my presentation was until you took the trouble to try and understand it. I hope I can do a better job of presenting the GR deductions. The math there is nowhere near as complex as Einstein's Rieman geometry but neither is it "easy". The calculus required includes use of the Euler–Lagrange equation which is rather advanced mathematics.

Okay, as it is with SR, I'm not really familiar with the math of GR. I just look at it in a kind of "intuitive" way, imagining a spacetime transformation in my mind. But I'm sure if I'm careful enough and ask enough questions, I can walk through it as well.

I hope I can drag you through it.

Certainly. A new thread?

-Anssi

[Doctordick]

Originally Posted by AnssiH

Oh btw, I started to comment on Dennet and Consciousness Explained, but it went totally off-topic so quickly that I decided to not post it here. Anyhow, have not read the book, but been meaning to many times.

There is one question I would like to ask Dr. Dennet regarding “Consciousness Explained”. Since he claims a supposed explanation of Consciousness, he should be able to answer any question regarding the presence or absence of consciousness. The question I have in mind is, “is one conscious when one is dreaming?” I think the answer to that question could be interesting.

Originally Posted by AnssiH

I was struggling with t', and after looking at it for a while, it seems like it was due to an error earlier in the OP;

I think that should be in there. That's how it's used in the subsequent steps in the OP, including the final result (me thinks).

And you are right on the money again. I have looked at my original notes (the work from which I essentially copied the OP) and all of the errors you found are actually errors in my effort to copy and are correctly expressed in the original. At least it is nice to know that my original is not that contaminated with such off the wall errors. Thanks again (and I edited the OP earlier this morning when I first looked at your post).

Originally Posted by AnssiH

I think I'll still walk through the bits about definition of simultaneity carefully, albeit the result there seems to me to be a very obvious consequence of everything we've talked thus far. But at least I might spot some more typos

I can only hope you don't. It is quite clear to me at this point that, when it comes to the kind of errors you have found, I can't see the woods for the trees. I guess, when I proof read these things, all I do is just scan the stuff. I do find a lot of errors on my own you know. In fact, I find quite a few on first reading.

Originally Posted by AnssiH

Okay, as it is with SR, I'm not really familiar with the math of GR. I just look at it in a kind of "intuitive" way, imagining a spacetime transformation in my mind. But I'm sure if I'm careful enough and ask enough questions, I can walk through it as well.

I have been thinking about the approach by which the Euler-Lagrange equation was presented to me and I don't know if I can remember the details. It was a long time ago and, as I remember it, not taken from a book; at least not from any book I have a copy of (my math professor was educated back before quantum and relativity were really serious physics subjects and I suspect his view was closer to the point of view more common in the late 1800's). So I may just have to do a little hand waving there. We will see what I can come up with when I get into it.

Originally Posted by AnssiH

Certainly. A new thread?

Yes, but a tad down the line. Before we go into GR, I would like to show you my deduction of Dirac's equation. That deduction is quite straightforward and answers a few interesting questions mostly avoided by conventional modern physics. I will try to work up my first post this weekend.

Have fun -- Dick

[AnssiH]

These animations should make it fairly easy to comprehend the diagrams (and they will get embedded to the OP too):

Originally Posted by Doctordick

Click on the video to get to YouTube for high resolution version

YouTube - Presentation of a stationary clock

As is explained in the OP, this is simply a representation of a clock from its own rest frame. I.e. rest frame in terms of x,y,z-directions (tau corresponds to the definition of mass and gets integrated out).

Click on the video to get to YouTube for high resolution version

YouTube - Presentation of a moving clock

The same clock shown from a different frame, after exactly the kind of transformation that is required for the picture to remain self-coherent.

I will try and provide some more clarification on this issue soon.

-Anssi

[Bombadil]

Originally Posted by Doctordick

Somehow I get the impression that you are still missing the central issue. What we are talking about is a situation where we have an explanation of the universe as we see it. That means our explanation is not bothered by the fact that our reference frame (the coordinate system we use to represent our experiments) is moving with respect to the rest of the universe or not; the explanation includes the issues brought up by that circumstance. This has to do with absolutely any experiment we choose to examine. We choose to examine a few special circumstances because they point out, in detail, the problems with the old fashion Euclidean transformations used by Newton and, in fact, give us exactly what those transformations have to look like. The required transformations are a fact of life; your explanation must obey them and what kind of machinations you have to go through to achieve that is essentially beside the point.

So the requirement that the Lorenz transformation is part of our explanation is a consequence of being able to construct an object in our explanation where we have defined an object to be a collection of elements that maintain their orientation over changes in t. Would this be equivalent to saying that an observer at rest with an object will always use the same explanation even after they both have accelerated?

