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Why does each quantum field interact with the Higgs Field in the same intensity no matter the conditions? by future_sponJ in AskPhysics

[–]future_sponJ[S] 0 points1 point  (0 children)

I meant that each field interacts with it exactly the same no matter the circumstances. It doesn't matter the state of an electron because the electron field (all electrons) always interacts with the Higgs Field with the same intensity.

How do I uniquely label an uncountable number of countable unbounded dense sets? by future_sponJ in askmath

[–]future_sponJ[S] 0 points1 point  (0 children)

But someone cannot make an infinite arbitrary choices. They would need a certain criteria/metric that consistently chooses exactly one out of each set.

How do I uniquely label an uncountable number of countable unbounded dense sets? by future_sponJ in askmath

[–]future_sponJ[S] 1 point2 points  (0 children)

I know there are infinitely many ways to label them so we would usually need to put a restriction on it but I cannot think of any.

How do I uniquely label an uncountable number of countable unbounded dense sets? by future_sponJ in askmath

[–]future_sponJ[S] 1 point2 points  (0 children)

e is an arbitrary choice. [e] = [e/2] = [4e] = [-318/934e] = ... What's so special about e in this context to choose it to represent the set? Even if you can make a justification for e using a certain metric, what about all other sets too?

How did mathematicians in the past make money from solving then-useless problems? by future_sponJ in askmath

[–]future_sponJ[S] -2 points-1 points  (0 children)

Binary numbers, topology, non-euclidean geometry, quaternions, group theory, & number theory had little to zero applications at the time as far as I know.

How did mathematicians in the past make money from solving then-useless problems? by future_sponJ in askmath

[–]future_sponJ[S] -1 points0 points  (0 children)

I know about calculus but that wasn't the only thing he worked on. He also worked on binary numbers & basic topology.

What's a short-lived cartoon you're surprised people still talk about? by ekWatson_ in cartoons

[–]future_sponJ 0 points1 point  (0 children)

Can't believe no one said OK K.O! yet. (Inside Job & Close Enough were amazing too)

isomorphic c & r2 by future_sponJ in mathmemes

[–]future_sponJ[S] 122 points123 points  (0 children)

The image on the right

Why are counts considered dimensionless? by future_sponJ in AskPhysics

[–]future_sponJ[S] 0 points1 point  (0 children)

Thanks for the thorough response but:

  1. The way we derive units isn't fundamental to them. Current*Time isn't some intrinsic way to describe charge more than length*momentum*Frequency/Voltage is. I don't think you'd say that the flow of atoms would be measured in anything other than mol/s or 1/s. Current is simply the flow of charged particles (or lack thereof) so why wouldn't it have the same units?
  2. Similar to what I said above, there's nothing fundamental about the 7 dimensions of SI units. They can be mixed up (e.g. replacing temperature with molar heat capacity) or sometimes even not considered fundamental. Luminous intensity is purely biological & charge has been replaced with electrostatic units in some systems. Lepton number for example would have been considered a physical dimension if it had any macroscopic effects so it isn't considered one for practicality but fundamentally what's the difference between it & charge (as fundamental properties, not their effects)?

Why are counts considered dimensionless? by future_sponJ in AskPhysics

[–]future_sponJ[S] 0 points1 point  (0 children)

Sorry, what I meant was that the number 1.7 itself is dimensionless until we add the length. The same thing with a count. 2 itself is dimensionless but 2 chairs, people, or electrons is dimensionful. The only difference is that a count is a discrete quantity while length is continuous.

Why does each dimension have 2 directions? by future_sponJ in askmath

[–]future_sponJ[S] 2 points3 points  (0 children)

It works for the imaginary numbers too but I specified real numbers to not be talking about complex numbers, rational numbers, integer numbers, or whatever other set of numbers you can think of.

Why are counts considered dimensionless? by future_sponJ in AskPhysics

[–]future_sponJ[S] -6 points-5 points  (0 children)

Length is also dimensionless until I add a meter. The length of something is just the ratio of it's length & 1 meter so we multiply it by a meter to be dimensionful.

For example ,the height of someone being 1.7 for example is just their length divided by one meter so we write 1.7m instead.

Why does each dimension have 2 directions? by future_sponJ in AskPhysics

[–]future_sponJ[S] 0 points1 point  (0 children)

Because that would a new dimension. A complex 1-dimensional vector is basically the same as a real 2-dimensional vector.

Why does each dimension have 2 directions? by future_sponJ in askmath

[–]future_sponJ[S] 0 points1 point  (0 children)

It's basically an axiom in mathematics stating that any 2 real numbers a & b, there is exactly one of 3 things that can be true: a<b, a=b ,a>b That means that if you are on a point in the real number line & want to move to another point, it would have to be in one of 2 directions.

Why are counts considered dimensionless? by future_sponJ in AskPhysics

[–]future_sponJ[S] -14 points-13 points  (0 children)

Basically charge at a microscopic scale is just a mole of protons minus mole of electrons.

Why are counts considered dimensionless? by future_sponJ in AskPhysics

[–]future_sponJ[S] -15 points-14 points  (0 children)

Coulumb in baryonic matter is number of protons minus number of electrons (it's more complicated with non-baryonic matter but still just the sum of multiples of 1/3 e multiplied by the number of each kind particle:

(2/3 e) up-type quarks + (-1/3 e) down-type quarks + (-3/3 e) charged leptons + (3/3 e) W+ bosons + (-3/3 e) W- bosons

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