A Common Misunderstanding Of Special Relativity

[AnssiH]

I think that I was perhaps not entirely clear as to what I was referring to as it is the other equation that I was looking at and not from the question of what effect that this has on measurements, as I am well aware that it is more or less a rotation in a sort of hyperbolic space, just look into the hyperbolic sine and cosine functions. Rather my question is how will it effect what is actually seen. Currently I don't think that it will have any effect at all, as what is important is the actual length which is only going to be scaled and is independent of location.

If you go back to the video, what you see in the video is what is being plotted in terms of the pictured frame; this frame plots the moving rod as length contracted. That plotting will allow the two inner photons to pass through. There you go.

 

I suspect that we are actually very close to agreeing on what is actually seen, and that the real disagreement here is not on what is seen, but when it is seen, how simultaneity is defined and what a picture is. Actually I think it all boils down to the definitions that we are using and we really agree on the rest of it.

 

To try and explain what I mean I will use the thought experiment as you put forward in your video. Firstly the obvious, clearly both ships will see the side of the rod inside of the pipe. You have said several times that this is the case and I agree with you. Now for a few things that are not so obvious and I think could be pointed out better in the video.

 

Firstly the observer that is at rest with the pipe will see the rod pass though the pipe directly ahead of him and it will be possible for him to see the trailing side of the rod at this time, the thing to realize though, is that the observer that is moving will see a slightly different picture of the event. He will see that pipe as ahead and to the right of him, as you have it in the video, he will also be able to see the trailing side of the rod, the important part in my mind though is the location that they will see the rod inside of the pipe, as your video seems to be hiding this and rather assuming that both pictures will be the same because they are capturing the same photons.

Well no, that's not the intented implication. Even though it doesn't explicitly display so, little thought should reveal to the viewer that the moving camera will;

 

1. Also take a photograph where the tube and the pipe co-incide (its photograph is composed out of the same photons after all). Since the pipe is ahead of him, that's where the tube must also appear to be.

2. This is the same result as you get from aberration analysis

3. ...or from figuring out where the emission events are in the frame of the moving camera -> they must be ahead of the camera.

 

I will admit that the pictures must be conformal mappings of each other and that they must preserve casualty but the pictures will show the rod inside of the pipe in different directions from the front of the crafts.

Yup

 

I think that it is worth pointing out one or two other things, although I think that you already realize them. Firstly the observer at rest with the pipe will see the rod as longer when it is in the pipe then the observer that is moving. Why, well because he will see the hole thing taking place closer to him then the moving observer.

Yeah but that's completely besides the point if the question is "can length contraction be photographed". You must put the reference stick at the same distance in all cases, otherwise you are just asking if the same object photographed from different distances will have different size in the picture. Of course the objects further away will look smaller in the photograph itself.

 

Also the more that I think about it, the more that I have to conclude that the observer at rest with the rod will have to see the pipe as stretched when the rod is inside of it. Since if your video is correct and this event took place in front of the moving observer he would see the rod and pipe lengths reversed.

 

If you are having a hard time understanding what I am talking about just consider for a moment that when the observer at rest with the rod sees the pipe directly in front of him, he will see it as the same length as the observer at rest with the pipe see the rod to be when it is directly in front of him (inside of the pipe).

Yup.

 

Btw it occurs to me that "tube", "pipe" and "rod" are terrible labels for these objects - who knows what's what anymore - but I get what you are saying from the context :D

 

In my mind this is very counterintuitive and I really can't fully explain its cause although I am sure that it must be the case.

Yeah, you get these results from considering the time delays to the emission events. That is why a length contracted object may look elongated when its approaching, because the time delay to emission event varies across the length of the object. The same mechanism causes visual shrinking when the object is receding.

 

I have to wonder at this point if you have miss identified the path of the photons to the rest observer and that in fact the rest observer will see both the tube and the pipe as the same length from his vantage point. Put simply, when any object is seen at a right angel to the direction of travel it is seen as having the same length no matter how fast it is moving. How you have it right now Lorentz contraction would be visible.

