If correct: a catastrophe in the Lorentz transformation

[aawahab76]

R' and R are two events which are lightlike separated, therefore they cannot occur at the same time. You are just experiencing some roundoff error and you probably have to use an arbitrary precision math package and look at the 10th decimal place to see the difference. I haven't checked your numbers, but I provided some numbers in a previous post which you can use to compare.

i) because O and P are spacelike separated, as we have already discussed
ii) it is a small difference in time, as I said several times already
iii) it does reduce to the Galilean transformation in the limit as c -> infinity

The following is the exact calculation but the gamma factor which is very small was deleted and because it is a multiplicarive factor in all numbers below, it will not affect any equality result if it is there
- R is (10^100/(3*10^8)=((10/3)*10^92 sec, 0) in F so in F' it is ((10/3)*10^92 sec,-10^91 m)
- R' is (1-(1/3)*10^82+(1/3)*10^92-(0.03/3)*10^(-8), 0')=((1-10^(-10))(1+(1/3)*10^92) sec,0') in F' but in F is given by ((1-10^(-10))(1+(1/3)*10^92) sec, 3*10^(-2)*(1-10^(-10))(1+(1/3)*10^92))

So what you said is true. However, for the moment, this is not related to our problem as I stated it in the list above but I think I can add to the list
14- As measured by the corresponding frame, P happened in very different times, but at approximately the same spatial location and received in approximately the same time by each observer. I am not yet intending any physical interpretation of this observation, if it is correct.

 

[bobc2]

The following is the exact calculation but the gamma factor which is very small was deleted and because it is a multiplicarive factor in all numbers below, it will not affect any equality result if it is there
- R is (10^100/(3*10^8)=((10/3)*10^92 sec, 0) in F so in F' it is ((10/3)*10^92 sec,-10^91 m)
- R' is (1-(1/3)*10^82+(1/3)*10^92-(0.03/3)*10^(-8), 0')=((1-10^(-10))(1+(1/3)*10^92) sec,0') in F' but in F is given by ((1-10^(-10))(1+(1/3)*10^92) sec, 3*10^(-2)*(1-10^(-10))(1+(1/3)*10^92))

So what you said is true. However, for the moment, this is not related to our problem as I stated it in the list above but I think I can add to the list
14- As measured by the corresponding frame, P happened in very different times, but at approximately the same spatial location and received in approximately the same time by each observer. I am not yet intending any physical interpretation of this observation, if it is correct.

aawahab76,

I don't think the signal from event P is received at approximately the same time by each observer. Now, R' as given in the F frame (refer to my sketch) is approximately R'--maybe that is what you are thinking.

 

[aawahab76]

aawahab76,

I don't think the signal from event P is received at approximately the same time by each observer. Now, R' as given in the F frame (refer to my sketch) is approximately R'--maybe that is what you are thinking.

Thanks and you are correct (in F, R time is 10 times that of R'). The new corrected list is:

1- An observer in the x-frame has built his frame with the usual rulers and synchronized clocks (by the known method of Poincare and Einstein) with coordinates (t,x). We call this observer and its frame F. I think it would be understood when F ( and similarly for F' below) means the frame or the observer (located at the origin of spatial coordinates).
2- The same has been done by the x'-frame observer with coordinates (t',x'). This is called F'. F' moves with the speed v=10^(-10) m/s with respect to F (so F moves with the speed -10^(-10) m/s with respect to F").
3- An event is an absolute physical process and is independent of coordinates (or frames). An event can be represented in coordinates given by the reading of the clock and the reading of the ruler located at the event. This is done separately by each observer using his or her coordinates.
4- F and F' agree to set their time coordinates such that the event of their meeting is given by (0,0) in F and by (0',0') by F'. (0,0) is named O, and (0',0') is named O'.
5- An event P happen at (t,x)=(1 sec, 10^100 m) in F and at (t',x') in F' ( that is in F, P happened after O). We assume that the event is a flash of light.
6- The Lorentz transformation gives the corresponding coordinates of P at F', that is (t'≈-10^81 sec, x'≈10^100 m).
7- F receives the light from P at the event R given in F by (10^100/(3*10^8)=3.3*10^92 sec, 0).
8- Using the Lorentz transformation, R is given in F' by ((10/3)*10^92 sec,-10^91 m).
9- F' receives the light from P at the event R' given by ((1-10^(-10))(1+(1/3)*10^92) sec,0').
10- R' is given in F by using Lorentz transformation by ((1-10^(-10))(1+(1/3)*10^92) sec, 3*10^(-2)*(1-10^(-10))(1+(1/3)*10^92)).
11- In summary, in F we have the following events O, P, R and R'. Order of these events is O, P, R' and R (any way R and R' order may not be important).
12- Similarly, in F’ we have O’, P, R’ and R. Their order is P, O’, and R' and R (any way R and R' order may not be important).
13- Thus, our original problem can be cast in the following threefold points:
i- how does O before P in F but P before O' in F' (notice that O' is the coordinate representation in F' of the same event O)?
ii- why does a very small relative speed lead to such a huge difference in time for the event P in F' relative to F?
iii- why the Lorentz transformation (LT) does not in general reduce to the Galilean transformation (GT) ( but I think this may not be true if we define the non-relativistic limit to be the limit when c goes to infinity in which case LT reduces in general to GT). Any way, this third point may not be of interest at this moment.
14- As measured by the corresponding frame, P happened in very different times, but at approximately the same spatial location and R' was received in ten times less than in R. I am not yet intending any physical interpretation of this observation, if it is correct.

