What is the difference between separation in space and separation in time?

[enceladus_]

I do not understand the difference between separation in space and separation in time. Could someone please explain the following positions to me? I would be very thankful and appreciative if so.

Position of event 1: Separation in time (lightyears) = 20. Separation in space (lightyears) = 0

I think of light years as a measure of distance. So if separation in space is zero, then that must be my exact location, so how can it be 20 light years away in time?

Position of event 2: Separation in time = 25. Separation in space = 15.

If I think of light years as distance, how can the two be different?

Position of event 3: Separation in time = 52. Separation in space = 48.

Same confusion as #2.

Position of event 4: Separation in time = 101. Separation in space = 99.

Many thanks!

 

[Chestermiller]

I do not understand the difference between separation in space and separation in time. Could someone please explain the following positions to me? I would be very thankful and appreciative if so.

Position of event 1: Separation in time (lightyears) = 20. Separation in space (lightyears) = 0

I think of light years as a measure of distance. So if separation in space is zero, then that must be my exact location, so how can it be 20 light years away in time?

Position of event 2: Separation in time = 25. Separation in space = 15.

If I think of light years as distance, how can the two be different?

Position of event 3: Separation in time = 52. Separation in space = 48.

Same confusion as #2.

Position of event 4: Separation in time = 101. Separation in space = 99.

Many thanks!

As a result of your inherent physical limitations as a 3 dimensional being, you cannot see into your own time direction (4th dimension). It is hard to conceive of where that 4th direction even is, but it is there. It is also hard to believe that you are traveling into your own time direction at the speed of light. You are moving along your "world line," and + 25 light years ahead of you is where you will be in 25 years. -25 light years relative to your present location along your world line is where you were in space time 25 years ago. Separation in time and separation in space are just components of your position vector in space time (the story is a little different if you are in a portion of space time that is curved). Also, the components of your position vector do not satisfy the ordinary Pythagorean relationship of Euclidean space, but it satisfies an analogous relationship called the Minkowski metric for non-Euclidean space time.

I hope this rough qualitative description helps.

 

[enceladus_]

As a result of your inherent physical limitations as a 3 dimensional being, you cannot see into your own time direction (4th dimension).

From the little I know, I am traveling through time as fast as possible.

It is hard to conceive of where that 4th direction even is, but it is there. It is also hard to believe that you are traveling into your own time direction at the speed of light. You are moving along your "world line," and + 25 light years ahead of you is where you will be in 25 years. -25 light years relative to your present location along your world line is where you were in space time 25 years ago.

It seems then that light years in this case are a quantity of time. It seems I must think of light years as both measures of distance and time then.

Separation in time and separation in space are just components of your position vector in space time (the story is a little different if you are in a portion of space time that is curved). Also, the components of your position vector do not satisfy the ordinary Pythagorean relationship of Euclidean space, but it satisfies an analogous relationship called the Minkowski metric for non-Euclidean space time.

Is that why you subtract one from the other?

I hope this rough qualitative description helps.

It did, thank you very much.

 

[tensor33]

I do not understand the difference between separation in space and separation in time. Could someone please explain the following positions to me? I would be very thankful and appreciative if so.

Position of event 1: Separation in time (lightyears) = 20. Separation in space (lightyears) = 0

I think of light years as a measure of distance. So if separation in space is zero, then that must be my exact location, so how can it be 20 light years away in time?

Position of event 2: Separation in time = 25. Separation in space = 15.

If I think of light years as distance, how can the two be different?

Position of event 3: Separation in time = 52. Separation in space = 48.

Same confusion as #2.

Position of event 4: Separation in time = 101. Separation in space = 99.

Many thanks!

Light years are not units of time, they are units of space. A unit of time would be a year or a day. Your statements make no sense.

 

[Chestermiller]

It seems then that light years in this case are a quantity of time. It seems I must think of light years as both measures of distance and time then.

Not exactly. Light years is distance into your time direction. Think of your watch as an odometer, telling you how far you traveled. It's just that your speed is always constant, so the distance you travel along your world line is always proportional to the amount of time that has elapsed on your watch.

Is that why you subtract one from the other? (in the Minkowski metric)

Yes.

 

[nitsuj]

Light years are not units of time, they are units of space. A unit of time would be a year or a day. Your statements make no sense.

Hmmm, technically you're right. But a light-year is also a very specific speed. I could "derive" without much difficulty, it to be a measure of time. (how long does it take for light to travel the length of one light year? ) I think the math would be

1 = 1/1

look at me; math prof. nitsuj :tongue:

the unit(temporal dimension) is kinda hidden in the term/ but it's in there twice

 

[enceladus_]

Light years are not units of time, they are units of space. A unit of time would be a year or a day. Your statements make no sense.