Yeah, that's why I made the video, because it appears to be plainly true that you can photograph Lorentz contraction easily. It is also plainly true that there is a single moment for every passing object, where the visual elongation (while it is approaching) will exactly compensate for the Lorentz contraction.

 

In my previous post I described how to find this moment with plain symmetry arguments (the two identical objects moving from opposite directions at the same speed)

 

I have to ask at this point how did you generate the velocities in your picture?

I just arbitrarily chose C, and set the massive objects' speed to 86% of it.

 

If the above seems somewhat confusing try to understand I am trying to picture the video from the prospective of the other observer, and I would be very interested in a video from that prospective if you think you can make one, if you do try to make one remember that in that video the pipe is half the length of the rod.

 

I really would be interested in such a video as I think that it is more or less what is being assumed when I watch the video that you made.

Well it would be reasonably easy to do it but I don't have the software I was using at hand right now. I can do it later. But also you can get somewhere by imagining a coordinate system that is moving along with the moving camera, and think about the apparent paths of the photons in terms of that coordinate system. Take into account that the emission events that are simultaneous in the video, are not so in the other coordinate system; The moving camera composes its picture out of photons, whose emission events it doesn't take as having been simultaneous.

 

-Anssi

[Bombadil]

Hello. It does not appear that you understood my question. First it does not matter what I mean by the term rest length, my question concerns what you mean when you say....."rest length of an object, which is also nothing more then a consequence of the definitions that we use". OK, if as you say rest length of an object is a consequence of the definitions we use, then what are the definitions you say we use a consequence of? Sorry if i am not making myself clear.

It's not that you are not clear and its probably not me at least not from my point of view. I can't say what you think I said, but I think that it's that we don't agree on what is being discussed here, so let me try to clear things up, as I answered your question when I said

 

My first answer to this question would be that they are a convenient set of definitions that result in useful consequences,

 

but perhaps you see that as a somewhat quizzical statement so let me first say that I would be rather surprised if you and I use the same definitions of rest length although we might agree that we can use a particular definition for rest length and I think that we would agree on the rest length of an object.

 

You should try to understand that the idea that “ you and I use different definitions of rest length” and the idea that “we might agree that we can use a particular definition for rest length” are two very different ideas and are at the heart of the question that you asked. Furthermore there is no reason that both statements cannot be true, if you cannot understand this then I don't have any idea what to tell you as the remainder of my post is likely not to make any sense.

 

If you think that what I just said has no relevance then I suggest that you realize that we must be talking about two different ideas and I suggest that you try to understand why I said what I said.

 

What you need to try to understand is that definitions really are not a consequence of anything, they are a statement that is true whether or not it makes sense. On the other hand there is no reason for us to use a definition just because we can make it, and I don't expect any one in there right mind to use a collection of definitions that they know are not internally consistent although it is quite possible not to know that a set of definitions are not consistent.

 

What you have to understand is that as strange as what I just said sounds, it is in fact an answer to your question. Here I will say it again to be completely clear.

 

Definitions are not in themselves based on anything. They are a statement that is taken to be true no matter what they say.

 

If this answer wont satisfy you, you'll just have to ask a different question.

 

Bombadil, this part of the analysis is simply SR since it just involves tracing back the photon emission events. In the picture taken by the camera (which is flat against the ground btw), the wheel is going to look distorted the way it is described in the paper. But if you place a camera into the coordinate system of the axle, the wheel must look symmetrical. In fact taking the wheel as rotating only complicates the picture; you get the same distortion without rotation, just with linear motion of the wheel. Relativistic spinning wheel problems are just a massive headache... :I

 

Well unfortunately I have not had time to read the entire article and I'm not entirely sure if you are referring to the entire article or which particular part, however I think that you may very well be right in that only special relativity is needed. As for it being a headache, I think that it could be done as an extenuation of the derivation on page 84 of “the foundations of physical reality”. While I have not tried to do the corresponding derivation I suspect that it could be done without too much headache, although perhaps I am misunderstanding what is being asked. I think that the question is, “what will a rotating wheel look like as the outer rim approaches the speed of light”.

