Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Gert in Ottawa, Canada on 09/01/2010 04:30:02
-
Gert in Ottawa, Canada asked the Naked Scientists:
Theoretically, would it be possible to bend a light beam back to the point it came from without having it bounce off something?
If yes, how many Earth-masses would it take to do such a bend (if we're talking about one single object doing the bend)?
What do you think?
-
The photon sphere is a region around a huge mass (i.e. a black hole) such that any photon that passes the black hole at the appropriate distance is bent so much that it enters an orbit around the black hole forever. (More details here: http://en.wikipedia.org/wiki/Photon_sphere)
It seems reasonable that photons approaching from some point further away should be able to "slingshot" out in a different direction. I don't know the details of the calculation, however.
-
It's a weirdly fascinating question. Can a light beam bend back to the point it came from without having it bounce off something?
What exactly would be 'bend back'. There is nothing there before the interaction. We seem to be a 'field' existing under certain conditions, with matter as the 'touch ables'. Then we have 'laws' that define how this field interact with itself. And it all works because of our 'arrow of time' keeps it on one track macroscopically.
-
When I worked out the orbital radius for an orbital velocity of 'c' it turned out to be well within the Schwarzschild radius, so I'd say that it's not possible for the light to be bent back to where it came from. The most severe change of course would be hyperbolic.
-
Is that not what happens inside a blackhole?
Answers on a postcard
P.S Forget the post card as the snow is so bad it would probably not arrive.
-
Thanks for the replies. :) I realize that I should have been more clear in my question, but I agree... Black holes certainly pulls the light back... (the question is if the photons have much of a chance of moving anywhere inside the black hole).
What I should have should have emphasized was that I was looking for an object (e.g. a planet, a star, a moon, a black hole) to bend the beam with its gravitation. After submitting my question, it hit me that you probably need two objects, or else the light might just get "sucked" into the object and never return:
[ Invalid Attachment ]
So, the question remain... How many earth masses (or similar "simple to understand" measurements) would it take for each object in order to bend the light back to its source.
Thanks again,
Gert
-
It is not possible to produce a definitive answer to your question as it depends how closely the photon grazes the body that deflects it, of course one body cannot do the job and two are required.
The alignment of the two bodies is of course critical, after being deflected by 90° by the first it must graze the second at just the right place.
I don't think we will ever see light from a star grazing two black holes in just this manner.
-
Just a point re Gert's diagram; at no point will the light follow a straight-line path; I said earlier it's course will be hyperbolic, but otherwise yes, it would be possible to bend light back through its point of origin using two bodies, although of course, and as shown, it wouldn't be bent back on itself but bent back across itself.
Syphum; if the universe is infinite, then this must be happening somewhere.
-
Hi. Just a quick question. If photons have no mass will they be subject to gravitational attraction, to bend around the object, or will they be traveling in a straight line through space that has been curved by the object?
Liam
-
Hi. Just a quick question. If photons have no mass will they be subject to gravitational attraction, to bend around the object, or will they be traveling in a straight line through space that has been curved by the object?
Liam
Photons have to follow the geometry of the spacetime, as any other object. Spacetime rules everything! [;)]
-
If our universe is a closed one all light should 'return' sooner or later.
Well from my point of view, probably 'later' :)
-
"it wouldn't be bent back on itself but bent back across itself".
Although and incredibly unlikely alignment a third body could bend it back along its self.
P.S
What about the 'slingshot' effect if the deflecting bodies are moving ?.
-
Hmm... re moving bodies; on one hand, wouldn't they have to be moving at a significant proportion of the speed of the deflected photon? But on the other hand, the photon can't experience any acceleration...
Edited to change first 'one' -> 'on'
-
syhprum - "It is not possible to produce a definitive answer to your question as it depends how closely the photon grazes the body that deflects it, of course one body cannot do the job and two are required."
You'll have to think of ideal conditions and perfect paths. I believe the chance of pulling off this kind of bend is pretty slim, but it would be cool if someone has the knowledge to calculate the masses involved. [:)]
LeeE - "at no point will the light follow a straight-line path"
Very true. There's so much stuff out there that would affect its path and not to forget the expansion of the Universe, which also affects the path (especially at long distances). I think we'll need to forget about these things, or else it will be impossible to answer this question.
yor_on - "If our universe is a closed one all light should 'return' sooner or later.
