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aostling
09-16-2008, 01:50 AM
http://www.sciencenews.org/view/generic/id/36400/title/Math_Trek__A_knot_of_light shows some intriguing objects, formed by families of circles on a torus. These fibrations were known to mathematicians; now it is theorized that it may be possible to form them by bending light, in accordance with solutions to the Maxwell Equations.

If such knots can indeed be produced they may lead to new designs for containment of controlled nuclear fusion.

When I look at the video of the fibration I see a possible wire-mesh (non-pneumatic) tire. What do you see?

dp
09-16-2008, 02:54 AM
Interesting concept - and since all energy has mass it should also be a black hole if as they suggest, all space in the loop is filled with light.

aostling
09-16-2008, 02:58 AM
Interesting concept - and since all energy has mass it should also be a black hole if as they suggest, all space in the loop is filled with light.

Er, I thought a photon had zero mass.

darryl
09-16-2008, 03:21 AM
reminds me of ball lightning

Evan
09-16-2008, 05:53 AM
Er, I thought a photon had zero mass.

Photons have zero rest mass meaning that they are pure energy. They do have the mass of thier energy. This isn't often explained in the text books. If mass and energy are held to be equivalent by theory then to be internally consistent any entity that has either or both must have mass in accordance the proportion of each.

The consequence of the mass energy equivalance of the photon is that the photon has momentum. This equivalence is also demonstrated in the loss of mass that occurs when a chemical reaction occurs that releases binding energy (combustion for instance). Although the number of elementary particles (atoms) in the reaction does not change the mass does in accordance with the change in binding energies. It's called the "mass defect".

09-16-2008, 08:16 AM
Pretty heavy concept for light

Evan
09-16-2008, 08:41 AM
Pretty heavy concept for light

Actually, no. The joker is that equation, e=mc^2. That is essentially an expression of the density ratio of mass in the form of matter to mass in the form of energy. It's a very large ratio. It's 1/90,000,000,000,000,000. The mass equivalent of the energy of a photon is so small that it almost doesn't exist. Almost, but not quite. To calculate the momentum force you divide kilowatts of light energy striking something by the speed of light squared. The result is in Newtons and for sunlight reflected from a square kilometer it amounts to about 1 kilogram of pressure. Since a square kilometer is 1 million sq meters that works out to .000001 kilograms or 1 milligram per sq meter per 1000 watts per meter.

I forgot to relate that to the mass-energy of a photon of visible light. One watt is one Joule per second which is 1.8 x 10^24 photons per second. That's 1,800,000,000,000,000,000,000,000 photons per second.

rotate
09-16-2008, 10:45 AM
Photons have zero rest mass meaning that they are pure energy. They do have the mass of thier energy. This isn't often explained in the text books. If mass and energy are held to be equivalent by theory then to be internally consistent any entity that has either or both must have mass in accordance the proportion of each.

Another thing that text books don't explain very clearly is whether "mass" in the context of energy equivalent is affected by gravity in the same way that a particle with mass is influenced.

Evan
09-16-2008, 11:14 AM
Another thing that text books don't explain very clearly is whether "mass" in the context of energy equivalent is affected by gravity in the same way that a particle with mass is influenced.

No question of that. It's called gravitational lensing.

rotate
09-16-2008, 02:20 PM
No question of that. It's called gravitational lensing.

Yes, but often massive object is shown to distort space instead of showing that the photons are gravitationally attracted by the mass. I don't know if you can explain gravitational lensing just by using Newtonian gravitational law. This is why I noted that the text books don't make the definition of "mass" very clear or use it consistently.

Evan
09-16-2008, 05:01 PM
Yes, but often massive object is shown to distort space instead of showing that the photons are gravitationally attracted by the mass. I don't know if you can explain gravitational lensing just by using Newtonian gravitational law. This is why I noted that the text books don't make the definition of "mass" very clear or use it consistently.

It isn't Newtonian since the photons are traveling at the speed of, um, photons. One must be very careful how one characterizes space and matter in such circumstances. At relativistic velocities Newtonian physics gives invalid answers. Saying that the light is following a straight path in a curved spacetime is no different than saying a massive body does the same. The difference is the velocities of the entities. The photon passes by a star or a galaxy in much less time with a nil ratio of momentum to mass and a 1 to 1 ratio of momentum to energy compared to a slower traveling material object. Once velocities exceed about .1 c the approximately linear relationship between velocity of matter and momentum starts to become obviously non-linear. As c is approached any object with rest mass gains momentum on an asymptotic curve becoming infinite at c. The photon on the other hand has a fixed momentum that is proportional to it's energy only.

Therefor the photon exhibts a much lesser amount of deflection than objects moving at non relativistic velocities. The deflection cannot be predicted by Newtonian mechanics.