Beginner: Some questions about relativity

[Genecks]

Hello, all.

I've been attempting to understand relativity the past week. I've also been reading about quantum mechanics. However, I'm going to try and direct this thread toward relativity.

1) Does relativity only cover space, time, gravity, and light?
2) In the realm of relativity, how is space defined?
3) In the realm of relativity, how is time defined?
4) In relation to time, is time in relativity better defined as entropy?
5) Does Einstein's relativity ever take into consideration subatomic particles or waves other than light?
6) In relation to space, how did Einstein define space?

The reason I've asked these questions is because it's as if Einstein defines space as everything there is, and that somehow it's all part of a geometrical fabric rather than a bunch of marbles in a jar: The jar of marbles acts as a single object (space-time fabric) rather than more than one object.

7) Am I right on that view in relation to relativity?
8) What is the point of the twin paradox hypothesis if there is a block universe?
9) Does Einstein's general relativity attempt to act as a deductive proof?
10) How can there be such a thing as space-time if there is no such thing as empty space?

Thanks for reading.

- Genecks

 

[pervect]

Hello, all.

I've been attempting to understand relativity the past week. I've also been reading about quantum mechanics. However, I'm going to try and direct this thread toward relativity.

Welcome to PF. You have a lot of questions, I'm going to take the approach of giving brief answers to each, there's to much to give an in-depth answer to every one.

1) Does relativity only cover space, time, gravity, and light?

Relativity should also cover the weak and strong forces (for instance as to how they transform), i.e. our theory of weak and strong forces is also based on relativity. If you cover space, time, and all four forces, I think you can say it covers "everything", at least I can't think of anything not covered. If you think of something not covered by those categories that you're curious about, ask again.

A fine, but possibly important point, but space and time are usually regarded in relativity as being combined into a single entity, space-time.

2) In the realm of relativity, how is space defined?

space-time is defined in general relativity as a 4 dimensional manifold. A manifold is popularly regarded as the surface of a higher dimensional object, but this is just a visual aid. The mathematical definition of a manifold is based on the concepts of points and a notion of "neighborhood", formalized in topology as "open balls". Plus some other axioms I'm not going to get into, a full description would be too involved.

Special relativity considers only "flat" manifolds, so you can use the simpler mathematical concept of $\mathbb{R}^4$, if you're familiar with that.
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3) In the realm of relativity, how is time defined?

Time can generally be regarded as what a clock measures. There are a couple of notions of time that are important in relativity , actually - coordinate time and proper time. Proper time is the time measured on a clock that's present at all events. Proper time does not need the concept of synchronizing clocks, because the clocks are present at all events. Coordinate time is the time measured by coordinate clocks, which need additionally a system of synchronization to define the coordinate system.

In general relativity the splitting of space-time into space+time is regarded as a matter of convention. In special relativity, the splitting of space-time into space-time is determined by your choice of reference frame. A frequently used anology in SR is that space-time is like a loaf of bread, and that the process of identifying "now", the set of all points that are simultaneous, is like cutting that loaf of bread.
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4) In relation to time, is time in relativity better defined as entropy?

No.

5) Does Einstein's relativity ever take into consideration subatomic particles or waves other than light?

Yes. For instance particles in a particle accelerator are governed by the laws of relativity. We can give them enormous energies, but no matter how much energy we give them, they don't exceed (or for massive particles, even reach) the speed of light, something that would not be predicted by other theories.

6) In relation to space, how did Einstein define space?

I'm not sure how Einstein historically defined space. My personal popular-level explanation would be that "space is what you measure with a ruler".

The reason I've asked these questions is because it's as if Einstein defines space as everything there is, and that somehow it's all part of a geometrical fabric rather than a bunch of marbles in a jar: The jar of marbles acts as a single object (space-time fabric) rather than more than one object.

I'm afraid I don't really understand your question.

7) Am I right on that view in relation to relativity?

I would guess that you probably have more to learn, and that your views may shift as you learn more, If you keep studying, that is.

8) What is the point of the twin paradox hypothesis if there is a block universe?

The twin paradox is an educational tool. The block universe is a philosophical position that isn't required to understand relativity, though it may make it easier.

9) Does Einstein's general relativity attempt to act as a deductive proof?

No.

 

[bhobba]

The reason I've asked these questions is because it's as if Einstein defines space as everything there is, and that somehow it's all part of a geometrical fabric rather than a bunch of marbles in a jar: The jar of marbles acts as a single object (space-time fabric) rather than more than one object.

