# What Scientific Concept Was the Hardest For You to Comprehend?

• kyphysics
In summary, this conversation was difficult because Kyphysics had to understand General Relativity, Astronomy, and Quantum Spin.

#### kyphysics

Thought this might be an interesting question. Feel free to post why it was hard and/or what let you finally understand it.

Hi kyphysics!
I guess, if God keeps me alive, the last year of the Grade in Physics will be difficult: need to understand General Relativity, Astronomy...

It's kind of hard to think of one in particular but what comes to mind is that when I was learning about current circuits and current versus voltage and resistance that was hard to wrap my mind around some of the concepts in that.

Relativistic velocity addition. I recall feeling a strong contradiction that simple addition just had to be the right operation to add a distance to a distance and divide by a time plus a time.

But, of course, one is actually adding a distance in this frame to a distance in that frame. And then dividing by the sum of a time in this frame and a time in that frame. So so simple addition is not automatically the right operation.

It also took a surprising number of years after thinking I knew special relativity to integrate the relativity of simultaneity. I recall thinking: "what if there is a systematic offset in time corresponding to distance in the direction of relative motion?" Could that resolve these difficulties? Then I turned around, looked at the Lorentz transforms and saw that very term staring me in the face. *facepalm*.

Klystron, Twigg, DennisN and 1 other person
That's good that you resolved it. That one is challenging I think. It's fun though.

jbriggs444 said:
I recall thinking: "what if there is a systematic offset in time corresponding to distance in the direction of relative motion?" Could that resolve these difficulties? Then I turned around, looked at the Lorentz transforms and saw that very term staring me in the face. *facepalm*.

For me, one of the most difficult concepts to accept was that there is no absolute time.
Why? I'm not sure, but part of it was probably that I was thoroughly "indoctrinated" with Newtonian physics.

Now, when I look back, I am of the opinion that it actually is quite weird to assume that there is one universal clock making time run equally fast everywhere in the Universe. There is no such clock, and it has also been shown that there is gravitational time dilation.

In more recent years, for me, quantum spin was one of the most difficult concepts to comprehend. I can't say I comprehend it today, I just accept it.

As with the loss of absolute time, my acceptance of quantum spin was achieved by going through the famous
five stages of grief :

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Klystron and BillTre
Green functions in boundary value problems. Except for the general part of the theory, it always seemed like a bit of magic was needed to actually use them.

DanielMB, Twigg and etotheipi
"As with the loss of absolute time, my acceptance of quantum spin was achieved by going through the famous
five stages of grief:"

Speaking of absolute did you know that this is also not absolute ?

DennisN
Speaking of absolute did you know that this is also not absolute ?
Do you mean you think that nothing is absolute? If so, then no, some things ARE absolute. Just as a simple example, the outcome of arithmetic is absolute. 2 + 2 (in base 10, just to be clear) has an absolute outcome. It's always 4.

No I meant that the "stages of grief" are not absolute. 2+2 in base 10 definitely is.

DennisN
No I meant that the "stages of grief" are not absolute. 2+2 in base 10 definitely is.
Ah. Well, I guess I was over-interpreting your comment.

Speaking of absolute did you know that this is also not absolute ?
Absolutely.

This is Absolute:

mcastillo356, gleem, DennisN and 1 other person
Believe it or not logarithms and exponentials. I didn't really get it until I did real analysis where it was developed rigorously. It wasn't I could not do it - that was easy, but a^x had been defined for rationals - but not for reals - yet you need reals for calculus. Plus what the dickens was going on with euler's number. Sure in calculus you had handwavey arguments, but they didn't really 'gell'. Then real analysis cleared it all up. Just to recap how it is done 'properly' you first define ln (x) = ∫1/y dy from 1 to x. Then take the derivative of ln (xy) to get also 1/x. Hence ln(xy) = ln(x) + C. Let x =1 so ln (xy) = ln (x) + ln(y). The inverse of ln(x) is defined as e^x. Let a = e^x, b= e^y. e^(x+y) = e^(ln(a) +ln(y)) = e^ln(a*b) = a*b = e^x*e^y. Everything else follows easily from that. It was a revelation when I saw it in my real analysis class. So simple and easy. Of course rigorously proving some of the steps used required theorems you did before to show things like ln(x) has a unique inverse. But it always amazes me they do dot do it in calculus, and just rely on intuitively the inverse exists (it's easy to see by simply drawing the graph) - and mention you will prove it rigorously in real analysis. In fact for me it's why I would teach calculus and precalculus together.

Thanks
Bill

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mcastillo356
phinds said:
Do you mean you think that nothing is absolute? If so, then no, some things ARE absolute. Just as a simple example, the outcome of arithmetic is absolute. 2 + 2 (in base 10, just to be clear) has an absolute outcome. It's always 4.

Of course the logical consequences of axioms (in this case Peano's axioms) are absolute. Nobody (well some modern philosophers like Rorty and perhaps even Wittgenstein might - but as this is a family forum I will not give my opinion on their views) doubts that. Much more interesting is does 1 +2 +3 + 4 ... = ∞ or -1/12 and why. Answer - we generally think of 1, 2,3 etc as from the set of integers but in fact they are also from the set of complex numbers. In the complex plane it is seen the infinity can be removed by analytic continuation. So this is a case of watching your assumptions.

