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

[LeeJeffries]

Yes, I mean what is holding the light back. It is like an invisible hand jumps up in front of things at c and stops them from going faster.

I suspect my paradigm might be completely wrong and I need to shift, in which case I need why it is wrong explained. It seems the same as if I were adding more and more to an object to increase it's mass, then suddenly the mass stopped increasing, and I think "What the heck is going on?"

The Ether ;)

 

[nitsuj]

For instance, E = mc^2 (i edited this part for my sake) We write it this way because we've defined energy/mass/speeds in various metrics. Let's just hold the speed of light c to equal 1 in natural units (which is to say, instead of defining c as 300,000 of something else of value 1, let's just define c as our fundamental unit of 1 to begin with). Then we simply see that E = m only we're discussing both E and m in different units.

I like trying to understand things, can you please explain to me what "just hold the speed of light c to equal 1 in natural units" means? And how then E = mc^2 can be changed to E=m?

Why are you taking the C part out of that equation you called a "conversion"?
E=M is wrong, it's E= mc^2. it "converts" to a little mass equates to a lot of energy, and vice versa. The "various metrics" thing you mentioned is crucial. If you index C to equal 1, it won't change the relationship that a little mass equates to a lot of energy.

http://www.1728.com/einstein.htm has a calculator at the bottom. You enter mass, select the UoM you used for mass, and it tell you the amount of energy it has in various UoM. Never do you see "C".

"The real question isn't so much "why is c equal to 300 km per second"" your right, its why does "time"(which I also assume to mean space) stop at 300k km/s, that's what the "c" part of the equation is doing.

 

[LeeJeffries]

I like trying to understand things, can you please explain to me what "just hold the speed of light c to equal 1 in natural units" means? And how then E = mc^2 can be changed to E=m?

Why are you taking the C part out of that equation you called a "conversion"?
E=M is wrong, it's E= mc^2. it "converts" to a little mass equates to a lot of energy, and vice versa. The "various metrics" thing you mentioned is crucial. If you index C to equal 1, it won't change the relationship that a little mass equates to a lot of energy.

http://www.1728.com/einstein.htm has a calculator at the bottom. You enter mass, select the UoM you used for mass, and it tell you the amount of energy it has in various UoM. Never do you see "C".

To demonstrate that C is a conversion factor

 

[SeventhSigma]

I like trying to understand things, can you please explain to me what "just hold the speed of light c to equal 1 in natural units" means? And how then E = mc^2 can be changed to E=m?

Why are you taking the C part out of that equation you called a "conversion"?
E=M is wrong, it's E= mc^2. it "converts" to a little mass equates to a lot of energy, and vice versa. The "various metrics" thing you mentioned is crucial. If you index C to equal 1, it won't change the relationship that a little mass equates to a lot of energy.

From http://en.wikipedia.org/wiki/Mass–energy_equivalence

[The formula is dimensionally consistent and does not depend on any specific system of measurement units. For example, in many systems of natural units, the speed (scalar) of light is set equal to 1 ('distance'/'time'), and the formula becomes the identity E = m'('distance'2/'time'2)'; hence the term "mass–energy equivalence" ]

Natural units are basically ways to redefine your unit scales. Instead of saying that the speed of light is 300,000 km/s, you might just say that it's equal to 1 light-second per second (a light-second is a unit of distance, and a second is a unit of time, and we know distance/time is a rate). It's basically redefining the speed of light from one distance/time metric to another, only instead of using 300,000, we use 1. The idea is to change the units so that we can simplify certain relations.

So when we set c = 1, we more clearly see that E = m, or that the rest energy of a particle in Planck energy units is equal to the rest mass of a particle in Planck mass units. The important thing to keep in mind is that energy and mass are seen as different forms of the same thing and are proportional to each other to the tune of the maximum speed anything can move in our universe (light, gravity's effects, etc).

