Why is there a universal speed limit, c, and why is it what it is?

DaleSpam

Excellent post, Rap.

SeventhSigma

Rap: That post honestly frustrates me because it makes me feel like you missed what I mentioned above (basically saying the same thing). Nobody is arguing about the labeling of the units. We've defined a meter in an arbitrary fashion and a second in an arbitrary fashion, and we know the speed of light is 3 * 10^8 times as fast. The question is why that particular ratio exists and why it isn't smaller or larger.'

Asking why it has the speed that it has is not an improper question in the sense that I am asking it in the context of ratios, much like how I equated this question to the circle / pi argument earlier. Yes, if you adjust EVERYTHING by the same relative scalar, we won't notice any difference. We're not talking about this, however. We're talking about why everything has the ratios to each other as they do. When we ask "why 300,000 km/s and not 200,000 km/s," we're implicitly discussing ratios in this case and not the labels.

Dmitry67

There is no ratio. space and time are the same. They should be measured in the same units. So when you use natural units, c appears to be equal 1.

c = 1.

SeventhSigma

It doesn't explain why there's a cap on how high c can go, however.

Rap

Ok, that would be addressed by the third paragraph in my post, that says "A proper question is why is the ratio of the speed of light to some other velocity equal to whatever it is? For example, a valid question is "why is the speed of light so fast (compared to anthropomorphic speeds - e.g. 1 meter per second)?". Your example is "why is the ratio of the speed of light to our anthropomorphically defined standard velocity (1 meter per second) equal to 3e8?" - the same type of question, and its a valid and interesting question.

Ok, yes, as I said, framed this way, this is a valid and interesting question. But note that you don't want to multiply the fundamental dimensionless constants by the same scalar. The fine structure constant is [itex]\alpha=e^2/\epsilon_0 h c[/itex]. If you multiply c by 2, [itex]\epsilon_0[/itex] by 1, h by 8 and e by 4, you will have the same fine structure constant. If you multiply everything by 2, you will not have the same fine structure constant. It is valid to ask why the fine structure constant has the value it has, but the point I was making is that it is not valid to ask why the speed of light is what it is without referencing it to some other speed, or length/time. And you have done this, so your question is a good one.

About answering that question - that gets into biology. Life forms are constrained by the chemistry of life. Nerve impulses only allow life forms to react to external stimuli on the time scale of fractions of a second. Our eyes must be large compared to the predominant wavelengths emitted by the sun. Single cells must be larger than a certain size in order to accomodate all the chemical reactions necessary for life, and humans, being multicellular animals, must be orders of magnitude larger. Are life forms larger than the dinosaurs reaching some sort of upper bound on the size of multicellular organisms, in the sense that they are at some evolutionary disadvantage? I don't know, maybe. All of these factors put constraints on the size of the meter and second, assuming that the meter and second are defined anthropomorphically. I don't know the full answer, but I think it is and interesting and complicated question.

SeventhSigma

Sorry -- that's what I meant by relative scalars. Not so much everything by the same number in itself but just everything by the same relative ratios. In other words, keeping the numerators and denominators the same no matter where we look. It's basically no different from multiplying everything by 1.

Regarding the evolution argument, there's an upper limit because of the types of structures required to support weight (for instance, large creatures like King Kong would collapse under their own weight because as you increase, say, the diameter of the thickness of a leg, the strength of this cross-section is proportional to that section's surface area whereas the weight is proportional to volume, so eventually it's not sustainable). However, these limits are in place because of the relative strengths of forces. There's a reason why, for instance, our brains did not evolve as smaller structures on a quantum scale. The nature of the constants ultimately guide complex chemistry and physics and therefore the kind of life we'd expect to see in its extreme expressions.

In other words, if the constants were tweaked in various ways, we'd expect to see different expressions of reality. The question is how much leeway these constants have. It'd be like popping into a complex 3D computer game and tweaking various constant variables and then running the game to see what happens. Odds are things wouldn't play quite right or wouldn't play at all if some logical rule winds up being violated.

The thing that depresses me is the notion that we may never know what "causes the constants." If I were a being inside the game Halo, then it doesn't matter how hard I pry into that environment -- I will never be able to see the code that underlies my program, nor would I ever be able to see anything outside the program/TV/etc. I can't tear into a rock and see the internal polygon code and texturing algorithms. I can certainly model my reality based on what I observe, but it doesn't tell us the driving factors that serve as the underpinnings to the reality itself.

