Do parallel lines always converge at infinity?

[geordief]

Suppose we have an experimental set up where there is a set of mirrors  parallel to each other and two beams of light are set off bouncing back and forth in between and perpendicular to  them for an extended period.

 

At first the two beams are aligned parallel to each other.

 

Can it be shown that these two beams will  always  always converge when any  effects of gravity are  allowed for?

 

If this can or has been experimentally confirmed does it show that  there is no such thing in Nature ( the physical world)  as the Euclidean  idea of parallel lines?(only approximations)

 

Or might there be other ways of attempting to reproduce experimentally  Euclidean parallel lines   in Nature? Something even more accurate than two beams of light...

[swansont]

3 hours ago, geordief said:

Suppose we have an experimental set up where there is a set of mirrors  parallel to each other and two beams of light are set off bouncing back and forth in between and perpendicular to  them for an extended period.

Extended period is still limited, before allthe light is absorbed. Also, the mirrors would have to be perfectly flat, as well as parallel.

However, you can make a cavity with flat mirrors as you describe. They are difficult to align.

3 hours ago, geordief said:

 

At first the two beams are aligned parallel to each other.

 

Can it be shown that these two beams will  always  always converge when any  effects of gravity are  allowed for?

How could you tell the difference between a cavity aligned so that the beams are parallel, with no gravitational effects, and one in which the alignment counteracts the gravitational deflection. 

[geordief]

I am no experimenter.Might there be two additional  beams of light placed at the extreme edge of the mirrors forming the cavity-?- these to keep a stable distance between them.

 

In the middle would be the two beams whose "parallel effects "we would be interested in.

 

But are you suggesting that the experiment is far too difficult to achieve any  worthwhile result? Even one based on statistical probabilities?

 

 

22 minutes ago, swansont said:

Extended period is still limited, before allthe light is absorbed. Also, the mirrors would have to be perfectly flat, as well as parallel.

However, you can make a cavity with flat mirrors as you describe. They are difficult to align.

How could you tell the difference between a cavity aligned so that the beams are parallel, with no gravitational effects, and one in which the alignment counteracts the gravitational deflection. 

 

[swansont]

1 hour ago, geordief said:

I am no experimenter.Might there be two additional  beams of light placed at the extreme edge of the mirrors forming the cavity-?- these to keep a stable distance between them.

Beams have a finite size, and you will get diffraction from this.

1 hour ago, geordief said:

In the middle would be the two beams whose "parallel effects "we would be interested in.

 

But are you suggesting that the experiment is far too difficult to achieve any  worthwhile result? Even one based on statistical probabilities?

I don’t see a way to make the confirmation you seek. You can’t turn gravity on and off.

[geordief]

41 minutes ago, swansont said:

 

I don’t see a way to make the confirmation you seek. You can’t turn gravity on and off.

Would gravity be the only force ( if "force" is the correct term)  causing light beams to converge?

Btw do the two beams generate their own inter  attractive force ?(if ,say it was 2  extremely powerful laser beams)

 

Edited March 10, 2019 by geordief

[swansont]

2 hours ago, geordief said:

Would gravity be the only force ( if "force" is the correct term)  causing light beams to converge?

Btw do the two beams generate their own inter  attractive force ?(if ,say it was 2  extremely powerful laser beams)

 

You can get self-focusing in background gas at high intensities.

Really high energy photons can interact, but then they would not reflect very well.

[Sensei]

"Flat mirror".. under e.g. electron microscope flat surface to human-eye and human-made-devices is full of "mountains", "bumps" and "valleys" at quantum level..

 

[swansont]

1 hour ago, Sensei said:

"Flat mirror".. under e.g. electron microscope flat surface to human-eye and human-made-devices is full of "mountains", "bumps" and "valleys" at quantum level..

 

What’s important is being flat somewhat below the wavelength of the light.

[OldChemE]

The title question and the discussion seem to be at odds.  Parallel lines (the title question) being massless creations of geometry do not converge-- ever.  The only exception is in art, where an artificial convergence point is selected for parallel lines in order to create the illusion of perspective.  But, in fact the parallel lines do not converge.  Beams of light, on the other hand, being subject to gravity, would presumably converge at some point (assuming they started out parallel but close enough for the very small gravitational effect to bring them together).  The problem is proving this by experiment-- for all the reasons given above.

[geordief]

2 hours ago, OldChemE said:

The title question and the discussion seem to be at odds.  Parallel lines (the title question) being massless creations of geometry do not converge-- ever.  

Don't they converge on the surface of a sphere?

I was thinking of parallel lines as two sets of physical  measurements  drawn  locally where  the distance between corresponding    opposite elements   was constant.

If these 2  sets of elements were used to produce 2 lines then ,on the surface of a sphere  they would meet and I understand the same would happen in curved spacetime.

Since spacetime can be  (is?) curved by light itself I imagined that two such lines made of light would eventually converge

I think I have learned from this thread that whilst this may be so it is impossible to verify experimentally.

Edited March 11, 2019 by geordief

[swansont]

7 hours ago, geordief said:

Don't they converge on the surface of a sphere?

I think the implication was Euclidean geometry.

[geordief]

11 minutes ago, swansont said:

I think the implication was Euclidean geometry.

Would it be fair to consider Euclidean geometry as a kind of  (subset of ) curved geometry in the limit ?(when the local region becomes infinitely small)

 

[swansont]

59 minutes ago, geordief said:

Would it be fair to consider Euclidean geometry as a kind of  (subset of ) curved geometry in the limit ?(when the local region becomes infinitely small)

Or the radius of curvature becomes infinitely large

[OldChemE]

Whether or not parallel line converge on a sphere depends on how you define parallel.  If you define parallel classically, as two lines of which corresponding points remain equidistant (such as latitude lines on earth maps), then they also do not converge on the surface of a sphere.  Lines of longitude (again speaking in terms of maps) might appear to be parallel on some maps, but they are 'great circles' and are not parallel.

[geordief]

1 hour ago, OldChemE said:

Whether or not parallel line converge on a sphere depends on how you define parallel.  If you define parallel classically, as two lines of which corresponding points remain equidistant (such as latitude lines on earth maps), then they also do not converge on the surface of a sphere.  Lines of longitude (again speaking in terms of maps) might appear to be parallel on some maps, but they are 'great circles' and are not parallel.

I had in mind 2 lines on a sphere which we draw parallel  for a short  distance (locally,as I think it is described).

When these 2 lines are produced (follow their own direction)  they converge.

Edited March 17, 2019 by geordief

[OldChemE]

On 3/16/2019 at 7:49 PM, geordief said:

I had in mind 2 lines on a sphere which we draw parallel  for a short  distance (locally,as I think it is described).

When these 2 lines are produced (follow their own direction)  they converge.

Agreed.  over a very short distance two great circles could appear to be parallel, but still ultimately converge.