What if C didn't exist?

[magnemoe]

If there were no absolute c, we would still use classical physics, there would be no special relativity

This is how I read it, light has the same speed as before, however its not the upper speed, e=m*c^2 is still true.

It would have no impact on current and medium future space travel, none of the ideas of interstellar ships will get into speeds where relativity become an important factor.

[Michael Kim]

Correct me if I'm wrong, but didn't Newtonian-era physics establish that light had a finite speed, but just fail to realize the significance of the constant c? Infinite light speed would break many, many, things even if we take away relativity.

At the time of Newton (or some time later, can't really remember), the speed of light is finite, but it's purely derived from experiments and observations. It's not derived from any theory, nor does it go into any theory. (e.g. The fastest human runs about 10m/s.) So changing it to infinite won't break any law.

In fact, in classical physics, the interaction of two objects (i.e. force) is instantaneous.

This is how I read it, light has the same speed as before

Please read, #1 said "If light were literally instantaneous"

however its not the upper speed, e=m*c^2 is still true.

e = m * c ^ 2 is a result of special relativity

[stupid_chris]

But there's no maximum speed of light, so you could keep on accelerating forever. You can travel between galaxies. Even more, you can travel back home.

The limiting factor here isn't how fast you accelerate. It's the human's living time. With relativity, the time frame of an object going near the speed of light slows down. This happens to prevent anything from actually breaking this law. Example: You are inside a ship travelling 99.999% of the speed of light. What happens if you are at the back of this ship and suddenly start running to the front of the ship? Your relative speed to the ship greatly increase. But you're already going 99.999% of the speed of light. The thing is if you run fast enough, you could acquire this 0.001% (well you'd have to run fast but you get the idea ). So to prevent that, the time frame of everything in the ship is slowed down. Anyone looking at what happens in the ship would see it happening in slow motion. So a trip to something 1000LY away would take a bit more than 1000 years for the ship if it goes 99% of the speed of light, but the crew would feel it took only 50 years (if my memory serves me right) But the same trip, without c, even if you end up going to 300% c, would take a few hundred years, even for the crew, who would die during the travel. So c is essential for really long travels, as time contraction greatly helps.

[K^2]

1) the universe is finite, then the brightness will be finite;

2) the universe is infinite, then the brightness will be infinite.

Of course. I understand how divergent sequences work. Any finite partial sum is finite. My claim is that it would still be very large if the density was uniform.

Also, why do you say that our universe is big enough to compare to, say, Olber's size?

Why don't you run an estimate? Estimates on known luminous matter in the visible universe is a matter of record. Go ahead and assume uniform distribution and compute luminosity of the sky. Then compare it to what we actually see. I think you'll be surprised at disparity.

Point is, if it wasn't for the fractal structure of the visible universe, we'd still see a much brighter sky. And if we assume that the same fractal hierarchy is preserved throughout the infinite expanse of the universe (if it is such) we still have average density drop off with distance fast enough for Olber's paradox not to be a factor.

Of course, there is no way to prove that universe doesn't become uniform at some large enough scale, way beyond our visible universe. But that raises a whole lot of new questions. I don't want to get into all the fine details, but speed of light limit doesn't trivially resolve Olber's in this case either.

[Michael Kim]

Of course. I understand how divergent sequences work. Any finite partial sum is finite. My claim is that it would still be very large if the density was uniform.

Why don't you run an estimate? Estimates on known luminous matter in the visible universe is a matter of record. Go ahead and assume uniform distribution and compute luminosity of the sky. Then compare it to what we actually see. I think you'll be surprised at disparity.

Point is, if it wasn't for the fractal structure of the visible universe, we'd still see a much brighter sky. And if we assume that the same fractal hierarchy is preserved throughout the infinite expanse of the universe (if it is such) we still have average density drop off with distance fast enough for Olber's paradox not to be a factor.

Of course, there is no way to prove that universe doesn't become uniform at some large enough scale, way beyond our visible universe. But that raises a whole lot of new questions. I don't want to get into all the fine details, but speed of light limit doesn't trivially resolve Olber's in this case either.

