constant motion and perspective

[michel123456]

You drive on the highway on a very long straight line.

In the mirror, you look at a fast car coming closer and closer. Then the car comes really close and passes you by.

Zouf.

Then gently goes in front of you, getting smaller and smaller, slowly vanishing to the horizon.

 

Don't you get the impression that the car was going faster when it was close to you?

Maybe not because you have seen this effect so many times that it means nothing to you.

 

The picture below.

 

 

The real distance between the light posts is equal.

Because of the effect of perspective, the apparent distance beween the posts (the colored lines on the picture) gets small and smaller until zero at the horizon.

So, when you are observing a car moving at constant velocity in perspective, you are observing the car going from one post to the other in the same interval of time.

IOW the car appears to travel less and less distance in the same time. Which is called deceleration.

 

When you look at a car coming from the horizon and getting closer to you, you are observing the opposite effect: acceleration.

 

Of course, that would be an abuse of language to call that "acceleration" because the car is moving at constant velocity. The "accelerated effect" is caused by the apparent deformation of perspective.

However the effect is real and counts for everything coming from far away and reaching your eye.

 

I wondered what is the mathematical relation between the coloured lines.

Intuitively, a graph of it should be a conic section. A parabola I guess.

Does anybody know?

Edited April 7, 2014 by michel123456

[michel123456]

Which means, if I am correct, that when you fall down, in fact what your eyes see is not a common accelerated motion towards the ground, but a second derivative of velocity.

Which also means, If I am correct, that anything coming straight into your retina at constant velocity appears as being in accelerated motion.

Edited April 8, 2014 by michel123456

[Sensei]

I wondered what is the mathematical relation between the coloured lines.

 

Look at OpenGL perspective transformation matrix.

http://www.opengl.org/sdk/docs/man2/xhtml/gluPerspective.xml

http://www.opengl.org/sdk/docs/man2/xhtml/glFrustum.xml

 

OpenGL transforms first 3d object coordinate to 3d world coordinate (multiply vector 3x1 by matrix 4x4) (glMatrixMode GL_MODELVIEW),

then multiply result by perspective matrix (glMatrixMode GL_PROJECTION).

After that you have x,y on screen and depth (which is used to z-buffer).

 

Analyze this transformation matrix, and you will have math.

 

It'll be easier than you think- distance between lanterns is same, and their heights are also the same.

Edited April 8, 2014 by Sensei

[michel123456]

I am almost deseperate not finding anywhere a video showing what I mean.

 

Found this one

 

Where the effect can be seen, if you make an effort, some yoga exercise first, and concentrate on what you are actually observing against what you are so used to observe.

The train is constantly defomed since the front of the train is seemingly accelerated relatively to the back of the train, as you can observe when the train passes sideways.

And this counts for constant motion.

 

Still looking for something equivalent concerning accelerated motion.

Edited April 13, 2014 by michel123456

[michel123456]

Which also means, If I am correct, that anything coming straight into your retina at constant velocity appears as being in accelerated motion.

I ment

 

When an object comes from far away straight towards you, moving at constant velocity, it will appear accelerating.

And that counts for light too:

when light comes to you, it will appear accelerating.

[John Cuthber]

You may find this helpful

https://en.wikipedia.org/wiki/Optical_flow

[swansont]

I ment

 

When an object comes from far away straight towards you, moving at constant velocity, it will appear accelerating.

And that counts for light too:

when light comes to you, it will appear accelerating.

 

 

Doesn't work for light. You don't see it coming at you. You only see it when it gets to you.

[michel123456]

You may find this helpful

https://en.wikipedia.org/wiki/Optical_flow

Interesting. But I see no mention of acceleration.

 

 

Doesn't work for light. You don't see it coming at you. You only see it when it gets to you.

If a rule applies because of geometry there should be no exception.

 

If you make a careful analysis of the light that gets to you, you should find that this light appears like being under acceleration.

[swansont]

Interesting. But I see no mention of acceleration.

If a rule applies because of geometry there should be no exception.

 

If you make a careful analysis of the light that gets to you, you should find that this light appears like being under acceleration.

 

 

No, it won't. Unlike massive objects, you can't watch light as it's getting to you. This optical illusion — and that's all it is — doesn't come into play. If it leaves a point some distance away from you and arrives some time later, then d/t is going to be equal to the speed of light.

[michel123456]

 

 

No, it won't. Unlike massive objects, you can't watch light as it's getting to you. This optical illusion — and that's all it is — doesn't come into play. If it leaves a point some distance away from you and arrives some time later, then d/t is going to be equal to the speed of light.

Constant motion is not under question.

If a train comes from 100km away at 100km/h, it will reach you in 1 hour.

Nonetheless it will look like accelerating when it comes straight to crush you.

I don't know why you think light would be an exception to that.

It is an "optical" illusion.

Optical: isn't it all about vision?

[J.C.MacSwell]

Constant motion is not under question.

If a train comes from 100km away at 100km/h, it will reach you in 1 hour.

Nonetheless it will look like accelerating when it comes straight to crush you.

I don't know why you think light would be an exception to that.

It is an "optical" illusion.

Optical: isn't it all about vision?

You see the train coming. You do not see the light coming. You only "see" it arrive.

[EdEarl]

You can't see a photon until it hits your eye.

[Delta1212]

As a helpful illustration:

 

If you close your eyes, you will only find out the train is coming when it hits you, and then you will feel it moving exactly as fast as it is moving. It will obviously not look like it is accelerating in this case.

