Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: ries van Twisk on 05/03/2009 05:30:03
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ries van Twisk asked the Naked Scientists:
Chris,
I am a frequent listener to your programme (http://www.thenakedscientists.com/HTML/podcasts/) and it's great!
i do have a question for you :
since everything seems to vibrate at some sort light light has waves, electrons move around atoms, and I believe that string theory is based on these vibrations as well.
I was wondering if there is evidence that Time Ticks, or is time continuously?
Thanks,
Ries van Twisk
Quito, Ecuador
What do you think?
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Quantum mechanics assumes that the smallest unit of time is that which light takes to travel the planck unit of distance.
Planck time 5.391 * 10^-44 seconds
Planck length 1.616 * 10^-35 meters
See http://en.wikipedia.org/wiki/Planck_units#Base_Planck_units
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If time is quantised then it wouild not flow smoothly but, rather, it would take discrete steps. These steps would obviously need to be incredibly tiny; maybe the Planck time - 10-43 seconds.
I think syhprum meant to say "Quantum mechanics assumes that the smallest unit of time is that which light takes to cross the planck unit of distance". I believe that is how the Planck time is defined.
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Planck scale units can be derived from solving for the point where a quantum theory of gravitation is needed (for some, but not all, formalisms). What actually happens at the Planck scale is quite another story — we don't have the ability to do experiments at that level. Planck's original determination happened before QM, and were just a convenient unit system from setting c, G and hbar to 1. So take any statement that says the Planck time is the smallest unit of time with a quantum of salt.
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OK, I shall bear that in mind.
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I think the second is defined in relation to the number of times the caesium atom changes states under a defined condition. I guess you could count those changes of states of the caesium atom to be ticks.
Those ticks would be pretty short though; I'm not sure how they would compare to a Planck length.
A "cesium(-beam) atomic clock" (or "cesium-beam frequency standard") is a device that uses as a reference the exact frequency of the microwave spectral line emitted by atoms of the metallic element cesium, in particular its isotope of atomic weight 133 ("Cs-133"). The integral of frequency is time, so this frequency, 9,192,631,770 hertz (Hz = cycles/second), provides the fundamental unit of time, which may thus be measured by cesium clocks.
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That isn't time ticking, though, is it. It's just atomic decay.
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That isn't time ticking, though, is it. It's just atomic decay.
I think the second is defined in those terms. They synchronize the time piece with the vibrations of the atom; vibrations we used to think of as orbiting electrons.
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But a second is an artificial construct. It isn't "time" per se.
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There is no experimental evidence for time being events.
You could say that Feynman diagrams could be seen as some sort of proof for time being 'events' perhaps, as they can go 'both ways' in time?
But we have tested the idea down to 'attoseconds'
(One quintillionth (10^-18) of a second) without being able to see any proof for it being 'events'.
I think it's a 'flow' :) like we are 'fishes' inside 'times ocean'
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I've heard it said, although I'm not sure of the reasoning behind it, that the Planck length is the smallest unit of length that has any meaning. If time is just another dimension, as is thought by some, why should that also not have a smallest measurement that is meaningful? If that is indeed the case, then it would not flow linearly but would have to pass in discrete steps.
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Yes DB, you are quite correct, I read the same.
Even though it gives me problem to see spacetime as having a 'smallest length'.
But then the definition seems to be more like 'having a meaning for us'.
http://www.scribd.com/doc/11157955/Planck-Length-and-Time
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Yes, that is certainly what that article seems to imply (paragraph 3).
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fi148.photobucket.com%2Falbums%2Fs26%2FDoctorBeaver%2Fthings%2Fplanck_time_text.jpg&hash=7607afe11148c26ac1dcdd399b8c0d9e)
(I had to take that from a screenshot as it doesn't allow copy & paste.)
I must have misunderstood what I read about the Planck length.
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Dear Doc
If you sign up (free) you can download as text instead of PDF and then you can cut and paste from the text document
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A free sign? I wasn't trying to download anything, just copy & paste from the site.
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This question falls within an area of theoretical physics that is little discussed but which is of special interest to me. I think it is little discussed because it concerns an aspect of reality that we don't, in general, even think to question.
