# Speed of light in the universe, experimental data

1. May 17, 2007

### lalbatros

I would like to compile direct and indirect data on the speed of light in the universe.
How much evidence do we have that it is constant, even close to a black hole?
What kind of observations could be relevant to answer such a question?

Michel

2. May 17, 2007

### Chris Hillman

The mercurial signficance of "c"

Hi, Michel,

Hang on a second: do you mean the speed of light measured over an infinitesimal course by some inertial observer? That is, you can think of a nonspinning inertial frame field as defining "local Lorentz frames" at eah event in some curved spacetime, and at the level of tangent spaces, the light cones and so on always look just like Minkowski spacetime. On larger scales, of course, they look nothing alike, as the black hole example dramatically illustrates. A much easier but still very instructive example is to look at "light cones in the large" for the Kasner vacuum I mentioned in another recent post. See Hawking & Ellis, Large Scale Structure of Space-Time if you get stuck.

I remind everyone once again that even in Minkowski vacuum there exist multiple operationally significant notions of "distance in the large". If follows that there exist multiple operationally significant notions of "speed in the large". See Peebles, Physical Cosmology for a discussion of the implications for observational cosmology.

(In case this isn't yet clear, I am saying you need to refine your question.)

3. May 17, 2007

### lalbatros

Hi, Chris,

Yes, indeed, I was asking about the speed of light in (local) inertial frames.

As long as the physics observed can be considered as sufficiently local, I assume that the speed of light is our familiar "c". But I was asking a little bit more background on that.

It is clear that we can observe atomic spectra from very far in the heaven, and conclude that far away physics must be the same. But I already do not see how we could conclude that the speed of light is the same. I would like to learn that.

And of course, my question is aiming particularly at extreme conditions, near black holes.

What are our tools and our evidences to make sense from this assumption that "c" is constant everywhere?

Thanks,

Michel

Last edited: May 17, 2007
4. May 17, 2007

### smallphi

GR postulates that the speed of light c=1 in any local inertial frame. That can be checked either directly by going there and measuring the local speed of light or indirectly by comparing our observations with GR theoretical predictions.

For example if c is not 1, then light won't follow null geodesics and the deflection of light around the sun won't match the value predicted by GR. Even Newtonian intuition suggests the deflection angle is sensitive to the speed of the photons.

Last edited: May 17, 2007
5. May 17, 2007

### Chris Hillman

Dunno if I can help....

Indeed, it's hard to avoid doing this unless you are theoretically creative, because this feature is built into the notion of a Lorentzian manifold, i.e. independent of gtr, and this notion is so mathematically and conceptually convenient that many people never question its validity.

I don't understand--- you believe atomic spectra work the same way near a stellar mass black hole and on Earth, but you don't believe c is the same near the hole and on Earth? Any particular reason?

I'm not sure that testing the hypothesis that c is the same THERE as HERE is very different from testing the hypothesis that the Rydberg constant is the same THERE as HERE. I think you need to be able to argue that if Rydberg constant varied from place to place such and such phenomenon would be observed, or that if c varied from place to place, such and such phenomenon would be observed.

6. May 17, 2007

### pervect

Staff Emeritus
The short answer is in http://arxiv.org/abs/hep-th/0208093

varying physical constants doesn't actually have any operational meaning, it's just a unit conversion.

However, there's another paper by a variable speed of light enthusiast whose name escapes me, but the point is that it might make sense to use a variable speed of light theory if it makes the physics appear simpler. Some unit choices are much more convenient than others for particular theories.

The point is that you aren't actually changing anything fundamental when you change "the speed of light" - you are just chosing a particular set of units. However, the choice of units can make the theory a lot easier to express, even though it may not have any truly fundamental significance.

7. May 17, 2007

### smallphi

The current SI definition of length is through distance traveled by light for certain time. Using that definition, the speed of light would be always the same constant everywhere by definition.

The old definition of length used a rigid etalon/ruler. Hypothetically, one can take an atomic clock and the rigid ruler and go MEASURE the speed of light in terms of 'RIGID METERS' around black hole for example. The light speed measured in 'rigid meters' per second DOESN'T HAVE to be the same everywhere. We BELIEVE it's the same and that GR is correct, that's why we redefined the meter in SI.

