Why is C constant

[Lowemack]

If we are in a rocket flying to the sun at 0.75C, why would we measure light from the sun AND light from earth to be C. It can't be because "moving clocks tick slower" for both cases, can it?

[swansont]

If we are in a rocket flying to the sun at 0.75C, why would we measure light from the sun AND light from earth to be C. It can't be because "moving clocks tick slower" for both cases, can it?

 

c can and will be the same because lengths contract and time dilates. Observers in different frames will disagree on the length traveled and the time it took, but they will agree on c.

[Schrödinger's hat]

If we are in a rocket flying to the sun at 0.75C, why would we measure light from the sun AND light from earth to be C. It can't be because "moving clocks tick slower" for both cases, can it?

 

The moving clocks being slower is generally considered a consequence rather than cause of light moving at constant speed.

 

As far as I am aware, the constancy of the speed of light is purely empirical. We did a bunch of experiments, and found that it always moved at the same speed, no matter how you were moving relative to earth/sun/CMBR/whatever (or rather how earth/whatever was moving relative to you) when you did the experiment.

 

As a result we either needed to modify the way we translate times and distances between frames to make them consistent.

[Lowemack]

c can and will be the same because lengths contract and time dilates. Observers in different frames will disagree on the length traveled and the time it took, but they will agree on c.

 

Surely both won't be the same because length contracts and time dilates, because without relativistic effects, light from the sun should be faster and light from the earth slower. How can both measure the same due to the same reason.

 

The moving clocks being slower is generally considered a consequence rather than cause of light moving at constant speed.

 

As far as I am aware, the constancy of the speed of light is purely empirical. We did a bunch of experiments, and found that it always moved at the same speed, no matter how you were moving relative to earth/sun/CMBR/whatever (or rather how earth/whatever was moving relative to you) when you did the experiment.

 

As a result we either needed to modify the way we translate times and distances between frames to make them consistent.

 

So basically the speed of light is a constant, and has nothing to do with our time or distant measurements changing with velocity.

 

My problem is that if you ask "why does someone in a rocketship travelling to the sun measure the same for c as someone on earth" then the answer is usually "because moving clocks run slow". But I cannot get my head around the fact that a clock running slow cannot explain my first question. A slow running clock cannot make light seem to measure faster AND slower than it would without relativistic effects.

[Schrödinger's hat]

My problem is that if you ask "why does someone in a rocketship travelling to the sun measure the same for c as someone on earth" then the answer is usually "because moving clocks run slow". But I cannot get my head around the fact that a clock running slow cannot explain my first question. A slow running clock cannot make light seem to measure faster AND slower than it would without relativistic effects.

 

You're right in that the usual hand-waving explanation is insufficient, but the full story requires starting from the beginning and slowly building up your understanding with careful logic.

 

If you're interested, I can explain further or point you in the direction of some resources.

SO I can find out what type of explanation to point you towards. What level of maths are you comfortable with?

Rate the following either comfortable (understand the concept fairly well and can use it), familiar (heard of it, got a vague idea), or no idea (I don't know what this is) as a guide for me:

Simple geometry -- using a protractor to find angles, scaling shapes

Arithmetic -- exponents, square roots, logarithms etc

Simple algebra -- ie. [math] 2=\frac{1}{\sqrt{1 - x^2}}[/math]

Vectors

Basic Derivatives

Chain rule/product rule

Linear algebra -- transformations using a matrix

Edited February 15, 2012 by Schrödinger's hat

[Lowemack]

You're right in that the usual hand-waving explanation is insufficient, but the full story requires starting from the beginning and slowly building up your understanding with careful logic.

 

If you're interested, I can explain further or point you in the direction of some resources.

SO I can find out what type of explanation to point you towards. What level of maths are you comfortable with?

Rate the following either comfortable (understand the concept fairly well and can use it), familiar (heard of it, got a vague idea), or no idea (I don't know what this is) as a guide for me:

Simple geometry -- using a protractor to find angles, scaling shapes

Arithmetic -- exponents, square roots, logarithms etc

Simple algebra -- ie. [math] 2=\frac{1}{\sqrt{1 - x^2}}[/math]

Vectors

Basic Derivatives

Chain rule/product rule

Linear algebra -- transformations using a matrix

Arithmetic -- exponents, square roots, logarithms etc = Comfortable

Simple algebra -- ie. [math] 2=\frac{1}{\sqrt{1 - x^2}}[/math] = Comfortable

Vectors = Comfortable ish

Basic Derivatives = Comfortable ish

Chain rule/product rule = familiar but too long ago to remember

Linear algebra -- transformations using a matrix = not really

 

Thanks in advance.

