Undergrad Is there a physical explanation for the relationship between light and space?

[Buckethead]

I am curious why a more intimate relationship between light and empty space is not something one ever hears about when I think about the three obvious examples of why there seems to be a relationship. 1) Light follows a curve when in a curved spacetime (a gravitational field), 2) photons at large distances from us can move away from us at speeds exceeding c due to the expansion of space, and 3) inertia felt by acceleration and acceleration felt by rotation are absolute in nature which (it seems to me) must imply they are relative to some kind of physical spacetime structure.

What I'm asking is given these 3 examples, why isn't it acceptable to consider a strong relationship between light and space, a relationship that would allow for (and even explain) the constancy of the speed of light while still allowing for a structure that would help to explain the 3 examples given here. Isn't it possible to define a type of space that both upholds relativity but also can be pictured as something physical that can be stretched, moved, and spun to accommodate things like curving spacetime, expanding space, and a Newtonian type of absolute space? A theory to describe what such a space could physically consist of or be made of so it could be pictured? I'm sure I'm not the only one to have thought about this so is it just simply impossible or illogical?

 

[SiennaTheGr8]

I'm not quite sure exactly what it is you're asking, but a "relationship" between light and space certainly exists in the sense that our universe has a speed limit, and light travels at it.

 

[Dale]

Isn't it possible to define a type of space that both upholds relativity but also can be pictured as something physical that can be stretched, moved, and spun to accommodate things like curving spacetime, expanding space, and a Newtonian type of absolute space?

Sure. Take GR, define any tetrad, call the spacelike components "space".

 

[Buckethead]

Thanks for the replies.

Sure. Take GR, define any tetrad, call the spacelike components "space".

I'm just a science enthusiast so had to look up tetrad real quick, but from what I was able to glean, isn't this just a tool to determine for example how light might move past a gravitational field? If so perhaps it can also be used when describing an expanding space, but can it also be used to explain the "absoluteness" of space and what that space is anchored too such as stars or just simply nothing at all and the mechanism behind that anchor? For example, is "space" (or the chosen "tetrad") anchored to distant galactic clusters for example and if so why and if not, what is it anchored to? (I suppose this is simply Mach's Principle vs something else whatever that something else might be)

 

[Dale]

A tetrad is another name for reference frame. It does not need to be anchored to anything in particular, but it certainly can be anchored to whatever you like if you so desire. The selection of a tetrad to use to define "space" is an arbitrary mathematical exercise and has no physical implications.

 

[Buckethead]

OK, with that in mind, if we were to use this model to determine for example how fast a light beam is traveling away from us due to expansion of space between us and this distant light beam and its associated cluster then is it safe to say you would anchor this tetrad to the cluster (since the tetrad/light/cluster are all moving away from us at the same speed)? Therefore this mathematical model, even though it's not physical, is still a representation of a chunk of space that is now anchored to a cluster and is also determining the movement of the light beam (with regard to its speed relative to us). So what I'm asking is if anyone has worked on the mechanism (either mathematically or philosophically) by which this light is tied to the tetrad (or the physical space it represents) and by which the tetrad is tied to the cluster? I hope I'm not asking a nonsensical question. My apologies if I am.

 

[Dale]

if we were to use this model to determine for example how fast a light beam is traveling away from us

The tetrad formalism guarantees that light always travels at c.

 

[Buckethead]

I assume this is for a non-expanding tetrad. Am I wrong when I say it takes light longer to get from a distant cluster to us than we would calculate from distance/c because of the expansion?

 

[Dale]

I assume this is for a non-expanding tetrad

No, it is for any tetrad. No matter what light always travels at c. Note, a tetrad is not a coordinate system, and there is no global notion of simultaneity defined by one.

 

[John Park]

No matter what light always travels at c.

I thought this was strictly for local measurements.

 

[Dale]

I thought this was strictly for local measurements.

I think you are thinking of a coordinate chart. A tetrad is not a coordinate chart, so it doesn't produce any artificial coordinate speed of light

 

[phyzguy]

Isn't it possible to define a type of space that both upholds relativity but also can be pictured as something physical that can be stretched, moved, and spun to accommodate things like curving spacetime, expanding space, and a Newtonian type of absolute space? A theory to describe what such a space could physically consist of or be made of so it could be pictured? I'm sure I'm not the only one to have thought about this so is it just simply impossible or illogical?

Physics is about using the language of mathematics to describe the physical universe. One of the reasons we use mathematics is that it is a precise language where terms have well defined meanings. I don't know what your question means, because it is stated in imprecise language. Can you formulate a description of the universe in mathematical terms which is somehow different from general relativity?

