I think you meant photons. Protons at c would be kind of a different thing. And immensely cool to watch, assuming the universe didn’t asplode. 
I rather thought that the question was, why is the speed of light 2.99 x10^8 m/s, as opposed to 2.3x 10^8 m/s. What deeper quality of the universe determines that the actual number should be the one we have, instead of some other number?
Is there an answer to that question?
Missed the edit window:
And by answer, I don’t mean “the units are defined that way”. It is conceivable that we could live in a universe where the speed of light, according to our present units, was faster or slower than it presently is. What property prevents that being so?
The likelihood that we wouldn’t be around to notice. Tweak the laws of physics a little, and you tend to get a universe where life doesn’t seem likely. If one presumes many universes as seems probable, then only the universes whose physics allows life will have observers around to ask questions like “why does that law of physics have that particular value?”
Here’s the simplified version as I understand it.
Look at E = mc[sup]2[/sup]. The real importance of that is the understanding that energy and matter are the same thing. That is, E is proportional to m. The more mass an object has, the more energy it contains. (This is actually a simplified version of a more complex proportionality that would include the case of massless particles, which have momentum rather than mass.)
To make a proportionality into an equation, a constant is introduced. That constant is the speed of light squared.
Therefore, you can test the equation by an approximate measurement of the speed of light and see whether a transformation of mass into energy, say, in a fusion reaction, gives the experimental result.
But you can also rewrite the equation as E/m = c[sup]2[/sup]. If you know the values of E and m, you can work out what c must be. That’s why in our universe, c must equal 2.99 x 10^8 m/s, as opposed to 2.3 x 10^8 m/s.
Can there be other universes where the reverse is true? I believe that is an implication of string theory, that different universes can have different basic physics constants. If that’s true, then the reason that c equals 2.99 x 10^8 m/s is because we happen to live in that universe and not another one, and nothing deeper.
But that’s also why so many people feel uncomfortable with the idea of string theory. They want that deeper answer.
That’s one way to look at it. In another sense it’s okay to say that light will always travel at c (which may well be a physical law for massless particles). But the interactions that occur with other matter, or energy, or whatever you wish to call it, makes it “appear” to travel at less than c. I put “appear” in quotes because it may not exactly be what you think.
Consider this analogy. Suppose I have some shoes on that force me to always run. I can only go one speed, fast (they never tire me out, either). You see me running down a hallway that’s lined with open doorways. I head through a doorway, and then a little while later pop out of the doorway next to it. You don’t know what happens outside the hallway[sup]*[/sup]. If I kept doing that, you’d say my apparent speed through the hallway was slower than my “normal”, unimpeded speed.
But what light does may be more like me entering a doorway, disappearing (I mean physically, actually “ceasing to exist”), and then an exact clone of me showing up a little while later. For all intents and purposes, it’s the same me. Light’s also more complex than just one person running through doorways, which is why saying it appears to slow down is not what you might expect.
Thanks for that, Exapno. In a sense, the “why” question can always be hidden by “because the units we chose say so”. The “reason” g can be measured at 9.8m/s^2 is “because” metres and seconds are the units we chose. We can measure g without any theory of gravity at all. But the deeper reason is that gravity is dependent upon mass, and the earth’s mass is just so as to result in a g of 9.8m/s^2.
I get that seconds and metres are defined by reference to stable physical criteria and that the speed of light plugs into those criteria (like the decay of cesium atoms), and the argument that says any measurement of the speed of light assumes the speed of light because it is a constant. But that still does not answer the question why this speed of light and no other. The idea that if the speed of light were to be 2.3 x 10^8 m/s, this would mean that the universe would be so distorted that the decay of cesium atoms would change and the length of a metre would change so that it would magically come out at 2.99 x 10^8 m/s again does not, ISTM, satisfactorily answer the question.
So the constant c is simply the square root of the ratio of the amount of energy “locked up” in a certain amount of mass. One unit of mass can produce ≈ 300,000,000² units of energy, so that gives us the specific value of c.
