Alternative way of looking at simultaneity is 1

[Dreads]

I don't know if this is new or not but an alternative way of looking at simultenaity is

1. if you have two events
2. draw a straight line joining the two events
3 find the mid point of that line
4 draw a plane perpendicular to that line at the midpoint

any number of observers moving in any direction, either accelerating or not, on that plane will percieve the events as simultaneous

The events can be moving wrt the plane as long as both events move parrallell to the plane

 

[dx]

Straight line joining the events in spacetime?

 

[Mentz114]

It's a common definition, but replace 'events' with 'spatial locations'. The spatial plane that lies symmetrically between the points is the 'plane of simultaneity'.

Now forget all about simultaneity because it has no physical significance for spatially separated events.

 

[JesseM]

It's a common definition, but replace 'events' with 'spatial locations'. The spatial plane that lies symmetrically between the points is the 'plane of simultaneity'.

Dreads wasn't talking about the plane containing both events, the idea was something about a plane perpendicular to the line joining the events. As such the argument doesn't work, if I'm interpreting it right. If you take a plane perpendicular to the line in spacetime joining the two events, and look at an inertial observer whose worldline lies in this plane, that observer would not view the events as simultaneous. Instead, if the blue x' line in this diagram is viewed as a line joining two events, then you'd need to take a plane which contains the blue ct' line (which obviously isn't perpendicular to the x' line) in order to ensure that an observer with a worldline in that plane would view the events as simultaneous in their own frame.

 

[Mentz114]

Hi Jesse,

Dreads wasn't talking about the plane containing both events,

Nor was I ( not intentionally, anyway ). On re-reading the first post I don't know what dreads means now. If the two events are completely arbitrary, all we can say is that there is a plane of simultaneity. If the events both happen at the same time on synchronised clocks, that plane is symmetrically placed.

M

 

[neopolitan]

If the two events are completely arbitrary, all we can say is that there is a plane of simultaneity.

Completely arbitrary doesn't quite work, because it doesn't exclude two events which are causally related and which are never simultaneous. Say I pick two events arbitrarily, then I do some research and find those events are where-when Fred was born and where-when Fred died. Even arbitrarily chosen, those events will never lie on any plane of simultaneity.

cheers,

neopolitan

(Still away)

 

[matheinste]

Hello all.

I assume the events referred to are spatially separated because timelike, causally connected events cannot be simultaneous by the usual (perhaps any) definition.

Matheinste

 

[Mentz114]

Completely arbitrary doesn't quite work, because it doesn't exclude two events which are causally related and which are never simultaneous. Say I pick two events arbitrarily, then I do some research and find those events are where-when Fred was born and where-when Fred died. Even arbitrarily chosen, those events will never lie on any plane of simultaneity.

cheers,

neopolitan

(Still away)

You're right, arbitrary does not work. But I have found an observer for whom the events are simultaneous. We'll exclude the case where Fred lives for zero time, because then the events are simultaneous in everyone's frame.

Suppose Fred lived for n years, and dies in a different place to the one he was born. An observer who is located n+k light years from the birthplace, and k light years from the hospice, will see both events simultaneously through his telescope.

But I'm not sure if I can make a plane out of these conditions, so you could be right on that.

I think. It's late here and this is my last post today.

 

[JesseM]

Suppose Fred lived for n years, and dies in a different place to the one he was born. An observer who is located n+k light years from the birthplace, and k light years from the hospice, will see both events simultaneously through his telescope.

Simultaneity in SR is a totally separate concept from seeing events simultaneously though...the events at the beginning and end of Fred's life won't have the same t-coordinate in any inertial frame.

