Why speed of light is measured same regardless of their speed?

[WannabeNewton]

There's nothing wrong with the part of rbj's post that got this response.

Granted that exact paragraph written by rbj that was quoted was not saying anything wrong but rbj was making the mistake of saying relative motion was something special to SR / novel and that the bare concept of relative motion for inertial observers is what implies the laws of physics are the same in all reference frames which is certainly not true; there are more conditions that need to be assumed, otherwise Galilean relativity would leave Maxwell's equations invariant as well under Galilean boosts.

 

[ghwellsjr]

George's post #12 was spot on, especially the 2nd paragraph.

I have to disagree with this.

And I have to disagree with your disagreement and I'll show you why.

Relative to the light.

This should be "relative to the light source". But even if ghwellsjr had said that, it wouldn't have added anything to the discussion. Rbj didn't ask "relative to what?" because he wanted to know. He asked to remind the OP that he shouldn't have left that information out.

It was obvious to me and I was attempting to point out to rbj what adjacent meant in his OP:

Can someone please explain me why speed of light is measured same regardless of their speed?
Will not a person moving with 0.6c measure speed of light as 0.4c?

Isn't it obvious that he is considering the person to be moving at 0.6c relative to the light which is moving at 1.0c and wondering why the difference of 0.4c isn't correct?

You're missing the whole point of the Principle of Relativity. It's not that each observer is at rest and so his measurements come out the same--it's that even when an observer is not at rest but traveling at some high rate of speed, his measurements still come out the same.

There's nothing wrong with the part of rbj's post that got this response. All ghwellsjr did here was to make a personal attack on rbj. This description of what the principle of relativity is about isn't any more accurate than what rbj said. I like rbj's version better than this one.

Yes there is something wrong with rbj's post. He expressed over and over again that having an acceleration of zero leads to a velocity of zero which is not true. Instead it leads to any constant velocity of which zero is just one of an infinite number of valid answers. The integral of acceleration is velocity and like all integrals, there's always that "plus any arbitrary constant value (+C)" tacked on.

Here's a spacetime diagram illustrating how a person that is at rest in an Inertial Reference Frame measures the speed of light to be c (defined for our purpose here to be 1 foot per nanosecond):

The "person" is shown in blue with each nanosecond of time marked off with dots. He has placed a mirror a measured six feet away shown in red. At his time of 4 nanoseconds, he sends off a flash of green light which travels at c toward the mirror and reflects off of it at coordinate time of 10 nanoseconds and arrives back at the "person" at his time of 16 nanoseconds. The "person" measures that the round-trip time for the light took 12 nanoseconds and so he calculates the speed of light to be one-half of 12 nanoseconds divided into 6 feet or 1 foot per nanosecond.

Now we use the Lorentz Transformation process to create an IRF moving at -0.6c to see the scenario that adjacent described in his OP. Now the "person" is traveling at 0.6c toward the flash of light which is traveling at 1.0c. He's wondering why the "person" won't measure the speed of the light to be traveling at 0.4c.

Now you can see that the difference between his speed and the speed of the light as it is moving away from him is 0.4c but he can't measure that by itself because he can't know when the light hits the mirror. Instead, he does a round-trip measurement that turns out to be identical as in the first IRF. And that illustrates what adjacent was asking about.

 

[Fredrik]

Granted that exact paragraph written by rbj that was quoted was not saying anything wrong but rbj was making the mistake of saying relative motion was something special to SR / novel and that the bare concept of relative motion for inertial observers is what implies the laws of physics are the same in all reference frames which is certainly not true; there are more conditions that need to be assumed, otherwise Galilean relativity would leave Maxwell's equations invariant as well under Galilean boosts.

I can't interpret what rbj said in that way.

his or her measurements come out the same because his or her physics are the same because each, being in their own inertial frame of reference, are in indistinguishable situations. they are, in their own unaccelerated position, operationally at rest and it's the other observer who is moving.

You assert that the following statement "An inertial observer can claim he is at rest and that all other inertial observers are moving relative to him" IMPLIES "Laws of physics are the same in all inertial reference frames in special relativity".

He says that each since all inertial observers are in indistinguishable situations, their measurements will come out the same. To say that the measurements will come out the same, is just another way of saying that their situations are indistinguishable. So the statement can be shortened to "all inertial observers are in indistinguishable situations". This is just a statement of the principle of relativity, not a statement of some crazy implication.

Even your paraphrased version of the statement, which was meant to look crazy, just looks like "PoR $\Rightarrow$ PoR" when I think about what it means. Even a non-inertial observer can claim to be at rest, so I would assume that the reason you're mentioning inertial observers is that they have a good reason to claim that they're at rest. The only good reason I can think of is that they will all be indistinguishable in some sense. So even in this case, the antecedent of the implication seems to be the principle relativity.