 

Well yeah, and a lot of the references seem to assume length contraction is just completely compensated out from the photographs once you trace back the emission events to get the appearance in the photograph. But the result you get from that analysis varies depending on where in the coordinate system you place the camera (e.g. whether the object is receding or approaching, and in what angle).

 

Well at least they admit that it will appear different then just length contracted. All in all I think that this is perhaps a touchy subject, and made no less touchy by what “science shows” say about it. Which is somewhere that you are suppose to get accurate information from. I really think that all of this trouble is due to scientists not really caring what something looks like and only being interested in the movement of the system.

 

I wrote the "same length" in quotation marks exactly because, like you, I also don't think it is good semantics to take conformal mapping as meaning "same length". I was wondering if they do in these papers. But if they don't, then conformal mapping just has got nothing to do with whether or not you can photograph length contraction, under the sensible definition for "length". So... It just seems like the semantical interpretation of these papers is all over the place.

 

As I said before I think that these papers where written by mathematicians and physicists for other mathematicians and physicists and trying to look at them in any other light will only lead to misinterpretation and incorrect results. If you understand the idea of a dot product then you should understand that the ideas of mappings that preserve length and angles are not completely unrelated however if you don't understand the idea of a dot product perhaps this is a topic better left for a different time as it is really just a lot of linear algebra and holds no direct significants unless we want to get particular about just what those proofs are saying, not that we shouldn't be this particular just that I'm not sure if there is any reason to right now.

 

 

Yeah, if it wasn't, it would not be self-consistent transformation; your expectations would be coordinate system dependent.

 

Well I don't think that I would go that far, rather I think that I would say that the transformation must include a force that is nothing more then an effect of the coordinate transformation if the transformation is not conformal. A few ideas come to my mind but nothing that I could say right off the top of my head if they are conformal or not. In any case I don't think that self consistency is what I would expect to lose but I might expect to lose elegance and simplicity. At this point I don't see any reason to go further into the topic unless we come across a transformation that is not conformal and we want to know if we can use it or not.

 

Well they both see the angles of the photons differently.

 

This is exactly what I was pointing out.

 

Well no, that's not the intented implication. Even though it doesn't explicitly display so, little thought should reveal to the viewer that the moving camera will;

 

1. Also take a photograph where the tube and the pipe co-incide (its photograph is composed out of the same photons after all). Since the pipe is ahead of him, that's where the tube must also appear to be.

2. This is the same result as you get from aberration analysis

3. ...or from figuring out where the emission events are in the frame of the moving camera -> they must be ahead of the camera.

 

While I will agree with you, I must say that I don't think that it is entirely obvious from the video. Although it shouldn't take too much effort to come to this conclusion, I suspect that it is very much the same situation as the people that think that Lorenz contraction is altogether invisible, that is not really the case either.

 

Also this seems to have an interesting side effect and that is that the object will in fact appear to just be rotating and will never truly appear to be out of proportion. Which is actually something that I have come across as well a few times.

 

Yeah, you get these results from considering the time delays to the emission events. That is why a length contracted object may look elongated when its approaching, because the time delay to emission event varies across the length of the object. The same mechanism causes visual shrinking when the object is receding.

 

Yeah, not something that I think is obvious but a little thought seems to reveal what is going on and that it must in fact be the case.

 

Yeah but that's completely besides the point if the question is "can length contraction be photographed". You must put the reference stick at the same distance in all cases, otherwise you are just asking if the same object photographed from different distances will have different size in the picture. Of course the objects further away will look smaller in the photograph itself.

 

I don't think that this is beside the point at all as your video makes it quite clear that the actual distance traveled by the photons is the same and that the actual source of the disagreement in the size of the object is not due to actual distance from the object, although the observers have every right to argue about this point, it is actually due to the Lorenz transformation effecting the size of the object that they see. Just as you have been pointing out both observers are in the same location and so must be receiving the same photons, and so they must have traveled the same distance to get to them and hence any disagreement must be a consequence of length contraction.

 

Well it would be reasonably easy to do it but I don't have the software I was using at hand right now. I can do it later. But also you can get somewhere by imagining a coordinate system that is moving along with the moving camera, and think about the apparent paths of the photons in terms of that coordinate system. Take into account that the emission events that are simultaneous in the video, are not so in the other coordinate system; The moving camera composes its picture out of photons, whose emission events it doesn't take as having been simultaneous.

