# Why is the speed of light the same to any observer?

And the 2nd question:
Do we know why is the speed of light 3*10^8 m/s? What determines this value? (I'm not asking about system of units)

S.

## Answers and Replies

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Anything that has momentum without mass is seen to travel at 'c' by any observer. This was a postulate of special relativity, and has many times been experimentally verified. If you want any more of an answer than that, you'll have to ask a philosopher. :)

Same goes for your second question. Some have theorized that the speed of light might have changed over the life of the universe, but there's been no evidence of this.

And the 2nd question:
Do we know why is the speed of light 3*10^8 m/s? What determines this value? (I'm not asking about system of units)

S.
The value of c can be derived by postulating Maxwell's equations. The derivation shows that c = 1/sqrt(eu) where e = permitivity of free space and u = permiability of free space.

Anything that has momentum without mass is seen to travel at 'c' by any observer. This was a postulate of special relativity, and has many times been experimentally verified.
That is a theorem (something derived) and not a postulate.

Pete

The constancy of the speed of light was one of Einstein's original postulates. The fact that v=c when m=0 can be derived from E=pc does not make it a theorem because it already assumes that which it is trying to prove.

The constancy of the speed of light was one of Einstein's original postulates. The fact that v=c when m=0 can be derived from E=pc does not make it a theorem because it already assumes that which it is trying to prove.
My interpretation of the OP's original question is that he was asking about why c is invariant and also how the value of c is obtained. c is obtained using Maxwell's equations. The invariance of c is a postulate and as such is not derived. However we can postulate the Principle of Relativity and Maxwell's equations and then derive the invariance of c. So it really depends on what you're starting with.
peter0302 said:
The fact that v=c when m=0 can be derived from E=pc does not make it a theorem because it already assumes that which it is trying to prove.
Please provide the derivation of which you speak.

A theorem is, by definition, that which is derived from other theorems, from postulates/laws/axioms or from both. As far as E = pc then this too is something derived and not postulated. This relation can be derived from Maxwell's equatons. As such it too is a theorem. If you hold that v = 0 given m = 0 and E = pc then please proof a proof since I'm a bit uncertain as to what you're assuming as given (i.e. what are you assuming is true in that derivation?). How exactly are you defining mass m anyway?

Definiton of theorem - a formula, proposition, or statement in mathematics or logic deduced or to be deduced from other formulas or propositions.

If you disagree then please define the term "theorem" as you understand it and, if possible, please provide a source where you learned such a definition. Thank you.

Pete

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here is my 2 cents :
1. constancy of speed of light wrt all observer is a postulate of relativity.
2. Maxwells eq gives a theoritical proof of what the value should be, but doesn't imply that it is contant for all frames.
3. even if the value of C is changing, it is same for everybody/frame at a given pint in time.

4. to understand why it is same for all frames, if you have to deal with higher dimension. Light is actually travelling perpendicular to 4D, it is travelling in 5th dimension, but trapped by the 4D universe so that it just grazes the surface of 4D. Anything travelling in 5th dimension will not be seen as travelling with varying speed to any observer in 4D. Don't compare with X/Y axis here. XY axis is straight, where as 5th dimension is curved. Efeectively what is happening is this
you tarvell at a speed in Y axis.
observer is in X axis, now assume Y axis is curved although always pernedicualr to X. the component of its velocity projected on X axis will remain identical irrerespective of the movement along X axis. in eucledian X-Y axis this component is zero. in our higher dimension, where things to bend, the component is = C.

Any object without mass, can't exist in a gravitational field, it must escape the field = escape the universe but since the higher dimensions are al curved, they graze the surface of 4D universe.

Read kaluza-Kein theory of 5 dimension you will get the hint. If you want to know further you have to get into string theory or some such ideas.

In fact the equations of SR can be derived from this - light is travelling perpednicular to 4D. I can't draw images here. poor at editing.

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Any object without mass, can't exist in a gravitational field, it must escape the field = escape the universe but since the higher dimensions are al curved, they graze the surface of 4D universe.
I don't see where you get that idea from. Photons certainly exist in gravitational fields. In fact if they didn't then I'd be unalbe to read your posts. As far as remaining in a gravitational field its a well accepted notion that a photon can orbit a massive spherically symmetric body. However ther orbit is unstable.
Read kaluza-Kein theory of 5 dimension you will get the hint. If you want to know further you have to get into string theory or some such ideas.
Nah. Unless you learn it at a layman's level then learing string theory requires an education in quantum field theory. And its a a minority of physicists know QFT. A great deal of people who post here, such as myself, have never learned string theory at a detailed level. Namely because QFT is very hard to learn. Its said to be extremely hard, if not impossible, to learn through self teaching.
In fact the equations of SR can be derived from this - light is travelling perpednicular to 4D. I can't draw images here. poor at editing.
I'd have to see such a derivation before I'd believe it. Its meangless in SR to speak of light traveling perpendicular to 4d spacetime because relativity only uses 4 dimensions and having something perpendicular to spacetime requires another dimension. One then has to specify the meaning of that dimension before one can discuss it too.

