What is the Path of Light through Strong Gravity?

[Grendizer]

Hello All,

My background in physics is very basics. So I apologize in advanced if a make silly logical or empirical error.

As shown in the attached picture, for the sake of simplicity, imagine the picture is a 2D world. Let's say we are being from 3D world looking directly at this world. We have 2D earth, with normal gravity. Assume there are three paths an object can travel through, either from left to right or vica verse, represented by the lines.

My Question is: since space is "bent", how will light travel through the bottom line? there is a "gap" in the path because space is bent at that point into earth. How will light travel through the "gap"?

Thanks,

 

[themrscientist]

You are correct that space would be "bent", but there wouldn't be "gap". I've always heard it best described as the Earth being a bowling ball on a mattress (or some other squishy surface). It creates a depression in the mattress.

The trick here is that light is a part of space. it has a momentum (even though it has no mass), and that momentum can be changed by massive things (like Earth, a star, or a black hole). So, if you take the illustration of the bowling ball on a mattress, and you roll a marble next to it, the marble's path would bend (anywhere from slightly to a ton depending on the speed and path of the marble.

I built a picture to help show you what I mean. Both of the yellow paths are different light paths, and the blue thing (I'm sure you've already guessed, is supposed to be Earth)

 

[Grendizer]

Thanks for the respond.

I think bowling ball on a mattress is a deceptive picture to the mind because the mattress is representing a "plane" where an object can travel on. Since the mattress is bent, there is technically a "virtual gap" because the object can't travel on a straight line on the mattress. It is bent.

Light is the opposed, no? It "does" travel in a straight line. So how would the light travel on the mattress?

 

[Grendizer]

If I was standing on the opposite side of the mattress and you through a marble from the other side, I will see the marble until it is bent. But for the light, I will still see it, right? How is that possible?

 

[themrscientist]

The question becomes tricky when you say a straight line. according to the light, it does move in a straight line, but when you move to a reference frame like the one you are talking about, the light's path would be non-linear for a time. The surface of the mattress represents space. light cannot just jump out of space, and back into it (which is what you are trying to make it do in this 2-D universe).

 

[themrscientist]

sorry, I didn't get to see you post about the marble, but I'm not quite sure what you mean by it. Could you re-phrase the question?

 

[Grendizer]

"but when you move to a reference frame like the one you are talking about, the light's path would be non-linear for a time."

How can you say this in other words?

 

[themrscientist]

If we look at this 2-D universe from our 3-D universe, when the light is near Earth (or another massive object) its path would look like it bends.

 

[Grendizer]

So like this? Where the red line is the path of light?

 

[themrscientist]

yes, in that 2-D universe, that's what it would look like.

 

[Grendizer]

Nice! Thanks :)

In 3-D world, it should work the same. Can that bent be measured?

 

[themrscientist]

You are welcome.

That bend can be calculated using the mass of the object and the distance the light is from the object.

 

[DrewD]

So like this? Where the red line is the path of light?

A very massive object would bend the light to a different direction. The red line shows the path bending and then bending back so that the light travels in the same direction as it did before passing by the object. The light would bend to a different direction like shown in the picture on this site.

 

[themrscientist]

A very massive object would bend the light to a different direction. The red line shows the path bending and then bending back so that the light travels in the same direction as it did before passing by the object. The light would bend to a different direction like shown in the picture on this site.

except that your picture is in 3-D. We have been talking about 2-D. If you reduce your picture to 2-D, you have more or less the exact same picture we are using.

 

[DrewD]

except that your picture is in 3-D. We have been talking about 2-D. If you reduce your picture to 2-D, you have more or less the exact same picture we are using.

It is like the picture that you posted, but it is not like the picture that Grendizer posted. In Grendizer's picture the apparent position of a distant object (as view in the 2D world) would not be changed by a massive object near the path of light. The picture that you drew does show this.

 

[themrscientist]

It is like the picture that you posted, but it is not like the picture that Grendizer posted. In Grendizer's picture the apparent position of a distant object (as view in the 2D world) would not be changed by a massive object near the path of light. The picture that you drew does show this.

That's true. I was originally confused about the axes and view of his original picture. My picture does not answer his question though.

