Newbie Asks: What is Spacetime?

[jerrok]

I'm new, so go easy on me...

I see the term spacetime used... does that mean that time exists in the same way that space exists?

 

[HallsofIvy]

I'm not sure what you mean by "time exists" and "space exists". Certainly just as my birth did not occur at the same place as my graduation from college, they did not happen simultaneouly!

But the term "space-time" refers to the fact that any physical "event" must occur at a specific place and a specific time- you cannot talk about one without the other.

 

[ghwellsjr]

No. It primarily relates to the concept that in special relativity, we use coordinate systems that include three spatial components and one time component in the ordinary sense which together specify an event.

 

[pervect]

Whether or not something "exisists" is basically a philosophical question.

While it's still philosophy, the easiest way to understand the concept of space-time in relativity is to think of space and time as being two parts of a larger whole, the whole being space-time.

The textbook example is to consider north- south distances, and east-west distances. (The textbook here is "Spacetime physics). If you allow rotations, north-south and east-west can mix together, as long as the sum of the squares of the distances remains constant.

In realtivity, space and time can mix together in a very similar way. Rather than rotations, this phenomenon is caused be motion, which is mathematically rather similar to a rotation of the space-time diagram. A key difference, though, is that it's the difference of the square of the intervals that's constant in relativity, while it's the sum of the squares of the distances that's constnt in ordinary gemoetry.

 

[bobc2]

I'm new, so go easy on me...

I see the term spacetime used... does that mean that time exists in the same way that space exists?

No, that does not mean that time exists in the same sense as space exists. In our special relativity model space exists and objects embedded in the space exist. Space exists with 4 dimensions, i.e, four spatial dimensions. Time only enters into the picture as a parameter. Every observer moves along his own 4th spatial coordinate axis (at rest with respect to his X1, X2 and X3 dimensions) at the speed of light. So, time passes as the observer moves along the 4th dimension. Time passes in the same sense that time passes as you drive along an interstate highway. Driving at 60 mph along the highway, you could mark off time along the way at one minute intervals--that would be a time mark every mile. But, just because you can put time marks along the highway does not make the highway a time dimension--it is strictly a spatial dimension. And the 4th dimension works the same way.

Space exists makes sense. Time exists does not seem to make sense. You must bring in a concept of consciousness and other metaphysical concepts to have a serious discussion about time.

 

[Passionflower]

I'm new, so go easy on me...

I see the term spacetime used... does that mean that time exists in the same way that space exists?

Time between point A and B is a path in spacetime, it is not a dimension of spacetime.

In Galilean spacetime time is truly a dimension but this is not the case in a Lorentzian spacetime.

 

[bobc2]

Time between point A and B is a path in spacetime, it is not a dimension of spacetime.

Passionflower, I've been impressed with your comments in some of the other posts. But, hopefully without sounding argumentative, I must emphasize again (see previous post) that the 4th dimension is purely spatial. Time simply plays the role of a parameter in exactly the same way it would if you were to write the X(t) and Y(t) parametric equations for the path of a projectile through 3-D space for the X and Y coordinates. Or, the example I presented of driving along the interstate and marking off time points based on clock readings. The ability of reading clock times as you move along the interstate does not make the interstate a time axis--it is still a spatial axis. Likewise X4 is still a spatial axis.

 

[DrGreg]

Time between point A and B is a path in spacetime, it is not a dimension of spacetime.

In Galilean spacetime time is truly a dimension but this is not the case in a Lorentzian spacetime.

No. To communicate successfully with others, it is best to use established terminology. Proper time between point A and B is the "length" of a timelike path in spacetime. (Coordinate) time is a dimension of spacetime.

Passionflower, I've been impressed with your comments in some of the other posts. But, hopefully without sounding argumentative, I must emphasize again (see previous post) that the 4th dimension is purely spatial. Time simply plays the role of a parameter in exactly the same way it would if you were to write the X(t) and Y(t) parametric equations for the path of a projectile through 3-D space for the X and Y coordinates. Or, the example I presented of driving along the interstate and marking off time points based on clock readings. The ability of reading clock times as you move along the interstate does not make the interstate a time axis--it is still a spatial axis. Likewise X4 is still a spatial axis.

