Physics/Astrophysics Questions
That should be 186,000 miles/sec.
From my understanding, from the perspective of the photon, it IS moving at infinite speed. The photon experiences no time.
EM waves have a velocity, in a vacumm, of 1/sqrt(eu) where e is the permitivity of free space and u is the permeability of free space. The value that pops out is c (299792458 m/s)
There’s no substance with smaller values of e or u than the vacumm so c can’t be bigger.
The speed of light is one of the fundemental constants of the universe. It is the speed limit of the universe. It is the lack of mass that allows the photon to achieve this speed. Everything with mass would have to be slower.
Nothing can go faster than it because, the universal laws are set up so that anything going at the speed of light will appear to be going at that speed according to all observers regardless of speed. So if a photon is observed by a stationary observer and by also by an observer going 100,000 miles per second away from of the photon, both will oberserve the photon coming at them at 186,000 miles per second. Now suppose that I had a ship that went 187,000 miles per second. The stationary observer would see me able to escape the photon which can’t jive with my view of the photon still coming at me at 186,000 miles per second.
As to why it is 186,000 miles per second, a better question might be why is is a mile the distance that light travels in a second, or why is a second the time it takes for light to travel 186,000 miles. The speed of light is what scales the relationship of the universe between time and distance. In doing calculations many physicists define units of time and distance so that the speed of light is 1. Any other measure of time relative time and distance are going to involve some arbitrary units (like the length that 1,000 Roman paces or the 1/86,400 of the time it takes the earth to spin on its axis) or else on some physical process such as the vibration frequency of an atom which will in the end involve certain physical laws related to the speed of light.
There is always the relativistic picture, that this is a feature of the geometry of space- time and the photon is already moving along a path of least resistance, in this case a null geodesic (along which there is no proper time) since the particle has zero mass.
As for why one gets so-and-so many miles per second, well, what’s a mile? It’s an arbitrary unit so you get an arbitrary number for the speed. Set c = 1 to keep things simple.
From the perspective of the photon, the entire universe (in the direction the photon is traveling) is squashed down thinner than a sheet of paper. Wherever it’s going - it’s already there.
The photon may have no mass but it does have energy and therefore is subject to the rules covering energy, which we call relativity.
Yes although from the same perspective the distances are also zero so from the photon’s perspective its speed is 0/0 or undefined.
Sounds like we’re veering close to Anthropic Principle territory.
Why is the speed of light 186,282.3950 and not something else? Why is pi 3.141592654…? Why is G 6.674×10−11 m3⋅kg−1⋅s−2? Because if they weren’t, we’d be living in a different universe.
eta: for all we know, in the “proper unit system of the designed universe”, these values may be 1.
Well in this universe we can set c to 1 but Pi is a ratio of circumference to diameter. Pi can’t be other than what it is unless we fundamentally change the geometry of our universe.
Unlike those other numbers, “pi” is not a physical constant, nor is it measured by units- it is dimensionless.
ETA we should regard pi as a true mathematical constant; in fact its value cannot change. It is true that different manifolds can have positive or negative curvature but that does not have to do with the value of pi.
Hate to ask, but…
How fundamental are pi (and e)? Is there some mathematician somewhere who has considered some alternate spatial geometry where these would be different?
I’m having difficulty imagining such a thing.
Both pi and e have mathematical definitions that have nothing to do with geometry. For example, pi = 4*(1 - 1/3 + 1/5 - 1/7 + 1/9 - …). This doesn’t change depending on the geometry of space.
That’s true, but the only reason we can set c=1 is because it is a dimensioned quantity. When we say c=1, what we’re really doing is just measuring velocity in units of light-seconds per second. But that’s just another name for the same thing. Saying c=1 doesn’t change its value, just the units it’s being measured in.
Pi doesn’t have units, so there’s no other way to write it in the same sense.
True. In a different geometry there may be a constant that is very relevant in calculations, but pi would still be 3.14159 (etc.)
By analogy, you could imagine a creature living in a medium (in our universe) in which light traveled very slowly - but if that creature did physics, it would find a particular speed (186000 mps) turning up in a lot of places. It wouldn’t call it the speed of light - but probably something like the “speed of causality” or something.
Imagine, if you will, a world in which, for some reason, we’d gotten into the habit of measuring all horizontal distances in inches, but all vertical distances in centimeters. I could take a meterstick, and set it on its end, and say that its height was 100 cm. Or I could take the same stick, lay it down flat, and say that its length was 39.37 inches. Or I could hold it at an angle, and find that it has a height of 70.7 cm and a length of 27.83 inches. I could even come up with formulas describing things like its length in inches whenever it’s angled in such a way that its height in cm is a certain value. And in those formulas, I would find that there’s a constant that shows up all over the place, equal to 2.54 cm/inch. This constant has units of height divided by length, so I might call it a slope, and I might find some interesting tilted surface that has that slope, and name that constant the Slope of <That Thing>. And then I might ask just why tilted metersticks care about whatever that thing is, that might seem completely unrelated to sticks.
But of course, 2.54 cm is one inch: They’re the same thing. And so that constant that shows up all over the place, 2.54 cm/in, is really just a fancy way of writing “1”, and if we didn’t have this silly custom of measuring length and height in different units, that’d be completely obvious. And it’s hardly a surprise that the number 1 shows up all over the place in formulas.
Just so, we have for various historical reasons chosen to measure spatial distances and times in different units, and so there’s a constant c that shows up all over the place in formulas, but if we measure them in the same units, we find that c = 1, and it’s all so much simpler.
Chronos: for historical reasons, submarines (US ones anyway) measure the amount of water above the ship in feet, and the amount of water below the ship in fathoms.
I was being funny, but…imagine a universe where pi is equal to 3. Now THAT would be an interesting universe.