Taking BrainGlutton’s formulation of it as three different questions, but in reverse order.
Mijin is correct in that it’s a consequence of the photon being massless. Even if it turned out that photons had some (astonishingly tiny) rest mass, none of special relativity would change and c would still be c. It just wouldn’t be “the speed of light”.
Flippantly, it’s not: c = 1. The numerical value is completely arbitrary since it depends on our choice of measurement units. Historically, that it has this value is thus a very indirect consequence of Babylonian counting and French Revolutionary politics.
While it may seem odd to think this way, in general the only meaningful questions in physics can ultimately be framed as questions about unitless numbers. Thus why the speed of sound involves the number 340 isn’t a useful question. Asking why it’s roughly a million times smaller than the speed of light is. This ratio doesn’t change when we change units and hence is expressing actual physics.
Why not? People have certainly thought about how much of the content of special relativity follows from just assuming that there’s some limit. Such an assumption may seem odd in classical physics, but it’s interesting to see how far it takes you.
Furthermore, the most astonishing insight of special relativity is that space and time are interchangable. But in classical physics these have different units. Any attempt to equate space and time is thus going to involve some factor that has the units of a velocity. So in any such theory there’s going to be some special velocity.
It’s then actually quite difficult to come up with a natural role for such a velocity in the physics that isn’t some maximum or minimum speed.
In what way is the number 1 any less fundamental than the number pi? If anything, I’d think it would be more fundamental. And the speed of light is equal to 1.
Yes, I know, 299792458 m/s doesn’t look like 1. But that’s not the Universe’s fault; it’s just our fault for using funny units. Picture, by way of analogy, that you had a piece of graph paper that was ruled in centimeters on the vertical axis, and inches on the horizontal axis. You might discover that a line that had a slope of 2.54 centimeters/inch has some interesting properties, and from that conclude that the quantity 2.54 centimeters/inch is some sort of fundamental constant. But of course, the quantity 2.54 centimeters/inch is just a fancy way of writing “1”, and only looks weird because, for some reason, you’ve chosen to use different units to measure width and height. Well, just as 2.54 centimeters is one inch, 299792458 meters is one second.
OK, so that covers why that particular speed would be interesting. Why does it have the property that the sum of any speeds less than that is still less than it? Well, ultimately it comes from the fact that there’s a difference between space and time, in the way that distances are measured. In three-dimensional space, if you want to know the distance s between two points, you set up a coordinate system, find the coordinates of the two points (let’s call them (x1, y1, z1) and (x2, y2, z2), and find s^2 = (x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2. Even though you used a coordinate system to find this answer, it’ll turn out to be independent of coordinate system: Any system you choose will give you the same answer. Well, there’s a similar coordinate-independent system for finding the “distance” between two points in spacetime, except there’s a minus sign on the time part: s^2 = (x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2 - (t2 - t1)^2. And ultimately, that minus sign ends up leading to all of the things that seem odd about Special Relativity.
Einstein basically took it as a postulate: that the speed of light is constant in any reference frame. From this you can derive all the other interesting features of the speed of light. For example, that the time interval between two events will depend on the speed of the observer, and that an observer moving faster then light would actually see the time interval become negative (ie, the order of events would reverse), hence forcing you to make the speed of light an upper limit to preserve causality.
But taking it as a postulate isn’t very satisfying. I think you can actually derive the constant speed of light from the much more intuitively obvious conjecture that laws of physics can’t depend on the reference frame of the observer (so if I’m closed up in a room moving at constant velocity, I can’t do an experiment to figure out how fast I’m moving). Since the speed of light is a consequence of Maxwell’s equations, then a unchangeable speed of light would seem to be a consequence of this. This is a pretty satisfying answer, IMHO
Alternatively, you can do what Chronos does in his second paragraph, and basically assume that the Universe obeys Special Relativity, and work backwards to get Einstein’s postulate. That certainly works, but its far from intuitively obvious that we live in a Mankowski space, so again, I’m not sure thats a very satisfying answer.
In fact, it’s Maxwell’s equations that caused Einstein to think that the Speed of Light was a fundamental constant, invariant to different observers, in the first place. The Michelson-Morley experiment empirically verified that, but the evidence seems to be that Einstein wasn’t aware of that experiment when he published his theory.
You seem to be answering the question “how do we know this to be true”, while I was attempting to answer the question “what is the underlying cause for this being true”. Two different answers to different questions.
I haven’t taken physics in 15 years so I’m a bit rusty so If I’m wrong please correct me but I did want to put in my 2 cents
I wold basically reiterate what Chronos and Simplicio stated. It all began with Maxwell’s equations. These equations stated that interactions between magnetic and electrical field produced a wave that propagated at 299,792,458 meters per second, and which seemed to explain light. Oddly though there didn’t seem to be any indication of a frame of reference, so for any observer this speed seemed to be the same. This was in total violation of neutonian dynamics which said that velocity vectors were additive.
