Question about relativistic acceleration:

Originally posted by twhitehead
You got it wrong. It will give a continuous spike from the focal point of a ray skimming the surface of the sun, and going off to infinity. In theory, if wavelengths were infinitely small, the point at infinity would be brightest because it corresponds to the largest circle. However, because wavelengths are finite and there is some spread going on, the re ...[text shortened]... t to the sun should be brightest, or possibly somewhere beyond that depending on the wavelength.

You both are wrong because you haven't done the geometry of point source lights at interstellar distances. I have, if you take a look at the angle a point source makes when it is away from the exact centerline then it diverges all on its own, so there comes a point where that light cannot be focused.

Originally posted by sonhouse
You both are wrong because you haven't done the geometry of point source lights at interstellar distances. I have, if you take a look at the angle a point source makes when it is away from the exact centerline then it diverges all on its own, so there comes a point where that light cannot be focused.

Not quite sure what you are saying without a diagram. However, I fully agree that as the circles get larger there will be a circle for which the light never converges. However, the transition between convergence to divergence happens when the focus gets to infinity - not at some magical finite distance as you claim.

Originally posted by twhitehead
Not quite sure what you are saying without a diagram. However, I fully agree that as the circles get larger there will be a circle for which the light never converges. However, the transition between convergence to divergence happens when the focus gets to infinity - not at some magical finite distance as you claim.

It took me doing the geometrics of this for a long time, making drawings on very large pieces of paper and I realized after analyzing it in detail that what you are saying is totally wrong. The change from convergence to divergence happens just as I said, it is indeed a very long spike of energy, light years long for stars but it turns out the reducing gravitational effect as you get further from the target star vs the increasing divergence of the light from a distant star ensures the spike is the same length as the distance between the objects, on the one hand the energy of any given circle of light from the distant star is equal in total as a piece of the whole 360 degree sphere, that is to say, every surface area of energy has the same energy so if you took a 1 foot slice of energy from a tiny circle that actually skims the surface of the sun, there will be more energy in total from a ring further from the sun and so even though that energy focuses further away it ensures at least equal energy in the whole spike but if you want to verify my assertion the spike is as long as the distance between the stars, you need to do a point by point analysis like I did ten years ago.

It has sit pretty fallow for that time since I am quite busy at my present job and my son in law whom I started the paper with has his own teaching duties and we both have not had time to formally put it out as of yet.

But try it for yourself, see what I mean, there is a competition between the divergence of light from the distant star and the reducing gravitational lensing angle as you get further from the surface of any star like I said, at the surface, 1R, the angle is 1.75 arc seconds but at 2R it is half, 0.875 arc seconds and that continues to infinity, a billion miles away from the surface there will still be some extremely small bending of light but you can see for instance, at 10R the lensing effect will now be 0.0875 arc seconds and at 100R, 0.00875 arc seconds. 100R is 70 million km above the surface and further out yet, 148 million km, or 1 AU, the sun's lensing effect is still there but clocking in at only 0.0083 arc seconds or 8.3 milli-arcseconds.

So at a relatively close in distance from the sun, 1 AU, the effect has gone down to practically nothing and for a totally flat wave front hitting the sun that, I haven't done that calc yet but it would be really far out away from the sun.

But the wavefront from a distant star is not a flat, it is curved and that curve approaches flatness the further the star is from the sun. The net result is the spike of energy has a longer path but only the length of the distance between the distant point source and the sun.

Originally posted by sonhouse
It took me doing the geometrics of this for a long time, making drawings on very large pieces of paper and I realized after analyzing it in detail that what you are saying is totally wrong. The change from convergence to divergence happens just as I said, it is indeed a very long spike of energy, light years long for stars but it turns out the reducing grav ...[text shortened]... a longer path but only the length of the distance between the distant point source and the sun.

No he's correct.

Applying classical physics the focal point will go to infinity.

In much the same way that as you get closer and closer to light speed it takes
more and more energy to accelerate further, increasing up to infinity...
As you approach the limit beyond which light rays diverge the focal distance will
increase at an increasing rate go to infinity at the limit.

In quantum terms it's more complicated as you can't have arbitrarily small changes in
angle, and you can't have arbitrarily small quantities of light.
So at some distance past the star the amount of light will go to zero.

But it will be because the probability of photons reaching that far becomes infinitesimal,
rather than there being a limit on focal length.

Originally posted by sonhouse
It took me doing the geometrics of this for a long time, making drawings on very large pieces of paper and I realized after analyzing it in detail that what you are saying is totally wrong.

Nowadays we have computers. I will give it some thought and possibly write a small program to demonstrate it. If I get lazy, I'll just do it in Excel.

Originally posted by googlefudge
No he's correct.

Applying classical physics the focal point will go to infinity.

In much the same way that as you get closer and closer to light speed it takes
more and more energy to accelerate further, increasing up to infinity...
As you approach the limit beyond which light rays diverge the focal distance will
increase at an increasing rate ...[text shortened]... tons reaching that far becomes infinitesimal,
rather than there being a limit on focal length.

Y'all keep forgetting the only way to have an infinite focal line, focusing to infinity is to have an equally infinitely flat wave front.