Thanks
Bill

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I still don't understand (intuitively) why the bottom of the wheel does not move relative to the ground!

weirdoguy and mcastillo356
It is hard to say , but that number Pi is not a geometrical constant … being still the same number we observe affecting our lives (equations): Fourier Series, Fourier Transforms, Leibniz Pi Series, Euler Identity, Gauss Law, Buffon’s Needle problem, Madhava-Leibniz series for Pi, Schrödinger equation, Normal Distribution, Einstein Field Equations, etc., the same constant value in the Earth and in the neighborhood of black hole

Circles are not geometry? That's how arose ##\pi##

atyy said:
I still don't understand (intuitively) why the bottom of the wheel does not move relative to the ground!
Could you elaborate on what this means? It sounds interesting.

For me, time and eternity are very difficult to grasp.

The instantaneous velocity of the wheel in contact with ground is zero relative to the ground (otherwise, the wheel slips)

mcastillo356 said:
Circles are not geometry? That's how arose ##\pi##

Sure. What he is referring to is part of Wigner famous essay:

Thanks
Bill

mcastillo356
It was the fact that I did not know know that you could define anything in math or physics.In physics perhaps some goals as motivation are needed to define things.Then in junior high school I read a book about Einstein and when I read about the four dimensions of spacetime I thought it could be done mathematically I did not know how he came up with this result.Then more dimensions than three generally from the viewpoint of geometry with distances and angles and curvature was a little difficult as it was more abstract than the three spatial dimensions we experience in the universe.I did not know the reason to do this but then it is interesting to generally study all n dimensions of a manifold where n is a natural number.Then in analytic number theory the methods used to solve number theoretical problems was a little strange to me then.I did not know then that possibilities of connections like these could happen in math or physics.

"How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?"
I need your help to understand these sentence, I thought I had understand: does it mean that if somebody states something inconsistent, this is, not in agree with something else, eg, previous studies, we can fall into a chain of failures? Is DanielMB trying to say that the concurrence of ##\pi## is yet to study?

mcastillo356 said:
"How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?"
I need your help to understand these sentence, I thought I had understand: does it mean that if somebody states something inconsistent, this is, not in agree with something else, eg, previous studies, we can fall into a chain of failures? Is DanielMB trying to say that the concurrence of ##\pi## is yet to study?
Does the second theory explain all the phenomena of the first one but has little in common with it?If it explains all the phenomena and provides explanation for new phenomena that the first does not it is a generalisation.But if it explains completely the same phenomena with the first I would say it is equivalent, but has a different statement.

At an intuitive level: Creating a force, like holding a weight at arms length, isn't necessarily doing any work, it may be just using energy with 0% efficiency. It sure seems like it's work though.

mcastillo356 and Frigus
I think different types of infinity are weird.

You can have infinity from 0 on up . . .
Then, you can have a "smaller" infinity from 1 on up. . .

Both are infinity, but one is larger than the other.

kyphysics said:
I think different types of infinity are weird.

You can have infinity from 0 on up . . .
Then, you can have a "smaller" infinity from 1 on up. . .

Both are infinity, but one is larger than the other.
I agree, and further it seems strange to me that cardinalities bump up in scale discretely according to simple formulas. It makes me wonder how intrinsic it is (beyond ZFC in general, and in nature).

I also find uncomputable numbers strange. They are numbers which presumably cannot show up or play any role in a physical universe, unless the universe has an infinite state space going into determining a single value. And these numbers are the vast majority of numbers (small and big). They make up the vast majority of the interval from 0 to 1 for example. And they're implicitly part of our continuous physics models, even though they can't really be in the way they are in the model in reality.

It makes me think that maybe values are not complete separable objects in physical reality, but rather a single value, or physical realization of a real number, is something that must be distributed in space and time (perhaps infinitely in each dimension), and not only can we not measure them completely as an instantaneous thing, or completely in any sense, but we can't even talk about them completely or use them in applied math or physics.

But yet time goes on, and things change. And in physics we talk about complete and objective, maybe even separable, but uncertain things.

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Klystron
As a child, truly understanding the concept of interval helped me understand number lines and consequently, physics and geometry. Understanding logarithms helped understand electronics.

As an adult, learning fractal dimensions and related mathematics greatly expanded my worldview.

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Jarvis323
Jarvis323 said:
I also find uncomputable numbers strange. They are numbers which presumably cannot show up or play any role in a physical universe, unless the universe has an infinite state space going into determining a single value. And these numbers are the vast majority of numbers (small and big). They make up the vast majority of the interval from 0 to 1 for example. And they're implicitly part of our continuous physics models, even though they can't really be in the way they are in the model in reality.

It makes me think that maybe values are not complete separable objects in physical reality, but rather a single value, or physical realization of a real number, is something that must be distributed in space and time (perhaps infinitely in each dimension), and not only can we not measure them completely as an instantaneous thing, or completely in any sense, but we can't even talk about them completely or use them in applied math or physics.
Have you studied any philosophy, Jarvis? I'm not a STEM major, but do have a social sciences and humanities background that includes philosophy (almost a minor of mine).

Going back to Aristotle, it's been argued that actual infinites cannot exist. Rather, Aristotle posits only the existence of potential infinites. These are like limits in that you continuously approach a "goal," but never get there.

This was the dominant way of thinking until Cantor, in mathematics, developed the notion of actual infinities in set theory. From there, it's been an open debate if I'm not mistaken. I'm of the opinion that actual infinites cannot/do not exist. They may be coherent/workable conceptual ideas, but in the real physical world do not exist.

For me, it was a simple one: 'numbers first'.
Still struggling with it every day