 

Well, it is quite a bit clearer now that I have thought about it for a while. Still, I think that if you get the opportunity it might make a good addition to the video that you have already made. Just a thought.

 

Now back to the original question of “will a moving observer and a rest observer see the stars as the same distance from them” and it seems that the answer must be, yes they will agree on the distance to the stars although they may not agree on the direction to the star and hence the actual location that it is at.

 

There is just one thing that is troubling me about this answer, and that is, if the observer that is moving towards the star decides to measure his speed by making a series of measurements of the distance to a particular star and say he was traveling at a very large fraction of the speed of light, wont he say that he is in fact traveling far faster then the speed of light?

[Grains4]

I have skipped everything that was said in here.  The reason why?  Cause I "googled" a specific topic on special relativity and found my answer.

 

"In 1905, however, when Einstein first introduced it, it was a strange and even shocking theory . it was strange and mocked.  

 

Ha!  Disproved and denoted.  See.  

 

You can go through most things in history and take like a sentence or a phrase or even a limerick or two, when taken out of context, the whole theory falls through.

 

Pick it apart for where it was written.......along in history you will soon be forgetten.

[Eclogite]

I have skipped everything that was said in here. 

I am forming the impression, based on this and your other posts, that this is a lifestyle choice that extends well beyond the confines of this thread.

 

Cause I "googled" a specific topic on special relativity and found my answer.

1. You don't think it might promote the effectivenes with which your message is conveyed if you told us what your question was? You found an answer - to what?

2. Oh, my. You know how to use google! The important question is, do you know how to critically assess what you read, or are you solely driven by an ill-informed, evidence-free, angst-ridden agenda?

 

"In 1905, however, when Einstein first introduced it, it was a strange and even shocking theory . it was strange and mocked.  

 

Ha!  Disproved and denoted.  See

I recommend you when you leave school you seek manual work. Your writing is inadequate for any work requiring clarity of communication.

 

My best guess of what you are trying to say is that because some people were puzzled and shocked by Einstein's introduction of relativity that it has therefore been disproven. If that is not what you mean, then please explain clearly. If that is what you mean - then don't be silly.

[AnssiH]

Well at least they admit that it will appear different then just length contracted. All in all I think that this is perhaps a touchy subject, and made no less touchy by what “science shows” say about it. Which is somewhere that you are suppose to get accurate information from. I really think that all of this trouble is due to scientists not really caring what something looks like and only being interested in the movement of the system.

Perhaps. It is important to at least recognize that when it comes to discussion about relativity, it is completely impossible to avoid some very unfortunate ambiguities regarding what something "is" and what something "looks like". For example, if you say "time dilation is real", you may be seen as implying it is more than a consequence of coordinate transformation. On the other hand, if you say "time dilation is only apparent", you may be seen as implying it is a visual illusion. And proper interpretation is neither, a proper interpretation can only be reached by understanding the theory already. So, what can a man do...

 

Well I don't think that I would go that far, rather I think that I would say that the transformation must include a force that is nothing more then an effect of the coordinate transformation if the transformation is not conformal.

I don't know what this means... If by force you mean something that has got a measurable effect in some sense, surely you cannot expect to create a demonstrable force just by choosing to represent some situation from a different coordinate system. The whole point of coordinate transformations is to yield the same data form different reference point. So, any set of data points must imply the same measurable effects from any coordinate system if your coordinate transformations are self-consistent... If they are not, then you can trivially demonstrate different reference points have different expectations for the same data points... that is, you demonstrate the invalidity of a theory.

 

Perhaps I completely misunderstand what you mean though.

 

I don't think that this is beside the point at all as your video makes it quite clear that the actual distance traveled by the photons is the same and that the actual source of the disagreement in the size of the object is not due to actual distance from the object, although the observers have every right to argue about this point, it is actually due to the Lorenz transformation effecting the size of the object that they see.

 

Just as you have been pointing out both observers are in the same location and so must be receiving the same photons, and so they must have traveled the same distance to get to them and hence any disagreement must be a consequence of length contraction.