Actually Einstein was a physicist and physicists usually get by with pretty 'ordinary' notions of such things. What he assumed was that, locally (ie in small regions) space is as described by good old Euclidean geometry you learned about at school. He then added in time to create something called space-time that incorporated the insights of special relativity. He then generalised those local areas of space-time to create a whole class of really weird geometries using a process pioneered by the great mathematician Riemann (its called Riemannian geometry and describes all sorts of geometries in the one formalism so that in small regions ie locally its Euclidean - basically its a generalisation of Euclidean geometry) - but this time with space-time and not just space (its called a Pseudo Riemannian Geometry and is a generalisation of the space-time idea of SR so that in small regions ie locally its the space-time of SR like in Riemannian geometry small regions are Euclidean). Like Riemannian Geometry this describes a whole class of geometries in the one formalism, so the final ingredient was to ask - what geometry did nature use? Einstein's answer was none - its actually dynamical like a field is - this is called no prior geometry and is the rock bottom essence of general relativity from which the theory basically follows.

This wasn't quite how Einstein looked at it initially, and there was a bit of confusion about it to start with. But people like Kretschmann spotted the errors Einstein made and Einstein accepted it as valid so that the idea of no prior geometry is basically the way the theory is looked at these days. Indeed a standard textbook on GR - MTW - is basically a mathematical exposition of this key idea.

You can find a discussion of such esoterica here if you are interested:
http://www.pitt.edu/~jdnorton/papers/decades.pdf

I also must add it's not the only approach, but that is a whole new discussion.

Thanks
Bill

 

[Genecks]

First off, question 10 was not answered; perhaps because I added it in late to the post prior to seeing the second poster's reply in this thread.

Secondly, thank you, all, for the replies so far.

Relativity should also cover the weak and strong forces (for instance as to how they transform), i.e. our theory of weak and strong forces is also based on relativity. If you cover space, time, and all four forces, I think you can say it covers "everything", at least I can't think of anything not covered. If you think of something not covered by those categories that you're curious about, ask again.

Are these weak and strong forces something from quantum mechanics or something before quantum mechanics?

For what I understand, things, such as force, gravity, energy (Newton's work), and electromagnetism (Maxwell?) came before Einstein developed relativity.

A fine, but possibly important point, but space and time are usually regarded in relativity as being combined into a single entity, space-time.

space-time is defined in general relativity as a 4 dimensional manifold. A manifold is popularly regarded as the surface of a higher dimensional object, but this is just a visual aid. The mathematical definition of a manifold is based on the concepts of points and a notion of "neighborhood", formalized in topology as "open balls". Plus some other axioms I'm not going to get into, a full description would be too involved.

Special relativity considers only "flat" manifolds, so you can use the simpler mathematical concept of $\mathbb{R}^4$, if you're familiar with that.

This is all just a geometric interpretation of reality, however, right?

Time can generally be regarded as what a clock measures. There are a couple of notions of time that are important in relativity , actually - coordinate time and proper time. Proper time is the time measured on a clock that's present at all events. Proper time does not need the concept of synchronizing clocks, because the clocks are present at all events. Coordinate time is the time measured by coordinate clocks, which need additionally a system of synchronization to define the coordinate system.

Again, this is geometric, right? This is kind of why I was asking if Einstein's relativity was an attempt at a deductive proof. The way I keep looking at Einstein's theory is that it seems somewhat Aristotelian.

In general relativity the splitting of space-time into space+time is regarded as a matter of convention. In special relativity, the splitting of space-time into space-time is determined by your choice of reference frame. A frequently used anology in SR is that space-time is like a loaf of bread, and that the process of identifying "now", the set of all points that are simultaneous, is like cutting that loaf of bread.

I've seen this sliced loaf of bread video on YouTube. Even though it's argued there is a slice, why can't each point in space have its own relative "time" in relation to all other things?

Yes. For instance particles in a particle accelerator are governed by the laws of relativity. We can give them enormous energies, but no matter how much energy we give them, they don't exceed (or for massive particles, even reach) the speed of light, something that would not be predicted by other theories.

I'm not sure how Einstein historically defined space. My personal popular-level explanation would be that "space is what you measure with a ruler".

I'm afraid I don't really understand your question.

Ok, so, I feel that this kind of goes into the realm of quantum mechanics, such as quantum chromodynamics.

