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Thanks, sufficient for me.

So the confusion here is that division by zero is often said to be undefined. So whereas, the point (0,0) certainly appears in the set of values where x=y, does the point (0,0) appear in the set of values where 1=y/x. Why or why not? In other words are the set of points where x=y the same as...

I was thinking of light slowing down when it passes through a medium. People have told me that this is due to interactions that happen to bend and slow the light. It feels odd that a bunch of particle interactions happen to make light refract like a water wave. It always felt like it should not...

Hi, It is easy to find discussions about time dilation and muon Half-Life. Is it meaningful to discuss whether bosons capable of pair production can have their decay rate changed if they pass through material?

I can provide a counter argument to the original suggestion that there is survival pressure for a virus to keep the host alive so the virus can reproduce. Surely there would be viruses that spread more easily during and after the decay of the host? Humans treat their dead with more attention...

You could argue that social isolation during experience of Covid symptoms would cause all viruses that make humans cough have an increased survival pressure not to produce symptoms. Perhaps viruses can learn to "hide"? In fact I read somewhere that Coronavirus evolved a very sophisticated...

One answer I got online is that someone described seeing the same thing that I am able to see with my elbow. In many ways this is quite thought provoking.

I have been reading about electrode implants into the visual cortex but this seems far more invasive and perhaps undesirable.

Hi, Are the any documented examples of descriptions of a subject's sensations during stimulation of the visual cortex, when given by people born blind? This is something I am curious about after hearing a creative musical piece sung by a disabled child. I am assuming that many people born...

Summary:: If you send a laser beam through a prism, can you measure any shift in wavelength at the other side of it? This sounds like a high school experiment and the concept is simple. I feel the laser should emerge monochromatic and at the same wavelength it went in. Do you get this result...

I also forgot the mathematics of taylor series years ago. I am not lazy, but I had my chance as an academic and I blew it. I write computer software these days. Any way, your thoughts are much apppreciated.

It just felt for a minute that projective geometry might let me graph things that converge at infinity and so "see" a limit converging as it goes to infinity. I have to be honest, I don't get projective geometry.

I went this far so I demand satisfaction. Is it impossible to use projective geometry and allow graphing of points outside reals (with infinite values like our friend Aleph) to render any solutuon to the convergence of Taylor series in a manner that is mathematically useful? Why is this and can...

interesting...

i can honestly say a best guess sometimes popped out of using the largest number my calculator could generate for infinity and then rounding it. Also, workings were sparse :)

for the record, i did manage to sort out some of the complicated limits back then. i sometimes used the obvious limits to help deduce parts of the solution to more advanced ones i think

thanks

I learned not to show all my workings in those exams ;)

Is it bad logic or bad lecturer?

I am worried that you may think I am being argumentative. Actually, I can see that aleph null is not a Real number, being itself infinite cannot appear on your definition of the real number line. The reason for my stubborness is that 30 years ago when I did my physics degree, I got exam...

That's a couple of great answers and I get it now. My only objection is that the separation on a number line between zero and n = n. This is also equal to the size of the set of positive integers between 1 and n. If you choose the full set of positive integers then the size of the set is aleph...

If the maximum separation between two points on an infinite line is finite, then what is its value? So the maximum separation is infinite. Does this mean two points on an infinite line can be separated by an infinite distance? Why, why not?

That's fascinating. Thank you :)

I'll keep trying. I know light is an em wave but the concepts of perms predate the understanding of em waves. So how can the values vary with wavelengths if really it is about fields that don't need wavelengths?

So, I've been thinking about this and permativity/permeability are properties that relate to electric and magnetic fields not historically about waves, which begs the question "wavelength of what exactly?" In the context of classical physics?

Does this mean the perms have different values at different wavelengths?

Is refractive index the same as optical density?

Cool :) Thanks.

The assumption i was making here is that the perms and OD relate to the speed of light in a substance.

Do you think I have got the right forum for this topic?

Does electric perm and magnetic perm give you enough info to work out OD? Thanks in advance

Thanks for the link. "Photoionization microscopy" looks pretty cool. Looking at that research in more detail, helium and entangled electrons are mentioned and were being studied. That was a few years ago now:)

OK, so I have been trying to educate myself on this matter. I watched this video to calculate the probability of finding an electron outside the Bhor radius in Hydrogen...

So in this link, there is a quotation of Hakwin's Brief history of time (where I also read it) that discusses short wavelength/high frequency measurement of an electron's position. I know that this is not-at-all in the context of a helium atom, but it does appear to be a general principle of...

I read somewhere that high frequency radiation can locate electrons.

If you measure the location of an electron in helium, does it impact the expectation value for the location of the other? Also, can this experiment be conducted in practice? Thanks.

There's this weird thing where the strong force suddenly stops acting over larger distances. I often wondered if it was a perfect cut-off or whether it just diminished very quickly.

I guess the strong force doesn't appear to always act from the same place like gravity and perhaps electric forces. So, I'm thinking there is no "centre" that attracts stuff.

Doesn't the strong force have a kind of "centre-of-gravity" inside the nucleus?

I'm guessing that protons might not be attracted to the centre of the nucleus in the same way an electron might be.

Does this mean that protons also cannot fall down into the centre of the nucleus?

Feynman said in one of his lectures that electrons can't just fall down into the nucleus since the uncertainty principal wouldn't let them have a known position and momentum at the same time. The problem I have with this is that protons seem quite happy in the nucleus. Is my objection fair...

https://www.mytutor.co.uk/answers/11559/A-Level/Physics/What-is-gravitational-potential-energy-Why-is-it-negative/ But a parallel plate capacitor is oppositely charged, so the plates attract. With the same logic don't they store negative energy and wouldn't you get the wrong answer from a...

If you were to look back in time towards the big bang, wouldn't you measure time dilation?

Thanks. Appreciated :)

Hi, When objects fall in a gravitational field, they convert gravitational potential energy into kinetic energy. Because energy is always conserved: amount of kinetic energy gained = amount of gravitational potential energy lost. Now the gravitational energy lost should be equal to the amount...

I took a spinning top out of a christmas cracker and watched it for a while. So I think a spinning top should just fall over like it does when it is at rest. Why does it "work"? It balances better when you spin it on its axis.

Thankyou!

So just to be clear there really is a field inside the ring but not inside the sphere?

Thanks :) Need to do some thinking.