Is it pointless attempting to conceive the notion of higher dimensions?

[Louloubelle]

http://www.tenthdimension.com/flash.php

A nice flash presentation which explains how to imagine up to 10 dimentions

beautiful

however.....

the flash animation invites us to consider the possibility of the existence of only 10 dimensions by illustrating and contrasting our ability to expereince 3 dimensions and our limited ability to experience the 4th dimension, time, and then inviting us to consider further dimensions based on superstring theory and our abililty to imagine contextually by projecting our understanding of 3 dimensions onto a larger theoretical framework

Surely this elegant construct must again be limited by our ability to perceive and imagine?

I once was speaking to a very brainy mathmeticial and phsysicist at a rave (he had been awarded a professorship at an insanely young age and while very clever seemed to lack social skills and to be rather depressed and possibly delusional / pshychotic, in a mad professor style - he was the real deal though, not a fantasist) anyway I digress, he told me that it was possible to hypothosise the existance of 23 dimensions. he did his best to explain how this was possible but I didn't really understand.

The 10 dimensions I can understand but I also wonder whether our senses, of hearing, sight etc, provide us with impoverished brief glimpes of what could be much greater dimensions of colour and sound that are just beyond our ability to perceive.

 

[Louloubelle]

And if you look at this link you'll find that string theory looks seriously like its on its last legs, at last!

This professor kid was very scathing of string theory, like "it's soooo last year"

this kind of discussion always reminds me of stories like this

http://www.dagonbytes.com/thelibrary/lovecraft/dreamswitchhouse.htm

 

[jcsd]

Not sure if discussing pseudo-metrics of Lorentzian manifolds (which model spacetime) is particularly helpful.

In English a metric is a distance and discussing the 'distance' into the future is a bit odd, especially when the distance is negative.

Infact the 'metrics' induced by Lorentzian metric tensors aren't even pseudometrics because of the distinction between timelike and spacelike intervals. Not many texts will note this though as they serve many of the same purpose as distance metrics due to the fact that a Lorentzian metric tensor induces one of these bad boys over a Lorentzian manifold in exactly the same way as a Riemannian metric tensor induces a metric over a Riemannian manifold.

 

[Knotted]

Infact the 'metrics' induced by Lorentzian metric tensors aren't even pseudometrics because of the distinction between timelike and spacelike intervals. Not many texts will note this though as they serve many of the same purpose as distance metrics due to the fact that a Lorentzian metric tensor induces one of these bad boys over a Lorentzian manifold in exactly the same way as a Riemannian metric tensor induces a metric over a Riemannian manifold.

I think I'm confusing metric tensors with metrics and furthermore the 'distances' in spacetime can be imaginary as well as negative. This breaks two of the three rules for metrics - mapping to the non-negative reals and the triangle inequality.

Technical stuff aside, I think what should be understood from all this is that although time and space are inseperable, time (or time-like dimensions) has different qualities to spacial dimensions and this is before we even consider the way that time only seems to go in one direction. A lot of people are confused by the idea that time is the fourth dimension and I think they should understand that this confusion is quite natural because time is a different sort of dimension.

 

[Loki]

Thank god I haven't got a hangover

 

[merlin wood]

Infact the 'metrics' induced by Lorentzian metric tensors aren't even pseudometrics because of the distinction between timelike and spacelike intervals. Not many texts will note this though as they serve many of the same purpose as distance metrics due to the fact that a Lorentzian metric tensor induces one of these bad boys over a Lorentzian manifold in exactly the same way as a Riemannian metric tensor induces a metric over a Riemannian manifold.

just what i was goimg to say. Can you speek ordinary English?

 

[jcsd]

I think I'm confusing metric tensors with metrics and furthermore the 'distances' in spacetime can be imaginary as well as negative. This breaks two of the three rules for metrics - mapping to the non-negative reals and the triangle inequality.

Technical stuff aside, I think what should be understood from all this is that although time and space are inseperable, time (or time-like dimensions) has different qualities to spacial dimensions and this is before we even consider the way that time only seems to go in one direction. A lot of people are confused by the idea that time is the fourth dimension and I think they should understand that this confusion is quite natural because time is a different sort of dimension.

The whole area is incredibly confusing a lot of this is to do with the mixing of terminolgy so for example for many people especially phycists it's perfectly correct to call a 'metric tensor field' a 'metric'.

Whether timelike seperations are imaginary/negative/postive depends on which signature you choose for the metric tensor and what you actually define as the metric function, the important thing is that there's a fundamnetal differnece between timelike and spacelike seperations and that lighlike seperations are null and degenerate (i.e. both timelike and spacelike).

