Time vs. Spatial Dimensions

[duraultra]

Now, I've read that time can behave much like a spacial dimension. But to me, time seems more like a measurement than a dimension. Regardless of what dimension someone might call time, does it even make to sense to relate time to the spacial dimensions such as 2d and 3d? Time doesn't seem like it fits the trend to be called the 4th dimension, let alone any dimension. I know most of us agree here that the 4th dimension is a spacial dimension, at least for the sake of discussion. But is time even worthy of being called a dimension? If it is, why would it make sense to call time the nth dimension (assuming its not called the 4th dimension, which many people do)?

[moonlord]

As far as I know, Einstein considered time a dimension because it simplified calculus a lot.

[duraultra]

Hmm. Well, even if that is the case (which I don't doubt) it still seems silly to go as far to call time the 4th dimension.

[pacecil]

Time is simply the motion of some object (or a point on the object). You can't have motion without giving a distance for the motion to occur through. Therefore you have to make some reference to distance in defining time. So it makes sense to put time in the same terms as the other three spatial dimensions. My question is: Which direction do you put it?

[Nick]

There is no motion; you can only consider it a motion if you consider time a dimension, but since that is what we are arguing, you can't say that. You can't base your argument on something that is being argued. An object can be standing perfectly still (just kidding, it can't; but lets pretend here, ok?), and it wouldn't be moving.

Besides, you can only move one way through time; on a spacial axis, you can move both ways.

[duraultra]

It seems to me that time, speaking in any dimension, can't define any unique points that already exst in the given dimension. Therefore the fact that time defines when something existed in a certain point, time can't really be credited to defining a new axis. I just think that time is worthy of another title besides a dimension (at least not a numbered dimension), because time itself does not define any unique spatial points such as width, length, or heigth can.

[thigle]

anyone who considers time-like and space-like dimensions as same deserves to be...

re-programmed :%

[PWrong]

It's not actually the fourth dimension, and it's definitely not a Euclidean dimension. Spacetime isn't Euclidean, it's Minkowskian, which means it has a different version of pythagoras's theorem.

I doubt I would have passed the relativity part of my physics exam last year if it wasn't for those spacetime diagram things. And the fact that the maths is absurdly simple compared to the concepts. Multiply everything by gamma and you'll nearly always get the answer .

[duraultra]

anyone who considers time-like and space-like dimensions as same deserves to be...

re-programmed :%

See, that's the thing, I was in a debate with someone over this and they were considering them to be very close, if not the same...

[jinydu]

Relativity defines a 4D object called spacetime. Every point in spacetime represents a particular point in space at some particular time; and every point can be represented using a 4-tuple. In Special Relativity, one can convert from one inertial reference frame to another by performing linear transformations on the 4-tuples.

[thigle]

jin what do you imply by that ? that in certain context (of relativity) one can treat 3 spacelike and 1 timelike values as a quadruple, so that they are equivalent for these purposes ?

that's right perhaps.

but consider the start of the working with quadruples which was Hamilton's discovery. and he didn't consider all 4 equivalent. not as a matter of his choice, like einstein's constant, but as a matter of fact that for 4-tupled algebra to work one needs to treat one value as real and others as imaginaries. operational richness is restricted when one starts to treat them as 4 instances of the same. like if one doesn't allow square root of -1, one cannot get to solve certain equations.

know it's different context, but it just implies that there are contexts where one cannot treat the fourfold as homogenic.

as for the time specifically, depending on what Kind of time we are talking about, it seems rational we cannot treat it as spatialised on all occasions.

there's also quite a lot of debate about spatialisation of time in philosophy of science and also in philosophy in general. that time has been spatialised is not just arbitrary. and it was not fully conscious and reasonable change either.

also, what is meant by

... inertial reference frame ...

in special realtivity ?

[jinydu]

I was just trying to clarify what is meant by (perhaps too hasty comments) such as "space and time are one and the same".

also, what is meant by

... inertial reference frame ...

in special realtivity ?

An inertial reference frame is a reference frame in which (the generalized form of) Newton's Second Law holds. That is, a reference frame in which the rate of change of a system's momentum is equal to the net external force exerted on the system.

[thigle]

...a reference frame in which the rate of change of a system's momentum is equal to the net external force exerted on the system.

ok. what is that good/used for ? (perhaps i am going off topic by trying to understand SR a bit ?)

[jinydu]

In just about all of the theories (not just Special Relativity) I have learned so far, the cherished laws of physics break down if one does not use an inertial frame.

For a simple example, take classical mechanics. If we discard Newton's First Law, it becomes possible for a particle at rest (in a particular reference frame) to suddenly start moving, even if no force is exerted on it. This is not only counterintuitive; it violates both the Law of Conservation of Momentum and the Law of Conservation of Energy. However, this sort of thing can happen when, for instance, one is sitting in a vehicle and the driver suddenly starts the engine.

Of course, one can get around these problems by converting the description of events in a non-inertial reference frame to an inertial reference frame. As far as I know, a critical assumption in physics is that there exists an inertial frame of reference.

In short, one can do little physics if one is not in an inertial reference frame, or at least a reference frame whose coordinate transformation into an inertial reference frame is known.

[thigle]

thanx. :wink:

is will then also a violation of First law ?

[PWrong]

who's Will? :wink:

[thigle]

will-as-such :wink:

[PWrong]

If you mean free will, the answer is no. The violation is due to the engine, not the driver.

If we discard Newton's First Law, it becomes possible for a particle at rest (in a particular reference frame) to suddenly start moving, even if no force is exerted on it. This is not only counterintuitive; it violates both the Law of Conservation of Momentum and the Law of Conservation of Energy. However, this sort of thing can happen when, for instance, one is sitting in a vehicle and the driver suddenly starts the engine.

How does that violate conservation of momentum? The car moves forward fast, and the earth moves backwards very slow, because it has a larger mass. Energy is conserved because the energy of the fuel is converted to kinetic energy. And anyway, there is a force being exerted by the engine on the car.:?

[jinydu]

How does that violate conservation of momentum? The car moves forward fast, and the earth moves backwards very slow, because it has a larger mass. Energy is conserved because the energy of the fuel is converted to kinetic energy. And anyway, there is a force being exerted by the engine on the car.:?

Actually, the force exerted on the car comes from the ground, not the engine, but that is besides the point.

The physical answer to your question you were locked inside the car and sealed in by impenetrable walls that stopped any information from going into or out through the walls, you would be unable to detect the external force on the car. The sudden jolts you experience would seem totally inexplicable. For a simpler example, consider an observer looking outside the window of an airplane that is taking off. From the observer's frame of reference, the airplane was stationary the entire time and the earth accelerated downwards. Clearly, the laws of physics have been violated from this observer's frame of reference; how could the plane's engines possibly exert a large enough force to accelerate the entire earth by such a large amount?

The mathematical answer is (I think, I haven't studied non-inertial reference frames in detail before) that given a frame of reference where particles move in accordance with Newton's Laws, there exist transformations into other frames of reference where Newton's Laws are violated.

is will then also a violation of First law ?

If and only if it causes the total momentum of an isolated system to change in time.