 

[Dreads]

if you have a cartesian coord system
observer A and observer B's eyes are located on the xy plane
Observer A and Observr B can be moving in any direction, at any velocity and any accelleration as long as the direction of travel is parrallell to the plane
lightening strikes on the z axis at 10 and -10 ie equidistant from the origin on the z axis
anypoint on the xy plane will be equidistant from -10 and 10 and so the light will reach any point on the xy plane simultaneously

 

[Dreads]

the events will appear simultaneous to both observer A and observer B

 

[JesseM]

if you have a cartesian coord system
observer A and observer B's eyes are located on the xy plane
Observer A and Observr B can be moving in any direction, at any velocity and any accelleration as long as the direction of travel is parrallell to the plane
lightening strikes on the z axis at 10 and -10 ie equidistant from the origin on the z axis
anypoint on the xy plane will be equidistant from -10 and 10 and so the light will reach any point on the xy plane simultaneously

Again, "simultaneity" in SR has nothing to do with seeing events simultaneously. For example, if I see the light from an event in 2005 according to my clock which occurred 5 light-years away according to my length measurement, and in 2010 I see the light from an event 10 light-years away, then both these events happened "simultaneously" in 2000 in my frame.

 

[neopolitan]

You're right, arbitrary does not work. But I have found an observer for whom the events are simultaneous. We'll exclude the case where Fred lives for zero time, because then the events are simultaneous in everyone's frame.

Suppose Fred lived for n years, and dies in a different place to the one he was born. An observer who is located n+k light years from the birthplace, and k light years from the hospice, will see both events simultaneously through his telescope.

But I'm not sure if I can make a plane out of these conditions, so you could be right on that.

I think. It's late here and this is my last post today.

I think that you are implying that Fred and the observer have a relative speed of c, which doesn't seem right. (Think of a photon spawned by the birth of Fred, which then passes Fred at the time of his death, then goes on to be observed by the observer - either that's what is being implied or you have photons from the birth catching up with photons from the death.)

In any event, observing two events together does not make them simultaneous.

cheers,

neopolitan

 

[Al68]

Simultaneity in SR is a totally separate concept from seeing events simultaneously though...the events at the beginning and end of Fred's life won't have the same t-coordinate in any inertial frame.

How about Fred living and dying on Earth at age 60, and an observer on a ship is moving toward Earth at 0.8c, then after Fred is dead (in the ship's frame), he decelerates to come to rest with Earth at a distance of 75 light years. Now, Fred's a baby again.

It's not an inertial frame, and the ship observer can't know that Fred is alive or dead until later, but it looks like according to the clock on the ship, lots of people on Earth who were dead "before" are alive "after".

Is this a case where LET would be a better (philosophical) description of reality?

 

[JesseM]

How about Fred living and dying on Earth at age 60, and an observer on a ship is moving toward Earth at 0.8c, then after Fred is dead (in the ship's frame), he decelerates to come to rest with Earth at a distance of 75 light years. Now, Fred's a baby again.

It's not an inertial frame, and the ship observer can't know that Fred is alive or dead until later, but it looks like according to the clock on the ship, lots of people on Earth who were dead "before" are alive "after".

There are an infinite number of ways to construct a non-inertial frame where the ship is at rest, none of them preferred over any other. You appear to be trying to construct one where the ship's definition of simultaneity always matches that of the ship's current inertial frame at that instant, but there's no need to build it that way. You could equally well construct a non-inertial frame where Fred is exactly the same age before and after the ship decelerates, for example.

Is this a case where LET would be a better (philosophical) description of reality?

The standard interpretation of SR doesn't imply that the non-inertial coordinate system you constructed is a "description of reality", it's just an arbitrary way of labeling points in spacetime.

 

[Al68]

There are an infinite number of ways to construct a non-inertial frame where the ship is at rest, none of them preferred over any other. You appear to be trying to construct one where the ship's definition of simultaneity always matches that of the ship's current inertial frame at that instant, but there's no need to build it that way. You could equally well construct a non-inertial frame where Fred is exactly the same age before and after the ship decelerates, for example.

The standard interpretation of SR doesn't imply that the non-inertial coordinate system you constructed is a "description of reality", it's just an arbitrary way of labeling points in spacetime.

I agree with your entire post. That's why I asked, "Is this a case where LET would be a better (philosophical) description of reality?"

 

[JesseM]

I agree with your entire post. That's why I asked, "Is this a case where LET would be a better (philosophical) description of reality?"

