# Fixed speed of light

1. Aug 6, 2008

### PhanthomJay

Following up on a recent prior post under a different subject, I would like to know why the speed of light is what it is. I'm not talking about its constancy or its value based on whatever units of measure are chosen, but rather, I am asking what are the factors in the universe that limit its speed to any value? To rephrase, we know that the speed of objects with mass is limited to lightspeed, but what limits the speed of light itself?

2. Aug 6, 2008

### Varnick

There are really two questions there. The first, "Why is the speed of light 300 km/s (approx)" is, to my knowledge not really known as such. We can say that it must be something, and it happens to be the value it is (someone may well disagree with me on that). The reason that things are limited to below that speed is because of the Lorentz Factor, an element of Special Relativity. It looks like
$$\frac{1}{\sqrt{1-(\frac{v}{c})^2}}$$

Essentially, this shows that for any body with mass (photons have 0 mass, of course) that it takes an infinite amount of force to reach c, and as an infinite amount of force is not readily available, we cannot reach or surpass c.

V

3. Aug 6, 2008

### Integral

Staff Emeritus
The speed of light, that is the speed at which electromagnetic energy propagates through space is given by:

$$c = \frac 1 { \sqrt { \epsilon_0 \mu_0}}$$

where $\epsilon_0$ is the permittivity of free space and $\mu_0$ permeability of free space. This factor was derived by Clerc Maxwell in 1867 and initiated the "Schism" in Physics which lasted until 1905 when A.Einstein published his work on Special Relativity.

4. Aug 6, 2008

### Varnick

Ah yes, I'd forgotten the wave equation, thank you for the correction Integral.

V

5. Aug 6, 2008

### PhanthomJay

Yeah, thanks, Integral, I think I may I have seen that equation before, and had also forgotten it. But it does beg another question or two (or more): Why are those permittivity/permeablity values what they are? What is it about 'free space' that leads to these values? Could we perhaps locally decrease those values (how?) and thereby exceed the speed of light? I'm assuming the answer must be "no", but why not? Just fishing for answers. What is the meaning of these values anyway? How can a vacuum have a permeability/permittivity coefficient assigned to it? Thanks.

6. Aug 6, 2008

### 81+

Hi Integral,

Your comments brings up a question I've had for some time. The intergalactic areas in the observable universe is made up of space itself (the complete absence of everything, a pure vacuum, the area that's left when everything else is removed) plus photons, neutrinos, dust, gas, radiation, etc. Empty space remains empty space but the amount of photons, bosons, neutrinos, dust, gas, etc. will vary from place to place. So the physical properties of space (actually all the stuff in space) must vary from place-to-place. Wouldn't this variation in stuff in space change the permitivity and permeability of space such that it would change the speed of light (actually reduce it from its maximum) so light speed could be different from one place to another in space?

Frank

7. Aug 7, 2008

### kmarinas86

It could potentially serve as a test for the Big Bang. For example, if the permeability and permittivity of light was significantly smaller in very large voids, it could drastically alter our views about the age of the universe. The problem is, it would probably be hard to measure. Perhaps the effects of any increase in the electric permittivity and magnetic permeability in the local vacuum may be interpreted as time dilation rather than as properties of the vacuum, such that these properties of the vacuum seem constant. For example, a decrease in these properties in a distant vacuum, when observed from far away, might cause an atomic clock to appear to work at an abnormally fast pace. It would also have the effect of refracting light, just as these parameters (electric permittivity and magnetic permeability) between pieces of glass and other transparent substances cause them to bend at the boundary where they change. A significant decrease in the values as you get further from solar system or galaxy may have serious implications for observations which rely on the distance ladder methods for calculating distances from light years to billions of light years.

8. Aug 10, 2008

### rbj

what you're asking about really is about units. (and Nature doesn't give a rat's patootie about units we humans, or the aliens on the planet Zog, happen to choose for use.) the only necessary physics is that c, $\mu_0$, and $\epsilon_0$ be real, positive, and finite. pick any two and you can assign them any real, positive, and finite values.

9. Aug 11, 2008

### Eimacman

Greetings, Integral.

I am new here but something has been pestering me for some time and that is the relivestic effect, if any, on the speed of light due to universal expansion. Would such have an effect, no matter how small, on permittivity and or permeability of free space, being such space is expanding? I have tried to plug in the relivistic formulas taking into account universal expansion but I do not know if I got the math right for they are showing a tiny change in light speed. I don’t currently know how to input formulae into this forum yet or I would send you the equations that I have come up with. If I am right, and that is yet to be proved, the speed of light is not fixed, but may have a slight variation due to the expansion of space time.

Eimacman

Last edited: Aug 11, 2008
10. Aug 11, 2008

### junglist

aside from the hangups with regard to 'units' i think the point and questions that phantomjay is posing are more about what causes something to behave as it does rather than whether it has a value of, say, 3.

I think this line of questioning is still very interesting and very valid.