 

[DrewD]

Then what is the question? It appears that the red line shows light traveling from one direction, bending toward the "Earth" and then bending back to the same direction. That is not correct no matter how many dimensions we are considering. If the picture is showing light bent into and hitting the "Earth", then it would be absorbed and not continue past. The red line does not look like that, but perhaps that is due to the drawing.

 

[Grendizer]

Hello DrewD,

My problem is visualizing how space is curved at gravity and how the light travel in this curvature? Initially I thought there was some sort of "gap in space" or "interruption" at gravity point, which affects the path of light. That's why I made a 2-D universe, just to make it as simple as possible and make my point clear.

I am going to try to rephrase my question differently. As shown in the attached figure, let's imagine space is curved without a body, a glitch in a hypothetical world. My question is then to you, how would the light travel?

 

[DrewD]

No matter how you set that up, light would not travel along that path. It looks like you are imagining that the light just bends out of the 2D space. That doesn't make sense. If the universe is restricted to two dimensions, that the light will only be moving "left or right" in those two dimensions.

The "ball on a sheet" analogy is a three dimensional interaction where the path is projected onto two dimensions. So the marble or whatever rolls along the sheet and dips down toward the ball. The "down" direction isn't visible. You should imagine that the path taken by the marble is plotted on a flat surface above the curved sheet. Plus, it is only an analogy.

 

[Drakkith]

Hello DrewD,

My problem is visualizing how space is curved at gravity and how the light travel in this curvature?

You can't visualize it because spacetime is 4d, not 2d or 3d. You can try to visualize the analogies, such as the bowling ball on a mattress, but these are merely analogies. Your best bet is to understand what a Geodesic is and how the geometry of surfaces affects straight lines.

I am going to try to rephrase my question differently. As shown in the attached figure, let's imagine space is curved without a body, a glitch in a hypothetical world. My question is then to you, how would the light travel?

I would really, really like to comment on the picture, but I'm afraid anything I say will simply be misunderstood since your picture is not an accurate representation of how the curvature of space works. Even the simplified 2d scenario of a bowling ball on a mattress (yes, this is a 2d scenario, as the surface of the mattress is 2d) is simplified so much that it is more confusing than helpful to most people.

 

[Drakkith]

The "ball on a sheet" analogy is a three dimensional interaction where the path is projected onto two dimensions. So the marble or whatever rolls along the sheet and dips down toward the ball. The "down" direction isn't visible. You should imagine that the path taken by the marble is plotted on a flat surface above the curved sheet. Plus, it is only an analogy.

Exactly, the depression in the sheet should not be viewed as an actual depression, but merely a change in the geometry of the surface. In reality a ball rolling on this curved surface would not dip down into the Z dimension (the Up/down in this scenario), but would simply start to curve inwards towards the object making the depression.

 

[Chronos]

We observe objects in two dimensions. It is purely an x-y axis thing. That is how the human brain is wired. Our bifocal vision grants us the ability to deduce the location of relatively nearby objects in 3 dimensional space. Our brain also has an onboard clock that allows us a limited ability to deduce the future position of objects in motion. Our perceptual abilities are entirely inadequate beyond that.

 

[256bits]

Hello DrewD,

My problem is visualizing how space is curved at gravity and how the light travel in this curvature? Initially I thought there was some sort of "gap in space" or "interruption" at gravity point, which affects the path of light. That's why I made a 2-D universe, just to make it as simple as possible and make my point clear.

I am going to try to rephrase my question differently. As shown in the attached figure, let's imagine space is curved without a body, a glitch in a hypothetical world. My question is then to you, how would the light travel?

Perhaps you mean to say a 2-d representation of the path of light in a 3-d special universe. In a 3-d universe gravity follows a 1/r^2 law according to Newton versus 1/r in a 2-d universe. Best to stick with the 3-d spatial universe with a 2-d picture of the path of light, rather than having to invent new physics where you do not know where it will take you.

If you have an object influenced by a gravitating mass such as a star, then the object follows an orbit which can be elliptic or circular. If the object is not in an actual orbit then the trajectory is parabolic or hyperbolic depending upon whether the velocity of the object is equal to the escape velocity or greater.

Light also follows these rules since it is influenced by gravity, but since its speed is so great you will be hard pressed to find anything other than a hyperbolic orbit due to Newtonian mechanics.