We see c in so many equations in the same way we see pi everywhere. It's like asking why pi is equal to 3.14159 etc. It is because of the nature of the circle. Circumference over diameter equals pi. Saying "Let's make pi equal to 5 instead of 3.14" is like saying "Let's make c equal to 200,000 km/s instead of 300,000 km/s." If we set pi to be something else, then we're really not talking about a circle anymore because there's no way we can get 5 if we divide circumference by diameter.

Similarly, c is equal to c because if it were anything else, the nature of our universe wouldn't exist as it is now.

 

[nitsuj]

To demonstrate that C is a conversion factor

Umm, no it was for me to demonstrate that SeventhSigma can use the calculator and assume that "c" is 1. the formula still shows a little mass is a lot of energy. It takes the 'ratio' of all three (opps, four) measurements (energy, mass, distance, time).

My opening in that post "I like trying to understand things, can you please explain to me what "just hold the speed of light c to equal 1 in natural units" means?" should prove difficult as speed is two measurements, not 1.

 

[SeventhSigma]

You have to assume SOMETHING is 1 at some point. We always measure something in terms of something else. You can say c = 300,000 km/s, but then you have to ask what a meter is equal to. A few hundred years ago it was suggested to make the meter equal to one ten-millionth of the length of the distance from the Equator to the North Pole. TEN millionth because we're accustomed to the decimal system (because we have ten fingers) and an Earth distance because it's something "applicable to all" and this ratio gives us something workable on human scales.

Either way we're still calling the meter "1." Changing c to equal "1" is just another way of redefining our units. It can help us better understand certain physical relationships. In this case, energy-mass equivalence. Saying c equals 1 is a way to define it as a standard tautological unit where c = the distance that light goes in one unit of time.

 

[nitsuj]

Natural units are basically ways to redefine your unit scales. Instead of saying that the speed of light is 300,000 km/s, you might just say that it's equal to 1 light-second per second.

Wow, I actualy never understood what "c" is. 300,000km/s is very definitive. I thought it was a measure of speed.

 

[SeventhSigma]

It's actually something like 299,792,458 m/s in a vacuum but it's just easier to say 300,000 km/s

 

[harrylin]

Why on Earth would you say that? [..]

I explained it immediately below by means of a quote by Newton about the purpose of his work - didn't you see it? The asterix is even in your quote of what I wrote...
Here it is again but now with emphasis by me:

[..]
* But how we are to collect the true motions from their causes, effects, and apparent differences; and, vice versa, how from the motions, either true or apparent, we may come to the knowledge of their causes and effects, shall be explained more at large in the following tract. For to this end it was that I composed it.

An important aspect of answering "why" is "the knowledge of causes and effects"; that's much more than "the mathematical model X correctly predicts".

 

[nitsuj]

We see c in so many equations in the same way we see pi everywhere. It's like asking why pi is equal to 3.14159 etc. It is because of the nature of the circle. Circumference over diameter equals pi. Saying "Let's make pi equal to 5 instead of 3.14" is like saying "Let's make c equal to 200,000 km/s instead of 300,000 km/s." If we set pi to be something else, then we're really not talking about a circle anymore because there's no way we can get 5 if we divide circumference by diameter.

After you setting me straight with what "c" actualy is, I see how perfect your annalogy to pi is. They're almost siblings :)

 

[pip1974]

