Why is the speed of light the same for all observers?

[rahulgarg12342]

I never understand why the speed of light is the same for all observers irrespective of their motion relative to the source of light. Now suppose I am sitting at the back of a vehicle which is traveling at the speed of 0.999999999999c and light approaches me from behind the vehicle. i.e. I am going away from the source of light while I can still see the light. Now I attach an instrument to my car for measuring the speed of light. Won't it measure 0.000000000001c.

Please help me understand why will the instrument still record 0.999999999999c and not 0.000000000001c according to the theory of relativity.

 

[jtbell]

Velocities don't "add" the same way in relativistic physics as in classical physics.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

http://en.wikipedia.org/wiki/Velocity-addition_formula

 

[Saw]

I suppose you may now be asking yourself why velocities add in a different way in relativistic physics. if you want to answer yourself this, just look at the way that the relativistic formula for addition of velocities is derived.

 

[rahulgarg12342]

I know we use the lorentz transformation to add velocities but doesn't it seem a bit absurd?

 

[Saw]

Why? You may be thinking that the Galilean alternatives (c+v) and (c-v) are self-evident but they are aren't. They are also derived. Think of it: how do you derive them?

(Will go to play tennis now...:)

 

[tom.stoer]

In physics we cannot explain why nature is the way it is. We can only try to find a mathematical representation which describes how it works, and we can derive predictions.

In this specific case we find experimentally that electromagnetic waves travel at the speed of light, and we find that this is true for all observers (all reference frames). Then we find theoretically that Maxwell's equations predict exactly this behavior. In addition we can use special relativity (including Lorentz transformations, relativistic addition of velocities, ...) to formulate a comprehensive theoretical framework.

So we know how to describe nature. And we should believe in this description b/c it makes correct predictions.

Unfortunately this is all we can say in physics.

 

[Naty1]

In physics we cannot explain why nature is the way it is. ...
So we know how to describe nature.

so true!
Just to emphasize those points, everybody who studies special and then general relativity and especially quantum mechanics must change their way of thinking.

It turns out you probably think space and time are fixed and immutable; turns out they are not, but 'conspire' together in such as way that enables all observations of lightspeed to be the same. It turns out the speed of light that is fixed and immutable...

I know we use the lorentz transformation to add velocities but doesn't it seem a bit absurd?

yes, it took an 'Einstein' to recognize that, so don't feel bad about it not seeming natural to you. If you are not familiar with the struggles of the greatest minds of the early 1920's, look up 'luminiferous ether'...

It’s nature that is bizarre, not the presentation.

A. Zee

 

[Naty1]

I never understand why the speed of light is the same for all observers irrespective

for clarity: nobody knows.

Nobody even knows why light exists.

 

[ghwellsjr]

I never understand why the speed of light is the same for all observers irrespective of their motion relative to the source of light. Now suppose I am sitting at the back of a vehicle which is traveling at the speed of 0.999999999999c and light approaches me from behind the vehicle. i.e. I am going away from the source of light while I can still see the light. Now I attach an instrument to my car for measuring the speed of light. Won't it measure 0.000000000001c.

Would you please describe this instrument that measures the speed of light. How does it work? Do you know of a place where you can buy one?

Please help me understand why will the instrument still record 0.999999999999c and not 0.000000000001c according to the theory of relativity.

Are those the only two choices? If I bought an instrument that measures the speed of light and it gave me one of those results, I'd want my money back. I could sell you an instrument that measures the speed of light. It would be a little box with a hole in one end. When you shine a light in it, a photo detector inside powers a little display that says "c".

But if you actually wanted to measure the speed of light you would have to start a timer when the light reached you, then put a mirror in front of you some measured distance away and stop the timer when the reflection got back to you. Since the light traveled twice the distance to the mirror, you would calculate the speed of light to be that double distance divided by the reading on the timer. As long as you are not changing your speed while you're doing this, you will always get the same answer, c. Why? That's just the way the universe is.

