Understanding Multidimensional Time

[Ghetalion]

Let's see if I get this thought right!

In accordance with Uncertainty Principle, if we know the location of the particle (space), we cannot know the direction (rate of change/time).

But, if we know X-pos of a particle, then Y-pos and Z-pos cannot be know either since the first axis of measurement will influence the measurement of the other two axes, and thus, invalidating the true location.

What if we add a dimension of time to each axis? By knowing the direction of X-[ps, we cannot know the direction of Y-pos or Z-pos!

Viola! Multidimensional time!

 

[TriTertButoxy]

Let's see if I get this thought right!

In accordance with Uncertainty Principle, if we know the location of the particle (space), we cannot know the direction (rate of change/time).

Actually, its if we know the location of a particle in space precisely, we cannot know its momentum (often related to its velocity ~ rate of change of position with time).

But, if we know X-pos of a particle, then Y-pos and Z-pos cannot be know either since the first axis of measurement will influence the measurement of the other two axes, and thus, invalidating the true location.

This is factually incorrect. In quantum mechanics, the three position coordinates are compatible observerables. Thus, I am allowed to know the X-pos, Y-pos and Z-pos of a particle to arbitrary certainty.

What if we add a dimension of time to each axis? By knowing the direction of X-[ps, we cannot know the direction of Y-pos or Z-pos!

Viola! Multidimensional time!

Haha, nice try, but the uncertainty principle is only between the position coordinate, and its (canonical conjugate) momentum. And it just so happens that the momentum of the particle is related to its motion through space over time. --perhaps that's where the confusion was.

 

[Ghetalion]

This is factually incorrect. In quantum mechanics, the three position coordinates are compatible observerables. Thus, I am allowed to know the X-pos, Y-pos and Z-pos of a particle to arbitrary certainty.

Is that true in practice however? How can one measure three dimensions simultaneously with precise accuracy in all three dimensions?

I was aware of Non-Communitive Uncertainty coming into play on this.

 

[Rach3]

Is that true in practice however? How can one measure three dimensions simultaneously with precise accuracy in all three dimensions?

I was aware of Non-Communitive Uncertainty coming into play on this.

"Non-commuting", not "communitive".

The position operators all mutually commute, so this doesn't apply. If an electron hits a phosphor screen, you see its location in three dimensions don't you? Same with cloud chambers or bubble chambers. Detectors for particle colliders have all sorts of schemes to pinpoint particles in 3D, like the ones at http://www.bnl.gov/rhic/experiments.htm .

 

[Ghetalion]

"Non-commuting", not "communitive".

The position operators all mutually commute, so this doesn't apply. If an electron hits a phosphor screen, you see its location in three dimensions don't you? Same with cloud chambers or bubble chambers. Detectors for particle colliders have all sorts of schemes to pinpoint particles in 3D, like the ones at http://www.bnl.gov/rhic/experiments.htm .

Yes, you see it in three dimensions. But that's not what is getting argued. It not like you see the X and all of a sudden you never see the Y and the Z. They collapse, their precision is forever lost.

The precision of measuring those dimensions is what I'm talking about.

 

[chroot]

Honestly, Ghetalion? Try to learn some quantum mechanics before attempting to find holes in it.

When people say "the position observable," they're not referring to a single dimension. They're referring to all spatial dimensions at once.

You're getting tripped up because many QM problems are cast in one- or two-dimensional form, simply to make the math easier to follow. When you measure the position of something in the real world, you get all three components.

- Warren

 

[Ghetalion]

Honestly, Ghetalion? Try to learn some quantum mechanics before attempting to find holes in it.

When people say "the position observable," they're not referring to a single dimension. They're referring to all spatial dimensions at once.

You're getting tripped up because many QM problems are cast in one- or two-dimensional form, simply to make the math easier to follow. When you measure the position of something in the real world, you get all three components.

- Warren

BUT DON'T TAKE MY WORD FOR IT!

http://en.wikipedia.org/wiki/Noncommutative_quantum_field_theory

 

[ZapperZ]

BUT DON'T TAKE MY WORD FOR IT!

http://en.wikipedia.org/wiki/Noncommutative_quantum_field_theory

You should be very concerned that the best you can do is cite something of Wikipedia.

Zz.

 

[BoTemp]

Ghetalion, that's just one of many theories, as far as I know there's no experimental evidence to support it (or refute it). According to Quantum Mechanics as currently accepted, the spatial operators commute and there's no reason why one can't measure all three coordinates simultaneously.

Of course this can't be done perfectly in practice, because any apparatus has some small error in it, but that doesn't make the slightest bit of difference to the theory. The HUP doesn't take "margin of error of equipment" into account; that limit can be made arbitrarily small.

I don't see how noncommuting spatial measurements would lead to multi-dimensional time. Never followed your logic in the first place.

 

[Rach3]

Odd, that wiki article doesn't talk about position in non-rel. QM, but rather some exotic theoretical work in string theory. They link to the review paper in Rev. Mod. Phys:

http://prola.aps.org/abstract/RMP/v73/i4/p977_1?qid=a81527af6e5a2fa2&qseq=1&show=10

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states...

It doesn't support your OP at all.