Odd physics question

[Telonius]

So, my over-caffeinated brain and I are still awake at 2am. As usual, some weird questions have occurred to me. One resulted in statting up a were-squirrel. Another goes thusly...

I've always heard that time is the fourth dimension. But if time were the "fourth" dimension, would motion be possible in a two-dimensional universe? (Or for that matter, a one-dimensional universe?) Since velocity is distance over time, if time doesn't exist there wouldn't be any motion... but if motion is possible, wouldn't time exist "before" width or depth?

[factotum]

Usually, if someone refers to a universe as being two-dimensional, they're referring to the spatial dimensions. Most people don't refer to our universe as being four-dimensional, either, mainly because time doesn't work the same as the other dimensions--you can't travel freely through it, for a start.

[Grinner]

Time is a weird concept. Some people say that it's a fabrication of the human mind, made to measure the passage of events. Others say that it has a very real mechanism, usually some kind of quantum shenanigans.

Either way, I don't think it's really the fourth dimension.

By the way, have you read the book Flatland: A Romance of Many Dimensions? It has a very entertaining analogy for the fourth dimension. You can find it on Google Books.

[kurokotetsu]

From what I understand.

First "motion", what do you mean?

I guess displacement of a particle, and I'll kind of work with that. There could be displacement in a n-dimensional space without a time dimension, just as you can plot a point "moving" in a plane by drawing a curve. Technically it doesn't have speed and it occupies both places (and all in between if we think that the motionwas continuous) always and moves "instantaneously", without ever moving form it's place. And all motions happen always if there is a motion at all. Strange and non-sensesical for any kind of physical study, but I guess you could describe it that way.

Also, if you're abscribing to the "normal" concept of dimension, which is really only a coordinate. To find something in our Universe you need four factors, thre spatial demsnions to know where it is and a time dimension to know when it is. You are not in the same place that you were this morning.

In relativity (where this tetra-dimensional view is most common) it is also linked to the other dimensions through a metric, in other words, through how the change when speed and mass changes. They are kind of the same in that respect, both can be distorted in intimately related ways.

Still, time is an odd dimension. As stated, although mathematically "identical" to the other dimensions, one can't travel through it easily (or if it is even possible). Also there seems to be a preferential direction (there are no preferential up-down, right-lefts in the universe) as time seems to increase entropy (there is an arrow of time, not space). And other curious details that still boggle the mind.

Also, last but not least, the way you number dimensions is irrelevant. Time could be the "first", "second" or "third" dimension and it doesn't change a thing. It is normally referred as fourth because we think of the spatial ones first, but that doesn't change a thing in the math. That is just thing you say.

[KillianHawkeye]

Time is not really the 4th dimension. Anyone who says that is arbitrarily limiting themselves to three spatial dimensions, when mathematically there is no reason to do so.

[Razanir]

Time is a weird concept. Some people say that it's a fabrication of the human mind, made to measure the passage of events. Others say that it has a very real mechanism, usually some kind of quantum shenanigans.

And others yet describe it as a big ball of wibbly-wobbly, timey-wimey... stuff

But really, though, time is just the next dimension up. We all travel through it, just at a lame constant rate on 1 s/s (yes, time travel is dimensionless) with no means of changing it. If our world was 2-dimensional (which is implausible for other reasons), time would be the third dimension, solely because we wouldn't have a third spatial dimension

[QNLA]

So time is an additional dimension, this is because to locate something (called an event, which is the term for a space-time "point") you need to add the time at which it occurred. Its called the forth dimension because there are 3 obvious space dimensions and time is being tacked on as an extra one, though in the literature I've often seen physicists label time with 0 rather then 4 (space being 1 through to 3). Also the ways these spaces are often referred to is 3+1 dimensional for normal space time and your 2 dimensional space is 1+1 space.

Now for the more interesting stuff, normally what you think of for space is called Euclidean space which in a 2D space would be a sheet of paper, you can represent this with a bunch of different coordinates, e.g. cartesian, (x,y) or polar (r theta), then you can start getting to weirder spaces which still kind of make sense, an example of this is the surface of a sphere for 2D, where the angles of a triangle add to more then 180 degrees, and there is at least one other type of space in 2D, in general these spaces are called Riemannian manifolds.

