What's so special about C?

[SkepticalScience]

So what makes the speed of light such a special constant in the universe?

Why can't we travel faster than light, without resorting to some “trick” like using wormholes or the like?

What is it that actually prevents clever engineers from developing an engine that can break the light barrier, just as engineers broke the sound barrier previously.

I have a feeling that it has something to do with things getting “massier” as more energy is applied to them – but what makes 186,000 mps so special??

Can someone help a skeptic out by explaining this madness in laymens terms!

THANKS!
SS

 

[rppa]

You probably won't like the answer but: It's not that light sets a speed limit. It's that the universe sets a speed limit. Light goes as fast as the universe allows it to, which is c. But c is a property literally of the fabric of space and time.

Why is it the number it is? The hope for a Theory of Everything is that eventually instead of a bunch of different constants of the universe (c is not the only one) we'll have one theory that explains all of them. But till then, the best we can do is say, here are the constants that have been handed to us.

 

[Johnny Pneumatic]

It is indeed due to mass. The reason is as you get up to relatavistic speeds the mass of an object gets greater and thus takes more energy to make it go even faster, and so on. At the speed of light itself the mass of any object is infinite. It would take an infinite amount of energy to push something with infinite mass so that's why it's impossible. Someday we might be able to get up to 0.9 or more C, maybe; but never 1.0.

 

[Terry]

Well, it's high enough level to be somewhat portable, but close enough to the machine to do system programming.

Oh, not the programming language? never mind...


--Terry.

 

[Dilb]

The only "special" thing about c is that oberservations have been made that c is constant in any reference frame. This (single) observation then leads to a lot of different things, ie all of relativity. The fact that physicists

1. Assumed c to be constant
2. Derived theories that would have to be true for c to be constant
3. Observed these new theories to be correct

make it very justifiable that c is constant. But it's entirely possible to imagine a universe where this isn't true, it just isn't correct to do so. Any space computer game will use Newtonian mechanics (or even simpler ones, maybe), since it's not really possible or necessary to use relatavistic calculations.

To expand on this:
It is possible to go faster than light, infact this leads to an interesting type of radiation, Cerenkov radiation, explained here. You can't go faster than the speed of light in a vacuum. Although I think even with this radiation you're only exceeding the bulk/average speed of light in a medium.

2 Sound is determined by the elasticity of a material, so by having more than one type of material and making a sound, you've already got something (a different sound, admittedly) moving faster than sound. Also, simple experiments will show that the speed of sound is not constant for reference frames, this is the doppler effect, so it's a just a matter of moving faster and seeing sound move slower relative to you. Go fast enough and you beat sound.

Essentially, there's no better answer than "light is always moving at lightspeed relative to you, regardless of how fast you move, as confirmed by experimental results". It's simply how the universe works. From the cockpit of your super-hyperpowered-spaceship, light is always constantly outrunning you, regardless of your speed or acceleration.

 

[Tez]

The only "special" thing about c is that oberservations have been made that c is constant in any reference frame. This (single) observation then leads to a lot of different things, ie all of relativity. The fact that physicists

1. Assumed c to be constant
2. Derived theories that would have to be true for c to be constant
3. Observed these new theories to be correct

make it very justifiable that c is constant. But it's entirely possible to imagine a universe where this isn't true, it just isn't correct to do so. Any space computer game will use Newtonian mechanics (or even simpler ones, maybe), since it's not really possible or necessary to use relatavistic calculations.

To expand on this:
It is possible to go faster than light, infact this leads to an interesting type of radiation, Cerenkov radiation, explained here. You can't go faster than the speed of light in a vacuum. Although I think even with this radiation you're only exceeding the bulk/average speed of light in a medium.

2 Sound is determined by the elasticity of a material, so by having more than one type of material and making a sound, you've already got something (a different sound, admittedly) moving faster than sound. Also, simple experiments will show that the speed of sound is not constant for reference frames, this is the doppler effect, so it's a just a matter of moving faster and seeing sound move slower relative to you. Go fast enough and you beat sound.

Essentially, there's no better answer than "light is always moving at lightspeed relative to you, regardless of how fast you move, as confirmed by experimental results". It's simply how the universe works. From the cockpit of your super-hyperpowered-spaceship, light is always constantly outrunning you, regardless of your speed or acceleration.

Be careful not to confuse speed and frequency re the doppler effect Dilb.

SkepticalScience, here is something I have always found amazing. Consider a collection of massive particles on the vertices of a square lattice, coupled by springs to their nearest neighbours. Think of this as a "mattress". You can imagine "waves" travelling through the mattress - if you bounce at one point, the oscillations will fan out from there.

