Might all physical quantities be quantized?

[somega]

TL;DR Summary

Could it be that all quantities (space, time, mass, frequency, ...) are quantized?

Please take a look at my first thought experiment:
You have 2 coins to place on the table.
The distance between them may be between 0 (inclusive) and 1 meter (exclusive).
So if you want to store the number 15 you simply set the distance to 0,15m.
You can later read the information by measuring the distance.

Now if space was not quantized you could store unlimited information using the two coins by simply increasing precision.
To store a number with 5 digits you would simply set the distance to 0,XXXXX.
In other words: You have limited resources (1 meter) but you can store unlimited information in it.
Wouldn't it be be like storing 100GB on a 1GB disk?

A similar experiment can be done with time.
You have to send a light signal to your friend then wait between 0 (inclusive) and 10 second (exclusive).
So to send the number 15 you simply wait 1,5 seconds.
If time was not quantized it would be possible to put endless information in the time difference which is itself limited to 10 seconds.
Wouldn't it be like sending 1TB/s over an 1 GBit/s cable?

You could do similar experiments with other quantities like force and mass but also frequency.

 

[berkeman]

Summary: Could it be that all quantities (space, time, mass, frequency, ...) are quantized?

Now if space was not quantized you could store unlimited information using the two coins by simply increasing precision.

And what transmitter and receiver are you going to use that have infinite resolution?

 

[somega]

And what transmitter and receiver are you going to use that has infinite resolution?

Of course in reality it will fail because you can't build such a device.
But in the experiment it could be a device which tells you 10^6 digits per second.

 

[DaveE]

Certainly the measurements are quantized.
https://en.wikipedia.org/wiki/Uncertainty_principle

 

[sophiecentaur]

And what transmitter and receiver are you going to use that has infinite resolution?

I can't find a reference to RANDOM NOISE in this thread yet. That's the nub of the question because it dogs every measurement. Below a certain level the uncertainty in any measurement requires longer and longer time to determine its value. Given a long enough processing time, you can measure your distance to any precision you want. i.e your TX / RX would need bandwidths approaching zero.

 

[256bits]

Summary: Could it be that all quantities (space, time, mass, frequency, ...) are quantized?

You have limited resources (1 meter) but you can store unlimited information in it.

The thought experiment stores only one piece of information - the distance to high precision, which you then compare to the exact base value of 1.000... meter to get a ratio, which is pretty much what all distance measurements are - a ratio of the measured distance to a standard distance measured in a unit agreed upon by committee. You could have used angstrom, cm, AU's, light years as the base unit. Which is probably not your point at all.
But for the number system, there is as many infinite points in a 1 cm length as there is in a light year length.
So if space is quantized, which length measurement breaks down first - the one using the shorter base distance, such as cm, or the one using the longer base distance, such as ly?

 

[sophiecentaur]

So if space is quantized, which length measurement breaks down first - the one using the shorter base distance, such as cm, or the one using the longer base distance, such as ly?

Nice curve ball there!
I think it boils down to the range within which the measurement can fit - i.e. the maximum possible value for length is the 'unit' and the minimum value is defined by the random error. If your maximum is 1LY ( cm, foot, angstrom) then you cannot describe 2LY ( cm, foot, angstrom). In practical terms, there are many obvious reasons why measuring small values with a coarse instrument would be a problem (surveyor's chain to measure the width of a watch hair spring etc.)