Infact the 'metric' function over a spacetime only really has one of the qualities of a metric function in that it is a symmetric function, but luckily a reverse triangle inequality does hold for timelike seperatations which is enough.

The thing about dimensiosn though is that they're completly independent of considerations like a metric, Lorentzian manfiolds are four dimensional because they are locally homeomorphic to E^4 (the properties of the metric tensor field depend of the diemsniosn of the manifold not vice versa). That is you have an object thta is fundamnatally four dimensional and you need the metric on it to discern the differnce between space and time. You can't really say that time (or space) are dimensions of spacetime because once combined into spacetime they are not that easily distinguished.

 

[jcsd]

just what i was goimg to say. Can you speek ordinary English?

I thought by calling Lorentzian metric tensors 'bad boys' I was bringing my description down to street level

More simply put then:

A metric is a function that allows you to calculate a generalized notion of distance between the members of a set. This function obeys ceratin rules and if you relax one fo those rules then you have what is called a pseudometric (specifically if you relax the rule that the distance between two different members of a set is greater than zero). The equivalent distance function over spacetime doesn't even obey enough of the rules of a metric to be called a pseudometric.

 

[merlin wood]

The confusion lies in what can be mathematically described and what can be described in the real world, eg Hilbert space versus real space.

 

[Knotted]

The whole area is incredibly confusing a lot of this is to do with the mixing of terminolgy so for example for many people especially phycists it's perfectly correct to call a 'metric tensor field' a 'metric'.

My backgound is maths not physics if that helps explain any misunderstandings.

Whether timelike seperations are imaginary/negative/postive depends on which signature you choose for the metric tensor and what you actually define as the metric function, the important thing is that there's a fundamnetal differnece between timelike and spacelike seperations and that lighlike seperations are null and degenerate (i.e. both timelike and spacelike).

Sure, you can apply all sorts of metrics. I think you are right with respect to timelike and spacelike paths and if I could confirm/concretetise what you say:

Given a point in spacetime as a reference, if you travel through time but not space (not as tricky as it sounds - just wait) with respect to your reference point then this is nothing special. If you travel through space but not time with respect to your reference point you are stepping outside a spacetime cone and travelling faster than the speed of light. In conclusion no matter how you measure spacetime, timelike travel and spacelike travel are very different and this is due to the fact that there is a finite speed of light.

Infact the 'metric' function over a spacetime only really has one of the qualities of a metric function in that it is a symmetric function, but luckily a reverse triangle inequality does hold for timelike seperatations which is enough.

Surely multiplication by scalars still work normally?

The thing about dimensiosn though is that they're completly independent of considerations like a metric, Lorentzian manfiolds are four dimensional because they are locally homeomorphic to E^4 (the properties of the metric tensor field depend of the diemsniosn of the manifold not vice versa). That is you have an object thta is fundamnatally four dimensional and you need the metric on it to discern the differnce between space and time. You can't really say that time (or space) are dimensions of spacetime because once combined into spacetime they are not that easily distinguished.

Absolutely. The popular notion that 'time is the fourth dimension' is positively Newtonian. However I think physcists used to regard time as a dimension (a component of a cartesian product) multiplied by the square root of -1. I'm not clear on why they dropped this.

 

[Knotted]

Surely multiplication by scalars still work normally?

Not one of the conditions for a metric, but one for a norm. Doh. Its been a long time...

jcsd is quite right about the lorentzian 'pseudometric' not even being a pseudometric as well.

 

[jcsd]

My backgound is maths not physics if that helps explain any misunderstandings.

Sure, you can apply all sorts of metrics. I think you are right with respect to timelike and spacelike paths and if I could confirm/concretetise what you say:

Given a point in spacetime as a reference, if you travel through time but not space (not as tricky as it sounds - just wait) with respect to your reference point then this is nothing special. If you travel through space but not time with respect to your reference point you are stepping outside a spacetime cone and travelling faster than the speed of light. In conclusion no matter how you measure spacetime, timelike travel and spacelike travel are very different and this is due to the fact that there is a finite speed of light.

Sticking to Minkwoski spactime and inertial refernec frames:

Space and time are mixed in spacetime in a way that it's not easy to pull them apart, e.g. in one reference frame a separtion can be purely spatial or purely temporal but in another it's temporal and spatial.

What distinguishes spaclike and timelike seperations is that there's always a refrence frame in which a spacelike seperation is purely spatial and never a reference frame in which it is purely temporal, equally there's always a refrence frame in which a timelike sepration is purely temporal and there's never a reference frame in which it's purely spatial (to avoid confusion despite what I said early it might better to think of lightlike seperations as the limitng case of timelike seperations)

Surely multiplication by scalars still work normally?

