Calling sonhouse (et al.)

Could you explain me what this means:

"a particle that travels at light speed, follows a geodesic of the space-time."

This is a mistery for me. I know that it has to do wirh vector and tensor analysis, and with the restricted theory of relativity. I hope there a wizz person out there that can explain it to me...

-J

P.S.: sorry sonhouse, maybe you are not the most indicated but I didnt can find another tittle for the thread.... I know you are interested/attracted by the topic.

Cheers

-J

Originally posted by CrazyLilTing
Could you explain me what this means:

"a particle that travels at light speed, follows a geodesic of the space-time."

This is a mistery for me. I know that it has to do wirh vector and tensor analysis, and with the restricted theory of relativity. I hope there a wizz person out there that can explain it to me...

-J

P.S.: sorry sonhouse, m ...[text shortened]... r tittle for the thread.... I know you are interested/attracted by the topic.

Cheers

-J

Space time is curved (imaging the peel of an orange or the shape of a saddle). A geodesic of a curved surface is a curve of shortest distance between two points on the surface (think of it as a string stretched on the curve always touching it). Light under general relativity follows these geodesic curves.

PS. Learn to spell/type.

Originally posted by XanthosNZ
(imaging the peel of an orange...

PS. Learn to spell/type.

did you mean "imagine" ?

Like Xanthos said, a geodesic is a length minimizing curve. For a plane these are straight lines, while for a sphere like the Earth they are great circles. When there is a strong gravitation field involved the shortest distance an object can take is through curved space-time. Otherwise, it is a straight line through space.

If you want an explanantion in mathematical terms, take a look at Math World's page on geodesics.

Originally posted by CrazyLilTing
Could you explain me what this means:

"a particle that travels at light speed, follows a geodesic of the space-time."

This is a mistery for me. I know that it has to do wirh vector and tensor analysis, and with the restricted theory of relativity. I hope there a wizz person out there that can explain it to me...

-J

P.S.: sorry sonhouse, m ...[text shortened]... r tittle for the thread.... I know you are interested/attracted by the topic.

Cheers

-J

The posts that came before me are true, but particles that travel
at the speed of light can contain no mass, such as Photons or
the theoretical Graviton. If it contains ANY mass, it can't go exactly
at the speed of light, therefore its geodesic is a bit differant than
the light speed particle. Neutrino's have little or no mass, however,
the latest is they think it has some vanishingly small mass, even
so, therefore, it cannot go exactly the speed of light. Very close but
0.9999999 C is not the same thing as 1.000000000 C.
Just a side bit.

Originally posted by XanthosNZ
Space time is curved (imaging the peel of an orange or the shape of a saddle). A geodesic of a curved surface is a curve of shortest distance between two points on the surface (think of it as a string stretched on the curve always touching it). Light under general relativity follows these geodesic curves.

PS. Learn to spell/type.

That geodesic changes if there are mass concentrations nearby,
such as our sun. I devoted a LOT of time analysing something
dear to my heart, gravitational lensing as it applies to our neck of
the woods, that is to say our sun. The geodesic changes slightly
when light from a distance source, like the star Sirius, only 8 light years
away and very powerful, when a tiny portion of that light skims just
above the surface of the sun, as Einstein showed, the path the light
takes makes a slight bend, the path changes about 1.7 arcseconds
from its original path. That is about 1/117,000 th of a full circle.
If you imagine two laser beams coming from distant space and one
beam going by the north pole of the sun and the other going by
the south pole of the sun, that change in its angle, going through
the local geodesic, if you do the trig, the two beams will meet at
about 52 billion miles out in space, the sun then is a giant, albeit
imperfect, lens. I could bore you to tears if I haven't already so I
will leave it at that, but trust me, I could go on for days about THAT
subject!

Thanks to all posters!
Xantos, sorry... My mother tongue is spanish. And I an a very bad typist btw... 🙂
Thanks sonhouse for your post. It is very interesting.
But a caveat about my original post: it is only a mathematical formulation, not a physical one... so how it enters here the physics, asuming there is is a super mass that curves the space? Such distortion is not contemplated in the (basic) formulae.
Am I missing something?

-J

P.S.: Xantos, feel fre to correct my english and spelling. It will be welcome. If you have the time, of course!

Originally posted by CrazyLilTing
Thanks to all posters!
Xantos, sorry... My mother tongue is spanish. And I an a very bad typist btw... 🙂
Thanks sonhouse for your post. It is very interesting.
But a caveat about my original post: it is only a mathematical formulation, not a physical one... so how it enters here the physics, asuming there is is a super mass that curves the space? Su ...[text shortened]... eel fre to correct my english and spelling. It will be welcome. If you have the time, of course!

The "super mass" that curves space is nothing less than the entire
mass of the universe. Thats the overall geodesic. Theory goes, if
you aim a beam of light away from you into open space, billions of
years later, that beam will hit the back of your head, come at you
from the opposite direction. Thats because the whole universe curves
in on itself. At least thats the theory. In a three dimensional analogy,
if you draw a line on the surface of a sphere, a globe of the earth
for instance, keep on drawing a straight line, it will come back to itself.
Thats the geodesic for the sphere in 3D. The universe is like that
but in a higher dimensional version where if you draw a straight line,
it will come back to itself even though you think you are going in
a straight line, you are actually curving but you don't see it. Just like
drawing a line on the surface of our planet earth, you keep drawing
a straight line but you don't notice the small curvature which will
eventually bring you right back to the same place.
BTW in my post on gravitational lensing, I said the curve was
1/117,000th part of a circle. Actually its more like 1/750,000 th part of
a circle. The 117,000 number is the equivalent of the F stop number
on a camera lens. Like F8 means the focal distance is 8 times the
diameter of the lens. So the "F stop" of the solar lens is
F117,000. If you divide the focal distance of the sun, about 52 billion
miles to first focus by 117,000 you get the radius of the sun, about
440,000 miles. So that is actually twice the F stop number, the
real Fstop of the sun is half that, or about F 58,000.
Been a while since I examined those numbers.

When someone says an object is curved, like an orange or a saddle, this is in reference to some outer space which has straight dimensions, no? How can space itself be curved?

Originally posted by AThousandYoung
When someone says an object is curved, like an orange or a saddle, this is in reference to some outer space which has straight dimensions, no? How can space itself be curved?

It is what it is.

Originally posted by AThousandYoung
When someone says an object is curved, like an orange or a saddle, this is in reference to some outer space which has straight dimensions, no? How can space itself be curved?

It is easy to imagine the skin of an orange or a saddle, however space isn't two dimesional meaning you need a new type of geometry that is not easily visualised to describe it.