What is the 2D Concept of Spacetime and How Does It Work?

[Dimitri655]

Hi guys,

I was wondering if anybody could help me understand the concept of spacetime. My physics knowledge is quite limited but so far what I have gathered is: Spacetime is like a piece of paper (assuming it is 2d) but instead of width and length it has space on one axis and time on another axis.

Does this definition seem to be pointing towards the right direction?

Thanks in advance,

 

[Nemika]

Actually spacetime combines space and time into a single entity,that is the universe. It has 4 dimensions instead of just 2. The first 3 are quite simple- length, breadth and height and fourth one is time. These four are represented on Cartesian plane as x, y, z and t respectively. It is a manifold structure basically. Space needs all the 4D's to specify an event or a point. An event has 2 parts, when and where and they can be specified only by these 4 dimensions.
For further information go to https://en.m.wikipedia.org/wiki/Spacetime.

 

[mrspeedybob]

I would clearify that it is not really something physical. You mentioned a piece of paper as a 2D analogue. A better analogue would be a grid that someone drew on the piece of paper. It's a mathematical construct that's useful for talking about places and events, but it's not really an actual physical thing.

 

[Dimitri655]

Awesome, thanks for the replies.

So from what I understand now space-time is a mathematical model ( abstract structure) formed by space (3d) and time 1(d). The analogy of the piece of paper would be less good because it implies that it is a concrete thing that might be subjected to properties that we apply to physical objects.

Does that seem like a better definition?

 

[phinds]

Awesome, thanks for the replies.

So from what I understand now space-time is a mathematical model ( abstract structure) formed by space (3d) and time 1(d). The analogy of the piece of paper would be less good because it implies that it is a concrete thing that might be subjected to properties that we apply to physical objects.

Does that seem like a better definition?

I think it's better to say that space-time is the framework in which things happen. It's not a material object, but saying that it is JUST a math structure doesn't seem quite right either. That's just my opinion, thought.

To paraphrase somebody or other, time is what keeps everything from happening all at once and space is what keeps it from all happening on top of me.

 

[Drakkith]

My two cents:

First, I would look at what Geometry is: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

Spacetime is defined by the General Theory of Relativity, which says that the geometry of space and the geometry of time are not static and unchanging, but are both dynamic (capable of changing) and linked together in certain ways. The concept of spacetime is a way of joining space and time so that they can be explained and described together instead of separately.

Ultimately, spacetime is a description of the shape, size, and position of objects and events within a universe that has dynamic geometry.

 

[Dimitri655]

Oh I see so [in phinds opinion] space-time would be both a framework , that is: the essential supporting structure of the universe and our representation of it is done trough a mathematical model. Would that be correct?

also, I like that quote! I've heard the first part but not the second part.

To paraphrase somebody or other, time is what keeps everything from happening all at once and space is what keeps it from all happening on top of me.

 

[Dimitri655]

My two cents:

First, I would look at what Geometry is: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

Spacetime is defined by the General Theory of Relativity, which says that the geometry of space and the geometry of time are not static and unchanging, but are both dynamic (capable of changing) and linked together in certain ways. The concept of spacetime is a way of joining space and time so that they can be explained and described together instead of separately.

Ultimately, spacetime is a description of the shape, size, and position of objects and events within a universe that has dynamic geometry.

Man that's beautifully framed! you blew my mind with the dynamic geometry part. So from this perspective space-time is a description of {shape, size, position} (related to space) and {events} (I think related to space and time) within a universe that has a property of being dynamic when it comes to geometry. Does that make sense?

 

[rootone]

Yes it is a mathematical model, but as such it's a model that is very much in accord with actual observations.
It is accurate enough to explain things such as the otherwise 'weird' precession in the orbit of Mercury, and it is necessary for GPS systems to work properly.

 

[Drakkith]

Man that's beautifully framed! you blew my mind with the dynamic geometry part. So from this perspective space-time is a description of {shape, size, position} (related to space) and {events} (I think related to space and time) within a universe that has a property of being dynamic when it comes to geometry. Does that make sense?

Makes sense to me, lol.

 

[Dimitri655]

Makes sense to me, lol.

Awesome! How about if I add this distinction:

Lets assume that the universe has a framework and let's calls that framework Bob (because it would be a cool name for the fundamental structure of the universe).
We make observations of small pieces of Bob, and mathematically model Bob as the spacetime. The model spacetime is in accordance with the observations we make from Bob.

In fact, our mathematical model spacetime describes Bob in terms of {shape, size, position} and {events}. Similarly, from our undestanding so far, Bob appears to have the property of being geometrically dynamic.
​

Does the distinction makes it better or worse?

Btw, once again thanks for the replies!