Wait a minute... the "actual distance" traveled by the photons is not the same across coordinate systems. Or rather, the use of the word "actual" is quite dangerous here because "actual distance" really just depends on your definition of a coordinate system. Of course if you measure the distance in one or the other coordinate system, you come up with different result.

 

So for the moving observer, since he sees the object where it "was" in some earlier time in his coordinate system, in his picture - even though it is composed of the same photons - he will indeed picture the object as further away than the stationary observer.

 

Here we come to see another funky aspect of "semantics". See, it kind of doesn't make sense to propose that in one picture the object is further away than in the other just because the photons appear into the picture frame in different angles. But on the other hand, what we mean by "distance" must be carefully defined in epistemological sense! And what we mean by "distance" as a measure within a coordinate system, will in fact *require* that we also say the object is further away in one picture than it is in the other.

 

If this sounds odd, you are just confusing coordinate systems with reality :) In "reality" the "actual distance" of the "same thing" of course cannot change according to your choice of coordinate system. Something very many people have troubles grasping.

 

There is just one thing that is troubling me about this answer, and that is, if the observer that is moving towards the star decides to measure his speed by making a series of measurements of the distance to a particular star and say he was traveling at a very large fraction of the speed of light, wont he say that he is in fact traveling far faster then the speed of light?

Yes if he is measuring his speed by assuming the distances are not shrinking in his coordinate system. But if he is using the relativistic definitions, he would of course say the distances have shrunk, allowing him to say that travel distance/time is still not exceeding C.

 

Of course the same thing applies here; coordinate systems are not reality. Coordinate transformations are self-consistent transformations to *your* own definitions, not to reality. Because of how you define things in relativity, you are required to length contract fast moving objects, meaning you are required to length contract the rest of the universe as you are traveling through it.

 

But the fact that you are doing something does not *actually* shrink anything else anywhere at all. The universe is not watching you and conveniently shrinking because you'd like it to. You will not exceed C because of how you define C. Yet, you will in fact get across 10 ly distance in less than 10 years according to your own clock, because of how you define distance.

 

-Anssi

[Rade]

To Bombadil:

 

You make this claim:

 

[edit]  "definitions really are not a consequence of anything"

 

I do not agree. 

 

Thank you for your clarification.   

Edited March 4, 2015 by Rade

[Bombadil]

To Bombadil:

 

You make this claim:

 

[edit]  "definitions really are not a consequence of anything"

 

I do not agree. 

 

Thank you for your clarification.   

 

 

Well to each his own but just out of curiosity, What do you think that the definitions that you use are a consequence of ?

I am of course speaking of the very fundamental, most definitions that you use. For instance what did you originally base your definition of the word “length” or “rest” on, or for that matter rest length. Note that I am not asking what rest length is but rather what it is that you base your definition of it on, a very different idea.

 

 

Perhaps. It is important to at least recognize that when it comes to discussion about relativity, it is completely impossible to avoid some very unfortunate ambiguities regarding what something "is" and what something "looks like". For example, if you say "time dilation is real", you may be seen as implying it is more than a consequence of coordinate transformation. On the other hand, if you say "time dilation is only apparent", you may be seen as implying it is a visual illusion. And proper interpretation is neither, a proper interpretation can only be reached by understanding the theory already. So, what can a man do...

 

 

 

Not much that can be done, as to understand it someone has to have both the ability to understand it the time to put into it, and must avoid the very points that you are bringing up. So, there is very little that can be done. Furthermore it is quite possible for someone to think that they understand it and in fact completely misunderstand it.

 

 

 

 

I don't know what this means... If by force you mean something that has got a measurable effect in some sense, surely you cannot expect to create a demonstrable force just by choosing to represent some situation from a different coordinate system. The whole point of coordinate transformations is to yield the same data form different reference point. So, any set of data points must imply the same measurable effects from any coordinate system if your coordinate transformations are self-consistent... If they are not, then you can trivially demonstrate different reference points have different expectations for the same data points... that is, you demonstrate the invalidity of a theory.

 

Perhaps I completely misunderstand what you mean though.

