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
