Why is time called a 4th dimension?

[trevorjohnson32]

They say an object has four dimensions x,y,z, and time, but if you stand far enough away from an object like say mars or another planet, its dimension of time or light isn't the same as its x,y,z, coordinates. Also say you were to find a church by its bells ringing. Wouldn't that create a 5th dimension of sound? or say a dog finds something by smell, 6? gravity waves? 7?

[beecee]

2 hours ago, trevorjohnson32 said:

They say an object has four dimensions x,y,z, and time, but if you stand far enough away from an object like say mars or another planet, its dimension of time or light isn't the same as its x,y,z, coordinates. Also say you were to find a church by its bells ringing. Wouldn't that create a 5th dimension of sound? or say a dog finds something by smell, 6? gravity waves? 7?

In simple language, a set of dimensions of an object, [length breadth and width] needed to specify or locate that object: Time then is needed to specify when in space that object is.

 

Sound, smell etc I would class as properties of that particular object.

[Strange]

6 hours ago, trevorjohnson32 said:

They say an object has four dimensions x,y,z, and time, but if you stand far enough away from an object like say mars or another planet, its dimension of time or light isn't the same as its x,y,z, coordinates. Also say you were to find a church by its bells ringing. Wouldn't that create a 5th dimension of sound? or say a dog finds something by smell, 6? gravity waves? 7?

Dimensions are (independent) values for defining the location of an object. So, for example, if you want to meet someone then you would need to specify the location, which is in three dimensions in space and the time you are meeting, for four dimensions in total.

The three spatial dimensions can be defined in many ways, for example on the surface of the Earth we normally use latitude, longitude and altitude as x,y,z. These are often "encoded" for human use in things like a postal address ("Apartment 501, 82 Main Street, Hometown") but if you use GPS then these will be decoded to the latitude, longitude and altitude used by the navigation system.

You might use references to describe to someone how to find it ("it's two doors down from the church where you can hear the bells ring" or, if you are a dog, "its where you can smell that chihuahua") but that doesn't change the location in space and time, it is just an aid to finding it.  These don't provide any more information about the location (you could find it via the x,y,z coordinates or via some sequence of landmarks or smells - but you can always map from one set of coordinates to another. In the same way you can map from a street address to an x,y,z location.

We might use different coordinates in different places. So, for example, latitude and longitude don't help much in space, so we are more likely to use a coordinate system based on the position of the Sun etc. And these might be based partly on angles (e.g. the angle up from the plane of the Earth's orbit) as well as lengths (distance form the Sun). But we will still end up needing three spatial dimensions to specify the position.

You can use all sorts of methods to find things (smell, landmarks, sound, bouncing radar signals off of airplanes or planets) but you will at some point find you need to convert those to the three dimensions in space (and the time that it was there).

Note that dimensions are also used in a more "abstract" sense to define locations in a conceptual space. For example, if you were studying people's sensitivity to different tastes you might define a multi-dimensional "taste space" where the dimensions were things salt, sweet, sharp, bitter, heat and savoury, etc. You could then define the "position" of each flavour within this space. So dark chocolate would be quite high up the sweet dimension and the bitter dimension, milk chocolate would be the same position on the sweet dimension but not as far up the bitter dimension, and so on. You could then plot different peoples responses to a new flavour within this space. This might help you say "if you like the food, then you might also like this one" or "this flavour generates a similar response to chocolate".

 

[StringJunky]

Short version of Strange's informative post: Dimensions, as used in science, are degrees of freedom (or parameters that are independently variable); there are four necessarily associated with motion or position in space,of which, time is one of them.

Edited January 18, 2018 by StringJunky

[geordief]

8 minutes ago, StringJunky said:

Short version of Strange's informative post: Dimensions, as used in science, are degrees of freedom (or parameters that are independently variable); there are four necessarily associated with motion or position in space,of which, time is one of them.

I understand c can be seen as a conversion factor between the spatial dimension and time.Is this value of c purely an observed quantity or is there/could there be  any (possible) a priori reason that it should be as it is (or otherwise)? 