Cutting to the chase, if you consider an object that has zero length in the direction that it is moving, it is apparent that it can only move in discrete steps in that direction; any change of position of a zero-length object must result in a displacement greater than the length of the object (which is zero) i.e. there must be a discrete (non-zero sized) gap between it's former and current positions.
In fact, having zero length just high-lights the broader issue of the change of precisely known values; any precisely known value can only change by values greater than zero, so once again, there must be a discrete and non-zero sized gap between any two precisely known values.
The significance of the Planck Length and Time units, is I believe, probably one of the single most counter-intuitively understood aspects of science and physics. While the Planck Length and Time units are part of a scheme that allows the normalisation of many of the constants in physics to the range of values between 0 and 1, it is the interpretation of the Planck Length and Time units as being the smallest divisions of those dimensions that has any meaning that is most interesting here; if the Planck Length is the smallest measure of distance that has any meaning, and the Planck Time is the smallest duration of time that has any meaning, then the slowest possible constant speed would appear to be 'c'. It would, of course, be possible to achieve lower speeds, but only by moving less than the Planck Length in the Planck Time duration, or by only moving the Planck Length in multiples of the Planck Time, but this then begs the question; 'if it only moves one Planck Length in two Planck time units, where was it after only one Planck Time unit?
In any case, the idea of something moving just one Planck Length distance in multiples of the Planck Time unit soon runs in to other problems; to achieve a perfectly smooth and continuous acceleration from zero would require an infinite number of Planck Time units for the initial movement of one Planck Length away from it's original position; any other solution still results is a series of discrete jumps.
The logical solution then, to describe constant movement at lower speeds than 'c', is to require the locations and velocities of the moving objects to be imprecise, rather along the lines of the Uncertainty Principle.
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LeeE has managed to baffle me with science yet again. (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.freesmileys.org%2Fsmileys%2Fsmiley-confused002.gif&hash=ecc3014df2c4ab8f4fb336f2f1a6ae18) (http://www.freesmileys.org)
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Me to DB.I am trying to get my head around how something with zero length can exist.For that matter zero height or zero width?.
Cheers
justaskin
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But a second is an artificial construct. It isn't "time" per se.
Yes; you're right; maybe the ticking of time is simply a conceptual construct to allow us to think about it. Time itself may flow smoothly along, impervious to our attempts to explain it.
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Perhaps one could see time as 'whole', but in it we have phenomena relating to either QM or our macroscopic spacetime? What we see as distance seems to be connected to our 'relative' motion and acceleration macroscopically. It seems to me that we can't say that distance is anything else than a 'property' between two frames of reference. And as we can't say that anything is 'standing still' in spacetime either, as our 'frames of reference', as far as I understand, always will be defined as being relative someone else's frame.
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I'm not sure I'm expressing myself 'explicitly enough' here (no surprise huh:)
What I try to say is that to me there is no correct 'definition' of 'distace'.
It's just a concept describing a relation between two frames.
You and whatever you are measuring against. That as you will be at some frame, not able to define its possible motion without referring to another 'frame of reference'.
That we have an 'Earth standard' doesn't make it a 'preconception universale'.
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Well, thinking of it I do have one for the 'shortest path' though :)
The one costing you the least energy :)
Like light through spacetime's geodesics.
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It's like the whole question of plank length. there is nothing hindering us from saying that a plank length is double the distance we have measured, relative those other definitions Plank used for defining.
That is, as long as we change those too to keep the relative 'balance' in check between them, sort of:)
Or is there anything that we can say won't be possible to change numerically as long as we keep their 'intergroup' relations correct?
So if we agree on that the frames of reference we use are 'arbitrary' in that meaning then there is no 'gold standard' for 'distance'. That we think so comes from what we are used to historically it seems to me.
Now one could say that the 'intergroup' relations will be there anyway, and I would agree on that. But what I want to put forward is that the concept of 'distance' doesn't have any meaning in spacetime other than defining a relation between two frames. So ' meaningful for us' seems a very appropriate concept here, like describing a 'tool' we use for giving us a 'meaningful' comparison.
