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

[Rap]

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.'

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.

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.

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 $\alpha=e^2/\epsilon_0 h c$. If you multiply c by 2, $\epsilon_0$ 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 accommodate 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 thing that depresses me is the notion that we may never know what "causes the constants."

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/Standard_Model#Construction_of_the_Standard_Model_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]

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

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.

 

[Dale]

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.

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.

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

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!

 

[SeventhSigma]

that's from Maxwell's equations -- epsilon and permeability are derived experimentally -- it is another way to get c but it doesn't explain why it is c.

 

[Dmitry67]

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

There are 2 separate questions;

1. Why there is "c" at all. This is because our space is not euclidean, but pseudoeuclidean with metrics (+++-). You can ask "why", it is like asking "why we have these particular physical laws"

2. The question about the particular value of "c". We discussed it before. There are no puzzles. Distance in space is defined as

s^2 = x^2 + y^2 + ...

not as

s^2 = x^2 + 1.3 y^2 + ...

nor

s^2 = x^2 + 0.9 y^2 + ...

as different directions in space are measured in the same units, c must be =1 and can't be different.

P.S.
Note: if scientists from the very beginning would have used Planks (natural) units, all formulas will be different: there won't be "c", "G" and "h" at all!

 

[Tanelorn]

I understand that beyond the edge of the observable universe galaxies are traveling well beyond the speed of light away from us relative to us, as is the light they emit. Further, when the CMBR that we see today was first emitted, it was traveling at over 500 times the speed of light away from us (but traveling towards us) and has only just had chance to reach us. Thought that would cheer you up :)

 

[SeventhSigma]

1. Yes, the question is like asking "why do we have these particular physical laws."

2. Yes, we can define c as 1 if we want to use it as a natural unit. This is an example of "labeling" as I define it, and this is not what I am discussing. We don't answer the question by just relabeling something as a fundamental unit of 1 because then we could just ask "Why is everything so slow in comparison?" and it brings us to the same problem.

 

[Tanelorn]

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

Permitivity and permeability are not constants of nature, They're artifacts of a particular choice of electromagnetic units (SI). In Gaussian CGS and Heaviside-Lorentz CGS units, they don't exist.

 

[Dmitry67]

1. Yes, the question is like asking "why do we have these particular physical laws."

2. because then we could just ask "Why is everything so slow in comparison?" and it brings us to the same problem.

1. We don't know. But if space was simply Euclidean, there would be no "time"

2. Pseudo-Euclidean structure of space-time itself does not limit speeds to <1, for example, hypothetical tachyons can move faster than light. However, because of the way how we interpret space and time, something moving faster than light is interpreted as “spacelike”, something that has spatial extent.

 

[nitsuj]

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.

Coincidently the "speed of light"/"c" is not speed at all, (again you taught me that) but the point that time stops. If time stopped at 200,000km/s then I am guessing it would be impossible for something to go faster since time stops.

Don't blame the limit on speed, blame it on time(distance/space).

 

[Dmitry67]

Coincidently the "speed of light"/"c" is not speed at all, (again you taught me that) but the point that time stops. If time stopped at 200,000km/s then I am guessing it would be impossible for something to go faster since time stops.

time does not stop because it does not move.
just the interval and proper time becomes 0 at v=c.
and it has nothing to do with an ability to move FTL: tachyons always move FTL, and they can't slow down to c (even they probably don't exist for the other reasons)

 

[nitsuj]

Clearly we would agree c is not infinite.

c IS infinite in every sense of the word. I feel as if c defines infinite. maybe the idea of 300,000 distance of some kind with a "time" of some kind, is a misnomer when thought of in the context of "c", because there is no time at 300,000 km/s.

excerpt from Brian greene's The Elegant Universe pg52

"So as a moun moves more quickly it gets ever more difficult to increase its speed. At 99.999 percent of the speed of light the mass of a moun has increased by a factor of 224; at 99.99999999 percent of the speed of light it has increased by a factor of more than 70,000. Since the mass of the muon increases without limit as it's speed approaches that of light, it would require a push with an infinite amount of energy to reach or cross the light barrier."

 

[nitsuj]

time does not stop because it does not move.
just the interval and proper time becomes 0 at v=c.
and it has nothing to do with an ability to move FTL: tachyons always move FTL, and they can't slow down to c (even they probably don't exist for the other reasons)

I can't define time as anything else but movement. I see time as a "consequence" of movement in space. Said differently, Derived from movement in space. So much so that "the interval and proper time becomes 0 at v=c", whatever that means, just looks like the math agrees.

"(even they probably don't exist for the other reasons)" seems like weaker support than "...time becomes 0 at v=c"


From wikipedia
A tachyon- is a hypothetical subatomic particle that moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds.

"Imaginary time is obtained from real time via a Wick rotation..."


This hardly seems fair as a point of arguement.

 

[bobc2]

I would tend to study the significance of the constant speed, c, for all observers by considering the 4th dimension a spatial dimension--not a time dimension at all. Proper time along any observer's 4th dimension is merely a parameter. The understanding of time itself necessarily involves an understanding of consciousness, neurology and psychology. For example you can carry a clock with you as you drive up the interstate at a constant speed of 70 mph and assign time values to every mile along the way--but that in no way makes that highway anything but a spatial dimension. Every observer is moving along his own 4th dimension at the speed of light--just like driving up the interstate--you can record proper time values along the 4th dimension trip, but that in no way makes X4 anything but a spatial dimension.

So, the essence of what's behind the constant value of "light speed" implies an understanding of the universe as a 4-dimensional structure (the so-called "block universe") populated by 4-dimensional objects (the photon being modeled below as a 4-dimensional world line). You see the "speed" in this case is really shown as the ratio of distances (X1/X4), i.e., literally a dimensionless quantity. And that ratio is of course: 1.000----. simply because the world line of the photon bisects the angle between X1 and X4 for all observers, regardless of speed.

