Naked Science Forum
General Science => General Science => Topic started by: jnorris235 on 15/03/2009 21:35:51
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I'm just having thoughts that are probably daft. But we talk of 3, then 4 dimensions and now of 7 and 11 etc. And yet I remember at school that we had polar coordinates instead of two of them. And I also wonder if it is possibly only in our small region of space that everything is at right angles (space being curved an' all). Anything larger than a football field and right angled triangle don't add up to 180 degrees for instance.
So my thought is that dimensions do not exist in a rigid and axiomatic mathematical way and are merely a construct.
Shall I go away now?
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Hello, and welcome to TNS.
Dimensions. Oooh, tricky. Well, we know that at least 3 exist beause we can move about in them. General Relativity says there are 4 by adding time to the 3 spatial dimensions we are famiiar with. String theory says 10, and Supergravity has 11.
But what are they? In another thread I gave 1 definition which is that a dimension is a value that enables us to fix an event in spacetime (a more mathematically based definition of a space is "the minimum number of coordinates needed to specify every point within it"). But that is just a mathematical construct, it doesn't really say what dimensions are.
I don't know the answer. When you consider that the compactified dimensions of some theories are so ridiculously small that nothing can exist inside them except gravity, it makes a definition even harder.
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Dimensions; Highth, width, breadth and time; The four dimensions of our easily recognizable universe.
This brings up a question I've had for quite some time now. Physicists will tell you that in space there is no such thing as right or left, only the dimension we call width. If that is so, how do particles know the direction of spin they possess. While traversing thru space, some will spin to the left while others will spin to the right. Something tells me they know right from left.
..................Ethos
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Something tells me they know right from left
Weak force gauge bosons certainly do as only left-handed ones work.
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Something tells me they know right from left
Weak force gauge bosons certainly do as only left-handed ones work.
Consider the thought experiment this fact raises;
If particles know right from left, starting from a point we can call a place of origin, are there more than three spacial dimensions? Remember the number line in math? Every thing to the right was positive and everything to the left was negative. And because the particle knows right from left, it follows that it also knows forward from backward. And if it knows right, left, forward and backward, will it also know up from down. Consider the spiral course it travels, everyone of these values must be considered for the spiral course to form. Are there really six spacial dimensions?
.....................Ethos
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No, that doesn't follow. Particles are left or right spin, not up or down spin.
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Are dimensions not a man made means to explain some of the elements of space and time which he cannot understand?
On Earth we can comprehend and explain the spacial dimensions of forward, backward, up, down, left, right and all the variants between. But in space, there is no up or down, neither is there a left and right nor a backward and forward.
Left is only left when viewed from one plane, from the opposite plane, left is right. The hands of a clock move in a 'clockwise' direction, but we only ever observe that clock from our plane, the face. Observe that clock from the opposite plane and the hands will appear to be moving in an 'anticlockwise' direction.
Then surely there can be no backward. Whichever direction you travel in, must be forward. Yes we can retrace our steps, we can even walk backwards, but the end result is that we are somewhere new or revisited, therefore, we have travelled forward.
Our perception of time is one which allows us to put events into an order of happening. A chronological diary and should be considered only as EARTH/MAN TIME, since we place occurrences in an order relative to dates fixed by man.
To my way of thinking, in the universe there are only the dimensions of MASS, which we can translate as weight and density; VOLUME, we can translate as the amount of space occupied by a MASS; NON-MASS VOLUME which we can translate as the empty space between two or more MASSES and TIME. This dimension of TIME is one which we cannot comprehend since it cannot be measured from any particular point, not even the big bang. It is a dimension without confines; it has no start point and no end point. Similarly, the dimension of NON-MASS VOLUME is only comprehendible in respect of its space between MASSES, but its further dimension beyond where MASSES occur is again incomprehensible to man, since like TIME, it has no confines. There is no end to space.
We use words such as 'forever', 'always', 'endless' and 'infinity', we even define the meaning of such words in our dictionaries, yet they describe a notion which is beyond our comprehension.
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Yes, dimensions really do exist. Dimensions though, are not material in that they do not seem to be made of anything.
