Is there a possiblity of something beyond a hyperspace

[Pandothemic]

Recently I really got into Michio Kaku and the string theory and a question popped up in my mind that he didn't really explain or talk about. If the 11 dimensional hyperspace is truly as the "arena" of universe that have their own dimensions, does the hyperspace itself have the same property of a space and therefore has it's own dimension too ? And by those standards if a hyperspace is still "just" a space ,is there anything beyond it ? 

 

P.S.:I am not a scientist nor a student of science, so please try to respond in simpler terms. Also I'm just very superficially knowledgeable in this subject, so sorry beforehand for any errors in thought.

[studiot]

Good morning Pandothemic and welcome.

Quote

16 minutes ago, Pandothemic said:

P.S.:I am not a scientist nor a student of science, so please try to respond in simpler terms. Also I'm just very superficially knowledgeable in this subject, so sorry beforehand for any errors in thought.

 

 

Gosh string theory is heavy going and not for the faint hearted.

 

As an amateur you need to be aware that scientists use ordinary words in very special ways and this can easily lead someone trying to misunderstand something a scientist has said so be careful.

Here you need to understand what is meant by a dimension and a space in general as well as 'space' and dimension in particular.

 

Do you understand the idea of graphs or plots?

Edited January 5, 2018 by studiot

[Pandothemic]

3 minutes ago, studiot said:

Good morning Pandothemic and welcome.

 

Gosh string theory is heavy going and not for the faint hearted.

 

As an amateur you need to be aware that scientists use ordinary words in very special ways and this can easily lead someone trying to misunderstand something a scientist has said so be careful.

Here you need to understand what is meant by a dimension and a space in general as well as 'space' and dimension in particular.

 

Do you understand the idea of graphs or plots?

Good morning,

Well, I think that graphs and plots are not topics I've been introduced to, so no. But about the other two, I hope I got the definitions right a dimension=1st dimension is a point/dot, 2nd dimension is 2 dots connected with a line and 3rd is a line that has a third line added that goes out of the 2D, adding depth. So I would call it like a form that the particular space takes. So space should be by that thinking a place, where all the matter and antimatter can "exist" and where basically everything happens therefore even the surface of Earth is also space. Of course correct me if I'm wrong. I know just the dumbed down definitions, really. Always glad to learn more since Wikipedie and other sources never really answer anything because of how broad they are.

[studiot]

OK that's a useful reply.

Science moved forward tremendously when the number zero was invented.

29 minutes ago, Pandothemic said:

But about the other two, I hope I got the definitions right a dimension=1st dimension is a point/dot, 2nd dimension is 2 dots connected with a line and 3rd is a line that has a third line added that goes out of the 2D, adding depth. So I would call it like a form that the particular space takes.

A dimension is a scale against which we can measure some property of interest.
(Sometimes we can measure several properties against the same scale.)

So a single point is not a scale it cannot vary. We say it is of zero dimension.

A line has one dimension.

A sheet of paper has two dimensions, because we can show two independent scales on it.
Note the word independent. This means we can choose any value from each scale, whatever the value of the other scale may happen to be.

A sheet of paper with two scales is a graph or plot.

 

Here are a couple of examples, of the same thing the range of temperatures for a normal human adult.

Notice that we only need one number to specify an actual temperature so the plots can be one dimensional or two dimensional.

 

We call the collection of scales we use the 'space' .

One particular space is the one we live in which has dimensions of length or position.
This is the one you are referring to, but it is not the one String Theory uses.

 

That is enough to digest in one go so I will pause for questions.

 

Edit

 

One question for you for next time.

Have you watched skating demonstrations or competitions on TV or wherever?

In particular have you watched the skaterskating around, then  spinning on the spot?

Edited January 5, 2018 by studiot

[Pandothemic]

13 minutes ago, studiot said:

OK that's a useful reply.

Science moved forward tremendously when the number zero was invented.

A dimension is a scale against which we can measure some property of interest.
(Sometimes we can measure several properties against the same scale.)

So a single point is not a scale it cannot vary. We say it is of zero dimension.

A line has one dimension.

A sheet of paper has two dimensions, because we can show two independent scales on it.
Note the word independent. This means we can choose any value from each scale, whatever the value of the other scale may happen to be.

A sheet of paper with two scales is a graph or plot.

 

Here are a couple of examples, of the same thing the range of temperatures for a normal human adult.