Along comes Einstein with his theories of relativity and gravity and the situation changes somewhat. A famous experiment involving an eclipse of the sun (by the moon) occurring in the beginning of the 20th century( early 1900's WWI). Eddington and his team traveled to the southern hemisphere to observe the positions of stars near the sun using an occult disk with a telescope. Eddington declared the experiment a success for general relativity in that the shift of the stars close to the sun's edge from their "real" position to an "apparent" position due to the gravitational influence of the sun on light was experimentally determined to be twice that as for Newtonian gravity, as calculations had determined. ( due to the errors of the technology at the time, and the physics of the sun, the experiment was not really a "true" verification, but who was to argue with Eddington ).

In any event. light does curve around a massive object, and if you are speaking spacially, then the red curve in one of your previous posts is not correct, but the others paths would be more representative of the lights' spatial path.

In addition, one can consider the massive object as having what is sometimes termed as a gravitational well. The object or light passing by the gravitating mass enters into the well and exits. How far into the gravitational well the object enters would be a function of how close it grazes by the mass, and of how large the mass is. Your red line can then be thought of the path as an object or light entering and exiting the well. One can then see that by doing so the object or light has a longer path that curves in and out a bit than a more straighter path farther from the object. Since a path closer to the large mass has this dip into the well and becomes longer, the time for the light from the object also takes longer to reach you than the straighter path farther out.

So while you have drawn several paths, some straight, some curved, and some with a dip, neither of them is actually correct or incorrect, except for the fact that you have to specify what you are describing ( which was alluded to by the post from Drakith ). You can also see that the stretched sheet does have something in common with the ideas of a gravitational well represented by the dip in the sheet if a mass is placed upon it.

 

[Grendizer]

Thank you guys for your replies.

@256bits, "gravitational well" that's exactly what I was thinking. This is why I showed my red line as it is "falling" in this gravitational well and quickly exiting. It is like looking through a curved fiber optics. You can see the other side through the fiber, but you will not experience the curvature of the fiber, except the time it takes for the light to reach you, which in this case is neglectable.

 

[Drakkith]

Thank you guys for your replies.

@256bits, "gravitational well" that's exactly what I was thinking. This is why I showed my red line as it is "falling" in this gravitational well and quickly exiting. It is like looking through a curved fiber optics. You can see the other side through the fiber, but you will not experience the curvature of the fiber, except the time it takes for the light to reach you, which in this case is neglectable.

Just to be clear, you realize the light does not follow the red line, right?

 

[Grendizer]

Hey Drakkith,

Here is the confusion, "...the depression in the sheet should not be viewed as an actual depression, but merely a change in the geometry of the surface..."

So curvature is not a depression? If you have "a change of geometry of a surface", for example a parabola, isn't that change an actual depression to the surface? Geometry would be a method that tells you about the depression.

 

[Grendizer]

Just to be clear, you realize the light does not follow the red line, right?

Logically speaking, light travels in space. If space is a straight geometric plane, light should travel in a straight geometric line. If space is a zick zack geometric plane, then light should travel in a zick zack geometric line. That's the bottom line of it.

In a zick zack space, if the light still goes in a straight line, then there is some serious problems with our understanding about light or space.

 

[Dale]

Logically speaking, light travels in space. If space is a straight geometric plane, light should travel in a straight geometric line. If space is a zick zack geometric plane, then light should travel in a zick zack geometric line. That's the bottom line of it.

In a zick zack space, if the light still goes in a straight line, then there is some serious problems with our understanding about light or space.

Light travels along what is called a "null geodesic", which means that it is a "straight line" in a curved spaceTIME. The time dimension of spacetime cannot be neglected. That is what makes the "rubber sheet" and other curved space analogies problematic.

 

[Grendizer]

Thanks for the respond @DaleSpam.

I guess I have to understand the problem from the general relativity prospective. Sucks. I thought I can understand it logically without needing to go into the depth and complex equations (at least for me sounds complex).

This is one of those things if your not expert at the topic, you simply won't get it. :(

 

[Drakkith]

Hey Drakkith,

Here is the confusion, "...the depression in the sheet should not be viewed as an actual depression, but merely a change in the geometry of the surface..."

So curvature is not a depression? If you have "a change of geometry of a surface", for example a parabola, isn't that change an actual depression to the surface? Geometry would be a method that tells you about the depression.