That's what the anthropic principle tries to address by saying "If it were any different, reality wouldn't be here to begin with -- so the fact that we're even able to make these observations means that conditions must be correct for observation to occur." A bit tautological, but important.

Dmitry67

The fundamental constants are, contrary to how they are called, are not constants at all. In Planks units,

G = h = c = 1.

However, you can vary other dimensionless numbers, which are called 'the parameters of the Standard Model'.

They are here:
http://en.wikipedia.org/wiki/Standar...del_Lagrangian
On the right side of the page

(Masses are given in GeV units, but they are actually dimensionless (and very small) numbers in Planks units)

Dmitry67

P.S.
You can express "c" in a non-antrophic way, for example, why light passes N carbon atom sizes during a half life of a neutron?

The answer will be a function of the parameters of the Standard Model.

SeventhSigma

Yes, we can always redefine the label, but the question is the nature of the ratios involved in the structure of the framework that defines our universe. Again, we're *not* talking about labels or scales. We could define pi = 1 if we wanted to -- but we're really after the answer "pi is the result of dividing the circle's circumference by the diameter and we can prove this based on the definition of a circle." Similarly, we're trying to ask why these constants have the implications that they do by understanding the relationships between different components.

The question is what the nature of the relationships are. This isn't the same as saying "Well we know what c is because we know p and therefore E/c as well as hf/c as well as h/lambda," etc -- it's asking why these relationships exist the way that they do to begin with.

The way I approach this problem is, ultimately, under the assumption that our universe is inherently something mathematical. I posit that the nature of existence itself requires certain logical constructs to be in place for the concept of "existence" and therefore those logical constraints are mathematical in their build and ultimately give way to the structure of the universe.

nitsuj

In what sense is 300,000km/s a cap? You taught me that it is not a measure of speed.

300,000km/s is "off" and not 300,000km/s is "on"

SeventhSigma

It's a cap in the sense that if we define a meter in an arbitrary way and time in an arbitrary way, we can therefore define speed in an arbitrary way. The speed of light is not infinite and therefore there is an upper bound to it that we can describe with our arbitrary definitions of speed. Again, the question is not about labels but the relative ratios.

DaleSpam

Rap and Dimitry67's point is only that those ratios (the ones that define the structure of our universe) are always dimensionless constants like the fine structure constant and not dimensionful constants like c.

http://math.ucr.edu/home/baez/constants.html

Dmitry67

SeventhSigma, what is a nature of ratio between WIDTH and HEIGHT?

SeventhSigma

A ratio can be anything. But some ratios are bound by constraints. For instance, again, I bring up the circle analogy. A circle is a concept such that it has two properties which we can define as circumference and diameter. The division of these two result in pi, a "constant" bound by constraints resultant from the mathematical implications of what a circumference and diameter are.

Similarly, I make the analogy that the speed of light is likely another such eventuality of something bound by mathematical constraints based on the nature of the universe's structure. The question is what the explanation behind that particular ratio/relationship is.

Right, we're in agreement there.

Dmitry67

if we are in agreement, then I don't understand, why you keep asking about the "ratio".
There is no "ratio" and the situation with "c" is much simpler then with pi.

Unless we for some weird reason measure width in kilometers and height in miles, the "ratio" between width and height is 1 because both are distances in space.

c=1 for the very same reason

SeventhSigma

OK, maybe this will clarify things if I explain in in this way: We know pi is dimensionless because it involves a mathematical operation between two figures that are given in the same dimensions. Say, a circumference in inches and a diameter in inches. They cancel out to form a dimensionless quantity. This will be the same regardless of the units we use assuming we are referring to the number in the same numeric base (in this case, decimal).

My argument is that c is likely another such "piece of a separate puzzle." It's like knowing the diameter of a circle without knowing the circumference because we don't yet understand the nature of the circle yet. I am saying that it is possible that c, as we know it, is what it is because of some other constraint(s) in our universe.

Clearly we would agree c is not infinite. The question is why this is so.

sahil_time

c=1/sq.root(epsilon zero*permeability of free space)
Since both are constants hence c is constant!