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## [triangulation at speed]

Surely a parallax measurement would be the same for either observer whether stationary or travelling near c. Why would movement change the triangulation?

Last edited by pzkpfw; 2012-Jun-26 at 07:19 PM. Reason: Add note

2. Originally Posted by Webbo
Surely a parallax measurement would be the same for either observer whether stationary or travelling near c. Why would movement change the triangulation?
Because the distance is shorter (because of relativity).

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Originally Posted by Strange
Because the distance is shorter (because of relativity).
Which distance? The only distance that is measured is the distance between the 2 viewpoints and these are accross the direction of movement. My understanding was that the shortened distance was only in the direction of movement. Am I incorrect?

4. Originally Posted by Webbo
Which distance? The only distance that is measured is the distance between the 2 viewpoints and these are accross the direction of movement. My understanding was that the shortened distance was only in the direction of movement. Am I incorrect?
You are correct. It is the distance to the distant object which is less, therefore the measured angles would be different.

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Originally Posted by Strange
You are correct. It is the distance to the distant object which is less, therefore the measured angles would be different.
The angles are used to derive the distance not the other way around. The distance is unknown; it's a calculation based on the baseline and the angles.

6. Originally Posted by Webbo
The angles are used to derive the distance not the other way around. The distance is unknown; it's a calculation based on the baseline and the angles.
Yes. That is what I said (or intended to ). You measure the baseline and the angles, calculate the distance: the "stationary" observe calculates 22 ly; the moving one calculates 1 ly. They measure the same baseline but different angles (because the distance to the object is different).

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Originally Posted by Strange
Yes. That is what I said (or intended to ). You measure the baseline and the angles, calculate the distance: the "stationary" observe calculates 22 ly; the moving one calculates 1 ly. They measure the same baseline but different angles (because the distance to the object is different).
But why would the angles be different? They are either determined by the direction that the light is received or by the target stars lateral movement against the background stars. I can't see how either is affected.

8. Originally Posted by Webbo
But why would the angles be different? They are either determined by the direction that the light is received or by the target stars lateral movement against the background stars. I can't see how either is affected.
We seem to be going round in circles. Because the distance to the star is less (because of relativity).

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Originally Posted by Strange
We seem to be going round in circles. Because the distance to the star is less (because of relativity).
But like I said, for that to happen either the lateral movement against the background stars would need to contract or the distance between the viewpoints, but that is not possible as that is not the direction of travel.

Look at the method used.

1.Distance is measured between viewpoints = real number
2.Lateral movement is measured = real number
3.Angles determined = derived from 1 & 2
4.Distance calculated = derived from 1, 2 & 3

1 & 2 are the only real measurement hence only they can cause differences in the angle and distance. How can forward movement affect those first 2 measurements?

10. Originally Posted by Webbo
But like I said, for that to happen either the lateral movement against the background stars would need to contract or the distance between the viewpoints, but that is not possible as that is not the direction of travel.

Look at the method used.

1.Distance is measured between viewpoints = real number
2.Lateral movement is measured = real number
3.Angles determined = derived from 1 & 2
4.Distance calculated = derived from 1, 2 & 3

1 & 2 are the only real measurement hence only they can cause differences in the angle and distance. How can forward movement affect those first 2 measurements?
The amount of lateral movement seen depends on how far away the star is, no?

(I'll leave it there as I am not sure quite which bit of this you are not clear on)

11. Originally Posted by Webbo
But like I said, for that to happen either the lateral movement against the background stars would need to contract or the distance between the viewpoints, but that is not possible as that is not the direction of travel.
The problem is anything but an exact 90 degrees has a contraction as part of its vector.
Let me try to explain what I see: (difficult because of my lack of correct terminology)
To judge speed, you are taking a time measurement between two objects or positions at two different times. No matter which object you choose as your 90 degree angle, the measurement at the other time point has changed it's angle and introduces contraction.

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Originally Posted by Strange
The amount of lateral movement seen depends on how far away the star is, no?
Which means that the stationary observer would have the target star in one particlular position on a photographic plate when compared to the background, and the moving observer would have the target star in a different position on the photographic plate when compared to the background as it passed virtualy the same point in space. Not sure how that is possible.