As a consequence of defining an object like this, if we take an object and then transform all of the elements that it is composed of so that it is in a moving frame (we accelerate the object for instance) it will appear to contract according to the Lorenz transformation. What seems more important to me is that if we suppose that an observer measures the object while at rest with it and then accelerates with it, since anything that might change the length of the object he is measuring will effect his ruler as well as anything else he might measure, he will still consider the object to have the same measurements.

The actual requirements, though, for a observer at rest with something not necessarily an object, to agree on the measurements before and after an acceleration, and for the object to be Lorenz contracted for a observer that remains at rest and doesn’t accelerate with it is not that it is an object but rather that the construct is unaffected by the rest of the universe. That is, we can still use the same explanation of the construct for an observer that remains at rest with it. This can be accomplished by being able to consider the construct separately of the universe that is of any influences resulting from the Dirac delta function, effecting the construct outside of it can be ignored. This is just saying though, that there is no preferred reference frame in which the fundamental equation is valid in, which is not necessarily a true statement about any explanation but for the time being is considered a useful approximation as it shows that the Lorenz transformation is a consequence of being able to explain things with the use of objects.

Originally Posted by Doctordick

The “if we can construct objects then” does not need to be there. We don’t need the existence of “objects” (collections of elements which can be considered as universes unto themselves) in order to create a V(x,t) such that a single element will appear to approximately obey Newtonian mechanics. Given any collection of elements, it is always possible to imagine (or create fictional elements) such that we can see the impact of the rest of the universe (including those fictional elements) as causing an interaction of the form V(x,t). If we cannot create objects, then we cannot create rulers; this is another problem.

Then is it even possible to create a V(x,t) such that the elements won’t appear to obey Newtonian mechanics? Also, if you are saying that even if we cannot construct objects that Newtonian mechanics will be an approximation to how elements behave I can’t see how we could use Newtonian mechanics and so call it an approximation without the use of a clock which so far requires the use of objects to construct.

Originally Posted by Doctordick

I essentially agree with what you are saying except of the fact that I don’t feel that the existence of objects can be considered an axiom. We could certainly conceive of a “universe” without objects and even talk about some of the constraints on explaining that universe; it could even be a subset of our universe which had negligible impact upon that portion of the universe we deal with on a day to day routine. Say the inside of stars (or perhaps the interior of nuclei) or the structure of those great voids between the clusters of stars. We just couldn’t hypothesize rulers or clocks in such a realm.

It seams clear that such systems will appear to be Lorenz contracted from an outside prospective like a ship going by at relativistic speeds. But in considering possible explanations of such objects, what will happen to the expanding sphere? I know that the fundamental equation is still the equation of an expanding wave, we just can‘t say that it is expanding at a constant speed because we can‘t define the distance that it has expanded or how long it has expanded for.

Originally Posted by Doctordick

We cannot solve the general equation anyway so what difference does this make? What I am saying is that the elements of your explanation must obey that equation. I think what you are missing is the fact that most all common explanations are what is called “static”: i.e., none of the fundamental elements change in any way so obedience to the fundamental equation is a trivial issue. Just as the structure of my house obeys Newtonian mechanics: it just stands there without moving.

But isn’t the only thing that is important is that there is some way that we can map the behavior of the elements in however we are explaining them into a solution to the fundamental equation? How we are explaining them and what we are explaining is of no importance as long as such a mapping exists.

Originally Posted by Doctordick

I think it is the issue of the existence of “rulers” without which we couldn’t talk about “coordinate frames of reference”. Without “frames of reference” transformation between frames of reference is a pretty meaningless concept.

Is there a way though, to define a coordinate system without the use of objects that we can use to define distance? Isn’t it possible that we may be able to use some sort of consistent repeating behavior of elements to set up a coordinate system even if it isn‘t what we would ordinarily consider to be a coordinate system?

[AnssiH]

Originally Posted by Doctordick

There is one question I would like to ask Dr. Dennet regarding “Consciousness Explained”. Since he claims a supposed explanation of Consciousness, he should be able to answer any question regarding the presence or absence of consciousness. The question I have in mind is, “is one conscious when one is dreaming?” I think the answer to that question could be interesting.

Why, what do you have in mind?

I personally wouldn't know what to answer, as it's kind of a matter of what one supposes "being conscious" means.

But, running with the idea that dreams are a product of the brain re-ordering information, and looking for new self-coherent connections between ideas (which would explain why in dreams there often exists rather strange combinations of ideas, why dreams often include things that have been in our mind recently, why we sometimes come up with a solution to a difficult problem in our dreams, and why good night sleep seems to aid learning), then I think it's to be expected that sometimes that ordering doesn't include the idea of "self" at all, and thus cannot really be remembered later (it's not "something that happened to me"), and can't really be considered a conscious experience.

On the other hand, maybe one doesn't want to call those instances "dreams" at all, in which case a dream is always something consciously experienced.

Of course I understand some people associated "being conscious" with the everyday idea of being awake...