CosmicVoyager. I have a thought experiment relating to your original question that I thought I'd share with you. You started wondering what it was that stopped the object, or spaceship or whatever it is accelerating as it approached the speed of light. The answer is nothing!
Here goes...
Imagine one day the people of Earth get a message from an alien spaceship that is hurtling towards us at 0.75c. It says that they are on a huge generational starship, and if we wanted to we could send a spaceship on an intercepting course, dock with their planet sized spaceship and join them.
So, we make necessary preparations and do exactly as they suggested.
Don't worry about the details so much - it's a colourful story - but the important point is that we are now on a huge planet sized spaceship that is moving at 0.75c relative to Earth, with our own spaceship, also capable of accelerating to 0.75 safely docked there.
Once there we watch the Sun rush away from us at 0.75c as we begin our new lives, having a whale of a time finding out all about the alien civilisation and lounging on the beaches by the shore of the lovely artificial oceans. We call it "Earth Two"!
Now here we are, on our new home in space, very different from but as comfortable as our old home, Earth, and of course just as valid as a frame of reference! We can play ping pong there in exactly the same way that we could on Earth! We can also look at the stars at artificial night-time and look upon similar constellations as we did on Earth with equal wonder.
Now after some time, we, the band of intrepid Earthlings, settle down and have families. And eventually we grow old and die, but our families go on. Then one day a group of our descendants decide upon a curious course of action. They decide to get back in the old spaceship and set off. Now they just happen to choose a course which is the exact opposite direction to our old Earth. They don't care - they don't want to go back there. To them it's just an obscure planet orbiting a distant star that happens to be moving away from us at 0.75c.
So they set off in the spaceship, and after a few months find themselves going at 0.75c relative to New Earth.
Now, as I said, they'd forgotten about Earth and the Sun, but if they had spared it a thought, they'd notice that that system was speeding away from them at a very high speed approaching the speed of light and definitely not at 1.5c as the uninitiated might expect.
If they'd thought to check before they set off they'd have observed Old Earth flying away at 0.75c when they were still stationary relative to New Earth. Then if they’d kept looking as they approached 0.75c relative to New Earth they’d see the acceleration relative to Old Earth slow down. The velocity relative to Old Earth would approach but never exceed the speed of light, even as the velocity relative to New Earth continues to increase.
Now the interesting thing here is, the whole slightly unnecessary bit in the middle of this story where our intrepid explorers settled on the alien star ship was exactly that - a bit unnecessary! The Earth explorer's ship (which I've decided runs by scooping up interstellar hydrogen atoms by the way) can actually carry on accelerating indefinitely as far as the crew are concerned without any need for a stay on a friendly alien star ship world. Their speed relative to their origin will carry on increasing, but never reach the speed of light. The engines will be working just as before, life on board ship will be much the same, but they will observe the acceleration relative to the origin decrease. At any point they can shut off the engines and just fly on through space for a bit, decide on a new frame of reference, then turn on the engines again and start accelerating towards the speed of light away from a new fixed point on the same heading. If they look back and start measuring their velocity according to the old reference frame again, they'll still be getting nowhere fast, but they'll be whizzing away from the new point! The two frames of reference are equally valid, just like the two reference frames that see me sitting fairly still in front of my monitor, and hurtling around the Sun at 100,000 km/h.
The point is, at no stage does God come along with a speed limit sign telling you to slow down because you are approaching the universal speed limit, things just aren't ever going to be moving away from you faster than that limit, no matter how long and hard you or they run for.
Phew!
I enjoyed writing about that. I hope you enjoy having a think about it!
By the way, before anyone jumps on it, I realize this doesn't answer your original question but perhaps gives you another way of visualising the consequences of there being a speed limit that you may find useful. And one final note just in case people are thinking that somehow I'm claiming that the spaceship will be going faster than the speed of light - it won't be - OK! If the explorers always had it in mind to get somewhere, a star, let's say, the spaceship would never be traveling towards that star at the speed of light (and the light from the star they are heading towards would still always be traveling to the peepers of the people on board at the speed of light!)
As for why! Well, I still think that's an interesting question :)

 

[Dale]

I explained it immediately below by means of a quote by Newton about the purpose of his work - didn't you see it? The asterix is even in your quote of what I wrote...
Here it is again but now with emphasis by me:


An important aspect of answering "why" is "the knowledge of causes and effects"; that's much more than "the mathematical model X correctly predicts".

If some parts of your mathematical model have a relationship to each other that we expect from causes and effects then you have modeled cause and effect and accomplished the goal of Newton as I understand it, which is a scientific goal. I don't think that he was asking "why" his laws worked, and that statement that you quoted doesn't seem to indicate that either.

