lets discuss dimensions! Preferably extra ones.

[Samson]

Time not only feels different, but it is different. If you would add a fourth spatial dimension, you would calculate a distance in that space as

d=sqrt( (dx1)^2 + (dx2)^2 + (dx3)^2 + (dx4)^2)

where dxn is the distance in the nth dimension.
However, time is different: In special relativity you calculate a distance as (with c=1):

d=sqrt( (dx1)^2 + (dx2)^2 + (dx3)^2 - (dt)^2)

Notice the minus there? This makes the resulting space quite different form a "normal" (i.e. Euclidean) 4 dimensional space.

How does this work then? Is this not saying that the further away in time something is the closer it is really?

 

[Robert Can't]

As for taking time as a fourth dimension: Look at it this way - I can also take time as my second dimension. If I plot a graph of displacement vs time I have a curve/arc in R^2 i.e a 2 dimensional object but the dimensions I am working in are displacement and time.

Spoiler :

Clearly you can see this is a 2-dimensional curve and one of those dimensions is clearly labelled time.


We can take whatever we want as however many dimensions we want another way to imagine a fourth dimension would be to define each point in an object with Cartesian coordinates and then the heat of the object at that point (x,y,z,c).
Similarly we can define a points position over a length of time as (x,y,z,t) i.e (distance from the start position parallel to one wall, distance from the start position parallel to another wall, distance from the floor, distance from the starting time)

Basically 4-dimensions are just a specific case of a Euclidean n-space and I can define my dimensions to have whatever physical representation I want - really in studying four dimensional spaces what those dimensions actually mean does not matter.

 

[warpus]

I still cant consider time a dimension simply based on how the first to third dimensions work, I cannot correlate time to also being a dimension.

If you break the dimensions down into mathematical equations, they become not only similar but also in a way equivalent. Time and space are linked, it's just not so obvious at this scale and in our weird human context.

 

[Marla_Singer]

It's funny time is generally the most questionned dimension, whereas it's as much part of life as any other. People argue that as time cannot be defined without motion and motion cannot be defined without time, therefore that means time is an artificial construct. But in the meantime it's impossible to define space without the notion of distance and distance without the notion of space, but you would look like an idiot if you would use that fact to conclude space is an artificial construct.

Dimensions are impossible to define because they are the very structure of our universe. Trying to define dimensions is like trying to explain to a binary computer the difference between 0 and 1. 1 is not 0, 0 is not 1, and that's it... there's nothing more to understand, and we don't care if such a definition generates a loop.

Now, I've spent a lot of time few months ago to improve my knowledge of the theory of the relativity. And this has lead me to wonder if what defines our world the most ultimately is not simply energy. Energy is the key generating spacetime, and that's what I consider the most meaningful in E=mc². However, what I haven't understood yet is... from where comes energy. We of course know the reactions releasing energy, but we don't know how energy could be generated in total emptyness. That's my big question in my current understanding of the universe.

 

[strijder20]

The difference between the two dimensions in this picture is negligible.

It is true that time is the fourth dimension. But it is wrong to think it to be similar to a fourth spatial dimension. Time not only feels different, but it is different. If you would add a fourth spatial dimension, you would calculate a distance in that space as

d=sqrt( (dx1)^2 + (dx2)^2 + (dx3)^2 + (dx4)^2)

where dxn is the distance in the nth dimension.
However, time is different: In special relativity you calculate a distance as (with c=1):

d=sqrt( (dx1)^2 + (dx2)^2 + (dx3)^2 - (dt)^2)

Notice the minus there? This makes the resulting space quite different form a "normal" (i.e. Euclidean) 4 dimensional space.


Here is a useful fact about extra spatial dimensions: The volume of an infinite dimensional sphere is equal to its surface area. (And yes, there is physics where this fact is indeed useful)[/QUOTE]

So staying stationary while travelling forward in time implies you've traveled an imaginary distance?

 

[warpus]

Isn't it impossible to stay stationary, since there is no fixed frame of reference?

 

[Marla_Singer]

Isn't it impossible to stay stationary, since there is no fixed frame of reference?

Spacetime only exists as long as there is an energy to make move something on a certain distance during a certain time. If there is no such energy, then there cannot be any spacetime in the first place.

Gravitation attracts us to the sun and makes the earth turn onto an orbit. This strength actually makes the spacetime in which earth travels circular and not euclidian. Indeed, the earth doesn't do a circle, gravitation makes it fall in one straight direction... it is actually the spacetime in which it falls which is itself curved by the gravitation of the sun, and thus bring the earth back to its initial position (relatively to the sun), hence drawing a circle.

I'm just giving that example to make understand that it's really the different forces interecting in the universe which generates the universe in itself, and the timespace which is created by them, is also distorted according to the strength and influence of those forces, and this at all levels.

So the logic should be thought otherwise. There cannot be a stationary world (without energy) in the first place because the world is energy.

 

[warpus]

I was more trying to say that it's impossible to "stand still" - we are always moving through space-time, no matter what.

As for us always moving through space itself.. aren't we? How would it be possible to "stay still" ? Depending on the point of reference you pick, you are always moving.

But then that makes me wonder - photons move only through space - not through time. I think. Is it possible to move only through time, but not through space? It seems like it should be - but how? ANd how would you know it?

