C is constant?

[QuarkQuarkQuark2001]

Why does Einstein think that nothing is faster than light speed?

I think this is the most important core of relativity, so I must have a clear concept.

Hope for your helps

[5614]

i cant remember exactly how or why, but einstein definately said that nothing with matter could move faster than the speed of light

[J'Dona]

I just tried typing up the formula with an explanation for you but it messed up, and I have to go immediately to catch a bus, so I'll just leave you with this link which should hopefully explain it: http://www.physlink.com/Education/AskExperts/ae388.cfm

[swansont]

Why does Einstein think that nothing is faster than light speed?

I think this is the most important core of relativity' date=' so I must have a clear concept.

Hope for your helps[/quote']

 

As 5614 implied, the solutions preclude any massive object that travels slower than c from ever attaining or exceeding c, but there are valid solutions to the equation for v>c. But these objects can never travel below c.

 

c being the speed in all inertial frames is a postulate of special releativity, but it also stems from it being true for electrodynamics. If you solve Maxwell's equations for an EM wave, the only way it works in a moving frame is if c is invariant. (and I think we can agree that radio waves are still waves if we're in our car.)

[J'Dona]

Out of curiousity swansont (because I really just don't know how it works yet), if the speed of light is invariant, then how do they know things like the universe being 156 billion light years across when light would have only travelled 13.7 billion ly's at the most since its creation? I would have assumed that the speed of light was not always the same as now (as some recent but perhaps discredited theories have suggested), though maybe I'm just not taking into account relativistic effects or some such.

 

Also, if at the universe's creation all the matter in the universe was confined to a very small volume, surely it would be a singularity and all matter would immediately recollapse unless the speed of light were higher then? Or maybe the matter just was moving so quickly and its mass was higher that the force decelerating it was less... but then that still wouldn't explain how photons escaped. I'm getting confused. :S

[QuarkQuarkQuark2001]

I just tried typing up the formula with an explanation for you but it messed up, and I have to go immediately to catch a bus, so I'll just leave you with this link which should hopefully explain it: http://www.physlink.com/Education/AskExperts/ae388.cfm

 

Do I need to register for asking experts?

[J'Dona]

Don't know, that's just some random link I found with the xplanation already typed up from some previous person's question, I assume. It didn't ask me to register, so I assume it's okay. :/

[swansont]

Out of curiousity swansont (because I really just don't know how it works yet)' date=' if the speed of light is invariant, then how do they know things like the universe being 156 billion light years across when light would have only travelled 13.7 billion ly's at the most since its creation? I would have assumed that the speed of light was not always the same as now (as some recent but perhaps discredited theories have suggested), though maybe I'm just not taking into account relativistic effects or some such.

 

Also, if at the universe's creation all the matter in the universe was confined to a very small volume, surely it would be a singularity and all matter would immediately recollapse unless the speed of light were higher then? Or maybe the matter just was moving so quickly and its mass was higher that the force decelerating it was less... but then that still wouldn't explain how photons escaped. I'm getting confused. :S[/quote']

 

One part of this is that "c is invariant" occurs in inertial frames. Once you get into the expansion of space you have left that realm.

 

Cunfusion isn't unusual. Cosmology and general relativity aren't easy concepts, even compared to special relativity. I have limited experience in these areas, so I can't of much more help.

[Martin]

..., then how do they know things like the universe being 156 billion light years across

 

I think that result was that it is at least that big

but it might be much larger, perhaps infinite

 

I dont see a contradiction. if you see one please explain.

I think the idea that the u is very large (radius at least 50 billion ly)

is compatible with the idea of constant speed of light and its age

being 13.7 billion years. dont know anything about non-constant speed of light theories---too marginal.

 

Also, if at the universe's creation all the matter in the universe was confined to a very small volume,...