Well I wonder how you would make the estimation. It is true that the universe has structures (galaxies on a small scale; walls and voids on a large scale), but whatever structure it has, the density of luminous matters is really low. In fact, we are in a rather dense area (i.e. the Milky Way galaxy), but our night sky is still dark. If you uniformly distribute all the stars of the Milky Way in the Local Group, our night sky will be much darker. So again, why do you say it will be bright?

[K^2]

Well I wonder how you would make the estimation. It is true that the universe has structures (galaxies on a small scale; walls and voids on a large scale), but whatever structure it has, the density of luminous matters is really low. In fact, we are in a rather dense area (i.e. the Milky Way galaxy), but our night sky is still dark. If you uniformly distribute all the stars of the Milky Way in the Local Group, our night sky will be much darker. So again, why do you say it will be bright?

Because you are integrating 4 pi r² * rho®/r². The luminosity we see is actually so low because rho is not uniform. It might feel counter-intuitive, but with cluster structure, only the stars in your own galaxy, in fact your arm of the galaxy, contribute to the night sky. Sure, they contribute a lot more, but they are an almost infinitesimal part of the universe. With uniform distribution all of the stars contribute, and the sky actually ends up brighter.

Just take estimate for total output of the luminous matter in visible universe, divide by volume, use it as density, and integrate.

[Michael Kim]

Because you are integrating 4 pi r² * rho®/r². The luminosity we see is actually so low because rho is not uniform. It might feel counter-intuitive, but with cluster structure, only the stars in your own galaxy, in fact your arm of the galaxy, contribute to the night sky. Sure, they contribute a lot more, but they are an almost infinitesimal part of the universe. With uniform distribution all of the stars contribute, and the sky actually ends up brighter.

Just take estimate for total output of the luminous matter in visible universe, divide by volume, use it as density, and integrate.

It is obvious that if you distribute all the stars in the Milky Way uniformly in the observable universe ("the universe"), the night sky will be darker. Sure there are other things in the universe, but the average matter density of the universe is much smaller than that of the Milky Way. And since you agree that most of the light of our night sky is about the Milky Way, you should agree that if we lower the density in this area, the night sky will be darker.

EDIT: Since your claim is "counter-intuitive", you've got to prove it with maths

Edited May 29, 2013 by Michael Kim

[K^2]

Aren't you an astronomy student? You are supposed to be able to do all of this.

Alright. So the rough estimate is one star per billion cubic light years. And because I'm too lazy to find actual average luminosity, I'll use Sol. It's not a particularly bright star, but majority of stars are in the same neighborhood, so I might be underestimating a bit, but that's fine. So we have P = 3.85x10²⁶W per 10⁹ ly³. Each star will distribute its light over the 4À solid angle. So per unit area, you get 1/(4À r²) of star's power. And, of course, at a given distance r in a shell of thickness dr, you'll have 4À r² àdr stars. Here, àis number of stars per unit of volume. I'll be using light years as my unit, so à= 10^-9 ly^-3. This gives me the integral to compute total luminosity of the sky.

Lets take R = 40bly. That gives me total luminosity of P_tot = PRà= 3.85x10²⁶W * 10^-9 ly^-3 * 4x10¹⁰ ly = 1.54x10²⁸ W/ly². Of course, W/ly² is not a convenient unit. Converting it to metric units we have P_tot = 0.172 mW/m².

Comparing that to what we actually see. The average starlight is about 15 S₁₀. That's 15 mag 27.78 stars for every arc second squared. Sun is mag 4.83 from 10 parsecs, which means we need to have 15 Suns for every arc second squared uniformly distributed at 1.27x10⁶ light years from here. The total in the sky would be 8x10¹² such stars. This gives me a P_tot of 1.7 μW/m² as per formulae already described.

So the sky is roughly 100x dimmer than it would be if the stars in just the observable universe were uniformly distributed. Is that a lot? Subtract 5 from magnitude of every star and you'll have the idea. We'd be living in perpetual twilight.