 

[WannabeNewton]

He says the laws of physics / measurements are the same in all inertial reference frames because anyone inertial observer can claim he/she is at rest and that the other is moving. How does the latter imply the former? In Newtonian mechanics, I can claim the exact same thing i.e. that I am at rest and the other observers are moving but this obviously does not immediately imply the laws of physics are the same in all inertial reference frames.

 

[Fredrik]

Isn't it obvious that he is considering the person to be moving at 0.6c relative to the light which is moving at 1.0c and wondering why the difference of 0.4c isn't correct?

OK, I see that this interpretation is possible too. But until now I thought it was obvious that the OP was talking about a person moving at 0.6c relative to the light source (in the same direction as the light) and wondering why this person will not assign velocity 1-0.6=0.4 to the light. This interpretation makes a lot more sense, since "relative to the light" is nonsense in SR. (I understand that the OP may not know that).

Yes there is something wrong with rbj's post. He expressed over and over again that having an acceleration of zero leads to a velocity of zero which is not true. Instead it leads to any constant velocity of which zero is just one of an infinite number of valid answers.

An acceleration of zero makes the observer an inertial observer, and an inertial observer has velocity 0 in the inertial coordinate system associated with his own motion. That's what rbj pointed out, and then you came along and pointed out that an inertial observer has a non-zero velocity in other inertial coordinate systems. Since this doesn't in any way disagree with what rbj said, it was a very bad time to claim that he was "missing the whole point of the principle of relativity". rbj definitely went too far with his insults later in the thread, but I have to agree with him that you misrepresented his position.

Here's a spacetime diagram illustrating how a person that is at rest in an Inertial Reference Frame measures the speed of light to be c (defined for our purpose here to be 1 foot per nanosecond):

I haven't participated in the discussion about the OP's question, and I don't think I will. I don't doubt that you are competent enough to handle that.

 

[Fredrik]

He says the laws of physics / measurements are the same in all inertial reference frames because anyone inertial observer can claim he/she is at rest and that the other is moving. How does the latter imply the former? In Newtonian mechanics, I can claim the exact same thing i.e. that I am at rest and the other observers are moving but this obviously does not immediately imply the laws of physics are the same in all inertial reference frames.

As I said, even your distorted version of his statement can be interpreted as "PoR $\Rightarrow$ PoR". But it's clearer in the original statement. He says that the indistinguishability of the situations implies that the physics is the same, and that this implies that measurements are the same.
$$\text{Indistinguishability}\Rightarrow\text{Physics}\Rightarrow\text{Measurements}.$$ The implications holds because all three statements mean the same thing.

 

[WannabeNewton]

What definition of implication is being used here? To use the same example, I can take two inertial observers in Newtonian physics, related by a Galilean transformation. One will say the other is moving and he is at rest and the other will say he is at rest with the first moving but Maxwell's equations don't transform covariantly under Galilean boosts so how does the implication follow? If, on the other hand, you are saying it should imply it as a matter of physical principle then I can agree with that but that just leads us down the road of replacing Galilean transformations with Lorentz transformations; here we are accepting on physical grounds that the situation should imply the laws of physics are the same - we aren't taking the situation and actually showing it implies the laws of physics are the same from first principles.

 

[HomogenousCow]

It is one of the fundamental postulates of special relativity, like the axioms in quantum mechanics.
One could alternatively start with the postulate that the metric of spacetime is the minkowski metric in vaccum, then we may declare the equivalency of all inertial frames and derive the expressions which show us the asymptotic behavior of particles as they approach the speed of light.
For the electromagnetic field, it is apparent in the general solution to Maxwell's equation for prescribed sources, all times are replaced with "retarded times".

 

[WannabeNewton]

It is one of the fundamental postulates of special relativity...

Yes exactly, we are accepting the implication as a basic truth; we aren't proving it from first principles.

 

[Boy@n]

Here's a spacetime diagram illustrating how a person that is at rest in an Inertial Reference Frame measures the speed of light to be c (defined for our purpose here to be 1 foot per nanosecond):

The "person" is shown in blue with each nanosecond of time marked off with dots. He has placed a mirror a measured six feet away shown in red. At his time of 4 nanoseconds, he sends off a flash of green light which travels at c toward the mirror and reflects off of it at coordinate time of 10 nanoseconds and arrives back at the "person" at his time of 16 nanoseconds. The "person" measures that the round-trip time for the light took 12 nanoseconds and so he calculates the speed of light to be one-half of 12 nanoseconds divided into 6 feet or 1 foot per nanosecond.

Now we use the Lorentz Transformation process to create an IRF moving at -0.6c to see the scenario that adjacent described in his OP. Now the "person" is traveling at 0.6c toward the flash of light which is traveling at 1.0c. He's wondering why the "person" won't measure the speed of the light to be traveling at 0.4c.