 

[Dale]

i- how does O before P in F but P before O' in F' (notice that O' is the coordinate representation in F' of the same event O)?
ii- why does a very small relative speed lead to such a huge difference in time for the event P in F' relative to F?
iii- why the Lorentz transformation (LT) does not in general reduce to the Galilean transformation (GT) ( but I think this may not be true if we define the non-relativistic limit to be the limit when c goes to infinity in which case LT reduces in general to GT).

These have all been answered. Are you unclear about the answers?

 

[aawahab76]

These have all been answered. Are you unclear about the answers?

A side from point 3 which is now settled and can be omitted, the answers given for the first two points are the usual graph-LT equation method (I do not know a name for such method), a method which I believe does not satisfy our physical intuition (specially point 1). Notice that the graph-LT equation method is completely accepted and our discussion as I stressed more than once should not be concentrated on that very understood solution but should be directed toward a more physically clear one. Yes, at the end we may find our self forced to accept the graph-LT equation method in the lack of any physically appealing picture (as I believe we do in quantum mechanics in many of its non-intuitive concepts).

 

[Dale]

the answers given for the first two points are the usual graph-LT equation method (I do not know a name for such method), a method which I believe does not satisfy our physical intuition (specially point 1).

We call it the "geometric interpretation" or "Minkowski geometry". I personally find it very intuitive and satisfying.

If you don't find it intuitive then you need to understand that your physical intuition is not reliable and that satisfying it is not a requirement nor even a goal of a correct theory of physics.

 

[JesseM]

A side from point 3 which is now settled and can be omitted, the answers given for the first two points are the usual graph-LT equation method (I do not know a name for such method), a method which I believe does not satisfy our physical intuition (specially point 1).

I gave you answers not involving graphs or the equations of the LT, but rather involving the fact that each observer uses their own set of rulers and synchronized clocks to assign position and time coordinates to events using local measurements, and that the method each observer uses to synchronize their own clocks ensures that each observer will measure the other observer's clocks to be out-of-sync, with the amount that two clocks are out-of-sync being greater the larger the distance between the clocks. Are you unconvinced that this physical method will provide coordinates that match those of the abstract Lorentz transformation? Or do you think this give an adequate physical picture of where the coordinates of the Lorentz transformation come from, but you think that this method of synchronizing clocks is problematic since it doesn't match your own physical intuition (not 'our' physical intuition, speak for yourself) that there must be some objective truth about which of two events happened first?

Keep in mind that as a philosophical matter you are free to believe there is some "metaphysical truth" about simultaneity, so that there is one frame whose definition of simultaneity is "metaphysically correct" while others are "incorrect". But the Lorentz-invariance of the laws of physics implies that all physical experiments will give the same result in every frame, so no experiment can pick out a preferred frame or a preferred definition of simultaneity, thus even if some frame is "metaphysically preferred" and its judgments about the order of events are more "correct" than other frames', we could never discover which frame that is! This is why I asked in post #29 whether you understood the meaning of Lorentz-invariance, which you didn't answer:

Do you also understand the meaning of Lorentz-invariance? As long as the equations of all the fundamental laws of physics (quantum field theory, for example), are Lorentz-invariant, that implies that it should be impossible in principle for any experiment to pick out a preferred inertial frame, the equations of the laws of physics will look the same when expressed in the coordinates of any inertial frame. This implies that no possible experiment could pick out a preferred definition of simultaneity, although as I said earlier you are free to adopt some sort of metaphysical belief that there is a "real truth" about which of a given pair of spacelike-separated events happened earlier (or if they 'really' happened simultaneously), as long as you acknowledge that this truth couldn't be discovered by any possible experiment your view won't conflict with relativity (but metaphysically I prefer eternalism to presentism, so I don't see the need for there to be any objective truth about which events are simultaneous and which aren't).