 

[Bill_K]

But if you actually wanted to measure the speed of light you would have to start a timer when the light reached you, then put a mirror in front of you some measured distance away and stop the timer when the reflection got back to you. Since the light traveled twice the distance to the mirror, you would calculate the speed of light to be that double distance divided by the reading on the timer.

Then there are the people who measure the speed of neutrinos. They obviously don't use a mirror!

 

[ghwellsjr]

Then there are the people who measure the speed of neutrinos. They obviously don't use a mirror!

Aren't they comparing the speed of neutrinos to the speed of light? We can also compare the speed of light coming from two different sources that are traveling at different speeds and determine that the speed of the light does not depend on the speed of
the source. These are both examples of races to see which one wins or if it is a tie but they don't measure the absolute one-way speed, don't you agree?

 

[tiny-tim]

don't we have an FAQ on this? …

https://www.physicsforums.com/showthread.php?t=534862​

 

[rushikesh]

I never understand why the speed of light is the same for all observers irrespective of their motion relative to the source of light. Now suppose I am sitting at the back of a vehicle which is traveling at the speed of 0.999999999999c and light approaches me from behind the vehicle. i.e. I am going away from the source of light while I can still see the light. Now I attach an instrument to my car for measuring the speed of light. Won't it measure 0.000000000001c.

Please help me understand why will the instrument still record 0.999999999999c and not 0.000000000001c according to the theory of relativity.

Yes, all experiments showed this and so we believe in this. But Special relativity did provide an answer for that. Length contraction and time dilation are nothing but an explanation for this phenomenon, is what I have known.

Your instrument will calculate speed of light, by using distance of the source and time taken by light to reach it. Since both the values decrease while in motion, when you will calculate the speed, it will turn out to be 'c'.

But even I'm still not able to use and calculate it mathematically. I am not sure who's length and time we would consider and how exactly the 'instrument' will find it. Maybe anyone would like to help in that?

 

[adjacent]

This may help
https://www.physicsforums.com/showthread.php?t=686876

 

[jtbell]

But even I'm still not able to use and calculate it mathematically. I am not sure who's length and time we would consider and how exactly the 'instrument' will find it. Maybe anyone would like to help in that?

If you post a specific example of a situation which confuses you, and your attempt in calculating it, with some description of what exactly is confusing you, we can help you with it. Please start a new thread for it rather than hijack this one.

 

[nitsuj]

I could sell you an instrument that measures the speed of light. It would be a little box with a hole in one end. When you shine a light in it, a photo detector inside powers a little display that says "c".

 

[ghwellsjr]

Yes, all experiments showed this and so we believe in this. But Special relativity did provide an answer for that. Length contraction and time dilation are nothing but an explanation for this phenomenon, is what I have known.

Your instrument will calculate speed of light, by using distance of the source and time taken by light to reach it.

No, that is not right. There is no instrument that can measure the one-way speed of light that you are describing here. You cannot measure the time it takes for light to travel a distance. I already described how you measure the round-trip speed of light in post #9:

But if you actually wanted to measure the speed of light you would have to start a timer when the light reached you, then put a mirror in front of you some measured distance away and stop the timer when the reflection got back to you. Since the light traveled twice the distance to the mirror, you would calculate the speed of light to be that double distance divided by the reading on the timer. As long as you are not changing your speed while you're doing this, you will always get the same answer, c. Why? That's just the way the universe is.

Since both the values decrease while in motion, when you will calculate the speed, it will turn out to be 'c'.

Where did you get the idea that both the length and the time decrease while in motion? Please tell me what you are thinking.

But even I'm still not able to use and calculate it mathematically. I am not sure who's length and time we would consider and how exactly the 'instrument' will find it. Maybe anyone would like to help in that?

Even if you had such an instrument that you calibrated to work correctly in one inertial state (by synchronizing two clocks some distance apart), it would no longer work if you accelerated it to a new inertial state or pointed it in a different direction.

 

[rushikesh]

Where did you get the idea that both the length and the time decrease while in motion? Please tell me what you are thinking.