Now you can see that the difference between his speed and the speed of the light as it is moving away from him is 0.4c but he can't measure that by itself because he can't know when the light hits the mirror. Instead, he does a round-trip measurement that turns out to be identical as in the first IRF. And that illustrates what adjacent was asking about.

Excelent diagrams.

 

[ghwellsjr]

Yes there is something wrong with rbj's post. He expressed over and over again that having an acceleration of zero leads to a velocity of zero which is not true. Instead it leads to any constant velocity of which zero is just one of an infinite number of valid answers.

An acceleration of zero makes the observer an inertial observer, and an inertial observer has velocity 0 in the inertial coordinate system associated with his own motion. That's what rbj pointed out, and then you came along and pointed out that an inertial observer has a non-zero velocity in other inertial coordinate systems.

Where did I say anything like that? Please quote what you are referring to.

Since this doesn't in any way disagree with what rbj said, it was a very bad time to claim that he was "missing the whole point of the principle of relativity". rbj definitely went too far with his insults later in the thread, but I have to agree with him that you misrepresented his position.

Where did he ever say I misrepresented his position? Please quote what you are referring to.

 

[Fredrik]

Where did I say anything like that? Please quote what you are referring to.

You said it just now.

He expressed over and over again that having an acceleration of zero leads to a velocity of zero which is not true. Instead it leads to any constant velocity...

Are you denying that this is to point out that "an inertial observer has a non-zero velocity in other inertial coordinate systems"? (Other than his own rest frame).

Where did he ever say I misrepresented his position?

It was in post #43. The comment was edited out by the mentors, because rbj made it personal. I shouldn't have mentioned it, since the comment has been edited out. What I should have said instead is that my opinion is that you are misrepresenting his views.

You keep making it worse by saying things like this:

He expressed over and over again that having an acceleration of zero leads to a velocity of zero which is not true.

Since you're using this to argue that he's wrong, it can't be interpreted as a suggestion that rbj's view is that "an inertial observer has velocity 0 in his own rest frame" (which would be 100% accurate). So I can only interpret this as a suggestion that rbj's view is that "an inertial observer has velocity 0, period".

 

[Fredrik]

What definition of implication is being used here?

This truth table:

p     q     p→q
1     1       1
1     0       0
0     1       1
0     0       1

By this definition, we have $p\Rightarrow p$ for all statements p. That's all you need to know about implications to understand what I'm saying. The rest is about understanding that was rbj said is of the form
$$p\Rightarrow p\Rightarrow p,$$ which is undeniably true. On the surface, his statement looks like
$$p\Rightarrow q\Rightarrow r,$$ but p,q,r are just three slightly different ways of saying the same thing.

p = "All the inertial observers are in indistinguishable situations."
q = "Physics is the same for all inertial observers."
r = "Measurements come out the same for all inertial observers."

These are just three statements of the principle of relativity. The only one I can object to is r, because measurement results won't be literally the same. But everyone knows that, so I assume that he was just being a bit sloppy with the statement. (And this doesn't seem to be what you're objecting to anyway).

To use the same example, I can take two inertial observers in Newtonian physics, related by a Galilean transformation. One will say the other is moving and he is at rest and the other will say he is at rest with the first moving but Maxwell's equations don't transform covariantly under Galilean boosts so how does the implication follow? If, on the other hand, you are saying it should imply it as a matter of physical principle then I can agree with that but that just leads us down the road of replacing Galilean transformations with Lorentz transformations; here we are accepting on physical grounds that the situation should imply the laws of physics are the same - we aren't taking the situation and actually showing it implies the laws of physics are the same from first principles.

I don't think any of this has anything to do with what rbj said. I explained why in post #63, and again in this post. It looks to me like you have just misinterpreted what he said.

 

[ghwellsjr]

Even if we assume that the physical distance between the Sun and Earth is always the same, how do we know what that physical distance is? Prior to Einstein and his postulate that light propagates at c in all directions in any IRF, scientists had concluded that the physical distance between the Sun and Earth was already contracted because they assumed that the solar system itself must be traveling with respect to some presumed absolute IRF and how could you prove them wrong?

So if we had some absolute frame of reference (so to say a viewpoint outside of Universe - please allow me this hypothetical situation, and let's say we have a rod of 1 meter for measuring distances anywhere in Universe), the physical space of our solar system would be different depending on two things:

1. Motion (e.g. if whole solar system moved at .1c or .5c the the distances between Sun and planets would be different? Smaller at .5c. So, 1 meter on Earth would always be 1 meter, no matter of solar system speed, but if measured with that absolute meter the distances would be different at different speeds, right?)

