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Author Topic: Optical illusion in GR diagram?  (Read 1476 times)

Pmb

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Optical illusion in GR diagram?
« on: 10/04/2013 21:45:47 »
I want someone elses opinion on something. I've been reading the following chapter in a book online at http://www.eftaylor.com/exploringblackholes/GPS130204v1.pdf

I noticed something in Figure 4.2. The way that the slope of each line in the figure decreases with increasing r causes an optical illusion. The two points on the verticle line at r = r_earth intercect a equal distances as they do at r = r_tower. However to the eye it looks like the two on the left are closer together. When measured with a ruler they are equal though. I think the illusion is caused by the closing in distance between the lines in the direction perpendicular to the lines ... if that description is clear? If you notice it too it might be useful to mention it.

Does it appear that way to anyone else but me?

Ethos_

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Re: Optical illusion in GR diagram?
« Reply #1 on: 10/04/2013 22:11:45 »

Does it appear that way to anyone else but me?
Yes it appears that way to me also. But if one would move both arks from the bottom to the top left side, you'd see the same interpretation of distances.

Pincho

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Re: Optical illusion in GR diagram?
« Reply #2 on: 10/04/2013 23:17:28 »
The lines are equal, and the dots are equal, but...

It's not quite an optical illusion. If you treat the black dots as clocks. You have the lines coming out of the black dots as clock hands. The time that they tell is different at each end. The Left side says 6:25, and the right side says 11:50. Treating these as angles you get something like 150 degrees, and 345 degrees.

There is less amount of white area (I mean that the angle is shallower) for 150 degrees than there is for 345 degrees. 345 degrees has a triangle that my red line can fit into. My red lines are the same line copied over...
« Last Edit: 10/04/2013 23:21:56 by Pincho »

bizerl

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Re: Optical illusion in GR diagram?
« Reply #3 on: 11/04/2013 04:28:48 »
If you consider a rhombus. The opposite sides are the same distance apart as they would be for a square of equal sides, however the area is reduced. So while there is the same distance between equivalent points on the lines, there is actually less space between the two lines.

Which I think is what Pincho said, but anything I can do to confuse the issue further...

yor_on

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Re: Optical illusion in GR diagram?
« Reply #4 on: 11/04/2013 15:05:55 »
"I can help  I can help"
Anyone remember that one, more than me?
I'm sure I can ::))
=

Yep I could, Billy Swan, right?

JP

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Re: Optical illusion in GR diagram?
« Reply #5 on: 11/04/2013 15:26:46 »
I see it too.  I agree with Pincho and bizerl: our brains are probably queued in to look at areas as well as linear distance, and the area of section chopped out of that curve by making a vertical cut is smaller at the left end than the right.

Pmb

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Re: Optical illusion in GR diagram?
« Reply #6 on: 11/04/2013 22:07:10 »
I see it too.  I agree with Pincho and bizerl: our brains are probably queued in to look at areas as well as linear distance, and the area of section chopped out of that curve by making a vertical cut is smaller at the left end than the right.
Thannks. That is essentially what I said/thought too. I was thinking in terms of distance whereas Pincho was thinking in terms of area.

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Re: Optical illusion in GR diagram?
« Reply #6 on: 11/04/2013 22:07:10 »