 

[BenitoChavez]

As for us always moving through space itself.. aren't we? How would it be possible to "stay still" ? Depending on the point of reference you pick, you are always moving.

If you pick yourself as the point of reference then you are always staying still (ie not moving through space).

 

[Marla_Singer]

But then that makes me wonder - photons move only through space - not through time. I think. Is it possible to move only through time, but not through space? It seems like it should be - but how? ANd how would you know it?

Photons move at the speed of light... so they do move through time, which explains why the image we see of the stars are actually past image and not the way they are currently.

Nothing is supposed to be able to move faster than the speed of light. Well to tell the truth I've never checked that by myself, I only trust those guys who really look serious when they state so. Theory of relativity isn't something I fully master, especially when it goes about speed distorting time.

 

[warpus]

BenitoChavez, that seems like cheating.

Marla, I'm under the impression that every object in the universe moves through space-time at the speed of light. So if you move through space at light speed - your movement through the temporal dimension is 0.

I am pretty sure that is right, but I could be thinking of a different particle.. but if photos do move through space at lightspeed.. it seems that the only conclusion you can draw is that they do not move through time at all.

What do I have wrong here?

 

[Marla_Singer]

Well... as I've said Warpus I'm a bit lost with the idea that time is distorted by speed. I don't fully understand it. So I hope others could answer more accurately than I can.

OK so here's what I've understood: if an object move really really fast, it distorts the time and time will move "slower" in the moving object than in the universe standing still around it. So if it moves at the speed of light, what would be the "timespeed gap" between the "time" as experienced by our photon and the "time" of objects standing still?

Considering the speed of light is an absolute limit, could we consider that "timespeed gap" to be absolute? Is this your question? If so, I have absolutely no idea!

 

[bhavv]

I believe that an object can be perfectly still. I don't think that something can travel faster than time, it just gets that object from one point to another in less time.

 

[uppi]

As for taking time as a fourth dimension: Look at it this way - I can also take time as my second dimension. If I plot a graph of displacement vs time I have a curve/arc in R^2 i.e a 2 dimensional object but the dimensions I am working in are displacement and time.

Spoiler :

Clearly you can see this is a 2-dimensional curve and one of those dimensions is clearly labelled time.


We can take whatever we want as however many dimensions we want another way to imagine a fourth dimension would be to define each point in an object with Cartesian coordinates and then the heat of the object at that point (x,y,z,c).
Similarly we can define a points position over a length of time as (x,y,z,t) i.e (distance from the start position parallel to one wall, distance from the start position parallel to another wall, distance from the floor, distance from the starting time)

Basically 4-dimensions are just a specific case of a Euclidean n-space and I can define my dimensions to have whatever physical representation I want - really in studying four dimensional spaces what those dimensions actually mean does not matter.

There are two different things that people have in mind when talking about dimensions. The first one is the mathematical tool used to describe a space. For that I can add as many dimensions of any type as I find to be useful. If my problem can be well described by 112 dimensions, I use 112 dimensions. There is not much to it, except the increasing resources I need for the calculation.

The second thing is the description of the space of the universe, the space we lie in. Here we cannot randomly add dimensions, but have to comply with reality. And here the evidence is very strongly in favor of 4 (non-compactified) non-Euclidean dimensions.

So staying stationary while travelling forward in time implies you've traveled an imaginary distance?

Yes. The physical meaning is that the distance is time-like, which means that it is different from the usual space-like distance.

 

[BenitoChavez]

Picking yourself as a reference isn't cheating. Its just as valid as picking a spaceship, or the earth, or Barrack Obama, or anything else as a reference.

As for traveling at near the speed of light, objects will experience both time dilation and length contraction. Meaning that the moving frame will measure time to be longer and lengths to be shorter than an outside, stationary frame. At the speed of light things get weird. Time measured in the moving frame will be infinitely long. Lengths measured in the moving frame will be infinitely short.

However to an observer in the outside, stationary frame, the object moving at the speed of light is moving through space and time at the speed of light. The speed of light is 3*10^8 m/s after all.

 

[warpus]

I haven't been talking about time dilation though, only that all objects in the universe move through space-time at the speed of light - a part of that is through space, and a part of that is through time. The faster you move through time - the slower you move through space, and vice versa.

 

[Samson]

Gravitation attracts us to the sun and makes the earth turn onto an orbit. This strength actually makes the spacetime in which earth travels circular and not euclidian. Indeed, the earth doesn't do a circle, gravitation makes it fall in one straight direction... it is actually the spacetime in which it falls which is itself curved by the gravitation of the sun, and thus bring the earth back to its initial position (relatively to the sun), hence drawing a circle.

This is the sort of graphic that is always shown "here", but this is not following a straight line in any dimension (the red arrow is crossing the blue/white lines). Can we not reduce the 4 dimensional movement of the earth to a 3D image? Is this what you guys mean by not euclidian?

 

[Lohrenswald]

Trust me, I've had calculus

 

[Borachio]

Me too. (And not just on my teeth.) But what's the w for?

And why isn't the y axis pointing in the opposite direction?

 

[Lohrenswald]

You just don't understand my visionary innovasion, Borachio