[swansont]

As far as I am aware, the constancy of the speed of light is purely empirical. We did a bunch of experiments, and found that it always moved at the same speed, no matter how you were moving relative to earth/sun/CMBR/whatever (or rather how earth/whatever was moving relative to you) when you did the experiment.

 

It's also a prediction of Maxwell's equations as applied to EM waves — you don't get a wave equation if it varies — so it has a very solid foundation. Radio transmitters and receivers still work when they are moving. Einstein applied this to kinematics and found that length and time are not invariant intervals.

[Schrödinger's hat]

You should be able to understand most of the introductory material on the subject.

Unfortunately I'm terrible at paying attention to which books are good.

Here's the first free resource that looked okay:

http://en.wikibooks.org/wiki/Special_Relativity

 

You can probably find suggestions for something to buy/find at a more academically inclined library by searching past posts. Or if someone else would be so kind as to post suggestions.

 

If that's insufficient/too complicated I can write up a basic tutorial.

[swansont]

Surely both won't be the same because length contracts and time dilates, because without relativistic effects, light from the sun should be faster and light from the earth slower. How can both measure the same due to the same reason.

 

Looking solely at special relativity effects, if I am moving, the length I measure will be shorter. You will notice that, according to you, my clock is running slow. Those two effects will reconcile the observation that we both measure c.

 

So basically the speed of light is a constant, and has nothing to do with our time or distant measurements changing with velocity.

 

No, length contraction and time dilation are a direct consequence of it.

 

My problem is that if you ask "why does someone in a rocketship travelling to the sun measure the same for c as someone on earth" then the answer is usually "because moving clocks run slow". But I cannot get my head around the fact that a clock running slow cannot explain my first question. A slow running clock cannot make light seem to measure faster AND slower than it would without relativistic effects.

The simplest answer is "because c is invariant" but that doesn't really explain anything. The question is "how can that be?" I'm on the moving rocket, so you might think I should measure a speed that's faster. However, I see the length as being contracted, so my measurement shows the light didn't go as far in the allotted time, and I measure c.

[Lowemack]

However, I see the length as being contracted, so my measurement shows the light didn't go as far in the allotted time, and I measure c.

 

But would that cause opposite effects to the speed measurements we made to the light we are travelling towards (sun), and the light we are moving away from (earth)?

 

If we are moving towards the sun and away from the earth how can "length contraction" be the reason both sources of light measure the same speed?

[Schrödinger's hat]

But would that cause opposite effects to the speed measurements we made to the light we are travelling towards (sun), and the light we are moving away from (earth)?

 

If we are moving towards the sun and away from the earth how can "length contraction" be the reason both sources of light measure the same speed?

 

The missing piece of the puzzle is the time of distant events.

In additition to the measured duration of events not agreeing between frames, the time that they occur differs by a factor that depends on the displacement.This effect is known as simultenaety of relativity.

 

Again, you can view this all as a consequence of the speed of light being constant, or the simultenaety as a consequence of the time dilation+length contraction (or the other way around), as they all must happen together to give a consistent view of the universe.

 

The only way I know of to become truly used to this idea, and gain some intuition from it is to go through all the derivations carefully from the beginning, making sure you understand each step, then think about it for a prolonged period (days or weeks). Time spent in the shower or mulling it over as you go to sleep is as, if not more important than the time you're studying.

A good check on whether you are building any misconceptions during this is to keep a reserve of scenarios and exercises you have not looked at the answers to, and work through them as you go. Eventually you will pull your intuition in line with the logic.

 

If you just want the 'because I said so' version I can tell you what happens, give a couple of examples and leave it at that.

[Lowemack]

The missing piece of the puzzle is the time of distant events.

In additition to the measured duration of events not agreeing between frames, the time that they occur differs by a factor that depends on the displacement.This effect is known as simultenaety of relativity.

 

 

 

But all this is happening on my rocketship (not distant), in one frame, travelling to the sun at some relativistic speed and measuring the speed of light from the sun and from the earth (in a lab on my rocketship).

