[alancalverd]

Still wearing my linguistic pedant hat, what you are actually doing with squeezed states is reducing the indeterminacy of one vector of a phenomenon in order to reduce the uncertainty of your measurement. It's remarkably like heterodyning.

Just thought of a macroscopic analogy. How do you count sheep? In a field, they are all milling about in various directions so you don't know if you've counted one twice, or missed out a few. So you can either take a photograph, which tells you how many were there at the time you took the photo (but you don't know where they are now) or you herd (squeeze) them through a gate and count them one at a time into separate pens. Well, it's no worse a model than the bouncing photon!

[JesWade21]

These are not, by any means, the only physical units. For starters, you can change the units so that mass, space, time, and temperature are all the same (Planck units). The quantities chosen are not even fundamental (for example, charge is unquestionably more fundamental than current, and moles are essentially a conversion factor between AMUs (atomic mass units) and kilogrammes). And because Candelas are entirely human-based, they are not physically fundamental at all. Finally, these units omit nearly all of quantum mechanics' fundamental parameters.

The seven basic units are simply convenient choices for dealing with many classical physics equations (I believe it is easier to measure current than charge, for instance). Charge, mass, space, and time are the fundamental units for electromagnetism and gravity equations, and temperature is useful for thermodynamics (although you can actually calculate it in many cases from an average kinetic energy, which in turn is derived from the previous units). Moles convert microscopic to macroscopic quantities, and I'm not sure what candelas are doing there.

[varsigma (OP)]

I think the more fundamental thing isn't actually any physical units, but rather difference.

A distance "lies between" two different points; a voltage "exists between" two different amounts of charge.

Without fundamental differences, measurement isn't that well-defined, I would say.

[alancalverd]

Mass is mass. No difference between anything. Likewise charge.

[varsigma (OP)]

Mass is mass. No difference between anything.

?? Not sure what that means; the mass of the earth and the mass of the moon are both masses. And yet, there's a difference between them; if I subtract one from the other, that's the difference, and it might be negative.

It might be the case that this difference has no physical significance (except that isn't true); it might be that the information the difference has in it, amounts to nothing useful. Except it does

[Bored chemist]

It might be the case that this difference has no physical significance (except that isn't true); it might be that the information the difference has in it, amounts to nothing useful. Except it does

There are two unsupported claims there.
Were you expecting us to "just believe you"?

[varsigma (OP)]

There are two unsupported claims there.
Were you expecting us to "just believe you"?

There are two unsupported claims? Surely the masses of the earth and moon being different isn't an unsupported claim?
Or perhaps I could weigh their masses and make sure, but how?

Is the other unsupported claim that the difference is useful information?
In physics, there are indeed things that you should 'just believe'. For instance, you should believe that distances exist and can be measured. That's actually what most people do believe, so physics teachers usually skip the definition of distance and measuring distance.

[alancalverd]

The difference between the masses of the earth and the moon, or indeed any two bodies, does not constitute a fundamental physical quantity, unlike the spatial difference between point A and point B, which as you say defines "distance". Mass is defined without introducing a second object or point.

Measuring distance is (or at least used to be) one of the most important lessons in elementary physics.

The definitions are straightforward. Time is what prevents everything happening at once, and distance is what prevents everything being in the same place.

[Colin2B]

Measuring distance is (or at least used to be) one of the most important lessons in elementary physics.

It still is. The concept of distance and it’s measurement is also a key feature of most elementary education.

[varsigma (OP)]

The difference between the masses of the earth and the moon, or indeed any two bodies, does not constitute a fundamental physical quantity,

So you say.

I say it does constitute something more fundamental than physical units, in this case units of mass. The mass difference is physically significant and it does contain information. I don't understand why that means it is or isn't a physical quantity; I don't understand the significance of the rest of your post.

I say that difference is more fundamental and you say the distance between two points is fundamental. Why aren't the two points more fundamental?

Mass is defined without introducing a second object or point.

A point is defined without introducing a second point, but you need a second point to define a distance. You need a second distinct mass to define a mass difference likewise.

Like I said, difference is more fundamental than a choice of units.

[alancalverd]

You seem not to understand the word "constitute" , nor the difference between a ratio and a difference.

[varsigma (OP)]

You seem not to understand the word "constitute" , nor the difference between a ratio and a difference.

You seem not to understand a rational argument. How to make one, that is.

Please explain your claim, so far just a bare statement, that the difference between two masses does not constitute a fundamental physical quantity.

I want you to explain all the terms you're using. Explain what a physical quantity is, then what a fundamental physical quantity is, with examples. I want it absolutely clear and irrefutable so that the difference between two masses is excluded from the set of fundamental physical quantities.