Notice that we only need one number to specify an actual temperature so the plots can be one dimensional or two dimensional.

 

We call the collection of scales we use the 'space' .

One particular space is the one we live in which has dimensions of length or position.
This is the one you are referring to, but it is not the one String Theory uses.

 

That is enough to digest in one go so I will pause for questions.

 

 

 

Woah, pretty difficult to wrap my head around but hopefully I got a hang of it. So that would mean that none of these "scales" just apply to the hyperspace itself ? And therefore nothing that we know a space has (gravity,time,matter,etc.) doesn't apply to the hyperspace ? And also that there is nothing "beyond" the hyperspace because that would mean it just doesn't exist, right ? 

[studiot]

3 minutes ago, Pandothemic said:

Woah, pretty difficult to wrap my head around but hopefully I got a hang of it. So that would mean that none of these "scales" just apply to the hyperspace itself ? And therefore nothing that we know a space has (gravity,time,matter,etc.) doesn't apply to the hyperspace ? And also that there is nothing "beyond" the hyperspace because that would mean it just doesn't exist, right ? 

Woah indeed, I'm trying to build up to hyperspace but I need to get the ducks in a row first.

Please look at the question in my last edit as it leads directly to explaining the difference between string theory space, other hyperspaces and ordinary space.

Here it is again.

One question for you for next time.

Have you watched skating demonstrations or competitions on TV or wherever?

In particular have you watched the skater skating around, then  spinning on the spot?

Edited January 5, 2018 by studiot

[Pandothemic]

2 minutes ago, studiot said:

Woah indeed, I'm trying to build up to hyperspace but I need to get the ducks in a row first.

Please look at the question in my last edit as it leads directly to explaining the difference between string theory space, other hyperspaces and ordinary space.

Here it is again.

One question for you for next time.

Have you watched skating demonstrations or competitions on TV or wherever?

In particular have you watched the skaterskating around, then  spinning on the spot?

Oh ok. Yes, I've seen skaters do that before.

[studiot]

Just now, Pandothemic said:

Oh ok. Yes, I've seen skaters do that before.

Excellent.

 

OK so let's think of a stack of bricks.

This has 3 dimensions in what we call ordinary 3D space.

Length, breadth and height.

I can choose to make my pile any combination of length, breadth and height I like.

So if you tell me to make a stack of bricks I will ask, how tall, how wide and how long boss.

3 numbers, quite independent.

And that is all that is needed to completely describe the stack.

 

But Physics is more complicated than this.

Some properties cannot be decribed by a single number and the activity of the skater is one such.

As the skater moves about the rink, just skating along, 3 numbers will do to say exactly what the skater is doing.

But as soon as she starts to spin, another property comes into play.

No only can she spin but she can vary the spin by extending her arms or drawing them in.

 

So we need additional data to specify her activity, including the extension of her arms.

 

This type of data is a form of hyperspace that is superimposed upon normal 3D space, but does not use up one of the existing dimensions.

The dimensions in String theory are similar. They refer to additional information to describe the 'strings'.

 

I have to leave now but please ask away an I, or someone else will try to answer later.

 

[Pandothemic]

9 minutes ago, studiot said:

Excellent.

 

OK so let's think of a stack of bricks.

This has 3 dimensions in what we call ordinary 3D space.

Length, breadth and height.

I can choose to make my pile any combination of length, breadth and height I like.

So if you tell me to make a stack of bricks I will ask, how tall, how wide and how long boss.

3 numbers, quite independent.

And that is all that is needed to completely describe the stack.

 

But Physics is more complicated than this.

Some properties cannot be decribed by a single number and the activity of the skater is one such.

As the skater moves about the rink, just skating along, 3 numbers will do to say exactly what the skater is doing.

But as soon as she starts to spin, another property comes into play.

No only can she spin but she can vary the spin by extending her arms or drawing them in.

 

So we need additional data to specify her activity, including the extension of her arms.

 

This type of data is a form of hyperspace that is superimposed upon normal 3D space, but does not use up one of the existing dimensions.

The dimensions in String theory are similar. They refer to additional information to describe the 'strings'.

 

I have to leave now but please ask away an I, or someone else will try to answer later.

 

Ooooh, that is pretty interesting. Thank you for a more detailed clarification. However in on of your responses you mentioned hyperspace"s" not just one. That means there is even more hyperspaces that contain other ordinary spaces ?  EDIT:And by that standard hyperspaces (if there are more) would have to also be located "somewhere" right? In another kind of space maybe ? 