 

If it is purely observed do we just "shoehorn" everything else  around it?

[StringJunky]

11 minutes ago, geordief said:

I understand c can be seen as a conversion factor between the spatial dimension and time.Is this value of c purely an observed quantity or is there/could there be  any (possible) a priori reason that it should be as it is (or otherwise)? 

 

If it is purely observed do we just "shoehorn" everything else  around it?

Apparently, it falls out of Maxwell's equations which predict it. I originally thought it was limited by the properties of the vacuum (permittivity and permeability) but gravitational waves are limited to c as well, which are not influenced by properties of the vacuum. It seems that c is a fundamental, axiomatic value.

Edited January 18, 2018 by StringJunky

[geordief]

3 minutes ago, StringJunky said:

Apparently, it falls out of Maxwell's equations which predict it.

Including the(or a?) numerical value? (those equations themselves are faulty in that they don't account fully  for  the relative motion  between the electric charge and the magnetic charge**  I think I  have learned)

 

** if there is a magnetic "charge" as such

[Strange]

5 minutes ago, geordief said:

Including the(or a?) numerical value?

No, it is a measured value (like the permittivity and permeability of free space). I really hope that one day some "deeper" theory will explain why these things have the values they do....

[geordief]

2 minutes ago, Strange said:

No, it is a measured value (like the permittivity and permeability of free space). I really hope that one day some "deeper" theory will explain why these things have the values they do....

Are there any attempts along those lines?  "Quantum Gravity "? (I assume)

[StringJunky]

8 minutes ago, Strange said:

No, it is a measured value (like the permittivity and permeability of free space). I really hope that one day some "deeper" theory will explain why these things have the values they do....

I thought you could calculate c with those equations.

[Strange]

4 minutes ago, geordief said:

Are there any attempts along those lines?  "Quantum Gravity "? (I assume)

There are lots (I don't know much about any of them). String theory, causal dynamical triangulation, loop quantum gravity, etc. And there are wackier ideas about everything emerging from information and entropy ...

2 minutes ago, StringJunky said:

I thought you could calculate c with those equations.

From other things you measure, I think.

[StringJunky]

2 minutes ago, Strange said:

From other things you measure, I think.

Right. No doubt mordred will come along and shrivel my brain with his version of "a little bit of maths".

[Mordred]

Lol actually you guys have accurately answered the Op's question. I would only like to add that by using the displacement of c via the usage of {ct} we get the dimensionality of length for the time component.

 

[Endy0816]

1 minute ago, Mordred said:

Lol actually you guys have accurately answered the Op's question. I would only like to add that by using the displacement of c via the usage of {ct} we get the dimensionality of length for the time component.

 

Just curious, are there any metrics that involve {d/c} instead?

[Mordred]

Not that I am aware of. In many metrics the coordinates will often employ the following

[math] {ct,x,y,z}={x^0,x^1,x^2,x^3}[/math] where the superscripts are indices and not powers. The indices can be interchanged to the subscripts ie [math]x_0[/math] following the covariant and contravariant rules under Einstein summation rules. GR,QFT and String theory all use the latter x coordinates.

There is advatanges to using the latter when you use Natural units.

https://en.m.wikipedia.org/wiki/Natural_units

particularly under symmetry/ assymetry group relations

Edited January 18, 2018 by Mordred

[Strange]

4 hours ago, Strange said:

Dimensions are (independent) values for defining the location of an object.

It may be worth adding that because they are independent, they are also the minimum set of values required. 

So, for example, you could specify the position of a place on a map by using x (along the bottom) and y (up the side) and d (a measure diagonal from the corner). But if you consider two points at the same y coordinate but with different x coordinates, then they will also have a different d value. The same is true if you keep x constant and vary y. So x and y are independent of one another (you can vary one without changing the other) but d isn't independent; it changes when x or y changes. Which means that d doesn't provide any more information. It may be convenient but it is redundant. 

The same argument can apply to adding other "dimensions" like ringing bells or dog smells; they may be useful but they don't tell you anything new. 

