Faster than light

jblack

Forgive my Sesame Street knowledge but I've never received a satisfactory answer to this question:

If nothing can exceed the speed of light, then how come physicists estimate the expansion of the universe to be many light years across within fragments of a second from when time = 0.

Cú Giobach

The speed of light limit only concerns "things" travelling through space, not with the expansion of space itself.
Things can't travel faster than light because it would take infinite energy to move them through space, but two objects receding relative to each other faster than light due to expansion/inflation are not travelling through space but with it, consequently no laws are broken.

Capt'n Midnight

The dumbed down version.

The laws of physics were very different at the start of the universe, multiple dimensions and all that. And the bit I'm not sure about is that light then would be travelling through matter because there still wasn't empty space, and this would have slowed light down far below the speed of light in a vacuum. So information would not be able to pass between parts of the universe faster that it was expanding until there was more empty space between the matter. Or something.

jblack

So light then caught up, so to speak, with the area created by expansion?

krd

Capt'n Midnight wrote: »

The dumbed down version.

The laws of physics were very different at the start of the universe, multiple dimensions and all that. And the bit I'm not sure about is that light then would be travelling through matter because there still wasn't empty space,

Hang on. Are you saying the Big Bang created the Vacuum?

What laws of physics were different at the big bang?

Did matter move through space faster than the speed of light - to inflate?

What's the explanation?

and this would have slowed light down far below the speed of light in a vacuum. So information would not be able to pass between parts of the universe faster that it was expanding until there was more empty space between the matter. Or something.

The big bang was very bright. We can still see/detect the light from it today.

acidpenguin

If 2 objects move away from each other, each at 99% the speed of light, are they going faster than the speed of light relative to each other?

Capt'n Midnight

acidpenguin wrote: »

If 2 objects move away from each other, each at 99% the speed of light, are they going faster than the speed of light relative to each other?

https://en.wikipedia.org/wiki/Horizon_problem


when the light was emitted the universe was much younger (300,000 years old). In that time light would have only reached as far as the smaller circles. The two points indicated on the diagram would not have been able to contact each other because their spheres of causality do not overlap.

krd

Capt'n Midnight wrote: »

when the light was emitted the universe was much younger (300,000 years old). .

Why did it take 300,000 years for that to happen?

I always assumed the light of the big bang was instantaneous.

Was there light emitted before the 300,000 year mark?

Morbert

acidpenguin wrote: »

If 2 objects move away from each other, each at 99% the speed of light, are they going faster than the speed of light relative to each other?

No. Velocities don't add linearly.

You can try it yourself.

If you have two velocities v and u, adding their velocities, according to Newtonian mechanics gives you

u + v

but according to relativity, it's

(u + v)/(1 - uv/c^2)

http://en.wikipedia.org/wiki/Velocity-addition_formula

This is somewhat unrelated to the Horizon problem posted by Capt'n'Midnight, which relates to how distant parts of the universe can be in thermal equilibrium. It is solved with inflationary models.

krd

Morbert wrote: »

(u + v)/(1 - uv/c^2)

Can you explain how c ends up in that equation?

In English.

Why c?

I know it's something to do with Einstein's relativity. But why c?

Anonymo

krd wrote: »

Can you explain how c ends up in that equation?

In English.

Why c?

I know it's something to do with Einstein's relativity. But why c?

Ok, it's a bit of a challenge to explain this! The reason that 'c' appears can be traced to the relation between special relativity and Maxwell's equations.

Right so Maxwell's equations, which govern electromagnetism show two big things, namely, that a changing electric field can give a magnetic field and that a changing magnetic field gives an electric field.
This seemed to suggest a fundamental relationship between magnetism and electricity. Maxwell found a system of equations (4 of them) that showed this relationship but to make the whole thing consistent some constraints have to be satisfied. One of these was for a constant that is called 'c' and has the dimensions of velocity. Since electromagnetism is governed by photons, this 'c' must be the speed of photons, i.e. light.
Now electromagnetism obeys a nice symmetry in these four equations called Lorentz transformation invariance. Lorentz transformations transform the time and space coordinates in a certain and specific way and shows that space and time are related (or more precisely how space and c multiplied by time are related). It is this relation that gives the formula for adding velocities. If you want to see the maths... do a lorentz transformation to transform your frame so that it's moving at speed v. The transformation is
x'=gamma(v) (x-vt)
t'=gamma(v) (t-vx/c^2)
where gamma(v) = 1/sqrt(1-v^2/c^2)
Do this again to move this frame at speed u relative to the new frame then the frame has
x''=gamma(u) (x'-vt')
t''=gamma(u) (t'-v x'/c^2)
where gamma(u) =1/sqrt(1-u^2/c^2)

Ok that's great but naively you'd have thought that doing a transformation of the original frame to move at speed u+v relative to what you started with would give you the correct answer. It doesn't! If you use the formulae here and write x'',t'' in terms of x,t you get
x''=gamma(w) (x-w t)
t''=gamma(w) (t-w x/c^2)
where gamma(w)=1/sqrt(1-w^2/c^2)
and we have
w=(u+v)/(1+u v /c^2)

What was important was to take the transformation of one frame RELATIVE to the other

Anonymo

Capt'n Midnight wrote: »

The dumbed down version.