As you've already noted that's not a property of metric spaces.

Absolutely. The popular notion that 'time is the fourth dimension' is positively Newtonian. However I think physcists used to regard time as a dimension (a component of a cartesian product) multiplied by the square root of -1. I'm not clear on why they dropped this.

The ntoion of a diemsnion is a little bit more specfic than the cartesian product, though it's related as handwavingly the dimension of a space is how many numbers you need to describe each element.

Using multiplying time by i in spacetime is a cheat just so we can deal with 4 diemsnional Euclidean space rather than Minkowski space, but it's a cheat that ignores important properties of Minkowksi space. For example if you continually rotate something through an axis in E^4 after a while you'll get back to the same psotion it staretd , but in Minkowski space if you do the equiavlent it'll never get back to the same postion it started.

The reason that people call time the fourth dimension is taht when you define your basis vector fields over spacetime in order to create a reference frame you have 3 basis vector fields made up of spaceliek vector and one basis vector field made up of timelike vectors. What I'd say is though that Minkowski space is four diemsnioanl before you define your basis vector fields and it's only really when you wnat to get numbers out of the equations that you have to define a basis. Also as I said earlier soemthing that is purely temporal in one refernce frame can be a mixture of temporal and spatial in another.

 

[Knotted]

Sticking to Minkwoski spactime and inertial refernec frames:

Space and time are mixed in spacetime in a way that it's not easy to pull them apart, e.g. in one reference frame a separtion can be purely spatial or purely temporal but in another it's temporal and spatial.

What distinguishes spaclike and timelike seperations is that there's always a refrence frame in which a spacelike seperation is purely spatial and never a reference frame in which it is purely temporal, equally there's always a refrence frame in which a timelike sepration is purely temporal and there's never a reference frame in which it's purely spatial (to avoid confusion despite what I said early it might better to think of lightlike seperations as the limitng case of timelike seperations)

OK I think we've got there. You cannot transform a purely temporal displacement into a purely spacial displacement by changing the frame of reference. You can, however, transform orthogonal (at right angles) spacial displacements into one another by changing the frame of reference.

The ntoion of a diemsnion is a little bit more specfic than the cartesian product, though it's related as handwavingly the dimension of a space is how many numbers you need to describe each element.

Sure, but in this case the space is a cartesian product. And as an utterly technical point mathematicians/physicists do not usually talk about "a dimension" but rather "set", "coordinate" or "axis". "Dimension" is the size (cardinality) of a minimal spanning set of vectors for the space.

Using multiplying time by i in spacetime is a cheat just so we can deal with 4 diemsnional Euclidean space rather than Minkowski space, but it's a cheat that ignores important properties of Minkowksi space. For example if you continually rotate something through an axis in E^4 after a while you'll get back to the same psotion it staretd , but in Minkowski space if you do the equiavlent it'll never get back to the same postion it started.

Hmmm. Not sure on this. Remember we are not talking about E^4(=R^4) but R^3XiR. I'm pretty sure the symmetry group will be the same as for Minkowski space.

The reason that people call time the fourth dimension is taht when you define your basis vector fields over spacetime in order to create a reference frame you have 3 basis vector fields made up of spaceliek vector and one basis vector field made up of timelike vectors. What I'd say is though that Minkowski space is four diemsnioanl before you define your basis vector fields and it's only really when you wnat to get numbers out of the equations that you have to define a basis. Also as I said earlier soemthing that is purely temporal in one refernce frame can be a mixture of temporal and spatial in another.

I think this is actually the problem with regarding time as an imaginary axis in Euclidean space. The mathematics (and probably the physical intuition as well) is inelegant when you start changing frames of reference. The real and imaginary coordinates will start getting mixed up.

 

[merlin wood]

The reason that people call time the fourth dimension is taht when you define your basis vector fields over spacetime in order to create a reference frame you have 3 basis vector fields made up of spaceliek vector and one basis vector field made up of timelike vectors. What I'd say is though that Minkowski space is four diemsnioanl before you define your basis vector fields and it's only really when you wnat to get numbers out of the equations that you have to define a basis. Also as I said earlier soemthing that is purely temporal in one refernce frame can be a mixture of temporal and spatial in another.

The reason why time is called the fourth dimension is just because it works out that way mathematically in relativity theory.

But in the real non-mathematical world you can conclude that space is space and time is time and never the twain shall meet.

Only space has height, breadth and depth. And while it's difficult to conceive of extra dimensions of time you can think of such dimensions of space if you think, in particular of a cause of quantum entanglement which cannot be described as acting upon objects while surounding them. Such can be thought of as acting so as to maintain the measured correlation st s distsnce between objects and maintaining the subatomic organisation of matter in general.