Look closely at the analogy. We are talking about a ball on a sheet. In this analogy the sheet represents 2d space, yet the depression curves the sheet in the 3rd dimension. In our analogy, the 3rd dimension, the Z axis, shouldn't even exist. But because our analogy takes place in the real world, using real objects, it is necessarily 3-dimensional in nature, which automatically generates confusion unless you approach the analogy very, very carefully.

Logically speaking, light travels in space. If space is a straight geometric plane, light should travel in a straight geometric line. If space is a zick zack geometric plane, then light should travel in a zick zack geometric line. That's the bottom line of it.

In a zick zack space, if the light still goes in a straight line, then there is some serious problems with our understanding about light or space.

Note that a 2d plane can exist, and be curved, and yet still be only 2-dimensional. The curvature is not part of another spatial dimension. The curvature we talk about in regards to spacetime is known as intrinsic curvature, not extrinsic curvature. Extrinsic curvature is like the curvature of the surface of the Earth. It is a 2d plane that is embedded in 3 dimensions. Intrinsic curvature is more complicated. Here's what wiki has to say on it:

...a space of three or more dimensions can be intrinsically curved. The curvature is intrinsic in the sense that it is a property defined at every point in the space, rather than a property defined with respect to a larger space that contains it. In general, a curved space may or may not be conceived as being embedded in a higher-dimensional ambient space; if not then its curvature can only be defined intrinsically.

It's important to understand that we live in 3-dimensional space and therefor cannot tell if our universe is embedded in another spatial dimension or not. Because of this, the curvature of spacetime is necessarily intrinsic and cannot be drawn accurately. It also means that drawing 1 or 2 dimensional curved surfaces is possible, but only if they are drawn as extrinsically curved.

 

[Drakkith]

Thanks for the respond @DaleSpam.

I guess I have to understand the problem from the general relativity prospective. Sucks. I thought I can understand it logically without needing to go into the depth and complex equations (at least for me sounds complex).

This is one of those things if your not expert at the topic, you simply won't get it. :(

I don't agree. Sure, you need to know the equations to actually do GR and solve problems, but I don't feel you need to know the math to grasp the basics. GR is, at its core, a theory of geometry, and it takes only a little imagination to extend the more basic concepts of geometry to GR. But you have to have some understanding of those basic geometry concepts, many of which weren't taught to you in high school or college unless you specifically took advanced math courses.

 

[Grendizer]

@Drakkith

Wow, that is really interesting! I have to read you comment few times so I understand the concept, lol. At least you showed me which door to walk through. You showed me which concepts are involved to understand my question. That's kool man, Thanks!

 

[Grendizer]

I don't agree. Sure, you need to know the equations to actually do GR and solve problems, but I don't feel you need to know the math to grasp the basics. GR is, at its core, a theory of geometry, and it takes only a little imagination to extend the more basic concepts of geometry to GR. But you have to have some understanding of those basic geometry concepts, many of which weren't taught to you in high school or college unless you specifically took advanced math courses.

I have a diploma in Robotics and Automation. I love my job; a lot of real life problem solving including design and automating processes using varies programming solutions. However, sometimes I regret not studying Physics. I always been fascinated by it! It been a while since I did physics and "not everyday" mathematics. In my free time, I try to review what I've learned and want to learn new things about physics and math. Hopefully, I'll catch up soon. :)

 

[Drakkith]

I have a diploma in Robotics and Automation. I love my job; a lot of real life problem solving including design and automating processes using varies programming solutions. However, sometimes I regret not studying Physics. I always been fascinated by it! It been a while since I did physics and "not everyday" mathematics. In my free time, I try to review what I've learned and want to learn new things about physics and math. Hopefully, I'll catch up soon. :)

Never regret doing something that has tangible benefits like robotics and automation. Heck, if anything we need MORE engineers and people like yourself. Engineers are who solve real world problems and can be some of the most creative people in the world. A lot of our current unsolved problems in physics is the result of the lack of data, not a lack of brainpower. We are effectively waiting for technology to catch up to theory to get more data to show us which way to go.

 

[A.T.]

My problem is visualizing how space is curved at gravity and how the light travel in this curvature?

You have to understand the concept of geodesics on curved surfaces. The lower picture in the below link gives you an approximate idea:

http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

However, note that this purely spatial curvature just explains half of the light bending. To explain the full amount you have to include the time dimension, and consider space-time curvature. But this gets very hard to visualize.