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That isn't time ticking, though, is it. It's just atomic decay.
Not decay; it's a spin-flip of the electron. But there's nothing inherently fundamental about the choice of Cesium or that transition — that was one of utility (it's a measurement which can be realized with good precision and accuracy)
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The idea of zero-length objects does seem to be very counter-intuitive but they seem to be implicit in any theory that can handle n dimensions; that is, any theory that isn't limited to just three spatial dimensions, no more and no less.
If we consider a three-dimensional object, everything seems fine; that's how the universe appears to us, but then how long is that three dimensional object in the fourth, fifth, sixth etc. dimension?
The existence of 'n' dimensions is debatable, of course, but we do accept four-dimensional space-time, so it's valid to ask the question; "How long is a three-dimensional object in the fourth dimension?
Interestingly, the idea of zero-length avoids a big problem that appears in n-dimensional theory that occurs if one insists on a QM style non-zero sized object; if an object has to have some size in every dimension then every object must exist in all of an infinite number of dimensions, unless the number of dimensions is arbitrarily limited. If you allow zero-length in a dimension though, you then don't need the object to exist in all of an infinite number of dimensions because it can have zero length and presence in them.
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That isn't time ticking, though, is it. It's just atomic decay.
Not decay; it's a spin-flip of the electron. But there's nothing inherently fundamental about the choice of Cesium or that transition — that was one of utility (it's a measurement which can be realized with good precision and accuracy)
Oh, sorry. I thought it was atomic decay.
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LeeE that sounds like it's coming from string theory?
I guess we need the concept of zero-length to explain how we can have those 'curled up' dimensions existing simultaneously with us, presuming that an object needs to be spatially extent in all dimensions. If we look at it as some does with photons, there, but only at the moment of interaction then it seems to become another question. As photons could be said to represent a 'zero length' object.
Or a photon 'somewhere else' might be seen as only one filling up that dimension totally, perhaps? :)
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If we consider a three-dimensional object, everything seems fine; that's how the universe appears to us, but then how long is that three dimensional object in the fourth, fifth, sixth etc. dimension?
It isn't "long" at all in those other dimensions. It will demonstrate an increase in mass proportional to its motion in other dimensions.
I often wonder about the heavier types of particle in the Standard Model; the muon, for example. It is identical to the electron apart from its mass. If electrons can travel in spatial dimensions other than the 3 with which we are familiar then their motion would show as increased mass but every other characteristic (charge, spin, etc) would remain the same. Isn't that exactly what we see? (Can we for now ignore the magnetic moment anomalies of the muon? Please?)
There are 3 generations of electron in the Standard Model (electron, muon & tau). Could the disparity in their mass be a function of their motion in our normal dimensions plus 2 other dimensions of different size? For instance, the muon is travelling in the 5th dimension so its mass is increased proportional to the size of that dimension. The tau could be moving in the 6th dimension alone, which would need to be large enough to account for all the tau's extra mass, or combined motion in a 5th & 6th dimension.
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DB, that was real interesting. Are you sure that mass will communicate itself through all dimensions (past the ones we can see:) of an object? Do you have a good link explaining that idea?
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Rest mass is constant and is a measure of the amount of matter present; that is basic physics. Therefore, however many dimensions a particle can be in, its rest mass will be the same in all of them. But the particle will also have momentum. Momentum is rest mass * velocity (or, rather, rest mass times the sum of its velocities in all dimensions). We can't detect a particle's velocity in another dimension so what we see is an increase in its perceived mass. The faster the particle is moving in another dimension, the greater its momentum and, consequently, we will see it as having greater mass.
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Hey All,
do you all saying that indeed time ticks and it not continuously?
I am trying to understand the most out of it.. and also it's very interesting to read about the zero length object....
so far it's great to see the answers and looking forward to read the 'final answer' :)
regards,
Ries van Twisk
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oops. Ik verontschuldig me, Ries. I got sidetracked [:I]
There is no way of proving 1 way or the other whether time ticks or flows smoothly. Any ideas on the subject must be purely hypothetical. My inclination is to say that time is quantised and therefore does not flow in a linear fashion. Others here disagree with me.
