Question about photons traveling on same path

[stever]

if photons are traveling on the same path, and in only one direction, are they sometimes passing each other? Or are they staying in sequence? Assume the sources for these photons are variously moving in relation to each other. .

 

[HallsofIvy]

Since all photons travel at the same speed, c, regardless of the speed of their sources, no, one photon cannot pass another.

 

[stever]

Since all photons travel at the same speed, c, regardless of the speed of their sources, no, one photon cannot pass another.

does this mean that the speed of the photons in relation to their sources can vary if the source's speeds vary?

 

[Nugatory]

does this mean that the speed of the photons in relation to their sources can vary if the source's speeds vary?

No. A flash of light travels at $c$ relative to everything - its source, its target, and anything else in its vicinity - no matter how these are moving relative to one another.

(You'll notice that I said "flash of light" instead of "photon". It's not a big deal in the relativity forum because everyone here automatically makes the mental substitution when we see the word "photon"... but photons aren't what you're thinking they are).

 

[Ibix]

does this mean that the speed of the photons in relation to their sources can vary if the source's speeds vary?

Depends what you mean by "speed of the photons in relation to their sources"..

If you mean "what speed will an observer riding on a flashlight measure for the light being emitted", then this is always c.

If you mean "what rate of change of separation will some other observer (moving relative to the flashlight) measure between the flashlight and the light it emits", then from this perspective the distance between the flashlight and the light it emits will grow at c-v, not c. This is becaue they, too, will measure the light to be traveling at c.

 

[stever]

Depends what you mean by "speed of the photons in relation to their sources"..

If you mean "what speed will an observer riding on a flashlight measure for the light being emitted", then this is always c.

If you mean "what rate of change of separation will some other observer (moving relative to the flashlight) measure between the flashlight and the light it emits", then from this perspective the distance between the flashlight and the light it emits will grow at c-v, not c. This is becaue they, too, will measure the light to be traveling at c.

If a flashlight varies in speed, what becomes different about the flashlight so that the speed of light stays the same for the observer on the flashlight?

 

[Mister T]

If a flashlight varies in speed, what becomes different about the flashlight so that the speed of light stays the same for the observer on the flashlight?

Nothing. There's no difference between a flashlight in uniform motion and a flashlight at rest. The Principle of Relativity asserts that all inertial reference frames are the same, so if there were something different about a moving flashlight that thing that's different would give us a way to distinguish between two inertial frames.

And there's nothing different about the light, either. It's the speed itself that's invariant, or in other words the same in all frames of reference.

 

[Nugatory]

If a flashlight varies in speed, what becomes different about the flashlight so that the speed of light stays the same for the observer on the flashlight?

Suppose that I am at rest and shining a flashlight in front of me. Meanwhile, you are flying past me at .5c and shining a flashlight in front of you. Your speed relative to me is .5c; the speed of the light from both your flashlight and mine relative to me is c; and the speed of the light from both your flashlight and mine relative to you is c.

However, we could just as well describe this situation from your point of view: I'm moving backwards at .5c while you are at rest. The speed of the light from both flashlights relative to both of us is still c. Thus, there's nothing different about either flashlight. They're both acting the same way and it makes no difference which one we consider to be the one that's moving.

This might be a good time to mention that if A is moving at speed $u$ relative to B, and B is moving at speed $v$ relative to C, A's speed relative to C is not the $(u+v)$ that you would expect from classical physics; it is $\frac{u+v}{1+uv/c^2}$. It's an interesting exercise to try setting $u$ or $v$ to c - that's the flashlight problem you posed.

 

[stever]

I think it is being said that changes to a moving object are only apparent to observers in motion relative to that object; the moving object itself can see no difference in itself.

what does a moving observer think or do that would explain how objects, moving in relation to said observer, calculate light to be at c for themselves?