13. Good point NEOWatcher.

Webbo, are you thinking that length contraction only happens in exactly the direction of travel?

14. Originally Posted by Webbo
Which means that the stationary observer would have the target star in one particlular position on a photographic plate when compared to the background, and the moving observer would have the target star in a different position on the photographic plate when compared to the background as it passed virtualy the same point in space. Not sure how that is possible.
As a crude analogy, think of taking two photographs from different distances but with different focal length cameras such that the main object in the picture appears the same size in both. Other objects will have a different spatial relationship in the two images because one is "compressed" in the direction the picture is taken.

Similarly, the travelling observer will see everything "squished" which will change their apparent relationships.

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Originally Posted by NEOWatcher
The problem is anything but an exact 90 degrees has a contraction as part of its vector.
Let me try to explain what I see: (difficult because of my lack of correct terminology)
To judge speed, you are taking a time measurement between two objects or positions at two different times. No matter which object you choose as your 90 degree angle, the measurement at the other time point has changed it's angle and introduces contraction.
We're not trying to determine speed, we're trying to determine distance and therefore doesn't need to be a time difference between measurements. It's currently required for parallax measurement because our baseline is the diameter of the Earths orbit.

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Originally Posted by Strange
Good point NEOWatcher.

Webbo, are you thinking that length contraction only happens in exactly the direction of travel?
No but it shouldn't be evident at all at right angles to direction which are the only measurements we can make.

17. Originally Posted by Webbo
No but it shouldn't be evident at all at right angles to direction which are the only measurements we can make.
Ah, I think I see (maybe). You are considering the displacement and the baseline as both being at right angles to the direction of travel? But the displacement is a result of the trigonometry of the setup; i.e. the angle between two different viewpoints looking at the same object.

The angles to the star (which you are measuring as a displacement) are between lines in the direction of travel (which will be shorter) and a line orthogonal to the direction of travel (which will not be shorter).

Do I need to draw a diagram, I wonder... (ETA: no need!)

For the travelling observer, the distance being measured (indirectly) is shorter and therefore the angle/displacement must be greater.

18. Originally Posted by Webbo
Surely a parallax measurement would be the same for either observer whether stationary or travelling near c. Why would movement change the triangulation?
Since length contraction is only in the direction of movement the angles are different.
Parralax2.png

Actually a better representation would be
as the observers would be using the angles F & E to derive the distance of C & D

I'll add that both ships at the tips can tell that they are travelling parallel to each other and trade data to get the parallax (purple lines is the direction of motion of the observers)

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Originally Posted by Strange
As a crude analogy, think of taking two photographs from different distances but with different focal length cameras such that the main object in the picture appears the same size in both. Other objects will have a different spatial relationship in the two images because one is "compressed" in the direction the picture is taken.

Similarly, the travelling observer will see everything "squished" which will change their apparent relationships.
I don't see why it would be squished. It's an image reproduced on a plate at a particular point in space in either case. Forward movement shouldn't have the same effect as changing focus.

20. Originally Posted by Webbo
I don't see why it would be squished. It's an image reproduced on a plate at a particular point in space in either case. Forward movement shouldn't have the same effect as changing focus.
[changing focal length]

Look at Wayne's diagram. Everything is foreshortened from the moving observer's point of view. Things are nearer him and hence nearer to each other.

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Originally Posted by WayneFrancis
Since length contraction is only in the direction of movement the angles are different.
Parralax2.png

Actually a better representation would be
as the observers would be using the angles F & E to derive the distance of C & D

I'll add that both ships at the tips can tell that they are travelling parallel to each other and trade data to get the parallax (purple lines is the direction of motion of the observers)
Parallax is not measured using that method. Only lateral measurements are made. Angles are derived not observed/measured.

22. Originally Posted by Webbo
I don't see why it would be squished. It's an image reproduced on a plate at a particular point in space in either case. Forward movement shouldn't have the same effect as changing focus.
But parallax is the use of 2 images. With a really wide ship or 2 ships or as we do it here 2 points separated by 6 months and ~2AU.

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Just to clarify. If everything is squished then the arc second must also be squished hence measurements would be exacly the same. What's required is for just the target star to be slightly shifted compared to the background.

