What really is time?

Originally posted by KazetNagorra
However, this does not mean that time is "just another distance", since there are differences with respect to time in the mathematical formulation of special relativity (I won't go into the details).

Can you give some examples?

Originally posted by KazetNagorra
Well, in the spacetime formulation you are on a very different place in spacetime after you make that circle.

Yes, in four dimensionals. But the difference between the space dimensions and the time dimension is that you can move freely in space, but only in one direction in time. In four dimensional timespace you can never return to the same point again.

...unless the time dimension is circular. Does anyone believe that?
...or if there are more than one time dimension, and these time dimensions are interchangeable. Does anyone believe this?

Interesting reading here:
http://en.wikipedia.org/wiki/Minkowski_space

Originally posted by KazetNagorra
Entropy is a somewhat "mystical" property, because it both takes up an important place in physics and is hard to measure (there are no entropy-meters). In common language it's usually referred to as a measure of disorder (i.e. more entropy = more disorder), but that's a bit inaccurate. On a microscopic level, entropy is proportional to the logarithm of ...[text shortened]... sible states (usually this figure is much higher of course), then the entropy is k * ln 10.

Entropy refers to how many possible arrangements of matter would have the properties of the matter in question. Roll two six sided dice; the total "7" would have more entropy than the total "2" because there are 6/36 ways to make 7 and 1/36 ways to make 2. If you took a million pairs of dice and put every die so the "1" was facing up (ordered situation) - and began to vibrate the surface the dice are resting on, you would end up in the long run with more 7's than 1's. Why? Entropy. Why? Because there are more ways to make 7 than 1. That's all entropy is...

http://athousandyoung.blogspot.com/2009/11/energy-and-space-or-why-are-fish.html

Originally posted by AThousandYoung
Entropy refers to how many possible arrangements of matter would have the properties of the matter in question. Roll two six sided dice; the total "7" would have more entropy than the total "2" because there are 6/36 ways to make 7 and 1/36 ways to make 2. If you took a million pairs of dice and put every die so the "1" was facing up (ordered situatio ...[text shortened]... ...

http://athousandyoung.blogspot.com/2009/11/energy-and-space-or-why-are-fish.html

Interesting and nicely explained for us couch observers. But then why does stuff exist at all. I mean ordered stuff, life and complex molecules for example?

Originally posted by Palynka
Can you give some examples?

Okay. In special relativity there is something called a Lorentz transformation, which is used to transform the view of one observer to the other. Some variables are constant when you make such a transformation. One such variable is the difference between the seperation x² + y² + z² - c²t². The minus sign before the time affects the geometry of spacetime.

Originally posted by AThousandYoung
Entropy refers to how many possible arrangements of matter would have the properties of the matter in question. Roll two six sided dice; the total "7" would have more entropy than the total "2" because there are 6/36 ways to make 7 and 1/36 ways to make 2. If you took a million pairs of dice and put every die so the "1" was facing up (ordered situatio ...[text shortened]... ...

http://athousandyoung.blogspot.com/2009/11/energy-and-space-or-why-are-fish.html

Yes, that's a nice layman's version of what I said.

Originally posted by divegeester
Interesting and nicely explained for us couch observers. But then why does stuff exist at all. I mean ordered stuff, life and complex molecules for example?

These ordered things are all created in processes in which the total entropy in the universe either remains constant or increases. Simply speaking, you can create order locally by creating at least as much disorder somewhere else.

Originally posted by FabianFnas
Yes, in four dimensionals. But the difference between the space dimensions and the time dimension is that you can move freely in space, but only in one direction in time. In four dimensional timespace you can never return to the same point again.

...unless the time dimension is circular. Does anyone believe that?
...or if there are more than one time dimension, and these time dimensions are interchangeable. Does anyone believe this?

Well, there is the restriction that I pointed out earlier; that is events that are causally related must have a spacelike seperation. A person moving around involves a causal relationship, so that implies you cannot be at two places at the same time, but you can be at the same place at different times.

Originally posted by KazetNagorra
Okay. In special relativity there is something called a Lorentz transformation, which is used to transform the view of one observer to the other. Some variables are constant when you make such a transformation. One such variable is the difference between the seperation x² + y² + z² - c²t². The minus sign before the time affects the geometry of spacetime.

Bear with me, I think I'm getting close to understanding this.

