B How are the concepts of space, time, and space-time related?

[uday01]

I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time " but never explain what the difference is between the two concepts or how they are related.
How are the concepts of space, time, and space-time related?
Uday

 

[phinds]

I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time " but never explain what the difference is between the two concepts or how they are related.
How are the concepts of space, time, and space-time related?
Uday

Space-time is a framework in which everything in the universe happens. It's not that space and time are related so much as it is that they are just aspects of the same thing. For example, you might think that an apple is a 3-dimensional object, but that is just not true. An apple is a 4-dimensional object because it exists in space-time. I suggest you google and study "world lines"

 

[Khashishi]

Events happen at a particular place and a particular time. I.e., they happen at a particular point in space-time. This is simply just putting the two together. The advantage is that now it makes sense to do a (hyperbolic) rotation between a space direction and the time direction.

 

[Ibix]

Prior to Einstein it was entirely sensible to believe that time and space were distinct things, like the screen of your TV and the clock on your DVD player. They work in completely different ways.

Minkowski realized that the maths of Einstein's Special Relativity could be interpreted as describing one four-dimensional whole called spacetime. In this picture, changing your definition of time without changing your definition of space islike changing your notion of up without changing your notion of across. It can be done at the cost of a significant increase in mathematical and conceptual complexity, but it's not recommended. Naturally, though, changing your notion of time will change your notion of space simply because they're just a choice of how to split up spacetime.

 

[sweet springs]

Hi.

Time and space are two different categories in human perception as seeing and hearing are.

In the 20th century Einstein pointed out that time and space are interchangeable between two observers in different frames of reference. An observer attributes long time and long distance but another observer attributes short time and short distance to the same event interval e.g. start and goal of a short track runner. This was an amazing discovery that contradicts our domestic way of sensing.

This interchangeability is like a x-length and y-length of a rotating bar of definite length like a needle of a watch $x^2+y^2=x'^2+y'^2=r^2$ but with change of signs $t^2-z^2=t'^2-z'^2=\tau^2$ where sped of light c = 1.

We had to admit that the real physical entity lies in space-time not in space and time separately.

 

[stoomart]

We had to admit that the real physical entity lies in space-time not in space and time separately.

I'm having difficulty reconciling how time can be used as one of the dimensions in spacetime, and still be relative; does the time 'coordinate' here represent the local time relative to an outside observer?

 

[Ibix]

Einstein pointed out that time and space are interchangeable between two observers in different frames of reference

I think "interchangeable" isn't quite right here. That would mean that the direction I call x could be the direction you call t, which doesn't happen. My x direction is orthogonal to my t and is not orthogonal to your t' direction, I agree. But it's never parallel to your t' direction.

 

[Ibix]

I'm having difficulty reconciling how time can be used as one of the dimensions in spacetime, and still be relative; does the time 'coordinate' here represent the local time relative to an outside observer?

There isn't a single direction that can be called time; rather there is a whole family of them. You can just pick a different direction from me to call time, and that freedom to choose is where the relativity of time comes from.

It's like having an infinitely large blank piece of paper and being told to draw a coordinate grid on it. Your grid and mine probably won't align unless we work together at the start. That's x and y being relative. The only odd thing about spacetime is that one of the four orthogonal directions needs to be measured with a clock.

 

[sweet springs]

Hi.

I'm having difficulty reconciling how time can be used as one of the dimensions in spacetime, and still be relative; does the time 'coordinate' here represent the local time relative to an outside observer?

You need to know time and place to identify an event with asking when, 1 dimension, and where, 3 dimensions.

Mathematics teaches us 3 space dimensions are relative in rotation. TOR says 1 time dimesion is also relative.
Length of a body $x^2+y^2+z^2=r^2$ is common constant in coordinates of rotation. Similar quantity called world interval between two events $c^2t^2-x^2-y^2-z^2=c^2\tau^2$ is constant in inertial frames of reference. Lorentz transformation or boost changes $(ct,x,y,z)$ into $(ct',x',y',z')$ keeping the relation $c^2t^2-x^2-y^2-z^2=c^2t'^2-x'^2-y'^2-z'^2=c^2\tau^2$. Time coordinate t or t' is ticks of their clocks.

 

[Khashishi]

I'm having difficulty reconciling how time can be used as one of the dimensions in spacetime, and still be relative; does the time 'coordinate' here represent the local time relative to an outside observer?

Think of spacetime as a graph with no axes drawn in or a map with no compass marking. Each observer has their own set of axes. Time is one of these axes. It's relative because people agree on what events occur in the universe, but they don't agree about the time or position each event occurs. It's simple to convert between people's viewpoints though using a Lorentz transformation.

 

[robphy]

This might help...
it's a new update of my desmos "spacetime diagrammer" ( https://www.desmos.com/calculator/nilbye4ecz ) .

The key idea is this...
Short answer: "space is perpendicular to time"
Slightly longer answer: "an observer's sense of space [her spaceline] is 'perpendicular' to an observer's sense of time [her worldline]"

One can define "perpendicularity" using a unit circle.
Then, the tangent line to that circle is perpendicular to the radial line.

Refer to the visualization ( https://www.desmos.com/calculator/nilbye4ecz )
The t-axis [to be interpreted as time in the spacetime cases] runs to the right and
the y-axis runs upwards.
You can tune the slopes [to be interpreted as velocities in the spacetime cases] of the [world]lines.
You can tune the choice of circle [to be interpreted as "being one tick after the origin event O" in the spacetime cases].

The black point [event] represents a point you can drag around... representing the point [event] of interest.
The green and red points represents points along the [world]lines, together with the "perpendicular direction" (defined by the chosen type of circle).Consider the Euclidean case (Set the "E= -1" in the visualization. The metric)
Here's how the green line will assign coordinates.

• Drag the green point so that the associated perpendicular meets the distant black point.
• According to the green line, the distant black point has the same "t"-coordinate [according to green] as the black point.
• Measure the distance (call it "y" according to green) along that perpendicular. (The visualization doesn't show this measurement explicitly, yet. But it conveys the idea.)

The red line will assign coordinates in an analogous way.
In general, the green and red lines will assign different t's and y's... but they will agree that on the value of $t^2+y^2$ (the square distance from O)

Now consider the special relativity case (set the slider to E= +1).
In general, the green and red lines will assign different t's and y's... but they will agree that on the value of $t^2-y^2$ (the square interval from O)

I encourage you to look at the E=0 case (set the slider to E= 0), which corresponds to Galilean case.
In general, the green and red lines will assign the same t's [absolute time] but different y's...
(they will agree that on the value of $t^2$ (the Galilean square interval from O)).