# Thread: is a point in physics a fermion or a boson ?

1. In mathematics, many points can occupy the same place, or the same state as it is said in physics. In fact, a point is
always located at some point in mathematics, in other words a point is located at some other
point. This means there must always be at least 2 different points at the same point, which just appear
as one single point. It would not be sensible to think that a point would not be located at any point. If that were true
the point would not exist because it would not have a location.

According to Pauli exclusion principle, two identical fermions cannot occupy the same state
simultaneously. If a point in physics is a fermion, the exclusion principle prevents two points
occupying the same state. Where is a point located in this case? Or should a point be defined
as a boson in physics, because two bosons can occupy the same state. Bosons are not
subject to the Pauli exclusion principle. Just defining a point in physics to be a boson, makes physics
the same as mathematics, where it is free to define everything which don't need to be true in real world.
So physics cannot be the same as mathematics, because everything is not possible.  2.

3. Originally Posted by Hot Then Thot This means there must always be at least 2 different points at the same point
Doesn't follow.

It would not be sensible to think that a point would not be located at any point. If that were true the point would not exist because it would not have a location.
You're, apparently, misunderstanding what a point is.

If a point in physics
A point is a mathematical/ geometrical concept. It's not a "thing".

Just defining a point in physics to be a boson, makes physics the same as mathematics
Physics != mathematics. Mathematics != physics.

So physics cannot be the same as mathematics, because everything is not possible.
While the first part is true the second doesn't follow from it.  4. Originally Posted by Dywyddyr You're, apparently, misunderstanding what a point is.

A point is a mathematical/ geometrical concept. It's not a "thing".
Maybe a point is not a "thing". I am making assumptions only. If points in physics were fermions,
then physics would become mathematics, because what would prevent 2 points occupying the same state since Pauli
exclusion principle deals only with "things" or real particles, it can't be applied to points. Fermions would no more obey Pauli exclusion principle, they could occupy the same state. Fermions would become bosons. Supersymmetry in string theory implied something
like this. String theory may be out of fashion now, it had some ideas.  5. Originally Posted by Hot Then Thot If points in physics were fermions, then physics would become mathematics
That's an overly-ambitious (and unjustified) extrapolation.  6. Originally Posted by Hot Then Thot In mathematics, many points can occupy the same place, or the same state as it is said in physics. In fact, a point is
always located at some point in mathematics, in other words a point is located at some other
point. This means there must always be at least 2 different points at the same point, which just appear
as one single point. It would not be sensible to think that a point would not be located at any point. If that were true
the point would not exist because it would not have a location.

According to Pauli exclusion principle, two identical fermions cannot occupy the same state
simultaneously. If a point in physics is a fermion, the exclusion principle prevents two points
occupying the same state. Where is a point located in this case? Or should a point be defined
as a boson in physics, because two bosons can occupy the same state. Bosons are not
subject to the Pauli exclusion principle. Just defining a point in physics to be a boson, makes physics
the same as mathematics, where it is free to define everything which don't need to be true in real world.
So physics cannot be the same as mathematics, because everything is not possible.
Your last line makes the most sense.

The job of science - including physics - is to model physical reality. Mathematics is a type of quantitative logic that is a powerful tool to help build such models. It is plain that things may be logically possible in mathematics that do not reflect the physical world.

It is therefore pointless (geddit?) to assign physical properties to purely mathematical entities.  7. Originally Posted by exchemist Your last line makes the most sense.

The job of science - including physics - is to model physical reality. Mathematics is a type of quantitative logic that is a powerful tool to help build such models. It is plain that things may be logically possible in mathematics that do not reflect the physical world.

It is therefore pointless (geddit?) to assign physical properties to purely mathematical entities.
There are many mathematical physicists and do they also have their own science called mathematical physics.
Perhaps I am talking now about theoretical physics and theoretical physicists. How many times did you see
them writing about Eugene Wigner'sThe Unreasonable effectiveness of mathematics in natural sciences.

I think that it is rather a weakness of mathematics to be used as an absolute truth in physics, where the truth is often
contextual or "relative". Another problem arises of the freedom in mathematics to define almost anything as true,
as I am arguing in this thread that one could define a point in physics to be a fermion or a boson, and neither of these
definitions are satisfying just because physics does not work according to definitions alone. A point is physics is not
a "thing" as Dywyddyr said. A point in physics does not become a "thing" even if it defined as a "thing".
Otherwise we will end up to "an overly-ambitious (and unjustified) extrapolation" as Dywyddyr said.

I think that the problem is serious, physics is infected with mathematics, and it can be misleading to trust in
tools of logic as exactly modelling the physical world. Think about the wave-particle dualism. What does it mean?
Dualism refers to a mathematical concept, can it be a foundation of quantum mechanics? The problem is
how to understand the meaning of this dualism, the meaning of the words and definitions. Does the wave-particle
dualism mean that a wave is a particle, although that does not make sense in real world. A wave is a wave, a particle
is a particle.  8. Originally Posted by Hot Then Thot  Originally Posted by exchemist Your last line makes the most sense.

The job of science - including physics - is to model physical reality. Mathematics is a type of quantitative logic that is a powerful tool to help build such models. It is plain that things may be logically possible in mathematics that do not reflect the physical world.

It is therefore pointless (geddit?) to assign physical properties to purely mathematical entities.
There are many mathematical physicists and do they also have their own science called mathematical physics.
Perhaps I am talking now about theoretical physics and theoretical physicists. How many times did you see
them writing about Eugene Wigner'sThe Unreasonable effectiveness of mathematics in natural sciences.