Pete

Why is the speed of light the same to any observer

And the 2nd question:
Do we know why is the speed of light 3*10^8 m/s? What determines this value? (I'm not asking about system of units)

S.
I quess your first question has 'independent of the relative speed and direction of the observer' added on the end.
I think that it is to do with light behaving like a wave. The frequency and/or the wavelength changes (red shift/blue shift) but the relationship between these two components stays the same, hence c stays the same.

As for the second question, I would imagine that the answer would be similar to why sound has a specific speed through water or any other medium. The only difference is that we are dealing with the natural frequency of something which has resonant inertia but is not matter.

Nick

HallsofIvy
Science Advisor
Homework Helper
I am a bit uncomforable talking about "postulates" for physics as opposed to mathematics. In mathematics we can "make up" whatever systems we want with whatever postulates we want- in physics we are constrained by reality!

Yes, the constancy of the speed of light is a "postulate" of relativity- and it was chosen as one because that was what experimental evidence showed.

As for why the speed of light is a constant, in Newton's immortal phrase "Hypothesen non fengo"- "I frame no hypotheses".

I am a bit uncomforable talking about "postulates" for physics as opposed to mathematics. In mathematics we can "make up" whatever systems we want with whatever postulates we want- in physics we are constrained by reality!
I don't follow. Why do you say that we can postulate whatever we want to in mathematics? This is certainly news to me. In math the basic postulates are things like Peno's postulates, the distributive laws, the associative laws etc. But we don't make up postulates. This follows from the definition of postulate (as used in this context)

postulate: to assume or claim as true, existent, or necessary : depend upon or start from the postulate of to assume as a postulate or axiom (as in logic or mathematics)

Pete

And the 2nd question:
Do we know why is the speed of light 3*10^8 m/s? What determines this value? (I'm not asking about system of units)

S.
This is a very good question. Turns out that light speed is set by defintion.

The value it is set to (299,792,458m/s) was obtained averaging the results of the most recent and most precise experiments.

Now, as to your thread title: "Why is the speed of light the same to any observer?"

The answer has been given by others already: it is a postulate derived from multiple experimental observations. Postulates are not explainable.

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I don't follow. Why do you say that we can postulate whatever we want to in mathematics? This is certainly news to me. In math the basic postulates are things like Peno's postulates, the distributive laws, the associative laws etc. But we don't make up postulates. This follows from the definition of postulate (as used in this context)

postulate: to assume or claim as true, existent, or necessary : depend upon or start from the postulate of to assume as a postulate or axiom (as in logic or mathematics)

Pete
Those are not the basic posulates of math. Math has no basic postulates. Those postulates, or axioms are a set of axioms for the natural numbers. That's all they cover. There are many problems domains that go beyond natural numbers such as quantum mechanics and string theory, where the concept of addition or commutativity are not applicable.

So using math you can develop axioms for all sorts of things, it doesn't matter, and maybe some applied mathematicians such as physicists will use them and the derived theorems to help solve their problems. But math itself certainly shouldn't concern it's self with our own experiences as HallsofIvy correctly stated.

So in math make up whatever axiom you want and perhaps the theorems derived will cover some part of reality we have yet to know. Betrand Russel has a famous quote:

"Thus mathematics may be defined as the subject in which we never
know what we are talking about, nor whether what we are saying is
true." -- Bertrand Russell

rbj
Do we know why is the speed of light 3*10^8 m/s? What determines this value? (I'm not asking about system of units)
it appears that you are asking about units.

the only fundamental physical fact imposed upon us by reality is that c is finite. it doesn't matter what the finite value is, and we may as well call it 1. the question as to why it comes out to be 299792458 m/s, is a question about units; why is the meter as long as it is (in terms of the Planck length) and why the second is as long as it is (in terms of the Planck time)?

rbj
here is my 2 cents :
1. constancy of speed of light wrt all observer is a postulate of relativity.
a consequence of an even more fundamental postulate that the laws of nature are the same for all inertial observers.