 

[bobc2]

A side from point 3 which is now settled and can be omitted, the answers given for the first two points are the usual graph-LT equation method (I do not know a name for such method), a method which I believe does not satisfy our physical intuition (specially point 1). Notice that the graph-LT equation method is completely accepted and our discussion as I stressed more than once should not be concentrated on that very understood solution but should be directed toward a more physically clear one. Yes, at the end we may find our self forced to accept the graph-LT equation method in the lack of any physically appealing picture (as I believe we do in quantum mechanics in many of its non-intuitive concepts).

I think I understand your question now, aawahab76. I agree. The phenomena and mathematical description of special relativity and the space-time sketches are quite contrary to our physical intuition developed from our life in a slow 3-dimensional world understood for the most part quite well. And I don't think we have a solid "physical" (whatever that means) understanding of the phenomena we've been analyzing.

I think that special relativity is shrouded in mystery every bit as much as quantum mechanics. Of course many physicists feel like it's not the job of the physicist to make "physical" meaning out of nature, but rather just go about the job of observing and classifying the behavior of nature. Identify the way the world is working and develop the rules for making predictions.

If there were actually an ontological external 4-dimensional universe with 4-D objects populating it, that would allow you the possibility understanding special relativity at a deeper level. But of course that possibility is fraught with problems.

At this point you may have to just accept the phenomena and theory of special relativity the way it presents itself to us or else move to the philosophy department--at least when pursuing truth on this forum.

p.s. I sometimes think we physicists are a little hypocritical. Epcially when carrying on discussions in the context of General Relativity. We tend to imagine a curved 4-dimensional universe with curved world lines, geodesics, black holes, worm holes, closed curve time lines, etc. But, having completed our analysis and discussions, we then throw away the external "physical" 4-dimensional objects occupying a 4-dimensioanl curved universe with local patches of 4-D Lorentz transform spaces.

 

[aawahab76]

We call it the "geometric interpretation" or "Minkowski geometry". I personally find it very intuitive and satisfying.

If you don't find it intuitive then you need to understand that your physical intuition is not reliable and that satisfying it is not a requirement nor even a goal of a correct theory of physics.

Yes every body may have a different viewpoint on the meaning of "physical intuition" and thus may find some statement physically intuitive and satisfying as you do with regard to our problem while others do not. This also explain why intuition is not a goal of a physical theory as it is more or less subjective (at least to some extent). However, scientists always try to think in terms of a "physical intuition" of some meaning. This I believe not to be of a philosophical nature but rather originate from the ability to describe nature in some cases in more than one way. Think of describing gravitational interaction in terms of "action at a distance" and in terms of "particle exchange". Particle exchange seems to be more intuitive but if nature can not be described but by the action at a distance, then let it be. Again here a scientist here or there will always be working to find the more "intuitive" picture.

 

[Dale]

Yes every body may have a different viewpoint on the meaning of "physical intuition" and thus may find some statement physically intuitive and satisfying as you do with regard to our problem while others do not. This also explain why intuition is not a goal of a physical theory as it is more or less subjective (at least to some extent).

Exactly. You should focus on understanding the objective math and experimental data, not the subjective intuition. Reversing the priority would be a mistake.

In your case, the relativity of simultaneity seems to go strongly against your intuition. Therefore your intuition needs to change. Familiarity with the math and the data can help that.

 

[aawahab76]

I gave you answers not involving graphs or the equations of the LT, but rather involving the fact that each observer uses their own set of rulers and synchronized clocks to assign position and time coordinates to events using local measurements, and that the method each observer uses to synchronize their own clocks ensures that each observer will measure the other observer's clocks to be out-of-sync, with the amount that two clocks are out-of-sync being greater the larger the distance between the clocks. Are you unconvinced that this physical method will provide coordinates that match those of the abstract Lorentz transformation? Or do you think this give an adequate physical picture of where the coordinates of the Lorentz transformation come from, but you think that this method of synchronizing clocks is problematic since it doesn't match your own physical intuition (not 'our' physical intuition, speak for yourself) that there must be some objective truth about which of two events happened first?