 

 

I think that there is a misunderstanding here, the most trivial example that I can think of is spinning a disc above your head, now choose coordinates so that the disc is stationary in them, it shouldn't be too hard for you to see that this can be done so I won't go into details here. In this way we have defined a set of coordinates so that every point experiences a force towards the outside of the disk. Now plot the trajectory of a ball that is released from the disc. It should not be hard for you to to understand that in these coordinates the trajectory must be different then from the trajectory that we get if we consider the disc to be what is spinning. The difference must be made up for with a force. I believe that this is called a pseudo force and it exists because of the coordinates that we have chosen.

 

I think that you can get the idea from what I just said or you could look up pseudo force, in any case I don't think that is anything to be concerned with right now. Actually I believe that doctor dick mentioned this idea in the thread about gravity.

 

 

Wait a minute... the "actual distance" traveled by the photons is not the same across coordinate systems. Or rather, the use of the word "actual" is quite dangerous here because "actual distance" really just depends on your definition of a coordinate system. Of course if you measure the distance in one or the other coordinate system, you come up with different result.

 

 

OK let me rephrase it then, ether observer will say that the distance traveled by the photons to arrive at one of the observers is the same for both observers as they can directly measure this in their coordinate system and will never have need to use a different one, however they will say that the other observer is going to see the object differently and rather then saying that this is due to some change in distance they will say that this is due to the Lorentz transformation.

 

Maybe I'm wrong but I find it hard to think that someone would actually argue that the distance that the photons travel is different for them to reach the other observer although I suppose there is no reason that you can't argue this. I mean we can't ask the photon if it had to travel longer to get to the other observer. But I wouldn't argue that they did.

 

 

If this sounds odd, you are just confusing coordinate systems with reality :) In "reality" the "actual distance" of the "same thing" of course cannot change according to your choice of coordinate system. Something very many people have troubles grasping.

 

 

I think that we are talking about the same thing here and there is no misunderstanding.

[HydrogenBond]

One thing that is not fully considered with motion and relativity, is energy conservation.  If I am sitting on a moving train or if I am stationary at the station, although the velocity effects are relative, an energy balance is not. If I am stationary, I will see the train moving at V. If you are in the train, you see the station moving at V. Each has different energy. One of the two references will violate the conservation of energy, and therefore might unknowing do magic tricks with imaginary energy. 

 

In a particle accelerator, as we approach the speed of light, the half life of light isotopes will slow due to the time dilation. Relative to an energy balance, only the moving particles have this energy, therefore their timed dilatation is real. From the reference of the particles, one may also see all the half lives of particles in the lab facility slowing, but the energy needs for this will violate energy conservation. This is not real, but is more of an illusion, since it implies more energy than was available. 

 

One has to do an energy balance to see which is real and which is an illusion. 

Edited April 17, 2015 by HydrogenBond

[Doctordick]

HydrogenBond, please explain exactly how you would propose to "do an energy balance"?

[AnssiH]

Not much that can be done, as to understand it someone has to have both the ability to understand it the time to put into it, and must avoid the very points that you are bringing up. So, there is very little that can be done. Furthermore it is quite possible for someone to think that they understand it and in fact completely misunderstand it.

Yeah this is not only possible but quite regular occurrence in all human communication and attempts to understand just about anything. Especially the nature.

 

 

 

 

 

I think that part of the point is that the Lorenz transformation wont preserve length, but it is suppose to be a conformal mapping at least that is what Terrell said in his paper and I suspect that this is actually a true statement about the Lorentz transformation although this perhaps says nothing about what will be seen.

Yeah, if it wasn't, it would not be self-consistent transformation; your expectations would be coordinate system dependent.

 

Well I don't think that I would go that far, rather I think that I would say that the transformation must include a force that is nothing more then an effect of the coordinate transformation if the transformation is not conformal.

 

I don't know what this means... If by force you mean something that has got a measurable effect in some sense, surely you cannot expect to create a demonstrable force just by choosing to represent some situation from a different coordinate system. The whole point of coordinate transformations is to yield the same data form different reference point. So, any set of data points must imply the same measurable effects from any coordinate system if your coordinate transformations are self-consistent... If they are not, then you can trivially demonstrate different reference points have different expectations for the same data points... that is, you demonstrate the invalidity of a theory.

