The speed of light (also known as "c") is a shorthand to describe the speed of electromagnetic radiation of all types, and that in turn is a shorthand to describe the speed limit of causality in our universe. Therefore, it seems entirely possible that c started out being much slower before accelerating to the point where it reached the speed limit of causality at which we have always observed it.

If this were true I don't think we'd have any way of knowing, but it would radically alter our concept of certain distances in space, given that we rely on c having always been ~300 000 km/s and so that assumption is built into our estimate of the distance to and between the stars we observe through telescopes.

I'd like to survey those with greater knowledge about astronomy and cosmology as to whether this theory could possibly be true, and if not, why not. Thanks

there is no reason why c has to have remained constant throughout the existence of universe, or that it is universal homogenous either.
All of cosmology and astronomy is based on assumptions such as this that we have to make, I was today just looking at something as simple as the distance to our nearest (none sun) star, and the error bounds that we measure within are so vast, we could be out by a distance equivalent to 100s of solar systems.

C is a fundamental constant that governs our world, but asking if it is different in different locations is the same as asking if h (plancks constant) or pi(ratio of a circles circumference to its diameter) is different in other areas of the universe.... It could be, we will never know, but we have to assume these constants remain constant.

maybe a silly question but how could pi be different? i get that the laws of physics could (in theory) be different somewhere else regarding the speed of light, but if a circle's circumference/diameter stops being 3.14(...) how could it still be a circle as opposed to just an ellipse in some other solar system/galaxy/etc?

If you bend a circle in the plane of the circle, you get a different value of "pi". I think. Applying that to the real world is a challenge, to express it mildly.

When it comes to the speed of light the current theoretical physics equations and the actual observations don't need the speed of light to have changed at least anything near substantially over time. Would surprise me a bit if they'd missed such a thing.

I've read/watched a lot of science stuff and have never come across the idea that 'c' might be different in different epochs or locations in the universe. If the cosmologists suspected such a thing I'd have come across it.

Googled it: https://en.wikipedia.org/wiki/Variable_speed_of_light

The results appear meager. Good they have checked out about it though.

The pi ratio thing is fairly easy to demo, but no so easy to express in type, but basically if you get a ball, and measure from top to the middle following the curve you will get a value that could be expressed as the radius in a curved space, but isn't the radius of the sphere....if you exist within a curved space tome, which we almost certainly do, the radius we measure will be curving in this way....I hope this sort of makes sense, it's really easy to demo on a ball by measuring the part of the circumference vs the radius and looking at the difference. If you then get a flat piece of circular paper and press it against the surface of the ball you should notice the radius will curve slightly, even though it us imperceptible to a being that exists on the surface of the ball.

A circle is a defined entity. Pi is going to be the same unless you want to change the definition of what a circle is. It would be weird to change the definition of what a circle is to force pi to be a small puppy.

Also, if the speed of light were different in the past than it is now, it would be different than it is now.

There would be visible consequences in distant phenomena (their properties) if the speed was different in distant observation of effects there that are only now arriving. We should think what these are and propose them for testing.

That said of course all is different in some little or more important sense eventually in extreme conditions because spacetime is not what think it is and anything you define in it is not well defined unless you control the entire reframing that explains the observation and reproduces such effective things as geometry and speed of light.

Pi doesnt exist in nature by the way. Only in the limits that currently make us happy in idealized continuous calculus dominated models. And these models work very well by the way up to a point soon reached.

The Pi of mathematical models is not in risk. The models are. "Circles" in curved spacetime or any realization of Pi in terms of geometry observed are subject to uncertainty but the idealized models are very safe forever in their fictitious worlds. Arc-tangent series or Ramanujan series for Pi are safe and removed from actual physics.

I don't know what that has to do with the OP, but since you mention it...

The completed infinite decimal expansion of pi does not exist in nature. Or, if it does, it cannot be observed to exist.

Progams that output this decimal expansion indefinitely do exist.

So, regarding the existence of pi itself, it depends how you define it.

I mean in the laws of nature eventually when we recover from calculus everything won so far. Programs and math are part of nature i meant that circles are not part of the final or higher level theory only its limits of simplification. In essence any mathematical realization of Pi will fail eventually to be faithful in nature. Math is about ideas and their consequences not precise realization of them always in terms of actual matter. I have no evidence of infinity in anything yet.

Like e similarly doesnt exist although the processes are very well described by it.

We do not have a realization of a circle in anything made of matter or energy although clearly many phenomena are well described by this logic ie even electromagnetic waves themselves (sine waves,wavefunctions etc but all eventually go away when you do the next level theory in which those idealizations are a limit) .


Programs that produce indefinitely do not exist because something will stop them eventually lol ie some breakdown of the system or the geometry/galaxy etc in which they exist.

I don't understand why you guys are being so irrational

The constants e and pi drop out of the simplest first and second order differential equations without any reference to geometry or physics.

If you live on the surface of a sphere, and measure circles on the ground that have a different ratio of circumference to diameter, that just clues you in that you're on a curved surface.

Precisely. There are no irrational numbers in physics if you try to be faithful to the principle of it all.

Everything that requires calculus and infinity is only an approximation. This is also the reason Quantum field theory is full of infinities and strings are not the answer.

Then there's no exactly a half in nature, either. Why pick on pi?

You're saying that the standard distinction between halting and non-halting programs in computer science is unimportant because, in physics, everything eventually halts anyway?

It is important only if the halting time doesnt exceed the lifetime of the system obviously.

Also half is just fine . 2 protons vs 1 proton.

Nonsense. The lifetime of the universe is irrelevant to the theory of what Turing machines can and can't do.

The point being that all protons are identical? No two are, as they occupy different positions in space.

If the halting time exceeds 10^1000 years when all the universe has become your computer then what are we talking about here! You will never reach it to see what happens.

We can never know the next 10^10000 digits of Pi starting from 10^100000 position.

The protons may not be ultimately identical but a great deal of what they they can do individually is shared by all of them hence you can have half of what 100 protons can do or 100 neutrons etc. No problem. Surely you can not have half of everything out there. Like what is half of planet earth. It is no longer a planet with the usual properties if you cut it in half. What is half of traffic jam?

The Halting problem, for example. It isn't a problem if everything halts.

https://en.wikipedia.org/wiki/Halting_problem

Let the halting happen when the digits of pi it calculates repeats the first 10^80 digits of Pi (obviously you expect eg every a few million digits to see somewhere 3141592) . Are we sure we know if this will ever happen before universe kills (renders non operable) the program it is running it or it runs out of space to store the digits in order to know and compare the sequence ?

I can make it more interesting by making the number of target digits repeated depend on n (the number of current digits calculated) in such a way that its heuristically not decidable if this actually ever happens anywhere (like eg it has heuristic probability 10% or something unlike the 10^80 that has 100% chance to happen but nowhere near that for as a long as the universe exists in a state that makes the program able to continue indefinitely and not saturate resources of the entire universe) .

If the speed of the computer is based on the speed of light and the speed of light speeds up fast enough you could get all the digits of pi before you're done eating turkey dinner.


PairTheBoard

But you still need to store the results somewhere. You cant have your turkey and eat it too.


Now if you gave me a phenomenon that reflects already the knowledge by nature of such a deep digits sequence i would be amazed.

One proton is a third of three protons.