 

[HallsofIvy]

Surely that is not what you meant to say? The idea of objects being able to "calculate light to be at c for themselves" smacks of mysticism! A basic "axiom" of relativity, based on experimental evidence, is that the speed of light, relative to any object, is a constant, c.

 

[stever]

light speed is always calculated. how is it calculated to be at c when for all moving observers it seems not to be at c (for that object).

 

[Nugatory]

light speed is always calculated. how is it calculated to be at c when for all moving observers it seems not to be at c (for that object).

I'm not sure I understand what you mean when you say "for all moving observers it seems not to be at c" - everyone in this thread has been saying that the speed of light is c for all observers.

You might want to try reading about the Michelson-Morley experiment, which was first done well before the discovery of relativity. The idea is simple enough: the Earth is moving through space at many thousands of kilometers an hour, and we can send flashes of light both parallel to and perpendicular to the direction of that motion. Does one of the flashes cover more distance in a given time than the other?

 

[stever]

Ibix said above: if you mean "what rate of change of separation will some other observer (moving relative to the flashlight) measure between the flashlight and the light it emits", then from this perspective the distance between the flashlight and the light it emits will grow at c-v, not c.

 

[Ibix]

Yes. Light always travels at c.

 

[stever]

Ibix said above: "if you mean "what rate of change of separation will some other observer (moving relative to the flashlight) measure between the flashlight and the light it emits", then from this perspective the distance between the flashlight and the light it emits will grow at c-v, not c."

 

[Nugatory]

Ibix said above: if you mean "what rate of change of separation will some other observer (moving relative to the flashlight) measure between the flashlight and the light it emits", then from this perspective the distance between the flashlight and the light it emits will grow at c-v, not c.

OK, I think I see what you mean. The important thing here is that c-v is the difference between the speed of the flashlight relative to the observer (that's v) and the speed of the light relative to the observer (that's c). It's natural, based on intuition from a lifetime of living around slow-moving objects, to assume that it must also be the speed of the light relative to the flashlight - but that's an assumption, and one that turns out not to be correct.

I mentioned the relativistic rule for adding speeds above. We can try it here: We see a flash of light moving at speed c. What is the speed of that light flash relative to a flashlight moving at speed v relative to us? Using the formula above, it is:$$\frac{v+c}{1+vc/c^2}=\frac{v+c}{1+v/c}=\frac{c(v+c)}{c(1+v/c)}=\frac{c(v+c)}{c+v}=c$$

 

[Nugatory]

Hit post too soon... I was going to add:

That the speed of light is the same for all observers has some very surprising consequences, and the relativistic velocity addition formula is far from the most surprising. When we start with the assumption (solidly supported by more than a century and a half of experiments) that the speed of light is the same for all inertial observers, we find ourselves drawn step by logical step to:
1) Relativity of simultaneity, essential for making sense of everything else (google for "Einstein train simultaneity").
2) The Lorentz transformations which relate the times and positions measured by observers in motion relative to one another.
3) The velocity addition formula I've been using, which is derived from the Lorentz transforms.
4) Length contraction and time dilation, also derived from the Lorentz transformations.
5) The impossibility of traveling faster than light.
6) That gravitational waves must also travel at the speed of light.
...
And it just gets more interesting from there. Part of the charm of special relativity is the mathematical price of admission is quite reasonable - everything I describe above can be competently covered with nothing more than high school math and an optional dash of first-year calculus.

 

[stever]

I'm not sure I understand what you mean when you say "for all moving observers it seems not to be at c" - everyone in this thread has been saying that the speed of light is c for all observers.

there is a difference. i am not asking about an observers own c. i mean how can observers in motion explain the c speed for relative moving objects. On the face of it, the light speed would seem to be more or less than c for others, but those others measure there own at c. the question is how to get from the appearance or Newtonian expectation to the reality. not only must there be some reason why this happens, but also a way to do the math.

 

[Nugatory]

On the face of it, the light speed would seem to be more or less than c for others

You'd think so, wouldn't you? That certainly squares with our intuition and it is EVERYONE's first reaction to relativity. It just happens not to be correct, although it is such a good approximation for speeds that are small compared with that of light that we seldom notice.