If we believe (as I said scientists prior to Einstein believed) that there is an absolute frame of reference in which a meter stick at rest in it is its true length and we know how do identify that frame, then we will know how to assign true lengths to everything else in the universe and also true times because we would know the true speed of light. Then we would know the true speed of the solar system with respect to that absolute frame and we could then calculate all the true distances and lengths for everything. But all these calculations would be a huge waste of time and we still would prefer to use Einstein's theory of Special Relativity as a much simpler and consistent theory than recalculating everything to express them in their true values.

2. Gravitation (e.g. if we had a Sun 100 times more massive than our Sun today the distances between Sun and planets would be different? Smaller with more massive Sun?)

Again, even if the Sun and Earth had true masses due to high speed that were greater than their rest masses in the absolute frame, we would still prefer to use Einstein's theory and assign masses just like we do now. Keep in mind that the orbits of the planets according to the absolute frame would be elliptical. It would be such a mess.

Doesn't it make sense, if you want to declare that there is only one correct constant distance between the Sun and Earth that you should make your best assessment as to the motion of the solar system?

It does, but the whole truth is then hidden to ignorant people as myself.

If the truth is that nature operates on an absolute frame, then the identification of the state of that frame is hidden from everyone--we would all be just as ignorant. And, as I'm trying to point out, that ignorance is really a blessing because it frees us of being concerned about identifying true lengths and times of everything.

That distance is only constant if we observe it from planet Earth, right?

When I made that statement I was not concerned about the orbit of the Earth around the Sun which would only be near circular in the Sun-Earth rest frame. I was taking a snapshot of the Sun/Earth distance aligned along the axis of mutual high speed motion with respect to an absolute frame.

And it changes depending on own frame of reference

Our assignment of distances (and times) changes depending on our chosen frame of reference, nothing changes in the universe, just because we choose a different frame.

I hope you are seeing that the problem is that we cannot identify a physically real distance between the Sun and Earth nor a physically real rate of time. Or to put it another way, nature won't reveal to us the answer to that problem.

So our understanding of our reality (distances, speeds, time) are all based on our (human) assumptions and conventions?

Not all, just those remote from us and it's because we cannot identify the propagation time of light which communicates those distant distances and times to us. The speeds between us and remote objects are not affected. We can tell when a distant object is at rest with respect to us or how fast it is moving, but if it is changing speed we cannot identify the times of when it was traveling at any particular speed. This is why Einstein's second postulate is so important, it allows us to assign the propagation time of light in a simple and consistent way without being concerned about whether it matches any "truth" because the truth is, it doesn't matter.

So Einstein's brilliant idea was that if nature won't do it for us, we'll do it our self. If nature won't disclose to us the state in which light propagates at c in all directions, we'll make up our own answer. And that answer is, we will merely assume that light propagates at c in any IRF we choose and we'll use that to define distances and times throughout that IRF. But, we can only use those definitions in one IRF. When we do this for the Sun-Earth rest frame, we don't care if it had a prior history of motion due to its formation. We could also do it for that prior state of rest in which case we wouldn't care about it current state of motion. It's important to stick to anyone IRF of our choosing and not to mix definitions from multiple IRFs. We can always use the Lorentz Transformation process to see what those definitions look like in another IRF but we don't want to say that the universe physically changes dimensions every time we change our chosen IRF. But we do want to say that when objects/observers/clocks change their motion, their dimensions really do change according to the definitions assigned by the chosen IRF and thus their measurements of things moving with respect to them will change as a result.

But what changes in truth? Distances? Time? Both? Neither, something else maybe?

Or nothing at all changes except our model of reality, or better to say, we adjust parameters (time, distances, speeds) in our model, so we can logically describe what is happening?

If that's the case (which I suspect it is), how do we know we have the right, or say, best possible, model (GR & SR)? OK, the model covers our experiments, observations, calculations and predictions (let's assume again) to perfection, and that's it?

We don't care to (or maybe we cannot?) find how the nature really functions, is it enough we have models which are practically useful? Maybe is.

In other words... We made models so nature fits into them nicely, we didn't discover models which really describe how nature functions?

I guess I am asking too much ;-) ...since, if we really knew how nature functions we could make 'new nature' ourselves (e.g. create a little universe in a lab.)

I think you've got the right idea. Just remember those two little words that Einstein stated in the introduction of his 1905 paper: simple and consistent. Any theory that is consistent with all the known facts of nature is just as good as any other theory but we prefer to pick the simpler theory. That's why we prefer Einstein's theory over all other consistent theories.

I don't know about making a little universe in a lab but we can certainly do a good simulation on a computer and make good animations.

 

[WannabeNewton]

It looks to me like you have just misinterpreted what he said.

What I was saying was that, using your definitions for the statements p and q, p implies q is not something you can prove from first principles but rather take as a postulate, as HomogenousCow mentioned. I interpreted rbj as saying you could prove systematically that one follows from the other, making no other assumptions etc. But you are right I think I just misinterpreted his phrasing.