Why would adopting a (probably fictitious) belief in a preferred frame be "better" here? Are you saying that the fact that there's no "proper" way to construct a coordinate system for a non-inertial observer is somehow philosophically problematic for the standard SR view? I don't consider it philosophically problematic that there's no standard way to construct a non-cartesian spatial coordinate system on the surface of the Earth where the non-straight coastline of Florida has a constant x-coordinate, for example, so why should it be any more problem that there's no standard way to construct a non-inertial spacetime coordinate system where the non-straight worldline of an accelerating observer has a constant position coordinate?

 

[Al68]

Why would adopting a (probably fictitious) belief in a preferred frame be "better" here? Are you saying that the fact that there's no "proper" way to construct a coordinate system for a non-inertial observer is somehow philosophically problematic for the standard SR view? I don't consider it philosophically problematic that there's no standard way to construct a non-cartesian spatial coordinate system on the surface of the Earth where the non-straight coastline of Florida has a constant x-coordinate, for example, so why should it be any more problem that there's no standard way to construct a non-inertial spacetime coordinate system where the non-straight worldline of an accelerating observer has a constant position coordinate?

I meant to say Lorentz Relativity Theory, not LET.

The philosophical issue is that according to the ship observer, a person who is dead "now" according to the standard SR simultaneity convention will be alive "later" according to the same convention. The "now" and "later" are each in an inertial frame. The ship observer experiences a moment simultaneous with the person being alive after experiencing a moment simultaneous with the same person being dead.

This seems very similar to how the Earth clock "jumps ahead" according to the ship's twin in the standard twins paradox resolutions. Except in this case, Earth's clock "jumps backward".

 

[granpa]

reality doesn't change. only your perspective changes.

 

[Dale]

I don't know if this is new or not but an alternative way of looking at simultenaity is

1. if you have two events
2. draw a straight line joining the two events
3 find the mid point of that line
4 draw a plane perpendicular to that line at the midpoint

any number of observers moving in any direction, either accelerating or not, on that plane will percieve the events as simultaneous

Hi Dreads,

This is definitely your best post so far. As long as you restrict the two events to being spacelike separated and as long as your observers use radar time and distance then you are correct.

Another way to describe that plane is as the plane that contains the intersection of the light cones of the two events. If an observer emits a radar pulse at any event on the "past light cone" intersection region then they will receive the radar echo from both events at the same time on the "future light cone" intersection region.

The events can be moving wrt the plane as long as both events move parrallell to the plane

Events don't move. It is like talking about the slope of a point. Points don't have slopes, lines do.

 

[JesseM]

I meant to say Lorentz Relativity Theory, not LET.

What's the difference between them? Does Lorentz Relativity Theory still involve a preferred inertial frame, just without necessarily treating it as an "ether" frame?

The philosophical issue is that according to the ship observer, a person who is dead "now" according to the standard SR simultaneity convention will be alive "later" according to the same convention.

But it's not "according to the ship observer", it's just according to one arbitrary way of labeling coordinates of events using a non-inertial coordinate system. There is no reason to treat this coordinate system as naturally representing the ship observer's "perspective" over any other non-inertial coordinate system.

 

[Al68]

But it's not "according to the ship observer", it's just according to one arbitrary way of labeling coordinates of events using a non-inertial coordinate system. There is no reason to treat this coordinate system as naturally representing the ship observer's "perspective" over any other non-inertial coordinate system.

Sure, if we want to call the standard SR simultaneity convention arbitrary. It was a single observer switching from one inertial frame to another, using the standard SR simultaneity convention for each.

In other words, the observer would use the standard SR convention to conclude it was year 2090 "now" on Earth and the standard SR convention to conclude it is year 2015 "now" on earth. The observer was at rest in an inertial frame for each of those.

Is this not exactly how the twins paradox is analyzed in standard resolutions? Does the fact that the ship twin is non-inertial invalidate the conclusion because there are other ways to represent the ship observer's perspective?

 

[JesseM]

Sure, if we want to call the standard SR simultaneity convention arbitrary.

