# Speed of light that hits our eyes

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1. May 21, 2014

### johnny_bohnny

It is a postulate of SR that the speed of light in an inertial frame is always c, no matter what inertial frame is in question. But clealry, as I've understood, the Earth is not an inertial system and our bodies cannot be considered to travel inertially. So my question is, what is the speed of light that hits our eyes in everyday life?

2. May 21, 2014

### xox

While the above seems to be a very simple question, it has a very complicated answer. A good place to read the answer starts here.
The short answer is that, while the Earth rotates, thus acting as a collection of non-inertial frames, the labs attached to it can be considered inertial for all practical purposes (i.e. there is no detectable effect on the speed of light). Actually, experimentalists make good use of the variable speed of the Earth in their measurements when testing light speed isotropy.

3. May 21, 2014

### dauto

SR states that the speed of light in VACUUM is always c. there is not caveat about being in a inertial frame (as long as the base line used to measure its speed is small enough). But there is a caveat about light being in vacuum and the light that meets your eyes is not in vacuum.

4. May 22, 2014

### johnny_bohnny

But in whatever case, if we consider ourselves non-inertial or approximate the Earth as an IRF, the speed of light that comes to us will be so large that it doesn't make a difference between our appearance of the world and reality?

5. May 22, 2014

### xox

Not exactly, the motion of the Earth generates an effect called "light aberration" (see the other thread on the subject). Aberration distorts the view captured by our telescopes. See here.

6. May 22, 2014

### ZapperZ

Staff Emeritus
If the speed of light is affected by the nature of our non-inertial reference frame, then there should be an anisotropy in that speed. This is because we know there is a sense of rotation of the earth, both on its own axis, and in its orbit around the sun. Thus, by changing the orientation of the apparatus that we do our experiment with, we should detect a difference in the speed of light.

This type of experiment has been done multiple times, starting with the infamous MM experiment, and until the present time. In fact, the Standard Model extension (SME) for possible Lorentz violation, and the Robertson-Mansouri-Sexl theory provide a way to measure for such a thing up to unbelievable accuracy. Want to guess what we have found so far?

See, for example, Ch. Eisele et al., Phys. Rev. Lett. v.103, p.090401 (2009):

Zz.

7. May 22, 2014

### A.T.

The speed of light is anisotropic in rotating frames, isn't it?

8. May 22, 2014

### xox

Actually, it is isotropic. The experiment cited (and many others) make use of rotating resonating cavities in order to generate ever tightening constraints on OWLS anisotropy.

"Laboratory Test of the Isotropy of Light Propagation at the 10−17 Level"
Phys. Rev. Lett. 103, 090401 – Published 25 August 2009
Ch. Eisele, A. Yu. Nevsky, and S. Schiller

Abstract

We report on the results of a strongly improved test of local Lorentz invariance, consisting of a search for an anisotropy of the resonance frequencies of electromagnetic cavities. The apparatus comprises two orthogonal standing-wave optical cavities interrogated by a laser, which were rotated approximately 175 000 times over the duration of 13 months. The measurements are interpreted as a search for an anisotropy of the speed of light, within the Robertson-Mansouri-Sexl (RMS) and the standard model extension (SME) photon sector test theories. We find no evidence for an isotropy violation at a 1σ uncertainty level of 0.6 parts in 1017 (RMS) and 2 parts in 1017 for seven of eight coefficients of the SME.

DOI: http://dx.doi.org/10.1103/PhysRevLett.103.090401

Last edited: May 22, 2014
9. May 22, 2014

### A.T.

What I mean is the Sagnac effect. Light beams traveling the same distance (in the rotating frame) need different amount of time, depending on the direction. Is that not a form of anisotropy?

10. May 22, 2014

### WannabeNewton

Yes it is a form of anisotropy but not of local light speed, which is what xox is referring to as well what the various experiments cited are testing. In short, local light speed is always isotropic including in the case of a rotating frame. What this means is, in more concrete terms using a rotating ring, at any point on the ring the light speed in the instantaneously comoving inertial frame is isotropic. This is true for all such points by axial symmetry. The Sagnac effect, as observed in the rotating frame, is a manifestly global phenomenon that says nothing about local light speed but rather about the non-time orthogonality in the rotating frame and as such is more a statement of geometry. In support of this, note that the Sagnac effect is not special to light as it also applies to e.g. matter waves (coherent beams of electrons would do the trick).

11. May 22, 2014

### xox

12. May 24, 2014

### johnny_bohnny

Ok, thanks for the reference. So what is the speed of light measured in those experiments? Is it exactly c?

13. May 24, 2014

### xox

Within the ever tightening error bars it is "c".

14. May 24, 2014

### pervect

Staff Emeritus
If you use local clocks (Einstein synchronized for a one-way measurement, for a two-way measurement the synchronization is irrelevant) and local rulers to measure the speed of light, you'll always get "c". The "local rulers" you can consider to be copies of the platinum bar standards that people used to use to measure distance. You make a copy, compare it to the original to make sure it's callibrated properly, and carry it with you.

A local clock would be a portable atomic clock that you calibrated beforehand, and carried with you to whatever place you are going to perform the measurement.

If you have some OTHER scheme that you want to measure the speed of light with, describe it in detail and if it's not too complicated we can probably tell you what you would measure the speed of light to be using that scheme.

The reason I specified using the platinum meter bars for measuring distance is that if you use the modern NIST definition of distance, the speed of light wouldn't need to be measured, it is a tautology that you'd get "c".