This is my point, the wave fronts of point sources are NOT flat, they are curved, even if the curve is 25 odd light years around in the case of Alpha Centauri at 4.4 light years away. That is not flat by any means and any simulation HAS to take that lack of flatness into account.

I keep saying, you have to competing effects, the lack of flatness of the source Vs the reducing lensing effect as you get further from the surface of the sun or whatever star you are talking about, obviously stars would have a spectrum of lensing effects, not all of them would clock in at 1.75 arc seconds like our sun. I did Alpha Centauri and it came in a bit less, 1.6 something if I recall, been a long time.

Originally posted by sonhouse
Y'all keep forgetting the only way to have an infinite focal line, focusing to infinity is to have an equally infinitely flat wave front.

This is my point, the wave fronts of point sources are NOT flat, they are curved, even if the curve is 25 odd light years around in the case of Alpha Centauri at 4.4 light years away. That is not flat by any means and ...[text shortened]... un. I did Alpha Centauri and it came in a bit less, 1.6 something if I recall, been a long time.

No we are not forgetting that at all.

If we imagine a hypothetical system with a completely flat universe devoid of any matter
except the sun.
And in which there are parallel light rays coming in from infinity past the sun.

Then because there is no limit to the range of gravity [classically speaking] then the
size of the gravitational 'lens' of the sun is infinite and ALL the light rays will be focused
at a distance determined by how close they pass by the Sun.


If we change that to a point source of light directly behind the Sun, then there will be a
limit [in terms of distance from the Sun] at which the diverging rays will be bent so as they
are parallel, inside of which they converge, and outside of which they diverge.

However as you approach that limit, the focal distance will steadily increase to infinity.
There is no upper [finite] limit on the focal length.

EDIT: Mathematically speaking I would expect the focal length to look like the tangent function.

Originally posted by googlefudge
No we are not forgetting that at all.

If we imagine a hypothetical system with a completely flat universe devoid of any matter
except the sun.
And in which there are parallel light rays coming in from infinity past the sun.

Then because there is no limit to the range of gravity [classically speaking] then the
size of the gravitational 'lens' o ...[text shortened]... EDIT: Mathematically speaking I would expect the focal length to look like the tangent function.

I didn't say there was some finite limit, I just said the close in stars would have a focal line that would go about the distance between them BECAUSE of the non flat wave front.

Originally posted by sonhouse
I didn't say there was some finite limit, I just said the close in stars would have a focal line that would go about the distance between them BECAUSE of the non flat wave front.

And we are saying that that focal line will [mathematically at least] extend to infinity.

As long as the point source is far enough away that it's outside the minimum focal distance.

Originally posted by googlefudge
And we are saying that that focal line will [mathematically at least] extend to infinity.

As long as the point source is far enough away that it's outside the minimum focal distance.

You need to analyse that a bit further. I did. You need to think outside the box you have put yourself in.

Originally posted by sonhouse
You need to analyse that a bit further. I did. You need to think outside the box you have put yourself in.

By the time the spherical nature of the wavefront becomes significant you are of the order of a lightyear from the sun (on a line between the sun's centre and the ray), so the effects of the gravity of other stars become important.

Originally posted by DeepThought
By the time the spherical nature of the wavefront becomes significant you are of the order of a lightyear from the sun (on a line between the sun's centre and the ray), so the effects of the gravity of other stars become important.

Consider Alpha Centauri. There are no other suns within 4 light years except us and AC. The nearest other star is Sirius, at twice the distance and therefore 1/4th any gravitational effect from AC. For all intents and purposes, there is no other gravitational effect from AC so the wave front will come to us more or less un-molested by other gravitational effects. You can see, can't you, that if you aim a line at say 20 degrees away from the centerline of AC and the sun, you could feel intuitively there would be no focus from the sun on those waves, right?

Originally posted by sonhouse
Consider Alpha Centauri. There are no other suns within 4 light years except us and AC. The nearest other star is Sirius, at twice the distance and therefore 1/4th any gravitational effect from AC. For all intents and purposes, there is no other gravitational effect from AC so the wave front will come to us more or less un-molested by other gravitational ef ...[text shortened]... the sun, you could feel intuitively there would be no focus from the sun on those waves, right?

The fact that there is a maximum distance away from the sun at which diverging
light rays will be focused, does not mean that the focal line will have a finite upper limit.

Originally posted by googlefudge
The fact that there is a maximum distance away from the sun at which diverging
light rays will be focused, does not mean that the focal line will have a finite upper limit.

I am not disputing that the focal line can have an infinite distance, I am just saying for close in stars, the focus poops out at about the distance between the stars, like AC has a spike about 4 light years long after which the light from AC is not focused any more.

Originally posted by sonhouse
I am not disputing that the focal line can have an infinite distance, I am just saying for close in stars, the focus poops out at about the distance between the stars, like AC has a spike about 4 light years long after which the light from AC is not focused any more.

Yes, I understand what you are saying. I'm saying that you're wrong.
I'm doing both at the same time. :p

I'll do the math to prove it shortly [ish].