The standard SR simultaneity convention is only intended for inertial frames, while you are talking about a non-inertial observer who changes velocities. Keep in mind that while the simultaneity convention for inertial frames is not arbitrary (it is physically 'natural' since the laws of physics will obey the same equations in all inertial frames constructed this way), it is a matter of arbitrary linguistic convention to say that if I am an inertial observer, "my" frame is the inertial frame where I am at rest. It's not as though it's any easier to calculate things using the inertial frame where I am at rest than it is to calculate things using the frame where I am moving at 0.99c, it's purely an arbitrary convention to treat one of these as representing my "perspective" somehow (after all neither reflects what I actually see visually). And for a non-inertial observer, not only is there no "natural" reason to say that their "perspective" at any given moment is represented by the inertial frame where they are instantaneously at rest, but this isn't even a standard accepted linguistic convention.

In other words, the observer would use the standard SR convention to conclude it was year 2090 "now" on Earth and the standard SR convention to conclude it is year 2015 "now" on earth.

I disagree that any such convention exists for non-inertial observers. The convention about equating an observer's perspective on simultaneity with what is true in the inertial frame where they are at rest is usually taken to apply only to ideal inertial observers who move at constant velocity for all time (or at least for the entire window of time that a given word-problem is looking at), as far as I've seen.

Is this not exactly how the twins paradox is analyzed in standard resolutions?

The most common resolution I've seen says nothing about switching inertial frames midway through the problem, it just notes that the traveling twin does not remain at rest in any inertial frame, so you can't calculate the elapsed time on the inertial twin's clock by using the standard time dilation which only works in inertial frames (and if you stick to anyone inertial frame, you see that for part of the journey the non-inertial twin must have been moving faster than the inertial one and thus aging slower during that phase). Some ways of answering the twin paradox do bring up the difference in simultaneity between the outbound rest frame and the inbound rest frame (which means that the time on the inertial twin's clock at the moment of the non-inertial twin's turnaround is very different in the two frames), but only to explain why you can't calculate how much the inertial twin ages by taking the sum of the the elapsed time on the inertial twin's clock from departure to turnaround in the outbound frame and then from turnaround to reunion in the inbound frame (which you could do if there was no disagreement in simultaneity between the two frames). The idea is usually not to imply that you should actually use some kind of non-inertial frame where there is a sudden "jump" in the inertial twin's age at the moment of turnaround, at least not unless you want to get into the issue of pseudo-gravitational fields and pseudo-gravitational time dilation in non-inertial frames.

Does the fact that the ship twin is non-inertial invalidate the conclusion because there are other ways to represent the ship observer's perspective?

Invalidate what conclusion? If you want to you can analyze things from the perspective of a non-inertial frame whose simultaneity convention agrees with that of the non-inertial twin's instantaneous inertial rest frame at every moment, but I still don't understand what this has to do with favoring Lorentzian relativity, or what you even mean by that if it's distinct from the Lorentz ether theory.

 

[DrGreg]

Suppose Fred lived for n years, and dies in a different place to the one he was born. An observer who is located n+k light years from the birthplace, and k light years from the hospice...

That's impossible, unless Fred is a photon!

 

[Al68]

The standard SR simultaneity convention is only intended for inertial frames, while you are talking about a non-inertial observer who changes velocities.

But I only used the standard simultaneity convention while the observer was at rest in an inertial frame. Does prior or subsequent acceleration preclude the convention being used while at rest in an inertial frame? Does the convention not apply to the ship's twin during inertial motion in the twins paradox? Is my noting the Earth clock "jumping backward" according to my observer any different from the Earth clock "jumping ahead" according to the ship's twin in the standard twins paradox?

I'm not claiming that people are actually rising from the grave, just a backward "jump" of the coordinate time on Earth relative to an observer who switches inertial frames. Or I suppose we could use GR to show that Earth's coordinate time is running backward relative to the observer during the acceleration. Isn't gravitational time dilation derived from using the SR simultaneity convention in a non-inertial frame (series of co-moving inertial frames)?

If you want to you can analyze things from the perspective of a non-inertial frame whose simultaneity convention agrees with that of the non-inertial twin's instantaneous inertial rest frame at every moment, but I still don't understand what this has to do with favoring Lorentzian relativity, or what you even mean by that if it's distinct from the Lorentz ether theory.

I'm not as familiar with Lorentz relativity theory as I should be, which is part of the reason I asked the question about its relevance. But it's my understanding that time is absolute, while it makes the exact same empirical predictions as SR.