I referred to the time dilation and length contraction. But not sure how it applied to that example. Equally confused.

But if you actually wanted to measure the speed of light you would have to start a timer when the light reached you, then put a mirror in front of you some measured distance away and stop the timer when the reflection got back to you. Since the light traveled twice the distance to the mirror, you would calculate the speed of light to be that double distance divided by the reading on the timer. As long as you are not changing your speed while you're doing this, you will always get the same answer, c.

I don't think practically it is possible to do this, due to the high speed of light. Do you know experiments that are actually done? Do they have the same set up or some other techniques?

 

[ghwellsjr]

Where did you get the idea that both the length and the time decrease while in motion? Please tell me what you are thinking.

I referred to the time dilation and length contraction. But not sure how it applied to that example. Equally confused.

Are you aware that Dilation means "expansion", not "contraction"?

Even if you had such an instrument that you calibrated to work correctly in one inertial state (by synchronizing two clocks some distance apart), it would no longer work if you accelerated it to a new inertial state or pointed it in a different direction.

I don't think practically it is possible to do this, due to the high speed of light. Do you know experiments that are actually done? Do they have the same set up or some other techniques?

Sure, read this.

 

[phyti]

Are you aware that Dilation means "expansion", not "contraction"?

Yes it does, but that also means there are fewer 'ticks' while moving a fixed distance at a slower speed.

 

[ghwellsjr]

Yes it does, but that also means there are fewer 'ticks' while moving a fixed distance at a slower speed.

I think you mean "at a faster speed"? But even without Special Relativity there will be fewer 'ticks' the faster a clock moves a fixed distance. I don't understand how this helps interpreting rushikesh's comment:

Length contraction and time dilation are nothing but an explanation for this phenomenon, is what I have known.

Your instrument will calculate speed of light, by using distance of the source and time taken by light to reach it. Since both the values decrease while in motion, when you will calculate the speed, it will turn out to be 'c'.

Are you supporting his comment?

 

[nitsuj]

You had asked me how my contraction comment applied to light approaching at a 90 degree angle in the closed thread. What is the comparative speed to the light source in that situation? you call time dilation "expansion" just because of the comparative of proper time over the same distance across spacetime.

For the made up calculations you don't see a problem with this statement you made were you double the distance because the ruler is contracted 50%?

If we have a length contracted ruler, say to 50%, then we will think that the distance to the mirror is 20 feet [double the length?] and we will calculate the speed of light to be 40 feet per 20 nsec or 2 feet per nsec.

 

[ghwellsjr]

You had asked me how my contraction comment applied to light approaching at a 90 degree angle in the closed thread. What is the comparative speed to the light source in that situation?

Your comment was similar to rushikesh's in that the calculation of the speed of light (length divided by time) would come out the same because both parameters were equally "retarded" and I just wanted you to think about the situation where the length for a calculation applied at 90 degrees to the direction of motion would not be retarded and yet the speed of light still comes out to be c. The light source never has any bearing on the speed of light. It is defined to be c in all inertial reference frames.

you call time dilation "expansion" just because of the comparative of proper time over the same distance across spacetime.

I was talking about comparing the spacing of the Proper Time tick marks on a spacetime diagram to the coordinate time markings.

For the made up calculations you don't see a problem with this statement you made were you double the distance because the ruler is contracted 50%?

If we have a length contracted ruler, say to 50%, then we will think that the distance to the mirror is 20 feet [double the length?] and we will calculate the speed of light to be 40 feet per 20 nsec or 2 feet per nsec.

No, I don't see a problem. If you are measuring the round-trip speed of light to a mirror that is 10 feet away and your ruler is actually only six inches long but claims to be 12 inches long, then you will measure the distance to be 20 feet in one direction or 40 feet for the round trip.

All I'm trying to point out is that if we recognize that time gets "dilated" (or expanded, because that's what the word means) and length gets contracted, then it's less likely that someone will jump to the conclusion that the calculation of the speed of light (being length divided by time) remains at c simply because the effects "cancel out".

