Relativity question

[Ixion]

Ok, I have a question about electromagnetic radiation traveling across space. I am not a physicist and my knowledge of mathematics is limited to basic calculus. I am also not a cosmologist, so this may be a fairly common question, and if so, I am just ignorant of the answer.

Here is the question:
If a particular source of EM radiation (be it light, radio waves, whatever) was detected from a particular point in the sky, would it be more appropriate to assume it originated from that direction, or that it originated from somewhere else, and spacetime has led it to us?

I am sure my question doesn't make sense, so let me try to explain it a bit. Suppose I am an amateur radio astronomer, and I had access to a very sensitive radio telescope. One night, I am out searching the skies, and I receive a remarkable radio transmission. After I verify that it did not originate from Earth, I look to where my telescope was pointed. I discover that there are no known pulsars in that direction, and no mapped stars within, say, 1000 light years. Would it be inappropriate to say that the radio wave originated from that point? As I see it, it would probably be inappropriate to say that. After all, the Earth is moving, the universe is expanding, the galaxy is moving, etc. Not to mention that gravitational effects may have warped the beam a little during their journey across the cosmos. After all, we cannot be sure there is not a black hole in that direction or an undetected brown dwarf or something similar.

On the other hand, the light we see from the sky is a representation of the origin of the radiation, since, based on my understanding of relativity, we are seeing where the light used to be. So it might be more appropriate to say that the radio wave could be tracked to a point of origin, but that point of origin is not in the same location of spacetime now as it was when the beam left. I am just unsure of the answer and any information people could provide would be helpful.

This is a hypothetical situation. I haven't intercepted any mysterious radio waves or seen any unexplained lights. I am just curious.

As a follow-up, are there certain mathematical models or formulas one would use to ascertain points of origin if they were different?

 

[Ziggurat]

I am sure my question doesn't make sense, so let me try to explain it a bit. Suppose I am an amateur radio astronomer, and I had access to a very sensitive radio telescope. One night, I am out searching the skies, and I receive a remarkable radio transmission. After I verify that it did not originate from Earth, I look to where my telescope was pointed. I discover that there are no known pulsars in that direction, and no mapped stars within, say, 1000 light years. Would it be inappropriate to say that the radio wave originated from that point? As I see it, it would probably be inappropriate to say that. After all, the Earth is moving, the universe is expanding, the galaxy is moving, etc. Not to mention that gravitational effects may have warped the beam a little during their journey across the cosmos.

First off, it's a direction, not a point.

When dealing with curved surfaces (which is what spacetime is in general relativity), it doesn't make much sense to talk about straight lines. But there is something which has some of the essential properties of straight lines which do make sense on curved surfaces, and those are called "geodesics". Light follows geodesics, which are the closed thing you can get to "straight" when on a curved surface.

Now, imagnie that you're on the surface of a sphere, and everything is confined to that surface. Now let's say someone somewhere else broadcasts a radio signal that expands outwards in all directions. Eventually, you pick it up, coming from one direction. A while later, you pick it up again, coming from the opposite direction, because the signal wrapped around the sphere. Now, which direction is the source? Well, it's in BOTH directions. In fact, the "direction" to that source is basically any geodesic.

So while it's true that light from a distant source may have been bent and curved by gravity, it still followed a geodesic. And since the universe itself is curved, calling the geodesic line it traveled along the "direction" to the source is as good a way to define the "direction" to that source as you can come up with.

As a follow-up, are there certain mathematical models or formulas one would use to ascertain points of origin if they were different?

Well, if you know something about the masses near the path of light, you might be able to describe the curvature of the light's path. But that's no simple task to figure out such masses, and even once you do it requires general relativity (which is ugly tensor math) to get the curvatures. But I'm not sure why you'd care: if radio waves are coming from that direction, then any other light from that source will come from that same direction. Whether or not you want to call that the direction to the source, different frequency light will still follow the same geodesic line, and take the same amount of time to arrive.

 

[Perpetual Student]

I believe the deflection of electromagnetic waves by gravity does not depend on the frequency. So seeing nothing in the direction of a radio source would present complications, since a visible source would be deflected in the same manner as a radio wave. Both waves (light and your mysterious source) should follow the same path as far as I know. If I am wrong about this, someone will soon correct me. Right?