This can get weirder when we add time in, it doesn't work like these other dimensions and instead the space required to describe it is called pseudo-Riemannian. This means time is not mathematically identical to the other dimensions due to it having a negative component in the metric, what this means is that as we increase the time change between 2 events (space-time points) then the space-time distance between these points becomes less, to the point where the square of this can be negative (there is an imaginary distance between them).

Now for the motion, motion in space time is given by a 3+1 dimensional vector (called a 4-vector) where they are changes in your coordinates with regards to changes in a parameter for the path you take, which can often be called proper time, though this only makes sense for physical objects moving (such as a space ship or car, ect.) though this doesn't work for light waves. So to be explicit 3 of these rates in the 4-vector are kind of like normal velocities while the last one is the rate at which you are going forward in time for the rest of the space with regards to how fast you feel like your going forward in time.

This last one is a bit difficult to understand if you don't understand the maths behind it and I think I'm too tired to fix this up at the moment, hopefully this answers your questions.


PS With regards to kurokotetsu's comment, time isn't always linked to space by the metric as the metric just determines how much space time distance squared is between 2 events if you change your coordinates slightly. Though the metric can "accelerate" you so that the rate you are going through time is different in different locations which is different for different masses or if you move the mass, though I haven't studied dynamics in any complex proper time dependent metrics. I also think your getting mixed up with Lorentz transforms which are different from the metric, though they are derived from the metric, and they are pretty much a change of coordinates when you change the inertial reference frame you are in.

Also time rate velocity for you and me is actually speed of light, c, so it has units of velocity, but that is equal to 1 in theorist terms.

[Traab]

I am trying to remember how I heard it described. This is probably total bs but lets see.

1st dimension is a point.
2nd is a line
3rd is a cube
4th is time, which, in this respect, is a single point in time. Its basically starting over again from the 1st dimension in that way.
5th is the start of time travel. Going back and forth in a line future to past, to future.
6th is when you start skipping timelines. Sort of like how sci fi writers describe events branching off. Being able to perceive the 6th dimension would be like being able to see all potential branching points of the timeline. So, if you chose to go left, there is another branch that goes right, and a third where you went straight. The 6th dimension lets you perceive all those choices and where they lead. Basically, this is where you are hitting the level of what we think of as god. Being able to see and know everything that did, is, will, or could happen.

Im sure thats way off, and probably something I read in a cheesy sci fi novel, but I always liked it.

[Jay R]

I am trying to remember how I heard it described. This is probably total bs but lets see.

1st dimension is a point.
2nd is a line
3rd is a cube.

First of all, a point has no dimensions. A line has one, a square has two, and a cube has three.


4th is time, which, in this respect, is a single point in time. Its basically starting over again from the 1st dimension in that way.
5th is the start of time travel. Going back and forth in a line future to past, to future.

Time begins to act somewhat like a spatial dimension in relativity equations, but the rest of this is a techno-babble way to justify time travel for science fiction.

First of all, please recognize that "dimension", like all other English words, can have more than one meaning, depending on context. It's not inherently about distance. A dimension is the minimum number of coordinates needed to specify a given point within an area or space.

A point has no dimension.

You can define a location on a line by specifying its distance from a defined "origin" point. So a line has one dimension.

On a plane or flat surface, we can define a location by its distance from a defined origin point in two directions at right angles to each other. So a plane has two dimensions. "My apartment building three miles north and one mile east from here."

There are three spatial dimensions, directions, that we can see. We can identify a specific location (point) by specifying its distance from a defined "origin" point in three different directions at right angles to each other. "The party will be at my apartment three miles north, one mile east, and three floors up from here."

But to identify a specific event, you also need to define when it occurred or will occur. This requires four dimensions. "The party will be at my apartment three miles north, one mile east, and three floors up from here, at 7:00 this Saturday."