2. Maxwells eq gives a theoritical proof of what the value should be, but doesn't imply that it is contant for all frames.
$$c = \sqrt{\frac{1}{\epsilon_0 \mu_0}}$$

3. even if the value of C is changing, it is same for everybody/frame at a given pint in time.
if c were changing (or any other dimesionful "constant"), no mortal would know the difference if all of the dimensionless constants remained constant.

This is a very good question. Turns out that light speed is set by defintion.
of course, one would ask, if we defined the speed of light to be however fast my Toyota goes flat out on the highway, would that make it so? it's actually the meter that got defined in such a way that given the existing definition of the second, and the speed of light (how we experience and measure it), the meter is whatever length it has to be so that light travels 299792458 of them in the time elapsed by a second.

The value it is set to (299,792,458m/s) was obtained averaging the results of the most recent and most precise experiments.
and that was when the meter was defined as the distance between two little scratch marks on a bar of platinum-iridium (the "prototype meter" ) in the BIPM in France.

Now, as to your thread title: "Why is the speed of light the same to any observer?"

The answer has been given by others already: it is a postulate derived from multiple experimental observations. Postulates are not explainable.
this postulate is a little bit explainable. it really is dependent on the more fundamental postulate that the llaws of nature are the same, both qualitatively and quantitatively, for every inertial observer, even those that are moving (at constant speeds) relative to each other. it is a consequence of the very reasonable postulate that all observers that are not accelerated have equal claim to being stationary. if two inertial observers, moving relative to each other, have equal claim to being stationary (and "it's the other guy who is moving, not me") then the laws of physics, including the quantitative expression of them (two such quantities are $\epsilon_0$ and $\mu_0$ which determine c), must be identical to both observers.

i tried to beat this horse to death in this thread.

of course, one would ask, if we defined the speed of light to be however fast my Toyota goes flat out on the highway,
:-)

and that was when the meter was defined as the distance between two little scratch marks on a bar of platinum-iridium (the "prototype meter" ) in the BIPM in France.
Yes, back in 1983.

this postulate is a little bit explainable. it really is dependent on the more fundamental postulate that the llaws of nature are the same, both qualitatively and quantitatively, for every inertial observer, even those that are moving (at constant speeds) relative to each other. it is a consequence of the very reasonable postulate that all observers that are not accelerated have equal claim to being stationary. if two inertial observers, moving relative to each other, have equal claim to being stationary (and "it's the other guy who is moving, not me") then the laws of physics, including the quantitative expression of them (two such quantities are $\epsilon_0$ and $\mu_0$ which determine c), must be identical to both observers.
This is an interesting one, I have seen occasional claims of :
-dependency of the second postulate on the first one
(re)constructing SR based only one the first postulate

but I could never find the respective papers/books. Do you know if the above claims are provable?

i tried to beat this horse to death in this thread.
OK, I am now going to look your horse in the mouth :-)

two inertial observers, moving relative to each other, have equal claim to being stationary
If these inertial observers don't have equal claim to being stationary does Maxwell's formula become untenable?
The reason I question it is that there is speculation about reference frames and the distortion of these near areas of high gravity. The existence of a reference frame at all may suggest that there is a theoretical 'at rest'

Nick

rbj
If these inertial observers don't have equal claim to being stationary does Maxwell's formula become untenable?
no, i don't think so. but if these inertial observers have unequal degrees of absolute velocity, and their absolute velocity is determined relative to some absolutely stationary frame of reference (that really doesn't exist, but we would call it "aether" if it did), then the velocities expressed in Maxwell's equations (the J vector would be charge density times a velocity vector v) and in the Lorentz force equation, those velocities would be in terms of or relative to the aether. doesn't make it untenable, just not correct.

rbj
rbj said:
and that was when the meter was defined as the distance between two little scratch marks on a bar of platinum-iridium (the "prototype meter" ) in the BIPM in France.
Yes, back in 1983.
actually, earlier than that. 1959, more like.

This is an interesting one, I have seen occasional claims of :
-dependency of the second postulate on the first one
(re)constructing SR based only one the first postulate

but I could never find the respective papers/books. Do you know if the above claims are provable?
depends on what you mean by "the laws of physics". if parameters that appear in the laws of physics are, themselves, part of the laws of physics, then it is an obvious logical construction to conclude that the parameters of the laws of physics (namely $\epsilon_0$, $\mu_0$, and c) remain invariant if the laws of physics are invariant.

some people might mean that the structure of the laws of physics remaining constant do not mean that the parameters inside them must remain constant, but that is not what i mean when i say "the laws of physics remain constant" for various inertial observers. is that what Einstein meant? i think so, but someone else might disagree. but it doesn't matter because Einstein closed the door on this but explicitly stating that the laws of physics and, at least the parameter we call c, both remain invariant for all inertial observers.