Anyway, I read the simultaneity stuff from the OP and didn't spot any errors. Albeit I did read it little bit less carefully than the rest, because that relationship between the definition of simultaneity and geometry seems fairly obvious to me.

Originally Posted by Doctordick

At this point, it is very important to examine the reverse case...

...

...Thus it is that he will hold forth that his clock is correct and the (so called) rest clock appears to be contracted by exactly the standard Lorentz contraction. The only reason I went through that, was because many people have difficulty comprehending how the moving observer (who' entire perspective appears to be Lorentz contracted) can see the rest observer as Lorentz contracted. (I strongly suspect that many trained physicists can't see it either; they are just throughly indoctrinated in conventional relativity. But that is only an opinion )

Well I have not heard any physicist talking about that relationship explicitly either, but then where would I...? The dumbed down presentations are so silly they make my head hurt, and I always end up thinking "someone needs to be fired for this..."

Incidentally, as I'm writing this there's a History Channel program "The Universe" on, and it's an episode about space travel. They are bringing up the speed limit of light speed as per relativity, and sure enough, they have once again dumbed it down so much as to make completely false assertions. Here's a direct 1:1 quote straight from Mr. Neil deGrasse Tyson (PhD in Astrophysics)

"Light's fast, but the universe is huge. So even if we could ride on a beam of light, if we wanted to cross the galaxy - the way they do it on the science fiction programs - it would take a hundred thousand years to do it".

And the narrator continues:
"And even at light speed, traveling to the nearest galaxy, would take several million years"

And then of course they had a computer animation where "a beam of light" is travelling "really fast through space"...

It is really really really beyond me, how any self-respecting scientist - who supposedly understand what relativistic speed limit means - can spew something like that from their mouth... Is it possible, that some of them don't really understand what it means? That they just heard somewhere that C is the speed limit and run that against their newtonian worldview without understanding what it means and where it comes from? Because if they understood it, surely they'd see it doesn't really play down the way they talk about it... Is that it? I'm quite puzzled. And to be honest, a bit annoyed.

How common is that misconception then? How many people reading this thinks what they are saying is valid, according to relativity? And why?

Well, then they go on to talk about space warps in terms of static spacetime, and about tachyons in a really stupid and incoherent manner (They seem to think tachyon simply refers to an "infinitely fast" object or something). I can't go on because I'm getting too depressed over that, so back to the topic

The only reason I find that relationship between simultaneity and geometry so obvious is because I understood it myself via visualizing Lorentz-transformation in my head. I have ran into many people who "know" relativity but did not understand it enough to see that relationship for some reason. I suspected it was just because they were somewhat casually interested of the subject and had never thought about it much.

At any rate, it should be quite obvious that if you set about to measure the length of a box, you are measuring "where the extends of the box are simultaneously". Change your idea of simultaneity, and you change your idea of the geometry of the box.

Anyway, let me walk through the final part of the OP still, maybe we'll uncover some typos...

Originally Posted by Doctordick

Finally, in order for the moving observer to measure the period of the rest clock, he must receive two signals...

...

Again, as all velocities along our displacement vectors are v_?, d₁+d₂=S. It follows that, from the perspective of our rest frame, this is exactly

Yup

or, solving for S,

.

While I was able to understand that that expressions is true, I do not know what the algebraic steps are in between there. It's just once again my unfamiliarity with math, I'm sure it's something really simple :P

During this time the observer will have moved a distance of . He however will call this distance (based upon his personal measurements of length and his perception of what he has measured) and will assume that the clock has receded from him by that distance. Since, as far as he is concerned, his standard clock is correctly measuring time, he will read the elapsed time between the received signals as . He will therefore see the clock as receding from him at a rate given by

Yup.

I'll continue from here soon...

-Anssi

[Doctordick]

Originally Posted by Bombadil

So the requirement that the Lorenz transformation is part of our explanation is a consequence of being able to construct an object in our explanation where we have defined an object to be a collection of elements that maintain their orientation over changes in t. Would this be equivalent to saying that an observer at rest with an object will always use the same explanation even after they both have accelerated?

Your use of the word “orientation” here bothers me! An object was defined to be a collection of elements which could be considered an entity unto itself for sufficient time to examine or use that fact. The only orientation of interest is its momentum direction in the four dimensional space being used here. No “orientation” is being maintained; the only thing being maintained is the fact that the elements making up that object have to remain in the vicinity of one another. Since they are all moving at the same speed (v_?) that fact has important logical consequences.

Originally Posted by Bombadil

... he will still consider the object to have the same measurements.

Well, of course, that is exactly the phenomena under examination.

Originally Posted by Bombadil

... but for the time being is considered a useful approximation as it shows that the Lorenz transformation is a consequence of being able to explain things with the use of objects.

Ok.