Time is not inherently a spatial dimension. You need to understand both calculus and relativity to get to the point where you can begin to understand a relationship that treats time (actually, time x the speed of light x the square root of -1) as similar in some limited ways to a spatial dimension.

But in terms of the general definition of a dimension, a coordinate required to specify a point, time can be a dimension, yes.

[Blightedmarsh]

You know the funny thing? A lot of theoretical physicists recon that there are about 11 dimensions, 1 temporal, 3 classical Euclidean spacial dimensions as well as a further 7 spacial dimensions curled in on themselves (M-theory).

As to relativity; it is an objective fact that some form of dilation does occur at relativistic speeds. Whether that requires the existence of time in and of itself is another question all together.

[Grinner]

As to relativity; it is an objective fact that some form of dilation does occur at relativistic speeds. Whether that requires the existence of time in and of itself is another question all together.

See, that has never made a whole lot of sense to me. How did anyone ever manage to so thoroughly mangle the concepts of speed and time together?

[Jay R]

See, that has never made a whole lot of sense to me. How did anyone ever manage to so thoroughly mangle the concepts of speed and time together?

A. Speed is distance over time. You cannot have speed without the concept of time.

B. If you want to understand relativity, learn calculus and college physics. Don't try without them.

[Grinner]

A. Speed is distance over time. You cannot have speed without the concept of time.

I understand that much, but it's supposed to be a one-way street, right? i.e. I can go as fast as I want, but that just means I'll reach my destination quicker.

Really, I'm just wondering whether certain quirks of theoretical physics are faulty conclusions resulting from a flawed model. That's all.

[Lorsa]

B. If you want to understand relativity, learn calculus and college physics. Don't try without them.

Are we talking general or special relativity? One is a bit trickier than the other...

As for time, it's by far the most important dimension. Without it we relaly couldn't experience motion or events. Calling it the first or fourth is hardly important.

[RebelRogue]

B. If you want to understand relativity, learn calculus and college physics. Don't try without them.
I'd say it's perfectly possible to get a feel for elements of special relativity with no knowledge of calculus.

[Blightedmarsh]

The problem is that the human brain is built to understand the world in a limited "down to earth" and highly simplified way. The way we perceive things is full of hacks and short cuts.

The problem comes in that the universe really does not match our perceptions of it. When It come to relativity or quantum physics common sense is about as useful as an alligator and bannofi unicycle at a Sudanese airport

[warty goblin]

I'd say it's perfectly possible to get a feel for elements of special relativity with no knowledge of calculus.

I have no particular knowledge of relativity, special or otherwise. I have however been given the flavor of the results of math divorced from the underlying proofs and theorems. In my experience I've never really understood those results until I understand the math behind them. The ideas are fundamentally bound up in the equations through which they are expressed. While they can be at some level summarized without the mathematical theory, it's a poor copy at best.

It's rather like the difference between reading the Cliff's Notes for Hamlet, and seeing a good, live performance of the selfsame play.


'Cides which, I'm still not sure why anybody would go to college and not take basic calculus. It's only one of the most important and beautiful intellectual advances of the last thousand odd years. I still remember when I first grasped just what the derivative was doing. It was, in the most pure possible way, magic.

[Xuc Xac]

Really, I'm just wondering whether certain quirks of theoretical physics are faulty conclusions resulting from a flawed model. That's all.

It's not really theoretical anymore; now it's practical. Time dilation doesn't come up much on Earth because nothing is that fast or that far away for the dilation to be significant. But now that we have space travel and orbital satellites, we can see it. If we didn't understand relativity, GPS wouldn't work.

Euclidean geometry and Newtonian physics are just shorthand methods that work on a human scale. If you try to use them over really enormous distances (interplanetary) or at really tiny distances (subatomic), they don't work.

[factotum]

I understand that much, but it's supposed to be a one-way street, right? i.e. I can go as fast as I want, but that just means I'll reach my destination quicker.

Er, well, no, you CAN'T go as fast as you want--that's one of the central tenets of Relativity. The speed of light in a vacuum is an absolute upper limit that you cannot exceed, and many of the other predictions of the theory come from that--one of them being time dilation as you get closer to lightspeed.

