# Why is light at a constant speed

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Why is light at a constant speed? Or better yet why does it travel at "c"? What is so special about that particular number?

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Someone here will - no doubt - have a clearer understanding of this or be able to answer your question in a more meaningful way, but until then, as I was passing, try this:

If we use a 'common sense' or 'day-to-day' view of speed, and imagine trying to attain an infinite speed (say, moving away from Earth) then you would expect this would take an infinite time, and an infinite amount of fuel, and you probably wouldn't see it as possible…

All we need to add is that because of the nature of spacetime - for something with mass - infinite speed is pulled all the way back down to 'c'. In Relativity, that makes 'c' special.

Obviously, the number itself is measured in whatever arbitrary measurement system we happen to be using...

But does that explain why light travels at 'c' in the absence of matter (I’m sure you’ll find several threads on this topic)... well, the idea that light travels at (effectively) infinite speed for our spacetime kind of makes sense. What do you think?

Also, if something moves with infinite speed, then our ‘common sense’ view would be that no time elapses between the beginning and end of a journey. In our spacetime this is still true, but only if you’re making the journey – that is, for light, or one of the other massless entities that carry forces around the universe.

Hope this is useful…

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Why is light at a constant speed? Or better yet why does it travel at "c"? What is so special about that particular number?

First I would like to say that's an excellent question.

There are different answers depending on how you interpret the question. In the pragmatic sense one can say that all standard theories of modern physics takes the speed of light to be constant. This is also one of Einsteins postulates(assumptions) on which he built his theory of relativity. And these theories are pretty consistent with experimental data we have so far. Thus we have not seen a reason yet to abandon the idea. It seems to be a consistent idea. If the speed of light is not constant, many working theories have to be reworked.

To look for a philosophical why, here is my personal suggestion of start and it is to ask more quesiton.

What is light and what is speed?

Speed should be a measure on position change with respect to time. And what is time? Supposedly time is simply relative change in a clock device. This means that speed is somehow something like "relative change relative another change". And what is "change"? Change is clearly related to the notion of information of knowledge and beeing able to distinguish one thing from another. I think it can be reduced to the relation of distinguishability.

So if we for a second ignore "what is light", the answer seems to be related to relative changes in information, somehow.

This is just talk but at this point but I think these things can be formalized into a more stringent formalism. It's a part of what I'm currently working on, to try to formalize what is intuitively clear, and IMO it is very exciting.

As for the particular number, it's cleary just a unit convention thing. Why is one inch 2.54 cm?

/Fredrik

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I am not much into all the standards but if I am not mistaken there is or used to be a definition of second that used the speed light in relation to radiation. Meaning, that the speed of light would be constant by definition. But I think other know these standards better.

/Fredrik

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Why is light at a constant speed? Or better yet why does it travel at "c"? What is so special about that particular number?

IMHO:

Light doesn't actually travel at a constant speed, not even in a vacuum. Check out the Shapiro effect:

http://www.geocities.com/newastronomy/animate.htm

However we always measure it to be doing 300,000km/s because light defines our seconds and our metres, and c is a conversion factor between the thing we call distance and the thing we call time.

Under the International System of Units, the second is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition refers to a caesium atom at rest at a temperature of 0K…

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second...

When c is reduced it affects the photons electrons and atoms of our bodies brains clocks and rulers. So we can never measure it directly. Trying to measure a reduced c would be like expecting to find less than sixteen ounces to the pound. Instead we experience the thing that we call gravity.

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IMHO:

Trying to measure a reduced c would be like expecting to find less than sixteen ounces to the pound. Instead we experience the thing that we call gravity.

I like that analogy. There will always be 16 oz. per lb, because that relies on another constant, gravity, which is actually a variable. So the only constant in our weight system is a constant relationship. I can go on to consider that light is likewise not actually a physical constant, but maintains only a constant relationship, but with what? I like this train of thought, because my bullshit alarm goes off when faced with an arbitrary cosmic speed limit

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The Shapiro delay, AFAIK, is not a consequence of c changing, but of the path being longer because of the curvature. The light follows the geodesic, and since it's not flat space, the path is longer, and thus takes longer.

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As fredrik implied, there are several physical theories that rely on c being a constant. All of E&M, for one — the wave solution to Maxwell's equations has the speed of light in it (as the product of the permeability and permittivity of free space, giving c^2). IOW, EM waves wouldn't be waves anymore — not be solutions to the wave equation — if c depended on the relative speed of the source and observer.