Edited January 5, 2018 by Pandothemic
an extension of a question

[Mordred]

Each space represents a different graph or plot. These different spaces can occupy different dynamics being described in the identical volume. In String theory which employs QM these different spaces more often than not describe different potentials of interactions within a compact potential region.

 For example if you have a spacetime volume, you first describe the spacetime geometry, then you can describe the potential variations due to say the electromagnetic field at some finite portion of the above region, or the strong force etc.

 The fundamental goal of string theory is to start with a fundamental string (waveform) that all other particles arise from. Each particle also has a wavefunction (several actually each describing different particle properties).

The fundamental string is usually considered to be the graviton spin 2 but not always...Don't confuse this with thinking that gravity causes all other particles lol.

It is a unification state of thermal equilibrium where all particles become indistinguishable (thermal equilibrium) commonly called supergravity which later on different forces decouple from. Ie electroweak symmetry breaking. ( this gives rise to different strings in the same volume) much like a waveform has harmonics.Think of an irregular waveform that cannot be described by a single sinisoidal equation.

The irregularities can be broken down into the harmonic sinusoidal waveforms that make up the standing wave. Some waveforms from different fields ie electromagnetic causes interference with other waveforms ie strong force, weak force etc. So a reading of a multiparticle field has numerous interferences within itself. Each of these interferences and interactions forms the individual strings and spaces used to model each individual string (waveform) of the same overall fundamental string (spacetime region)

 

[studiot]

2 hours ago, Pandothemic said:

Ooooh, that is pretty interesting. Thank you for a more detailed clarification. However in on of your responses you mentioned hyperspace"s" not just one. That means there is even more hyperspaces that contain other ordinary spaces ?  EDIT:And by that standard hyperspaces (if there are more) would have to also be located "somewhere" right? In another kind of space maybe ? 

Glad we are getting somewhere.

Physics is fun.

 

So back to the skater.

There is a difference between the spin and the position on the ice.

We have a scale metres or whatever of across the ice and along the ice and a height scale when she jumps in the air.

The important thing is that, like the length, breadth and height of the brick stack, along and across each require only one number on a scale.
(Just like the thermometer scale I posted earlier)

But spin does not take up any of these and further

Whilst it is true that there is a scale of spin speed which only needs one number,

Spin cannot be described in only one number.

As the song goes, "it takes two baby"

Because spin can be either clockwise or anticlockwise.
So this is not even on  scale.
Further sometimes the skater doesn't spin about a vertical axis, but swings her legs about an inclined axis as she hops from one leg to the other.

This is the simplest example I can think of of what I mean by something more complicated.

So spin can only be completely described by an abstract concept, which has dimensions of its own that do not take up any space in the 'real 3D world of up, across and forward yet still interface with that 'real' world.

Such dimensions are called sometimes phase dimensions and the space they occupy is called phase space.

Because they are all made up abstract ideas there is not limit to the number of dimensions in phase space - it is just limited to you imagination and ingenuity.

 

Hyperspace just literally means beyond (real) space.
I have added the real in brackets because that is its usual meaning but some (such as string theorists) include abstract dimensions from phase space.

As to the extension of 3D real space to 4D or 5D or more.

Scientists have looked but can find no evidence for the existence of hyperspaces greater than 3D (ignoring time).

One simple test is that just as 3D objects can obstruct the view of each other and reveal each other as they move in 3D space and also cast shadows on each other,

so we would expect to observe the 3D equivalent if we were 3D beings embedded (note that word embedded) in a 4D real space.

The lack of shadows is particularly telling since 2D beings could observe shadows cast by say the Moon or clouds on the 2D surface of our 3D Earth.

[Rob McEachern]

1 hour ago, studiot said:

Spin cannot be described in only one number.

As the song goes, "it takes two baby"

Because spin can be either clockwise or anticlockwise.

But a spin measurement can. If there are a number of skaters (an ensemble), all spinning one way or the other, and I ask you to give me a one-bit (one number) answer to the following question, you will indeed be able to describe the spin with a single number: If you look down on the skaters from above, do they all appear to be spinning clockwise (1) or anticlockwise (-1)? The number of numbers (components) required to describe spin is critically dependent on whether or not the description pertains to before, or after, an actual observation. One might say that the "collapse of the wavefunction" corresponds to the collapse of the number of numbers required by the description. Now if I asked you how fast they were each spinning, or to determine their average speed, your answer (assuming you could actually, reliably measure their speeds) may require either more numbers, more bits per number, or both.