Well from my point of view, probably 'later' :)"
Probably not if its energy is sucked up by some object. [;)] But you're right... if the Universe isn't expanding or if it once again contracts towards a singularity (for the latter, you better wear those sunglasses [8D]), the light will eventually come back.
-
LeeE - "at no point will the light follow a straight-line path"
Very true. There's so much stuff out there that would affect its path and not to forget the expansion of the Universe, which also affects the path (especially at long distances). I think we'll need to forget about these things, or else it will be impossible to answer this question.
It doesn't need many bodies to result in a curved path; just the two bodies will result in a curved path.
-
It doesn't need many bodies to result in a curved path; just the two bodies will result in a curved path.
What I was getting at was that - in space - there are more objects than the two bodies that will affect the beam's path.
-
LeeE - "at no point will the light follow a straight-line path"
Very true. There's so much stuff out there that would affect its path and not to forget the expansion of the Universe, which also affects the path (especially at long distances). I think we'll need to forget about these things, or else it will be impossible to answer this question.
It doesn't need many bodies to result in a curved path; just the two bodies will result in a curved path.
A single object can do this too. I've heard lectures about black holes doing this.
-
When I worked out the orbital radius for an orbital velocity of 'c' it turned out to be well within the Schwarzschild radius, so I'd say that it's not possible for the light to be bent back to where it came from. The most severe change of course would be hyperbolic.
Are you sure about that? I've definitely heard physicists talk about this happening outside of the Schwarzschild radius... The wiki claims it's at 3/2 the Schwarzschild radius: http://en.wikipedia.org/wiki/Photon_sphere
-
Hmm... that's interesting JP. I worked it out for a question here on the forum, and I think I gave my maths in the posting. I'll see if I can find it again, or work out how I worked it out.
-
LeeE - "at no point will the light follow a straight-line path"
Very true. There's so much stuff out there that would affect its path and not to forget the expansion of the Universe, which also affects the path (especially at long distances). I think we'll need to forget about these things, or else it will be impossible to answer this question.
It doesn't need many bodies to result in a curved path; just the two bodies will result in a curved path.
A single object can do this too. I've heard lectures about black holes doing this.
I was wondering about that too.
Is it possible to do that with objects with mass? If so, would light be fundamentally any different?
-
As far as I can make out, I used:
vo = √(m2G)/mr)
where vo is the orbital velocity, G is the gravitational constant, m is the mass and r is the radius, obtained from
http://en.wikipedia.org/wiki/Orbital_velocity#Mean_orbital_speed (http://en.wikipedia.org/wiki/Orbital_velocity#Mean_orbital_speed)
Note that I've omitted the second mass variable in that formula as the mass of the light is assumed to be zero.
The formula for the Schwarzchild radius from http://en.wikipedia.org/wiki/Schwarzschild_radius#Formula_for_the_Schwarzschild_radius (http://en.wikipedia.org/wiki/Schwarzschild_radius#Formula_for_the_Schwarzschild_radius)
is:
rs = 2Gm/c2
so for an Earth sized mass of 5.9736 * 1024 kg the Schwarzchild radius is:
= (2*6.67E-11*5.9736E+024) / (2997924582)
= 7.97E+14 / 8.99E+16
= 0.00886647 metres i.e. just under 9 mm
and the orbital velocity for an Earth sized mass at a radius of 0.00886647 metres is
= √ ((5.9736E+024 * 5.9736E+024) * 6.67E-11) / (5.9736E+024 * 0.00886647)
= √ 2.38E+39 / 5.30E+22
= √ 4.49E+16
= 2.12E+8
which is < speed of light.
It seems that I originally did a spreadsheet to compare the orbital velocities for different masses and it turned out that the orbital velocity at the Schwarzchild radius is always 2.12E+8 for any mass.
As always though, you'd better check my maths.
-
Just a belated thought on this: if the orbital velocity can be greater than or equal to 'c' outside the Event Horizon then it seems to me that you will end up with the situation where the circumference of the Event Horizon is less than the wavelength of light (EMR) being trapped within it. When the circumference is half the wavelength of trapped EMR, will the wave not end up being out of phase with itself?