Keep in mind that as a philosophical matter you are free to believe there is some "metaphysical truth" about simultaneity, so that there is one frame whose definition of simultaneity is "metaphysically correct" while others are "incorrect". But the Lorentz-invariance of the laws of physics implies that all physical experiments will give the same result in every frame, so no experiment can pick out a preferred frame or a preferred definition of simultaneity, thus even if some frame is "metaphysically preferred" and its judgments about the order of events are more "correct" than other frames', we could never discover which frame that is! This is why I asked in post #29 whether you understood the meaning of Lorentz-invariance, which you didn't answer:

Not really because you just used the essential structure behind the LT and graph to explain the same thing that equation and graph are doing (especially the definition of the simultaneity concept, they are all resulting from the same consistent structure of special relativity which I don not question here).
Regarding philosophy subject, I do not intend to delve in and I did not do before. My intention is "physical intuition" and at the moment when we cannot speak of any meaning of this intuition, then I must and will stop discussing the whole problem because at that time we will be outside the realm of physics. I do not believe that physical intuition is meaningless but yes whenever I speak of this, I mean my intuition and possible of those who believe in the same.
I believe that special relativity is a consistent structure so yes I do not question the ruler-synchronized clock method and the resulting LT but rather I am looking for a satisfaction that I call "intuitive physics" or if we can say I am looking for a different physically intuitive picture. Of course no one can be certain that special relativity is the final theory and that there is a more acceptable one hidden there (but strictly speaking I am not trying to find or discuss such theory in this post).
My issue is that I am not yet convinced (I am again do not questio LT ... etc) that when the two observers (using two frames as discussed above) meet, one frame (F) does not yet know of an explosion (that is there is no point on F that registered the explosion because it needs another second to do so) that was already registered in the other frame (F"). The two frames already built their global time coordinates t and t' and at each time point, each frame will register all events distributed on the x and x'-coordinates. So before observers meeting and at approximately , t'≈-10^81 sec in F', if we picture the whole x'-coordinates we will observe some where an explosion event. This explosion is real and I believe it must have been recorded by the x-coordinates some time before the observers meet. I want to understand the missing logic in this last statement.

 

[aawahab76]

Exactly. You should focus on understanding the objective math and experimental data, not the subjective intuition. Reversing the priority would be a mistake.

In your case, the relativity of simultaneity seems to go strongly against your intuition. Therefore your intuition needs to change. Familiarity with the math and the data can help that.

I do not think so. Yes science must be built on experiment and objective concepts but who said that intuition is completely subjective (as I said in my comment). I think it is better to have an intuitive picture (what ever that means) rather than less intuitive one.

 

[Dale]

I do not think so. Yes science must be built on experiment and objective concepts but who said that intuition is completely subjective (as I said in my comment). I think it is better to have an intuitive picture (what ever that means) rather than less intuitive one.

Your intuition is wrong, so why should we seek for a model which is intuitive to you? Your intuition needs to change, not the model.

 

[aawahab76]

Your intuition is wrong, so why should we seek for a model which is intuitive to you? Your intuition needs to change, not the model.

My intuition is not necessarily wrong, it could be the other way round, that is the theory is wrong (but certainly I am not putting any theory to the test of intuition). However, that is neither our aim here nor that there is any thing to make us believe so.
On the other hand, it is possible that our problem is related to the meaning of intuition itself or so but as I mentioned above I am certain that I accept "particle exchange" over "interaction at a distance" as an intuitive preference (of course if experiment and logic are satisfied by both). That might be subjective or due to experience or any thing else. Notice that when I say that intuitiveness is not necessarily a subjective matter I mean that sometimes "not being intuitive" could be a single that a mistake is hidden somewhere. If it is correct to say, sometimes we could find a mistake in some body logic by what we call intuition or some thing similar. So here I am using intuition concept as a constructive technique to discuss theories and ideas.

 

[JesseM]

My issue is that I am not yet convinced (I am again do not questio LT ... etc) that when the two observers (using two frames as discussed above) meet, one frame (F) does not yet know of an explosion (that is there is no point on F that registered the explosion because it needs another second to do so) that was already registered in the other frame (F").