 

[phyti]

I think you mean "at a faster speed"? But even without Special Relativity there will be fewer 'ticks' the faster a clock moves a fixed distance. I don't understand how this helps interpreting rushikesh's comment:

Are you supporting his comment?

My comment poorly worded. Should be something like "the converse of time dilation is fewer ticks".

As to the op:

Using a=v/c and substituting based on x=ct

x' = γ(x-vt) = γx(1-a)

t' = γ(t-vx/cc) = γt(1-a)

x'/t' = x/t

The moving frame is a scaled version of the 'rest' frame, therefore
the expressions involving x and t are equivalent (including light speed).
This requires x and t to change by the same proportion (γ).

also refer to the drawing

https://www.physicsforums.com/attachments/64995

 

[ghwellsjr]

As to the op:

Using a=v/c and substituting based on x=ct

If you are going to limit x to be equal to ct, then you are only concerned with events that are light-like.

x' = γ(x-vt) = γx(1-a)

t' = γ(t-vx/cc) = γt(1-a)

x'/t' = x/t

You should add that both of these factors are equal to c (because you made that limitation to begin with).

The moving frame is a scaled version of the 'rest' frame, therefore
the expressions involving x and t are equivalent (including light speed).

You should say that this is true only for light speed.

This requires x and t to change by the same proportion (γ).

But that proportion is not equal to γ. In fact, you can derive it if you just added a couple more steps:

t' = γt(1-a)

t'/t = γ(1-a)

So, for example, at a=0.6, γ=1.25 and t'/t = 1.25(1-.6) = 1.25(.4) = 0.5.

This is actually the relativistic Doppler factor (or its reciprocal) and not gamma.

also refer to the drawing

https://www.physicsforums.com/attachments/64995

I don't understand your drawing.

 

[ghwellsjr]

I never understand why the speed of light is the same for all observers irrespective of their motion relative to the source of light. Now suppose I am sitting at the back of a vehicle which is traveling at the speed of 0.999999999999c and light approaches me from behind the vehicle. i.e. I am going away from the source of light while I can still see the light. Now I attach an instrument to my car for measuring the speed of light. Won't it measure 0.000000000001c.

Please help me understand why will the instrument still record 0.999999999999c and not 0.000000000001c according to the theory of relativity.

I'd like to draw you some spacetime diagrams that illustrate how Special Relativity handles moving observers that all measure the speed of the same flash of light even though they are moving at different speeds relative to the light source but the speed you presented will require a huge diagram so I'll do it with smaller speeds.

As I said in post #9, the way you measure the speed of a flash of light that is coming from behind you while you are sitting in the back of a vehicle is to start a stopwatch when you first see the flash of light coming from behind and then let it reflect off of a mirror some measured distance, I'll use six feet, in front of you and stop the timer when you see the reflection.

Here is a spacetime diagram depicting this scenario starting with you stationary with respect to the light source. You are shown as the blue line and your mirror is shown as the green line. The dots mark off one-nanosecond increments of your time. The flash of light is shown as the black line:

When the flash reaches you, you reset your stopwatch to zero. It takes six nsecs for the flash to continue on to the mirror and another six nsecs for the reflection to get back to you. You stop the stopwatch at 12 nsec. Since the light had to travel double the distance to the mirror, you calculate the speed of light to be 12 feet divided by 12 nsecs or 1 foot per nanosecond.

Now we'll repeat the measurement but this time assuming that you are traveling at 60%c with respect to the same light source and according to the same reference frame as before. Gamma, γ, at this speed for you is 1.25 meaning that the dots marking off 1-nsec intervals of time will be stretched out to 1.25 times the Coordinate Time markings. In other words, the Coordinate Time is dilated from 12 nsecs in the first diagram to 15 nsecs in this diagram. Special Relativity says that the distance to your mirror will be contracted by the reciprocal of gamma or 0.8 times what it was at rest. Since it was 6 feet at rest, the distance to your mirror now will be 4.8 feet of Coordinate Distance as you can see in the following diagram:

