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Old May 20th 2019, 02:04 PM   #11
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Originally Posted by pittsburghjoe View Post
You didn't want a new dimension to exist anywhere else
Let me be a bit clearer: You can't mess with the number of dimensions in space-time. (Let's agree to ignore things like Supergravity and String Theory for now.)

Take a look at my comment about spin. The spin of a, say, electron is 1/2. Then there are two states to consider:
$\displaystyle |~+1/2~> = \dfrac{1}{\sqrt{2}} \left ( \begin{matrix} 1 \\ 0 \end{matrix} \right )$

and
$\displaystyle |~-1/2~> = \dfrac{1}{\sqrt{2}} \left ( \begin{matrix} 0 \\ 1 \end{matrix} \right )$

These vectors are not based in space-time but in a 2D Hilbert space. Despite adding two more dimensions we have to put them a bit "off to the side" when counting dimensions. Hilbert space does not live in space-time, but rather gives us "room" to create new dimensions to fully express quantities of interest. These dimensions are called "internal spaces."

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Old May 20th 2019, 02:23 PM   #12
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These vectors are not based in space-time but in a 2D Hilbert space. Despite adding two more dimensions we have to put them a bit "off to the side" when counting dimensions. Hilbert space does not live in space-time, but rather gives us "room" to create new dimensions to fully express quantities of interest. These dimensions are called "internal spaces."

You don't need to go to fancy spaces and names to see this effect.
It is also the effect which causes much confusion, although I have never seen it included in any textbook or course.

Consider a simple bicycle pedal crank arm.

Draw yourself the chainwheel, pedal and crank with the origin at the pivot.

Now draw in a few force vectors for the force the foot applies to the pedal as the chainwheel rotates.
Note that this applied force varies in both magnitude and direction at different points around the rotation.

Now tell me where those force vectors 'live' and I will tell you the next stage.

Note I have tried drawing all this out for folks in the past and they never 'get it' until they try to draw this for themselves.
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Last edited by studiot; May 20th 2019 at 02:27 PM.
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Old May 21st 2019, 05:12 AM   #13
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Antimatter is known to be unstable ..maybe so unstable it never collects large enough to become visible? Maybe Quantum Fluctuation lives in this dimension. You are saying space-time won't support a negative dimension?
If internal spaces are seen as a joke I'd rather shoot for a dimension.
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Old May 21st 2019, 06:07 AM   #14
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It's very disappointing when you make the effort to help someone and they don't even answer you.

Joe you have the germ of a very important idea, but you need the terminology to express it properly.
You may be suprised to learn that the object you should place on your drawing looks rather like your avatar and is called a tensor.
It comes complete with all its own dimensions.
There is an alternative way to describe this with Venn Diagrams from set theory, but it is rather abstract, though simpler.
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Old May 21st 2019, 06:52 AM   #15
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This is the most credence I've gotten, a germ, yay!!!
Please just spit out what you know instead of giving me riddles.
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Old May 21st 2019, 08:51 AM   #16
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Originally Posted by pittsburghjoe View Post
Antimatter is known to be unstable ..maybe so unstable it never collects large enough to become visible? Maybe Quantum Fluctuation lives in this dimension. You are saying space-time won't support a negative dimension?
If internal spaces are seen as a joke I'd rather shoot for a dimension.
Antimatter is just as stable as matter. The fact that it doesn't live for so long is that it is surrounded by matter. When it runs into matter they both interact and both are destroyed. It is quite visible in small amounts and we can keep it for as long as we like in magnetic "bottles" to keep it away from matter.

And yes, space-time does not support a negative dimension.

Internal spaces are no joke. As to QM I can't say that they are actually physical... So far as I know there is no way to detect them. But as Mathematical constructs the ones I've been talking about and what studiot mentioned are very valuable. (I've got my head sort of stuck on the QM thing as that's my area but studiot's example is more pertinent to what you are talking about.)

Originally Posted by pittsburghjoe View Post
This is the most credence I've gotten, a germ, yay!!!
Please just spit out what you know instead of giving me riddles.
No one is "spitting out" riddles. We are trying to give you facts. Studiot is simply giving you good hints so you can work out the answer... Which is one of the better ways of teaching.

My suggestion is for you to do some more studying. You have presented a group of what you believe to be facts that aren't actually facts. You need to improve on your basic Physics.

-Dan
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Old May 21st 2019, 09:21 AM   #17
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Lost in Translation

We have a number of members who's native language is not English
and we often see the confusion and misunderstandings this can cause.

The native language of Physics is Mathematics,
I struggle when the "native speakers" discuss deeper physics.

I am quite happy to throw matrices about (I use them daily at work),
but I have not managed to properly get my head around tensors.
I think I could master possibly tensors, if I really applied myself to the problem,
but when you start taking Hilbert spaces, I am fairly sure that I would struggle, even with full time tuition and dedicated study.
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Old May 21st 2019, 10:32 AM   #18
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https://www.degruyter.com/view/j/zna...59_s_007_s_006
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Old May 21st 2019, 10:33 AM   #19
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Originally Posted by Woody View Post
...but when you start taking Hilbert spaces, I am fairly sure that I would struggle, even with full time tuition and dedicated study.
Actually it's mostly Linear Algebra. It just sounds really bad. (Okay, it can get nasty in some places but most of it isn't that bad. It just sounds that way.)

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Old May 21st 2019, 10:38 AM   #20
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Originally Posted by pittsburghjoe View Post
I've looked through the Introduction and I see nothing wrong with it. But nothing in it nullifies what I've been saying. I'll try to take a look at the full thing later. However my comments remain: You need to work on the basics, not the advanced stuff. If you don't understand the basics you will get things wrong.

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