 

[PeterDonis]

Light follows a curve when in a curved spacetime

So does anything else.

photons at large distances from us can move away from us at speeds exceeding c due to the expansion of space

So can other objects. (And this "speed" is a coordinate speed anyway, and has no physical meaning; it's just a convenient bookkeeping number.)

inertia felt by acceleration and acceleration felt by rotation are absolute in nature

What does this have to do with light?

I'm having difficulty seeing why you think any of this implies some relationship between light in particular and empty space.

 

[Buckethead]

Physics is about using the language of mathematics to describe the physical universe. One of the reasons we use mathematics is that it is a precise language where terms have well defined meanings. I don't know what your question means, because it is stated in imprecise language. Can you formulate a description of the universe in mathematical terms which is somehow different from general relativity?

You can know what my question means using imprecise language the same way you know what I mean if I were to say something like "Dark matter is what holds the clusters together" There is nothing precise about that statement but you now have a foundation for which to develop a mathematical model. So it is useful. In the same way I'm asking what can space be made of that would cause it to uphold both relativity and to allow for things like inertia, expansion, etc.

 

[phyzguy]

You can know what my question means using imprecise language the same way you know what I mean if I were to say something like "Dark matter is what holds the clusters together" There is nothing precise about that statement but you now have a foundation for which to develop a mathematical model. So it is useful. In the same way I'm asking what can space be made of that would cause it to uphold both relativity and to allow for things like inertia, expansion, etc.

So if I understand you, you are asking me to take your idea and make it into a mathematical model that makes firm predictions. Why should I spend my effort to do this? I strongly doubt that it will lead anywhere. I'm trying to make the point that if you believe your idea has value, it is up to you to make it more precise. Simply throwing out ideas and expecting others to do the work is not very reasonable. Remember the old adage that genius is 1% inspiration and 99% perspiration. Also, as you try to develop your idea into more precise mathematical language, you will learn why it is unlikely to lead anywhere.

 

[Buckethead]

So does anything else.

Understood. It doesn't take away from my question.

So can other objects. (And this "speed" is a coordinate speed anyway, and has no physical meaning; it's just a convenient bookkeeping number.)

What are you basing that on? If a photon takes 20B years to travel 10B l.y. then light is traveling at .5c when measured over this distance even if experiment and maxwells equations show light to locally always go at c. In other words, there is a contradiction here than must be resolved. You can chose to say one of those is physical and one is not, but which one are you going to chose and why?

What does this have to do with light?

It's related to the nature of space, not light.

I'm having difficulty seeing why you think any of this implies some relationship between light in particular and empty space.

I was using light as an example because it exclusively is used to show that space is not "ponderable matter" due to its constant speed. But matter in general can be used when questioning things like the nature of space with regard to inertia, or curvature of space or expansion of space if it is found to be useful in leading to an answer.

 

[Buckethead]

So if I understand you, you are asking me to take your idea and make it into a mathematical model that makes firm predictions. Why should I spend my effort to do this? I strongly doubt that it will lead anywhere. I'm trying to make the point that if you believe your idea has value, it is up to you to make it more precise. Simply throwing out ideas and expecting others to do the work is not very reasonable. Remember the old adage that genius is 1% inspiration and 99% perspiration. Also, as you try to develop your idea into more precise mathematical language, you will learn why it is unlikely to lead anywhere.

I'm not asking you to do anything and as I stated earlier, I'm a enthusiast, not a physicist. I'm asking if anyone has thought about the nature of space that can be put into more physically understandable terms. If you do not think this is possible, then perhaps that is the case and I can accept that.

 

[Dale]

what can space be made of

Space can't be made of anything. Otherwise it would be that thing and not space.

Please do not misconstrue my discussion about tetrads as justification for any claims that space is made of something. It is actually intended to show that what you are asking for is already covered by GR simply by making a completely arbitrary choice to call something "space"

 

[Nugatory]

You can know what my question means using imprecise language the same way you know what I mean if I were to say something like "Dark matter is what holds the clusters together" There is nothing precise about that statement but you now have a foundation for which to develop a mathematical model. So it is useful.

You have the development of the ideas backwards. We started with the mathematical model and then came up with the imprecise language when we needed a way of describing the results of the model to non-specialists. It's easy to get the imprecise description from the precise description, but much harder to go the other way.

That's not to say that it doesn't happen; some of the most important developments in science have started with intuitive leaps from an imprecisely formulated idea, with the mathematical analysis following after. However, it doesn't happen very often and when it does, it's based on a deep understanding of the then-current theories which are being improved upon.

 

[Dale]

In other words, there is a contradiction here than must be resolved. You can chose to say one of those is physical and one is not, but which one are you going to chose and why?

The coordinate speed is not physical because coordinates are not physical.

I'm asking if anyone has thought about the nature of space that can be put into more physically understandable terms.

Hmm, what is not physically understandable about GR? Space and time together form spacetime and spacetime is curved according to the energy/momentum content.

 

[Buckethead]

Space can't be made of anything. Otherwise it would be that thing and not space.