Imagine you have a program that let's you make 3D graphics, such as Blender, and these images can move over time. The way I see Einstein's relativity argument is that he is ignoring the existence of atoms, he's ignoring the existence of particles (except light), and he's focusing on what's on the Euclidian plane and the "time" dimension. It's as if everything is connected together in some cybernetic way without objects having any independence from each other, and that since they're all connected, they can all be classified as a single object.

So, perhaps I can put it with an analogy. Maybe it's stupid. I'll try. Perhaps it's the Platonist in me.

Imagine I invite you to my bedroom. If you were in my bedroom, you would see my bed, the items in my room (desk, shelves, a fan, some garbage bags, the carpet, and so on), the spatial positions of everything in my bedroom, and whatever else is observable to the human eye in my bedroom from one focal point. So, what I do, then, is that I kind of figure out where your vision was, and I take a picture of my bedroom with a film camera.

I get the film developed, and I eventually have a picture developed of the bedroom. From there, I find you and show you the photo to talk about Einstein's relativity and geometry.

From how I'm interpreting Einstein's relativity, he's treating space-time as something that is connected and unified. So, what I do to give the idea of what I mean is that I start warping the picture with my fingers, bending it, making waves with it, and I eventually flatten it out. However, isn't this a wrong view of space-time? Because the reality of space-time is that it has objects.

If you've ever watched Blues Clues (it was a children's show), there are often images around the house that are in picture frames.

It seems like Einstein's relativity is saying that space-time is a flat image or 3D object (ignoring objects in this 3D object) in time.

In contrast, with the Blues Clues example, sometimes the characters of the show will say a phrase, such as "Blue skadoo we can, too" and jump into the picture. In the picture, space-time (if it can even be called that in this example, because such seem as though it would contradict) is filled with physical objects that are tangible rather than a unified whole. Furthermore, the characters can interact with the environment once they move themselves into these environments. However, from how I've been reading about relativity, everything is more of a hologram or geometric whole rather than having parts existing to it.

I saw a video on 4D geometry and somehow have found a way to envision it, but only in an attempt to visual the geometry in multiple side-by-side frames in my mind's eye. I don't think I'm having cognitive dissonance about this. I think Einstein's relativity, because it comes from a mathematical viewpoint, totally ignores objects that exist within the volume of the universe and instead looks only at the volume as space-time. Furthermore, with the lack of looking at what is inside of the volume, entropy is ignored and time is a fabricated variable.

If I take into consideration three-dimensions, then space is all of the dimensions. However, if I add an additional dimension, then there is time.

I feel as though Albert Einstein made the hasty generalization of clumping objects into a dimension. At least, I perceive that to be true. However, that perception is dependent on my view that objects exist within the universe, that space is never space but a location where some object exists, and that time is not time but instead the movement of objects (perhaps some kind of radiation that the brain perceives?) or entropy. This view, however, may have become biased from my encounter with quantum mechanics.

I would guess that you probably have more to learn, and that your views may shift as you learn more, If you keep studying, that is.

Possibly so, but I'm attempting to look at the foundations before becoming brainwashed with dogma. No offense.

...
You can find a discussion of such esoterica here if you are interested:
http://www.pitt.edu/~jdnorton/papers/decades.pdf

I also must add it's not the only approach, but that is a whole new discussion.

Thanks
Bill

Thank you, Bill. I will attempt to read through the article, perhaps within the week (it's fairly lengthy).

 

[bhobba]

How can there be such a thing as space-time if there is no such thing as empty space?

As I mentioned in my reply GR assumes euclidean geometry in small local regions so obviously it has the concept of empty space. In GR gravity is simply something that results from what coordinate system you use. Accelerate with respect to an internal frame and you feel a force - ie change your coordinate system and a force appears - but its still empty - all you have done is change your coordinate system. On Earth stick yourself in a falling elevator and gravity disappears - again all you have done is change your coordinate system. Gravity is simply an 'illusion' depending on your freely chosen coordinate system (for the more knowledgeable - yes I know of the issue of tidal forces - I am talking at the beginner level here).

What you may be thinking of is Quantum Field Theory where empty space is far from empty - but that is a whole new ball game.

Thanks
Bill

 

[bhobba]

This is all just a geometric interpretation of reality, however, right?

Mate this is getting into philosophy which is off topic on this forum.

That said its exactly the same as good old Euclidean geometry you learned of at school. Whatever relationship you attribute that theory to reality (whatever that is) GR is exactly the same. They are both mathematical models.

Thanks
Bill