11. Aug 12, 2008

### PhanthomJay

If the question is not clear and we're getting hung up on units of measure, let me ask a different one: I don't much care whether the speed of light is 3 times 10 to the something meters per second, or x million horselengths per solar day; the fact is, it does have some finite speed, no matter how arbitrary may be the units used in measuring that speed, and I want to know what limits that speed in a vacuum. Why is it not infinite? Darn photon has no mass anyway. I don't know why it takes one second to reach the moon. Why not something less?? Why not instantaneous?

12. Aug 12, 2008

### rbj

you're correct that asking "why is the speed of E&M (and the other seemingly 'instantaneous' interactions; gravity and nuclear) finite rather than infinite?" that question means something. to ask "why is this speed equal to this one finite value rather than some other finite value" is actually not meaningful. if our meter continues to be 6.187154x1034 Planck Lengths and our second continues to be 1.85486x1043 Planck Times (both of these dimensionless measures remain the same) we would have no idea that there was any change in c. if some dimensionless measure does change, yes, then we'll know the difference. but the salient fact would be that this dimensionless "constant" is measured to have changed. if, conceptually, the fine-structure constant has been determined to have been different 4 million years ago than it is now (what Oklo might be telling us), that means something, but it doesn't necessarily mean that c has changed. it might mean that the elementary charge has changed and if one chooses to measure (and express) physical reality in terms of Planck Units, then a change in $\alpha$ does mean that it is a change in the elementary charge.

about why it takes light about a second to reach the moon is asking about the sorta historical accident for why our moon is as far away as it is.

13. Aug 12, 2008

### PhanthomJay

Okay, now we're into the quanta. The Planck second, which last I checked was 10 to the minus 43 seconds. I suppose someone's going to say that's an arbitrary number based on the time it takes light to travel the Planck Length, which is some other ridiculously small number based on the distance covered by light in a planck second. This is like going in a circle. But again, I don't care what it is, all I know is that it is a finite value. Why? What's going on in half a Planck second????

14. Aug 12, 2008

### rbj

well, i've never heard of a "Planck second" before, but if you mean the Planck time, then i know what you mean. my issue is not so much about quanta although i've been told by people that know more than me that nothing happens in less than a Planck time. my issue is more about a set of expressions about physical reality (even if they are approximations of physical reality because of newer physics that provide for better descriptions that degenerate to the expressions i understand better) that have no anthropocentric or anthropometric components to the expression (namely these dimensionful constants like c, G, $\epsilon_0$, and $\hbar$). if those constants go to 1, they go away. doesn't matter if you're earthling or Zogling, whether you measure things in SI, miles and gallons, or whatever. these equations are the same. in fact, because i want to see arbitrary constants removed, i think that slight adjustments to the Planck units so that it is $4 \pi G$ and $\epsilon_0$ that are normalized to 1, rather than $G$ and $4 \pi \epsilon_0$ as is done in Planck units, i think that would make more sense.

but it doesn't really matter which set of natural units to use. when you measure stuff in terms of natural units, you are essentially measuring dimensionless quantities. (but ultimately, even with SI, we are eventually measuring stuff in dimensionless quantities anyway, it's just that when someone says what would happen if the speed of light decreased from 299792458 m/s to 299791458 m/s, they need to be precisely specific about what they mean, what would actually be changed. ultimately, when scrutinized, what would actually be changed is some dimensionless ratio of like-dimensioned quantities. c is actually measured against some other speed, like $e^2/(\epsilon_0 \hbar)$. if/when such a ratio changes, that is what changed and you cannot simply blame the change on any particular component of the ratio that one selects arbitrarily.)

that is the only reason i brought Planck units into the discussion.

15. Aug 12, 2008

### Eimacman

PhanthomJay

I am afraid that I jumped in to this thread without reading everything herein and I apologize.

How ever the only thing that I can think of is that in our universe there is no true vacuum, in that there are gravitational fields, virtual partials forming and annihilating, electromagnetic fields, nearly massless partials like neutrinos, the occasional proton or electron, dark matter and or dark energy, and the fabric of space time itself. So it is quite possible that if a photon was to travel threw a true vacuum with absolutely nothing in it including space time it might travel just travel instantaneously that is if the photon could even exist.

Therefore it could be, for this reason the observed speed of light appears fixed.

Eimacman

Last edited: Aug 12, 2008
16. Aug 12, 2008

### PhanthomJay

Ok, lets focus on the finite speed of light, if we all agree that the speed of light is , in fact, finite. What is it about the universe that limits the speed of E&M in a vacuum to a finite value? I thought it might be due to the permitivity/permeability of free space, but these seem to be derived numbers (?) chosen to make c come out to its experimentally observed 'finite' value?

17. Aug 12, 2008

### PhanthomJay

Thanks, I like your reasoning. Perhaps the journals should be changed to read that the speed of light is constant in free space, rather than in vaccuo (if I spelled that right the way Einstein did).