 

I think that there is a misunderstanding here, the most trivial example that I can think of is spinning a disc above your head, now choose coordinates so that the disc is stationary in them, it shouldn't be too hard for you to see that this can be done so I won't go into details here. In this way we have defined a set of coordinates so that every point experiences a force towards the outside of the disk. Now plot the trajectory of a ball that is released from the disc. It should not be hard for you to to understand that in these coordinates the trajectory must be different then from the trajectory that we get if we consider the disc to be what is spinning. The difference must be made up for with a force. I believe that this is called a pseudo force and it exists because of the coordinates that we have chosen.

 

Ah I see what you were referring to.

 

I added the earlier exchange above for clarity, to point out what I was referring to exactly.

 

You mentioned Lorentz transformation being conformal, and when I think about Lorentz transformation I'm thinking of transformation between two inertial frames only. Rotating frames are somewhat ill-defined concept in this regard because each point in a rotating coordinate system represents also a different inertial frame. Sure, it leads into a pseudo-force concepts if they are chosen for mapping data in.

 

But going back to straightforward application of Lorentz transformation between inertial frames, if you take a snapshot of some space-time coordinate system with bunch of events marked down on it, and draw light connections between the events, you can see kind of a mesh or a topology between events. Every event "communicates" via these light connections exclusively, and you draw each connection in the same angle (representing your idea of isotropic C).

 

Now, obviously you can transform this picture into any shape or form, so long as this same topology between events is preserved. As long as it is preserved, no natural observer can possibly detect any difference; anything they can measure is mediated to them via the connections that all look the same to them regardless. Any self-consistent mapping between inertial frames must preserve the connections, but not necessarily isotropic C.

 

Lorentz transformation is the particular transformation that preserves isotropic C too, so it preserves the angles of light connections across the entire pictre. It is basically just a matter of particular angle of scaling the entire picture (so not to change the angle of light connections), which brings some events closer together or further apart, but does not change the existence of any connections. Thus, it can be always performed without changing any measurable effects to any natural observers.

 

This is what I was thinking of when you brought up it being confromal mapping, and my comment meant that if it was not conformal, it would be mapping that changes this topology of light connections; I thought being non-conformal would change your expectations as per chosen coordinate system.

 

Hmmm, I'm not really confident with non-inertial applications, but I suppose if we are conceiving some non-inertial situations in terms of infinitesimal inertial elements, and apply Lorentz transformations accordingly, we can still say that the light angles in the spacetime diagrams are preserved "locally" as well (meaning each infinitesimal element can consider the light speed as C immediately around itself). I suppose that would mean it would always be "conformal" mapping as well?

 

Well you know, who knows... Definitions, definitions.

 

OK let me rephrase it then, ether observer will say that the distance traveled by the photons to arrive at one of the observers is the same for both observers as they can directly measure this in their coordinate system and will never have need to use a different one, however they will say that the other observer is going to see the object differently and rather then saying that this is due to some change in distance they will say that this is due to the Lorentz transformation.

 

Maybe I'm wrong but I find it hard to think that someone would actually argue that the distance that the photons travel is different for them to reach the other observer although I suppose there is no reason that you can't argue this. I mean we can't ask the photon if it had to travel longer to get to the other observer. But I wouldn't argue that they did.

Well I mean, the path taken by a photon is traced quite differently in different inertial frames.

 

Say, you are standing directly under the sun, 10 light seconds away from it, and the sun is at rest in your frame.

 

You would say a photon traveled a distance of 10 light seconds to get to you.

 

Add an observer moving very fast by you directly from the side, and catching the same photon. In his coordinate system the photon approached in sharp angle from the front (which is also where he sees the sun).

 

In his coordinate system also you are exactly 10 light seconds away from the sun, standing directly below it (he agrees with your measure there). Albeit he can't see the sun directly above you because he sees it how it was in earlier time (Or just consider aberration).

 

So you can imagine, tracing that same photon in his coordinate system creates a diagonal path, which must be longer than 10 light seconds.