 

I can understand that different reference frames can have different clocks and different measuring rods, but I can't see how either or both of those effects can explain how both measurements are the same.

[DrRocket]

 

So basically the speed of light is a constant, and has nothing to do with our time or distant measurements changing with velocity.

 

 

You have a bit of a "chicken and egg" problem.

 

If you assume that the laws of physics are the same in all inertial reference frames and that any phenomena propagates at the same speed, call it x, in all inertial frames, then it is a logical consequence that time and length transformations between reference frames are described by Lorentz transformations with "x" in the usual role of "c". So time dilation and length contraction come with the assumption. Lorentz transformations, not surprisingly, also carry the speed "x" in one frame to the same speed "x" in any other frame.

 

So, basically everything follows from the constancy of "x". You now have special relativity, except for a need to find something that propagates at some fixed speed in all inertial frames.

 

Enter light. Maxwell's equations show that light meets the requirement of propagating at the same speed in all inertial frames. So do many experiments, starting with the well-known historical Michelson-Morley experiment. Thus light fills the bill for the required phenomena used in deriving special relativity and the Lorentz transformations and the speed "x" is the speed of light in a vacuum, "c". With this train, it is the constancy of "c" that results in time dilation and length contraction.

 

Note that as a result of the logic used, there can only be one such invariant speed. So any phenomena that propagates at the same speed in all reference frames must propagate at the same speed as does light. It is thought that gravitational waves also propagate at c, so one might equally call c "the speed of gravity". It just happens that light is a more easily measured phenomena and so we deal with "the speed of light".

 

Conversely, if you start with time dilation and length contraction, hence the Lorentz transformations you find that there is a unique speed that is the same in all reference frames. With the standard Lorentz transformations, that speed is the speed of light "c". So in that sense you might say that the constancy of the speed of light results from the Lorentz transformations, and those transformations are based on so-called time dilation and length contraction.

 

Take your pick as to what "caused" what. But you either get the whole package or none of it.

[ydoaPs]

You have a bit of a "chicken and egg" problem.

 

If you assume that the laws of physics are the same in all inertial reference frames and that any phenomena propagates at the same speed, call it x, in all inertial frames, then it is a logical consequence that time and length transformations between reference frames are described by Lorentz transformations with "x" in the usual role of "c". So time dilation and length contraction come with the assumption. Lorentz transformations, not surprisingly, also carry the speed "x" in one frame to the same speed "x" in any other frame.

 

So, basically everything follows from the constancy of "x". You now have special relativity, except for a need to find something that propagates at some fixed speed in all inertial frames.

 

Enter light. Maxwell's equations show that light meets the requirement of propagating at the same speed in all inertial frames. So do many experiments, starting with the well-known historical Michelson-Morley experiment. Thus light fills the bill for the required phenomena used in deriving special relativity and the Lorentz transformations and the speed "x" is the speed of light in a vacuum, "c". With this train, it is the constancy of "c" that results in time dilation and length contraction.

 

Indeed, length contraction and time dilation are just ways of converting between co-ordinates of differing reference frames. These transformations follow from the above assumptions of c being constant and invariant as well as all inertial frames being equally valid. But, to restate the OP, why is c constant? DrRocket tells us it's the Maxwell equations.

 

Maxwell equations:

 

[math]\bigtriangledown\cdot{E}=\frac{\rho}{\epsilon_0}[/math]

[math]\bigtriangledown\times{E}=-\frac{\partial{B}}{\partial{t}}[/math]

[math]\bigtriangledown\cdot{B}=0[/math]

[math]\bigtriangledown\times{B}={\mu_0}{\epsilon_0}\frac{\partial{E}}{\partial{t}}[/math]

 

These are the equations that describe how electric fields and magnetic fields interact. Think of [math]\bigtriangledown\cdot[/math] as describing whether or not a vector field is pointing inward or outward, think of [math]\bigtriangledown\times[/math] as describing which in which direction and how tightly a vector field is curled, and think of [math]\frac{\partial}{\partial{t}}[/math] as being the rate of change of the vector field. A vector field is a space where there is a vector at every point. A vector is a mathematical object with both a number and a direction. Having no charges to worry about with light, we can set the charge density equal to zero which makes the equations:

 

[math]\bigtriangledown\cdot{E}=0[/math]

[math]\bigtriangledown\times{E}=-\frac{\partial{B}}{\partial{t}}[/math]

[math]\bigtriangledown\cdot{B}=0[/math]

[math]\bigtriangledown\times{B}={\mu_0}{\epsilon_0}\frac{\partial{E}}{\partial{t}}[/math]

 

Now, let's take the curl of the curl equations and see what happens.