Many people think that you measure the same speed for light because both the distance and the time are reduced by the same factor and "cancel" each other out but the exact opposite is what is true as you can see in the diagram. And it's important to use the Coordinate Time because that is the frame in which the light travels at c. Because the mirror is moving away from the location where you started the stopwatch, it takes longer for the light to reach the mirror (although you have no awareness of this). And because you are moving towards the location of the reflection, it takes less time for the reflection to get back to you (again, you have no awareness of this). So, in fact it is a distance expansion divided by the Time Dilation factor that cancels each other out and results in the speed of light continuing to be the same. The distance expansion is shown in the diagram as the sum of 12 feet for the light to get from you to your mirror and 3 feet for the reflection to get from the mirror back to you for a total distance the light has to travel of 15 feet and it takes 15 nanoseconds resulting in a speed of 1 foot per nanosecond. It is important to realize that the distance to your mirror must contract in order for the measurement to come out the same. If it didn't, the light would have to go farther in both directions taking longer and you would get a smaller measurement for the speed of light.

But, as I said before, you have no awareness of this Time Dilation from 12 nsecs to 15 nsecs. To you, it is still 12 nsecs because that's what your stopwatch measures. And you have no awareness that in this frame, the distance to your mirror is closer to you than it was while you were at rest because any ruler that you use to measure the distance is contracted by the same amount.

Now let's repeat the measurement for you traveling a little faster, at 80%c. At this speed, gamma is 1.667 (one and two-thirds). Here is a new spacetime diagram:

As you can see, the Time Dilation has grown to 20 nsecs and your mirror is now 3.6 feet away and the distances the light has to travel have increased to 18 feet going and 2 feet returning for a total of 20 feet so the speed of light is 20 feet per 20 nsecs or 1 foot per nsec. Again, you have no awareness of these numbers. To you, it is still a total of 12 feet in 12 nsecs.

Have you noticed the trend in how the diagrams show that the mirror gets closer to you and the dots marking your 1-nsec tick marks get farther apart? Now, in an attempt to get as close to your desired speed as possible and still draw a decent diagram, I have made one more at a speed of 98%c where gamma is 5.025:

Notice that this is at a different scale from the previous diagrams. Notice that your tick marks are spaced slightly more than 5 nsecs apart and that the total time is expanded to 60.3 feet and distance to your mirror is contracted to less than 1.2 feet. The distances the light has to travel have also expanded to just under 60 feet going and just over 0.3 feet returning for a total of 60.3 feet resulting in a speed of 60.3 feet divided by 60.3 nsecs or 1 foot per nanosecond.

If we tried to make a diagram for your target speed of 0.999999999999c, gamma would be 707106.78 which would make the diagram incredibly large if you want to actually see the details. But you could do all the calculations and show that the Time Dilation, Length Contraction and distance expansion for the light paths would still result in the light speed being 1 foot per nanosecond. But again, you would have no awareness of any of this. It's no different for you than it was when you were at rest in the frame.

 

[rushikesh]

ghwellsjr, btw what software do you use to draw these diagram??

 

[ghwellsjr]

ghwellsjr, btw what software do you use to draw these diagram??

I wrote my own application using a programming language called LabVIEW.

 

[nitsuj]

Your comment was similar to rushikesh's in that the calculation of the speed of light (length divided by time) would come out the same because both parameters were equally "retarded" and I just wanted you to think about the situation where the length for a calculation applied at 90 degrees to the direction of motion would not be retarded and yet the speed of light still comes out to be c. The light source never has any bearing on the speed of light. It is defined to be c in all inertial reference frames.

It's about the comparative geometry between the two, including the difference in claiming what is simultaneous.

I was talking about comparing the spacing of the Proper Time tick marks on a spacetime diagram to the coordinate time markings. No, I don't see a problem. If you are measuring the round-trip speed of light to a mirror that is 10 feet away and your ruler is actually only six inches long but claims to be 12 inches long, then you will measure the distance to be 20 feet in one direction or 40 feet for the round trip.