And one can represent such a cause as acting from a third dimension upon two dimensional objects in a two dimensional world as follows:

Although you can also think there needs to be a fifth dimension of space to distinguish between entangled and unentangled quantum objects.

 

[kropotkin]

merlin wood: you do understand that when you talk shit other people notice, right?

 

[merlin wood]

Well I notice when you talk shit, as above, kropotkin.

 

[Dubversion]

there are THREE????

 

[merlin wood]

Ask, given the action of the forces and just as they hsve been measured and described, how could mstter in any form remain organised out of its subatomic parts.

Then consider that, universally, the three dimensional world of the senses must be made just of its smallest parts and the forces that surround such subatomic parts of matter.

And then think that something needs to act so that matter remains organised out of its smallest parts and into atoms, molecules and living organisms and despite the action of the forces, and then ask where could such a cause act but from outside the world of the senses?

That is, just as a cause would act that does not surround objects but that produces the non-local effects of quantum entanglement and so that the behaviour of quantum objects remain correlated at a distance.

 

[Knotted]

The reason why time is called the fourth dimension is just because it works out that way mathematically in relativity theory.

But in the real non-mathematical world you can conclude that space is space and time is time and never the twain shall meet.

The mathematics does not diverge from reality here - relativity is very well tested.

Only space has height, breadth and depth. And while it's difficult to conceive of extra dimensions of time you can think of such dimensions of space if you think, in particular of a cause of quantum entanglement which cannot be described as acting upon objects while surounding them. Such can be thought of as acting so as to maintain the measured correlation st s distsnce between objects and maintaining the subatomic organisation of matter in general.

Maybe jcsd can help you with this one. I'm having great difficulty following you. It seems you are trying to force quantum mechanics to comply with classcial physics. I don't think quantum particles are akin to classical particles no matter how many spatial dimensions you use. Also considering that entanglement is not a force, then why should be thought of as some sort of causal action?

And one can represent such a cause as acting from a third dimension upon two dimensional objects in a two dimensional world as follows:

Although you can also think there needs to be a fifth dimension of space to distinguish between entangled and unentangled quantum objects.

Sure I can visualise what you are talking about - but why the need for an extra *spatial* dimension? Essentially you are talking about a hidden variable - but why does it have a spatial expression?

 

[merlin wood]

The mathematics does not diverge from reality here - relativity is very well tested.



Maybe jcsd can help you with this one. I'm having great difficulty following you. It seems you are trying to force quantum mechanics to comply with classcial physics. I don't think quantum particles are akin to classical particles no matter how many spatial dimensions you use. Also considering that entanglement is not a force, then why should be thought of as some sort of causal action?



Sure I can visualise what you are talking about - but why the need for an extra *spatial* dimension? Essentially you are talking about a hidden variable - but why does it have a spatial expression?

At present orthodox physics cannot accept that there could be a cause that's not a force, and so cannot be described by a mathematical formula.

But you can simply consider how the existence of such a cause makes sense.

Hence entangled quantum objects that remain correlated at a distance can be considered to require a cause to act so as to maintain or conserve this correlation.

While the electron wave can be thought to maintain or conserve the electron's orbital around the nucleus. And a cause that act universally so as to conserve or maintain the organisation of matter as atoms and molecules would make sense of how matter in general can remain naturally organised out of its subatomic components and despite the action of all the forces.

And such would be a cause that would neither push nor pull objects and so would have no measurable strength that could reduce or cease with increasing distance between objects, and so makes sense of all those experiments that have measured long distance quantum entanglement.

 

[Knotted]

At present orthodox physics cannot accept that there could be a cause that's not a force, and so cannot be described by a mathematical formula.

So what is the problem with orthodox physics with respect to entanglement and how does this new perspective (which looks quite mathematical to me) solve this problem?

 

[laptop]

It's clear to me from merlin wood's web page that they've started from the "revelation" that there's a "Cause" and are scrabbling around looking for sciency-sounding "justification".

So not interested in what's going on either in the world or in mathematics at all, then.

Just to alert you not to put too much effort in, knotted - take a look at earlier exchanges.

 

[Crispy]

This theory needs maths, badly.

 

[bluestreak]

Chorus: "We need a mathmatician"

 

[merlin wood]

So what is the problem with orthodox physics with respect to entanglement and how does this new perspective (which looks quite mathematical to me) solve this problem?

One of the problems with quantum entanglement is that, considered on its own, it's effect seems like a bit of magic. And way back in 1935 Albert Einstein called it a 'spooky action at a distance'.