Until we know what time is, we won't be able to answer the question. Don't ask me when that is likely to be; we don't even understand gravity yet and that is probably very simple compared to time.
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Hi there.
If I can put my two cents worth in the hat, I don't think time ticks in nature. The "tick" of time is nothing more than man's insatiable desire to measure everything. Whether it be a planck length, a second on my watch, a year on my calendar, or a light year, it is nothing more than a measurement. If we didn't have these "ticks" for measurement, we would have no math.
Time flows. Man has ticks. [;D]
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I agree with Burt; time needs to flow smoothly. We have become smitten with Quantumania since we discovered that each certain frequency of electromagnetic phenomena comes in discrete bundles of action. Now we feel a great need to describe everything in terms of quanta.
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Now now! Don't blame it on the quanta. Man has been measuring the world around him for thousands of years. We are just getting better at measuring the quantum world in the last two centuries.
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I think what Doc Beaver was saying about something existing in overlapping but different dimensional sets is perfectly reasonable. In fact, I think it must probably be a feature of any model that attempts to describe n-dimensional geometries/geodesics. At least I think that's what he was saying [:)]
I'm strongly inclined to think that from our point of view, time moves in 'ticks', for the reasons given earlier. However, what we regard as our time dimension, and which we move through in steps, could as easily be a spatial dimension for something occupying a different but overlapping set of dimensions, where they could move through that same dimension smoothly.
The same sorts of n-dimensional models seem to predict that the higher number of dimensions that something occupies, the higher the total 'quantity' of whatever it's made out of. For example, if you consider the transformation of mass to energy, you can map it to a three-dimensional object being turned in to many two-dimensional objects, or in the case of electron/positron creation/annihilation, from two very small 3D objects to two very strong 2D objects, all in line with e=mc2.
I also think it's interesting that the mathematics itself implies multi-dimensional aspects; in Albert's equation we square something to produce an area, like the length and width of a floor, and then multiply the area by the height of the wall. You can almost see it building a three-dimensional object.
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I have since changed my mind about time ticking. I've posted a bit of nonsense about it in the New Theories section
http://www.thenakedscientists.com/forum/index.php?topic=21043.0 (http://www.thenakedscientists.com/forum/index.php?topic=21043.0)
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You may be right LeeE; but I was kinda hoping that string theory wouldn't really catch on. It is hard enough trying to figure things out in three dimensions plus time. Maybe since we've become familiar with maths and computers where adding another dimension simply requires a comma and a number, we yield to it too readily. [:)]
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We seem to have been distracted into discussing dimensions rather than whether time ticks. I am as guilty of that as anyone.
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I don't think the issue of whether time ticks or not can meaningfully be discussed without referring to dimensions - it is precisely about the nature of movement through dimensions.
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Well, the idea if dimensions and what they might be defined as is worthy of a discussion on its own I think :)
We know that time is here, of all dimensions we have time is the one you can't take away. You can choose any optional dimension of those others, and we will still be here, well, maybe disappearing now and then as f ex. width is gone, but mostly here at least. But try to take time away and see what happens, huh...
So 'time' is a very special relation to us, like your favorite aunt perhaps? and as spacetime is a whole as I see it with time, distance, mass, acceleration and motion all being connected to each other through sliding scales, you manipulate one, the others will react / slide. I know that this is not all true, but it's true enough :) We may not be able to shorten a distance by our own, but we sure can do it by accelerating. And that distance will be shorter for real, no joke, as long as you are in that accelerating frame. And time outside your spaceship will seem to 'speed up'. And that's also for real. So time is not 'only' time, it's in fact 'Spacetime'.
Now if I want to have fun I would split 'spacetime' in three parts. And if I could get away with it I would name all three as 'dimensions' bur as I won't get away with it I will just call them 'states'. Those three are Space, Matter and Time. In this place created by those states we have two exceptional 'exceptions' more, namely, photons, but as I see photons as a secondary state arising from those first three its not a primary, and then gravity, as an expression of the combination of space and matter (as I see it, for now that is, things have been known to change at 'times':) and not as a 'force' of its own.