Huh? Who's measure of twelve feet? Who's measure of 20 feet. To your point everyone measures c to be the same. If time is retarded, so is length. If you wish to consider angles of approach to direction of motion, then consider simultaneity. Such as an analog clock in motion, the dials don't move at a constant speed around the face.

All I'm trying to point out is that if we recognize that time gets "dilated" (or expanded, because that's what the word means) and length gets contracted, then it's less likely that someone will jump to the conclusion that the calculation of the speed of light (being length divided by time) remains at c simply because the effects "cancel out".

We must conceptualize this completely different. It was one of the other pf'ers that mentioned a term "Rate Contraction" imo it's a great term. The effects on time/length do change equally and in turn motion has no impact on mechanics.

I'm poor at wording these things, so here is a copy n paste from South Whales U website

"If they agree on the speed of light, but disagree on measurements of time, they must inevitably disagree on length as well. If you observe someone's clocks run slowly by a factor γ, you will also observe her rulers to be short by a factor of γ: that's the only way that she can measure the speed of light to have the same value you get."

 

[ghwellsjr]

Your comment was similar to rushikesh's in that the calculation of the speed of light (length divided by time) would come out the same because both parameters were equally "retarded" and I just wanted you to think about the situation where the length for a calculation applied at 90 degrees to the direction of motion would not be retarded and yet the speed of light still comes out to be c. The light source never has any bearing on the speed of light. It is defined to be c in all inertial reference frames.

It's about the comparative geometry between the two, including the difference in claiming what is simultaneous.

Of course it's about the geometry, but it's not about simultaneity in this geometry. And in this geometry that I asked you to think about, there is no Length Contraction, only Time Dilation. So why would you claim that the way Special Relativity "explains" how a moving observer can measure the speed of light to be c is that Length Contraction and Time Dilation are both retarded to the same degree? That's my question for you and you didn't address it.

I was talking about comparing the spacing of the Proper Time tick marks on a spacetime diagram to the coordinate time markings.


No, I don't see a problem. If you are measuring the round-trip speed of light to a mirror that is 10 feet away and your ruler is actually only six inches long but claims to be 12 inches long, then you will measure the distance to be 20 feet in one direction or 40 feet for the round trip.

Huh? Who's measure of twelve feet? Who's measure of 20 feet.

Huh? I never said anything about twelve feet. I said, if you have a ruler that is only six inches long (one-half foot) but is marked as being 12 inches long (one foot) and you measure a distance that is 10 feet, you will think it is 20 feet.

To your point everyone measures c to be the same. If time is retarded, so is length. If you wish to consider angles of approach to direction of motion, then consider simultaneity. Such as an analog clock in motion, the dials don't move at a constant speed around the face.

Time isn't retarded, it's expanded. That's what dilated means.

I don't see why you want to confuse this issue by bringing up an analog clock. An analog clock in motion (provided the motion is not parallel to the axis of the shafts of the dials) is not even round, it is oval shaped. Not only do the dials not move at a constant speed, they don't even remain at a constant length. Their lengths change as they go around. So what? We're not talking about that. We're talking about how a moving observer has a Length Contracted ruler to measure the distance to a mirror and a Time Dilated stopwatch (or timer or clock) that is colocated with him. The answer that we supply has to work for all orientations of the ruler and mirror with respect to the direction of motion. Can you please address that issue and not bring up side issues?

All I'm trying to point out is that if we recognize that time gets "dilated" (or expanded, because that's what the word means) and length gets contracted, then it's less likely that someone will jump to the conclusion that the calculation of the speed of light (being length divided by time) remains at c simply because the effects "cancel out".

We must conceptualize this completely different. It was one of the other pf'ers that mentioned a term "Rate Contraction" imo it's a great term. The effects on time/length do change equally and in turn motion has no impact on mechanics.

As I so carefully pointed out in post #26, motion has everything to do with why (according to Special Relativity) a moving observer measures the speed of light to be c even when light is traveling at c in the frame in which he is in motion. It's a combination of his Time Dilated stopwatch, his Length Contracted ruler, and his motion, for the case where he is measuring along the direction of motion. If he's measuring perpendicular to his direction of motion, then it is a combination of just his Time Dilated stopwatch and his motion since his ruler is not Length Contracted in this case.