Originally Posted by Bombadil

But in considering possible explanations of such objects, what will happen to the expanding sphere?

Somehow I don't think you are following the deduction at all. If you followed what I was doing, you wouldn't ask such a question.

Originally Posted by Bombadil

I know that the fundamental equation is still the equation of an expanding wave, we just can‘t say that it is expanding at a constant speed because we can‘t define the distance that it has expanded or how long it has expanded for.

Why don't we just drop these issues for the time being as they have nothing to do with the problem presented in this thread.

Originally Posted by Bombadil

But isn’t the only thing that is important is that there is some way that we can map the behavior of the elements in however we are explaining them into a solution to the fundamental equation? How we are explaining them and what we are explaining is of no importance as long as such a mapping exists.

Ok.

Originally Posted by Bombadil

Is there a way though, to define a coordinate system without the use of objects that we can use to define distance?

Again, I don't think this has anything to do with what this thread is talking about. You are trying to discuss things far beyond the issues presently being argued here.

[AnssiH]

Since I've carefully followed the earlier steps of the analysis up to this point, I can see quite clearly what this thread is about, and I thought I should try and clarify this thread for all the interested lurkers out there.

First of all, this is all part of an epistemological analysis, meaning it is not supposed to uncover any sort of ontological reality. Instead, it is shown how relativistic time relationships arise from circumstances that are necessary for any world model that conceives "unknown data patterns" in terms of "persistent objects", as long as the model preserves self-coherence very carefully every step of the way.

Issues discussed earlier in different threads:

Any world model needs to define objects, based on some unknown data patterns (it needs to be known "what constitutes an object"). In the earlier thread (Deriving Schrödinger Equation), it was shown that while many valid sets (of defined objects) would always exist for any finite amount of data, any self-coherent set of defined objects will end up obeying quantum mechanical relationships. Or another way to put it, it was shown that quantum mechanical relationships are already embedded in the original symmetry requirements, and will be a feature of a self-coherent worldview regardless of the content of the raw data patterns (It is simply a matter of ordering the information in a specific way).

(Note; the idea that some "ontological identity" exists behind the raw data patterns is always an open question, and probably easiest to just suppose there aren't any ontological identities out there. The idea of "persistent identity" is clearly something required by a mental conception of reality, but I would not expect the actual reality to require it)

Once you have a world model, that defines objects, that obey quantum mechanical relationships (which newtonian mechanics are an approximation of), you already hold a perspective where there are "objects" that are persistent through time, that are moving around in a coordinate system, and that are interacting upon touch.

If you have no patience to follow the analysis up to that point, you can still follow this thread if you just let yourself take the above on faith for time being.

This thread is explaining exactly how, and exactly why, those defined objects must obey relativistic time relationships, as a result of carefully preserving self-coherence every step of the way. I.e. how relativity is not a feature of ontological reality, but instead spring from the way we classify and order data through our world models.

About the presentation form:

Note, that parameters, and all the other definitions related to the fundamental equation, are there for the sole purpose of being able to investigate relationships between things that we have defined in our head.

I.e. that the analysis is using a tau dimension to communicate this issue, is of little significance here. It does NOT mean that there exists an ontologically real tau dimension.

It does not even mean, that there literally exists a tau dimension as such in our minds. The presentation form (of ) is not important, what is important is the exposed relationships between defined things; While we do not consciously think about the world in terms of a tau dimension, the timewise relationships that are expressed in the form, are necessary for any self-coherent world model; i.e. these same relationships are always to be found in one form or another (as long as that self-coherence is carefully preserved).

Onto the relativistic relationships

First note that the relationships that were exposed before this thread, were expressed in terms of a coordinate system that is at rest with the entire set of defined entities. I.e. the probability function of that form would behave exactly correctly ONLY in that one coordinate system.

Then it was shown what sort of transformation between coordinate systems (that are moving within each others) must be performed for the world model to remain self-coherent. It was shown why the transformation must be Lorentz-transformation (to space), as otherwise the new perspective would not map properly over the same raw data anymore. Don't take this as consequential to the chosen presentation form, as it is more properly a consequence of the original symmetry arguments, and the same relationship could certainly be expressed in many different forms. (Note; this is not exactly how Lorentz transformation is used in relativity, I can talk about the difference separately if it's not already obvious)

Next, note that the relationships exposed before this thread, were shown to map perfectly onto the relationships given by modern physics (often taken as features of ontological reality as oppose to features of our world model), which yields us a way to see exactly how does a defined macroscopic object such as "a clock" map into this picture (of space).

When that clock assembly is expressed in terms of the space, we can show the logical consequences of that self-coherent transformation between moving coordinate systems. It is shown, that the dynamic behaviour of the clock absolutely must be plotted in a way where the supposed geometry and the dynamics (incl. the observable cycle count) of the construction must exhibit relativistic behaviour as a function of the chosen coordinate system.