Edited January 5, 2018 by Rob McEachern
fix a typo.

[swansont]

15 minutes ago, Rob McEachern said:

But a spin measurement can. If there are a number of skaters (an ensemble), all spinning one way or the other,

Which is additional information you are omitting in your scenario.

Quote

and I ask you to give me a one-bit (one number) answer to the following question, you will indeed be able to describe the spin with a single number: If you look down on the skaters from above, do they all appear to be spinning clockwise (1) or anticlockwise (-1)?

What if the spin axis is not vertical?

Quote

The number of numbers (components) required to describe spin is critically dependent on whether or not the description pertains to before, or after, an actual observation. One might say that the "collapse of the wavefunction" corresponds to the collapse of the number of numbers required by the description. Now if I asked you how fast they were each spinning, or to determine their average speed, your answer (assuming you could actually, reliably measure their speeds) may require either more numbers, more bits per number, or both.

And the speed is part of what was referred to earlier. Vectors have a magnitude and a direction.

Which means that you can have a one-bit answer if you narrow the situation down to where you are only looking for one bit of information. Which I don't think is all that earth-shattering.

[Rob McEachern]

3 minutes ago, swansont said:

Which is additional information you are omitting in your scenario

You (and many, many others) have assumed that the observer is the entity that has committed the omission. But it is possible that the observed is the cause of the omission, and there is consequently nothing else there capable of ever being reliably measured. Your assumption is quite reasonable in the classical realm. But that may not be the case in the quantum realm. My  point is, that all or most of the seeming weirdness of quantum phenomenon, may be due to that assumption.

 

5 minutes ago, swansont said:

Vectors have a magnitude and a direction

Which may be completely unmeasurable or even detectable, in the quantum realm, due to limited interaction duration, limited bandwidth and limited signal-to-noise ratio (the cause of the omission). In which case it is possible (and, I would argue, even likely in quantum scenarios) that there is only a single bit of information that can ever be reliably extracted, from any set of measurements, made on such objects.

[swansont]

31 minutes ago, Rob McEachern said:

You (and many, many others) have assumed that the observer is the entity that has committed the omission. But it is possible that the observed is the cause of the omission, and there is consequently nothing else there capable of ever being reliably measured. Your assumption is quite reasonable in the classical realm. But that may not be the case in the quantum realm. My  point is, that all or most of the seeming weirdness of quantum phenomenon, may be due to that assumption.

 

Which may be completely unmeasurable or even detectable, in the quantum realm, due to limited interaction duration, limited bandwidth and limited signal-to-noise ratio (the cause of the omission). In which case it is possible (and, I would argue, even likely in quantum scenarios) that there is only a single bit of information that can ever be reliably extracted, from any set of measurements, made on such objects.

The example was a skater, which is classical. 

[Phi for All]

1 hour ago, Rob McEachern said:

You (and many, many others) have assumed that the observer is the entity that has committed the omission. But it is possible that the observed is the cause of the omission, and there is consequently nothing else there capable of ever being reliably measured. Your assumption is quite reasonable in the classical realm. But that may not be the case in the quantum realm. My  point is, that all or most of the seeming weirdness of quantum phenomenon, may be due to that assumption.

 

Which may be completely unmeasurable or even detectable, in the quantum realm, due to limited interaction duration, limited bandwidth and limited signal-to-noise ratio (the cause of the omission). In which case it is possible (and, I would argue, even likely in quantum scenarios) that there is only a single bit of information that can ever be reliably extracted, from any set of measurements, made on such objects.

!

Moderator Note

It seems the OP is doing well on this topic without an unnecessary branch-off into entanglement. Please stop.

 

[studiot]

2 hours ago, Rob McEachern said:

But a spin measurement can.

 

Rob, you misunderstand me.
Which surprises me because I have said enough times in this thread,  that a dimension reuqires a scale, not a point number and that a point has zero dimensions.

So 1 and 0 or 1 and -1 or 1/2 and -1/2 or the more complicated spins that Mordred mentioned don't cut it as a dimension in their own right.