How can a frame "know" anything? You're anthropomorphizing, only an individual with a brain (or some other information-processing system like a computer) at a distinct position in space can really be said to "know" about an event. If two observers meet at a single position, then either they are both inside the future light cone of an event or they're both outside the light cone, if they're inside then they both know about the event (and it happened at an earlier time-coordinate than their meeting in both frames), if their meeting happens outside the event's future light cone then they are both ignorant of it, even if in one observer's frame it happened at an earlier time coordinate than their meeting (in this case there is a spacelike separation between the event and their meeting, which is synonymous with the idea that their meeting is outside the future or past light cone of the event). Do you disagree with (or just doubt) any of this?

This explosion is real and I believe it must have been recorded by the x-coordinates some time before the observers meet. I want to understand the missing logic in this last statement.

Sure, in the frame where it happened earlier than the meeting, the synchronized clock at rest in that frame that was right next to the explosion as it happened (call it clock #1) showed an earlier reading than the synchronized clock at rest in the same frame (call it clock #2) that was next to the two observers at the moment they met. But the observer at rest in this frame will only learn about this later, when the signal from the camera next to clock #1 arrives at his own position (according to the scheme I outlined in [post=3114649]post 61[/post] which you seemed satisfied with). Here's the logic:

1. In order for the two frames to disagree on the order of the two events (i.e. the event of the explosion and the event of the two observers meeting), there must be a spacelike interval between the events

2. If there is a spacelike interval between events, then neither event lies in the other event's future light cone, so no signal traveling at the speed of light or slower could travel from one event to the other event

3. Thus, regardless of which frame you use, the signal from the camera that was next to the explosion as it happened (and which shows the reading on the synchronized clock next to the explosion) will not have had time to reach either observer at the moment they first meet, so they will both be ignorant of it.

 

[Dale]

My intuition is not necessarily wrong

Yes, your intuition is necessarily wrong. And until you intuitively grasp the relativity of simultaneity it will continue to be wrong.

This discussion about intuition has become stale. You have all of the math and logic and the experimental evidence. If you would like to discuss that then I am more than willing to help. If you wish to continue to whine about your personal intuition then you can do that without my assistance. Personally, I think that your priorities are completely backwards on this topic.

Your intuition is wrong, the sooner you accept that the sooner you can address it.

 

[aawahab76]

How can a frame "know" anything? You're anthropomorphizing, only an individual with a brain (or some other information-processing system like a computer) at a distinct position in space can really be said to "know" about an event. If two observers meet at a single position, then either they are both inside the future light cone of an event or they're both outside the light cone, if they're inside then they both know about the event (and it happened at an earlier time-coordinate than their meeting in both frames), if their meeting happens outside the event's future light cone then they are both ignorant of it, even if in one observer's frame it happened at an earlier time coordinate than their meeting (in this case there is a spacelike separation between the event and their meeting, which is synonymous with the idea that their meeting is outside the future or past light cone of the event). Do you disagree with (or just doubt) any of this?

Sure, in the frame where it happened earlier than the meeting, the synchronized clock at rest in that frame that was right next to the explosion as it happened (call it clock #1) showed an earlier reading than the synchronized clock at rest in the same frame (call it clock #2) that was next to the two observers at the moment they met. But the observer at rest in this frame will only learn about this later, when the signal from the camera next to clock #1 arrives at his own position (according to the scheme I outlined in [post=3114649]post 61[/post] which you seemed satisfied with). Here's the logic:

1. In order for the two frames to disagree on the order of the two events (i.e. the event of the explosion and the event of the two observers meeting), there must be a spacelike interval between the events

2. If there is a spacelike interval between events, then neither event lies in the other event's future light cone, so no signal traveling at the speed of light or slower could travel from one event to the other event

3. Thus, regardless of which frame you use, the signal from the camera that was next to the explosion as it happened (and which shows the reading on the synchronized clock next to the explosion) will not have had time to reach either observer at the moment they first meet, so they will both be ignorant of it.

Firstly, do you think that two events can be similtineuos with respect to a frame but not so with respect to a comoving observer in this frame? Does that make sense?

 

[JesseM]

Firstly, do you think that two events can be similtineuos with respect to a frame but not so with respect to a comoving observer in this frame? Does that make sense?

No, "simultaneous relative to an observer" is normally just a shorthand for "simultaneous in the observer's inertial rest frame", unless you're talking about the observer seeing the light from some pair of events simultaneously with their eyes (for example, if one star 200 light-years away in Earth's frame exploded in 1800, and another star 100 light-years away exploded in 1900, then on Earth we would see the light from these explosions simultaneously in 2000).