 

That's what seeing a photon is like. You only detect it when it hits you. You can't watch it coming at you, and so it can't "look" like it's doing anything on the way to your eye.

[michel123456]

You can't see a photon until it hits your eye.

 

well understood. But this photon comes from far away. From a star or a galaxy. The photon is not born upon your eye.

So you see it coming from somewhere.

[EdEarl]

Not coming, your brain only registers the photon after it is traveled from the source to your eye. Thus, you see where the photon came from. You cannot see it as it travels, it is invisible.

 

PS

What you are suggesting would mean light bounces off the photon in transit (light doesn't bounce off light), and the reflected light would race to your eye faster than light (not possible) to get to your eye before the photon in transit.

Edited March 26, 2016 by EdEarl

[michel123456]

I am talking about a property of the geometry of space as seen by an observer. i am not talking about the property of light or anything.

Since it is a property (or an illusion) created by the geometry, everything must be subordinated to the same effect.

[swansont]

I am talking about a property of the geometry of space as seen by an observer. i am not talking about the property of light or anything.

Since it is a property (or an illusion) created by the geometry, everything must be subordinated to the same effect.

It's created by being able to see things in that geometry. You don't see light while it's in transit to you.

[Strange]

 

Constant motion is not under question.

If a train comes from 100km away at 100km/h, it will reach you in 1 hour.

Nonetheless it will look like accelerating when it comes straight to crush you.

I don't know why you think light would be an exception to that.

It is an "optical" illusion.

Optical: isn't it all about vision?

 

It may seem to be accelerating but if you were to make a measurement such as timing the rate at which the car passes the light posts (or the train passes the sleepers) then you would see that the speed was constant.

 

Also, if you were to measure the Doppler shift of the light from the object, you would see it was constant (until it passes you).

 

That is why science relies on measurements rather than appearances.

Edited March 26, 2016 by Strange

[J.C.MacSwell]

I am talking about a property of the geometry of space as seen by an observer. i am not talking about the property of light or anything.

Since it is a property (or an illusion) created by the geometry, everything must be subordinated to the same effect.

I am not sure exactly of the point you are trying to make.

 

Are you are saying that space (say, everyday Cartesian space) is not "as seen" but "as seen and calculated", or not as observed but as observed through the perspective of experience?

 

Compare to Minkowski Spacetime, which would always, I think, be "as seen (measured) and calculated", and we don't get to experience it in everyday life in the same intuitive manner.

[michel123456]

I am not sure exactly of the point you are trying to make.

 

Are you are saying that space (say, everyday Cartesian space) is not "as seen" but "as seen and calculated", or not as observed but as observed through the perspective of experience?

 

Compare to Minkowski Spacetime, which would always, I think, be "as seen (measured) and calculated", and we don't get to experience it in everyday life in the same intuitive manner.

I say that observation is deformed: what you measure as constant motion is observed as if it was accelerated motion. The result is first that all objects in constant motion are seen as if they were expanding/contracting. The same goes for objects that come directly towards you.

And that seems acceptably true for all objects, except for light if I have to believe all the other members here.

Edited March 26, 2016 by michel123456

[Strange]

I say that observation is deformed: what you measure as constant motion is observed as if it was accelerated motion. The result is first that all objects in constant motion are seen as if they were expanding/contracting.

 

Reminds me of a comedy sketch I saw years ago: two characters sitting on a beach watching a ship sailing away. They comment on how it is getting smaller and smaller. And then start panicking about the fate of the passengers who are being crushed to death as the ship shrinks.

 

What you seem to be missing is the difference between subjective appearances and reality. You can measure the distance to the moving object (and its speed) and work out how much it should appear reduced in size. If you see differences between that objective data and what you see, then you might need to worry about the fate of the passengers.

 

As you seem to be trying to draw some sort of cosmological analogy here: we know the distance to stars, we can measure the actual velocities at those distances, and we can compare those to our models.

[J.C.MacSwell]

Maybe it's time Father Ted helped us out...

 

Edited March 26, 2016 by J.C.MacSwell

[michel123456]

You drive on the highway on a very long straight line.

In the mirror, you look at a fast car coming closer and closer. Then the car comes really close and passes you by.

Zouf.

Then gently goes in front of you, getting smaller and smaller, slowly vanishing to the horizon.

 

Don't you get the impression that the car was going faster when it was close to you?

Maybe not because you have seen this effect so many times that it means nothing to you.

 

The picture below.

 

Shot108.jpg

 

The real distance between the light posts is equal.

Because of the effect of perspective, the apparent distance beween the posts (the colored lines on the picture) gets small and smaller until zero at the horizon.

So, when you are observing a car moving at constant velocity in perspective, you are observing the car going from one post to the other in the same interval of time.

IOW the car appears to travel less and less distance in the same time. Which is called deceleration.

 

When you look at a car coming from the horizon and getting closer to you, you are observing the opposite effect: acceleration.

 

Of course, that would be an abuse of language to call that "acceleration" because the car is moving at constant velocity. The "accelerated effect" is caused by the apparent deformation of perspective.

However the effect is real and counts for everything coming from far away and reaching your eye.

 

I wondered what is the mathematical relation between the coloured lines.

Intuitively, a graph of it should be a conic section. A parabola I guess.

Does anybody know?

Does anybody know?

[Strange]

Does anybody know?

 

Post #3

[michel123456]

Maybe it's time Father Ted helped us out...

 

Father Ted will also explain why time does not seem to diminish when far away?