secretkeeper12 said:
Some say time makes up a fourth dimension, but every thing caused by time is really a change in three dimensions.
No, time actually is a fourth dimension. We exist in four-dimensional spacetime. The postulates of relativity (which are based on empirical fact, most famously by the Michelson-Morley experiment) cannot be satisfied without adding a fourth dimension. These are:
1.) The speed of light is observed to be the same by all observers in all inertial reference frames
2.) The laws of physics are the same in all inertial reference frames
An alternative formulation of the second postulate is "There is no privileged reference frame." What this means is that the uniform motion (motion with constant velocity) of one's own reference frame can be detected only by observing another reference frame, and that when this relative motion is observed it is not physically meaningful to ask which frame is moving and which is stationary.
An inertial reference frame is a member of the class of coordinate systems none of which is accelerated with respect to any other coordinate system in that class. That is to say that in an inertial reference frame, Newton's laws are valid, and in observer in one reference frame will always observe Newton's laws to be valid in any other reference frame.
There are many approaches to the mathematical derivations, which vary in their formality and accessibility, but the most famous and easiest to understand is Einstein's own thought experiment involving a laser reflected by a mirror in a moving train car.
Fix a reference frame to the side of the train tracks, call it S. Fix another reference frame to a point inside the train car, call it S' (read as "S-prime"). A device on the center of the floor of the train car emits a pulse of light. In S', the light rays reach the front and back of the train at the same time. The two events, a light ray reaching the front and a light ray reaching the back, are said to be simultaneous. The events are separated only in space.
However, to an observer on the side of the tracks in S, something different happens. The rays of light must have the same speed in both S and S'. But in S, after the light flashes but before the rays of light are emitted, the front and back of the train car have moved. The observer in S sees that the back of the car catches up the rays and the front is moving away from them, so the two events in this frame are no longer simultaneous. The events are now separated in space and in time.
This leads us to a bit of a paradox. What, exactly, happened? Did the rays of light hit both walls at the same time, or did the rays hit the back first, and then the front? If we consider time to be separate from space, then only one of these can be true. This violates the second postulate, as it would imply that a physical process happened differently in two different frames, and therefore different physical laws were in effect.
To resolve this paradox, we abandon the idea that physics happens in three dimensional Euclidean space with time as just a parameter. When we say that an n-dimensional space is Euclidean, what we mean is that the distance between two points is given by the Euclidean metric, the length of the hypotenuse of the right triangle connecting the origin to the point. If the point is given by the ordered n-tuple (x[sub]1[/sub], x[sub]2[/sub], x[sub]3[/sub], ..., x[sub]n[/sub]) then the distance from the origin is (x[sub]1[/sub][sup]2[/sup] + x[sub]2[/sub][sup]2[/sup] + ... + x[sub]n[/sub][sup]2[/sup])[sup]1/2[/sup]. Instead of Euclidean space, we now say that physics happens in four-dimensional Minkowski space.
Minkowski space is very different from Euclidean space. In Euclidean space, the elements of the space are
points and they are connected by straight line segments. In Minkowski space, the elements of the space are called
events and they are connected by what is called the spacetime interval. If two events are separated by dt units of time and dr units of distance, then we say that the spacetime interval is given by ds = (c[sup]2[/sup]dt[sup]2[/sup] - dr[sup]2[/sup])[sup]1/2[/sup] where c is the speed of light. The reason we do this is that the spacetime interval between two events is invariant, meaning that it has the same value in every reference frame. If we two events are separated by dr and dt in S and by dr' and dt' in S', then even if dr is not equal to dr' and dt is not equal to dt', we still must have ds' = ds. By describing physical processes in terms of spacetime interval we are now able to satisfy the second postulate.
tl;dr It is not possible to disentangle time and space, anything that happens in space also happens in time.
You will be more accurate to say time is the derivative of space rather than an addition to it.
Nope. A derivative is an operation on a function that is defined on a smooth manifold, it is not a property of the manifold itself. Space itself is not a function of anything, you cannot take its derivative with respect to anything.
And in any case, to say that time is the derivative of space would mean that time is tangent to space at each point in space, which wouldn't be physically meaningful.
Time is change in space, and the 2nd law of thermodynamics states every change increases overall entropy of our universe. We define more entropy as a state with more possible ways of creating it. In order to go back in time, we would need to recreate a condition of less entropy. We cannot create a state with less possible ways of existing, which is what scientists mean by saying we cannot decrease entropy. So, we cannot recreate past conditions with less ways of existing, and that means we cannot time travel.
No. The reason that we can't go backwards in time has nothing to do with entropy or thermodynamics.
Let's go back to our discussion of Minkowski spaces and intervals. Given any two events separated by ds in a reference frame S, it is
always possible to find a reference frame S' in which those two events are simultaneous, that is, separated only in space. To be in this reference frame, the observer must not have any speed relative to this frame, the observer is then said to be at rest in this frame and for this reason we call this the rest frame.
One of the consequences of relativity of simultaneity is that while the time that separates two events A and B depends on the reference frame, their order does not. If A happens before B in any one reference frame, then A happens before B in
every frame, except for the rest frame in which A and B are simultaneous. The only way to observe the order of events as being reversed is to be travelling faster than the speed of light relative to the rest frame of the two events. This is of course not possible.
Let's say I wanted to go back in time to see the signing of the Declaration of Independence. This happened in 1776. So let's say I were to somehow build a time machine. What would happen is I would turn the device on in 2018, step through, and then arrive in 1776. This is a violation of relativity of simultaneity. 1776 happened before 2018, so this must be true in every reference frame. But in the reference frame attached to me, my departure (which happened in 2018) would have to happen before the signing of the Declaration of Independence (in 1776).
Entropy doesn't have anything to do with it. All that it means for the entropy of a system to increase is that it's entered into a state in which work needs to be done on the system in order to return it to its previous state.
Does that all make sense?
Er, no. Sorry to say. You've got a lot of studying ahead of you want to really be able to understand this.