 

[darkhorror]

If you want to see it in a more "physical" sense seems like you should just start with the basic that the speed of light is constant. Use math in a way where you come up with a scenario that your looking to understand. Use the speed of light and how it works twards time dilation, length contraction,... not just looking at the math but the math came to be. That may help so that you can see what's happening in a more physical way.

It also seems like there are already good descriptions and even videos of what you wondering about.

 

[aawahab76]

If you want to see it in a more "physical" sense seems like you should just start with the basic that the speed of light is constant. Use math in a way where you come up with a scenario that your looking to understand. Use the speed of light and how it works twards time dilation, length contraction,... not just looking at the math but the math came to be. That may help so that you can see what's happening in a more physical way.

It also seems like there are already good descriptions and even videos of what you wondering about.

As long as I know, all such videos ... etc will try to simplify LT and graph rather than giving an "intuitive" physical picture. Just keep attention that we are concentrating on understanding if there is a physical contradiction (if that can be said) in the statemen that "P before O before and P' before O'", that is all.

 

[aawahab76]

No, "simultaneous relative to an observer" is normally just a shorthand for "simultaneous in the observer's inertial rest frame", unless you're talking about the observer seeing the light from some pair of events simultaneously with their eyes (for example, if one star 200 light-years away in Earth's frame exploded in 1800, and another star 100 light-years away exploded in 1900, then on Earth we would see the light from these explosions simultaneously in 2000).

So at 1 sec in F, all space (as represented by x coordinate) is filled with events (being empty for example except at 10^100 m). However, space as it is is a physical structre that exist irrespictive of any coordinate and at this moment in F, P is being registered in x=10^100 m. But this space is already filling the F' space itself and as such it must be registered in the x' coordinte but after O,O' event as I can picture it (this is possibly where intuition come on). I am sure you may say that what I am saying is just with respect to a particuler frame that I find some how "intuitiv" but notice how we are now speaking about the totality of events (all x's) registered by a particuler frame at its global time coordinate rather than a single event.

 

[JesseM]

So at 1 sec in F, all space (as represented by x coordinate) is filled with events (being empty for example except at 10^100 m). However, space as it is is a physical structre that exist irrespictive of any coordinate and at this moment in F, P is being registered in x=10^100 m.

I don't understand what you mean by this. The statement "at this moment in F" is not one that's "irrespective of any coordinate", because talking about what's happening at different locations at a particular "moment" has no meaning outside the context of a particular coordinate system (unless you believe in some coordinate-independent notion of absolute simultaneity).

But this space is already filling the F' space itself and as such it must be registered in the x' coordinte but after O,O' event

Your phrasing is difficult to follow--when you say "it must be registered in the x' coordinate", what is the "it", is it event P? If so, by "registered in the x' coordinate" do you just mean P is assigned some coordinates in the primed frame?

 

[aawahab76]

I don't understand what you mean by this. The statement "at this moment in F" is not one that's "irrespective of any coordinate", because talking about what's happening at different locations at a particular "moment" has no meaning outside the context of a particular coordinate system (unless you believe in some coordinate-independent notion of absolute simultaneity).

Your phrasing is difficult to follow--when you say "it must be registered in the x' coordinate", what is the "it", is it event P? If so, by "registered in the x' coordinate" do you just mean P is assigned some coordinates in the primed frame?

"It" means all of space (in this case 1D space covering the whole x-axis in F and x'-axix in F').

 

[aawahab76]

I don't understand what you mean by this. The statement "at this moment in F" is not one that's "irrespective of any coordinate", because talking about what's happening at different locations at a particular "moment" has no meaning outside the context of a particular coordinate system (unless you believe in some coordinate-independent notion of absolute simultaneity).

Your phrasing is difficult to follow--when you say "it must be registered in the x' coordinate", what is the "it", is it event P? If so, by "registered in the x' coordinate" do you just mean P is assigned some coordinates in the primed frame?

Sorry, but for the first paragraph (and excuse me for this but I do not know how to quote in the appropriate way, one may help here) yes why can't we define absolute simultaneity using t in F and t' in F' so event (t,x) is simultaneous with (t,y) for what ever x and y.

 

[darkhorror]

Sorry, but for the first paragraph (and excuse me for this but I do not know how to quote in the appropriate way, one may help here) yes why can't we define absolute simultaneity using t in F and t' in F" so event (t,x) is simultaneous with (t,y) for what ever x and y.

where do you use t' and F"?