So quantum.mechanics finds that in order to explain the observable evidence - and this includes the chemical nature of matter - correlations of behaviour need to be described as occurring between the subatomic components of matter and between electrons in particular. And the whole of the Pauli exclusion princple, which describes the arrangement of electrons around the atomic nucleus, works on this basis

So you can't describe anything of the charge or electromgnatic force to explain the Pauli principle and thus how the different elements chemically react in their different ways.

No theory developed just from the evidence of matter on the smallest scale can explain how quantum enanglemeent and the Pauli principle are possible And this is so despite the development of a complex and highly successful quantum theory that can explain everything but how matter can exist and organise itself into atoms and molecules, and how it does this despite the action of all the forces.

So at preaent the physicist can ultimately only say that matter is, somehow, 'self-organising' by obeying the principles of quantum mechanics.

Where it relates the quantum wave to the astronomical evidence my hypothesis at http://tinyurl.com.ek76d is in dire need of mathematical development, but where it just deals with the subatomic organisation of matter in general it needs mathematics like a hole in the head.

Although to the extent that support for the theoretical argument as a whole is dependent on all the evidence examined when taken together, then its accepability is dependent upon confirmation by measurement and calculation.

 

[Knotted]

One of the problems with quantum entanglement is that, considered on its own, it's effect seems like a bit of magic. And way back in 1935 Albert Einstein called it a 'spooky action at a distance'.

So quantum.mechanics finds that in order to explain the observable evidence - and this includes the chemical nature of matter - correlations of behaviour need to be described as occurring between the subatomic components of matter and between electrons in particular. And the whole of the Pauli exclusion princple, which describes the arrangement of electrons around the atomic nucleus, works on this basis

So you can't describe anything of the charge or electromgnatic force to explain the Pauli principle and thus how the different elements chemically react in their different ways.

No theory developed just from the evidence of matter on the smallest scale can explain how quantum enanglemeent and the Pauli principle are possible And this is so despite the development of a complex and highly successful quantum theory that can explain everything but how matter can exist and organise itself into atoms and molecules, and how it does this despite the action of all the forces.

Let's ask oursleves, 'what is an explanation?' An explanation is really a translation - if you explain something you translate observation and theory into a (hopefully more general) framework. So if you say quantum mechanical theory needs an explanation then this is saying that the theory needs to be translated into another form. That's probably true considering the conflict between QM and general relativity, but I really don't see why this particular aspect of quantum mechanics is disagreeable as it is. It may be strange but its perfectly logical. What is there in non-locality that is to be feared?

Btw I can't get your link to work.

 

[Knotted]

It's clear to me from merlin wood's web page that they've started from the "revelation" that there's a "Cause" and are scrabbling around looking for sciency-sounding "justification".

So not interested in what's going on either in the world or in mathematics at all, then.

Just to alert you not to put too much effort in, knotted - take a look at earlier exchanges.

Thanks for the warning but the discussion keeps my brain ticking over.

By the way the whole discussion about 'causes' is very odd given that even in classical mechanics it is not always possible to say that object X causes object Y to behave in such and such a way because if you have a third object it is not always possible to disentangle causes and effects.

I am however quite happy to consider what Merlin Wood says. Its not the first time someone has looked at hidden variables to explain what is going on - cf David Bohm - although he did not claim his theory was non-mathematical and nor did he attack quantum entanglement but rather the apparent randomness of quantum mechanics (if I remember correctly).

 

[Crispy]

This Thread is required reading, Knotted.

 

[merlin wood]

Let's ask oursleves, 'what is an explanation?' An explanation is really a translation - if you explain something you translate observation and theory into a (hopefully more general) framework. So if you say quantum mechanical theory needs an explanation then this is saying that the theory needs to be translated into another form. That's probably true considering the conflict between QM and general relativity, but I really don't see why this particular aspect of quantum mechanics is disagreeable as it is. It may be strange but its perfectly logical. What is there in non-locality that is to be feared?

Btw I can't get your link to work.

Sorry try this link. And I shouldn't take much notice of Laptop, he's an inveterate liar.

As I see it there's nothing to be feared about non-locality except by physicis and cosmologists who've spent a lot of their time developing theories that a sufficiently developed general non-local theory of natural organization would prove wrong.

I think that's one good reason why phyicists have a tendency to try and argue non-locality out of exisnce. It is the strongest indication of how much is unexplained by orthodox quantum theory.

 

[laptop]

And I shouldn't take much notice of Laptop, he's an inveterate liar.

Now, what would consitute evidence for that statement? Documentation of six lies, say?

Produce, withdraw or disappear.

Not understanding the concept "evidence" is no defence.