So to me 'time' is the 'cornerstone' together with mass and space. But then I have this feeling that space and mass are one and the same :) on some strange plane, not as we experience it but there is to me a symmetry in those two, I can't imagine one of them without the other, so to speak, can you? So perhaps in the end, we are down to two 'thingies' here? Time and 'matterspace'???
Well, it's just an idea. You don't need to throw things just because one gets an idea...
*Look Mummy, A taaable :)*
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I don't think the issue of whether time ticks or not can meaningfully be discussed without referring to dimensions - it is precisely about the nature of movement through dimensions.
Why do you say that? We can discuss spatial dimensions without reference to time, so why not vice versa?
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I don't think the issue of whether time ticks or not can meaningfully be discussed without referring to dimensions - it is precisely about the nature of movement through dimensions.
Why do you say that? We can discuss spatial dimensions without reference to time, so why not vice versa?
I'm not quite sure I understand "why not visa versa"
You can discuss milk without referring to tea, but you can't discuss tea without referring to milk. But I don't think that's relevant.
However, although I didn't specifically refer to spatial dimensions, there really doesn't seem to be any absolute difference between the spatial and temporal dimensions; it just seems to be that way from our point of view, as the phenomenon of relativistic time-dilation implies. In any case though, it comes down to the nature of the movement through both spatial and temporal dimensions. What we term 'time' is the movement through the temporal dimension, and you can't talk about the movement of something without reference to the dimension that it's moving through; the definition of movement is the change of location, and location only has significance in the context of dimensions.
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Hey all,
I was thinking a bit about it (but I am a nOOb in this)
They say that we humans experience 4 dimensions (XYZ + time) does that then automatically mean we can exchange any dimension for Time, or is Time special?
Ries
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Hey all,
I was thinking a bit about it (but I am a nOOb in this)
They say that we humans experience 4 dimensions (XYZ + time) does that then automatically mean we can exchange any dimension for Time, or is Time special?
Ries
With our special gadgetry, computers and the maths, we need only mark down a comma then a number to create another dimension. I suspect that leads us to ponder too easily into extra dimensions, and leads us to consider that they might be reality. The real world, to me, consists of three spacial dimensions and one time dimension. That is where we live.
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You can discuss milk without referring to tea, but you can't discuss tea without referring to milk. But I don't think that's relevant.
I don't take milk in tea. But even if I did, I could hold forth on the subject of tea without mentioning milk.
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You can discuss milk without referring to tea, but you can't discuss tea without referring to milk. But I don't think that's relevant.
I don't take milk in tea. But even if I did, I could hold forth on the subject of tea without mentioning milk.
I'm sure you could, but I bet you'd have to make a conscious effort to do so [;)]
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Hey all,
I was thinking a bit about it (but I am a nOOb in this)
They say that we humans experience 4 dimensions (XYZ + time) does that then automatically mean we can exchange any dimension for Time, or is Time special?
Ries
No, and yes, respectively.
There is a clear difference between them, or so it seems to us, but this doesn't necessarily mean that the difference is because the dimensions are fundamentally different; the perceived difference could actually be be due to us, or at least something about us that is different with regard to the temporal dimension and the spatial dimensions.
In the model I've been playing with, the apparent difference between the spatial and temporal dimensions is really due to the nature of our movement through those different dimensions; we move in a fundamentally different way through space when compared to the way we move through time and it is this that accounts for the apparent difference we see between the spatial and temporal dimensions.
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You can discuss milk without referring to tea, but you can't discuss tea without referring to milk. But I don't think that's relevant.
I don't take milk in tea. But even if I did, I could hold forth on the subject of tea without mentioning milk.
I'm sure you could, but I bet you'd have to make a conscious effort to do so [;)]
Not at all. I could make a reference to milk insofar mentioning that some people take it in their tea, but that certainly would not be necessary.
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In the model I've been playing with, the apparent difference between the spatial and temporal dimensions is really due to the nature of our movement through those different dimensions; we move in a fundamentally different way through space when compared to the way we move through time and it is this that accounts for the apparent difference we see between the spatial and temporal dimensions.
