The nature of space, time and spacetime

[playmesumch00ns]

So what exactly is meant by time as a 4th dimension?

I've read in a couple of places a nice visualization of the effect of time dilation using velocity as a 4-component vector. Since the maximum possible velocity is the speed of light, as something travels through space at close to the speed of light, the "time-component" of its velocity must necessarily be smaller.

Does this example have any meaning, or is it simply a useful illustration for the layman?

In modern physics, what are the distinctions between space and time? And is it worth asking the question in the first place?

The most obvious difference to me is that one can travel backwards in space, but not in time; but then it occurs to me that since the universe is constantly expanding, can one really travel "backwards" in 3-dimensional space?

I've also read that some theorists posit that in the first moments after the big bang, space and time were "smeared" together, and that time only emerged as a separate dimension as the universe grew. What exactly does this mean, and how does it relate to the first part of my question?

All illuminating answers greatly appreciated!

Cheers,

Anders

 

[pervect]

Space and time often "mix together" in relativity, that's why they are combined into a conceptual entity called "space-time".

Here is how it works, basically.

Consider an observer, who is looking at two events that happen "at the same time" according to the observer. He sees the events as occurring at different locations in space, but at the same time. The spatial interval between the two events is non-zero, the time interval is zero.

Now, another, moving observer who looks at the exact same two events will not see them as happening "at the same time". Both the spatial interval and the time interval between the two events are non-zero.

There is a conserved quantity, though, which is the square of the spatial interval minus the square of the time interval, i.e.

L = dx^2 + dy^2 + dz^2 - dt^2

is the same for all observers, moving or not. This is the Lorentz interval. So what happens is that some observers observe a certain physical "interval" between two points as having only space components, other observers observe the same "interval" as having time components as well.

 

[LURCH]

Since the maximum possible velocity is the speed of light, as something travels through space at close to the speed of light, the "time-component" of its velocity must necessarily be smaller.

The main idea behind this analogy is not just that the maximum possible velocity of an object is c/, but that the total velocity of any object is c at all times. I don't know where you heard this analogy, so you may already be familiar with the following illustration, but just in case you're not;

If you drive an automobile at exactly 60 mph on a highway going exactly east (a heading of 90^o), then for every minute that passes, you will be 1 mile further east. If the Highway turns to a heading of Northeast (45^o), and your speed remains constant, then for every minute that passes you will be only .5 miles further east, because 1/2 of your 1-mile-per-minute total velocity will be devoted to making Northward progress.

The idea of "time as a fourth direction" can be more easily excepted if we think of all objects in the universe as traveling at a constant velocity c. So, when you add up all for directions (x,y,z, and t), your total velocity will always equal c. When you commit any fraction of that total velocity to movement along one of the spatial directions, such as "eastward", your progress along direction t ("futureward") decreases.

 

[playmesumch00ns]

So it actually means something then! I think I first read that analogy in Stephen Hawking, or Brian Greene's books.

Okay, so the next part of my question: if space and time are not separate any more, but a malleable (by gravity) fabric we call spacetime, in what ways (other than ability to travel in both directions) are space and time similar and in what ways are they different? What is the nature of time as compared to space?