In other words, the reasons for that relativistic behaviour are entirely epistemological, as oppose to being a feature of the ontological reality itself.

About simultaneity and standard perspective of relativity

I think the real significance of this result shows up when we consider the concept of "simultaneity" and how it's historically been treated.

Let me start from the beginning of this whole conundrum, just in case someone doesn't know.

One-way speed of information

First, there is no way for you to tell "when" some distant event occurred, unless you know how fast the information about that event reached yourself.

Second, there is no way to measure the speed of information from one location to another, unless you have placed synchronized clocks in those locations.

Third, there's no way to tell if two spatially separated clocks are synchronized, unless you know how fast the information reached you from both of them. -> You are back to square one.

The idea of synchronizing the clocks in one place and then moving them to their respective locations, is invalidated once you realize that the dynamic behaviour of those clocks is governed by the same phenomena that we are set to measure. I.e. we will not know how the clocks are affected by us moving them until we know the one-way speed of information.

It follows from those facts that there is no way to measure one-way speed of information. You can only measure two-way speed of information (information starting its propagation from the same clock where it ends up).

And it follows that, to consider two spatially separated events as simultaneous, is to make an assumption about how fast the information about those events reached you.

Now, the epistemological analysis displays in very explicit manner this exact same problem. One-way speed of information is completely hidden from the view, in the sense that two observers can completely disagree with the one-way speed, and still map the same raw data in their respective coordinate systems. It displays exactly how and why we are free to make any assumption about the one-way speed (as long as the two-way speed remains unchanged) without generating any observable predictions.

In other words, each observer is entirely free to plot the data in their personal coordinate system in a manner where the speed of the information is considered equal in all directions against themselves. Of course when they do that, they also define which events they consider as simultaneous.

Of course, in standard relativity, that is exactly the assumption that is made by the postulate that the speed of light is isotropic across inertial frames, and people tend to assign varying degrees of ontology to this postulate.

Notice how, it is one thing to say "speed of light is the same for all observers", and another thing completely to say "all macroscopic objects measure the speed of light as the same". The latter assertion has to do exactly to the fact that "all clocks are defined macroscopic objects governed by exactly the same dynamics we are set to measure" (which is a very important issue, as here - under a careful analysis - it yields an explanation to time dilation measurements)

If you instead take the first assertion as literally true, then when being asked the question "what is happening in Alpha Centauri right now?", your answer of course depends entirely on the coordinate system you happen to choose for your answer.

Imagine that mankind had scattered all across the universe, and everyone were supposed to throw a party whenever it is the New Year's Eve on earth. If each space colony were to throw the party whenever they figure is appropriate according to their coordinate system, then hardly no one would be throwing the party at the same time (in terms of ANY coordinate system).

You would be having a party onboard of your ship, while another ship passing you would figure it's still 2 weeks until the party should be thrown. Of course, if they are planning to change their direction drastically within the next 2 weeks, they might be facing quite a difficult decision...

So, is the speed of light ontologically isotropic? I.e. does the state of reality actually change as a function of which coordinate system you happened to choose to describe it? I have some doubts

I expect everything above to be abundantly obvious to anyone who understands relativity, and I suppose that is why you often hear physicists say that relativity is just a handy convention, without dwelling more on the subject of ontology. Certainly you can build many sorts of ontological interpretations (like static spacetime), and I guess some people choose to view it simply as an expression of realistic dynamics, intentionally leaving the question of underlying ontology unanswered.

Yet, I'm sure everyone wonders to some extent, what does the validity of relativity actually imply about reality? Everybody does assign some level of ontology to some aspects of relativity, and certainly until now, it has not been trivial to answer the question "where does observable time dilation come from if not from isotropic speed of light?".

Notice that the epistemological analysis explains that issue, without saying anything about ontological simultaneity. It is entirely possible that "real simultaneity" is absolute, relativistic, ontologically meaningless, bubbly, or anything at all. What is significant is that relativistic time dilation is found to be a logically unavoidable consequence of "self-coherent object definition", "macroscopic clocks", and "the need to express the same reality in terms of different coordinate systems". It occurs in your head, without ANY ties to what sort of simultaneity exists ontologically.

The title of this thread could perhaps more properly be "Relativity demystified", as it, in my opinion, explains completely why relativistic world conception is valid, without adding any mysterious implications to reality.

And it should be clear at this point, that supposing an ontological reality of spacetime is also a case of taking the relativistic concepts way too literally. Likewise, you will often notice that physicists are using the idea that the one-way speed of light literally is C in all inertial frames, in their further musings. For instance, a violation of locality - meaning superluminal speed of information - is considered to destroy causality. But that is true IF and only if you actually assume each observer has got ontologically different simultaneity -> only if you suppose reality really does care about your chosen coordinate system in some sense (via static spacetime or something else).