What I am saying is that there are more complicated objects that act at / interface with the 3D real word at one point that have many parts.
A vector has two, but I doubt if the OP understands vectors so should I introduce them or worse cartesian tensors, the simplest of which have 9 parts (getting up towards strings there).
Perhaps you would like to discuss spin in terms of the inertia tensor?

[Rob McEachern]

57 minutes ago, studiot said:

What I am saying is that there are more complicated objects that act...

I do understand. What I am saying is that there are also less complicated objects that act... But a moderator has requested that I stop, so I shall.

[studiot]

 

18 minutes ago, Rob McEachern said:

I do understand. What I am saying is that there are also less complicated objects that act... But a moderator has requested that I stop, so I shall.

The moderator suggested we limit the discussion to classical phenomena.

 

I usually use classical phenomena because I try to find examples the OP may have personal experience of and are simple to compass.

 

Remember also that analogies are never exact.

Edited January 5, 2018 by studiot

[geordief]

13 hours ago, studiot said:

 

The moderator suggested we limit the discussion to classical phenomena.

 

I usually use classical phenomena because I try to find examples the OP may have personal experience of and are simple to compass.

 

Remember also that analogies are never exact.

Is it possible to use phase space to  make predictions in scenarios involving classical spin that are impossible using other methods? 

[studiot]

17 minutes ago, geordief said:

Is it possible to use phase space to  make predictions in scenarios involving classical spin that are impossible using other methods? 

No and yes.

The method is known as the method of generalised coordinates, and is tied up with 'degrees of freedom'.

No because it does not, of itself, introduce any method that is the only way of doing the calculations.

Yes because it is sometimes the most practicable method, especially with a computer since it is basically an array (matrix) method.

However we have become very cunning in reducing the calculation burden by the clever use of physical knowledge.
For instance with my skater we can remove an entire (vertical) dimension if we do no allow her to jump.

As regards classical spin generalised coordinates, the full works would introduce moment of inertia and products of inertia and an axis of spin that can point anywhere in 3D.

Happy googling on those terms.

[geordief]

Would complex numbers be classed as an example of phase space?

I think we have to ignore any possible relevance of QM to my question for the purposes of this thread....

[studiot]

25 minutes ago, geordief said:

Would complex numbers be classed as an example of phase space?

I think we have to ignore any possible relevance of QM to my question for the purposes of this thread....

Yes complex numbers could be so classed, though they would not normally be referred to in this way.

Multiplication by 'i 'can be regarded as a rotation through 90^o, to 'somewhere' Bthe out of the original domain (in this case the real numbers)

This is where the classification scheme becomes a bit murky because it has grown up from disparate sources.

Because the complex numbers are numbers in their own right.

 

But also generalised coordinates are a linear construct, which is why they are favoured for computer implementation.

We have for variables X₁, X₂, X₃.......Xn.  which fully describe a system

The generalised coordinates are

aX₁ + bX₂ +cX₃ +......

Where a, b, c... are coefficients (numbers real or complex)

This is linear and can easily be handled in computer form.

If a, b, c... are allowed to become functions in their own right then the construct becomes non linear and we have a sort of generalised 'generalised coordinates'

I do believe I have tried to explain (to you) before how this applies to cartesian vectors ( in Euclidian space), perhaps you are ready for it now?

 

Edited January 6, 2018 by studiot

[geordief]

1 hour ago, studiot said:

I do believe I have tried to explain (to you) before how this applies to cartesian vectors ( in Euclidian space), perhaps you are ready for it now?

I am  not sure .I have tried to find the posts or threads you are referring to. It is not this one is it?

 

 

I would need to know the ground I was standing on before taking up your time and my own  -although going over old half worked ground is something I would normally  expect to be particularly rewarding.

Edited January 6, 2018 by geordief

[studiot]

21 minutes ago, geordief said:

I am  not sure .I have tried to find the posts or threads you are referring to. It is not this one is it?

 

 

I would need to know the ground I was standing on before taking up your time and my own  -although going over old half worked ground is something I would normally  expect to be particularly rewarding.

 

I can't find it either, but I have given up finding old threads on this 'new improved' Scienceforums.

Yes that thread does contain a hint before that long exposition from Xerxes, but is not the one I was thinking of.

 

I think it would be too far off topic to reproduce the presentation here, but if you would like to start a new thread to discuss what happens when you place a vector at some point in a vector field and then try to rotate it we could try again there.