[Chrono]

I'm going to go out on a limb here, considering the topic, and say, if light was instantaneous, then there would be no red shifting, and if there was no red shifting then the sky would be white with light with all of the stars in the sky, no matter how far they are, and if that was true I would also say the same applies to the entire EM spectrum then if that was true... we would all die from massive radiation. Or at the very least would have evolved differently and then by that point this conversation would be a moot point.

[Michael Kim]

K^2, of course your equations are correct, and of course I can do them (well, previously I claimed that it goes with ln®, I made a mistake there).

But my point is, if you compare the uniform distribution and the current distribution, you will get the result that the former is darker. This is what I've been saying and I bet you didn't think it through. And when I made the comparison I don't need the values of P and ÃÂ, where you may get things wrong.

[K^2]

Except, it's not darker. With uniform distribution, you get a much brighter night sky. Night sky in a fractal-like universe is much, much dimmer than in a uniformly distributed universe, given the same number of stars in both. Again, I recommend you try this on your own, but if you really need me to, I will go through the equations. It is a very important result in cosmology, so if you don't trust me, I suggest you discuss it with somebody you do consider an authority.

For defining the density distribution in a fractal as a function of the distance, keep in mind that fractals typically have Hausdorff Dimension less than dimension of the space. In this case, less than 3.

[WestAir]

A uniform night sky will be brighter than a fractal night sky. I'm not an astronomy student, but I could easily imagine two stars 1 AU apart will appear brighter than two stars with one slightly hidden behind the other. Fractal clusters hide a lot of light sources behind other sources in a way that a uniform distribution wouldn't need to, and that means less luminosity reaching us.

[Fractal_UK]

Except, it's not darker. With uniform distribution, you get a much brighter night sky. Night sky in a fractal-like universe is much, much dimmer than in a uniformly distributed universe, given the same number of stars in both. Again, I recommend you try this on your own, but if you really need me to, I will go through the equations. It is a very important result in cosmology, so if you don't trust me, I suggest you discuss it with somebody you do consider an authority.

For defining the density distribution in a fractal as a function of the distance, keep in mind that fractals typically have Hausdorff Dimension less than dimension of the space. In this case, less than 3.

Except that it is widely accepted within the field of cosmology that the cosmological principe holds and that, on sufficiently large scale, the universe is indeed homogeneous and isotropic. By lowering the fractal dimension of the universe, anisotropy is required on the largest scales. Such anisotropy is at odds with the vast majority of experimental observations of the universe at very large scale. A fractal universe is not an idea that you will find much support for amongst the cosmological community.

[K^2]

Except that it is widely accepted within the field of cosmology that the cosmological principe holds and that, on sufficiently large scale, the universe is indeed homogeneous and isotropic. By lowering the fractal dimension of the universe, anisotropy is required on the largest scales. Such anisotropy is at odds with the vast majority of experimental observations of the universe at very large scale. A fractal universe is not an idea that you will find much support for amongst the cosmological community.

Which, I would claim, is a very strong indication that our universe is finite and likely closed. I am aware of the experimental evidence for universe becoming homogeneous at large scale, and I cannot see this causing anything but trouble if the universe is infinite, which is the case we've been discussing earlier. Sorry if I wasn't clear on this distinction.

With an infinite universe, the only way luminosity of the sky can remain finite is if the density goes to zero as you increase the scale. This doesn't happen if universe becomes homogeneous at large scale. And none of the other solutions work in an infinite universe. Even if we imagine that there is a lot of cold gas/dust in between the stars, all the energy absorbed has to be re-emitted. Sure, it would be emitted in IR if that gas is cold, but that only shifts the band, not the total output. If your luminosity diverges in IR, that will still cause everything to heat up and eventually glow in visible. So average density of infinite universe must go to zero.

Of course, this is quasi-static case. Some interesting things can happen with acceleration. But most of these workarounds require collapsing universe. That would, indeed, allow for average density to be zero on large scale but be high locally anywhere in the universe. Opens a whole new can of worms, however.