Whereas the epistemological analysis shows explicitly that the supposed simultaneity of each observer is simply an idea in their head, which hinges completely on their assumption about the one-way speed of light. That opens up quite a few doors that are normally thought to violate relativity.

I do think it would be a valuable thing for anyone interested in relativity to understand this analysis. It might take time, but it is quite illuminating, I can assure you. Think about it.

-Anssi

[Doctordick]

Originally Posted by AnssiH

I personally wouldn't know what to answer, as it's kind of a matter of what one supposes "being conscious" means.

My point exactly! Primitive outlooks have almost always included dreams as being as real as what we call reality. Certainly, in my dreams, I feel as if I am conscious; how is it that I remember what happened if that were not the case? And Dennet's definition of consciousness seems to me to include dreaming. The issue is, what philosophical position is appropriate here.

Originally Posted by AnssiH

Of course I understand some people associated "being conscious" with the everyday idea of being awake...

The reason I brought the question up.

Originally Posted by AnssiH

Incidentally, as I'm writing this there's a History Channel program "The Universe" on, and it's an episode about space travel. They are bringing up the speed limit of light speed as per relativity, and sure enough, they have once again dumbed it down so much as to make completely false assertions. Here's a direct 1:1 quote straight from Mr. Neil deGrasse Tyson (PhD in Astrophysics)

"Light's fast, but the universe is huge. So even if we could ride on a beam of light, if we wanted to cross the galaxy - the way they do it on the science fiction programs - it would take a hundred thousand years to do it".

It's all in your perspective. If you could offset the effects of acceleration (some kind of internal force field local to the ships cabin which would accelerate every element in your local environment at exactly the same rate), the ship could attain astounding accelerations. Now of course that is a science fiction idea but it isn't one which violates any law of physics except perhaps the energy problem which is not trivial. Let us suppose we have some way of using the free matter in space to obtain this energy (if we are moving fast enough, the amount of material we intercept could be quite large).

So let us say any desired acceleration is possible. If that is the case, we can go anyplace in the universe in as little time as we desire (insofar as ship time is concerned). Using a “earth rest frame of reference map of the universe” together with a ship time clock for time measurements, we can achieve any velocity right up to infinity and, strange as it might seem, we can use Newtonian physics to plot our course through the universe. That is an interesting consequence of using that mixed coordinate system. I suspect, if humans ever do achieve interstellar travel, they will use my geometry for plotting their course; it is much simpler than using Einstein's picture. For any physicists reading this note that one “g” acceleration (in the mixed coordinate system) is not one “g” acceleration in the ships frame so the standard relativistic comparisons are not valid. (I just pointed that out because I know you will do the relativistic calculations and point out my answer is different).

But back to the reason I mentioned this case. It is much easier to see rapid travel as “forcing” one into the future instead of in terms of a limiting velocity. For example, Alpha-Centauri is roughly four light years away. It is somewhat surprising that one “g” (32 feet per second per second) is almost exactly equal to one light year per year per year. So if we accelerated off towards Alpha-Centauri at one “g” (as measured on our mixed coordinate system) until we got half way there (two light years) it would take two years (ship time). We could then de-accelerate for another two years and arrive at rest at Alpha-Centauri. We could spend what time we needed there and then return to earth in another four years (ship time). So we would say the round trip was eight years long. How much time would pass on earth?

The answer is quite simple: our actual path in my space would be four segments, each two light years in the x direction plus two light years in the tau direction, c being one light year per year. Since these directions are orthogonal to each other, our actual total distance of travel would be light years. So the earth observers would say the trip took roughly eleven years and four months. That is, we could see ourselves as being forced into the future a distance of roughly three years and four months.

Suppose we wanted to go to the other side of the galaxy, some 200,000 light years away. Half way would be 100,000 light years; =447 years so, at one “g” it would take roughly 1,800 years ship time for the round trip. At four g's (something the crew could probably get used to) we could do the round trip in roughly a little over 900 years (ship time). But how long would we be gone, earth time? which is roughly 410,000 years. Just a tad short (by a mere 10,000 years) of the apparent speed of light. In this case we have been pushed about 409,100 years into the future. But what will the crew say their velocity was? They went some four hundred thousand light years in a little over 900 years. That would be almost 450 light years per year.

It's all how you look at these things. And I also get annoyed with professional physicists.

Originally Posted by AnssiH

Well, then they go on to talk about space warps in terms of static spacetime, and about tachyons in a really stupid and incoherent manner (They seem to think tachyon simply refers to an "infinitely fast" object or something). I can't go on because I'm getting too depressed over that, so back to the topic

You should notice that “tachyons” don't exist in my representation. “Apparent” velocities in excess of light are just plain -???- “not possible” -???- (see the above analysis). That is one reason I do not like Einstein's picture: it suggests the existence of phenomena which violate the logic of his own construct. A very poor characteristic for any theory to contain.

