For a good introduction to developing an intuition about special relativity via low speed of light, I really recommend George Gamow’s “Mr Tompkins in Wonderland” (or “in paperback”). These short stories explore things like how the world would look if the speed of light were 10 mph.
> Four Books in the Series
>
1940: Mr Tompkins in Wonderland
1945: Mr Tompkins Explores the Atom
1953: Mr Tompkins Learns the Facts of Life
1967: Mr Tompkins Inside Himself
There's a joke there in those last two titles but I'm not going to make it.
But does that make any physical sense? All the other speeds we are familiar with would be proportionally slower, since they are all ultimately determined by fractions of the speed of light, right? For example, if the speed of light were 10mph, the speed of sound would be something like 0.6in/h, days would be much, much longer, chemical reactions would take hours etc. Overall, I don't think it would really make any difference for a human in this world: everything would actually be perfectly identical.
I don't know whether it makes physical sense. There are other fundamental constants, too. Changing just "c" might lead to stuff like "atoms can't exist" or "the universe as we understand it would not evolve," etc. Or, not.
Changing "c" is different from just changing your units.
Yes, changing c would definitely lead to stuff like "reality does not exist as we know it".
c goes into many other constants and determines most of the laws, especially in e&m. Realistically, atoms would not be able to hold up against the pressure to collapse, pretty much all matter (if it still existed) would condense to very very very cold solids instantly. We'd be shut out of most light from the sun for potentially hundreds of thousands of years.
I'm just starting my big graduate theoretical physics journey so i really can't do all the relativistic quantum math yet, take what i say with a grain of salt!
AAUI the basic laws can be expressed with dimensionless constants, and in modern physics c is a conversion factor for convenience. I don't know if there's a way to adjust all of the "real" physical constants conjointly which would amount to "just like the Standard Model with a different c".
I want to say it's not incoherent to say e.g. "Newtonian mechanics, but relativistic, with a different c", except of course e.g. Newtonian gravity with its action at a distance doesn't fit, and I wonder if really even contact forces fully work if you try to follow through every detail.
Because the basic understanding of physics is that all particles move at constant speed c in spacetime; the proportion of their speed that is happening in the three spatial dimensions is determined by their mass. So, any particle's speed through space is a fraction of the "speed of light" c; the higher its mass, the lower the fraction.
The other items I mentioned are then caused by the speed of these particles. The speed of sound in a medium is determined by how fast particles collide into other particles in the medium. The speed of the earth around its axis (the length of a day) is determined by the speed of the particles making it up in the warped spacetime of the earth's gravitational field. The speed of chemical reactions is also limited by how fast atoms and electrons move and can interact with each other.
The length of a day, at least, is unrelated. There was a big splash in the news not long ago because it was determined that the length of Earth's day was changing and we might need to change it by a second.
Venus has a much, much slower rotation on its axis, but Mars is almost the same.
I doubt it was a big splash of news given that leap seconds have been a fairly routine thing for quite a while. Lately there’s been talk about a possible negative leap second, as Earth’s rotation speed has been increasing for a few years now. Many things can have a measurable on Earth’s rotation, including dynamics of the molten outer core, earthquakes, ocean currents, and melting of polar ice caused by the climate change.
Even before we invented precise enough clocks that there was any need for leap seconds, we knew that Earth’s rotation is slowing down due to tidal drag – the moon is literally robbing angular momentum from Earth, and getting farther from Earth in the process. Back in the Cambrian, day length was around 21 hours. Shortly after the formation of the moon, 4.5Ga ago, it would have been only around five hours, assuming the giant impact hypothesis is correct.
Leap seconds are just an imperfection in how we measure days. The recent splash was largely because it was being blamed on changes due to global warming.
In any case, it all goes to my point- the Earth's mass has no bearing on its rotational speed.
There was once a flash game that integrated principles of relativity into its mechanics for teaching purposes. It was a series of 2D rooms with the goal being to move from point A to B. I remember there being changing distances as well as colors, for example moving a certain way would change the color of a lock so that the key of that color could unlock it. It was good fun, and it was written by a physicist and hosted on a humble personal site. I can't remember where I saw it, but if anyone knows the reference, please share a link.
My understanding (as a layperson) is that if the fine structure constant changes even a little bit, you basically don’t have atoms or molecules as we understand them. So the game would be something like:
a=1/1: Nothingness as far as the eye can see
…
a=1/136: Nothingness as far as the eye can see
a=1/137: BOOM! Life, the universe and everything
Maybe I’m off, and maybe I have the numbers backwards (again, I’m a layperson), but I feel like the speed of light may be an unusual case among universal constants in that you can actually show an interesting gradient of effects as it changes.
That is not how I remember physics (former PhD student here):
The speed of light has a dimension, so it in itself does not change physics (thought experiment: everybody switches to feet-per-decade as the unit of choice, nothing really changes). It is the dimensionless constants that determine the real physics.
Have not heard the statement that is alpha was a tiny factor larger/smaller that would make atoms no longer exist. It's this were true, this would actually be a way to actually calculate it from first principles ('at which value of alpha are there solutions to this equation').
Edit: typo
There is the Hoyle state, a peculiar resonance state that is very important for nucleosynthesis. Without it, stars would not produce a lot of carbon. It appears to be finely tuned for complex chemistry and thus life to evolve.
The speed of light does change physics, as does any fundamental constant. Expressing a speed in different units does indeed yield different numbers, but that is not equivalent to a change of speed.
Changing alpha means that electromagnetic force get stronger or weaker, thus the atoms still exist but with different orbital levels. Considering how intricate the orbital levels of atoms are, it's not shocking that a tiny change in alpha completely redefines chemistry, but chemistry would still exist.
The point is that all of the speeds we measure are actually measured in units of the speed of light, if you go right down to it (seconds and meters are defined in terms of the speed of light). So, the value of the speed of light doesn't really matter - which is why c=1 is often used in many kinds of physics.
The fine structure constant is dimensionless and would be different if c were different. When doing a unit conversion, one also has to alter other constants so as to be consistent with observed reality; whether one alters other constants or not is the difference between talking about a change in units and a change in c.
It looks like this still doesn't cancel out? It's an interesting point as to whether our hypothetical change in c would affect the relationship between photon energy and wavelength, but either way we get a nonzero power of c.
Another game in this vein of "teaching math/physics through gameplay" is Hyperbolica, where you explore a 3D world with hyperbolic (and later spherical) geometry. It's mind bending.
Ratios only matter in vibrations (frequencies) because the vibration is a non-uniformity within a period. Translational speed isn't like that.
The main point of special relativity (Lorenz transform) is that it is a mapping between [0, c] and [0, infinity], so ratios to speed of light are not absolutely definable. Light has infinite speed in its own reference frame.
Not really AFAIK, since it's an asymptote regarding your speed vs speed of light, so it's a pretty continuous curve. The point where things become weird is at close to the speed of light so in your example at like 1.9~1.999 m/s, and physics "break" at 2m/s, but there's not a sigle point between 0~1.999 where anything "surprising" happens.
I feel like your field of vision expanding and everything around you freezing might be considered surprising. These don't become noticeable until near the top end.
Things get "weird" non uniformly at all the various fuzzy intervals where the effects of relativity are significant in scale compared to the measurement error, in time and space dimension, of whatever phenomena you are studying or experiencing. There are many of these phenomena at different scales, and which ones you care about is subjective.