one reason i think that it is semantically silly (and logically silly) to say that the parameters inside the laws of physics aren't part and parcel to the laws of physics and do not share the same degree of invariancy as the laws of physics is that, for any particular law, let's say Newton's 2nd law, one can insert a parameter (that would be unit dependent, just like c is) initially set it to 1 (so it changed nothing, by inserting it) and hypothesize that it might vary:

$$F = k \frac{dp}{dt}$$

if k varies, does that mean that Newton's 2nd law remained constant or not?

it is no different of an issue regarding the appearance of c in the laws of physics. if the laws of physics remain invariant for different inertial observers, then i cannot see how that semantic does not mean that c, G, h, do not also. either the law, the entire law is unchanged, or it has changed.

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speed of light same for all observers

The answer is in 'velocity measurement' http://wizdum.awardspace.info" [Broken]

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DaveC426913
Gold Member
it appears that you are asking about units.

the only fundamental physical fact imposed upon us by reality is that c is finite. it doesn't matter what the finite value is, and we may as well call it 1.
No, I think he really is asking why the speed of light is the speed that it is, independent of whatever unit you measure it in.

Yes, you can measure the speed of light in light-seconds per second, in which case its speed is 1ls/s, or in furlongs per heartbeat. But I do think he's asking why that speed.

I would speculate wildly that the speed was soon after the creation of the universe and is somehow related to the vacuum energy or the mass of the Higgs Boson. Or the amount of plasma vented from the warp nacelles.

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rbj
No, I think he really is asking why the speed of light is the speed that it is, independent of whatever unit you measure it in.

Yes, you can measure the speed of light in light-seconds per second, in which case its speed is 1ls/s, or in furlongs per heartbeat. But I do think he's asking why that speed.
but Dave, respectfully, then either he is asking what ultimately is a meaningless question (why is lightspeed 1 light-second per second?) or he is asking about units (why is lightspeed X furlongs per heartbeat?). the latter really is about why a furlong has the length it has (in terms of the Planck length or some other natural unit) and why a heartbeat transpires the number of Planck times (or other appropriate natural unit) that it does. asking why dimensionful constants are what they are is meaningless. asking why dimensionless parameters take on the values that they do is meaningful. we don't measure or even perceive any dimensionful quantity except in relation to another like dimensioned standard. the raw results (and net results) of all of our physical experiments, of reading instruments, or of kust our everyday experience are dimensionless numbers.

I would speculate wildly that the speed was soon after the creation of the universe and is somehow related to the vacuum energy or the mass of the Higgs Boson. Or the amount of plasma vented from the warp nacelles.
i'm with Michael Duff, John Barrow, Gabriele Veniziano, and John Baez about this. the speed of propagation of the fundamental interactions of nature is finite, real, and positive (it is necessary physics to come to that conlusion) but the actual value of that finite value is not operationally meaningful. it just defines the scaling, the tick marks, that the rest of reality conforms to. if the speed of light somehow suddenly doubled (from the POV of some God or "Q" or some omnipotent being who does not submit to the laws of nature), we mortals wouldn't know the difference. not unless some dimensionless parameter (like the fine-structure constant) changed, and then the meaningful thing that changed was that dimensionless parameter.

DaveC426913
Gold Member
but Dave, respectfully, then either he is asking what ultimately is a meaningless question (why is lightspeed 1 light-second per second
Why is this a meaningless question?

NateTG
Science Advisor
Homework Helper
And the 2nd question:
Do we know why is the speed of light 3*10^8 m/s? What determines this value? (I'm not asking about system of units)
It is generally agreed (and experimentally verified) that the speed of light is the same in all inertial frames of reference. The prediction that the speed of light is constant comes out of Maxwell's equations as others have mentioned. This struck people as odd, and a huge number of experiments were run allmost all of which support that the speed of light is constant. The most famous of which is the Michelson-Morely experiment.

http://en.wikipedia.org/wiki/Michelson-Morley_experiment

dst
It is quite a valid question to ask why light moves at 3x10^8 m/s and not say, 4 m/s or 4x10^100m/s (using the same "metre" as a multiple of however many planck lengths each and every time). Of course, I don't know if I've dug my own grave by using planck lengths as a measure of length, are they dependant on the speed of light? If so then surely all that matters, as I keep hearing, is that C is not infinite or zero.

Any ideas?

Hello all.

Any value attached to c is purely due to our choice of units and by a certain choice of units it could be 1 or 99 or whatever. But if we ignore units, to ask why it is whatever it is is a valid question.

As far as i have been taught Maxwell's equations require it to be a ratio of certain physical properties of space.

Matheinste.