24. Originally Posted by Webbo
Just to clarify. If everything is squished then the arc second must also be squished hence measurements would be exacly the same. What's required is for just the target star to be slightly shifted compared to the background.
No
triangles.png

Those 2 triangles where identical before I squashed one of them. Angle A ≠ B. This is basic euclidean geometry

Ah wait. I think I know where you are getting confused. An obserer will not agree with an observer, in a different inertial frame, on the angular separation of 2 objects. This is why the accelerated observer will come up with a different parallax measurement then the non accelerated obsserver.

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Originally Posted by WayneFrancis
No
triangles.png

Those 2 triangles where identical before I squashed one of them. Angle A ≠ B. This is basic euclidean geometry
If the camera takes an image of say the forward hemisphere and everything is squished then there will be an empty band around the outside. Only an inept scientist would continue to use the empty band as part of the total arc measurement. If an area of the photo is squished, then the unit of measurement must also be squished.

26. Originally Posted by Webbo
If the camera takes an image of say the forward hemisphere and everything is squished then there will be an empty band around the outside. Only an inept scientist would continue to use the empty band as part of the total arc measurement. If an area of the photo is squished, then the unit of measurement must also be squished.
There is no empty band.

In this image the left one is a stationary observer.
The right one is an accelerated observer.

arc.png

The accelerated observer will see a larger angular distance between the 2 objects then the non accelerated observer. The closer an object is to the direction of travel the more it will have its distance contracted. They can still see a continuous 360 degrees around them. The objects in front of them look a lot closer, the objects perpendicular to their direction of motion seem to be the same, objects directly behind them seem to be very far away. Through out the entire 360 degrees it is a completely smooth transition

27. Perhaps you could do some simple drawing on what you think is happening. Notice I've squished the 2 red dots but I haven't squished the sphere around the observer. This is why the parallax angle changes.

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Originally Posted by WayneFrancis
There is no empty band.

In this image the left one is a stationary observer.
The right one is an accelerated observer.

arc.png

The accelerated observer will see a larger angular distance between the 2 objects then the non accelerated observer. The closer an object is to the direction of travel the more it will have its distance contracted. They can still see a continuous 360 degrees around them. The objects in front of them look a lot closer, the objects perpendicular to their direction of motion seem to be the same, objects directly behind them seem to be very far away. Through out the entire 360 degrees it is a completely smooth transition
So you are saying the stars in front are squashed together but perpendicular are the same. Which means at somewhere between the 2 points there must be larger than expected gaps. I would argue that such a distortion should not be measured using fixed arcseconds. Any attempt to do so would be scientifically inept.

29. Originally Posted by Webbo
We're not trying to determine speed, we're trying to determine distance...
Fair enough. this thread topic is about speed, and to determine speed you need a distance, so the lines got a little blurred. But the concept still applies...
Originally Posted by Webbo
...and therefore doesn't need to be a time difference between measurements. It's currently required for parallax measurement because our baseline is the diameter of the Earths orbit.
Even removing time from the equation, you are still talking about 3 points in space. Unless they are a straight line, there will be at least one angle that is not 90 degrees from the direction of travel. Therefore, contraction can not be removed from the equation.

Originally Posted by Webbo
If the camera takes an image of say the forward hemisphere and everything is squished then there will be an empty band around the outside. Only an inept scientist would continue to use the empty band as part of the total arc measurement. If an area of the photo is squished, then the unit of measurement must also be squished.
No, there is no empty band until you reach c itself where a photon can't "catch up" to you. The "squish" is non-uniform around the field of view. It gets more compressed as you look forward, and less compressed as you look back. The distortion does not exist at 90 degrees and gets more "squished" as you look forward. As you go from 90 to 180, the field of view is stretched.

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Originally Posted by Webbo
So you are saying the stars in front are squashed together but perpendicular are the same. Which means at somewhere between the 2 points there must be larger than expected gaps. I would argue that such a distortion should not be measured using fixed arcseconds. Any attempt to do so would be scientifically inept.
Why? A spherical coordinate system is a spherical coordinate system. There isnt any requirement that the distribution of stars be distributed in any specific way. The universe is distorted at relativistic velocities. Changing the coordinate system to make it look 'normal' wouldnt be useful

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