 

[JesseM]

Sorry, but for the first paragraph (and excuse me for this but I do not know how to quote in the appropriate way, one may help here) yes why can't we define absolute simultaneity using t in F and t' in F' so event (t,x) is simultaneous with (t,y) for what ever x and y.

Again this isn't clear, as darkhorror said you don't seem to mention the t' coordinates of either event, and how is "using t in and t' in F' " supposed to give an absolute definition of simultaneity? "Absolute" here means something that all observers can agree on, but obviously a pair of events that have the same t-coordinate have different t'-coordinates and vice versa.

 

[aawahab76]

where do you use t' and F"?

t' is the time coordinate in F' and F'' is a mistake I corrected above, it is F'. Thanks darkhorror

 

[darkhorror]

I wasn't actually talking about the " vs ', the naming of them doesn't really matter. But where do you mention t' and F' after you say that there is that frame? you only mention (t,x) and (t,y).

 

[aawahab76]

I wasn't actually talking about the " vs ', the naming of them doesn't really matter. But where do you mention t' and F' after you say that there is that frame? you only mention (t,x) and (t,y).

That was my bad composition , I mean the following:

why can't we define absolute simultaneity using t in F and t' in F' so:
1- in F, event (t,x) is simultaneous with (t,y) for what ever x and y
2- in F', event (t',x') is simultaneous with (t',y') for what ever x' and y'?

 

[JesseM]

That was my bad composition , I mean the following:

why can't we define absolute simultaneity using t in F and t' in F' so:
1- in F, event (t,x) is simultaneous with (t,y) for what ever x and y
2- in F', event (t',x') is simultaneous with (t',y') for what ever x' and y'?

Because "absolute simultaneity" means a single truth about simultaneity that is the same for all observers. Two events that are simultaneous in F will not be simultaneous when their coordinates are translated into F', and vice versa.

 

[aawahab76]

Because "absolute simultaneity" means a single truth about simultaneity that is the same for all observers. Two events that are simultaneous in F will not be simultaneous when their coordinates are translated into F', and vice versa.

I completely agree as that is resulting from the postulate of special relativity. However, what do you think of the following picture:

1- O (I think it is obvious when O mean the event (0,0) or the observer in x=0, similarly for O' below) built F coordinates using rulers-clocks so whenever the clock at O reads 1 pm (or any other reading), all clocks at the whole space read 1 pm (or the other reading). This can be proved by using your (I think) proposed cameras when the pictures arrive.
2- As in 1, O' built F' so whenever the clock at O' reads 2' pm (or any other reading), all clocks at the whole space read 2' pm (or the other reading).
3- Notice the whole space is a physical entity that is independent of coordinate or frame being used. So usually we have F clock overlapping F' clock (of course the whole structure is imaginary).
4- When O meet O', their respective time coordinates read 0 and 0'. Each observer is certain at this moment that all other clocks (treating those for F independently of those of F') that are covering the whole space are reading the same, in this case 0 and 0'. This again can be proved using the cameras.
5- At the meeting of O and O', P (an explosion) is 1 sec in the future of F. So at the meeting, P is no where in the whole "space" but have already been there according to F'. That is because the reading of the clock at O' when P happened according to F' was -10^81 sec which is certainly before the meeting moment. I am picturing here that all F' clocks at the moment -10^81 sec in F' were reading -10^81 sec and it seems that at least one such clock was overlapping the location of O (the observer) whose clock was certainly before 0 (in F) because O (the event) is in the future.

 

[JesseM]

1- O (I think it is obvious when O mean the event (0,0) or the observer in x=0, similarly for O' below) built F coordinates using rulers-clocks so whenever the clock at O reads 1 pm (or any other reading), all clocks at the whole space read 1 pm (or the other reading). This can be proved by using your (I think) proposed cameras when the pictures arrive.

I don't understand what you mean by "proved". The idea that all clocks show identical readings simultaneously is not an empirical claim, it's just a matter of definition--in SR we have defined the word "simultaneous" in a given frame to mean "same time according to local readings on clocks which have been set according to the Einstein clock synchronization convention". If the observer didn't care about using the definition of simultaneity from inertial frames, he could easily pick a different convention for setting his clocks, and define simultaneity in terms of this new convention. There'd be no reason to judge this alternate definition of simultaneity "wrong" as long as we understand that it no longer matches the definition used in inertial frames (and thus equations of physics that apply in all inertial frames would no longer apply in the non-inertial frame defined by this alternate convention).

