I didn’t pay attention in School and I regret that now. Please help me understand some aspects here. I read about Time being the fourth dimension but I am just having difficulty grasping this information.
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Time can be mathematically modeled as a fourth dimension, which helps to understand the linking of space and time in Einstein’s theories, but Einstein did not really argue that time is the fourth dimension per se. And time is not really like space: you can’t move in an arbitrary direction in time like you can in space, nor could you move in a given space direction without also moving through time (like you could do with two given spatial dimensions when you’re moving in a straight line.) In fact, in almost all respects, you’re ‘locked in’ to your passage through time, stuck moving through time in one direction forever. So it isn’t necessarily very useful to think of time as the fourth dimension, even if that is a mathematical model that we can use to model it.
If what you really want to understand is Einstein’s theories, though, the basic idea here is that space and time are linked together as one thing, spacetime. That is to say, movement through space can affect the passage of time from different perspectives. Very-fast moving objects have pass through time more slowly, as do objects in massive gravitational fields. Things that travel at the speed of light, like light, apparently ‘have no clock’, i.e., they have no passage of time within themselves.
I could try to explain with an example, if you’d like.
To attend a party, you need to know where it is in space. That’s three dimensions. You also need to know what time it is, though.
It happens that no matter your perspective, no matter how you try to simplify things, as long as you’re making full use of our space (not limiting yourself to the surface of the Earth for instance), you will always need four numbers to properly attend a party.
We used to think space and time were separate, that changing the parameters of one doesn’t affect the other. Einstein proved this incorrect, twice. First, Special Relativity (1905) proved that time dilates for fast-moving reference frames. Second, General Relativity (1915) proved that time itself warps and bends around massive objects. We now refer to the two combined as spacetime.
Think of it this way. You’re invited to a dinner at a friend’s house. You know where your friend lives, easy. That’s space, three dimensions. But you can’t just show up whenever. You need to ask your friend when you’re allowed to show up. That’s a fourth coordinate, time.
Imagine you’re a flat person, 2 dimensional, and you live on the surface of a balloon. Your movement is restricted to the ballon surface – you live in a curved 2D space. Now, imagine the balloon is being blown up at a constant rate. You can think of time as being the radial dimension, the 3rd dimension. Being a 2D person, you can’t move in the 3rd dimension but you experience it as the passage of time.
In the you-didn’t-ask-but-I’m-going-to-tell-you-anyway department, imagine that a 2D item having mass resisting the expansion of the ballon and that other things near that mass want to fall into the dent made by the mass. Now, you have a reasonable model for gravitation and time slowing down near heavy objects. Something having the mass of a black hole would resist the expansion completely – time would stop at the surface of the black hole.
There’s more but I think this is a good start.
The idea is simple instead of thinking about locations in a 3D coordinate system you think in terms of events.
If we look at 1D of space and 1D of time we get an x-t coordinate system. This is very similar to an x(t) function. For a spring each point of its graph (the sin curve) is an event it tells you where the mass on the spring was at any given point in time.
So lets be more direct and we just say that we map events in a 4D spacetime. But the idea of using a 4D coordinate system comes from coordinate transformations.
We used to transform coordinates according to the Galilean transformation. Its what you use to calculate the difference in velocity between two movies objects. Lets say we are driving on the motorway and you want to overtake me. I travel with v1 and you with v2 so you’ll pass me with v=v2-v1. From my reference frame you move at v.
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So lets try to generalise a bit. If we both have a coordinate system K and K’ lets say at t=0 their origins are at one place and K’ is moving at v realtive to K along the x axis. So lets select a point in the coordinate system K, r0 and lets see how that point’s coordinates will change in K’. From K’ it’ll look as though r0’s x coordinate drifts in the negative direction. So the x coordinate of r0 will shift some distance in the negative direction for any t time vt is distance from v=s/t so x’=x-vt. So the origin of K in K’ will be at x=-vt y=0 and z=0. For v=3 units/s in 1 s r=(0,0,0) will appear in K’ as r’=(-3,0,0). And how does time transform well t=t’.