Did post #26 make sense to you?

I'm poor at wording these things, so here is a copy n paste from South Whales U website

"If they agree on the speed of light, but disagree on measurements of time, they must inevitably disagree on length as well. If you observe someone's clocks run slowly by a factor γ, you will also observe her rulers to be short by a factor of γ: that's the only way that she can measure the speed of light to have the same value you get."

That's a rather surprising comment to make since at the top of their webpage, they gave an example of Zoe's light clock oriented perpendicular to her direction of motion and although she and her car are Length Contracted along her direction of motion, the width of her car and the distance between her mirrors are not Length Contracted.

 

[phyti]

ghwellsjr;4611058

Many people think that you measure the same speed for light because both the distance and the time are reduced by the same factor and "cancel" each other out but the exact opposite is what is true as you can see in the diagram. And it's important to use the Coordinate Time because that is the frame in which the light travels at c. Because the mirror is moving away from the location where you started the stopwatch, it takes longer for the light to reach the mirror (although you have no awareness of this). And because you are moving towards the location of the reflection, it takes less time for the reflection to get back to you (again, you have no awareness of this). So, in fact it is a distance expansion divided by the Time Dilation factor that cancels each other out and results in the speed of light continuing to be the same. The distance expansion is shown in the diagram as the sum of 12 feet for the light to get from you to your mirror and 3 feet for the reflection to get from the mirror back to you for a total distance the light has to travel of 15 feet and it takes 15 nanoseconds resulting in a speed of 1 foot per nanosecond. It is important to realize that the distance to your mirror must contract in order for the measurement to come out the same. If it didn't, the light would have to go farther in both directions taking longer and you would get a smaller measurement for the speed of light.

The question is: “why do all observers measure light speed as constant?”.
All your drawings are showing the different cases from the U perception.
That’s already settled since U is not moving and exempt from lc and td.
It would be more convincing showing perception of the moving observer.

In the following the A perception is overlaid onto the U perception using the same time axis,
and providing a visual comparison.
A has a stick 4 units long (L) with a mirror at the front end.
In each case, a light signal is sent from the origin to reflect from the mirror and return to A
In each case U measures stick length as L/gamma, and A-time equals U-time/gamma.

In fig.1 A is at rest in the U frame.
Light is emitted at A(0, 0), and detected at A(0,8.0).
A calculates* coordinates as A(4.00, 4.00).

In fig.2, A moves at .6c.
Light is emitted at A(0, 0), and detected at A(0, 8.0).
A calculates* coordinates as A(4.0, 4.0).

In fig.3, A moves at .8c.
Light is emitted at A(0, 0), and detected at A(0, 8.0).
A calculates* coordinates as A(4.0, 4.0).

* using SR simultaneity convention

https://www.physicsforums.com/attachments/65069

 

[ghwellsjr]

The question is: “why do all observers measure light speed as constant?”.
All your drawings are showing the different cases from the U perception.

Yes, if by "the U perception", you mean the rest frame of the light source. That's my understanding of what the OP asked about so it shouldn't be surprising that I limited my answer to his question.

That’s already settled since U is not moving and exempt from lc and td.

Yes, if by "U", you mean the light source, since it is at rest in the U coordinate system.

It would be more convincing showing perception of the moving observer.

If by "perception" you mean the rest frame of an observer, then I'm not sure what more there is to show than either your first diagram or my first diagram in post #26 which are essentially identical, don't you agree?

In the following the A perception is overlaid onto the U perception using the same time axis, and providing a visual comparison.

Your overlaid diagrams make it look like the light flash is taking two paths. Is that intentional?

A has a stick 4 units long (L) with a mirror at the front end.
In each case, a light signal is sent from the origin to reflect from the mirror and return to A
In each case U measures stick length as L/gamma, and A-time equals U-time/gamma.