The laws of physics were very different at the start of the universe, multiple dimensions and all that. And the bit I'm not sure about is that light then would be travelling through matter because there still wasn't empty space, and this would have slowed light down far below the speed of light in a vacuum. So information would not be able to pass between parts of the universe faster that it was expanding until there was more empty space between the matter. Or something.

Nope. You're confusing a few things in your reply here - although it may be more your phraseology rather than your understanding that's in question. :cool:

The laws of physics at the start of the universe are conjectured to be very different. We do not know what they were really near the big bang. We can be pretty sure that we've the correct physics from around a second after the big bang through to today. The idea of multiple universes, 10 dimensions etc. is part of different conjectures to extend the knowledge of physics that we know is true to the region just after the big bang that we don't.

Anyway this is all independent, though conflated in your post, with the idea that the speed of light would have slowed down because of matter in the early universe. This is absolutely true. To a high degree of confidence the velocity of light 'c' is constant in a vacuum. Like a pressure cooker - the fact that the universe occupied a smaller volume in the early universe, means that the temperature was much higher. This means that electrons and other particles were moving around very energetically and there were frequent collisions between the photons and them. Assuming the photons (particles of light) were moving through a vacuum but constantly bombarded by these baryons this would mean that there effective speed was very low (because of being frequently diverted off course it takes much longer to get to the same destination). In fact this effective speed was so low that we have to wait till the universe cooled down enough, i.e. expanded enough, so that the photons are no longer being continually bombarded, in order to see them today. This took around 300,000 years after the big bang. And that era of the universe is called the last scattering surface. When people talk about the cosmic microwave background they are talking about the light that is still coming to us (more or less free of bombardments) from the last scattering surface.

There is no relationship between information transfer and the speed of expansion. One is to do with how fast photons travel, i.e. the speed of light. The other is to do with how the fabric of spacetime is expanding, i.e. there is no information being transferred in the latter.

I might put up a post later on the solution to the horizon problem, but this post is already long enough. :eek:

krd

Anonymo wrote: »

Now electromagnetism obeys a nice symmetry in these four equations called Lorentz transformation invariance. Lorentz transformations transform the time and space coordinates in a certain and specific way and shows that space and time are related (or more precisely how space and c multiplied by time are related).

Yeah, I knew the relationship with Maxwell's equations. Where I get stuck is with Lorentz, Poincare, etc.

It just doesn't pop out, or click with me, where, or why it's c. I can read the equations and see c there - and I can see other things that are implied by the equations. I think I'd need to see some animations - and some kind of guide that takes the derivation the whole way from Maxwell's equations through to Lorentz.

Morbert

krd wrote: »

Yeah, I knew the relationship with Maxwell's equations. Where I get stuck is with Lorentz, Poincare, etc.

It just doesn't pop out, or click with me, where, or why it's c. I can read the equations and see c there - and I can see other things that are implied by the equations. I think I'd need to see some animations - and some kind of guide that takes the derivation the whole way from Maxwell's equations through to Lorentz.

The speed c is derived from Maxwell's equations. I wrote a rough derivation of the speed.

http://www.boards.ie/vbulletin/showpost.php?p=75791351&postcount=8

Note that, in natural units, c = 1.

krd

Morbert wrote: »

The speed c is derived from Maxwell's equations. I wrote a rough derivation of the speed.

http://www.boards.ie/vbulletin/showpost.php?p=75791351&postcount=8

Note that, in natural units, c = 1.

I remember. Thanks again.


Where it's not clicking with me is where c comes into relativity. The Lorrentz factor. I have a vague idea, that c has to be there - I'm just not precisely sure why it should be there. Is the invariance of c based on experimental proof from Michelson-Morley interferometry.

When I look over the equations - I just don't see explanation of where c comes in that I can understand.

This stuff is confusing. I was looking at wikipedia last night, and it seemed to be saying in one little piece. That if an observer is stationary in front of a stationary electric charge/field. They won't see the magnetic field - but if they move relative to the electric charge - they will see the magnetic field. That's confusing.

Morbert

krd wrote: »

I remember. Thanks again.


Where it's not clicking with me is where c comes into relativity. The Lorrentz factor. I have a vague idea, that c has to be there - I'm just not precisely sure why it should be there. Is the invariance of c based on experimental proof from Michelson-Morley interferometry.