I think that it is rather a weakness of mathematics to be used as an absolute truth in physics, where the truth is often
contextual or "relative". Another problem arises of the freedom in mathematics to define almost anything as true,
as I am arguing in this thread that one could define a point in physics to be a fermion or a boson, and neither of these
definitions are satisfying just because physics does not work according to definitions alone. A point is physics is not
a "thing" as Dywyddyr said. A point in physics does not become a "thing" even if it defined as a "thing".
Otherwise we will end up to "an overly-ambitious (and unjustified) extrapolation" as Dywyddyr said.

I think that the problem is serious, physics is infected with mathematics, and it can be misleading to trust in
tools of logic as exactly modelling the physical world. Think about the wave-particle dualism. What does it mean?
Dualism refers to a mathematical concept, can it be a foundation of quantum mechanics? The problem is
how to understand the meaning of this dualism, the meaning of the words and definitions. Does the wave-particle
dualism mean that a wave is a particle, although that does not make sense in real world. A wave is a wave, a particle
is a particle.
I have at times wondered myself about the "reality" of models that seem purely mathematical and lack any visualisable, pictorial, counterpart. But I've come to the conclusion that such scruples are probably misplaced. One has to keep in mind, I think, that the goal is to model reality. If there is no visual way to do it and only mathematics will give the quantitative predictions one seeks, then one has to conclude that a mathematical model is required. I have had enough familiarity (at university, a long time ago now) with the maths of quantum chemistry to realise that, when you use it enough, the maths itself can become a kind of way to "visualise", in that the form of an equation tells you how reality appears to be, without the need for a physical picture. I've only been able to do this fleetingly, but there are those (I suspect our own Markus Hanke may be one) who do this quite naturally.

There is, I suppose, a risk that some mathematical physicists might let the maths run way ahead of the experiments and create a mathematical house of cards, that lacks experimental confirmation. But then it's the job of the experimental physicists to keep checking the predictions of the wilder flights of theory.

P.S. Regarding your example of wave-particle duality, my tutor told me any radio engineer was a good sense of how to make sense of this apparent paradox. (Wave packets, Fourier series and the Principle of Indeterminacy)  9. Originally Posted by Hot Then Thot I think that the problem is serious, physics is infected with mathematics, and it can be misleading to trust in
tools of logic as exactly modelling the physical world.
No one just accepts the results of models. Models are developed to ... well, model the world. The results of the model are tested by comparing against the real world

Physics, like most sciences, works in two ways: experimental, where data is found and attempts made to build a theory or model to explain the data; theoretical, where the conclusions of the mathematical theory are developed suggesting new areas for research. Both these routes are productive (for example, the positron was predicted before it was found; the neutrino was found before it was part of the theory).

You cannot have science without maths because it has to make quantitatively testable predictions.

Think about the wave-particle dualism. What does it mean?
Dualism refers to a mathematical concept, can it be a foundation of quantum mechanics? The problem is
how to understand the meaning of this dualism, the meaning of the words and definitions. Does the wave-particle
dualism mean that a wave is a particle, although that does not make sense in real world. A wave is a wave, a particle
is a particle.
The (apparent) dualism comes from trying to use words and everyday concepts ("particle", "wave") to describe something for which those concepts are not relevant. The maths avoids this problem.  10. Originally Posted by Strange No one just accepts the results of models. Models are developed to ... well, model the world. The results of the model are tested by comparing against the real world

Physics, like most sciences, works in two ways: experimental, where data is found and attempts made to build a theory or model to explain the data; theoretical, where the conclusions of the mathematical theory are developed suggesting new areas for research. Both these routes are productive (for example, the positron was predicted before it was found; the neutrino was found before it was part of the theory).

You cannot have science without maths because it has to make quantitatively testable predictions.

I found two good jokes. These tell more about The Unreasonable effectiveness of mathematics in natural sciences

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

"I'm going to prove this apple is not a fruit by assuming it isnt a fruit, and showing that if it isnt a fruit, it is therefore not a fruit."  11. Originally Posted by Hot Then Thot  Originally Posted by Strange No one just accepts the results of models. Models are developed to ... well, model the world. The results of the model are tested by comparing against the real world

Physics, like most sciences, works in two ways: experimental, where data is found and attempts made to build a theory or model to explain the data; theoretical, where the conclusions of the mathematical theory are developed suggesting new areas for research. Both these routes are productive (for example, the positron was predicted before it was found; the neutrino was found before it was part of the theory).

You cannot have science without maths because it has to make quantitatively testable predictions.

I found two good jokes. These tell more about The Unreasonable effectiveness of mathematics in natural sciences

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

"I'm going to prove this apple is not a fruit by assuming it isnt a fruit, and showing that if it isnt a fruit, it is therefore not a fruit."
The first is a mathematician being playful, which is perfectly fine, and illustrates nicely the difference between mathematics and science.

The second, however is just self-evidently stupid and provides no insights whatever.  12. Originally Posted by exchemist The first is a mathematician being playful, which is perfectly fine, and illustrates nicely the difference between mathematics and science.
And even in engineering we use idealisations to solve difficult problems and then use various ways to work out how they might be made to apply to the real world.

The second, however is just self-evidently stupid and provides no insights whatever.
It is not even a good example of the fallacy of begging the question.  13. I have another question:
where is the universe located or situated?

The answer may be found by first solving the original question: where is a point located.
A point is always located at some point, in other words at some other point, meaning that
there must always be at least 2 points occupying the same point, which just appear as a single point.

Therefore the universe could be located at another universe, perhaps "inside" an other
universe. There can be two universes in one.  14. No.
When two things are identicle they are the same thing.
A point is not an object, it is a location.

The problem is a location requires at least one other location to act as a reference, a place where you can tell how far away the other place is.
Two points define a line, three points define a plane, etc.  Bookmarks
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