Relation between dimensions

[Strange]

18 minutes ago, JohnMnemonic said:

Because we don't know about anything, what would be smaller, than a photon...

What do you think the size of a photon is?

[JohnMnemonic]

Quote

What do you think the size of a photon is?

Well, it's hard to speak about definitive volume of a photon - it's more about the wavelenght and amplitude of light. But the smallest known volume of space, in which a photon can be located in a single moment of time, would be probably the Planck's lenght

[koti]

4 hours ago, StringJunky said:

Physically, wouldn't a  point be the smallest unit of space?

In Euclidean geometry a point has no dimensions, no volume or area. A good practical example of this is a focal point on a camera lens - it has no size so it's not a unit of space but it's very much a point. In QM an electron (point particle) cannot be spatially localized because Heisenberg...and its size is zero...but it has mass so it has volume. Only interactions of electrons can be localized so in that context a point can be a unit of space - kinda but not really because super-strings...but the bottom line is that we don't know if spacetime is pixelated at it's smallest scale. 

Edited May 12, 2018 by koti

[StringJunky]

13 minutes ago, koti said:

In Euclidean geometry a point has no dimensions, no volume or area. A good practical example of this is a focal point on a camera lens - it has no size so it's not a unit of space but it's very much a point. In QM an electron (point particle) cannot be spatially localized because Heisenberg...and its size is zero...but it has mass so it has volume. Only interactions of electrons can be localized so in that context a point can be a unit of space - kinda but not really because super-strings...but the bottom line is that we don't know if spacetime is pixelated at it's smallest scale. 

If it is pixellated then that would constitute a point since that would be the smallest unit of space. I realise in maths a point is an abstract article with zero spatial extension.

[Strange]

7 hours ago, JohnMnemonic said:

But the smallest known volume of space, in which a photon can be located in a single moment of time, would be probably the Planck's lenght

Any evidence for this?

[studiot]

8 hours ago, JohnMnemonic said:

I think, that -1 is actually "bigger" than 0.

 0 is not a unit. We can make a unit from any measured value - even candies or apples  But then 1 apple becomes the unit of apples. 0 apples, means that there's no apples to count (measure).

While speaking about XYZ dimensions, then 1 and -1 define distances  in opposite directions, from the center of a frame (point 0). So, it''s the distance, which becomes the unit.

 

Well of the fundamental units measured in Science (eg mass, length, time etc) one is number of particles, N.

This appears in many equations and has no quantum uncertainty or Plank size associated with it.
The smallest value of N is zero.

 

7 hours ago, koti said:

In Euclidean geometry a point has no dimensions, no volume or area. A good practical example of this is a focal point on a camera lens - it has no size so it's not a unit of space but it's very much a point. In QM an electron (point particle) cannot be spatially localized because Heisenberg...and its size is zero...but it has mass so it has volume. Only interactions of electrons can be localized so in that context a point can be a unit of space - kinda but not really because super-strings...but the bottom line is that we don't know if spacetime is pixelated at it's smallest scale. 

Nice summary, I particularly like the focal point example. +1

[Mordred]

I concur Studiot, nice post Koti the quality and accuracy of your posts has greatly improved in the last few years. 

 This seems to me a good time to introduce Compactification and the concept of Dimensional reduction. These are two important techniques to understand for a great number of theories. Particularly in understanding higher dimensions such as the Kaluzu Klien mentioned in the latter link. In modern treatment the compact dimension is the U(1) symmetry group and describes a circular motion too small to be measurable (under symmetry treatments) hence the U(1) gauge is oft described as the circle group.

https://en.m.wikipedia.org/wiki/Compactification_(physics)

https://en.m.wikipedia.org/wiki/Dimensional_reduction

edit oops first link not second lol anyways the term cylinder that Kaluzu originally used is under gauge groups treatnent now referred to as a circle bundle as described in the following link

https://en.m.wikipedia.org/wiki/Kaluza–Klein_theory

Edited May 12, 2018 by Mordred