Saying that the light speed is 'just a conversion factor' just defines away the physical problem, doesn't prove it. It's like saying 'the speed of an electron moving around is always the same because we can define the unit of length as the distance traveled by an electron for given time'. The example is idiotic but follows the same logic.

The real physical question is 'Does light always/everywhere travels the same rigid ruler distance for given time ?'.

Last edited: May 18, 2007
8. May 18, 2007

### lalbatros

Chris,

I do believe the c is the same everywhere.
It is rather that I don't fully understand my belief.
Specifically, it is nice that atoms far from earth show the same spectra. We can be confident that the universe far from the earth relies on the same laws. However, this is no direct evidence that c is (exactly) the same so far from earth. If this is at least an indirect evidence, I would like to understand a bit more about it.

Last edited: May 18, 2007
9. May 18, 2007

### rbj

well, as long as we're defining the meter to be the distance in vacuo covered by light in 1/299792458 second, then no matter what, the speed of light is 299792458 m/s. i'm just a lowly electrical engineer that's not even an armchair physicist, but i'm of the same mind as Michael Duff or John Barrow (https://www.amazon.com/Constants-Nature-Omega-Numbers-Universe/dp/0375422218):

Michael Duff: "Comment on time-variation of fundamental constants", hep-th/0208093 (2004)

Duff, Okun, and Veneziano: "Trialogue on the number of fundamental constants", JHEP 203 23 (2002), physics/0110060

it really isn't meaningful to ponder time-variation of dimensionful constants. while a variation in $\alpha$ or some ratio of like-dimensioned quantites (both dimensionless) has meaning, such is not the case for dimensionful constants which are products of the anthropometric units that we Earthlings cooked up in a historical accident.

it's only the dimensionless physical constants that matter.

here's another one: http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/constants.html

Last edited by a moderator: Apr 22, 2017
10. May 18, 2007

### rbj

how does the rigid ruler stay "rigid" when c varies and all dimensionless quantities stay constant?

the more real physical question or two is: why is there about 1035 Planck lengths in a meter and why is there about 1044 Planck times in a second? those are asking questions about dimensionless quantities that, if they change, we would know the difference. when those questions get answered, then we can infer an answer as to why there light travels about 109 meters in the time of a second.

11. May 18, 2007

### smallphi

Any 'derivation' that rigid ruler will change to keep the speed of light everywhere the same uses the laws of physics as we know them here and now on Earth. The behavior of rulers with respect to light doesn't have to be the same everywhere simply because the laws of physics don't have to be the same everywhere. By assuming they do, you simply assume the result, instead of checking it experimentally. One can't 'prove' there isn't an modification of the physical laws as we know them by ASUUMING there isn't modification and those laws always apply.

It's like 'proving' Newtonian mechanics is always right by only using Newtonian mechanics formulas.

The speed of electron (or anything else) is as 'dimensionless' as the speed of light, yet nobody claims it's a constant. Just because a quantity is dimensionless in some units doesn't make it a constant.

Last edited: May 18, 2007
12. May 18, 2007

### rbj

what i'm saying is, essentially when physicists (as well as the rest of us) measure any physical quantity, they measure it against some other like-dimensioned quantity. in that, they are measuring a dimensionless number similar to when we commonly measure a length by use of a ruler and counting tick marks on it. so if $c \$ somehow changes but all dimensionless constants remain the same, and all we can ultimately measure are dimensionless values, then we can't tell if $c \$ changed and that "change" is meaningless in our existence. a better way to put it is that if $$\alpha = \frac{e^2}{\hbar c 4 \pi \epsilon_0} \$$ changes (which is something we can measure), we do not know if that change in $\alpha \$ was due to a change in $c \$ or if it was due to something else. what it is that changed depends on how we define our units, and as Duff puts it: "[Nature] doesn't give a fig which units are chosen."

this is sorta a tautology but i do not consider it to be particularly bad to make this point by use of tautology. in my opinion, the weak anthropic principle is a tautology. saying it tells us nothing new, really, but it does help me think about a persistant question often posed by the intelligent design folks.