Dimensions are not required for something to exist, if that thing is to have no size or it is not to change, but if any change or size is to be permitted then at least one dimension is needed to allow the change from the original to the new state or to accommodate the size.
The simplest solutions only require a single dimension, this being either a temporal dimension for change, or a spatial dimension for size.
Change can be illustrated by defining a number x. x, regardless of it's numerical value has zero size in space, so spatial dimensions are not required, but if we perform an action on x, for example, by adding two to it, we need the 'before' state to exist somewhere different to the 'after' state. Without being able to locate the 'after' state somewhere different to the 'before' state, both states would have to be in the same place with the result that x would simultaneously be both x and x+2.
With size, instead of defining a single value we are really defining a range of values, which encompasses every value within the range. In this case then, instead of needing different places to locate the different 'before' and 'after' states of a single value so that they do not exist simultaneously, we need different places to locate many different values that do exist simultaneously.
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Dimensions are not required for something to exist, if that thing is to have no size or it is not to change, but if any change or size is to be permitted then at least one dimension is needed to allow the change from the original to the new state or to accommodate the size.
I have a real problem with zero-size "things". How can something with no size exist other than as a mathematical concept?
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Things don't need to be zero-sized in all dimensions for these effects to occur. For example, how many cubic feet does a 1x1 foot area occupy? What size are you in the fifth dimension?
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LeeE - I understand that. I didn't realise that's what you meant. I thought you meant totally zero-size.
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Well, totally zero-sized seems to be possible, in theory, or at least in any theory that can handle n-dimensions where n >= 0.
I'll agree that it's difficult to imagine how something just consisting of an abstract value could actually exist as 'something' but any analysis of something can only end with such an abstract. Right at the bottom of any analysis that doesn't infinitely regress you end up with something that can only be expressed in terms of itself, at which point it becomes abstract. For example, what is energy made out of?
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Yes, but if n=0 then there is nowhere for it to exist except as an abstract concept.
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I love this question:)
I've always wondered what a dimension really is, we have the ability to 'wander' freely as 'living matter'. Only controlled by where our curiosity may take us, and so differentiating us from 'dead matter' like a celestial object. How come? And 'distance' btw, is no longer a thing set in stone. In our Einsteinian universe it seems more of a relation to density, motion, velocity and acceleration.
So what is a definition of 'dimension'. We call those three we see here on our Earth height, width and length, what they really seem to say though is that we seem to be able to move in a 'sphere' like direction, if you see yourself as always being in the middle of that sphere freely choosing a direction. And that movement is also a function of the 'time' we do it in. But then we have the fifth, up to, (?) dimensions. None of them can be observed by us other than mathematically, but there they can 'live' and flourish. Length width and height seems to be interchangeable as descriptions when you think of it, they only help us define where in that larger 'sphere' of spacetime we are/move.
This is very strange to me, let's say that you send away a really fast spaceship, it accelerates up to a velocity near to 'c' in a short 'time'. Now, you are observing it from the Hubble telescope, or from its 'after runner' :). This marvelous telescope allows you to follow it at all times to some star 50 lightyears away and back. We know that this ship, from its own frame of reference, will observe 'time' as running 'normally' internally, all biological 'clocks' should work as on Earth f ex. We also know that, seen from our perspective, the 'time' on that ship will 'slow down', and if being on that ship, we will see how the universe's 'time' seems to 'speed up'. That is the 'twin paradox' as I understands it. So 'time' will work to a different standard here, depending on where you are. Will this mean that this ship when observed from our telescope will slow down in space, same as its 'time dimension' will?
As far as I understands it, it won't. When observing we will see it accelerate and go on just as we expected, very fast and soon near that 'c'. It will behave 'normally' motion-wise and we will be able to follow it to 'there' and back to us, without seeing it 'freeze' in space as its 'time dimension' have slowed down relative us. Do you see how I think here?
I'm not discussing anything more than 'time' here btw :) There are some other phenomena coupled to it, but the important thing is that 'time' here seems to be more than just 'my time' and 'your time'. There is also the relation between those two 'time views' that allows us to observe that ship as behaving 'normally' motion wise. And that to me is very strange. It's like we all have our very own 'time dimension' depending on velocity, acceleration, motion and density and then we have the ability to observe those 'time dimensions' as a 'whole'. That is our spacetime.