 

[Boy@n]

I don't know about making a little universe in a lab but we can certainly do a good simulation on a computer and make good animations.

Thank you very much for all your explanations. I think I have a bit better understanding about this topic now (room to improve it is enormous ;-)

Would be interesting to see if we run a sophisticated computer simulation of Universe (from Big Bang onwards) long enough, if (self-aware) life spontaneously evolves as it did in our Universe.

 

[Fredrik]

What I was saying was that, using your definitions for the statements p and q, p implies q is not something you can prove from first principles but rather take as a postulate, as HomogenousCow mentioned.

The way I see it, all of the statements p,q,r are so similar and so imprecise that it's impossible to say (with certainty) that one of them is saying something different from one of the others.

 

[rbj]

What I was saying was that, using your definitions for the statements p and q, p implies q is not something you can prove from first principles but rather take as a postulate, as HomogenousCow mentioned. I interpreted rbj as saying you could prove systematically that one follows from the other, making no other assumptions etc. But you are right I think I just misinterpreted his phrasing.

i only meant what i said and vice versa.

everything i said in #8, #24, #26, and #27 are correct and were correct from the beginning. and are simple conceptually, and, in the sense of the Einstein quote, not too simple. all of that makes me suspicious that they were deliberately misrepresented, but if i say why or by whom, the powers that be will be unhappy.

 

[Boy@n]

You are all great people because you take the time to share, and help explaining...

Missunderstandings do happen, let's leave em behind...

Thanks again to all!

 

[ghwellsjr]

i only meant what i said and vice versa.

everything i said in #8, #24, #26, and #27 are correct and were correct from the beginning. and are simple conceptually, and, in the sense of the Einstein quote, not too simple. all of that makes me suspicious that they were deliberately misrepresented, but if i say why or by whom, the powers that be will be unhappy.

Rbj, welcome back. Let's see if we can have civil discussion about some of these posts. Let's start with #26:

There is no possible measurement that allows us to start a stopwatch when some light leaves the Sun and stop it when the light arrives at Earth and yields a measurement of 8 minutes and 19 seconds.

maybe we (on Earth) can't, but an observer far away that is equidistant from the light source and the Earth can.

suppose instead of the Sun, it was a quick little nuclear flash. and the Earth was one big silvered ball that reflects whatever hits it. the observer (who is equidistant from the source and the reflector) sees a flash and, at a later time, sees the reflection of that flash come from the shiny ball. if the distance between the source and the reflecting ball is 1.496 × 10¹¹ m, then that difference in time is 499 seconds.

And here was my response in post #32:

You are just measuring the round-trip time it takes for light to travel from the midpoint to the Earth and back and calling it the one-way time it takes for light to travel from the Sun to the Earth. Isn't that obvious?

Please respond to my very simple question.

 

[rbj]

Please respond to my very simple question.

In the same way, we cannot measure how long it takes for the light to get from the Sun to the Earth. There is no possible measurement that allows us to start a stopwatch when some light leaves the Sun and stop it when the light arrives at Earth and yields a measurement of 8 minutes and 19 seconds.

maybe we (on Earth) can't, but an observer far away that is equidistant from the light source and the Earth can.

suppose instead of the Sun, it was a quick little nuclear flash. and the Earth was one big silvered ball that reflects whatever hits it. the observer (who is equidistant from the source and the reflector) sees a flash and, at a later time, sees the reflection of that flash come from the shiny ball. if the distance between the source and the reflecting ball is 1.496 × 10¹¹ m, then that difference in time is 499 seconds.

there is an infinite plane of points that are all equidistant from the source and from the reflecting ball. you have chosen a specific and quite special point that is colinear and midway to both source and reflector. you have put the observer at the closest possible point, yet that was not what i had illustrated: an observer far away that is equidistant from the light source and the Earth.

so rather than changing the illustration to 3 colinear points, try approaching the illustration described; which is an isosceles triangle with equal distances from light source to observer and from reflecting ball to observer. the side opposite of the observer is what connects "Sun" to "Earth" and has length 1.496 × 10¹¹ m.

so, without conveniently changing the description from what it is to what you want it to be (try doing that in a Real Analysis course), what does the 499 seconds represent?

 

[Samshorn]

...what i had illustrated: an observer far away that is equidistant from the light source and the Earth. Try approaching the illustration described; which is an isosceles triangle with equal distances from light source to observer and from reflecting ball to observer. The side opposite of the observer is what connects "Sun" to "Earth" and has length 1.496 × 10¹¹ m... What does the 499 seconds represent?

The 499 seconds would represent the time for light to travel from Sun to Earth... but only if you assume that the speed of light from the Sun to the observer is the same as the speed from the Earth to the observer. Unfortunately, the experiment you described does not suffice to establish that those speeds are the same. So you cannot claim (based on that setup) that the 499 seconds represents the time for light to travel from Sun to Earth.