3- Notice the whole space is a physical entity that is independent of coordinate or frame being used. So usually we have F clock overlapping F' clock (of course the whole structure is imaginary).

No, I totally disagree, because when you say "the whole space" you mean a snapshot of space at a particular time, but this depends on your simultaneity convention which is not "independent of coordinate or frame being used". The set of events in spacetime is frame-independent, as is the "geometry" of spacetime encoded in the spacetime interval between any pair of events, but there is no single physically correct way to take a 3D cross-section of 4D spacetime and call that "the whole space" at a particular moment.

 

[Dale]

1- O (I think it is obvious when O mean the event (0,0) or the observer in x=0, similarly for O' below) built F coordinates using rulers-clocks so whenever the clock at O reads 1 pm (or any other reading), all clocks at the whole space read 1 pm (or the other reading). This can be proved by using your (I think) proposed cameras when the pictures arrive.
2- As in 1, O' built F' so whenever the clock at O' reads 2' pm (or any other reading), all clocks at the whole space read 2' pm (or the other reading).
4- When O meet O', their respective time coordinates read 0 and 0'. Each observer is certain at this moment that all other clocks (treating those for F independently of those of F') that are covering the whole space are reading the same, in this case 0 and 0'. This again can be proved using the cameras.

Yes, this is fine. In the future you can say this more concisely by saying "F and F' are two inertial frames in the standard configuration". See:
http://en.wikipedia.org/wiki/Lorent...ormation_for_frames_in_standard_configuration

3- Notice the whole [STRIKE]space[/STRIKE] spacetime is a physical entity that is independent of coordinate or frame being used. So usually we have F clock overlapping F' clock (of course the whole structure is imaginary).

As JesseM mentioned, this was incorrect as originally written. I have corrected it in red.

5- At the meeting of O and O', P (an explosion) is 1 sec in the future of F. So at the meeting, P is no where in the whole "space" but have already been there according to F'. That is because the reading of the clock at O' when P happened according to F' was -10^81 sec which is certainly before the meeting moment. I am picturing here that all F' clocks at the moment -10^81 sec in F' were reading -10^81 sec and it seems that at least one such clock was overlapping the location of O (the observer) whose clock was certainly before 0 (in F) because O (the event) is in the future.

Correct. P occurs after O in F and P occurs before O in F'. This is the relativity of simultaneity.

Except for the rather minor edit required for point 3 it seems that you understand what the theory predicts and claims.

 

[aawahab76]

Yes, this is fine. In the future you can say this more concisely by saying "F and F' are two inertial frames in the standard configuration". See:
http://en.wikipedia.org/wiki/Lorent...ormation_for_frames_in_standard_configuration

As JesseM mentioned, this was incorrect as originally written. I have corrected it in red.

Correct. P occurs after O in F and P occurs before O in F'. This is the relativity of simultaneity.

Except for the rather minor edit required for point 3 it seems that you understand what the theory predicts and claims.

No I meant exactly as I wrote "space" not "spacetime". Of course for using LT we will need the "spaetime" but it is my intention here to show that (my)intuition does not find it incorrect to think of 3D section of the whole 4D. I accept that two frames will use different coordinates but Why do you want me to think that at the moment I am writing this replay, I cannot think of a person reading something interesting of his own and being so far from Earth (in a spacelke interval from me) that a picture of him reading that book need 10^100000 light years to arrive to earth. Yes theory of relativity does not accept that or we can say the theory does not have a meaning for that, but that is the theory which even if it works fine, it does not mean it will continue to do so nor does a correct theoy (for now) mean that intuition is wrong. It may or may not be which always leave space for critisicing theories. Again I know that there are more or less subjectivity in intuition meaning but do you really think that the person from far a way (mentioned above) does not exist?

 

[Dale]

No I meant exactly as I wrote "space" not "spacetime".

Then what you meant was wrong. The whole space is not "a physical entity that is independent of coordinate or frame being used". It depends on your simultaneity convention, as JesseM described, which is part of the coordinate system.

I realize that you may think that I am being unkind to point it out so bluntly, but you are mentally stuck until you let go of some incorrect concepts that you are clinging to. Do you honestly believe that you are incapable of being wrong? If not, then consider that this might be one of those instances.