This is from a book I am reading. It doesn't make sense to me either! Here is what I'm referring to. I could have been explaining it poorly.

 

[nitsuj]

From the little I know, I am traveling through time as fast as possible.
It seems then that light years in this case are a quantity of time. It seems I must think of light years as both measures of distance and time then.

the first line is the same as saying c is invariant. Can you see that connection? "both measures of distance and time then"
Yea for sure, I never noticed, on my own, what a light-year/second actually was. It had to be pointed out to me that it is a speed, and of course a specific one. From that into Pythagoras theorem & time/length definitions was a great SR lesson. (and a lesson on dimensions/simple metrics / intervals)

 

[Crazymechanic]

Basically your separation in time and space is nothing more than saying that one event takes place like 20 years ago in New York but the second one took place 15 years ago in Dallas.
Now you have two things you have time that counts as years and days and and physical places like cities or galaxies in the universe.
Now you measure time with days and years but distanced with km, miles or in cosmological units as light years .


By the way here might be an interesting thread for you
http://www.thenakedscientists.com/forum/index.php?topic=22349.0

 

[nitsuj]

This is from a book I am reading. It doesn't make sense to me either! Here is what I'm referring to. I could have been explaining it poorly.

I'm not sure about the other posters positions, but imo you are understanding it correctly.

they're isn't any difference between the two, besides them being "opposite". A similar kind as symmetrical relationships.

I see time/length as having this kind of relationship/(a link to wiki),

lol so length/time are "something from nothing which is something*" (as in your textbook saying "Never mind the (light-like) interval is ZERO")

*statement I read on that wkiki-page speaking about the philosophical view about going from the number "0" to "1", i.e. 0 is two equal but opposite "units/things/whatever".

 

[enceladus_]

Basically your separation in time and space is nothing more than saying that one event takes place like 20 years ago in New York but the second one took place 15 years ago in Dallas.
Now you have two things you have time that counts as years and days and and physical places like cities or galaxies in the universe.
Now you measure time with days and years but distanced with km, miles or in cosmological units as light years .


By the way here might be an interesting thread for you
http://www.thenakedscientists.com/forum/index.php?topic=22349.0

Ahhh, I see. Now in the case of your example, the separation in space is near zero, if I am reading it right. That is, if distance is in terms of light years. Many thanks.

 

[tensor33]

Now I see where this book is getting lightyears as a unit if time. In the Minkowski metric the time component is often multiplied by c (the speed of light) to make the units the same for all components. So if you have events that happen a year apart, their time separation would be c times 1 year= 1 lightyear.

 

[Dale]

The idea of a lightyear being a unit of time (as opposed to the year) comes from geometrized units. It crops up fairly regularly in relativity. The basic idea is similar to the idea of natural units, except that in natural units c=1 still has dimensions of length/time whereas in geometrized units c=1 is dimensionless.

Here is a wiki on the topic.

http://en.wikipedia.org/wiki/Geometrized_unit_system

You can always go from geometrized units to other units simply by putting the units back into the variables and then looking to see where your units don't match. Then you multiply by powers of c and G to get the units correct.

 

[enceladus_]

Thanks for the wisdom, guys.

 

[nitsuj]

The idea of a lightyear being a unit of time (as opposed to the year) comes from geometrized units. It crops up fairly regularly in relativity. The basic idea is similar to the idea of natural units, except that in natural units c=1 still has dimensions of length/time whereas in geometrized units c=1 is dimensionless.

Here is a wiki on the topic.

http://en.wikipedia.org/wiki/Geometrized_unit_system

You can always go from geometrized units to other units simply by putting the units back into the variables and then looking to see where your units don't match. Then you multiply by powers of c and G to get the units correct.

Can c really be called a dimensionless quantity (in this case a value of 1)? You know I have no education in this respect, only from what I read on Dimensionless Quantities.

Just so I'm clear on the definition, c=1 is dimensionless because the temporal dimension has been "converted" to length. as in this line from the wiki article;

"The ratio of two quantities with the same dimensions is dimensionless, and has the same value regardless of the units used to calculate them. "

But c is in fact not "really" a dimensionless quantity, where as c=1 is, just like you said "geometrized" units. Perhaps better called a pseudo Dimensionless quantity.Is my understanding of dimensionless quantities in this context okay?
I had looked into the definition because I was "excited" that I maybe able to say a photon is dimensionless, but it looks as though it's just the opposite. It's both dimensions at once!

 

[Dale]

But c is in fact not "really" a dimensionless quantity, where as c=1 is, just like you said "geometrized" units. Perhaps better called a pseudo Dimensionless quantity.

The dimensionality of a quantity does depend on the system of units and the laws of physics used. For instance, in SI units electric charge has its own dimension but in cgs units charge has dimensions of $M^{1/2}L^{3/2}T^{-1}$.