When I look over the equations - I just don't see explanation of where c comes in that I can understand.

I suppose you could say it is derived from the permeability of the electromagnetic field in free space.

This stuff is confusing. I was looking at wikipedia last night, and it seemed to be saying in one little piece. That if an observer is stationary in front of a stationary electric charge/field. They won't see the magnetic field - but if they move relative to the electric charge - they will see the magnetic field. That's confusing.

It's the same kind of transformation that takes place between space and time. The electric field and magnetic field, like space and time, are facets of the same thing. It's why the dynamo on your bike works, or how electricity is generated.

krd

Morbert wrote: »

It's the same kind of transformation that takes place between space and time. The electric field and magnetic field, like space and time, are facets of the same thing. It's why the dynamo on your bike works, or how electricity is generated.

That's what I believe it is too........That's why I'm trying to understand it.

I'm so out of practice, with maths and formulae, that I can't just sit down and hammer it out myself - though I can see what I want to know is in the equations - I'm not really up to tackling them. An maybe the equations don't absolutely reveal everything - like if an observer is moving relative to a static charge, and they see the magnetic field - is the observer changing the flux of the that magnetic field. I think once I have a better understanding, it will fit together neatly.

Why in Newtownian Relativity, would c in the Lorrentz factor be infinity?

Anonymo

krd wrote: »

I remember. Thanks again.


Where it's not clicking with me is where c comes into relativity. The Lorrentz factor. I have a vague idea, that c has to be there - I'm just not precisely sure why it should be there. Is the invariance of c based on experimental proof from Michelson-Morley interferometry.

When I look over the equations - I just don't see explanation of where c comes in that I can understand.

This stuff is confusing. I was looking at wikipedia last night, and it seemed to be saying in one little piece. That if an observer is stationary in front of a stationary electric charge/field. They won't see the magnetic field - but if they move relative to the electric charge - they will see the magnetic field. That's confusing.

On your last point... if there is only an electric field to start with and everything is stationary (i.e. no movement) then the observer will only detect the electric field. However, what's interesting is that when the observer begins to move (relative to the source of the electric field) it will start to see a magnetic field. This is because electricity and magnetism are part of the same force, neatly called electromagnetism
This relation is called Ampere's law. You can kind of think of this in term's of the Lorentz force law - which tells us the force on a wire due to the presence of an electric charge and a moving magnetic field. This is
F=E+vB sin(theta), where theta is the angle between the direction of motion and the magnetic field.

Right so if there is no velocity (v=0) then you will only feel the electric field E. It takes motion relative to you, the observer, to feel a magnetic field (this is because the magnetic field is perpendicular to the direction of the electric field). If the electric field is pointing towards you then that means the magnetic field is pointing away. If the source of the fields moves towards you then that means over time there is a component of the magnetic field also moving towards you.

OK now back to where 'c' comes from. Morbert gave a nice derivation of the wave equation for B, the magnetic field (the same equation will also hold for E, the electric field). To simplify the maths let's write this as if it's in one space dimension (x). Then equation (9) reads [Note there's a typo in that equation which was correct elsewhere. It should have c->c^2]
B,xx - (1/c^2) B,tt =0
=> B,tt - c^2 B,xx =0

[Note the notation I use has ,xx to denote d^2/dx^2 , etc]
This has solutions like sin(x-c*t)
To check this note that sin(x-c*t),tt =-c^2 sin(x-c*t), while sin(x-c*t),xx=-sin(x-c*t)

Ok so the solution to the equation is a sine wave. You know the shape of this if it were sin(x). Right but this sine wave is moving... look at the x-ct
This means that if the wave is at x1 at time zero then at time t2 it moves to
x2=x1-c * t2, i.e. it move c*t2 in time t2, i.e. it's moving at speed c.
So this means we've a wave that's moving along at speed c.

This means that our solution for the magnetic field, B, moves along at speed c (as does the electric field, E). Great so now we know that electromagnetism moves at 'c', which must be the speed of light.

Where does this come into relativity. Well have a look again at that solution, the argument was x-ct. What if we think of ct as a type of coordinate itself, i.e. let's call it y.
Then the 1D equation will read
B,xx - B,yy =0. So the spatial dimension (x) is on the same footing as the time-like dimension (y=c * t). In fact this is really the symmetry that's present in Maxwell's equations. So if you want to transform your time dimension, so that e.g. you move from x to x+ v*t everywhere then you need to be careful about what's happening to c*t so that all your equations still hold. To get everything consistent requires you too move along in this fashion in a specific way, given by the Lorentz transformations that I spoke about in a previous post.