Although that is true, it obfuscates the real relationship of LC and TD. U is the coordinate system. L is the Proper Length and A-time is the Proper Time. So your statement is:

The Coordinate Length is the Proper Length divided by gamma and the Proper Time is the Coordinate Time divided by gamma.

But if we compare apples to apples, we would say:

The Coordinate Length is the Proper Length divided by gamma and the Coordinate Time is the Proper Time multiplied by gamma. That makes the reciprocal (or inverse) relationship between LC and TD more obvious.

In fig.1 A is at rest in the U frame.
Light is emitted at A(0, 0), and detected at A(0,8.0).
A calculates* coordinates as A(4.00, 4.00).

In fig.2, A moves at .6c.
Light is emitted at A(0, 0), and detected at A(0, 8.0).
A calculates* coordinates as A(4.0, 4.0).

In fig.3, A moves at .8c.
Light is emitted at A(0, 0), and detected at A(0, 8.0).
A calculates* coordinates as A(4.0, 4.0).

* using SR simultaneity convention

I don't disagree with any of this but since the OP asked about measuring the value of the speed of light (a round-trip) I didn't bother to mention that the propagation of light is defined to be c (one-way) in any Inertial Reference Frame.

 

[bhobba]

I never understand why the speed of light is the same for all observers irrespective of their motion relative to the source of light.

Well suppose there is a maximum speed, C, information can be sent - it may be infinite which seems the obvious choice - but for the heck of it we will allow for the situation where nature is such that, for some reason, only allows information to be sent at some finite maximum speed.

Now from the Principle Of Relativity that speed must be the same in all inertial reference frames. Since inertial frames are all traveling at constant velocity wrt each other it means if we have a transmitter of information at that maximum speed stationary in a frame, in another frame it will be moving but the speed of that information will be exactly the same ie its speed it independent of the speed of the source.

In fact you can derive the Lorentz transformations using this C - which I have cunningly chosen to suggest the speed of light. It shows there can only be one speed that is the same regardless of the speed of the source.

Now have a look at Maxwell's Equations. The speed of EM radiation does not depend on its source, and it is well known that speed is the speed of light. So, C must be the speed of light.

The bottom line here is C, in the way I have derived the Lorentz transformations above, is simply a parameter whose value needs to be fixed by experiment - it just turns out to be the speed of light.

You will find this way of looking at it in Rindler - Introduction To Special Relativity:
https://www.amazon.com/dp/0198539525/?tag=pfamazon01-20

It also shows how Bell can be accommodated in SR - even though that suggests non local effect can happen instantaneously it can't be used to send information

Thanks
Bill

 

[phyti]

Proper Length divided by gamma and the Coordinate Time is the Proper Time multiplied by gamma.

Yes in the U frame, not in the A frame, which represents all other frames. If light speed is measured in the U frame once as c, it won't be any different the next time. Thus I show from the perspective of A that it is c also regardless of his speed. Overlaying the A view eliminates a 2nd drawing and gives a direct visual comparison.

I don't disagree with any of this but since the OP asked about measuring the value of the speed of light (a round-trip) I didn't bother to mention that the propagation of light is defined to be c (one-way) in any Inertial Reference Frame.

I see the convention as defining equal path lengths since light speed is already declared constant. This should be obvious in Minkowski plots and the MMX, where the question is path length, not light speed. It's also the reason why LENGTH contraction solves the problem.

 

[phyti]

ghwellsjr;
You stated you didn't understand one of my recent drawings, so here is one of yours to show how easy it is to add the moving observers description of events in the same drawing. The sequence of details (red) is: the arc centered on the origin, the vertical from the detection event to the arc, the horizontal to the time axis, a light path to the initial light path, and a vertical to the x axis. With coordinate axes, calculations are not usually needed, and um is not relevant as long as they match, year:light yr, sec:light sec, and in your method, nanosecond:light ns.
Once you have the coordinates, the construction lines can be erased to eliminate clutter.


https://www.physicsforums.com/attachments/65112