Is Quantum Physics an Abstraction?

[RArvay]

Not being a physicist, I restrict my comments to the layman perspective.

Physics does not explain physical reality. It seeks to explain our perceptions of physical reality so that we can make sense of it. Its byproduct and validation is technology, an affirmation that we are indeed making practical sense of nature.

In recent decades, however, especially with the advent of quantum physics, the explanations have become so abstract that they are difficult to convey in a manner that all physicists can agree upon, much less be understood by non-physicists. Yet, technology and experimentation seem to continue to support the mainstream theories, albeit with some fudging at times.

It has been noted by greater minds than my own that physics is so completely reliant on mathematics that one premier physicist (I think it is Max Tegmark) claims that mathematics not only rules reality, but that it is in fact reality itself.

Mathematics is, however, almost purely abstract. Numbers count and measure things, but the concept of the number is itself an abstraction—a very necessary and useful one to be sure, but how far can abstractions go before they are challenged by physical reality? Is physics building an elaborate and elegant house of cards?

A simple example will illustrate the point. Suppose a concrete workman is instructed to pour a square platform with an area of twenty-five square feet, and a volume of twenty-five cubic feet. Simple mathematics will dictate that the dimensions of the platform be five by five by one foot. There is, however, another mathematically valid answer, and that is that the platform measure negative five feet, by negative five feet, by positive one foot, producing the same result.

To my knowledge, no one has ever accomplished this feat (although I once did have negative five dollars in my bank account). Imagine the savings in concrete costs! Each new platform would actually create new concrete—or even gold, depending on the instructions. (This assumes that there is not a universal law of conservation of concrete, LOL.)

It has not been done, but the mathematical model is just as valid for negative feet as for positive.

While the simple example seems ludicrous when applied to concrete platforms, some eminent physicists have claimed that it makes sense for virtual particles, and even for entire universes.

I must modify that statement a bit, but even after doing so, the point remains valid.

The modification is that while virtual particles can be created from empty space, they are not, as some seem to claim, created from nothing. Indeed, the mathematical value zero is not “nothing.” Zero has distinctive properties, but a “nothing” cannot (I contend) have affirmative properties.

The magnitude of this issue becomes infinitely greater when applied to entire universes. The cosmological claim has been made that entire universes can spontaneously arise out of nothing, using the basic axiom that minus X plus X equals zero, and that therefore, the value zero can produce two universes, each with its mathematical sign opposite of the other.

What this idea omits, however, is that for these two opposite-sign universes to spontaneously arise, there must first be the potential for them to arise. Some pre-existing principle must already be in place.

Moreover, a mathematical system might be constructed in which there are not two signs, but three. Instead of plus and minus, we might have zippity X, dippity X and doo X, in which all three of these add to zero. Can zero universes therefore produce three universes? Dozens? Infinities?

As we can see, abstractions unrestricted by physical verification produce absurdities. As we stretch toward the limits of measurement and experimental confirmation, we become increasingly reliant on mathematical models which might be perfectly valid, but only mathematically.

On the other hand, Max Tegmark may be right. I shudder to think that.
.

[minkwe]

This paper is relevant to the point you raise. http://arxiv.org/pdf/physics/0611043.pdf

An apple trader may begin the day with 5 apples and end it with 3, after
giving away 10 and receiving 8 apples. At no point in time was the trader in possession
of a negative quantity of apples. Still, the analysis of the process as a whole is greatly
simplified by showing that 5−10 = −5 and −5+8 = 3. Similarly, it must be acceptable
to use negative probabilities as well, so long as they simplify thought and calculations
in properly chosen situations.

[RArvay]

(although I once did have negative five dollars in my bank account)

Mathematics can help us in accounting for dynamic phenomena.
As the article says, in properly chosen situations.

The problem arises when abstractions are applied to those dynamic phenomena
as if the mathematics alone validated those applications.

It's not always easy to know when the situation has been properly chosen.

I recall reading some years ago that a mathematical technique known as
"renormalization" was used to make the math of general relativity work.

This technique, as it was explained, permits division by zero so long as later in the equation
the same variable is multiplied by zero, to reverse the "illegal" division.

Since division by zero is undefined, one wonders whether some of the
formulas in physics are mathematical illusions.

OTOH, I am reading a layman's physics article about whether our universe itself is a hologram,
making everything (including us) illusions.

I have faith in the axiom that reality does, ultimately, make perfect
sense. In humans making sense, not so much LOL.
.