Finite universe is simpler. You can get away even with a completely homogeneous structure, and the interstellar dust has much greater impact on luminosity of the sky. But there is still a very big difference between globally uniform distribution and a fractal one. Even if it's only fractal up to a certain scale. For example, in homogeneous universe the interstellar dust can still only convert the band of the radiation, not change the total luminosity across the spectrum. In a fractal universe, again, even just locally fractal, interstellar dust can actually dim the light.

Consider our own galaxy as an example. The sky would be brighter if the dust wasn't there. Why? Because dust doesn't only block the visible band, but it gets rid of absorbed energy by emitting IR in all directions, including out of the disk. As a result, the total luminosity across all bands goes down. This only happens if the void between galaxies is much greater than size of galaxies and local stellar density is much, much greater than average in the cluster.

[Michael Kim]

K^2,

I'm not sure if we are talking about the same thing... Plus, I'm a grade 2 undergrad, so I don't know Hausdorff Dimension, nor am I sure if I understand "fractal" correctly.

But here, I wrote myself a computer programme, where I randomly throw 100,000 stars in a spherical universe (radius = 1), and calculate the total brightness as seen from (0, 0, 0)

I have two cases:

1) stars are uniformly (i.e. totally randomly, with no bias in any dimension) distributed

2) stars are randomly grouped into galaxies, where the first galaxy (the Milky Way) is at the center of the universe, and other galaxies are randomly distributed

And no matter how I change the parameters or how many times I run the programme, the result of the second case is always much larger.

Meanwhile, for the second case, the Milky Way always contributes the most (>99%) brightness, which means it alone is much brighter than case 1.

Note that in my programme, no star can be within the distance of 1e-5, which is rather high compared to reality. Just to make sure the result is "night" sky.

[Fractal_UK]

Finite universe is simpler. You can get away even with a completely homogeneous structure, and the interstellar dust has much greater impact on luminosity of the sky. But there is still a very big difference between globally uniform distribution and a fractal one. Even if it's only fractal up to a certain scale. For example, in homogeneous universe the interstellar dust can still only convert the band of the radiation, not change the total luminosity across the spectrum. In a fractal universe, again, even just locally fractal, interstellar dust can actually dim the light.

Yes indeed but my point is related to the previous post where you attempt to show that the night sky is darker than it should be where the matter in the universe uniformly distributed. I'm not disputing the point that a fractal universe is darker, indeed one of the resolutions to Olber's paradox is a fractal universe with fractal dimension <= 2 but the result that you derive suggests that the universe is 2 orders of magnitude darker than it should be were the cosmological principle to hold. That is a worrying result and suggests that something is amiss with the admittedly highly simplified theory that you show because it contradicts experimental evidence that suggests that the universe is indeed homogeneous and isotropic at very large scales.

I can believe that the irradiance from starlight received by the Earth is attenuated by the instellar medium but this fact does not permit, via your equations, any conclusions to be drawn about the structure of the universe on a very large scale. It merely suggests that the universe is not homogenous and isotropic at smaller scales, which is immediately apparent anyway. Of course, the scale at which it becomes such is a matter of ongoing debate.

[sporkafife]

I'm pretty sure that if light moved instantaneously (i.e. c=inf, c wouldn't stop existing ) then the sky would always be lit up as if it were daytime. Because the universe is homogeneous and infinite (probably), then whichever direction you look in you will eventually meet a star, and because the light traveled instantly the sky would be full of bright lights and would never be dark. The sky would probably still be blue due to Rayleigh scattering though.

In terms of spaceflight and relativity, if you were to make the speed of light infinitely high then special relativity equations would all cancel down to every time and distance appearing the same to every observer no matter how fast their reference frame is accelerating. This would mean almost instantaneous travel becomes theoretically possible.

Also, just pondering the Equation E=mc^2, if c was infinite it means you would need an infinite amount of energy to create any mass. And seeing as the first sub-atomic particles all condensed from energy at the big bang, there wouldn't be any universe because energy would not be able to condense into matter in the first place to do anything interesting...

