Additional dimension - how do you conceptualise them?
Discussion
I've had a strong interest in science for many years, having done an Aeronautical degree at uni and then maintaining physics interests in motorsport and other job related activities.
One thing that has always been a struggle, is how to 'accept' or conceptualize more than the 4 dimensions that we are used to.
One important aspect to point out is that there are two main realms of 'dimensions' and what they are defined as.
The first is in the world of mathematics(geometry), and the second is in the world of physics.
In geometry the 4thD is not time, and one way to visualize it is by moving an entire 3D volume of an object along an axis to produce a new 'entity' made up of a swept volume.
Then the 5thD would be a similar concept of moving that swept 4D 'volume' along another axis to produce a 5D entity. And so on.
In the world of physics however, the 4thD is time, and beyond that there is a requirement in String (M) Theory to need 11 dimensions in total to describe how quantum mechanics plays out as it does.
These additional dimensions can be harder to conceptualize and there are a few different ways it can be done.
One method is to say that space itself is 'quantacised', that being space is made up of Plank sized portions of volumes.
(A Plank sized element is the absolute smallest size that has a meaningful measurement in quantum mechanics).
And although this may seem like such volumes are reverting back to our familiar 3D spatial dimensions, you'd be sort of correct. However, here at this scale, it is the interactions of these plank volumes and how they are compacted or moving relative to each other that 'form' the 7 additional dimensions to make up the 11 in total.
Its sort of hard to accept how these additional dimensions are created but one way to think about this is to accept how something becomes "not something" when you divide it so much that you end up with its constituent parts.
So for example, a video I saw recently put forward that you have a bar of gold. If you divide the bar in half, you have two smaller bars of gold. But if you keep dividing these bars, you would get to the point that you have a gold atom - now this is no longer a "bar of gold".
So you keep dividing the gold atom, its no longer even 'gold'. Continue down past quarks and the force 'particles' holding them together, keep dividing down until all that is left is a quantum volume of space. From here nothing can be divided. These quantum volumes must be of a Plank-sized volume but can stretch, twist, bend and provide a form of 'pressure', which gives rise to the additional dimensions that are needed to explain the effects.
So that is my current understanding of a possible method to conceptualize additional dimensions.
There are others and just as a final point to end this post I just want to mention that "flatland" is where many people start, but I found this method to lead to many confusing aspects. But at the same time some very interesting ones. Such as the fact that in our 4D world, a single photon is the same as any other photon in the universe - in terms of properties. This means in our 4D world a photon does not carry distance information with it, which is why we need to revert to parallax methods of measuring distant stars. But if a person living in 5D land (with reference to the 'flatland' concept), were to view an object, they may be able to see photons in 5 dimensions, which could include 'distance', meaning they'd be able to see through walls for example.
All interesting stuff - if not also a bit heavy on the philosophical side of things
..... TLDR version : its a mind f-ck ! .....
One thing that has always been a struggle, is how to 'accept' or conceptualize more than the 4 dimensions that we are used to.
One important aspect to point out is that there are two main realms of 'dimensions' and what they are defined as.
The first is in the world of mathematics(geometry), and the second is in the world of physics.
In geometry the 4thD is not time, and one way to visualize it is by moving an entire 3D volume of an object along an axis to produce a new 'entity' made up of a swept volume.
Then the 5thD would be a similar concept of moving that swept 4D 'volume' along another axis to produce a 5D entity. And so on.
In the world of physics however, the 4thD is time, and beyond that there is a requirement in String (M) Theory to need 11 dimensions in total to describe how quantum mechanics plays out as it does.
These additional dimensions can be harder to conceptualize and there are a few different ways it can be done.
One method is to say that space itself is 'quantacised', that being space is made up of Plank sized portions of volumes.
(A Plank sized element is the absolute smallest size that has a meaningful measurement in quantum mechanics).
And although this may seem like such volumes are reverting back to our familiar 3D spatial dimensions, you'd be sort of correct. However, here at this scale, it is the interactions of these plank volumes and how they are compacted or moving relative to each other that 'form' the 7 additional dimensions to make up the 11 in total.
Its sort of hard to accept how these additional dimensions are created but one way to think about this is to accept how something becomes "not something" when you divide it so much that you end up with its constituent parts.
So for example, a video I saw recently put forward that you have a bar of gold. If you divide the bar in half, you have two smaller bars of gold. But if you keep dividing these bars, you would get to the point that you have a gold atom - now this is no longer a "bar of gold".
So you keep dividing the gold atom, its no longer even 'gold'. Continue down past quarks and the force 'particles' holding them together, keep dividing down until all that is left is a quantum volume of space. From here nothing can be divided. These quantum volumes must be of a Plank-sized volume but can stretch, twist, bend and provide a form of 'pressure', which gives rise to the additional dimensions that are needed to explain the effects.
So that is my current understanding of a possible method to conceptualize additional dimensions.
There are others and just as a final point to end this post I just want to mention that "flatland" is where many people start, but I found this method to lead to many confusing aspects. But at the same time some very interesting ones. Such as the fact that in our 4D world, a single photon is the same as any other photon in the universe - in terms of properties. This means in our 4D world a photon does not carry distance information with it, which is why we need to revert to parallax methods of measuring distant stars. But if a person living in 5D land (with reference to the 'flatland' concept), were to view an object, they may be able to see photons in 5 dimensions, which could include 'distance', meaning they'd be able to see through walls for example.
All interesting stuff - if not also a bit heavy on the philosophical side of things
..... TLDR version : its a mind f-ck ! .....
Have a read of this, it has a few interesting things about additional dimensions.
https://www.amazon.co.uk/dp/B00O2LM3LW/ref=dp-kind...
Matt's also got a few youtube videos relating to it which are interesting too.
https://www.amazon.co.uk/dp/B00O2LM3LW/ref=dp-kind...
Matt's also got a few youtube videos relating to it which are interesting too.
I don't bother. It is like quantum theory - just trust the mathematical description. Trying to conceptualise it at a macro level leads to confusion. i.e. an electron going round a proton isn't a wave or a particle, it is a probability density function. What that looks like is meaningless, because we can't see them. Ditto 11 dimensions vs 4, it is an outcome of the maths, you don't need to conceptualise them
wisbech said:
I don't bother. It is like quantum theory - just trust the mathematical description. Trying to conceptualise it at a macro level leads to confusion. i.e. an electron going round a proton isn't a wave or a particle, it is a probability density function. What that looks like is meaningless, because we can't see them. Ditto 11 dimensions vs 4, it is an outcome of the maths, you don't need to conceptualise them
Accepted that is one way to treat it all, but conceptualizing things allows the human brain to notice possible relationships or possible interactions in the 'unseen', which then drives an investigation using the language of maths to attempt to model it.Maths can also do the same of course, equations can 'chuck out' unforeseen results leading to the human brain asking questions about that result, leading to then re-model what may be occurring.
I think both maths and concept have to play hand in hand to progress science.
Johnnytheboy said:
Simplistically (because I am an idiot), I imagine the next dimension as being at right angles to the existing ones.
That kind of works for 4th/5th, as does imaginary colour shifting, beyond that, I just get lost, and I can even follow the maths of topology (mostly).Watching the donut-coffee cup transformation also helps somewhat
We did have an interesting thread about this last year.
https://www.pistonheads.com/gassing/topic.asp?h=0&...
I always remember Carl Sagan's talk on Flatland: https://www.youtube.com/watch?v=N0WjV6MmCyM
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