Let us say that, as this ship actually will observe a real 'time' differentiation (twin paradox) when it comes back and join our frame of reference, we also would have expected it to 'slow down' when we observed it traveling before. Slowing down as seen from our perspective as the 'time' it will experience will be 'slowed down' as compared to us observing it. But that should give it a longer time of travel from our point of view, right. And then the space faring twin should become older than us. But we know that he is younger, according to relativity? So then, do we have a different way of explaining it? What would happen if we saw that ship to just 'disappear'(?) and then be back, all in a instant. Nah, that won't explain the age difference either, will it :) So what we actually see is the ship taking off, acting as we expect it while we follow it, but when coming back being 'younger' than us. And at no time have we lost 'contact' with that ship.
And it's not only 'time' that behaves as there was a 'hidden standard'. There is also 'distances' that will become 'shorter' when traveling, as seen from us observing, when we consider the real 'time difference' shown here as we compare the twins journey in time.
So what is a 'dimension'?
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we have the ability to 'wander' freely as 'living matter'. Only controlled by where our curiosity may take us
Not in North Korea. [:P]
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Well, can't argue against that DB:)
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Of course dimensions exist!
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Now you're being silly again. Go to your room!
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Yes, this room:------------------------------------------------ ↓
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Miss Scarlet did it in BR.2 with the candlestick!
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I'll not ask what Miss Scarlet did in BR2 with a candlestick. I fear for my sobriety should I get an answer.
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I'll not ask what Miss Scarlet did in BR2 with a candlestick. I fear for my sobriety should I get an answer.
She banged in a nail. Couldn't find a hammer.
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(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fbestsmileys.com%2Fanxious%2F2.gif&hash=1ed59877cccda206c2ef302797047fa2)You had me worried there when I read 'She banged...' I wasn't sure if I should read any further...
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So my thought is that dimensions do not exist in a rigid and axiomatic mathematical way and are merely a construct.
A thing is the concept of dimension in mathematics, another is its application in physics. The two things are always different.
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Yes, but if n=0 then there is nowhere for it to exist except as an abstract concept.
Matter, as we know it, is three-dimensional but this on it's own doesn't seem to directly account for it's possession of rest-mass; a spatial size of n cubic metres doesn't equate to a particular quantity of kilograms. We can use Density, of course, to relate the two, but density is just the measured quantity of rest-mass in a volume, not the reason that the rest-mass exists and has a non-zero size. Rest-mass then, appears to need three spatial dimensions within which to exist but whatever it is, that is manifesting/expressing itself as rest-mass, doesn't appear to have a particular spatial size.
If we look at light though, we've got something that certainly seems to exist, and once again, it seems to need three dimensions to exist within, but unlike matter it has no rest-mass; whatever it is that manifests/expresses itself as rest-mass in matter seems to be absent in light, so its size in light is zero.
I agree that point objects would only seem to be able to exist as an abstract, but any non-infinitely regressive analysis of the universe will lead to such abstracts. If we now go back to thinking about light again, it could be described as semi-abstract; it doesn't exist as matter, but it definitely exists as something.
With a zero-sized point-object, it seems to me that we could assign a value to it, representing the size of a particular quality, but if that quality isn't spatial size then the quantity of whatever quality it is will just occupy a geometric point that exists at a particular spatial (or temporal) coordinate. Only if the value (quantity) of its quality is zero would it not exist at all.
The ultimate abstract would be where all different qualities were reconciled at this level, in which case all you'd need would be the value because there would only be one possible quality.
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Dimensions don't have to be 'xyz'. You can describe a position using polar coordinates just the same.
The point of having dimensions is that you can specify the position (and other conditions) of an object using a number of quantities which can be independent of each other. So you can change your x dimension without altering your y dimension by moving along a horizontal line on your ordinary graph paper. The x and y dimensions are independent (the posh word is orthogonal). If you used polar coordinates you still have independent dimensions so, for example, you can keep the radius constant and vary the angle and the points will lie on a circle. Using r and theta, you can specify any position on a flat sheet of paper (a plane). Radius and two (orthogonal) angles can specify any point in simple space.There are other sets of coordinates you can use but you still need three dimensions.
