Comment by gumby
2 years ago
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.
https://en.m.wikipedia.org/wiki/Mr_Tompkins
There's a joke there in those last two titles but I'm not going to make it.
Also from Gamow, and something that blew my (then) 12 year old mind: 1-2-3-Infinity
https://en.m.wikipedia.org/wiki/One_Two_Three..._Infinity
Wow thank you I cant believe I've been ignorant of this my whole life. Thank you so much
Also see Redshift Rendezvous by John E. Stith. It's a novel, not a tutorial, but relativistic effects play a major part at several points.
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!
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I think the actual answer to your question is that the outcome you're hypothesizing would be absolutely useless for teaching the reader about relativistic effects, so there's no reason for someone to write such a book for a lay audience.
Why would these dependent on the speed of light?
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.
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I am not a physicist:
I've read that C is really the speed of causality, and that electromagnetic radiation is really a disturbance in the EM field that is propagating along a path. A photon is really information about a prior event, that caused the disturbance i.e. emitted the photon, propagating across the EM field at the rate C. Likewise gravity, the strong force, and the weak force are also propagated at the speed of causality. E.g. if the Sun suddenly doubled in mass for some reason, it wouldn't just take eight minutes for us to see the change in EM radiation, it would also take eight minutes for us to feel the gravitational change.
The whole bit about the physical laws being the same follows from that, and the assumption that there isn't any way to transmit forces across spacetime except through transmission of causality.
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