I think you are really undervaluing the mathematical models here. Cause and effect is a relationship that can certainly be captured mathematically, and in fact is an important feature of the modern concept of spacetime.

 

[SeventhSigma]

I think the OP is asking why c is 300,000 km/s and not, say, 200,000 km/s and why it's an absolute limit at all (i.e. why isn't light instantaneous?).

I don't know the answer, but I am trying to say that it's likely a similar analogy to circles and pi. Pi is a ratio between two properties of an object that is defined in a particular way. In other words, a circle has pi as a necessary condition. Changing pi means you are no longer talking about a circle.

I figure our reality is much the same way. Our universe is to c as a circle is to pi. I just don't know how you'd derive c based on everything else.

 

[nitsuj]

I think the OP is asking why c is 300,000 km/s and not, say, 200,000 km/s and why it's an absolute limit at all (i.e. why isn't light instantaneous?).

I don't know the answer, but I am trying to say that it's likely a similar analogy to circles and pi. Pi is a ratio between two properties of an object that is defined in a particular way. In other words, a circle has pi as a necessary condition. Changing pi means you are no longer talking about a circle.

I figure our reality is much the same way. Our universe is to c as a circle is to pi. I just don't know how you'd derive c based on everything else.

That annalogy, is perfect. I have been in awe today absorbing the idea of "c". what's speed calculated without time? "c" lol what a trip


"I just don't know how you'd derive c based on everything else" I thought you've intentialy said it already, with...

"Instead of saying that the speed of light is 300,000 km/s, you might just say that it's equal to 1 light-second per second"


"everything else" moves around relative to each other, and that is seen as time. measure the fastest (known) thing amongst everything else, and cross your fingers that it's a property of spacetime and not of the fastest (known) thing amongst everything else. I'd bet dollars to dimes that if the fastest (known) thing amongst everything else wasn't a property of spacetime that "c" would have come about later then it did (truism).

How it actualy came about is much much different(im sure you know), but it is a wonderful coincidence in hindsight.

 

[nitsuj]

Greetings,

Why is there a c? Why is there a speed limit to the universe? Why is there a limit to how quickly a cause can follow an effect at distance? Why is there a "causality constant"?

What is(are) the limiting factor(s) that make it what is? The speed limit is a consequence of what? Is what we know to be the speed limit the result of measurements? Or is it a logical problem that can be figured out in a thought experiment?

What was God thinking? lol

Thanks

It took a lot of thinking but I got it.

Because it's the fastest. That's my final answer. Nice and circular. :)

 

[Rap]

I think the OP is asking why c is 300,000 km/s and not, say, 200,000 km/s

If you are asking why the number is 3e8 m/s rather than 2e8m/s, the answer to this question is anthropomorphic. The question is essentially "why is the meter the length that it is?" and "why is the second the length that it is?". Change the value of the meter or the second, and the number changes*. The meter was chosen as a length easily comprehensible to humans - about the distance between outstreched arms. The second was chosen as a time interval easily comprehensible to humans - about a heartbeat. The numerical value for the speed of light follows. I bet if we contact an alien race and knew their size and metabolic rate, we could make a good estimate of what their fundamental length and time interval were, and what numerical value they assigned to the speed of light in terms of those length and time units.

If you are asking why it has the speed it has, this is an improper question. The nature of the universe is described by the values of the fundamental dimensionless constants (i.e the fine structure constant, the gravitational coupling constant, mass ratios of elementary particles, etc.). If you double the speed of light, but adjust other fundamental constants (e.g. Planck's constant, mass of electron, etc.) so that the fundamental dimensionless constants remain the same, you will be living in a universe that is identical to this one. The length of the meter and second will change, but if you redefine the meter and second anthropomorphically, absolutely everything will be the same.

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)?". This is a more interesting question, and can be discussed.

*I know, c is now defined as a constant value which, along with cesium radiation defines the meter and second, but those numbers were chosen to be close to meters and seconds that were otherwise defined.

 

[Dale]

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]

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.