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Comment by dpark | Hacker News Reader

> I am no mathematician, but the math needs to start with that fundamental principle.

This is a weird sort of hubris. “I’m not qualified to do this job but I can certainly tell you how it needs to be done.”

> And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.

This is not true in multiple ways. First, it’s known that these particles exhibit quantum behavior. This is measured and confirmed over and over. Many measures are in fact quantized.

Second, existing as a wave does not mean no discrete quantities. Even in everyday materials we observe situations like standing waves that are effectively quantized.

https://en.wikipedia.org/wiki/Standing_wave

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> This is a weird sort of hubris. “I’m not qualified to do this job but I can certainly tell you how it needs to be done.”

A quantum state is a mathematical entity that represents a physical system. Since waves are not physical can you see where I can assume that the math needs to start from a different place? If it is even useful at all?

> it’s known that these particles exhibit quantum behavior. Many measures are in fact quantized.

To measure is to quantize, so this is circular reasoning. If particles are always waves we would still see the quantum behavior.

> Second, existing as a wave does not mean no discrete quantities.

Where is the precise point a standing wave ends and begins? The best we can do is guess with calculus and differential equations. Again, yoiu are quantifying things that in and of themselves are not quantized outside of our conception.

> To measure is to quantize, so this is circular reasoning.

This is a fundamental misunderstanding. Measurement (which is a precisely defined mathematical concept) is not the same thing as quantization. For a very basic example, in all known physics theories, including QFT, SR, and GR, space and time can be measured, and they are not quantized. In fact, there is no theory compatible with SR in which space and time can be quantized, given the nature of the Lorenz transform: SR predicts continuous length contraction from the PoV of observers moving at any velocity relative to each other; for any distance of length 1, some other observer can exist for which the length would be 1/x, with x as a real number.

> space and time can be measured, and they are not quantized.

Yet…

Because we do not have the formulas does not mean they are not quantized.

https://www.scientificamerican.com/article/is-time-quantized...

Again, our current theories all agree that space and time are continuous, not quantized. Quantized space or time are not consistent with either QFT or GR.

Now, we do know that QFT and GR are not consistent with each other, so at least one new theory is necessary, at least one of them must be wrong. So the new theory could involve quantized space or time - but it could very well not. We don't know at the moment, and all we know is that our best theories, limited as they may be, require continuous space and time (and other quantities).

> all we know is that our best theories

Which is why we need new theories, and "everything is a wave" is a new theory.

Either you understand this stuff at a level so much deeper than me that I can’t comprehend what you’re getting at or you are way out of your depth because none of this makes any sense to me.

Waves aren’t physical but everything is waves? We can’t measure standing waves but have to “guess” with calculus and differential equations?

Let’s take calculating the area of a circle. Since pi is in an irrational number that goes on forever, we can only get a closer approximation to an area circle by extending the decimals of pi. But since pi goes on forever, we can never know the exact area of aLet’s take calculating the area of a circle. Since pi is in a irrational number that goes on forever, we can only get a closer approximation to an area circle by extending the decimals of pi. But since pi goes on forever, we can never know the exact area of a circle.

Do you agree or disagree with that statement?

Hard pass. The exact area of a circle is pi*r^2. We can calculate decimals of pi arbitrarily far, certainly further than our ability to measure. “Exact area” means we use symbolic math, not that we quibble about significant digits.

Pi is an infinite number. Each time we calculate the area of a circle with another decimal of pi we get a new answer.

You seem to be avoiding the question of how we can know the exact area of a circle knowing that pi is infinite.

I am saying that the area of a circle is impossible to know. And that has both philosophical and physical ramifications.

Very fact that this well-known scientific truth is hard to accept those people is telling.

https://www.scienceabc.com/pure-sciences/can-the-area-of-a-c...

“Hence, not only is it impossible to ever determine the exact value of the area of a circle, but it is equally impossible to measure any area with 100% accuracy.”

> Pi is an infinite number.

Your own link confirms this is not true. Irrational is not the same thing as infinite.

> You seem to be avoiding the question of how we can know the exact area of a circle knowing that pi is infinite.

I’m not avoiding it. I’m saying it’s a meaningless question. 16 digits of pi will be more precise than essentially anything we can measure. Just 3 digits of pi will probably be more precise than you can measure at home.

If you need perfection, you stick with symbolic math. If you need to convert to absolute physical units, your ability to measure will be your limit, not the irrationality of pi.

> Very fact that this well-known scientific truth is hard to accept those people is telling.

It’s not hard to accept. It’s not interesting. There are no physical problems related to this fact. And no interesting philosophical problems.

Your problem isn’t that you lack the knowledge but that you are overconfident in your ignorance. You lack the curiosity to ask why no one is impressed or convinced by your beliefs, instead assuming everyone else is missing the deep insights you believe you possess.

This is why you can cite someone’s article about everything being quantum waves as support for your personal beliefs while also confidently stating that the article’s author is completely wrong for believing in quantum waves. Because you are not looking for information. You are looking for confirmation. You are rendered blind by your hubris.

> Your own link confirms this is not true. Irrational is not the same thing as infinite.

Huh? From the article:

"Pi is a non-terminating and non-recurring irrational number. When we say that pi is infinite, we intend to say that pi has an infinite expression, not an infinite value."

That is what I meat by infinte, as in the number never ends.

I am not commenting about being more precise. I am talking about exactness. Yes, with every didgit we add to pi we become more precise, and there is a limit to what we need, but to know that there is not exact value we can give to the area of a thing, how can we say that is a thing at a deeper level? If we know things because we "measure them" and measuring is never exact, what do we really know?

> to know that there is not exact value we can give to the area of a thing

Pi has an exact value. It is irrational, not inexact.

This is increasingly irrelevant and inaccurate rambling I’m engaging with. I’m out. Take care.

> To measure is to quantize

You're confusing "quantify" with "quantize".

To measure is to quantify, not to quantize.

In quantum physics, "quantized" means that a field has a smallest possible excitation, called a quantum, rather than being able to vary continuously.

For example, the quantum of the electromagnetic field is the photon.

A quantum field is fundamentally quantized, so the waves that arise in quantum fields are similarly quantized.

> Again, you are quantifying things that in and of themselves are not quantized outside of our conception.

No, we have extremely strong evidence that the physical fields themselves are quantized. If you try to model physics using classical waves - which we do, e.g. in semiclassical electrodynamics, which models the electromagnetic field as continuous instead of quantized field - you find there are limits to what can accurately be modeled. To get an accurate model, you need to quantize the field.

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