2 questions come to mind:
Wonderful point, thought food. Thanks for putting this in the exact, simplest formulation in the philosophy of science.
Leo
This means …?
For comparison: Suppose that, for some unfathomable reason, society had decided to measure all vertical heights in centimeters, but all horizontal lengths and distances in inches. A measurement of a slope, then, would have units of centimeters/inch. After a while, though, you would notice that there’s something special about the ratio (with units of slope) 2.54 centimeters/inch. It shows up in all sorts of equations for things like how the height of something changes when you rotate it. Since 2.54 centimeters/inch is a slope, you might describe it as being the slope of something-or-other. But the significance of 2.54 centimeters/inch isn’t that it’s the slope of any particular ramp; the significance is just that 2.54 centimeters is one inch, and if you’d used the same units for vertical and horizontal to begin with, you’d have noticed that easily. Why is it 2.54 centimeters/inch and not some other number? Because those are the units you, for whatever reason, chose.
This is very closely analogous to the situation with space and time. For historical reasons, we have chosen to measure spatial dimensions in meters, and the time dimension in seconds. We notice that there’s a constant that keeps showing up in our calculations, and we call it the Speed of Light, since it has units of speed. We measure it to be 299792458 m/s, but really, what’s going on is that one second is 299792458 meters.
That’s a pisser. Gotta think about that more…Thanks.
Leo
This is superb - thank you.
Mass is energy. They are the same thing. Or, if you like, manifestations of the same underlying thing, as ice and water vapor are manifestations of the underlying H[sub]2[/sub]O.
Why the square root? Because it’s derived from the Pythagorean Theorem.
This is one of those moments that I assume physicists refer to when they talk about the beauty of an equation. If not, it works for me because it demonstrates so beautifully that math and physics are one glorious whole that start from basic axioms and build up a universe.
It helps to have a triangle to picture when you think about the Pythagorean Theorem. I just read Robert P. Crease’s The Great Equations, which I highly recommend for its explanations of why these equations matter and its sense of the beauty and wonder that they can evoke.
And fortunately, Google Books give the appropriate page in its preview mode. Click on the p. 167 link to open the full text. You can read the next several pages as well and they open up Einstein’s thinking from this thought experiment to the formulation of the equation itself.
Huh? I thought mass has energy.
If you think about it - and also take that energy “has” mass - how is that different?
Disclaimer: I’m not really qualified to answer this question, but I am fairly sure that’s right.
ETA: maybe think of it like this: what are the properties of mass? I think the every-day assumption that mass equals a “solid thing” is confusing you.
Exapno I’m surprised at you. You know that statement is not true. Don’t you remember a previous thread where myself, Stranger and Chronos all explained why isn’t true.
Mass and energy are not things they’re properties of a system, and one cannot be converted into the other.
Does that mean that I’ve literally moved 299792458 meters through the time dimension over 1 second? Time exists as a real dimension like x, y, and z?
OK, I just took another look at that thread. As I suspected you properly corrected me, but never were able to give an alternative way of expressing it purely in non-mathematical terms. That’s why I put in the “manifestations of the same underlying thing” clause.
But if even that is not a good enough way to express it, can we try to come up with a phrase that satisfies you and still addresses “What are these units that can be manifested by either mass or energy?”
Your version there was “a system that has energy of E and a mass of m.” and “Imo it’s much clearer to say that the mass of a system (if you’re consistent in defining the system) is absolutely conserved. However one form of the system’s energy can be converted to another, and the individual particles that make up the system can change resulting in a local mass defect.”
That’s technical English but not popular science English. And one is convertible into the other.
I’m not quite following you. What is it that you’re trying to express in English versus math?
Let’s try, "where does the energy in a fission reaction come from"?
The potential energy of the nucleus is converted to EM and kinetic energy.
Or: The binding energy is converted to EM and kinetic energy.
BTW I couldn’t find that thread, how about posting it.
I think that when you start with binding energy and talk about how it’s converted to EM, you’re already past most people’s technical vocabularies.
I also think that I’ll start a new thread since this is a hijack.