Now if you consider the waves which have a long wavelength - i.e. distance between peaks and troughs - (equivalent to a low oscillation frequency), and in particular the waves which have a wavelength that is long compared with the distance between the particles, then you find the following remarkable thing: All inertial observers of these waves will see them travel with a constant velocity - lets call it c. In modern language, the description of these waves is Lorentz invariant.

Why is this amazing? Because we start off with a description that is NOT Lorentz invaraint - we start off with a bunch off massive particles, embedded in some kind of Newtonian spacetime. That is, the underlying theory of our massive particles and springs is a theory in which the standard "sensible" Newtonian/Galilean transformations of space and time coordinates hold.

In effect, many people think that this picture does describe what happens with light in our universe - they believe that at a small enough scale (known as the Planck scale) we will see the "discreteness" of the mattress. Such discreteness could manifest itself in the propogation properties of light that has a short wavelength (high energy/high frequency) - in particular, this light may travel with a velocity that doesnt quite match c. In fact, there are already people trying to observe this in high energy photons that have travelled cosmological distances...

 

[69dodge]

Originally posted by Tez
Now if you consider the waves which have a long wavelength [ .. ] then you find the following remarkable thing: All inertial observers of these waves will see them travel with a constant velocity

?!

I am missing something here ...

 

[Tez]

?!

I am missing something here ...

You'll have to be more specific - you dont understand why, or you dont understand what!

 

[Dylab]

I don't understand the why. Can you elaborate. Why is it invariant?

 

[69dodge]

I think I understand what you said, but I also think I disagree with it. So, probably I don't actually understand it.

Are the waves transverse or longitudinal? How exactly are we defining "wave velocity"? Are we talking about the phase velocity of a single frequency or the group velocity of a wave packet?

Not sure why any of this should matter; I'm just trying to get a definite picture in my head.

Since spacetime is Galilean, nothing prevents one observer from moving at "c" relative to another. Then what? One observer sees the other keeping pace with a wave, while the other sees the wave passing himself at "c"?

I don't get it at all.

 

[Dilb]

Be careful not to confuse speed and frequency re the doppler effect Dilb.

Oops, right. That should be more like "the relative velocity of sound changes, so it takes longer for a sound to reach you if you're moving away, compared to a stationary person, when you start at the same position." It could be measured with the doppler effect, but the same applies to light, despite it's relative velocity not changing.

 

[IIRichard]

I personally find Pi more interesting. Could you have a universe where Pi doesn't = 3.14159 . . . . . .? Or is an irrational number like the square root of two?
______________________________
edi9ted to correct stupid speeeling masteak

 

[neutrino_cannon]

The sound and light barriers are different beasts. Well before the X-1 eve got slung off of its B-29 mothership, hot 30-06 loads had been exceeding the speed of sound since 1906, as the name would suggest. Flinging something through a medium at a velocity greater than that medium's rate of transmission of certain waves doesn't necessarily violate any physical laws, though it usually has some nifty and/or strange effects (google for "Cherenkov Radiation").

All that stood in the way of supersonic flight in the 1940's was the lack of mature jet engines with afterburners and a complete understanding of some of the aerodynamic strangeness that happens when flying past the speed of sound. Those may not have even been such a huge problem, numerous anecdotal reports suggest that diving f-86's could and did break the sound barrier in Korea. Years of experience with bullets showed engineers that breaking the sound barrier was just a matter of brute force and streamlining.

By contrast, flinging something with at the speed of light appears impossible because the amount of energy required keeps going up and up until it requires an infinte amount of energy to propell something with mass at c. Particle accelerators have this problem. Google something called the "oh my god particle". Basically it's a proton with the kinetic energy of a baseball, owing to it's moving at a fly's eyelash below c. Yes, that's a single proton with enough punch to knock over your neighbor's cocker spaniel, all because of the goofiness of Einsteinian physics. Throwing more and more energy in gives increasingly reducing returns in projectile velocity, which suggests that something mighty powerful indeed it producing the "oh my god" particles. Unlike the sound barrier, there is no prior human invention that can break c, and there is no clear means by which to do so.

 

[espritch]

I personally find Pi more interesting. Could you have a universe where Pi doesn't = 3.14159 . . . . . .?

From what I understand, we already live in a universe where Pi doesn't neccessarily equal 3.14159... Gravity warps space. If you measure a direct radial line from the center of the earth to a point in space and then measure the circumference of a circle around the earth that passes through that point, you will find that the lenght of the circumference does not actually equal Pi times the radius; it is a little less due to the warping of space by Earth's gravity well. So if Pi is defined as the relationship between the radius of a circle and it's circumference, it will only be 3.14159... in a perfectly flat region of space time, which, as far as I know, doesn't actually exist.

 

[neutrino_cannon]

c.f. Terry Pratchet's recent book Going Postal, in which a wheel where pi=3 is a very dangerous thing indeed.