No. To communicate successfully with others, it is best to use established terminology. What you call X4 (and everyone else calls x⁰) is temporal, not spatial. Yes, it's one of the four dimensions of spacetime, but it differs from the other three in being timelike, not spacelike. (That's why we call it "spacetime", not "spacespace".) Proper time (not "time" alone) can play the role of a worldline parameter. Note that nothing moves in or through spacetime as time is already one of the dimensions in spacetime. Motion of a particle in space corresponds to a static worldline in spacetime.

 

[bobc2]

...No. To communicate successfully with others, it is best to use established terminology. What you call X4 (and everyone else calls x⁰) is temporal, not spatial.

As always you make very good points, DrGreg. However, when trying to help one understand what's going on with special relativity I think it helps to emphasize that the 4th dimension is actually spatial, with time used a a parameter just as it is with parametric equations in normal 3-D examples.

...Yes, it's one of the four dimensions of spacetime, but it differs from the other three in being timelike, not spacelike. (That's why we call it "spacetime", not "spacespace".)

Of course the 4th dimension is distinguished from the X1, X2, X3. For the observed worldlines in our model (4-dimensional static objects)--they commonly are found to extend for billions of miles along paths in the forward light cone (they're slanted angles related to perceived speeds that are always less than c). But, the X1, X2, and X3 spatial extents of 4-dimensional objects are miniscule compared to the length along X4 (x0 if you wish). Further, just because we have such a distinction between the dimensions along with the additional special distinction that observers move along the 4th dimension--these distinctions do not translate into robbing the 4th dimension of its spatial character (nor does it imply some kind of existence of a mixture of space and time--we really would have no way of giving physical meaning to that kind of concept). Again, movement of something along the 4th dimension doesn't imply anything more than proper time is a parameter.

...Proper time (not "time" alone) can play the role of a worldline parameter.

Proper time does indeed play the role of a time parameter: X4 = cT (where T is proper time).

...Note that nothing moves in or through spacetime as time is already one of the dimensions in spacetime. Motion of a particle in space corresponds to a static worldline in spacetime.

I certainly agree that no physical object moves along the 4th dimension. It couldn't--the objects that populate the 4-dimensional universe are themselve static 4-dimensional objects. Yet, in our special relativity model we have some aspect of observers (related to consciousness and time in some way?...) that is moving along the 4th dimension at light speed. We really can't explore that aspect of nature in a forum of this type, since it veers too far outside the guidelines set out for this forum. We just simply state that the "observer" moves along his 4th dimension worldline at light speed, understanding that there is no movement at all of the observer's physical body structure--because, again, that is a static 4-dimensional structure.

Herman Weyl said something like, "...the observer crawls along his world line..."). But of course we would hardly call that crawling (maybe he was thinking a 90 year life time is a long time to crawl from one end of the world line to the other, even at the speed of light).

 

[Passionflower]

Yes, let me qualify what I wrote before, with time I mean time as measured by a clock, not time as coordinate time.

So in other words we have distances which can be measured by rulers and these are dimensions. But time, as measured by a clock, is a path in spacetime which is not a dimension. However time as a coordinate can be seen as a dimension.

Didactically important here IMHO, is to understand that time as measured by a clock is both a path and a dimension in Galilean spacetime while this is not the case in a Lorentzian spacetime.

 

[bobc2]

Yes, let me qualify what I wrote before, with time I mean time as measured by a clock, not time as coordinate time.

So in other words we have distances which can be measured by rulers and these are dimensions. But time, as measured by a clock, is a path in spacetime which is not a dimension. However time as a coordinate can be seen as a dimension.

Didactically important here IMHO, is to understand that time as measured by a clock is both a path and a dimension in Galilean spacetime while this is not the case in a Lorentzian spacetime.

Passionflower, I jumped to the wrong conclusion in interpreting your previous post. Thanks for setting me straight.