Do you think quantified things exist in reality?

[Hacker Jack]

TL;DR

What does quantum physics say about quantifying things? Explain to a layman?

For example, measurements and how we have set points of measurements, and an infinite amount of increments in between them. Do you this measuring system exists in reality? What is an alternative way of looking at the world in a quantified way (or non quantified way) other than the current measuring system where we put an infinite increment of distant between two set points. What does that say about measuring at heart if there is an infinite amount of increments between two set points, what are we really measuring?

 

[anuttarasammyak]

Say we measure position of an electron be between x and x+dx, as we decrease dx for precise measurement, our experiment inevitably makes many pairs of electron-positron there so it is a mess.
Measurement is interaction of objects and measuring apparatus. QM explains about such interaction well but it does not say about values taken by object without measurement that have been existing without doubt in classical mechanics and thus in our daily life.

 

[hutchphd]

Summary:: What does quantum physics say about quantifying things? Explain to a layman?

Do you this measuring system exists in reality?

I find the a continuum of measurements much more disconcerting than quantization. To me it is unclear whether quantum mechanics somehow describes a strange clockwork or describes our limitations in seeing the clockwork but it seems nonetheless inevitable.

 

[phinds]

What does that say about measuring at heart if there is an infinite amount of increments between two set points ...

It says you need to look up Zeno's Paradox. It will explain things.

 

[Nugatory]

For example, measurements and how we have set points of measurements, and an infinite amount of increments in between them.

When you read any modern physics paper, you will see that all the measurements are written to look something like $9.1093837015\pm{0.0000000028}\times{10}^{-31}$ or more concisely $9.1093837015(28)\times{10}^{-31}$ (this happens to be the mass of the electron in kilograms).

So no one is ever claiming that there is an exact value out to an infinite number of decimal points, and the infinite number of possible values between the upper and lower bound is not a problem.

 

[hutchphd]

But doesn't classical mechanics (historically at least) assume that there are an infinity of significant figures to be measured? Always worried me...

 

[DaveE]

But doesn't classical mechanics (historically at least) assume that there are an infinity of significant figures to be measured? Always worried me...

But who said classical mechanics was correct? It may just be a really, really, really, really good approximation.

 

[PeroK]

But doesn't classical mechanics (historically at least) assume that there are an infinity of significant figures to be measured? Always worried me...

The set of real numbers is mathematically a trickier concept that you might initially imagine. For example, althought there is an uncountable infinity of real numbers, there is a countable subset called comptutable numbers, that are the only numbers that you can describe - and work with computationally.

This means that you couldn't have a real number lottery, for example. You can have a lottery where everyone can choose a number from a countable set (e.g. any integer, or any computable real), then the lottery organiser chooses one as well, and if there is a match, then you have a winner or winners. But, if you try to do this with an uncountable set, there is simply no way to describe the chosen number; and, there is no way to compare the lottery organiser's number with anyone else's.

I'd don't know that it makes much difference whether we consider QM or CM, but you get the same problem if you say that a measurement can be any real number. Leaving aside the physics, there is no way to describe mathematically a specific number from an uncountable set.

If, therefore, we assume some physical quantity can take any real value, then the actual specific quantity is ultimately indescribable.

 

[sophiecentaur]

So no one is ever claiming that there is an exact value out to an infinite number of decimal points, and the infinite number of possible values between the upper and lower bound is not a problem.

Furthermore, whenever a quantity is measured, there is uncertainty. That uncertainty is not with respect to some fundamental value but to do with repeatability. So it's self-referenced or referenced to existing measured values. The uncertainty is always there and it's affected by external factors, the measurement equipment and the time taken to 'average' the reading. Pay more and you'll tend to get better certainty. The Heisenberg Uncertainty principle has to be included on top of this, of course.