I like this explanation. Plus; we can control our movement through the spacial dimensions; so far we are completely captive to the temporal one; we move through it, not at our own choosing but in complete lock step with everything else we know about.
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In the model I've been playing with, the apparent difference between the spatial and temporal dimensions is really due to the nature of our movement through those different dimensions; we move in a fundamentally different way through space when compared to the way we move through time and it is this that accounts for the apparent difference we see between the spatial and temporal dimensions.
It could also mean that we move through time in a fundamentally different way because time is fundamentally different from spatial dimensions. I fully appreciate that GR says space & time are inextricably linked, but I think I'm right in saying that it doesn't explain why they are.
My feeling is that there is a fundamental difference between them.
But, then again, what is a dimension? It can be defined as 1 of the values needed to fix the position of an event in spacetime. Using that definition, time has to be just another dimension. But it must be remembered that this definition of a dimension is no more than a mathematical construct that allows us to think about time in a fairly simple way. The truth may be very different,
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Yes; DB I think the truth is fundamentally different. We can think of the temporal dimension as a continuum and imagine moving back and forth through it, just like the spacial dimensions; however, we can not control our movement through time; we can only experience it as plodding ever onward at it's own pace.
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I've mentioned it before, but the best way of showing how the spatial and temporal dimensions are fundamentally the same is by referring to the phenomenon of relativistic time-dilation.
Relativistic time dilation is the phenomenon where the movement of something through space affects the local rate of movement through time; the rate of time for a moving object is lower when compared with the rate of time for a stationary or more slowly moving object.
The relationship between speed through space and the rate of time is simple and direct; the sum of the movement vectors through time and though space always equals 'c'. Thus, when stationary the spatial movement vector = 0 and the movement vector through time = 'c', but as the spatial movement vector becomes non-zero the temporal movement vector must decrease to maintain the same summed vector of 'c'.
Because these two apparently different vectors can be so summed indicates to me that they are of the same type.
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LeeE, you are definitely correct in that there are a symmetry to time and distance, but that symmetry seems to exist with density too? If we were on a neutronstar for example, not that we are, but if, time would slow down for us considerable, as measured from a observer outside that gravitational field. Shouldn't there also be a Lorentz contraction observed in that gravitywell, thinking of it? I find your idea interesting but you will need to explain why 'matter/density' have the same effect I think.
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http://sci.tech-archive.net/pdf/Archive/sci.physics/2005-04/msg00366.pdf
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The relationship between speed through space and the rate of time is simple and direct; the sum of the movement vectors through time and though space always equals 'c'. Thus, when stationary the spatial movement vector = 0 and the movement vector through time = 'c', but as the spatial movement vector becomes non-zero the temporal movement vector must decrease to maintain the same summed vector of 'c'.
That is a very good explanation LeeE. I had never before thought of that kind of vector analysis but it is simple and direct, as you say. But the same relationship would exist with the Lorentz version of space and time.
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what if time is at a constant speed? would it mean speeding up to times' speed would make time stop to you since its not flowing past you at its rate? Would it mean that if I was to stop dead right now in this point, in the expanding universe, then I would age rapidly? Maybe time is speed and we measure it like we would measure a flow of water; the more we flow with the water the less pressure we measure ( to us the flow seems to be slowing down the faster we move with it). Time does not slow down the faster we move to the speed of light but rather we are catching up to the speed of time and therefore time effects become less irreverent.
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Maybe stars collapse tears into the fabric that contains time thus allowing time to flow into a timeless pocket. Who knows just maybe "The Big Bang" was a result of another dimension ripping (aka black hole) and allowing time and material to flow from it to our timeless pocket.
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Shouldn't there also be a Lorentz contraction observed in that gravity well, thinking of it?
I can understand time slowing in a gravity well, but can't quite get length contraction to work. If it is like the Lorentz contraction, it would be only in one direction. I'm not sure what GR says about contraction in a gravity well; I don't remember reading anything about that.
