Anyone frequent any science or physics forums/groups i could pose these types of questions to?
Read Flatland, reading Flatterland right now and have a question. To a cluster of 2d creatures, could the third dimension be considered time (or more specifically duration)?
If the third dimension is time, why not? Time has certain properties that space does not have, thus you can distuingish both. There nothing beyond convention that makes “time” the 4th (or in Flatland 3rd) dimension. Of course, this is mathematically speaking.
what would time itself be considered?
For one frame of consciousness of a 2D creature, it wouldn’t see anything but a group of colored pixels arranged in 1 dimension. It would see a bunch of colored pixels arranged in a line. For example, it might see a row of 10 black pixels, then a row of 20 white one, and so on, until it reached the limit of its visual field.
But where would its idea of 2D objects come from?
It wouldn’t come up with the idea of 2D objects until it were to experience a sequence of 1D frames, and systematically were to group them into specific categories as to form its idea of 2D objects. Just like we can’t think of a 3D object without imagining a sequence of 2D appearances, it wouldn’t be able to think of a 2D object without thinking of a sequence of 1D appearances.
In that sense, for a 2D creature, I would say that the sequence of 1D appearances (time) wouldn’t supply them their 3rd dimension, but would supply them their 2nd dimension!
(If this doesn’t make any sense, I can expand on a lot of these points.)
I think that’s the implication of the Flatland analogy but I don’t buy it. Time is a lot harder problem than just saying “it’s another dimension!” A “dimension”, mathematically speaking, is any independent variable. Depending on how you slice it, your phone number is a 4-dimensional object - country code, area code, prefix and suffix. Do each of these “dimensions” have their own real existence? Who knows, maybe they do!
The problem is that we are abusing language. The world, as we experience it, is a holistic blob of states of affairs that we experience in a movie-like flow and in which all the frames of the movie are clearly causally related to one another. If you think about it, space is as mysterious as anything else, we just feel pretty comfortable taking it for granted. The unique problem of time is that it is entangled with causation - we believe that the present state of affairs is the sum result or effect of all previous states of affairs. But, really, we believe that the distant past doesn’t matter to the present… it can be neglected for the sake of analysis. All that matters to understanding the present state of affairs is the immediately prior state of affairs. Then, we can apply a regressive argument to say that the state of affairs at each “moment of time” is dependent solely on its immediately prior state of affairs. But what is the meaning of “immediately prior” in a continuous variable?? What is the number immediately prior to pi, for example?
Clayton -
No, it isn’t.
Isn’t what we call “time” just the sequence of frames?
If we are supposing that the 2D creature already has the idea of 2D objects, we are supposing that it already experiences sequences of 1D frames. And, if we need the sequence of 1D frames to build its idea of 2D objects, how could we have anything left over after we build its idea of 2D objects which would add a “3rd dimension” that we could call “time”?
What frames?
Clayton -
Let me state it another way.
For one moment of our consciousness, we don’t see anything but a bunch of colored pixels arranged in 2 dimensions.
So, for one moment of the consciousness of a 2D creature, it wouldn’t see anything but a bunch of colored pixels arranged in 1 dimension.
Just like we need to experience a sequence of 2D “pictures” to experience a 3D object, they would need to experience a sequence of 1D “pictures” to experience a 2D object.
To a cluster of 2d creatures, could the third dimension be considered time (or more specifically duration)?
Edit: I think I misunderstood your question. Yes, 2D creatures constrained to a 2D membrane in our universe could experience, measure, and think about time as their third dimension.
At first I thought you were asking whether a third spatial dimension could be interpreted by them as a kind of time. I think that’s not possible.
For that dimension to be called “time”, these creatures must have some kind of device (a “clock”) for measuring it. Simply imagining an extra dimension is entirely different from being able to measure it.
Also, to be similar to our concept of “time”, I think there must be some kind of statistical macroscopic arrow of time. For us, it is our proximity to a boundary condition (the Big Bang) that gives us an arrow of time. For the 2D creatures, there doesn’t seem to be any difference between opposite directions along a third spatial dimension.
Finally, time is not simply another space dimension but, due to the hyperbolic geometry of the universe, is radically different from space dimensions. In special relativity, the metric tensor n = ((-1 0 0 0) (0 1 0 0) (0 0 1 0) (0 0 0 1)) meaning the interval (squared length) of a 4-vector is not vv=xx+yy+zz+tt, but it is vv = vnv = xx+yy+zz-tt. (I’m not sure how to write it in text, but there is a distinction made between contravariant and covariant vectors). This is why we have a 4D light-cone and not a “light hypersphere” Even if the 2d creatures somehow imagined a third space dimension, it wouldn’t necessarily be anything like our “time”.