It's a worthwhile exercise to apply that velocity addition formula to a bullet fired at 300 meters per second (.000001c) from a car moving at 30 meters/second (.0000001c) - you'll see why it's reasonable to just add the speeds and not mess with that $uv/c^2$ correction in the denominator.

Not only must there be some reason why this happens, but also a way to do the math.

There is. I sort of hinted at it above: Start with the assumption (confirmed by enough experiments that we can reasonably choose to run with it and see where it takes us) that the speed of light is constant for all observers; then derive the Lorentz transformations from that assumption; and then watch the velocity addition rule fall out of that.

It's historically quite interesting to follow in Einstein's footsteps (the seminal paper was published in 1905 - "On the electrodynamics of moving bodies", and Google will quickly find it for you). However, the much more modern "Spacetime Physics" by Taylor and Wheeler comes with the advantage of a century of hindsight and refinement and is a much easier way of learning the key concepts and the math.

 

[stever]

is there a way to start with c+v or c-v that one would have expected and then produce the c by means of a verbal description or simple math as to why or how it happens?

 

[PAllen]

is there a way to start with c+v or c-v that one would have expected and then produce the c by means of a verbal description as to why or how it happens?

I don't know about verbal, but it can be done with simple math.

Start with an observer watching a moving ruler (moving along its length). Imagine the ruler has a mirror on one end and flash bulb, detector, and timer on the other. It times from the flash to receipt of the reflection. Then, per the observer watching this measurement, classically, they would expect that the time for the flash to reach the mirror is d/(c-v), and the time for the return is d/(c+v), for a ruler of length d. Thus, they would expect a measured speed of 2d divided by the sum of those times.

However, per SR, they note that the ruler they think of as d, is marked as longer: d /√(1-v₂/c²). This longer ruler is length contracted to d per our reference observer. Thus, they understand that the moving device will consider twice this longer distance to be the distance traveled. They also notice that the clock is running slower than theirs. Each of the trip times would be measured as that trip time multiplied by √(1-v₂/c²). If you do all the algebra, you find that you have explained how the ruler device measures c, from the point of view of the reference observer relative to whom it is moving.

 

[Nugatory]

is there a way to start with c+v or c-v that one would have expected and then produce the c by means of a verbal description as to why or how it happens?

Not that I know of. The problem is that we don't live in a universe in which c+v or c-v should be expected, so that's a bad starting point; you're better off trying to understand why you should stop expecting it. Instead, start with what we do know about the behavior of the universe we live in, and work forward from there to see what we should expect in that universe.

 

[stever]

I don't know about verbal, but it can be done with simple math.

Start with an observer watching a moving ruler (moving along its length). Imagine the ruler has a mirror on one end and flash bulb, detector, and timer on the other. It times from the flash to receipt of the reflection. Then, per the observer watching this measurement, classically, they would expect that the time for the flash to reach the mirror is d/(c-v), and the time for the return is d/(c+v), for a ruler of length d. Thus, they would expect a measured speed of 2d divided by the sum of those times.

However, per SR, they note that the ruler they think of as d, is marked as longer: d /√(1-v₂/c²). This longer ruler is length contracted to d per our reference observer. Thus, they understand that the moving device will consider twice this longer distance to be the distance traveled. They also notice that the clock is running slower than theirs. Each of the trip times would be measured as that trip time multiplied by √(1-v₂/c²). If you do all the algebra, you find that you have explained how the ruler device measures c, from the point of view of the reference observer relative to whom it is moving.

the speed of light on the outgoing trip and on the incoming trip needs correction to c so as to satisfy the observer that the ruler is experiencing speed c in both light directions. the ruler is longer but shortened (has shorter units?) and time slowed. that would have the same effect on the ruler's measurement of light speed in both directions. the shorter units would increase the distance traveled and therefore the speed, I think, and the slowed time would directly increase the speed. it would make the slower trip out measure faster and closer to c, but the faster trip in would measure even more above c. so while the ruler might experience an average light speed of c, it would not be c in both directions.