 

[math]\bigtriangledown\times\bigtriangledown\times{E}=-\frac{\partial}{\partial{t}}\bigtriangledown\times{B}=-{\mu_0}{\epsilon_0}\frac{\partial^2{E}}{\partial{t^2}}[/math]

[math]\bigtriangledown\times\bigtriangledown\times{B}={\mu_0}{\epsilon_0}\frac{\partial}{\partial{t}}\bigtriangledown\times{E}=-{\mu_0}{\epsilon_0}\frac{\partial^2{B}}{\partial{t^2}}[/math]

 

Since [math]\bigtriangledown\times(\bigtriangledown\times{V})=\bigtriangledown(\bigtriangledown\cdot{V})-\bigtriangledown^2{V}[/math] for any vector field V, we can write:

 

[math]-{\mu_0}{\epsilon_0}\frac{\partial^2{E}}{\partial{t^2}}=-\bigtriangledown^2{E}[/math]

[math]-{\mu_0}{\epsilon_0}\frac{\partial^2{B}}{\partial{t^2}}=-\bigtriangledown^2{B}[/math]

 

which we rearrange to get:

 

[math]\frac{\partial^2{E}}{\partial{t^2}}-\frac{1}{{\mu_0}{\epsilon_0}}\cdot\bigtriangledown^2{E}=0[/math]

[math]\frac{\partial^2{B}}{\partial{t^2}}-\frac{1}{{\mu_0}{\epsilon_0}}\cdot\bigtriangledown^2{B}=0[/math]

 

which are the electromagnetic wave equations. The speed term is [math]\frac{1}{\sqrt{{\mu_0}{\epsilon_0}}}[/math] where [math]\mu_0[/math] is the permeability of free space and [math]\epsilon_0[/math] is the permattivity of free space. Plug in the numbers and that's how we get c.

 

Do any of those numbers depend on the speed or reference frame?

[Schrödinger's hat]

Indeed, length contraction and time dilation are just ways of converting between co-ordinates of differing reference frames. These transformations follow from the above assumptions of c being constant and invariant as well as all inertial frames being equally valid. But, to restate the OP, why is c constant? DrRocket tells us it's the Maxwell equations.

 

Well that's where it showed up first, but does that really make it a reason why? I mean we can reformulate Maxwell's equations to look like a wave equation for a wave travelling at c. At that point it becomes a bit tautilogical.

I prefer 'we found a speed that was constant'. We can leave the philosophers to argue about why.

Unless someone can elucidate a good reason for space being locally Minkowskian which doesn't boil down to "'cos that's what agrees with experiments" in one or fewer steps (ie. some simpler principle that has a constant speed as a consequence).

[ydoaPs]

Well that's where it showed up first, but does that really make it a reason why? I mean we can reformulate Maxwell's equations to look like a wave equation for a wave travelling at c. At that point it becomes a bit tautilogical.

I prefer 'we found a speed that was constant'. We can leave the philosophers to argue about why.

Unless someone can elucidate a good reason for space being locally Minkowskian which doesn't boil down to "'cos that's what agrees with experiments" in one or fewer steps (ie. some simpler principle that has a constant speed as a consequence).

 

Good thing there's a philosopher in the room. The wave equations derived from the Maxwell Equations are the descriptions of what light "is". The speed term is made solely of terms that are constant and invariant. That's as close to why (technically why is about the intent of a causal agent, but it's vernacularly close enough here) as one can get.

 

So, the philosophically correct answer here is that "why" is a silly question to ask.

Edited February 15, 2012 by ydoaPs

[DrRocket]

 

So, the philosophically correct answer here is that "why" is a silly question to ask.

 

Science answers "How".

 

"Why" is for philosophers and theologians.

[ydoaPs]

Science answers "How".

 

"Why" is for philosophers and theologians.

 

 

Leave the philosophy to the philosophers. "Why" can be answered by science, but is the wrong question to ask here.