Well at this point you could claim there were problems with Maxwell’s equations, or possibly that this propagation was relative to some universal aether. But Einstein took the view that what needed to change was our whole intuitive understanding of time and space. So he took as an assumption that light speed was constant and started running thought experiments involving people on trains moving 0.9c and shooting laser beams back and forth out of their pocket watches. He found that in order to make these work he needed to assume that velocity vectors were no longer additive, and that mass, time and distance changed depending on your point of reference. As a result of this you find that the energy required to accelerate to the speed of light is infinite, and as stated in earlier posts, the concepts of before and after also depend on your frame of reference such that if communication were possible faster than c, causality would have to be abandoned.
If I were alive at the time I would have thought he was a crazy crackpot who should be ignored, but as it happens later experiments show he turned out to be right.
By the way Brain Glutton, if you have a basic grasp of algebra, special relativity is fairly easy to understand (In my highschool physics course it was covered over a couple of weeks) So If your really interested I would recommend spending a few evenings with a introductory physics text book. (Does anyone have any recommendations?)
This thread seems to be running around in circles chasing its own tail, and I can easily understand BrainGlutton’s continued frustration at trying to make sense of it. His/her continual plaintive cries of “but whyyyyy” echo my own. Maybe it would make more sense if we understood why an object also becomes thinner as its speed approaches c. I kinda sorta got the impression from one of Brian Greene’s books that as an object’s speed increases, it starts to ‘tilt’ out of normal 3-dimensional space, and when this angle of tilt reaches 45º, it ceases to have spatial extension. So can it be said that space somehow ‘wants’ to hold us back, and as we stubbornly attempt to overcome this resistance, space responds by telling us that resistance is futile and counters by pushing us out of space itself? This I can actually sort of wrap my brain around, if it’s actually true—c is c because that’s the point at which you skip right out of the water. I suppose Chronos is going to come along now and tell me that it doesn’t really get thinner, and that I’m a blithering idiot. This will immediately reduce me to a vapid pool of bubbles and tears, at which point I will forget the whole thing and become a YEC theist, but that’s beside the point. So why does an object get thinner and thinner as its speed increases, and can this help explain why the universal speed limit exists, or at least better illustrate what happens when an object’s speed approaches this limit?
The problem is that the simple answer is “The world just works that way”, which is unsatisfying.
While a more satisfying answer that derives why this must be the case mathematically, will inherently be somewhat complicated and is not something that you explain on an intuitive level in a few paragraphs, since they are counter-intuitive. As I said in my previous post, if they didn’t have experiments to back this up I would think that the whole thing was bullshit.
Still if you really are interested special relativity, which will get you as far as time and space dialation, E=MC^2, and the light speed limit the concepts aren’t all that complicated and with a good reference and a little time should be understandable to most Dopers.
OK then, do we understand why time slows down as an object’s speed increases? Humor me here, I’m getting at something. I think I can synopsize this whole thing into a digestible format, but unfortunately it’ll be along the lines of ‘we just don’t know.’ But at least I think I can clarify things by at least sorting out what we know from what we don’t understand and summarizing it in one paragraph or so.
One way to think about it is that everything is moving at the speed of light all the time through four-dimensional spacetime. When you accelerate an object you rotate its velocity vector so that some of its motion occurs in space instead of all of it occurring in time. The more motion through space, the less motion through time.
Of course, what constitutes a space dimension and what constitutes a time dimension varies from reference frame to reference frame … .
Well if you think about it it’s basically the same question as the first one.
Person A standing still. Ship B goes in one direction at .8c for a year(to A). Ship C goes in the opposite direction at .8c for a year(also relative to A). So to person A at the end of the year the ships are each .8 light years away. If time didn’t change the ship B would be 1.6 light years away from ship C, which means they would have exceeded c for that year. So time dilation has to follow.
Joe: Why did they set the speed limit at 60MPH?
George: They didn’t. They set it to one.
Joe: WTF?
George: Units of measurement are arbitrary, see?
Joe: Oh.
George: Get it?
Joe: Yeah, I get it.
George: Right?
Joe: Real helpful, George.
I’m not sure if this is accurate or helpful, but I’ve heard, possibly on this board, that all particles are moving at the speed of light through spacetime. Most of the atoms in your body are moving fairly slowly though space and at full speed forward in time. If you accelerate to a high proportion of c in space, then the speed of your travel through the time dimension decreases. For particles that travel at the speed of light, such as photons, change through time does not exist.
Because light moves at that maximum speed. If the max speed was different, light would move at* that* speed instead. Light doesn’t define the max speed; the max speed defines how fast light can go - i.e. no faster than that.