Originally Posted by AnssiH

While I was able to understand that that expressions is true, I do not know what the algebraic steps are in between there. It's just once again my unfamiliarity with math, I'm sure it's something really simple :P

We started with the expression

subtracting from both sides, we obtain

and then dividing by one obtains

And that should take you to the end of the OP. I just read your latest post and agree with most all of it; however, I don't think it would be possible to chart a path which would allow you to party all the time by accelerating your ship in a manner where it would be the New Year's Eve on earth all the time! The general relativistic transformation has to yield a stopped clock on the earth as seen from your ship! That, I think might require an infinite acceleration. But maybe you could get far enough away from the earth such that there was enough mass between you and the earth to yield a black hole solution.

Have fun -- Dick

[AnssiH]

Originally Posted by Doctordick

It's all in your perspective. If you could offset the effects of acceleration (some kind of internal force field local to the ships cabin which would accelerate every element in your local environment at exactly the same rate), the ship could attain astounding accelerations. Now of course that is a science fiction idea but it isn't one which violates any law of physics except perhaps the energy problem which is not trivial. Let us suppose we have some way of using the free matter in space to obtain this energy (if we are moving fast enough, the amount of material we intercept could be quite large).

So let us say any desired acceleration is possible. If that is the case, we can go anyplace in the universe in as little time as we desire (insofar as ship time is concerned).

Yeah, and what bothers me is that they talk about relativity and the relativistic speed limit as if it was some sort of speed limit against some metaphysical space, and back that idea up with a computer animation which gives everyone exactly the idea of racing through space really fast alongside a beam of light (i.e. they give the idea that at light speed, light is at rest with you). Certainly someone might argue that they were talking about the travel taking this and this long in earth's frame, just to simplify things or whatever, but I really don't think that sort of simplification helps in communicating what relativistic speed limit means. It only serves to confuse people.

I don't mind them talking about special relativistic view only, i.e. ignoring gravitational effects or energy questions for simplicity, as you can just imagine that you shift the perspective between different space ships as they pass each others (they can certainly communicate when they pass, so this just serves as a means to discuss our ideas of relativistic ontologies).

So, for all casual lurkers who have fell prey to exactly these sorts of assertions about relativistic speed limit, let it be said that relativity certainly allows for a spaceship to get from Earth to Alpha Centauri in any arbitrarily short period of time, even in 1 second (we can allow them to gain speed before passing the start line on earth) according to its own perspective (its own clocks and its own idea about the distance of the travel)

What the relativistic speed limit more properly means, is that no given object can move faster than C in terms of any inertial frame. That is a consequence of Lorentz transformation being valid (which is a scale-like procedure to the apparent speeds, as oppose to a velocity addition procedure). I.e. in terms of Earth's frame, the clocks on space ship would be said to be at almost standstill. In ship's frame, the distance between Earth and Alpha Centauri would be said to be shrunk into some tiny distance)

The point is, it is not a speed limit against any "space", it is a speed limit against any chosen coordinate system. For anyone who has followed this analysis, that should ring some bells...

The macroscopic dynamics that we are expressing in any given coordinate system, must transform in a very specific manner (for self-coherence reasons) when we choose to express them from a different coordinate system. Quote from my previous post: "it is shown, that the dynamic behaviour of the clock absolutely must be plotted in a way where the supposed geometry and the dynamics of the construction must exhibit relativistic behaviour as a function of the chosen coordinate system."

You could say that it is simply consequential to how persistent objects have been defined, that they exhibit such relationships. It doesn't matter what coordinate system you choose to describe those objects, but as long as they appear in speeds less than C in one coordinate system, they must appear in speeds less than C after transformation to any coordinate system.

Using a “earth rest frame of reference map of the universe” together with a ship time clock for time measurements, we can achieve any velocity right up to infinity and, strange as it might seem, we can use Newtonian physics to plot our course through the universe. That is an interesting consequence of using that mixed coordinate system.

Hmmm, yeah that is interesting idea.

I suspect, if humans ever do achieve interstellar travel, they will use my geometry for plotting their course; it is much simpler than using Einstein's picture. For any physicists reading this note that one “g” acceleration (in the mixed coordinate system) is not one “g” acceleration in the ships frame so the standard relativistic comparisons are not valid. (I just pointed that out because I know you will do the relativistic calculations and point out my answer is different).

My brain went all twisty and it's late so I can't figure this out; would the ships acceleration in the mixed coordinate system show up as constant if it shows up as constant in the ships own measurement?

But one interesting thought that popped to my mind while thinking about this was that all the massive things in the universe appear to be quite close to being rest against each others... I mean, shouldn't we expect massive things to form quite uniformly across "all the inertial frames" so to speak. And if they were spread across all inertial frames in somewhat uniform manner, then from our perspective, most galaxies etc, should appear to be moving at very near the speed of light, so close that they would be almost indistinguishable as galaxies... Hmmmmm, my brain went all twisty again.