[Ghostwheel]

To the O.P.: Time is real, and time is not like the others.

If time were an imaginary thing, there would be no real thing to have such an imagination. No real thing would have a time to exist in.

If physics, mathamatics and other sciences treat time as just another dimension, that is a by-product of the math, not a representation of the observable Universe. Sorry, Charly.

If there are "unobservable" dimensions (because they are somehow 'curled up'), how can they even be real? If there are "unobservable" parts of our Universe, how can they be refered to as 'real'?

The time is yours. Use the now to keep asking good questions. Use the now to do everything that you want to do. Use the now to love and to live. {IN THAT ORDER}

The time is now, give it a hug.

[Grinner]

Er, well, no, you CAN'T go as fast as you want--that's one of the central tenets of Relativity. The speed of light in a vacuum is an absolute upper limit that you cannot exceed, and many of the other predictions of the theory come from that--one of them being time dilation as you get closer to lightspeed.

Well, that wasn't quite what I was getting at, but thank you for bringing it up.

Whilst researching time dilation, I happened across an explanation of the "can't go faster than the speed of light" thing. It stated that as an object travels faster, it gains mass.

It follows from basic Newtonian physics that a heavier object requires more kinetic energy than a lighter object to travel at the same speed as a lighter object. Therefore, if an object gains mass, it would require more energy just to maintain its speed, nevermind acceleration. At some point, the energy requirements would be so enormous as to make the object's acceleration impractical, if not impossible.

There's just one tiny problem. Where is this additional mass magically appearing from? How does that follow conservation of matter? Is the energy invested in the object's acceleration being transmuted into matter somehow? If so, how so?

[Lorsa]

Special relativity does say that mass is just another form of energy after all. And energy in itself is really nothing more than a currency. You never observe energy, it's something we have invented for the sake of easy calculation that links various things together.

[factotum]

It follows from basic Newtonian physics that a heavier object requires more kinetic energy than a lighter object to travel at the same speed as a lighter object. Therefore, if an object gains mass, it would require more energy just to maintain its speed, nevermind acceleration.
.
.
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There's just one tiny problem. Where is this additional mass magically appearing from? How does that follow conservation of matter? Is the energy invested in the object's acceleration being transmuted into matter somehow? If so, how so?

It never requires energy to MAINTAIN speed in a vacuum--there's no drag slowing you down, as there is in a car. Your course and speed might be affected by the gravity of nearby objects, but that's a different issue and would be negligible for an object travelling at any appreciable fraction of lightspeed anyway.

As for the extra mass, you're still thinking in Newtonian terms. Einsteinian physics don't work that way--the mass of any object, from the smallest particle to the largest galaxy, is dependent on how fast it's travelling. Going faster does not increase the amount of *matter* in the object, it just makes it more massive. (It might be that the increased kinetic energy of the object accounts for the mass via the energy-mass equivalence E=mc^2, but I'm not 100% sure that's the case).

[the_druid_droid]

To clarify a bit, the speed of light being an upper limit on information transfer in all frames is typically viewed these days as a postulate of relativity, rather than something explained by the theory.

What that means is that it's something we've accepted as a foundational assumption and judge based on whether the predictions drawn from it are realistic and physically meaningful. In that regard, special relativity and the speed of light issue have been experimentally tested and confirmed amazingly well, through a number of different and independent methods. In this regard, the speed of light as a universal speed limit is more or less equivalent to Newton's Laws in the more familiar world of classical mechanics, and you can't really explain it, except to say it's a law of nature in the sense that it's the way we have observed the universe to behave in the sum total of our interactions with it.

[Sir Enigma]

To clarify a bit, the speed of light being an upper limit on information transfer in all frames is typically viewed these days as a postulate of relativity, rather than something explained by the theory.

