We might at first think of all the universal constants there are such as the speed of light, mass of a proton etc. A recent articles proposes that the speed of light does change in a vacuum and didn’t light move faster when the universe was younger anyway?
Is there anything out there that is in fact an undisputed constant? This question actually is related to my philosophy class (I am the teacher) and the arguments of Heraclitus and Parmenides.

Thanks for your help.

PS. If anyone is so inclined, do concepts such as 1+1=2 count as universals?

I don’t believe that physical constants must, in fact, be constant over time. There are proposals that the speed of light or the fine structure constant has changed. Some of these proposals would have unusual implications like the nonconservation of energy. On the other hand, mathematical constants are definitional 9Or at least mostly so), so that pi and e and Euler’s constant, gamma, have to be what they always were. Those are all irrational (I believe gamma is) so that we can never know their precise value, but the value cannot change, it can only be determined more accurately. Of course the same is true for (at least most) physical constants even if they are truly constant except of course when expressed in units where they are defined.

Time itself of course. Time measurement is based on the ‘second’, which is defines as “The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.”

Light itself may not always travel at c, but I thought c was the universal speed limit that has not yet observed to have been violated and only reachable at all by massless particles.

There are two different sorts of constants. On the one hand, you have definitional constants like c and hbar. For these, it’s not even meaningful to speak of them changing, because they’re the things you compare everything else to. Right now, c is equal to one times c. Ten billion lightyears away, c is also equal to one times c, and at the dawn of the Universe, c was equal to one times c.

On the other hand, you have dimensionless constants, like the Fine Structure Constant. These, it is meaningful to say that they change. Nobody knows for sure whether they do or not, but the concept is at least meaningful. There are plenty of these that certainly appear to be true constants (nobody’s ever produced any significant evidence of the Fine Structure Constant changing, for instance), but there’s always some level of dispute (that being how science works, after all).

How could that possibly be measured? Everything is relative. Was light faster when the universe was young, or was your unit of measure slower?

How do we know that the speed of light today is the same as the speed of light yesterday? Perhaps the cesium atom and light are slowing down at the same rate.

You could say that, so long as you specified what you’re comparing the size of the atoms to. You could, for instance, say that atoms are getting bigger compared to the Compton wavelength of the electron. Which would ultimately be the same thing as saying that alpha is changing.

To be clear: Most Christians don’t believe this; they don’t need to, because most Christians aren’t young-Earth creationists and so don’t believe the Earth was created in exactly six twenty-four hour days in October 4004 BC. That is the kind of dogma which this lie is propping up.

I was listening to Penrose’s interview on Science Friday and he had something interesting to say. His point was that the early universe may have been extremely low in density - thereby macro properties such as temperature may have different meaning. I did not quite understand everything he said, but the jist of it was that there could be communication between before and after the big bang.

He also explained how time could be faster (sort of like how time slows down near black holes) in such an environment.

I am not a Physicist - so feel free to correct my understanding.

That’s not really the correct way of putting it. We “know” the value of pi just as well as we know the value of 1 (which is rational), or the square root of 2 (which is irrational). Irrationality just means you can’t write it as a ratio of integers – you’ll never be able to write a “last” digit in the decimal expansion, or know that after a certain point it repeats itself – but I don’t think there’s a meaningful way to argue that we don’t know the value of pi.

I am no expert, but I have seen this proposed by physicists, such as Lee Smolin (more in the vein of out-there-physics). One idea is that higher energy photons might be faster than lower energy photons. (They would have to very high enery indeed, as I don’t think this has ever been experimentally observed, not even with the Fermi gamma telesope looking across the universe. )

It was suggested that a 'higher c" in the early universe might do away with any need of inflationary theories.

There have certainly been serious scientific proposals that the value of alpha might have changed over the lifespan of the Universe (though even the proponents of these proposals don’t generally think them likely). And the popular press, when reporting on such proposals, for some reason tends to interpret “changing alpha” as meaning “changing c”. So there’s not necessarily any religious maliciousness going on here, just common incompetence.

Kronecker, wrote “God made the integers; all else is the work of man.” This in part is in reference to the manner in which all[sup]*[/sup] the other numbers can be constructed.

If you want the Integers, the only number you need is One. All the others flow from there.

One could argue that once you have allowed the existence of logic, all of mathematics instantly exists. This is a curious philosophical argument that still runs. Does a mathematical theorem that has not yet been suggested, let alone proved exist? It is true in any sense? (Don’t go here. Really.) It does however address (but not answer) the OP’s question about whether there are mathematical universals. If I express Peano’s axioms, does the entire countably infinite set of Integers suddenly exist? Did it always exist? Does the entire set not exist, but only those numbers that have been somehow expressed exist? Is there some manner in which these numbers could be different with different expression instances? Most people will answer, No, Yes, No, and No. But not everyone.
If the successor to One is denoted as Two. Does that make Two a pre-existing constant? What about the rest of the Integers? What about the algebraic numbers? How about the transcendentals?
Transfinites? There are a lot of these[sup]**[/sup]

Even in alternative universes, we have no way of coming up with a way that the way mathematics works can be different.

One sort of assumes that there are parameters that set the nature of the universe. We may not know them all, or indeed any of them - even what the parameters are, let alone their values. But there seems to be a great deal of suspicion that at least quite a few of the currently know physical constants are actually derived from more fundamental constants by mechanisms we don’t yet understand. This is partly fuelled by the problem that there are too many of them for comfort.

For some values of all.
** For very large values of “a lot”