 

[Furcifer]

snip... it requires general relativity (which is ugly tensor math) snip...

ugh, Amy Winehouse is ugly, tensor fields are way beyond "ugly".

 

[Ixion]

Well, this has been very enlightening. Thank you very much for your responses, as they answered what I was thinking. I don't know what tensor math is, but based on your descriptions, I am not sure I want to know. I will leave that up to people more interested in solving them than I am.

 

[Ziggurat]

Well, this has been very enlightening. Thank you very much for your responses, as they answered what I was thinking. I don't know what tensor math is, but based on your descriptions, I am not sure I want to know. I will leave that up to people more interested in solving them than I am.

Well, knowing what tensors are won't hurt, even if you don't want to do anything with them. They're basically generalizations of matrices, and they actually get used all over the place.

For example, you may be familiar with vectors (which are rank-1 tensors). You can think of a vector as being an object which has a number associated with each direction (for example, velocity: you've got a component of velocity in different directions). Lots of stuff can be described as vectors, but certain things need more than that. For example, if you want to describe the stresses inside a material, a single vector doesn't have enough information. If you pick any direction, you have a surface perpendicular to that direction. The internal stresses can be described by a vector (basically the force the material on one side of the surface exerts on the other), but only along that direction. Pick a different direction, and the force vector may point in a different direction (for example, for hydrostatic pressure, the force is always along the direction you look, but int for shear stresses). So to describe the internal stresses in a material, you need a vector associated with each direction, or a rank-2 tensor. You can write it as a matrix if you want (a 2D array of numbers). Well, you can keep getting more complicated: associate a rank-2 tensor with each direction, and you get a rank-3 tensor (which would be a 3D array of numbers). And you can make higher and higher order tensors, ad infinitum, if you care to. Rank-2 tensors (ie, matrices) are much more commonly used than higher rank tensors, but higher-rank tensors are still useful (and sometimes necessary - including in General Relativity).

 

[Ziggurat]

ugh, Amy Winehouse is ugly, tensor fields are way beyond "ugly".

My father called Christoffel symbols "Christ-awful" symbols. I admit I found the nickname fitting.

 

[Ixion]

Well, knowing what tensors are won't hurt, even if you don't want to do anything with them. They're basically generalizations of matrices, and they actually get used all over the place.

For example, you may be familiar with vectors (which are rank-1 tensors). You can think of a vector as being an object which has a number associated with each direction (for example, velocity: you've got a component of velocity in different directions). Lots of stuff can be described as vectors, but certain things need more than that. For example, if you want to describe the stresses inside a material, a single vector doesn't have enough information. If you pick any direction, you have a surface perpendicular to that direction. The internal stresses can be described by a vector (basically the force the material on one side of the surface exerts on the other), but only along that direction. Pick a different direction, and the force vector may point in a different direction (for example, for hydrostatic pressure, the force is always along the direction you look, but int for shear stresses). So to describe the internal stresses in a material, you need a vector associated with each direction, or a rank-2 tensor. You can write it as a matrix if you want (a 2D array of numbers). Well, you can keep getting more complicated: associate a rank-2 tensor with each direction, and you get a rank-3 tensor (which would be a 3D array of numbers). And you can make higher and higher order tensors, ad infinitum, if you care to. Rank-2 tensors (ie, matrices) are much more commonly used than higher rank tensors, but higher-rank tensors are still useful (and sometimes necessary - including in General Relativity).

Oh, I understand now. I just didn't know that is what they were called. I think I did some tensor math a long time ago when I was taking physical chemistry classes. I have a bachelor's degree in biochemistry, and part of the degree required two semesters in physical chemistry. Part of the class involved using wave functions to see how chemists defined movement of electrons around the nucleus of an atom, using Heinsenberg Uncertainty Principle and Pauli Exclusion. It has been too long for me to remember exactly what it entailed, but I do remember that I had a very difficult time solving the problems, as they were very long and convoluted. I often read the threads in the science subforum, and I knew there are quite knowledgable people on theorectical physics and astrophysics, so I figured my question would pique someone's interest enough that I might get an answer. Thank you again for making it easy enough for me to understand it.