 

I dont think it has been established that the U began with a very small volume. At moment of big bang it may have had infinite spatial extent

(just a very high density)

 

... I'm getting confused. :S

 

we should have some links to standard cosmology sources and FAQ

 

Ned Wright teaches undergrad and grad course in cosmology at UCLA

and he has a pretty nice website with a tutorial and introductory level FAQ

 

just google "Ned Wright"

 

Charlie Lineweaver a worldclass cosmologist in, I think, new zealand

also has a basic article with good diagrams called "inflation and the cosmic microwave background"

it is PDF downloadable at arXiv and also HTML online at California Inst. of Technology

 

for that,just google "Lineweaver"

 

another cosmologist with worldwide rep who has stuff on the web is

Michael Turner----I dont know if google will find you his articles because i havent tried. He has a good onecalled "Understanding the new cosmology"

 

the main thing is that the popular science writers spread confusion because they simplify the message down to where it no longer makes sense and the images they use can be misleading, so it seems to me you

have to go to people who use at least a few equations and who arent trying to sell a lot of books to the public

 

if google doesnt get you what you want ask some more here and i or somebody else will get links to some cosmology FAQ

[J'Dona]

I dont see a contradiction. if you see one please explain.

I think the idea that the u is very large (radius at least 50 billion ly)

is compatible with the idea of constant speed of light and its age

being 13.7 billion years.

Well, if the speed of light has always been c (2.997 x 10⁸ ms^-1 that is), then even if the expansion of the universe proceeded at the speed of light in all directions (and I would assume the rate of propogation of spacetime), then it should still only be 27.4 billion ly across, not 156 billion. For it to be expanding at that rate and reach that size in this time, the rate of expansion would have had to have been on average about 5.7c (I know the rate of expansion slowed down and is now speeding up again, but that means that at one point it was slower and at one point it was faster than 5.7c so the problem is still there). That's why I was confused... because I'm assuming that the current theories of the big bang state that the universe was created from a single point or very, very small volume. We've all heard the stories about how it all came from something the size of an atom, and whereas this may be just the sort of misleading popular scienctific examples you're talking about, I hope they weren't exaggerating the situation that much (i.e. to the point where it wasn't a singularity). On another point, I thought that maybe during the big bang energy had not converted into matter yet, and that quarks and such did not come until some time after (maybe a fraction of a second, maybe a few hundred thousand years, but not at the start). I'm not sure on this, I'll have to read up on it. Hopefully one of your links will help there.

 

I dont think it has been established that the U began with a very small volume. At moment of big bang it may have had infinite spatial extent

(just a very high density)

If it had infinite spatial extent and any density at all, it would have infinite mass and energy. If the big bang didn't begin from a very small volume though, why was it called the "big bang"? (though of course that was only a name invented by Fred Hoyle, trying to make it sound daft)

 

Sorry, I really shouldn't be asking these questions, and should instead be reading the sources you've provided. But the first point I made at least I'm still not sure about, and unless there were some bizarre time dilation effects for the better part of the universe's life, I don't see how anything explains it. :/

[Martin]

 

Sorry' date=' I really shouldn't be asking these questions, and should instead be reading the sources you've provided. But the first point I made at least I'm still not sure about, and unless there were some bizarre time dilation effects for the better part of the universe's life, I don't see how anything explains it. :/[/quote']

 

Not at all! By asking you give a pleasant occasion for anyone like myself who wishes to answer. the reason to go to links is their credibility.

World class mainstream professional cosmologists say we cannot rule out the possibility that U was infinite at time of Bang, and is infinite in spatial extent now. Maybe you can believe them whereas you might not believe me.

 

No professional cosmologist that I know of believes that the speed limit of special relativity applies to the expansion of the U.

 

People often get confused because they have been told that nothing

can go faster than c relative to something else. Yet, in apparent contradiction, it is obvious from everything cosmologists are telling us that they are observing galaxies which they believe are currently receding at 2c, 3c 4c etc.

Eventually many people catch on, see the contradiction, and are then confused.

 

Special rel is a local theory governing local encounters and does not apply to recession speeds of distant objects. I have to go but will be back later.