The other question as to why there is a limiting factor can be seen in the sequence of diagrams showing increasing observer speeds (blue coordinates) with respect to the black coordinates. The key here is nature's strange characteristic of rotating the X1 axis to maintain symmetry about the photon world line for increasing rotations of the X4 axis. You can plainly see that the X1 axis merges with the X4 axis in the limit. I think this is this "limiting" condition is what you may be trying to graple with. The fundamental question is "Why does nature rotate the X1 axis like this?" (The rotations are described mathematically by Lorentz transformations).

Of course, bcrowell had it right when he advised us to first choose the postulates. I have not formalized my statements of postulates well.

 

[Dale]

c IS infinite in every sense of the word.

No way. C is finite. It is not infinite in any sense of the word.

 

[DrGreg]

c IS infinite in every sense of the word.

If you had said "c behaves a bit like infinity in some senses" you might have a point. To say "c is infinite in every sense" is complete nonsense. Do you really think the "equation"

$$299792458 = \infty$$​

makes any sense at all?

 

[nitsuj]

If you had said "c behaves a bit like infinity in some senses" you might have a point. To say "c is infinite in every sense" is complete nonsense. Do you really think the "equation"

$$299792458 = \infty$$​

makes any sense at all?

Can you explain what I would have meant if I had said "c behaves...". Does it show "behaviour" in graphs and equations?

299792458 = c = no time = no movement = infinity = ? as in the graph above
is infinity actualy used in math?

 

[Dale]

299792458 = c = no time = no movement = infinity

Absurd. c does not equal "no time". What you mean is that:
$$\lim_{v\to c} \, \gamma(v)=\infty$$

That certainly is not the same as c being either infinite or equal to "no time".

 

[nitsuj]

No way. C is finite. It is not infinite in any sense of the word.

yea? ask the one traveling at C, their reply might take what seems like an infinitly long time.

 

[Dmitry67]

1
I can't define time as anything else but movement. I see time as a "consequence" of movement in space. Said differently, Derived from movement in space. So much so that "the interval and proper time becomes 0 at v=c", whatever that means, just looks like the math agrees.


2
"Imaginary time is obtained from real time via a Wick rotation..."
This hardly seems fair as a point of arguement.

1 Well, it is a definition based on our "common sense"
The key finding of GR is taht time is a a 4th dimention, not "rate of change of things" or other wordy stuff usually used by the philosophers.

2 And what? (forget that they probably don't exist for now)
Tachyons always move faster than c, so for then c is also a barrier, but a LOW limit of seed - it requires for them an infinite amount of energy to slow down to c.

 

[Dale]

yea? ask the one traveling at C, their reply might take what seems like an infinitly long time.

That doesn't mean that c is infininte, it means that time dilation is infinite at c (more precisely the limit stated above). That c is finite is one of the key facts of relativity.

 

[Huttate]

So we have photons that travel at a speed that we ascertain to be the maximum possible speed in our universe. But for them, although we are not allowed to think of their frame of reference [it is meaningless] time has no meaning and is not experienced. Any attempt to attribute a half-life to them renders an infinite.

Trying to attain their view of the universe is therefore impossible.

These photons are the gauge bosons of interractions that create and destroy atomic structures and therefore everything we know in the physical world, including ourselves.

The mind boggles to think that those photons which constitute the CMB have themselves experienced no passage of time.

Is all this right so far?

We have something that is ageless, stretches effortlessly across time as we see it and is [responsible] for the creation of all matter and life.

I'm an atheist but were I not I think I could add another level of spin to the photon.

Let there be light!

 

[nitsuj]

That doesn't mean that c is infininte, it means that time dilation is infinite at c (more precisely the limit stated above). That c is finite is one of the key facts of relativity.

Ah okay,

I thought that I was talking about time being infinite at "c",

I also thought that because "c" is finite to an observer that it is measurable, but that if traveling at "c" it would not be, and that this oddity was one of the facts of special relativity.
Seems I am greatly mistaken, back to the beginning for me.

 

[SeventhSigma]

Ah okay,

I thought that I was talking about time being infinite at "c",

I also thought that because "c" is finite to an observer that it is measurable, but that if traveling at "c" it would not be, and that this oddity was one of the facts of special relativity.

Seems I am greatly mistaken, back to the beginning for me.

The point of special relativity relies on the notion that c is the same for all observers. You can derive tile dilation from, for example, the famous light-clock diagram.

Ultimately we find t=T*(1-v^2/c^2)^.5 or T*gamma. As v approaches c, gamma approaches 0. So hypothetically, at v=c we have T*gamma = T*0 = 0 = t, which implies that no matter how much time passes for T (the clock according to the observer moving at c), we'll see t's clock frozen in time.

 

[nitsuj]

1 Well, it is a definition based on our "common sense"
The key finding of GR is taht time is a a 4th dimention, not "rate of change of things" or other wordy stuff usually used by the philosophers.

2 And what? (forget that they probably don't exist for now)
Tachyons always move faster than c, so for then c is also a barrier, but a LOW limit of seed - it requires for them an infinite amount of energy to slow down to c.

1. Is "time in SR, different to "time" in GR?
Dmitry67 I am trying to understand what time is and the best I can come up with is movement in space. "rate of change" is simular enough to how I think of it. Why is that wrong in SR? (keep it simple please or I'll be lost in a few words)

2. I can't even come up with a reply to this. Seems like a different subject then SR, and something I never read or thought of ( outside of they may not be real, are based on Imaginary Real Time - all things outside my understanding, next to SR apparently)