What that means is that it's something we've accepted as a foundational assumption and judge based on whether the predictions drawn from it are realistic and physically meaningful. In that regard, special relativity and the speed of light issue have been experimentally tested and confirmed amazingly well, through a number of different and independent methods. In this regard, the speed of light as a universal speed limit is more or less equivalent to Newton's Laws in the more familiar world of classical mechanics, and you can't really explain it, except to say it's a law of nature in the sense that it's the way we have observed the universe to behave in the sum total of our interactions with it.

Actually, the universal speed of light isn't entirely pulled out of thin air, it's a result of Maxwell's Laws for electromagnetism - in the absence of any electric charge, they reduce to the electromagnetic wave equation, which predicts that an electromagnetic wave will always move at a fixed speed, with no dependence on a frame of reference. It took Einstein to realize that this was what Maxwell's equations meant, though - at first, people thought it meant there was a universal reference frame, and that was the one that the waves traveled at the speed of light with respect to.

[Asta Kask]

Time is not really the 4th dimension. Anyone who says that is arbitrarily limiting themselves to three spatial dimensions, when mathematically there is no reason to do so.

Hardly arbitrarily. There are solid empirical reasons to assume three dimensions. For instance, we can precisely specify any point in space with three coordinates.


You know the funny thing? A lot of theoretical physicists recon that there are about 11 dimensions, 1 temporal, 3 classical Euclidean spacial dimensions as well as a further 7 spacial dimensions curled in on themselves (M-theory).

No offense to you, but call me when they make testable predictions.

[the_druid_droid]

Actually, the universal speed of light isn't entirely pulled out of thin air, it's a result of Maxwell's Laws for electromagnetism - in the absence of any electric charge, they reduce to the electromagnetic wave equation, which predicts that an electromagnetic wave will always move at a fixed speed, with no dependence on a frame of reference. It took Einstein to realize that this was what Maxwell's equations meant, though - at first, people thought it meant there was a universal reference frame, and that was the one that the waves traveled at the speed of light with respect to.

True, Maxwell's equations encapsulate a lot of relativity, but the issue of inertial frames is a key one, and their equivalence certainly is a postulate of relativity. So in that sense, it's sort of semantic which one you take as which, especially considering that the equations themselves can be regarded as the foundation of electromagnetic theory - again, based on experimental observations but not really derived from anything more fundamental.

[KillianHawkeye]

Hardly arbitrarily. There are solid empirical reasons to assume three dimensions. For instance, we can precisely specify any point in space with three coordinates.

It's just like a 3-dimensional creature to say such a thing! My point was that, mathematically speaking, we can perform calculations that use any number of dimensions. Go look up "N-dimensional space."

[warty goblin]

It's just like a 3-dimensional creature to say such a thing! My point was that, mathematically speaking, we can perform calculations that use any number of dimensions. Go look up "N-dimensional space."

Just because something is mathematically true does not mean it corresponds to reality. Physics, being concerned with reality, gets to safely ignore that stuff which doesn't.

[Sir Enigma]

True, Maxwell's equations encapsulate a lot of relativity, but the issue of inertial frames is a key one, and their equivalence certainly is a postulate of relativity. So in that sense, it's sort of semantic which one you take as which, especially considering that the equations themselves can be regarded as the foundation of electromagnetic theory - again, based on experimental observations but not really derived from anything more fundamental.

The issue of inertial reference frames is a separate issue from the speed of light. Einstein's formulation used two postulates - the first was that the laws of physics are the same in all inertial reference frames, and the second was that the speed of light was a constant. The first one (the principle of relativity) was really the groundbreaking one - everyone to that point had been assuming that it was not the case. The speed of light issue follows directly from Maxwell's equations; in fact, Lorentz and Poincaré showed that the theory can be derived using the first postulate and Maxwell's equations.

Regarding experimental observation, any theory is going to have its roots in something that is experimentally observed but not derived from anything else - you can't derive anything without a starting point. You always have to take some fundamental set of laws that you simply accept as correct based on observation, and from these, you derive everything else. My point is just that the invariance of the speed of light isn't really one of these laws - it's derived from Maxwell's laws. The relativity principle, on the other hand, is - it doesn't follow directly from anything else.

[the_druid_droid]

The issue of inertial reference frames is a separate issue from the speed of light.