[Martin]

If the big bang didn't begin from a very small volume though' date=' why was it called the "big bang"? (though of course that was only a name invented by Fred Hoyle, trying to make it sound daft)

[/quote']

 

It is confusing that they called it "big bang" but at least it sounds nice and has alliteration and words of one syllable are often preferable

 

 

Have you tried Siobhan Morgan's online calculator?

there is a standard way that cosmologists have of calcuating the distance (and recession speed) of an object from its redshift given the standard values of the main parameters:

 

H-sub-naught = 71 for the hubble parameter

Lambda = 0.73 for the estimated "dark energy" as a fraction of total energy density

Omega-sub-M = 0.27 for density of matter (both ordinary and dark) as a fraction of total.

 

the popular astronomy magazine "Sky and Telescope" published a short computer program to do the calculation and Siobahn, an astronomy prof at Iowa State or some such place, kindly put it up as an online calculator at her website. so her students and others can use it.

 

the Cosmic Microwave Background has redshift z = 1100

that is the whole point----it used to be hot light, as from a glowing ionized gas but it has been stretched out and lengthened and "cooled" down to 2.725 kelvin----long infrared or microwaves

 

galaxies have been observed with redshifts as big as z = 10

A team led by the beautiful French astronomer Roser Pello currently holds the record.

 

there are many galaxies that have been observed with redshifts z = 2, 3, 4, etc.

 

If you put these redshifts into Siobahn's calculator you will see at once how far the object was when it emitted the light, and how far it is now

 

and the calculator will also tell you what its rate of recession was when it emitted the light we are receiving from it, and what its rate of recession is now.

 

I should get a link to Siobahn's online calculator. And also to a photo of Roser, looking very happy because her observation team has found the z = 10 object.

 

it is possible that even google could give these links if told the name of

Siobahn Morgan or of Roser Pello. I dont know about that.

[Martin]

here is a link to the Astronomy reference sticky-thread which is a catchall for astronomy links

http://www.scienceforums.net/forums/showthread.php?p=56565#post56565

 

Here are two good online cosmology calculators

 

Siobahn Morgan's

http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html

 

and Ned Wright's

http://www.astro.ucla.edu/~wright/CosmoCalc.html

 

homepages for Morgan

http://www.earth.uni.edu/smm.html

and Wright

http://www.astro.ucla.edu/~wright/intro.html

 

To use Siobahn's calculator put Lambda = 0.73

Omega = 0.27

H = 71 (or leave her default value of H = 70' date=' nearly the same)

those are the dark energy and the matter densities as fractions of rho crit,

and H is the present value of the Hubble parameter

 

then put in any redshift z,

like z =1 or 3 or 10 and it will tell you how far away the thing

was when it emitted the light we are now getting from it

and how far away it is now

and how fast it was receding then

and how fast it is receding now, at the present moment[/quote']

[Martin]

I said "Roser Pello" to google and it gave me this picture (brunette)

 

http://webast.ast.obs-mip.fr/people/roser/

 

in the old picture she was blonde, i liked it better

and it was taken right after they found the galaxy so she

was radiantly happy

 

I am disappointed that someone, perhaps roser, has changed the picture at the french astronomy (midi-pyrenees observ.) website

 

http://webast.ast.obs-mip.fr/people/roser/

[Martin]

J'Dona

in cosmology Hubble's law is more important than this locally applying speedlimit rule of special rel.

 

hubble's law says

 

v =H D

 

that is, the current recession speed (at this very instant) is equal to the distance D at this present instant, multiplied by the current value of hubble parameter H

 

and also at every past instant-----the recession speed then is equal to the distance then multiplied by the value of H then.

 

this law is taken seriously

 

and it means that for a big enough D you can have quite big v.

 

 

people who think that the hubble law is about the redshift and that the redshift is a doppler effect are mistaken

when you see the law in a textbook it does not have doppler in it or z in it

It simply and always says this:

 

v = HD

and the values of the three things in the law are their current values.

 

Ned Wright spends a fair amount of time being clear about this. to be rigorous about it you need to know the distance-measure that cosmologists use (FRW---friedmann robertson walker) and a few technical details like that..

 

but the upshot is if you accept the hubble law (about the most basic thing in cosmology) you can no longer believe that the special rel "speed limit c"

applies to expansion---recession-speeds are the rates that distances increase as space expands

 

nothing ever catches up to and passes a photon

space can stretch out without anything ever catching up to a photon

so really there is no contradiction