When you calculate hard things like the Universe and all that, you can arrive at equations which involve more than just x, y and z. The other dimension which you get from String Theory, for instance, have to be there in order to explain, in one fell swoop, how objects will interact.
So, on a simple level, xyz are enough to describe the position of objects. If you want to describe how they move about, you need to introduce time - a fourth dimension. If you need to describe the effects of electromagnetic fields and gravity all together, you can (they claim) do it using extra dimensions which, of course, we can't SEE. What they say is that moving along, say, the x dimension, we are, in fact moving through lots more dimensions. Although another object may be distant in the x dimension, its relation to us in its other dimensions may affect the way we move in the x dimension - i.e the other dimensions somehow explain how we experience the force of gravity from the Sun. String Theory replaces the theory which describes things in terms of Fields and masses. (Remember - Fields are not necessarily any more 'there' than anything else; we just use them as a model to predict and explain what goes on)
And, of course, when we talk of something with zero length, it may not have zero values for its other dimensions.
I am not too convinced that the two uses of 'dimension' are really that distinct from each other - except that Maths is a limited set of ideas (axioms). So, perhaps Mathematical Dimensions are just a sub set of Dimensions.
That's never stopped us from using all the rest of Maths (subset) to deal with the physical (complete set) World, though.
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Very nice description SC. It is this Idea that string theory seems to build on, that those 'dimensions' xyz are independent from each other. That makes it mathematically reasonable to see a 'one dimensional' string having qualities as 'vibration' aka 'mass' and 'tension. But that is if spacetimes dimensions really are independent isn't it?
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Those quantities could be functions of more than one dimension, of course, so it might be expected they could 'talk to each other'.
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If a particle has momentum in an extra dimension but none in the 3 spatial dimensions we are used to, then that momentum will look to us like rest mass. Maybe particles that do have rest mass are free to travel in an extra dimension whereas photons aren't. Why that should be, I don't know. Maybe the answer lies buried somewhere in string theory.
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That's an interesting idea Dr. B.
Instead of photons not being able to move in the 'momentum' dimension, they simply may not have any presence in it.
If it's not possible for something to exist in a limited set of dimensions, it must exist in every possible dimension, which brings us back to having to deal with an infinite number of dimensions again. However, by allowing something to exist in just a limited set of dimensions, out of a possible infinite set, we don't have to worry about infinite dimensions any more; only the ones that are being occupied are relevant.
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That's an interesting idea Dr. B.
Instead of photons not being able to move in the 'momentum' dimension, they simply may not have any presence in it.
If it's not possible for something to exist in a limited set of dimensions, it must exist in every possible dimension, which brings us back to having to deal with an infinite number of dimensions again. However, by allowing something to exist in just a limited set of dimensions, out of a possible infinite set, we don't have to worry about infinite dimensions any more; only the ones that are being occupied are relevant.
Precisely. Less infinities=good news
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Ethos discussed if the universe differed between left and right before. I don't think the universe uses our definitions at all. I'm not even sure that our definitions of a left or right handed spin have anything to do with what's really 'there'. We put on descriptions of 'stuff' like colourforce etc, but we can't see what we describe so it is quantitatively different than our macroscopic reality where a bike can be described as well as seen. At a QM level this type of definitions disappear and what is left is a mental guessing game where we find puzzle pieces that we label as being of certain properties. But there they may change shape, colour, and name at a moments notice, as a better theory comes.
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yor_on:
That's absolutely correct. But without labels we wouldn't know what other people were talking about. Where spin is concerned, left & right are meaningless except for us to be able to differentiate between how the particles behave. We may just as easily have used up & down or backwards & forwards. I'm not sure how chirality entered the picture but I suspect it has to do with the terminology from polarity.
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Yor_on & Dr B: these are examples of the abstracts you end up with as a consequence of any top-down analysis. We assign them a quality and a value, but we don't really know what it is that we're dealing with, other than in abstract terms.
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LeeE - I agree. But without labels we'd be buggered.
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LeeE - I agree. But without labels we'd be buggered.
Yup - even if we don't know exactly what it is that we're talking about, at least we know we're talking about the same thing.