[elfmotat]

"Why" questions can't really be answered in physics. "Why is G/ħ/e/etc. the value that it is?" It depends on what kind of answer satisfies you.

 

The constancy of c was implied by Maxwell's equations and later postulated by Einstein. Essentially, he said "let's see what it would imply if c was the same to all inertial observers." We know his postulate is correct because we've experimentally determined it to be the case.

Edited February 15, 2012 by elfmotat

[DrRocket]

 

Leave the philosophy to the philosophers.

 

Gladly, except when it comes to science.

 

Scientists also philolosophize, as part of the creative process of research. They just don't pay any attention to philosophers.

 

"Why" can be answered by science, but is the wrong question to ask here.

 

Science seeks only to descrive HOW nature behaves, quantitatively and predictively.

 

WHY it behaves that way is a question to be contemplated by philosophers and theologians. I did not mean to imply that philosophers or theologians were in any danger of reaching a conclusion, or of actually answering such questions.

 

I definitely agree that any actual answers will come from science. But those answers, again, will simply describe how nature behaves and not why it behaves in that manner.

[Schrödinger's hat]

Good thing there's a philosopher in the room.

Did you just call me a philosopher?

So, the philosophically correct answer here is that "why" is a silly question to ask.

 

Exactly my point.

[ydoaPs]

Did you just call me a philosopher?

 

No

[IM Egdall]

Enter light. Maxwell's equations show that light meets the requirement of propagating at the same speed in all inertial frames. So do many experiments, starting with the well-known historical Michelson-Morley experiment.

 

As I understand it, the Michelson-Morley experiments said nothing about light propagating at the same speed in all inertial frames. The MM experiments were done in a single reference frame -- the light source, the interferometric apparatus the light went through, and the detector (film?) were all at rest with respect to each other. So the experiments didn't prove or disprove Einstein's light postulate.

 

If we are in a rocket flying to the sun at 0.75C, why would we measure light from the sun AND light from earth to be C. It can't be because "moving clocks tick slower" for both cases, can it?

 

Maxwell's theory says light is a continuously moving electromagnetic wave. The continuously changing electric part of the wave produces a continuously changing magnetic part. This in turn produces the electrical part. They produce each other.

 

The key here is continuously changing. Einstein imagined moving at the same speed as a beam of light (at age 16!). Buit if he did, the beam would appear at rest with respect to him. So then the electric and magnetic fields would be static -- not changing. So they would not generate each other, and the EM wave would not exist from his poiint of view. As someone said, a light beam must move to exist.

 

So, Einstein concluded, you can never catch up to a light beam. It always goes at the same speed no matter what your (uniform) motion.

Edited February 16, 2012 by IM Egdall

[imatfaal]

As I understand it, the Michelson-Morley experiments said nothing about light propagating at the same speed in all inertial frames. The MM experiments were done in a single reference frame -- the light source, the interferometric apparatus the light went through, and the detector (film?) were all at rest with respect to each other. So the experiments didn't prove or disprove Einstein's light postulate.

MM showed that there was no variation in the speed of light detected relative to changes in direction/drift speed of the postulated ether wind. As the whole apparatus was on the earth moving at high speed through the ether and turned at the same time ; it is easily shown that each reading must be at different angle to the drift of the ether wind - at some points it must be parallel at others perpendicular. the speed of light SHOULD have described a sinusoidal variation as the angle with the ether wind varied as the apparatus turned - it did not have the variation. Variations would also be seen on a daily basis, and yearly - these were also missing. The simplest explanation was that the light did not require an ether to travel through. Basically MM showed that the absence of ether theory was a better fit to experimental data

[IM Egdall]

MM showed that there was no variation in the speed of light detected relative to changes in direction/drift speed of the postulated ether wind. As the whole apparatus was on the earth moving at high speed through the ether and turned at the same time ; it is easily shown that each reading must be at different angle to the drift of the ether wind - at some points it must be parallel at others perpendicular. the speed of light SHOULD have described a sinusoidal variation as the angle with the ether wind varied as the apparatus turned - it did not have the variation. Variations would also be seen on a daily basis, and yearly - these were also missing. The simplest explanation was that the light did not require an ether to travel through. Basically MM showed that the absence of ether theory was a better fit to experimental data

 

Yes, MM failed to detect the ether. But it said nothing about the absolute speed of light.