There was no such thing as modern day language, the scientific method, Newtonian physics, or higher mathematics during The Buddha's time-period those things seem to have come into existence around the 17th Century.
So there was no possibility of anyone asking The Buddha or any arahant to prove or explain things in modern scientific terms. It's also not exactly clear what certain things in modern terms mean because modern language is different.
However the Pali canons mention all types of concepts that only relatively recently came in:
- Big Bang and Big Crunch (expansion and contraction of the universe)
- Time dilation (time moving at a different pace on other worlds)
- Cyclic model
- World systems like galaxies
During The Buddha's time he encouraged those with doubt to ask questions.
In modern times if an arahant well-developed in the six higher knowledges or paccekabuddha or sammasambuddha appears they should be able to easily scientifically prove their ideas through modern means if someone challenged them to.
Something like that actually happened when the arahant Kumara encountered an ancient atheist Prince Payasi, here's an exerpt:
"Well, Reverend Kumara, I had friends who followed the right path, who
were very good people and citizens in every respect. By any right, as
certain Holy men have said, they should have gone to the Heaven of the
Thirty Three Devas. Yet, when one of them died, I said to him, "You
have always been trustworthy and dependable. Certain Holy men say
that, because of your lifestyle and because you followed the right
path, you will be reborn in the Heaven of the Thirty Three Devas. If
this is so, please come and tell me if it is true, or send a messenger
to tell me if it is true. To date, they have neither contacted me nor
sent a messenger."
"Hmm. Well, Prince… Consider this. In the Heaven of the Thirty Three
Devas, time passes at a different pace, and people live much longer.
In the period of our century, one hundred years, only a single day,
twenty four hours would have passed for them. Thirty of these hundred
year days make up one of their months, twelve such months make a year
and a thousand such years is roughly the life span of those born into
the Heaven of the Thirty Three Devas. Suppose your friend decided, "I
will go back to that unclean world just long enough to deliver my
message to the Prince – I shall set out tomorrow. Or perhaps, after I
have seen some more of this place, in two or three days, I will set
out to go see him." – would he have been able to?"
"Of course not, Reverend Kumara, because, by the reasoning you have
given, we should all be long dead by the time he had spent three days
there. However, I do not think that those born in the Heaven of the
Thirty Three Devas would be so long lived, or that time could pass at a different
pace. How do you know about their lifespan or their time?" (DN 23,
The idea of time moving at a different pace on other worlds is something that only recently came in.
But remember there was no such thing as the scientific method or higher mathematics back then so one could challenge an arahant to experimentally prove something like we can now in modern times.
It seems like The Buddha is the only teacher in history who debated in a bold calm fearless manner claiming to know that his ways are true. Still in modern times I don't know if there's any teacher like that.
If someone really is an arahant and also well-developed in the six higher knowledges scientifically proving something should be an easy task for them.
This means in modern times if a skilled arahant or paccekabuddha arises and someone challenges them they should be able to scientifically prove that they are right...it would probably bedazzle and astonish the world...
I wonder however if there really are any arahants that exist in this world...