Given the invariance of the average speed of light around any closed path, it is well known that if the speed of light depends on direction, it must be of the form C(theta) = c/[1 + k cos(theta)] for some constant k between 0 and 1, where theta is the angle of the direction of the light ray relative to some fixed reference. If you evaluate your experiment using this direction-dependent speed of light, you will find that the time interval measured by the observer's clock is always 499 seconds, regardless of the value of k. Therefore, your experiment does not help us to determine whether the speed of light is the same in all directions. It tells us nothing more than any closed-loop measurement tells us.

Of course, it IS perfectly possible to perform a meaningful measurement of the one-way speed of light, but not by the method you described. You can read about this in any good book on relativity.

 

[ghwellsjr]

there is an infinite plane of points that are all equidistant from the source and from the reflecting ball. you have chosen a specific and quite special point that is colinear and midway to both source and reflector. you have put the observer at the closest possible point, yet that was not what i had illustrated: an observer far away that is equidistant from the light source and the Earth.

so rather than changing the illustration to 3 colinear points, try approaching the illustration described; which is an isosceles triangle with equal distances from light source to observer and from reflecting ball to observer. the side opposite of the observer is what connects "Sun" to "Earth" and has length 1.496 × 10¹¹ m.

so, without conveniently changing the description from what it is to what you want it to be (try doing that in a Real Analysis course), what does the 499 seconds represent?

Thank you for providing additional details so that I can now understand what you had in mind. And although I did misrepresent what you had in mind, I did it inadvertently because to me, 46 million miles is far removed from us here on Earth. I had no idea that you wanted to go way farther than that.

In any case, it just changes the scenario from one that is obvious to one that is not so obvious but it does not change the fact that the 499 seconds is still a measurement of the round-trip propagation of light from the midpoint to the reflector and back. All you have done is added an equal amount of delay to when the observer starts and stops the stopwatch.

Let me see if I can make this a little more obvious. We will consider the inertial rest frame of all the objects and the observer. Let's imagine that the "infinite plane of points that are all equidistant from the source and from the reflecting ball" is a translucent sheet that will allow us to "see" the light from the nuclear flash and, 499 seconds later, "the reflection...from the shiny ball". I think you can realize that the light from the nuclear flash will first illuminate a spot at the midpoint (where I inadvertently thought you wanted the observer). Then this spot will expand in a perfect circle, first rapidly, then slower as the circle gets larger.

Now let's consider what happens when the reflection illuminates the sheet. Isn't it obvious that it will start at the same spot and expand as a circle, again first rapidly, then slower as this second circle gets larger but following exactly the same pattern of expansion as the first one? Now wherever we want to put an observer with a stopwatch, he will be measuring exactly the same thing except that the farther away he is, the later he will make the measurement which is the round-trip time for the light to propagate from the midpoint to the Earth and back. It does not include the time it takes for the light to propagate from the nuclear flash to the midpoint.

 

[ghwellsjr]

Excelent diagrams.

Thanks, I'm glad you liked them.

Now I want to take that same diagram that depicts the situation that adjacent described in his Opening Post (OP) and show you how it depicts the Length Contraction of the distance between the "person" in blue and the mirror in red which the "person" measured to be 6 feet with his ruler. There are a couple ways that other people, stationary in the IRF in which the "person" is moving can make this assessment. They both involve radar measurements. This is similar to the way a cop can clock you for speeding. It works by sending a light (or radar) pulse at an object and waiting for the return echo and then measuring how long the round trip took and dividing it by two and assuming that it took the same amount of time to get to the object as it took for the light to get back from the object. So we place the time of the measurement at the midpoint of the measurement and we consider the measurement of the distance to be how far the light traveled in the measured amount of time. By making successive measurements, we can establish a speed.

Here's the first spacetime diagram:

I have drawn the second observer as a black line at coordinate distance of 15 feet. At coordinate time of 1 nanoseconds, he happens to send out the first radar pulse in blue and a short time later he sends out the second radar pulse in green at 9 ns. He receives the first reflection at coordinate time of 13 ns and the second one at 15 ns. After doing the calculation I previously described, he calculates that the mirror was 6 feet away at time 7 ns and it was 3 feet away at 12 ns. The differences between these calculates establishes that the mirror is moving toward him at 3 feet in 5 ns. which is 0.6 feet per ns or just 0.6c.

So now, armed with the measurement of the mirror's speed of 0.6 feet/ns, he waits until the mirror reach him which happens at time 17 ns. Then he waits for the "person" to reach him which happens at time 25 ns. Since it took 8 ns for the object to pass him at 0.6 feet/ns, he concludes that its length is 0.6 times 8 or 4.8 feet, the same as the gamma process determined.