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what if time is at a constant speed? would it mean speeding up to times' speed would make time stop to you since its not flowing past you at its rate? Would it mean that if I was to stop dead right now in this point, in the expanding universe, then I would age rapidly? Maybe time is speed and we measure it like we would measure a flow of water; the more we flow with the water the less pressure we measure ( to us the flow seems to be slowing down the faster we move with it). Time does not slow down the faster we move to the speed of light but rather we are catching up to the speed of time and therefore time effects become less irreverent.
I don't think that is quite mainstream thinking; but it makes just as much sense to me as does the mainstream version. [:)]
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LeeE, you are definitely correct in that there are a symmetry to time and distance, but that symmetry seems to exist with density too? If we were on a neutronstar for example, not that we are, but if, time would slow down for us considerable, as measured from a observer outside that gravitational field. Shouldn't there also be a Lorentz contraction observed in that gravitywell, thinking of it? I find your idea interesting but you will need to explain why 'matter/density' have the same effect I think.
The wiki article on gravtational time dilation says:
Clocks which are far from massive bodies (or at higher gravitational potentials) run faster, and clocks close to massive bodies (or at lower gravitational potentials) run slower. This is because gravitational time dilation is manifested in accelerated frames of reference or, by virtue of the equivalence principle, in the gravitational field of massive objects.
Which basically says both forms of time-dilation are due to your inertial mass being equivalent to your gravitational mass.
Another way of looking at it is that space is distorted in a gravity well and this distortion, in changing the shape of space, changes it's size too, so everything moving within that distorted region of space is effectively moving further, equivalent to moving faster. Don't forget that even if you're sitting still within that gravity well, all the atoms and molecules that everything is made from will still be moving.
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Planck scale units can be derived from solving for the point where a quantum theory of gravitation is needed (for some, but not all, formalisms). What actually happens at the Planck scale is quite another story — we don't have the ability to do experiments at that level. Planck's original determination happened before QM, and were just a convenient unit system from setting c, G and hbar to 1. So take any statement that says the Planck time is the smallest unit of time with a quantum of salt.
I liked this definition, simple and clear. If time 'tick', I don't think we ever will measure it anyway, as that have to be under the Planck scale.
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The relationship between speed through space and the rate of time is simple and direct; the sum of the movement vectors through time and though space always equals 'c'. Thus, when stationary the spatial movement vector = 0 and the movement vector through time = 'c', but as the spatial movement vector becomes non-zero the temporal movement vector must decrease to maintain the same summed vector of 'c'.
That is a very good explanation LeeE. I had never before thought of that kind of vector analysis but it is simple and direct, as you say. But the same relationship would exist with the Lorentz version of space and time.
Sorry - must have missed this earlier.
The same relationship exists with the Lorentz equations because they are the same thing. Have a quick look at the Lorentz equations and you'll see that they are basically Pythagorus's right-angle triangle solution, where instead of solving for the hypotenuse, you're solving for one of the sides (time), the hypotenuse (c) and other side (speed) being known.
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Planck scale units can be derived from solving for the point where a quantum theory of gravitation is needed (for some, but not all, formalisms). What actually happens at the Planck scale is quite another story — we don't have the ability to do experiments at that level. Planck's original determination happened before QM, and were just a convenient unit system from setting c, G and hbar to 1. So take any statement that says the Planck time is the smallest unit of time with a quantum of salt.
I liked this definition, simple and clear. If time 'tick', I don't think we ever will measure it anyway, as that have to be under the Planck scale.
I agree that if time does 'tick' then we wouldn't be able to measure it, although this is not necessarily because it might be less than the Planck time unit. If we move through time in discrete steps, or ticks, then nothing could happen between successive ticks; all we could see would be a sequence of different states, but not the transitions between them.
That things happen in durations smaller than the Planck time unit, or over distances smaller than the Planck length unit is indisputable; if you travel a distance of one Planck length unit and it takes you one Planck time unit to do so, your speed is 'c', so how does anything travel slower than 'c' or accelerate and decelerate?
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Yes LeeE, you're perfectly right in saying that if time only allow us consciousness at the 'tick' and that whatever duration there might be between those 'tick' therefore neither will be measurable or observed. And that in fact becomes a 'negative proof' for a 'flow' as that would be the only thing measured under such a system :)