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Here's an animation of the Shapiro effect:

http://www.geocities.com/newastronomy/animate.htm

Here's a wikipedia-style article:

Obviously the above can't be taken as 100% reliable, but I imagine this Einstein quote is correct:

"In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)." - Albert Einstein (The General Theory of Relativity: Chapter 22 - A Few Inferences from the General Principle of Relativity)

The relative speeds of source and observer is something different, and as Special Relativity tells us, has no bearing on c.

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In chapter VII: "Every child at school knows, or believes he knows, that this propagation takes place in straight lines with a velocity c = 300,000 km./sec ... " (emphasis added)

Einstein was clearly discussing a vector quantity when he wrote of the velocity. An entity with constant speed need not have a constant velocity — its direction can change. Which is exactly what's happening in this case.

http://lheawww.gsfc.nasa.gov/users/craigm/bary/

"The "Shapiro" delay is the time delay analog of the well-known bending of light near the sun."

http://physicsweb.org/articles/news/5/7/8/1

"...the signal from the pulsar passes through a region of space that is distorted by the gravity of the white dwarf. This distortion means that the signal takes a longer route to Earth, and therefore arrives later. This is the Shapiro delay."

edit:

from your own link: $c\Delta t = \Delta x$ "Which is the extra distance the light has to travel."

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IMO, the whole philosophy of GR is to formulate the theory in an coordinate invariant way so that the so called laws of physics look does not depend on such things as choice of parametrisation or frames of reference.

When he made SR, which holds true only for intertial frames, this was clearly unsatisfactory because clearly the laws of physics must hold in ANY frame. This I think was the motivation for Einstein to look for general relativity. Einstein knew SR was incomplete.

The universal, invariant principle, is that the state of a system will "diffuse into the future" in a direction suggested by the principle of insufficient reason - the shortest path, or the path of least resistance - what we call a geodesic.

Einstein's idea was to look for the spacetime geometry that alone could explain away gravity as an additional force. He also assumed that SR holds locally (in the differential sense) - meaning that the speed of light is constant in the differential sense. Of course one can not non-trivially make parallell transports of vectors in tangent spaces from different spacetime points.

I think Einsteins lineout here is excellent, but some parts needed for the future (quantum gravity) are missing. First Einstein never ever spends a thought on considering the status of the event space, and to what extent points in event space are equally certain. I think of this is the classical limit (non-quantum) of the future theory we look for.

This is sloppy and very informal but I'll spit it out anway:

For an alternative (admittedly speculative) elaboration of the upper bound of change consider this.

Pick a clock device of your choice, and define your choice of "time" units. Then use this as a parametrisation of your observed distinguished changes.

What will the next immediate future look like? We have a range of possibilities with different conditional probabilities (based on present). Since time is simply an internal parametrisation, some of the observables has to do with changes in the state of the clock device. Thus, the clock is a subset of the system.

If we work in the classical domain, the expected path into the past is the most probable path. The most probable path should be in the direction of maximum prior probability. If we now are to quantify the change into the future, relative the change of the clock device, it seems intuitive that this ratio can never exceed 1. It equals 1 only when the future of the pure clock device coincides with the future of the system.

If there was no upper bound on this relative change, it would mean that a pure change in the clock device (other things held constant) is more probably than the change that was by definition chose to be the most probably change, a contradiction in other words.

/Fredrik

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Fredrik: apologies, I'm not clear on the above post and cannot respond with any worthwhile contribution.

Swansont: no, he was clearly talking about a change in c. Your first link is very interesting but in no way conclusive, and your second link rather fudges the issue and IMHO confuses longer distance with longer time. Distance and time are both confounded on light. See GRAVITY EXPLAINED.

Lekgo: re the original question, time has been demonstrably proven to pass more slowly in a high-gravity environment. The official definition of a metre is

the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.

If the metre in the high-gravity environment is the same length as the metre in the low-gravity environment, and if time passes more slowly in the high-gravity environment, it means that the speed of light in the high-gravity environment is less than the speed of light in a low-gravity environment.

Note however, that in both environments, you will still measure c to be 300,000km/s. It's just like measuring the length of your shadow, but the only thing you can use to do this is the shadow of your ruler.

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I'm not entirely sure but I seem to remember that, thanks to Mr Maxwell, you can calculate c from the permittivity and permeabillity of free space. I think it's the square root of 1/epsilon o Mu o

(sorry I have't got the hang of Greek characters or subscript zeros here)

Since these are porperties of a vacuum and a vaccum can't move it's not suprising that c is constant whether you are moving or not.