Now if you think of energy as related to time but momentum as related to spatial positions, then it turns out that if you want to do the same type of transformation x-> x-v*t you need to do it in a specific way so that your equations of motion stay consistent. The relations which do this are exactly the same Lorentz transformations as for Maxwell's equations.
Ok I was about to go off on a tangent about how this is used to give E=m c^2 but I think that might be enough for now!

Cookie_Monster

jblack wrote: »

If nothing can exceed the speed of light, then how come physicists estimate the expansion of the universe to be many light years across within fragments of a second from when time = 0.

well why do you assume nothing can go faster than light? Just because current theorys have it as a limit doesn't mean it's correct...

RebelButtMunch

I thought I heard that its not that light sets the limiting speed, its more that light travels at the fastest speed possible for it, and anything else. So its more like 'the speed of light' is easier than saying "299 792 458 m / s"

jblack

Cookie_Monster wrote: »

well why do you assume nothing can go faster than light? Just because current theorys have it as a limit doesn't mean it's correct...

Mainly because people who are a lot smarter than I have come to this conclusion, and I do not have the mental capacity to pick holes in this other than proffering questions like the OP.

Thanks so far to everyone who has replied.
Anonymo - Excellent answer, many thanks.

there is another similar thread here:

http://www.boards.ie/vbulletin/showthread.php?p=77081480

RebelButtMunch

jblack wrote: »

Mainly because people who are a lot smarter than I have come to this conclusion, and I do not have the mental capacity to pick holes in this other than proffering questions like the OP.

Thanks so far to everyone who has replied.
Anonymo - Excellent answer, many thanks.

there is another similar thread here:

http://www.boards.ie/vbulletin/showthread.php?p=77081480

I think jblack's statement is fair and correct. This is why we experiment . Even if a thousand experiments prove its right we only need one to prove its wrong. Thus far though we have only proven it to be correct.

desolate sun

Hi folks


I once went to a night time astronomy lecture in NUIG many years ago and the lecturer was talking about the expansion of the universe and how the galaxies were moving away from each other faster than the speed of light. Of course someone piped up that nothing can travel faster than light. The lecturer said it was the spaces in between the galaxies that were exceeding light speed.

Interesting. The way I see it is the spaces would be a vacuum, therefore containing nothing, nothing with mass, so not disobeying the e=mc2 law.

Would this be correct?

[EDIT] I just read the other thread and the space was mentioned.

Cookie_Monster

desolate sun wrote: »

Interesting. The way I see it is the spaces would be a vacuum, therefore containing nothing, nothing with mass, so not disobeying the e=mc2 law.

it's not a perfect vacuum though, there's lots and lots of stuff floating around in it.

Cú Giobach

desolate sun wrote: »

Hi folks


I once went to a night time astronomy lecture in NUIG many years ago and the lecturer was talking about the expansion of the universe and how the galaxies were moving away from each other faster than the speed of light. Of course someone piped up that nothing can travel faster than light. The lecturer said it was the spaces in between the galaxies that were exceeding light speed.

Interesting. The way I see it is the spaces would be a vacuum, therefore containing nothing, nothing with mass, so not disobeying the e=mc2 law.

Would this be correct?

[EDIT] I just read the other thread and the space was mentioned.

Think of two cars with top speeds of 150mph both moving in opposite directions, they are moving apart at 300mph and the distance between them is expanding at 300mph, but nothing, neither the cars nor anything in the space between them is actually moving at 300mph.
No matter where you measure the speed of expansion between two galaxies, even if they are receding at 10 times light speed relative to each other, the rate is still approx 74.2 km/sec/Mpc (and increasing).

Morbert

desolate sun wrote: »

Hi folks


I once went to a night time astronomy lecture in NUIG many years ago and the lecturer was talking about the expansion of the universe and how the galaxies were moving away from each other faster than the speed of light. Of course someone piped up that nothing can travel faster than light. The lecturer said it was the spaces in between the galaxies that were exceeding light speed.

Interesting. The way I see it is the spaces would be a vacuum, therefore containing nothing, nothing with mass, so not disobeying the e=mc2 law.

Would this be correct?

[EDIT] I just read the other thread and the space was mentioned.

It is important to distinguish between the coordinate speed of light, and the local speed of light. The local speed of light is always c, but if you are in a non-inertial frame, the coordinate speed of light might not be. The example I normally give is if you stand outside at night and spin on the spot, you will see the stars orbit you much faster than the speed of light. When we look at the expansion of the universe, what is effectively happening is the universe's definition of a unit distance is getting larger, so we don't have an inertial frame. I.e. if two galaxies are moving away from each other due to expansion, what is effectively happening is the length-scale between them is changing. Hence, while the local speed of light in any galaxy is c, galaxies can still "move" away from us faster than the speed of light.