An “analytical-metaphysical” take on Special Relativity!

[AnssiH]

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

Originally Posted by Bombadil

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 direction. That is, we want a point from which every one in a reference frame will agree on to measure their movement in the 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 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 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]

Originally Posted by Bombadil

.... However the clock has been shown to measure distance moved in the 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 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 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 direction, it also would measure (2) when A is at rest.

[AnssiH]

Originally Posted by Rade

I have a question. Suppose an object A that moves a distance C-->D in the 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 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 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 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]

Originally Posted by AnssiH

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.

Originally Posted by AnssiH

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.

Originally Posted by AnssiH

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?

Originally Posted by AnssiH

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 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.

Originally Posted by AnssiH

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]

Originally Posted by Bombadil

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"

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 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

[Bombadil]

Originally Posted by AnssiH

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".

Consider it like this suppose that one observer wants to measure the length of a train and he knows that he can’t be on both ends of the train at the same time he also knows that by the time that he receives a signal of where the front of the train is it will have moved. As a result one option that he has is to use a clock to describe the movement of the train and mark the end of it when he thinks that the other end is at a particular location lets say a flag that he placed earlier and then measure the distance between them. In order to do this he has to find a way to predict when the front of the train is even with the flag. In order to predict the location of the front of the train he will have to know how far it moves for every oscillation of his clock.

We will still have to define everything that was defined before and in the same way but it is a different way of doing the same thing. And we are now in a way hiding how we define simultaneity by defining the location of the train.

However it is done in order to define length one will define what a clock measures at the same time and this will result in a constant speed of the oscillator. But also in order to make measurements of a moving object one has to define a method of determining where the object is when it is measured or equivalently when to make measurements. It makes little sense to mark one end of a object then mark the other end of the object at a latter reading of a clock and say the distance between the two marks is the length of the object unless this is required for the definition of simultaneity that we are using.

Are there other ways to defining a coordinate system? I’m going to say yes, however, if we choose to use the fundamental equation this method will drop right out in a completely consistent way. And that is what we are really after, a consistent way that everyone can define a coordinate system.

Originally Posted by AnssiH

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.)

Yah, I can see how it could be seen like that although it seems that the idea of simultaneity could also be taken without the idea of space-time and rather be taken as a question of what interactions can occur between objects if they are traveling at some defined speed. This probably is not a common way of looking at things though.

Originally Posted by AnssiH

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

Yah, I haven’t been vary clear by what I mean. basically what I am saying is that any observers no matter what reference frame they are in, can agree on what the rest of the universe represents with only changes that have no consequences on what is being explained. That is, both observers can explain the rest of the universe in the same way up to a question of scale which has no effect on what the order that the rest of the universe has and a question of velocity which can have no effect on how the universe changes over time or the order of the universe. It can only have a effect on how the universe is explained and when they say a event happened.

In other words there is a way that even without defining a definition of length that two observers can determine if they are talking about the same collection of elements. We just have to remember that ideas like length and speed don’t exist yet. We are simply identifying that they are the same patterns of elements, and map one pattern to another in such a way that we can say that they are the same object.

So when I say that two observers agree on the location that a event takes place I mean for instance that if one observer says that a light on a moving train blinked when the light was even with a flag next to the train. All observers must agree that the light blinked when the light was next to the flag. Our coordinate system has nothing to do with if the light was next to the flag only when in our coordinate system the light blinked.

Originally Posted by AnssiH

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.

We are kind of straying from the original topic. Do you think we should back track and try to get back on the intended topic, just keep going like we are or do you think that we should move to the Dirac delta equation thread? Or is there something else that you think we should do?

Originally Posted by AnssiH

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

But are such things a consequence of cause happening after effect. Is it a case of taking space-time too seriously, or is it a question of how you interpret the equations? Either way I get the impression from that link that space-time is taken a little too seriously and time is considered nothing more then a axis of the equation. That is, there is no evolution parameter, it is a static model mapped in a four dimensional space.

I think you may also misunderstand what I mean by a signal traveling backwards in time. My understanding of the conventional view is that if a signal travels faster then light then it must arrive at the location that it was sent to before it was sent. Literally it is arriving at a earlier value of t, for instance let’s suppose that when it arrives we can then send a second signal back along the same path again faster then light, then it will arrive before the first signal is sent. My point is that this is not the case in the model that we are using. We can have waves that we say originate at a latter value of t and say that they travel backwards along t but this is all just a mathematical convenience. There is no reason or way to conclude that this is what reality is like and not just a mathematical convenience for what we are doing.

Further more there is no way for a signal that is only traveling faster then light to arrive at its destination at a point where less oscillations of our clock where counted then when we sent it unless it is traveling backwards along the t axis which seems to be more of an interpretation of the equations then a reality. The direction of travel along the axis has no effect on the equations. At least that is how I am understanding this. There is no backwards in time if a clock measures time. There is only waves traveling backwards along t which defines when elements interact and is our evolution parameter.

In looking at that Wikipedia page and following some of the links, I found what looks like an interesting result and link between the Schrödinger equation and Dirac equation threads. It appears to be a relatively obvious and necessary link but I’m not going to go into it in this thread as it is way off topic and will fit nicely into the Dirac equation thread.