Please do not misconstrue my discussion about tetrads as justification for any claims that space is made of something. It is actually intended to show that what you are asking for is already covered by GR simply by making a completely arbitrary choice to call something "space"

OK. I can wrap my head around that. So really what I need to ask is not what space is made of but what the properties of "space" is so that space can be understood on those terms, in the same way that an electron can't be understood except by way of its properties. With this in mind then, I have some additional questions, but I have to think them through first.

 

[Buckethead]

You have the development of the ideas backwards. We started with the mathematical model and then came up with the imprecise language when we needed a way of describing the results of the model to non-specialists. It's easy to get the imprecise description from the precise description, but much harder to go the other way.

OK, yes and indeed even the idea of of dark matter started from the precise measurements of the rotational curves of galaxies. But following that same model, we have precise mathematical descriptions of space, yet we still don't seem to have the non-precise "visual" in the same way that we have a "dark matter" visual for the rotational curve anomaly.

 

[Buckethead]

The coordinate speed is not physical because coordinates are not physical.

Why? If you define 2 coordinates in space that are 100m apart, why is that not physical? Or are you referring to spacetime intervals?

 

[Nugatory]

Why? If you define 2 coordinates in space that are 100m apart, why is that not physical? Or are you referring to spacetime intervals?

Saying that they are 100 meters apart is equivalent to saying that there exists some coordinate system such that for all $T$ if the coordinates of an event on the worldline of one point is $(X_0,T)$, there will be an event $(X_1,T)$ on the worldline of the other point with $X_0-X_1=100$. That not a physical statement, it's a statement about coordinate systems.

To get a physical statement, we'd need something like: If we have a light source anda detector at one point and a mirror at the other, a light signal emitted by the light source will be reflected by the mirror and arrive back at the mirror $200/c$ seconds (proper time along the worldine of the first point, not a difference in coordinate time). In curved spacetime there are coordinate systems in which the "100 meters apart" statement is true, yet the physical statement is not, and vice versa.

 

[Dale]

So really what I need to ask is not what space is made of but what the properties of "space" is so that space can be understood on those terms, in the same way that an electron can't be understood except by way of its properties.

Yes, I think that is a good approach.

 

[Dale]

Why? If you define 2 coordinates in space that are 100m apart, why is that not physical?

Because without changing anything physical I can choose a different coordinate system where the distance between the same two points is 50 m apart. All of the (physical) experimental results would be identical even though the (non physical) coordinates are different.

 

[Buckethead]

Saying that they are 100 meters apart is equivalent to saying that there exists some coordinate system such that for all $T$ if the coordinates of an event on the worldline of one point is $(X_0,T)$, there will be an event $(X_1,T)$ on the worldline of the other point with $X_0-X_1=100$. That not a physical statement, it's a statement about coordinate systems.

To get a physical statement, we'd need something like: If we have a light source anda detector at one point and a mirror at the other, a light signal emitted by the light source will be reflected by the mirror and arrive back at the mirror $200/c$ seconds (proper time along the worldine of the first point, not a difference in coordinate time). In curved spacetime there are coordinate systems in which the "100 meters apart" statement is true, yet the physical statement is not, and vice versa.

And coordinate systems change when velocities change? Can I say there is one specific coordinate system when looking out into space from the viewpoint of Earth? Can I say that from Earth there is a physical distance between us an a distant galaxy? Is this distance actually changing due to the expanding universe?

 

[Buckethead]

Yes, I think that is a good approach.

Then can I say that one of the properties of space is that it can move (due to expansion) and can carry a photon with it such that when observed from Earth, this photon will take longer to reach us than it would if space were not expanding?

 

[Dale]

can I say that one of the properties of space is that it can move

There have been many exquisitely sensitive experiments to try and detect this motion. None has succeeded. If space has such properties then it is a far more successful clandestine operation than any human conspiracy ever carried out.

Mathematically you can certainly make this claim as I described initially, but most scientists don't like to have the resulting conspiracy theory as the core of their physics.

 

[Buckethead]

There have been many exquisitely sensitive experiments to try and detect this motion. None has succeeded. If space has such properties then it is a far more successful clandestine operation than any human conspiracy ever carried out.

Mathematically you can certainly make this claim as I described initially, but most scientists don't like to have the resulting conspiracy theory as the core of their physics.

But if a distant galaxy (or any photon in that area) are moving away from us due to expansion, then doesn't this mean this is a successful experiment to show that space (or I should say its math model) are also moving? What kind of experiment could one do to measure the "motion" of space? Could galaxies moving due to expansion be caused by a "space wave" model instead where it is not the space model that's moving only the wave? Or perhaps a third option like a force? Also, why would suggesting that one of the properties of space is motion lead to a conspiracy theory and what kind of conspiracy theory would that be?