18. Aug 13, 2008

### rbj

the order of derivation of these numbers (in SI) is this:

first they essentially defined $\mu_0 = 4 \pi \times 10^{-7}$ as a consequence of how they defined the Ampere (as the current necessary in two infinite and parallel conductors to make them exert a force of 2x10-7 N/m on each other).

and, before 1960, they defined the meter as the distance between two scratch marks on a bar of platinum-iridium in Paris. and the second was also independently defined from the speed of light. in that case, with the given meter and given second, physicists set out to measure c.

then in 1960 they redefined the meter in terms of wavelengths of some light and later still (1983, i think) the redefined the meter to be such a distance that light in a vacuum travels 299792458 of them new meters in the time elapsed by one second.

again, why c is finite and not infinite, is a deep quesion about the fundamental nature of space and time and the four fundamental interactions we know about. if there is a third party that is equal distance from you and i, if he sees me do anything that interacts with you, he will see your response to what i do at a later time (the delay being proportional to the distance between you and i). things take time if they happen one place and cause reactions somewhere else. why, i dunno, but that's the way it is. i don't think a lot of physics would work (such as a matter-energy duality) if c was either infinite or zero.

19. Aug 13, 2008

### PhanthomJay

rbj....thanks for the detailed response.

20. Aug 14, 2008

### Eimacman

Rbj

I offer these small corrections, (I am afraid I haven’t learned to use the quote function yet).

First I would not use the word infinite, in the case of two parallel conductors, it brings up the possibility of paradox. Two long conductors is best.

The speed of light was determined mathematically in the mid 1800's by James Clerk Maxwell, and was later measured with some accuracy in the 1880's by Albert A. Michelson and Edward Morley not in the 1960's. You might be thinking of the experiment of Joseph Hafele and Richard Keating and their test of time dilation in the 1960's.

The length of the standard meter was also determined by Michelson also in the late 1800's as the number of waves of a certain red line in the cadmium spectrum, which was later changed, some time later, to a more narrower sodium yellow line, it turned out to be two narrow lines but they were very close together, then in 1960 it was changed again to be exactly 1,650,763.73 wavelengths of a certain orange line in the spectra of krypton 86. And I don’t think that they have had to change it since.

As I have stated earlier the speed of light appears fixed because of space time and every thing in it, as to the why, well that is a head scratcher. Could be the answer would reveal some of the great mysteries of the universe.

Eimacman

21. Aug 14, 2008

### rbj

you press the quote button.

arbitrarily long conductors. that, at least basically, is what "infinite" means. there are no infinite quantities of anything real that i know of. but the hypothetical problem that gets you to $\mu_0 = 4 \pi \times 10^{-7}$ henries per meter has infinite parallel conductors in it and $\pm \infty$ is what you see in the limits of the integral.

there are too many little things here to comment on individually. i accept the history of the SI unit definitions (and the present definitions) as put forth by NIST. maybe you should check it out. i also think that wikipedia is likely pretty accurate about this stuff also. (there is plenty in wikipedia that is crappy, but on stuff like this, they get it pretty close.)

22. Aug 15, 2008

### Eimacman

Rbj

Eimacman

Oh and I still cannot get the quote function to work for me, but that is but a minor annoyance.

23. Aug 15, 2008

### dilletante

I always thought that the speed of light is what it is because time slows to zero at that speed, and nature is designed to preserve causality.

24. Aug 18, 2008

### TalonD

but isn't it true that time slows only 'internally' for the thing that is moving? For example in a rocket. the astronaut and his clock both slow down, presumably also the brownian motion of the atoms of the rocket. So an external observer would not only see the astronauts clock slow down and measure a length contraction but would also see the rocket as colder than objects in his own reference frame? So the photon would be subject to time dilation in that it would not 'age' (whatever that means for a photon) but an outside observer would still see it moving in his normal time frame at some finite speed. Considering there is nothing special about EM but it is the speed limit that is pecial then the finite speed of light would need to be limited or controlled or influenced, not sure of the right word to use there, by some physical property of space time. Wouldn't it? And since speed is a function of distance and time, would that mean that there is a minimum possible distance and a minimum possible time as fundamental properties of space time? Maybe there is a falacy in my reasoning there, Please point it out to me.

25. Aug 18, 2008

### dilletante

Talon,
It sounds like you are referring to Planck Time. You will need to hear from a quantum physicist to get an opinion on that. Here is a quote from an unreliable source, Wikipedia:

"One Planck time should be the smallest measurable unit of time, according to quantum mechanics. But according to news reports, analyses of Hubble Space Telescope Deep Field images in 2003 brought up a possible discrepancy. Images should have been blurry at very far distances, but the news articles stated that they were not, challenging the theory that Planck time is indeed the smallest measurable unit of time in the universe."

I was just offering a layman's common sense guess at why there is an upper limit to the speed of light, based on the assumption that space and time are intertwined. The faster you go, the slower your clock goes, so the upper limit of speed is when it takes zero time to get there. That happens to be c, but if clocks stopped at 100 miles per hour in another hypothetical universe, maybe that would be the speed of light there.