Now I want to show you another way. This involves measurements of both the "person" in blue and the mirror in red taken at the same "time":

First, the observer in black sends an orange radar pulse at time 4.2 ns and a second green one at time 9 ns. He receives the echoes at 15 ns and 19.8 ns. He concludes that the blue "person" is 7.8 feet away at time 12 ns and the red "mirrors" are 3 feet away at the same time leaving a difference of 4.8 feet.

All methods agree.

 

[Samshorn]

All you have done is added an equal amount of delay to when the observer starts and stops the stopwatch.

The times are equal only if you assume the speed of light is the same in all directions, but that's precisely what the experiment is trying to test, so we can't just assume it.

Isn't it obvious that it will start at the same spot and expand as a circle, again first rapidly, then slower as this second circle gets larger but following exactly the same pattern of expansion as the first one?

No, it isn't obvious... in fact, it isn't even true, unless you assume the speed of light is the same in all directions, which would be assuming what you are trying to test. If you allow for the possibility that the one-way speed differs from the two-way speed, then the light emanating from the reflecting sphere could be approaching the sheet at a different speed than the light from the original flash, so you can't assume the circles would follow the same pattern of expansion.

See post #82 for the actual explanation of why this experiment doesn't provide any more information than a closed-loop measurement.

 

[ghwellsjr]

The times are equal only if you assume the speed of light is the same in all directions, but that's precisely what the experiment is trying to test, so we can't just assume it.

No, it isn't obvious... in fact, it isn't even true, unless you assume the speed of light is the same in all directions, which would be assuming what you are trying to test. If you allow for the possibility that the one-way speed differs from the two-way speed, then the light emanating from the reflecting sphere could be approaching the sheet at a different speed than the light from the original flash, so you can't assume the circles would follow the same pattern of expansion.

See post #82 for the actual explanation of why this experiment doesn't provide any more information than a closed-loop measurement.

I did make that assumption:

We will consider the inertial rest frame of all the objects and the observer.

What I said is:

You are just measuring the round-trip time it takes for light to travel from the midpoint to the Earth and back and calling it the one-way time it takes for light to travel from the Sun to the Earth. Isn't that obvious?

And don't you agree that the issue doesn't change just because the observer is farther away from the midpoint between the source and the reflector?

 

[Samshorn]

I did make that assumption: "We will consider the inertial rest frame of all the objects and the observer."

I don't see the relevance of the quote, but I agree that you did indeed "make that assumption", i.e., your reasoning assumed that the speed of light is the same in all directions, something which can't really be assumed in this context, since it is what the experiment was trying to determine.

What I said is: "You are just measuring the round-trip time it takes for light to travel from the midpoint to the Earth and back and calling it the one-way time it takes for light to travel from the Sun to the Earth. Isn't that obvious?"

You made that statement when you thought the observer was directly between the Sun and Earth, in which case your statement would be true. However, the OP pointed out that his scenario was not this, because in his scenario the observer does not sit directly between the Sun and Earth.

And don't you agree that the issue doesn't change just because the observer is farther away from the midpoint between the source and the reflector?

No, because your original reasoning was valid for a simple linear scenario, but not for the triangular scenario, for the reason explained in my post. An experiment in which the paths of light are not all co-linear imposes additional constraints on any possible directional dependence in the speed of light. A triangular test (and, implicitly, a whole family of triangle tests with different angles) gives us more information about the form of any possible anisotropy than a linear test. So the explanation for why such tests don't fully constrain the anisotropy must take this into account.

 

[rbj]

In any case, it just changes the scenario from one that is obvious to one that is not so obvious but it does not change the fact that the 499 seconds is still a measurement of the round-trip propagation of light from the midpoint to the reflector and back. All you have done is added an equal amount of delay to when the observer starts and stops the stopwatch.

no, you're measuring path length difference. that is not the same as round trip. there is no round trip, just two different paths to the observer.

yes, it is a closed curve, but not all closed paths are back-and-forth round trips. and yes, it requires an assumption that the time of travel on the two equal-length legs is the same. i am not saying how (i don't know how), but somehow it is established that the lengths are the same. and it is assumed that there is nothing of substance different about those two paths. and the contra-assumption becomes less and less reasonable as the distance increases. if the observer was at Alpha Centauri, had a very powerful telescope, could somehow establish that the observer was on a perpendicular from the midpoint between Earth and Sun (again, not saying how he/she could do that), it's becomes very unreasonable to say, without knowledge of an obstruction, that the path lengths would have different times of propagation, even if there was a movement in the aether.

The 499 seconds would represent the time for light to travel from Sun to Earth... but only if you assume that the speed of light from the Sun to the observer is the same as the speed from the Earth to the observer.

yup. of course it does. same assumption one makes when applying the round-trip two-way SOL measurement to a universal SOL. the assumption is there is nothing different about the vacuum of space between the source and the observer and the vacuum of space of between the reflector and the observer. and (somehow) we make sure that the distances are the same.