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So for some v velocity along the x axis K: (x,y,z,t) and K’: (x=x’-vt, y=y’, z=z’, t=t’). Ok great now transform EM waves accordingly and you get that there is some absolute rest medium through which EM waves propagate, we called it aether. Now this is the same for mechanical waves where you having some relative velocities to the medium effect how you see the waves. This is called Doppler shift.
So you do an experiment and you don’t see any of that and assume that then the speed of light must be the same for all frames.
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You create now two scenarios one where an event happens at the same place at different times. Like a clock, and lets use a beam of light bouncing off a mirror and coming bact to a detector. It travels l to and back from the mirror. So all together a distance of 2l. If we travel at some v velocity we see a triangle as for us the detector moves back vt’ lf a distance. And since c is constant we know that the the two sides are both ½ct’.
We got two event (t0,r0) = (0,0) and (t0′,r0′)=(0,0) since we can say for the two to start at (0,0) and r=(x,y,z) so r0=(0,0,0).
The second event is (t,r)=(2l/c, 0) and (t’,r’)=? 2l/c for simply v=s/t -> t=s/v.
Now we need pythagoras: l²=(½ct’)²-(½vt’)² and l is just ½ct.
From this we get t’=t/sqrt(1-v²/c²) and of course x’=vt’ and now we have it. The other exercise is to figure this out for two events that happen at the same time in different locations. And through a few additional steps we get the Lorentz transformation which is an upgrade for the Galilean one.
Now instead of doing geometry all the time we introduce the 4 vector formalism. We have vectors with the usual 3 spacial and a 0th time like component. The spacetime 4 vector is x_i = (ct,x,y,z) and we transform this into some coordinate system by applying the L Lorentz transformation which is a matrix it turns one vector into another.
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And from this the rest of the formalism unfolds and now we have special relativity. Its basically about using the Lorentz transformation instead of the classical one but the consequences are profound. (There is a lot more mathematical approach to this where we instead define rapidity and essentially arrive at the same conclusion.)
So we aren’t considering a 4D coordinate system with time since we are so bored but because time changes from coordinate system to coordinate system and we cant ignore it. And SR is how we account for that.
If you were in a 3D space and could only see a plane (an infinite, 2D flat surface that has x/y axes for the sake of simplicity) at a time, then moving across the z axis would allow you to see different slices of a 3D space, but you would still only see a 2D slice in any given moment.
Time is the similar: in any given moment, you can only see and interact with a 3D space, but as you go forward/backward in time, you get to see different 3D spaces.
Einstein’s major realization was that to know anything about movement in our universe, you need 4 pieces of info: you need 3 spatial coordinates (where are you up/down, left/right, and forward/back) and 1 time coordinate (simply “when”). So say you’re going to a party, you need to know the street address (which satisfies our 3 spatial coordinates) and you need to know when the party is (don’t show up at the wrong date or time).
These coordinates are what everyone else calls a “dimension”. It’s simply a direction we can move in or a way we can measure our movement in that direction.
You go on a flight from New York to Los Angeles. The plane basically takes off and then flies in a straight direction to Los Angeles where it lands.
So if we wanted to build a mathematical model of your trip, we can basically plot it on a graph in two dimensions – on the Y axis is what you can think of as “percent of trip completed”, with “I’m still in New York” at 0 and “I’ve landed in Los Angeles” at 100, and 50 is “I’m halfway through the flight.” That’s one dimension. Since the flight takes about six hours, then we can plot the X axis as “how much time is elapsed.” At zero, you’re just taking off from New York so you’re at New York. At hour three you’re halfway through the flight so you’re halfway to LA. And then at hour six, you’re all the way at Los Angeles. And in fact we now have an implicit equation where we can insert time and return your position along the axis between New York and LA, or we can insert your position along the axis between New York and LA and find out what time you were there.
That’s what it means for time to be a dimension – in a model of a moving object where time is a dimension, we create an association between time and position in space. It’s nothing to do with Einstein, it’s just a function of how we study physics and model the movement of objects in math. I just did it with one spatial dimension and one time dimension, but there’s no reason I couldn’t extend the model and use two or even three dimensions in space and one dimension in time. That would be your “four dimension model.”
Thanks everyone for commenting and explaining. I am going to read all one by one and it is definitely going to take some time to understand every concept explained since I don’t come from a science educational background. Thanks a lot people! 🙂
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