For time, where does our idea of the direction come from?
It comes from the fact that there is a regularity in the life-cycle of things growing and then detiorating.
(I can expand on that if it wasn’t clear enough.)
But why couldn’t the 2D objects in a 2D world not be subject to the same kind of thing?
why couldn’t the 2D objects in a 2D world not be subject to the same kind of thing?
I see no reason why they couldn’t. As my edit explained, I misunderstood the question. I was pointing out that it doesn’t make a lot of sense to call additional, inaccessible spatial dimensions “time”.
I think it’s physically possible - but not technologically yet - to create a 2D membrane on which are constrained 2D sentient beings who can perceive and contemplate time. Virtual reality would probably be an easier way to do this.
If there is a regularity in the sequence of 1D appearances, it would be possible to measure it.
(And, if there weren’t a regularity, they wouldn’t be able to come up with the idea of 2D objects anyway.)
Ah, I see.
What exactly would it mean for “time” to be their “3rd dimension”?
I.Ryan brings up a fascinating and interesting point about the thermodynamical properties of time. Specifically, entropy and the laws of thermodynamics. Either way, time seems to be a property of thermodynamics.
The equations of general relativity and Newtonian physics are symmetrical temporal. It’s only when we introduce thermodynamics into the physical equations that we see the arrow of time.
What exactly would it mean for “time” to be their “3rd dimension”?
When asked what directions there are, they will reply west and east, north and south, and before and after.
Unless they say before and after, west and east, north and south. Then time will be their 1st dimension 
“It’s only when we introduce thermodynamics into the physical equations that we see the arrow of time.”
True for most purposes. But even at a microscopic level, in some exotic cases, the universe shows a bias between the two directions in time. From http://en.wikipedia.org/wiki/CP_violation “This discovery showed that weak interactions violate not only the charge-conjugation symmetry C between particles and antiparticles and the P or parity, but also their combination… a violation of the CP symmetry is equivalent to a violation of the T symmetry… The kind of CP violation discovered in 1964 was linked to the fact that neutral kaons can transform into their antiparticles (in which each quark is replaced with the other’s antiquark) and vice versa, but such transformation does not occur with exactly the same probability in both directions”
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Hm, interesting.
But would it be useful to reserve the same word - “dimension” - for all of those 3 parameters?
Just wondering if you have any thoughts on that.
Introduction of quantum mechanics into the dynamics of time adds a boat full of more considerations that are far too bizarre. The Dirac equation still blows my mind. There is so much to say on the matter.
I’ve had very little exposure to quantum chromodynamics but the Lagragian formalism it still the same as in non-relavistic quantum mechanics and quantum field theory. Quantum chromodynamics digs way deep into the cosmos, and as you go deeper things become more bizarre, including C-P violations. However, just like every quantum theory, as you begin to move to larger spatial scales, fluctuations in space(fields in this case bc of quantum topology)-time begins to cancel out and emerge into smooth geometries and basic Newtonian physics. Well for the most part.
I will read more on C-P violations.
Either way, time experienced on cosmological and quantum scales introduce new views of time that the human mind have difficulty in understanding.
But would it be useful to reserve the same word - “dimension” - for all of those 3 parameters?
Yes, only because it’s easiest to do special and general relativity (SR/GR) with bunches of numbers called vectors (for us, 4-vectors). Even though time is fundamentally different as shown by the metric tensor of Minkowski space, it’s still convenient to lump it together with the spatial coordinates and do math on them. (Edit: FYI vectors are more than just bunches of numbers because they obey certain transformation rules. It’s not meaningful to count a quantity of apples and a quantity of oranges and just form a vector out of it.)
You can also choose different coordinate systems, including crazy ones where time and space are mixed together. (The simplest such mixing is akin to adopting the point of view of a moving observer). If done cleverly this has the benefit of allowing some of the coordinates to be neglected while solving a particular problem.
Another good reason for calling time a “dimension”, is that time is conceptually similar to spatial directions in that it supports the idea of orthogonality. I can imagine myself “moving” back and forth in time while not moving left or right, just like I can imagine myself moving up and down while not moving left or right.