The term “spacetime” and the concept of time being the “fourth dimension” appear to contradict each other. Is time actually a 4th dimension, or are all dimensions captured in time?
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Let’s say you and I are having a meeting. In order to meet you need to know two things: where to meet me and WHEN to meet me. If I tell you where but don’t tell you when you could miss me entirely. The same thing is true of describing any object in space. You can’t just give X, Y, and Z coordinates. You also have to give a T coordinate, aka time.
When scientists and mathematicians talk about dimensions they aren’t talking about other universes or realities, they are talking about the coordinates you use to locate something in the universe, we call that space time.
So yes time is its own dimension. From our perspective time is a bit different in that we can only move one way on it, and we can’t really change our speed, unlike the other three dimensions. But in physics it can still be treated the same as the other dimensions when it comes to certain equations and models.
Spacetime has three dimensions of space and one dimension of time. Time isn’t the “fourth dimension” because these dimensions are not in any order.
The concept of spacetime is used because space and time are intertwined. Up until special relativity was discovered, they were thought to be separable. The distance between any two points was thought to always be the same, as was the time interval between any two events. Distances can be shortened by travelling close to the speed of light. Events that appear to coincide, but happen at different locations can appear to occur at different times. Observers may not even agree on the order in which they occur.
Time is a dimension like the three spatial ones. It’s easier to understand if you think of it as nothing more than another axis on a graph. If I ask where a spot on a wall is, you can tell me using two dimensions, two coordinates, two axes. X,Y. It’s 3 feet up and 2 feet from the left.
For a spot in the middle of a room, like the location of your phone sitting on a table, though, you’ll need a 3rd coordinate for depth. It’s now 3 feet up, 2 feet from the left, and 7 feet away from the wall. Still easy to visualize.
But now we can be more precise with another dimension of time. If I check that spot (3, 2, 7), but I check it *yesterday,* will I still find your phone there? How about tomorrow? A hundred years from now? We can just add a 4th coordinate for time, no differently than we did when we added one to move out into the room away from the wall. It’s 3 feet up, 2 feet from the left, 7 feet away from the wall, and at 10:00 on August 27, 2023.
And while it’s tricky to graph all 4 of these at once in a way you can visualize, you can arbitrarily drop one or two spacial axes and now time fits nicely into a 2 to 3 dimensional graph you can see. And that’s useful beyond being a mathematical trick. Your travel on one axis directly affects your location and travel on the other axes.
For instance, just like it would be impossible to find your phone in your house if the vertical coordinate was 10000 feet, since it would be high in the sky, its also impossible to find it in your house if the time coordinate is 65 million BC, because your house likely didn’t coexist with the extinction of the dinosaurs.
You can also graph time against spacial dimensions to determine cause and effect. Actually demonstrating a Penrose diagram is a little beyond what I can do here, but basically, you can easily see on as simple as a 2-D graph whether an event is possible or not to ever interact with you by making specific assumptions on the graph (i.e. that the speed of light is at 45 degree angles to the corners of the graph and that the edges compress to infinity).
It sounds complicated, but it’s super easy to *see* how time works just like space when drawing cause and effect “light cones.” Basically, if it’s outside the cone, you can never, ever interact with it, since that would mean traveling faster than light, i.e. time traveling.
In this example, your phone being on the table *could* have been influenced by the dinosaurs, since their coordinates were close enough, appearing inside the cone (even if there’s no way for us to actually show a real life connection), but space-dinosaurs from the edge of the universe couldn’t have influenced it because they’re too far away in either space or time, and they’d appear outside the cone you’d draw.
Dimensions are just a mathematical construct.
You can make up any dimensional space you want: First dimension could be even numbers and second dimension is odd numbers. That’s a valid 2D space.
The trick is to find a dimensional space that is useful and consistent with some situation.
For example, sailors on the planet earth might use 2D longitude and latitude because it makes math and navigation easier. Is Earth 2D? No, you can fly or dig a hole but that doesn’t lessen the usefulness of longitude and latitude for boats that sail on the surface of earth.
4D (Space + Time) is just a useful space definition for describing relativity, much like longitude and latitude is useful space definition for describing a location on the ocean.
Now, space time certainly seems “special” because it fits with relativity so well and relativity has been proven to describe “reality” by real world experiments. (So far.)
Mathematicians can create infinitely many 4D spaces. Einstein’s space time is just a particular 4D space that works well with the theory of relativity. Before that, 3D space and time were considered separate. Edit: And that space definition worked well with Newtonian physics.
Now some other physicists might come along and come up with a 10 dimensional space that handles relativity + quantum physics in a single unified theory. But that hasn’t happened yet.
Spacetime is a structural quality we use to conceptually represent what we refer to as the gravitational field. To accomplish this we use mathematics.
Pull out a clock and measure how long it takes you to read this sentence. You call this value time. Pull out a ruler and measure how long your keyboard is. You call this value length. These are simply coordinates. Indices. Values to organize and study the universe and their interactions with each other.
In SI units we define the meter relative to what a “second” is and the speed of light, however in general relativity we **define** both dimensions of space and time to be the same thing (called geometrized units). This is why *c* takes on the value of 1 in cosmological contexts. Historically we failed to recognize that the units for time and space should be the same, so it’s preferable to view *c* in SI units as a conversion factor.
In this way you might colloquially view it as a fourth dimension because they are defined as the same units. Having said all this, spacetime only has three spatial dimensions but is a “4-vector”. Events happen in the universe at a specific location at a specific time, so unsurprisingly we require four coordinates to describe them. Despite having the same units, time and space aren’t literally identical.
Not quite sure if any of this helped. Your question was fairly open-ended.
Yes it’s a dimension. You have spacial (space) and temporal (time) dimensions. Our universe is 3-spacial and one temporal (relativity theory). Each dimension is a part of the whole.
Say you have an office building with 3 floors, 3 hallways per floor, and 3 doors per hallway. Now your office is going to have a meeting, you would need to know all the dimensions to know where it’s at.
If you just knew it was on the 3rd floor(Z axis) you don’t know where it is. If you knew it was in the first hallway (Y axis) you still don’t know, and if you knew it was the second door (X axis) you still don’t know. Coordinates (2,1,3).
You know the space it’s going to be at, but not the time. If you know it’s on Tuesdays at 9 (T axis), now you know all the dimensions of your meeting. Because that office is going to be a different meeting at 9 on Wednesday, it’s a different object. Without all four pieces you don’t have a complete object.
Missing time is just as important as say missing the floor number.
There is ‘almost’ two different types of time when you look at Newtonian physics and relativity which is probably what caused your question. There is the ‘Captured’ time, which is how we use physics as a tool, you need to know how things happened in the past and how things will happen in the future so we mapped events to a time line.
With relativity we found out that the rate of time passing can change, this is more of the 4th dimension, the rate changes in different places so space and time are intertwined.
If we try and use variable rate time and put it into our normal model of a time line, everything falls apart. Different observers observe different rates of time so there is no universal time to capture everything. So in relativity time needs to be tethered to an observer to make sense of anything, it’s kinda where the name comes from, and just like position being tethered to an observer time is also for a 4th dimension.
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