[talanum1 (OP)]

Because the zero point in space is not clearly defined. Space has positive points with negative points in between, so zero for the negative points is slightly to the right of the zero of positive points. Should you chose to measure the distance using negative points, the distance should be shorter or larger than using positive points. Thus the distance is uncertain by a Planck length.

It is for this reason that one may choose the origin anywhere.

[pzkpfw]

What are "positive points"?
What are "negative points"?
Why are there "negative points?" between "positive points"?
If "negative points" are between "positive points", why must zero (of -ve) be to the right of zero (of +ve)?
Why does "right" make sense in 3D (or rather 4D) space?
Why does measurement with "negative points" make shorter distances than with "positive points"?

[Bored chemist]

Thus the distance is uncertain by a Planck length.

In a lot of cases the uncertainty is much bigger than the Planck length

On the other hand, the uncertainty in mass can be a lot smaller than the Planck mass.
I have weighed things, on a balance in a lab, which weighed less than the Planck mass.

[talanum1 (OP)]

What are "positive points"?
What are "negative points"?

Positive points are those points best described by positive integers, negative points are those best described by negative integers.

Why are there "negative points?" between "positive points"?

So that one can choose the origin of one's coordinate system anywhere.

Why does "right" make sense in 3D (or rather 4D) space?

Because one can choose one's x-axis pointing to the right.

[talanum1 (OP)]

If the particle is located on a negative point and one measures with positive points, one must measure to the closest positive point and there are two, so in either case, one would be off by a Planck length.

If "negative points" are between "positive points", why must zero (of -ve) be to the right of zero (of +ve)?

It could be on the left too.

Why does measurement with "negative points" make shorter distances than with "positive points"?

See the figure: distance OA is shorter than distance PB.


Length.png (1.58 kB . 570x122 - viewed 1922 times)

[Bored chemist]

Positive points are those points best described by positive integers, negative points are those best described by negative integers

Is the end of your nose better described as positive or negative?
The question doesn't make sense, does it?
So your definition does not make sense either.

Because one can choose one's x-axis pointing to the right.

Or not.
So your statement about "

zero for the negative points is slightly to the right of the zero of positive points

does not make sense.

So that one can choose the origin of one's coordinate system anywhere.

That also makes no sense.

[puppypower]

If the measured object, is off by the Planck length, then you know where it is by simply adding the extra length to your measurement.

Reference is relative, therefore each reference can see things in a different way in terms of their energy balance. The uncertainty is because each reference does not see eye to eye or play by the exact same rules.

One way to create this situation is with differences in velocity. For example, in the twin paradox each twin ages differently, therefore time propagation and movement through space is not the same for both references. We cannot just assume we, the measurer, are the center of the universe and expect the other to play along by our reference rules. The result of this arrogance is the uncertainty .

For example, the nucleus of an atom is basically stationary; stationary twin. The electron moves at a  fraction of the speed of light. They are not in the exact same references, so the rules for each are slightly different. Electrons age slower than protons, which is a big difference in charge not often mentioned. If we assume both age the same, we will get wave probability functions for electron position. The nucleus is not modeled the same way since it is assumed to be with us at the center of the universe.

[Bored chemist]

Electrons age slower than protons, which is a big difference in charge not often mentioned.

No
Electrons don't age.