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If the metre in the high-gravity environment is the same length as the metre in the low-gravity environment, and if time passes more slowly in the high-gravity environment, it means that the speed of light in the high-gravity environment is less than the speed of light in a low-gravity environment.

That is assuming that the person measuring the Metre ruler is in the same inertial (or gravitational) frame of reference and the Ruler.

An observer out side that frame of reference will see a distortion. If the out side observer can see that distortion (contracted length), then a change in C is not needed.

Just as to the local observer, they would not see a change in Time with the object being observed, they would also not see any change in distance, but the out side observer sees both.

So, the Metre is not the same length in a high gravity environment as observed from a low gravity environment and time passes more slowly in the high gravity environment as observed from the low gravity environment.

The situation you described does not actually occur. If it did, then you would be right, but as it doesn't then it actually comes across as a Strawman argument.

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Fredrik: apologies, I'm not clear on the above post and cannot respond with any worthwhile contribution.

Ok, I'll probably get back on this. I guess a more sensible explanation of my suggestion will require starting from scratch.

IMO, a good theory deals with observable and quantities and abstractions thereof only. Objects and phenomena should also be logically devised in therms of the latter. The probabilities I talked about is that on the short time scale, time is more like a random walk, and to a "micro-observer" hardly distinguishable. But there is a "drift" in the random walk. In the classical domain, this drifting random walk appear completely continous. And from first principles of the random walk interesting things can be said.

I'm still struggling with the starting points though. Once I've fiinshed it properly I'll attempt a better explanation. What I wrote was admittedly informal.

/Fredrik

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John, yep, the equation is c = √(1/ε0μ0) where ε0 is permittivity related to capacitance and μ0 is permeability related to magnetiseability, and these can also be combined as impedance

√(μ0/ε0). Higher impedance means lower velocity, and I think it's unreasonable to say impedance can never change. PS: I tried to use math but had problems with the ε and μ characters.

Fredrik: I have somewhat unusual and speculative ideas concerning time. This is perhaps not the place to discuss them.

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I don't see how a vacuum can, so to speak, "know" that it is moving in order to change its impedance accordingly.

If I am running and I hit a tree I will become acutely aware of the relative velocity of the tree and me. How can I measure my speed with respect to a vacuum in order to allow for this when measuring its impedance, permittivity or permeability ?

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I didn't mean to suggest that. I was thinking of gravity actually.

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I may be missing something here but if I was right about that equation above doesn't the constancy of the speed of light follow from Maxwells equations? And if it does then does that mean that it was Maxwell, rather then Einstein, who first theorised that c is a constant. (OK, that's not how he put it)

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I may be missing something here but if I was right about that equation above doesn't the constancy of the speed of light follow from Maxwells equations? And if it does then does that mean that it was Maxwell, rather then Einstein, who first theorised that c is a constant. (OK, that's not how he put it)

Well the Lorentz transformations come from the requirement that maxwells equations have to be true in all reference frames. This lead Lorentz to come up with c having to be constant for this to be true.

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I may be missing something here but if I was right about that equation above doesn't the constancy of the speed of light follow from Maxwells equations? And if it does then does that mean that it was Maxwell, rather then Einstein, who first theorised that c is a constant. (OK, that's not how he put it)

It required the recognition that light was an electromagnetic wave, and then that it applied to mechanical systems. Einstein's paper was "On the Electrodynamics of Moving Bodies"

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I think the original question was why the speed of light was numerically what it is? Why is c = 300,000km/s and not, say, 600,000km/s? I guess this question is not that meaningful because, if c was really 600,000km/s, one could always ask why it is that number and not something else.

I think added to that was a second question, why is it always 300,000km/s? Meaning, why is it a constant? I think the answer to that is what Farsight said about ounces and pounds. The measurements may be sufficiently cyclic to give the illusion of constancy.

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i do not understand. If it was cyclic how could it give the illusion that it is constant

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i do not understand. If it was cyclic how could it give the illusion that it is constant

What is/are the "it" to which you refer here? I haven't reread the thread, but don't think anyone is contending that the speed of light changes in a cyclic fashion.

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the speed of light "changes" then in a cyclic fashion? I was referring to the measurement of the speed of light.

So the speed of light actually does change depending on the observer is that it?

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