Your example was somewhere along the lines of what I was expecting after I read about Minkowski spaces, but it seems that Lorenz Transformations are just rotations in a Minkowski space.

If this is correct, then the different treatment of time in LT comes naturally from the nature of Minkowski spaces (due to its signature). So the question is why are these (non-Euclidean) spaces a good representation for space-time as opposed to an 4D Euclidean one?

I think this is key for me finally understanding why time is fundamentally different from space.

Originally posted by AThousandYoung
I define absolute time as the amount of entropy the universe has increased as a whole. The local time is how much entropy has increased locally. All the local times in the universe make the absolute time. When an object moves very quickly, it's modified contribution to the total entropy is accounted for with relativistic equations.

I'm half maki ...[text shortened]... time is less at high velocities, and thus there is less aging, less thinking, less everything.

There is no such thing as "absolute" time. Generally, you cannot synchronize clocks based on an "absolute time" and time is relative to the observer.

Originally posted by FabianFnas
Yes, in four dimensionals. But the difference between the space dimensions and the time dimension is that you can move freely in space, but only in one direction in time. In four dimensional timespace you can never return to the same point again.

...unless the time dimension is circular. Does anyone believe that?
...or if there are more than one time dimension, and these time dimensions are interchangeable. Does anyone believe this?

I don't believe in a circular time dimension, but it seems researchers never consider the possibility of more than one time dimension. All cosmological models out there (at least the most popular ones) assign only one dimension to time.

Originally posted by KazetNagorra
Well, there is the restriction that I pointed out earlier; that is events that are causally related must have a spacelike seperation. A person moving around involves a causal relationship, so that implies you cannot be at two places at the same time, but you can be at the same place at different times.

What does same place really means?

I'm sitting here quite still, but the earth rotate and is is in orbit around the sun, the sun moves around the centre of the galaxy, the galaxy moves in the local galaxy cluster and the local in the super cluster, and everything around eachother. But relative to what? Is there a still point in universe that we can all relate to?
(The center of universe is not a valid answer, neither is the location of BigBang.)

Is there a same place at all?

Originally posted by Palynka
Bear with me, I think I'm getting close to understanding this.

Your example was somewhere along the lines of what I was expecting after I read about Minkowski spaces, but it seems that Lorenz Transformations are just rotations in a Minkowski space.

If this is correct, then the different treatment of time in LT comes naturally from the nature of Minkow ...[text shortened]... think this is key for me finally understanding why time is fundamentally different from space.

now i'm really interested to read about minkowski spaces and non-euclidean geometry, but sadly don't have enough "time" at the moment!

however, i will throw my hat in the ring once more...

thought experiment: consider a universe in which motion does not exist. not at the microscopic nor macroscopic level. change ceases to be. i posit that time does not exist in this universe either, and is an irrelevant concept. but then isn't time (and change itself) irrevocably linked to motion? isn't the so-called "4th dimension" in fact entirely dependent upon the other three?

but i think, (though it may often be useful to think of it as a 4th dimension for practical purposes, or even for elegant quantification of change) that time is subordinate to our "usual three" dimensions; that time is merely a dependent function of measurable physical measurable variables.

then why do we need a physical construction for time to describe a universe that is aptly described by changes in position? for ease of use and relating global and local change to others, i understand it... but i wholeheartedly don't see the need to fundamentally separate it from the ideas of mass, space, and change in relative position of bodies within that space. i think the conception of absolute time creates more difficult and more abstract (and perhaps even more inelegant) consequences in our understanding of our universe, without reconciling any particular flaws in the "more simple" understanding of three dimensions.

occam's razor isn't even close to always right... but it has quite an edge. creates in me the same qualms i have about string theory and religion! 🙂

...all that said, from what i can read between the lines of the posts about minkowski spaces, i may change my tune entirely if there is evidence for why time must be fundamentally separated from motion!

Originally posted by FabianFnas
What does same place really means?

I'm sitting here quite still, but the earth rotate and is is in orbit around the sun, the sun moves around the centre of the galaxy, the galaxy moves in the local galaxy cluster and the local in the super cluster, and everything around eachother. But relative to what? Is there a still point in universe that we can all ...[text shortened]... se is not a valid answer, neither is the location of BigBang.)

Is there a same place at all?

In the context of special relativity, "same place" means the same x, y, z coordinates in some inertial frame of reference.