i dunno if the ideas of length, time, mass, etc. are merely man-made, but clearly the definitions of the meter, second, and kilogram are. before the meter was redefined to its present form, we had a definition of meter and second that did not depend on the speed of light. we made many different measurements of it and got different answers, mostly due to experimental error. in the sixties, when people became more and more confident about their measurement the meter was redefined because a good atomic clock was easier to reproduce than platinum bars with precise scratch marks on them. but now think about this, with this redefinition, the meter is the distance light travels in 1/299792458th second. that defines the speed of light to be 299792458 m/s . if $c \$ changes, it is still 299792458 m/s. you can think of it similarly if you measured everything in Planck units no matter what $c \$ is, it is still 1 in Planck units (and same for $G \$ and $\hbar \$).

now, the fact is that a meter is about the size of us humans (small wonder). i don't know why an atom's size is approximately $10^{25} l_P \$, but it is, or why biological cells are about $10^{5} \$ bigger than an atom, but they are, or why we are about $10^{5} \$ times bigger than the cells, but we are and if any of those dimensionless ratios changed, life would be different. but if none of those ratios changed, nor any other ratio of like dimensioned physical quantity, we would still be about as big as $10^{35} l_P \$, our clocks would tick about once every $10^{44} t_P \$, and, by definition, we would always perceive the speed of light to be $c = \frac{1 l_P}{1 t_P} \$ which is the same as how we do now, no matter how some black hole or "god-like" manipulator changes it.

now if some dimensionless value like $\alpha \$ changed, that's different. we would perceive the difference. but to attribute that change to a change in $c \$, that case is not defensible. you could argue that the change in $\alpha \$ is due to a change in the speed of light, and i could argue it's a change in Planck's constant or the elementary charge and there is no way to support one over the other. and it shouldn't matter. my paraphrase is "Nature doesn't give a rat's ass that you choose a system of units that define some set of constants nor that i choose a different set of units that defines a different set of constants."

Last edited: May 18, 2007
13. May 18, 2007

### smallphi

I agree with that point. The physical question again is having an atomic clock and rigid ruler, will light always traverse that ruler for the same time. Change in the time of travel shows a RELATIVE change between the laws governing light and the laws governing the ruler. Some will say the ruler changed, others will say the speed of light changed but ALL will agree that there WAS A CHANGE.

14. May 18, 2007

### rbj

cool.
but we do not agree about this. the physical question to ask is why are there (5.39121×10−44 × 9192631770)-1 Planck Times in one oscillation of the "radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom"? that's the dimensionless question and we can tell if that quantity changes (at least it's a meaningful change). the other physical question to ask is if there will always be (1.61624×10−35 )-1 Planck lengths in this rigid meter stick you refer to. assuming it's a "good" meter stick and that it doesn't lose or gain atoms, then the question is how many Planck lengths go into the size of a Platinum atom (which should be some dimensionless constant times the Bohr radius). that's a dimensionless question and if the number of Planck lengths per Bohr radius changes, a meaningful dimensionless parameter has changed and you might perceive it as a change in the number of meter sticks light travels in a second. but the dimensionless questions are the fundamental ones. how many meters light travels per second is an issue that comes about as a result of the other two (how many Planck lengths per "rigid meter stick" and how many Planck times per second). the latter two are the real questions.

a change in what?? $$\alpha$$? what is it, fundamentally, that you would expect to measure that you postulate indicates a change in c? it's a ratio of like-dimensioned quantities, which is dimensionless. and when that dimensionless quantity changes, all you can really say is that this particular dimensionless quantity has changed. you cannot ascribe that change to any particular dimensionful factor that composes that dimesionless quantity. if $$\alpha$$ changes, all's you can really say is that $$\alpha$$ changed. you cannot say "$$\alpha$$ changed, so that means c changed". you do not have that information.

15. May 18, 2007

### smallphi

Let's imagine I have an electron and I measure its speed to vary with time. I can interpred that as 'the electron speed is not constant' or 'my rulers are not constant'. The correct thing to say is 'the electron speed with respect to the rulers' depends on time. Change is always relative, how you interpret is up to you. Some interpretations simplify your life, some complicate it. Sure you can define 'electron-length' in terms of the distance traveled by the electron for given time. Then the electron speed will be always a constant but you will notice that the electron-lengths of the objects around you depend on time yet the their ratios always remain the same. At the end you will decide it is more convenient to define length in terms of rigid rulers, thus producing many constant lengths around you, and interpret the electron speed as varying.