 

[Drakkith]

If you call the framework itself spacetime, then you can cut it down a bit. We have mathematical theories and models of spacetime, meaning that they define and describe spacetime itself (the framework).

 

[martinbn]

One possible definition is: space-time is the set of all events.

 

[Dimitri655]

If you call the framework itself spacetime, then you can cut it down a bit. We have mathematical theories and models of spacetime, meaning that they define and describe spacetime itself (the framework).

I thought so at first but I think its best to separate the framework because I don't think the mathematical model (space-time) can both be a model and the thing it is modeling. Tho that's just my opinion.

One possible definition is: space-time is the set of all events.

This is also a pretty cool definition too.

 

[PeterDonis]

I don't think the mathematical model (space-time) can both be a model and the thing it is modeling.

If you call the mathematical model "spacetime", then of course it isn't the same as the thing it's modeling. But then what do you call the thing it's modeling? The usual name for that thing is also "spacetime"--for example, when martinbn says that spacetime is the set of all events, he's not talking about the mathematical model; he's talking about the thing it's modeling.

 

[Herman Trivilino]

Hi guys,

I was wondering if anybody could help me understand the concept of spacetime.

Actually, you probably already understand a relationship between space and time. You experience it whenever you travel. You know where you live, you know where Grandma lives. You travel from your home to hers. You know both the distance between your houses and the time it takes to get there. When you divide the distance by the time to get the speed you are doing a spacetime calculation.

The reason you hear people talk so much about spacetime is because the relationship between space and time is more complicated when you start looking at different observers' measurements of distances and times, and the results of their calculations. Different observers that are moving relative to each other that is, or are located in gravitational fields of different strengths. Strange and weird things appear such as length contraction and time dilation. And something strange happens to the notion of simultaneity. Physicists and mathematicians have figured out ways to do these calculations using geometries in which there are 3 dimensions of space and 1 dimension of time. The techniques have caught on, people like them, and people use them to make predictions that match observations. The engineering of the GPS system with its array of high-precision clocks in orbiting satellites is one good example.

The type of calculations you do when you take a car trip allow you to use a notion of spacetime in which the 3 dimensions of space do not effect the 1 dimension of time, and vice-versa. The only reason that works is because the speeds you travel are slow compared to the speed of light. And because the gravitational field strength doesn't change much. Those calculations are based on an approximation that works quite well under those conditions. But when faster speeds and larger gravitational field gradients are involved, or when higher precision results are required as in the case of the GPS clocks, that approximation no longer works. Then, if we want accurate results, we must do calculations where the 3 dimensions of space alter the 1 dimension of time, and vice-versa. Using a 4-dimensional spacetime to do those calculations gives us accurate results.

 

[Dimitri655]

The reason you hear people talk so much about spacetime is because the relationship between space and time is more complicated when you start looking at different observers' measurements of distances and times, and the results of their calculations.

Oh man thanks a lot for this answer it actually helps!

Now one last question guys; if someone were to ask me to define spacetime, would I be wrong telling them that there is an ambiguity in definitions between spacetime as a mathematical model and spacetime as the framework of the universe (a.k.a set of all events)?

 

[Herman Trivilino]

Now one last question guys; if someone were to ask me to define spacetime, would I be wrong telling them that there is an ambiguity in definitions between spacetime as a mathematical model and spacetime as the framework of the universe (a.k.a set of all events)?

In this thread there was a discussion about the distinction between a model and the thing it's modeling, but that's not an ambiguity in the definition of spacetime. That's an ambiguity in the way people talk about all models.

 

[phinds]

I hate to muddy the water and drag this out but I have to object to the use of "the set of all events" as a description of space-time. The set of all events is what happens IN spacetime. Space-time is the framework in which events occur. An analogy would be that space-time is a basket (a framework) full of apples (events). The basket isn't the apples.

 

[PeterDonis]

I hate to muddy the water and drag this out but I have to object to the use of "the set of all events" as a description of space-time. The set of all events is what happens IN spacetime. Space-time is the framework in which events occur.

Mathematically, there is no difference between these two things. The "framework" is the set of all events--just with additional structure added (the metric). A manifold, mathematically, is just a set of points with additional structure that defines relationships between them.

Physically, we intuitively think of "events" according to their physical properties--things like mass, energy, etc., which are not included in the definition of spacetime itself, they are additional objects (like 4-momentum vectors, stress-energy tensors, etc.) that are defined mathematically as geometric objects on the manifold. But the term "event" itself thus has a double meaning: it can be used to refer to a point in spacetime, or to what happens at that point, meaning the values of scalars at that point which are obtained by contracting vectors, tensors, etc. When we define spacetime as "the set of all events", we are using the first meaning of "event", not the second.

 

[phinds]

Mathematically, there is no difference between these two things.

Thanks for that correction, Peter. I did not realize that.