Imo, the idea of 'grittiness' of the world is based on false conclusions taken erroneously from the messages in Quantum Physics. In the simplest models (Gases), there are only a limited set of interactions that can take place between EM radiation and isolated molecules of a gas. An individual atom can only absorb photons of a certain energy (+/-) but that doesn't mean other photons (with a continuum of energies) can't be going past that atom. Photons of any frequency within a band of energies are absorbed by a dense, amorphous solid.

It's like using a piano keyboard as 'proof' that only certain frequencies of sound exist. Then talk to a violinist.

 

[hutchphd]

It's like using a piano keyboard as 'proof' that only certain frequencies of sound exist. Then talk to a violinist.

As an occasional trombonist I feel neglected here.

I'd don't know that it makes much difference whether we consider QM or CM, but you get the same problem if you say that a measurement can be any real number. Leaving aside the physics, there is no way to describe mathematically a specific number from an uncountable set.

Operationally a measurement is always a ratio. To measure, say, a force you must eventually compare it to another force. So this seems not the issue to me.

For example, although there is an uncountable infinity of real numbers, there is a countable subset called computable numbers, that are the only numbers that you can describe - and work with computationally.

But there are still an infinity of computational numbers, so for me the OP question still remains. If I wish to specify the state of an isolated (localized) Quantum Mechanical atom, a small number of integers will suffice. Classically one can always ask for more.

 

[Vanadium 50]

As an occasional trombonist I feel neglected here.

How do you know when a trombonist's kid is at the playground? He can't swing and doesn't know how to use the slide.

But I digress...

The problem with that is that you only get infinite frequency resolution for notes held for infinite time. Pete Rugolo's piece Interlude notwithstanding, that's not something possible.

 

[hutchphd]

Definition of a gentleman: One who knows how to play the trombone but doesn't.

 

[sophiecentaur]

The problem with that is that you only get infinite frequency resolution for notes held for infinite time.

Heisenberg wasn't certain about that.

 

[jaketodd]

Science is of course incomplete. But the way the brain works - what is known about thinking - a neuron either fires or it doesn't. So, at least that part of who we are, the brain thinking, is quantized and quantified just like transistors in a computer. But remember that description is probably incomplete as to the full picture.

 

[trainman2001]

Food for thought (actually this entire forum is that). Even in a metrology lab where mechanical standards are maintained, things that appear to be finite and highly precise are simply approximations. Take Johannsen Blocks. Laboratory grade are accurate to 5 decimal places, but that doesn't mean they're an exact measure. There's still variation beyond five decimals at 6, 7, 8, … infinite decimal places of what the dimension really is. I supposed when you reach the Planck limit you there. But are you really?

 

[phinds]

I supposed when you reach the Planck limit you there. But are you really?

No. The Plank Length is an arbitrary measure of length just like the foot or the meter. It does not imply any physical limitation, although I do believe it is considered the smallest distance that we are EVERY likely to be able to measure. That certainly doesn't mean there's nothing smaller, just that we won't be able to measure it. I believe that presently we can measure things to as small as 10E20 Plank Lengths. So if we ever get 20 orders of magnitude better at measuring things ...

 

[FMPeck]

I find the a continuum of measurements much more disconcerting than quantization. To me it is unclear whether quantum mechanics somehow describes a strange clockwork or describes our limitations in seeing the clockwork but it seems nonetheless inevitable.

Einstein confused me at first when he said the properties we see and feel do not lie in the matter, but rather it is in the field. So, no wonder we experience a continum. Heisenberg proved to a certainty statistically that matter position is uncertain. You can know position to a certainty, you can know when to a certainty, but not both at the same time. The lead or lag in the field generated by matter according to math must be continuously differentible.

 

[sophiecentaur]

a neuron either fires or it doesn't.

You are drawing an unjustified conclusion from that. Neurons fire as a result of the sum of many inputs and the levels of the inputs is a continuum - not binary or even quantised. But, even if our brains were the same as present day PCs, that wouldn't mean anything other than the conclusions we might come to are discrete - nothing to do with any 'reality' that may or may not exist.