The point of this thread is wether light speed varies WITH RESPECT to rigid rulers and atomic clocks, NOT how you interpret that. This is an EXPERIMENTAL question not something you can define away. If it turns out there is such a variation, then defining distance in terms of light-distance makes as much sense as using the electron-distance above.

Sure we model spacetime with a manifold which has null geodesics. We associate those geodesics with light not with electrons because that is consistent with our local experiments. If we try to construct a GR theory in which electrons move on null geodesics we will have to redefine the electron-lengths of the objects around us every time we shoot an electron to measure length. We know from EXPERIMENT that rigid rulers do not change their light-lengths with time and that makes light a good candidate for definin distance of travel. That is a LOCAL result thogh, based on our LOCAL EXPERIMENTS. Doesn't have to be the same everywhere/at every time.

Last edited: May 18, 2007
16. May 18, 2007

### Chris Hillman

I am at a loss for words

Michel, please reread what I wrote, then reread what you wrote. Do you see why I find what you wrote so strange? If not, I'll have to give up trying to explain.

17. May 18, 2007

### rbj

what is the "ruler" made from? would metal atoms be accurate? let's say it's a "good" ruler (by that i mean it doesn't get longer or shorter because of adding or losing atoms). how do we know that the size of the atoms are independent of the of the electron speed?

but i don't think physical reality gives a rat's ass whether my life is complicated or not. what physical reality cares about are physical quantities and the relationship between such.

it's like you're using a ruler made up of iron atoms to measure the size of iron atoms. if your ruler is a "good" ruler and doesn't gain or lose atoms in between its tick marks, i am not sure how the size of iron atoms can change, as per any measurement you make with this ruler.

there can't be, unless some more fundamental dimensionless parameter (thought to be constant) changed. and then, the salient parameter is this fundamental dimesionless parameter, not any of these dimensionful parameters that depend on the unit system we happen to use by historic accident.

what precisely do you mean by that? what "EXPERIMENT" are you typing about? what's a "light-length"?

the point i am trying to nudge this thread toward is that the notion of variable speed of light is more meaningless than something that is contrary to experiment. we can talk about variable Fine-structure constant or variable proton/electron mass ratio, and argue over whether or not the experimental data is congruent to such. that is not meaningless, even if it may be the case that such variation lacks solid evidence. but VSL or variable G or variable h, in-and-of-itself is meaningless. and it's not just me saying it.

18. May 18, 2007

### rbj

pervect, i dunno how it slipped by me that i am just repeating stuff above.

one caveat: i would say that "varying [dimensionful] physical constants doesn't actually have any operational meaning, it's just a unit conversion." if a dimensionless physical constant like $\alpha$ or $m_p/m_e$ changed, there is no system of units where such change would be washed away. that does have operational meaning.

19. May 18, 2007

### smallphi

The local experiment establishing constancy of light expressed in 'rigid rulers/second' is Mikelson-Morley. Another theoretical construction based on previous experiments using rigid rulers is classical electrodynamics in which speed of EM wave is always the same.

If anyone claims that the constancy of speed of light is 'just unit conversion', independent from the above experiments, then I would like to hear explanation why choose light exactly? Why not take an electron and say it's speed is constant and just a conversion between time and length units?

Once one accepts that the fundament of 'constant speed of light' are the above experiments, one has to accept the fact those experiments are not confirmed globally only locally.

Last edited: May 18, 2007
20. May 18, 2007

### rbj

MM was an experiment to detect a medium of sorts for light or E&M to propagate in. turned out that the experiment had a negative result.

dunno about "rigid rulers" (i don't really see that term in the lit) but there is a pretty substantial theoretical reason for why the laws of physics (which include the permittivity and permeability of free space) is the same for every inertial observer. how i tried to explain that before.

it's not just light, or E&M. it's any ostensibly instantaneous action. like gravitation.

Last edited: May 18, 2007