Unfortunately, the experiment you described does not suffice to establish that those speeds are the same. So you cannot claim (based on that setup) that the 499 seconds represents the time for light to travel from Sun to Earth.

first of all, i was not really describing an experiment. i was simply refuting want ghwells said, specifically regarding a stopwatch. if the SOL was very slow, it's the same thing a 100-meter race timer would have to do: position him/herself on the line perpendicular to the 50-meter point, start the stopwatch when he or she sees the starter's pistol go off and stop it when he/she sees the runner cross the finish line. and it requires the assumption that there is no reason to believe that the equal path lengths would have different travel times, even for a slow speed-of-light.

you know, Michaelson-Morley could not claim the absence of aether based on the negative result of the experiment. perhaps the aether moves around with the Earth as the Earth revolves around the sun, that would account for the negative result. but it's an unreasonable assumption. so maybe M-M didn't prove anything. maybe, for the flat-earthers, the aether still is out there, and it moves around with the experimental platform which is why we just cannot measure our motion through it.

when making the round-trip two-way SOL measurement it may seem reasonable that the time of travel is longer in one direction than the other because we might be moving through the aether in nearlythe same direction (maybe another reason why M-M set up a perpendicular path).

however, for the case i outline, as the paths to the observer get longer and longer (yet somehow we guarantee they remain equal in length) the assumption of a difference in speed along those paths gets less and less reasonable because the two directions are virtually the same. and (if you could pull it off, and i never said how one could set that up) it would measure precisely what ghw says cannot be measured with a stopwatch.

 

[Samshorn]

For the case i outline, as the paths to the observer get longer and longer (yet somehow we guarantee they remain equal in length) the assumption of a difference in speed along those paths gets less and less reasonable because the two directions are virtually the same... it would measure precisely what ghw says cannot be measured with a stopwatch.

Not true. See the explanation in post #82. Again, the setup you described will give exactly the same result (499 seconds) regardless of the value of the anisotropy parameter k, where the speed of light varies with direction according to C(theta) = c/[1 + k cos(theta)]. This is already implied by the requirement for all closed-loop measurements to yield c, so your set-up tells us nothing beyond what the round-trip measurements tell us, and does not imply that the speed of light is isotropic.

I suspect you're getting confused because you are picturing the directions of the light rays (to the observer) getting closer and closer together as you place the observer further and further away, and you think that, in the limit, we can consider the rays to be parallel and hence the difference in speeds is negligibly small and hence it doesn't affect the measured result of 499 seconds. But that is erroneous reasoning, because as the observer is placed further and further away, the speeds of light along those two paths do indeed get closer together, but the distances they must travel are getting longer and longer, so a tiny difference in speeds still makes the same difference in total travel times.

I think the only way to really understand this is to work out for yourself what time interval the observer would measure, given that the speed of light varies with direction according to the equation C(theta) = c/[1 + k cos(theta)]. When you do this, you will find that, regardless of the distance of the observer, the result is always 499 seconds, independent of the value of k. This means the measurement is powerless to tell us anything about the value of k, and hence it tells us nothing about whether the speed of light is isotropic.

 

[phyti]

Can someone please explain me why speed of light is measured same regardless of their speed?
Will not a person moving with 0.6c measure speed of light as 0.4c?

Measuring the speed of light involves physics, so it should be possible to explain the results in terms of physical phenomena. We begin in a fixed frame (of reference), aka the universe. It is motionless (unless someone can find a separate entity to serve as a reference for its motion). The propagation pattern of light is spherical from its origin, with a constant propagation speed of c. A simultaneous 360º multi-photon signal from the center of a circular ring will reflect from the ring and return to the center simultaneously. A clock at the center will record 2t units of time for a path length of 2r units of distance. If the ring moves at constant speed v in the x direction, it causes motion induced phenomena in the form of two complementary effects. The em fields of mass modify themselves from spherical to elliptical with an x radius of r'=r/γ, and the clock at the center runs slower than the static clock with 2t'=2t/γ. Both effects are due to the motion extending the distances for light interactions, and are not detectable by the moving viewer. Since the distance and time units are reduced by the same factor γ, r'/t' = r/t = c. The relations for time t and distance x are the same for all inertial frames because of the scaling by 1/ γ. The γ factor is a consequence of constant light speed, therefore the 1st postulate of SR results from the 2nd.
SR is a theory of measurement and perception. Any viewer of the moving ring will see the reflection events occurring over an interval of space and time. Only the viewer moving with the ring will perceive those events as simultaneous, i.e. as if he is in a rest frame. It’s at this point where Einstein knowing you can’t measure light speed relative to the viewer, DEFINES the time out and back as equal, thus supporting the PERCEPTION of the pseudo rest frame.