This is all theoretical, and everything I said is the ramblings of somebody with only two years of university physics... so don't think everything I say is right

[Sof]

I'm pretty sure that if light moved instantaneously (i.e. c=inf, c wouldn't stop existing ) then the sky would always be lit up as if it were daytime. Because the universe is homogeneous and infinite (probably), then whichever direction you look in you will eventually meet a star, and because the light traveled instantly the sky would be full of bright lights and would never be dark. The sky would probably still be blue due to Rayleigh scattering though.

In terms of spaceflight and relativity, if you were to make the speed of light infinitely high then special relativity equations would all cancel down to every time and distance appearing the same to every observer no matter how fast their reference frame is accelerating. This would mean almost instantaneous travel becomes theoretically possible.

Also, just pondering the Equation E=mc^2, if c was infinite it means you would need an infinite amount of energy to create any mass. And seeing as the first sub-atomic particles all condensed from energy at the big bang, there wouldn't be any universe because energy would not be able to condense into matter in the first place to do anything interesting...

This is all theoretical, and everything I said is the ramblings of somebody with only two years of university physics... so don't think everything I say is right

It was argued earlier in the thread that infinite C wouldn't make the sky bright. We don't see far away stars because light hasn't reached us yet, they are just too far away and aren't bright enough to see. Changing the speed of light wouldn't change its brightness.

[sporkafife]

It was argued earlier in the thread that infinite C wouldn't make the sky bright. We don't see far away stars because light hasn't reached us yet, they are just too far away and aren't bright enough to see. Changing the speed of light wouldn't change its brightness.

It can be argued as much as you like by the smartest people in the world (and by the love of Jeb, it has been). I would argue straight back saying that no matter how dim a star was, if light traveled infinitely fast then there would always be photons of light reaching us from even the dimmest stars.

At the end of the day, this is still a topic that people much smarter than me still disagree on. I don't know what would happen, and nobody will ever know for sure. Human bias can convince you that you know the answer. But that's all it is: bias. Even armed with all the physics, theoretical physics and mathematics that exists in our collective minds it is impossible to know what would happen if the speed of light was infinite because we cannot observe it and collect data on it. As far as I can tell there are many fine arguments for and against it. That's why I'd rather treat it as a nice little brain straining exercise that just makes you think instead of a full blown debate.

Anyway, I think the idea that the universe probably couldn't have condensed out of the energy created in the big bang cancels out the point of any argument anyway

[Stochasty]

Finite universe is simpler. You can get away even with a completely homogeneous structure, and the interstellar dust has much greater impact on luminosity of the sky.

Yes indeed but my point is related to the previous post where you attempt to show that the night sky is darker than it should be where the matter in the universe uniformly distributed. I'm not disputing the point that a fractal universe is darker, indeed one of the resolutions to Olber's paradox is a fractal universe with fractal dimension <= 2 but the result that you derive suggests that the universe is 2 orders of magnitude darker than it should be were the cosmological principle to hold. That is a worrying result and suggests that something is amiss with the admittedly highly simplified theory that you show because it contradicts experimental evidence that suggests that the universe is indeed homogeneous and isotropic at very large scales.

I can believe that the irradiance from starlight received by the Earth is attenuated by the instellar medium but this fact does not permit, via your equations, any conclusions to be drawn about the structure of the universe on a very large scale. It merely suggests that the universe is not homogenous and isotropic at smaller scales, which is immediately apparent anyway. Of course, the scale at which it becomes such is a matter of ongoing debate.

Don't forget that in the physical Universe redshift also plays a factor in the decline of \rho® with distance. On scales much greater than >1Gpc the Universe is sufficiently homogeneous and isotropic that the Uniform distribution is reasonably valid, and dust attenuation doesn't make enough difference (if we assume that dust is opaque and has a homogeneous and isotropic distribution on large scales, then the solid angle obscured per radius shell dr is a constant; considering overlapping dust, this would have the effect of dropping the Hausdorff dimension of unobscured stars from 3 to 2, still not enough to make the sky dark in an infinite Universe).

EDIT: Bah, I'm wrong. I was thinking the dust would lead to a 1/r scaling; the scaling is actually exponential, which would be enough to drop the Hausdorff dimension below two.

Edited May 30, 2013 by Stochasty