Yes, that's what I said.


Regarding experimental observation, any theory is going to have its roots in something that is experimentally observed but not derived from anything else - you can't derive anything without a starting point. You always have to take some fundamental set of laws that you simply accept as correct based on observation, and from these, you derive everything else.

Again, this is my point.


My point is just that the invariance of the speed of light isn't really one of these laws - it's derived from Maxwell's laws. The relativity principle, on the other hand, is - it doesn't follow directly from anything else.

Really, only the speed of electromagnetic waves being c is what comes from Maxwell's equations. There isn't anything in the equations intrinsically that says this must be an upper limit to all information transfer. That comes from the Lorentz transformations, which are only required if we insist that the speed of light be invariant in all frames.

[Randomguy]

This video should clarify things. (http://www.youtube.com/watch?v=M9sbdrPVfOQ)

There are 3 spatial dimensions and 1 time dimension. A 2-dimensional universe, like Flatland, would have 2 spatial dimensions and 1 time dimension. I suppose a universe without a time dimension would just be in constant stasis.

[Sir Enigma]

Really, only the speed of electromagnetic waves being c is what comes from Maxwell's equations. There isn't anything in the equations intrinsically that says this must be an upper limit to all information transfer. That comes from the Lorentz transformations, which are only required if we insist that the speed of light be invariant in all frames.

But the invariance of the speed of light comes directly from Maxwell's equations as well - there's absolutely no dependence on reference frame in there. According to the principle of relativity, Maxwell's equations must be valid in any inertial reference frame; and if you solve the equations for any given reference frame, you get a speed of c. This is where the invariant speed of light comes from; and as you noted, this means that the Lorentz transformations are required, and therefore the upper limit on information transfer. Calling this limit a postulate of the theory is just not the case - it is a derived result.

[factotum]

But the invariance of the speed of light comes directly from Maxwell's equations as well - there's absolutely no dependence on reference frame in there.

Isn't the whole idea of reference frames something Einstein came up with, though? It wasn't very long before he was working on Relativity that the accepted theory was that the universe was filled with a fluid-like "luminiferous ether" that light propagated through, after all!

[Sir Enigma]

Isn't the whole idea of reference frames something Einstein came up with, though? It wasn't very long before he was working on Relativity that the accepted theory was that the universe was filled with a fluid-like "luminiferous ether" that light propagated through, after all!

Yes - that's encapsulated in the first postulate, the Principle of Relativity. It's the combination of that postulate with Maxwell's equations that give the invariance of the speed of light, not the equations on their own.

[Urpriest]

Really, only the speed of electromagnetic waves being c is what comes from Maxwell's equations. There isn't anything in the equations intrinsically that says this must be an upper limit to all information transfer. That comes from the Lorentz transformations, which are only required if we insist that the speed of light be invariant in all frames.

You've got it backwards: the invariance of the speed of light is a consequence of the universe being invariant under Lorentz transformations, not the other way around. And Lorentz invariance is an inevitable consequence of the Minkowski metric, the rough sort of spacetime we live in.

To say a bit about the whole "two dimensional world" question, Flatland and the like are technically 2+1 dimensional worlds. When a physicist looks at a 2d world, they're looking at a world with one space and one time dimension. You certainly can move in that world, you just move along the one space dimension. Such a theory describes the movement of vibrations on a string, for example.

To whoever said that it's silly to call time the 4th dimension when there might be more than three space dimensions, that's why some physicists call time the 0th dimension instead...but that's kind of awkward to say, so usually that language isn't used in casual conversation.

As for the whole "what if time isn't real" thing, time could be "fake" (perhaps the universe only exists at one moment, or time is some emergent property of entropy or causality), but time would still be the "fourth dimension". It's completely different language.

As for the "I won't believe the world has 11 dimensions until a testable prediction is made", well, debatably, it's happened (http://arxiv.org/abs/1211.2231). While it can be argued that this isn't as rigid a prediction as it could be, it's at least on the level with other contemporary non-string predictions, and it has proposals for further results. So yeah, we're getting there.