But back to the reason I mentioned this case. It is much easier to see rapid travel as “forcing” one into the future instead of in terms of a limiting velocity. For example, Alpha-Centauri is roughly four light years away. It is somewhat surprising that one “g” (32 feet per second per second) is almost exactly equal to one light year per year per year. So if we accelerated off towards Alpha-Centauri at one “g” (as measured on our mixed coordinate system) until we got half way there (two light years) it would take two years (ship time). We could then de-accelerate for another two years and arrive at rest at Alpha-Centauri. We could spend what time we needed there and then return to earth in another four years (ship time). So we would say the round trip was eight years long. How much time would pass on earth?

The answer is quite simple: our actual path in my space would be four segments, each two light years in the x direction plus two light years in the tau direction, c being one light year per year. Since these directions are orthogonal to each other, our actual total distance of travel would be light years. So the earth observers would say the trip took roughly eleven years and four months. That is, we could see ourselves as being forced into the future a distance of roughly three years and four months.

Suppose we wanted to go to the other side of the galaxy, some 200,000 light years away. Half way would be 100,000 light years; =447 years so, at one “g” it would take roughly 1,800 years ship time for the round trip. At four g's (something the crew could probably get used to) we could do the round trip in roughly a little over 900 years (ship time). But how long would we be gone, earth time? which is roughly 410,000 years. Just a tad short (by a mere 10,000 years) of the apparent speed of light. In this case we have been pushed about 409,100 years into the future. But what will the crew say their velocity was? They went some four hundred thousand light years in a little over 900 years. That would be almost 450 light years per year.

Seems like a fairly simple way to figure out these things.

You should notice that “tachyons” don't exist in my representation. “Apparent” velocities in excess of light are just plain -???- “not possible” -???- (see the above analysis). That is one reason I do not like Einstein's picture: it suggests the existence of phenomena which violate the logic of his own construct. A very poor characteristic for any theory to contain.
We started with the expression

Yeah it's a bit mixed up concept because people usually keep talking about tachyon's "motion" and "speed", but really the only coherent way to incorporate the idea of tachyons into the picture is just to take something in the past as being affected by something that "happened in the future", i.e. think of it in terms of static spacetime... No matter which way you discuss that concept, it makes zero sense to talk about their motion. I think the idea they have in their head is literally a spacetime changing as a function of another time over and beyond spacetime. I would advise a person to take a deep breath and start over at that point :I

subtracting from both sides, we obtain

and then dividing by one obtains

And that should take you to the end of the OP.

Okay, that's pretty clear now, it was just a procedure I had never seen before and didn't pop into my mind. I'll try and walk through the rest of the OP soon...

I just read your latest post and agree with most all of it; however, I don't think it would be possible to chart a path which would allow you to party all the time by accelerating your ship in a manner where it would be the New Year's Eve on earth all the time! The general relativistic transformation has to yield a stopped clock on the earth as seen from your ship! That, I think might require an infinite acceleration. But maybe you could get far enough away from the earth such that there was enough mass between you and the earth to yield a black hole solution.

Heh, "slightly" out of my depth to work that out, and certainly things get complicated when you start taking all things into consideration... I was intentionally just thinking about it in terms of special relativity and with the idea of changing continuously from one inertial frame to another when you are accelerating, where you'd just assume the simultaneity of that frame (and if you are a party-loving hippie, that's probably the interpretation you want to use

But yeah, even then you couldn't keep it up absolutely forever no matter how far from earth you started :I Well, pretty long party anyway!

At any rate, one more comment to all the lurkers. I'd think anyone can understand, that it makes very little sense to suppose that reality is affected by whichever coordinate system you choose to describe it. Reality probably is whatever it is no matter how you plot it in your spacetime diagram, unless you want to go with some sort of idealistic philosophy.

Yet, the relativistic transformation between coordinate systems is valid. So, shouldn't one be interested to understand why?

At least I've been interested to find an answer to that question, therefore it is pretty hard for me to understand the reluctance to look at work which explains exactly that conundrum...

Maybe part of the problem is that people are drawn to mysterious views of the ontological reality... Look at almost any mainstream presentation of relativity / QM, it's always bunch of way too enthusiastic physicists talking about modern physics in ways that suggest very mysterious ontology to nature. They ALWAYS imply that this is the ontology that scientists have somehow practically proven to be true.

I guess, the more mysterious the presentation makes things sound, the more it sparks the interest of general public, and therefore those descriptions gain the most attention. Everybody loves the possibility of "Many-Worlds" and relativistic time and length contraction and 11 dimensions without understanding where those concepts are coming from...

-Anssi