 

[Tez]

You don't need to "believe me" or otherwise - anyone who knows enough to be skeptical, probably knows enough to do the derivation themselves! Its fairly standard.

(That said, I had to google for 15-20 minutes to find a coherent but also rigorous discussion to link to!)

See e.g. Stetz' book:

http://www.physics.orst.edu/~stetza/COURSES/ph655/Book.pdf

The relevant part is chapter 4, pages 33-39. Note, I dont claim you must agree with the conclusions he draws, but the analysis is fine.

Someone asked the good question of why, if the background spacetime is Galilean, could one not have observers travelling faster than c. If you trust regularized quantum field theory (which is all this stuff actually is) then its for the simple reason that the "observers" are made out of the same junk! That is, from this perspective, we are all made up of the oscillations of a slightly more complicated version of the "masses and springs" mattress, (but not much more complicated!) and are similarly limited in our maximum velocity (in fact, being massive excitations, our dispersion relation is such that we cannot quite reach c).

Which brings me to the issues I have with this point of view. It seems the background spacetime retreats into a metaphysical structure if you adopt this approach. That I'm a little worried about, but there's enough historical precedent for such, and I am not rooted in postivistic philosophy; my epistemology will survive. However certain technical questions arise as to how, why or even if the theory is such that classical reference frame objects (clocks, metre sticks) can be built from the "oscillations" (excitations of the field), and these questions disturb me. For instance, if you read those pages above, the final wave equation contains a parameter "t" corresponding to time. This parameter originally arose from the background galilean spacetime. However, it must now be measured with clocks that are built from the field itself. If you try and make rigorous these constructions you find that there is no simple operational interpretation of this time. And yet we use this wave equation very successfully all the "time"! There are several proposals by leading physicists for how to give a consistent interpretation of time in such a scenario, but none of them have completely satisfied me...

 

[69dodge]

Ok, I read your link. Also, p.180 of http://www.ifa.hawaii.edu/~kaiser/lectures/elements.pdf. It seems you weren't saying what I thought you were saying.

Which is what I figured.

Tell me if have it right, now.

Originally posted by Tez
All inertial observers of these waves will see them travel with a constant velocity - lets call it c.

Yes, if those inertial observers are related to the mattress frame (no pun intended) via Lorentz transformations. (I originally thought these transformations were supposed to be Galilean too, just like the laws governing the oscillations of the mattress.) But then, it's no surprise that an observer still sees the wave travelling at c; that's built into the Lorentz transformation. The only interesting thing is that the transformed wave, in all its details, is (a different) one of the possible original waves.

In modern language, the description of these waves is Lorentz invariant.

Right. So if different inertial observers are related via Lorentz transformations, then they can all use the same description to describe the waves. But we can't derive the fact that they are related via Lorentz transformations unless we assume that they can all use the same description.

 

[Tez]

Ok, I read your link. Also, p.180 of http://www.ifa.hawaii.edu/~kaiser/lectures/elements.pdf. It seems you weren't saying what I thought you were saying.

Which is what I figured.

Tell me if have it right, now.Yes, if those inertial observers are related to the mattress frame (no pun intended) via Lorentz transformations. (I originally thought these transformations were supposed to be Galilean too, just like the laws governing the oscillations of the mattress.) But then, it's no surprise that an observer still sees the wave travelling at c; that's built into the Lorentz transformation. The only interesting thing is that the transformed wave, in all its details, is (a different) one of the possible original waves.Right. So if different inertial observers are related via Lorentz transformations, then they can all use the same description to describe the waves. But we can't derive the fact that they are related via Lorentz transformations unless we assume that they can all use the same description.

I think you've got it. I guess in principle we can imagine what things are like if you don't happen to be "in the mattress frame" (which is probably better thought of as "made of the mattress"). For instance, this is a reasonable enough model of long wavelength phonon propogation, and we can certainly imagine sitting outside the crystal and bopping along at any old veocity we want. I'd have to think about what this meant for a coherent description of physics from this observers viewpoint. I suppose they essentially end up in a messy situation much like people were in when they realized Maxwell's equations didnt transform under a Galilean transofrmation, but regular matter (supposedly) did...

 

[Dustin Kesselberg]

I have a few questions which do not seem to have been answered even though this thread pertains to them...


1.How did einstein know the speed of light?


2.Why did he assume that it was always constant?


3.How did he know it was always constant?


4.Why is mass infinite at the speed of light?


5.How did einstein know mass is infinite at the speed of light?

 

[Darat]

I have a few questions which do not seem to have been answered even though this thread pertains to them...


1.How did einstein know the speed of light?

When?

2.Why did he assume that it was always constant?

His genius.

3.How did he know it was always constant?

...snip...

When?

5.How did einstein know mass is infinite at the speed of light?

He didn't.