Edited January 18, 2018 by Strange

[StringJunky]

6 minutes ago, Strange said:

....they are also the minimum set of values required. 

That's a good point.

[geordief]

1 hour ago, StringJunky said:

 

If all regions were graded according to smell and none were identical would that identify the region  most efficiently?

Getting there might not be so efficient.

[trevorjohnson32]

26 minutes ago, geordief said:

If all regions were graded according to smell and none were identical would that identify the region  most efficiently?

Getting there might not be so efficient.

your sense of smell may not be as  great as mine, but when you are walking dog you might not see when it is time that squirrel bibs dinner but cause you are dog, nose is easy to see.

[trevorjohnson32]

10 hours ago, Strange said:

Dimensions are (independent) values for defining the location of an object. So, for example, if you want to meet someone then you would need to specify the location, which is in three dimensions in space and the time you are meeting, for four dimensions in total.

To an observer far away your meeting the person at a different time then the time for those meeting would meet at. Even for identical clocks.

[Strange]

7 minutes ago, trevorjohnson32 said:

To an observer far away your meeting the person at a different time then the time for those meeting would meet at. Even for identical clocks.

Not quite sure why you think that. Someone far away would see us delayed ("in the past") because of the time it takes for light to reach them.But if they can see my watch (*) and the clock at the place I am meeting, then they would see that they say the same time when we meet. 

(*) Yes, it's a really big watch.

Or do you mean, if I am far away from the people I am intending to meet? Again, I will see the time on their clocks delayed. But I can take that into account. I know how long it will take to get there and I can plan to leave based on the time on my watch which will (ignoring relativity) be in synch with theirs, even if it doesn't;t look like it.

[trevorjohnson32]

6 hours ago, Strange said:

Not quite sure why you think that. Someone far away would see us delayed ("in the past") because of the time it takes for light to reach them.But if they can see my watch (*) and the clock at the place I am meeting, then they would see that they say the same time when we meet. 

(*) Yes, it's a really big watch.

Or do you mean, if I am far away from the people I am intending to meet? Again, I will see the time on their clocks delayed. But I can take that into account. I know how long it will take to get there and I can plan to leave based on the time on my watch which will (ignoring relativity) be in synch with theirs, even if it doesn't;t look like it.

Alright, I'm not sure if you understand so I'll give another example. The light from a star in the sky shows us its position from however long ago, generally years. Without knowing how far away it is, how are you going to give it's x,y,z, position based on its position in time? because time isn't a coordinate its a measurement of the light an object reflects, it doesn't give away location any better then sound waves like I said.

And, what exactly is anyone leading to with this train of thought? It sounds like an attempt to marvel at the word dimension like its going to lead to something bigger.

[beecee]

20 minutes ago, trevorjohnson32 said:

Alright, I'm not sure if you understand so I'll give another example. The light from a star in the sky shows us its position from however long ago, generally years. Without knowing how far away it is, how are you going to give it's x,y,z, position based on its position in time? because time isn't a coordinate its a measurement of the light an object reflects, it doesn't give away location any better then sound waves like I said.

To a star, simple "stellar parallex"....to another galaxy, standard candles such as Type1a Supernova, Ceipheid Variables, in conjunction with cosmological redshift.

[trevorjohnson32]

2 minutes ago, beecee said:

To a star, simple "stellar parallex"....to another galaxy, standard candles such as Type1a Supernova, Ceipheid Variables, in conjunction with cosmological redshift.

parallax refer to measurement with one eye then other of finger in front of face? Or was I wrong to bring bacon for that word salad?

[beecee]

5 minutes ago, trevorjohnson32 said:

parallax refer to measurement with one eye then other of finger in front of face?

https://en.wikipedia.org/wiki/Stellar_parallax

 

http://hubblesite.org/hubble_discoveries/dark_energy/de-type_ia_supernovae.php

http://sci.esa.int/education/35616-stellar-distances/?fbodylongid=1673

 

Quote

Or was I wrong to bring bacon for that word salad?

As a lay person, my replies are generally dumbed down...Not sure how much further dumbing down I can do.