 

Yet it's the same photon that traces exactly 10 light second path in your coordinate system.

 

Definitions, definitions... Anything is whatever we say it is if we can come up with a self-consistent explanation.

 

-Anssi

http://foundationsofphysics.blogspot.com/

[HydrogenBond]

HydrogenBond, please explain exactly how you would propose to "do an energy balance"?

 

The only way to do this is to use a reference that is not relative; speed of light. This is the same for all references and can serve as a standard to compare apples to apples.

 

Say we have two similar mass rockets, out in space, with relative velocity V. If neither knew which had used their thrusters and therefore who contained tangible momentum, either can assume they are stationary or moving. In all cases, the  energy balance is maintained. 

 

Say instead, one rocket has mass=m and the other mass=2m, relative velocity can no longer define the energy balance, since one scenario has twice the kinetic energy. If might or consensus politics is right, we can end up with extra energy, less energy or exactly the right amount of energy, like in the three bears and goldilocks. In this fable, one porridge is too hot, the other too cold and the third was just right. 

 

If we calculate too little energy, the theory of the universe might have observations then need an invisible vacuum cleaner that removes energy. If the energy is too high, we may need an extra invisible energy to account for observations. If we choose the speed of light, as the standard, goldilocks finds the baby bear's porridge. 

Edited May 6, 2015 by HydrogenBond

[Rade]

Well to each his own but just out of curiosity, What do you think that the definitions that you use are a consequence of ?

I am of course speaking of the very fundamental, most definitions that you use. For instance what did you originally base your definition of the word “length” or “rest” on, or for that matter rest length. Note that I am not asking what rest length is but rather what it is that you base your definition of it on, a very different idea.

Sorry for slow reply.   Imo, definitions are a consequence of the process of explanation of the meaning of a concept (e.g., a word).    Thus, to answer your question, one would base their definition of 'length' on the process of providing explanation to others the meaning of the concept 'length'. 

[Doctordick]

Hi Bombadil,

 

Sorry I haven't communicated with you for so long. I am curious as to whether or not you still read this forum. You are one of the few people who has some comprehension of what I am talking about. 

 

The major reason I am posting this is that I have become aware recently of exactly what the public is misinterpreting about my posts. I could use your assistance in clarifying the issue.

 

Have fun --Dick

[sluggo]

 

The static frame has the detector aligned to light beam from source at x=0.
The entrance hole is fixed at 2 units from x axis. The detectors are adjustable vertically.
The second opening is redundant.
As the ship moves in the +x direction, the beam will form a smaller angle with the x axis, intersecting the front panel closer to the floor. If the container experienced length contraction, it would increase the departure from the detector.
d=distance from source to detector, f=distance of beam to floor at front, s=ship length
case 1: d=sf/(f-2) = 40/2=20
case 2: d=30/1=30
If h=f-2, and s=30m, then h=sb/(d-s)
If d=10^6 m then h=.06mm.
Using distance to the sun, h=4(10)^-10, effectively parallel.
This method would only be effective for a very short astronomical range.

[HydrogenBond]

Clocks moving in orbit around the earth will slow slightly. This has been used to demonstrate relativity.

 

The question becomes, if reference is relative do all the clocks on the entire earth also slow down, because someone in orbit, near the space clock, is using relative reference and is pretending the earth is moving? 

 

The answer is no. Only the clock in orbit will show a tangible time change. Space clock show there is a preferred reference. This is based on energy. Only the clock on the rocket used extra energy to get into motion. 

[A-wal]

The question becomes, if reference is relative do all the clocks on the entire earth also slow down, because someone in orbit, near the space clock, is using relative reference and is pretending the earth is moving?

The clocks on Earth are slowed in relation to a clock in orbit, because of gravitational time dilation.

 

The answer is no. Only the clock in orbit will show a tangible time change. Space clock show there is a preferred reference. This is based on energy. Only the clock on the rocket used extra energy to get into motion. 

There is no preferred frame of reference! You can use any object in inertial motion and construct a frame of reference around it and it's at rest in that frame. Objects can only move in relation to other objects. Movement is defined by a change in the amount of space that separates objects.