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zb23
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- potential
is the concept of potential just a mathematical model
Of course you are correct, but I am in a disputative mood. The notion of an absolute potential is perhaps a mathematical construct ? Absolute velocity also? Perhaps the distinction is important...or is my head just burnt from the week.Dale said:No. Differences in potential are measurable.
Well, it seems it has been that kind of a week in generalhutchphd said:I am in a disputative mood
So, the question was is it "just" a mathematical construct. I think it is not "just" a mathematical construct, but as you point out, it does have a gauge symmetry. So that makes it a little weird. However, this gauge symmetry leads (per Noether's theorem) to a conserved quantity. In this case, charge. I cannot think of something more physical than a conserved and invariant quantity. And since that quantity directly implies a potential with the property you pointed out, I still tend to say that "just" mathematical is not an accurate description.hutchphd said:The notion of an absolute potential is perhaps a mathematical construct ? Absolute velocity also? Perhaps the distinction is important
Vanadium 50 said:I don't like the word "just", except in the context of "it is just to help the less fortunate."
What does it mean to be "just a mathematical model"?
Is the electric field "just a mathematical model"?
Is electricity "just a mathematical model"?
Is gravity "just a mathematical model"?
Is it hard or is it impossible? If it is hard, then it still can be understood?Demystifier said:The Aharonov-Bohm effect is hard to understand without assuming that the potential is somehow "real".
I would say impossible, but it's somewhat subjective because it depends on what one means by "understood".martinbn said:Is it hard or is it impossible? If it is hard, then it still can be understood?
This type question can be asked about pretty much everything in physics. While it's obvious that all we talk about are models, it seems unreasonable to think that these models would be as successful if there wasn't any kind of relation between nature, and the abstractions (ie our models).zb23 said:Summary: potential
is the concept of potential just a mathematical model
Electrodynamics is a gauge theory. The potentials ##\Phi## and ##\vec{A}## can thus not be interpreted as "observable fields". Directly observable are only gauge-independent quantities as the electromagnetic field, ##(vec{E},\vec{B})##, while this physical observation is described by a quotient space, i.e., an entire equivalence class of potentials, each different from each other by a gauge transformation with an arbitrary scalar field, i.e., ##\Phi'=\Phi+1/c \partial_t \chi## and ##\vec{A}'=\vec{A}-\vec{\nabla} \chi## describe the same physical situation.Fra said:This type question can be asked about pretty much everything in physics. While it's obvious that all we talk about are models, it seems unreasonable to think that these models would be as successful if there wasn't any kind of relation between nature, and the abstractions (ie our models).
But as one refines the question, one may arrive to ask how large "mathematical redundancy" is there in our "models" as compare to the mechanism in nature I think the question itself requires choosing an observer. Because two obsevers of different complexity can not possibly, encode the same information. So there is bound to be both redundancies and losses as one compare models. Which is why it seems reasonable to think that various things like "potentials" are relative to the observer.
Would we label such observer dependence as "just a model"?
Another example, I suspect most will agree for example that the continuum which is the basis for system equation based dynamics in general are more a mathematical abstraction/model, which a doubtful relation to nature. So spacetime also is just a mathematical model? As spacetime is quite central to physics, all thing depending on it is also living with the same issues.
/Fredrik
My point was to elaborate one what "observation" means by embracing the whole inference process? Not just inferring a state, given the laws and structure.vanhees71 said:I'm not sure, what you mean by "observer dependence".
Whether or not your comment really belongs in the interpretations subforum, it's off topic in this thread. This thread is about a specific concept in standard QM, not about meta-meta-meta questions about how we come up with models or how we do science. (Even in the interpretations subforum meta-meta-meta questions can be off topic.)Fra said:I just noticed that this thread wasn't in the interpretational subforum, so I will make a short comment not to diverge things.
The concept of "potential" refers to the idea of something having the ability or capacity to become or develop into something else. It is often used in mathematics and physics to describe the amount of energy or force that is stored or available in a system.
No, the concept of "potential" is not just a mathematical model. While it is often used in mathematical equations and models, it also has real-world applications in fields such as physics, chemistry, and biology. It is a fundamental concept in understanding how energy and forces work in the natural world.
In mathematics, the concept of "potential" is often used to describe the energy or force that is stored in a system. It can also refer to the amount of work that can be done by a force in a given situation. For example, in the field of calculus, the concept of potential is used to calculate the potential energy of an object based on its position and the forces acting on it.
There are many examples of "potential" in everyday life. For instance, a stretched rubber band has potential energy due to its stretched state, which can be released to do work. A ball at the top of a hill has potential energy due to its position, which can be converted into kinetic energy as it rolls down the hill. In chemistry, potential energy is stored in chemical bonds and can be released during a chemical reaction.
Yes, the concept of "potential" is a universally accepted concept in science. It is used in various fields, such as physics, chemistry, biology, and economics, to describe and understand the behavior of energy and forces. While there may be different interpretations and applications of the concept, the fundamental idea of something having the ability or capacity to become or develop into something else remains consistent.