 

[PAllen]

the speed of light on the outgoing trip and on the incoming trip needs correction to c so as to satisfy the observer that the ruler is experiencing speed c in both light directions. the ruler is longer but shortened (has shorter units?) and time slowed. that would have the same effect on the ruler's measurement of light speed in both directions. the shorter units would increase the distance traveled and therefore the speed, I think, and the slowed time would directly increase the speed. it would make the slower trip out measure faster and closer to c, but the faster trip in would measure even more above c. so while the ruler might experience an average light speed of c, it would not be c in both directions.

If you want to model how a one way measurement by the ruler device comes out c, you have to bring in how the clocks on each end of the ruler are synchronized. By doing round trip, and one clock, I avoided this. If you want to consider it, you would find that in addition to length contraction and time dilation, the two clocks that are synchronized in the ruler frame are not synchronized per the reference observer. If you include this effect (that, at the same time per the reference observer, the two clocks read different time - in addition to being slower), then you will see how both directions measure as c. One reason not to bother with this is that clock standard clock synchronization is defined to produce a one way measurement of c, so this added complexity has no information content. All the real content is in the two way analysis I described.

 

[stever]

clock synchronization is defined to produce a one way measurement of c

so if a clock at the mirror is set back in time by the right amount, it makes the outgoing time less and the light speed greater, and increases the travel time of the return trip, lowering its speed, to c if it is done right. if this is what would happen by definition, just to get equal speeds, and this is not a proof of anything, how can we know that light speed is not different in opposing directions?

 

[PAllen]

so if a clock at the mirror is set back in time by the right amount, it makes the outgoing time less and the light speed greater, and increases the travel time of the return trip, lowering its speed, to c if it is done right. if this is what would happen by definition, just to get equal speeds, and this is not a proof of anything, how can we know that light speed is not different in opposing directions?

We cannot. Only arguments to the effect that "if assuming isotropy simplifies the analysis, then let's assume it" can be brought to bear. It is certainly true that equations become simpler with the isotropic assumption. See: https://en.wikipedia.org/wiki/One-way_speed_of_light

 

[stever]

if light would be traveling at different speeds in opposing directions, what would the implications be? Do you think it is possible?

 

[Nugatory]

if this is what would happen by definition, just to get equal speeds, and this is not a proof of anything, how can we know that light speed is not different in opposing directions?

We don't. It is pretty much impossible to measure the one way speed of light; you need some way to synchronizing the clocks at both ends and all methods of doing that synchronization are directly or indirectly based on the assumption that the one-way speed of light is equal to the speed that we can directly measure in a round-trip experiment. And if you start by assuming what you're trying to prove... You wouldn't have a proof, you'd have circular logic.

Instead, it's a postulate that the one-way speed of light is equal to the measured two-way speed. It's a pretty reasonable postulate, as the alternative would have weirdnesses like the speed of light being different in different directions even in empty space.

 

[HallsofIvy]

is there a way to start with c+v or c-v that one would have expected and then produce the c by means of a verbal description or simple math as to why or how it happens?

No, there is NO way to start with a wrong concept, whether you "expect" it or not.
Please go to the library and get a good introductory text on special relativity. You seem to simply not accept anything anyone is saying here. (You might want to think about why you "expect" c+ v or c- v. What reason do you have for thinking it should be that?)

 

[PAllen]

if light would be traveling at different speeds in opposing directions, what would the implications be? Do you think it is possible?

There are no implications, because we can't tell anything except if we assume isotropy (for clock synchronization and in all our laws of physics), we get the simplest equations. Personally, I take this as a definiiton of physically meaningful isotropy. If our universe was observably anisotropic, that would mean that assuming isotropy leads to excess complications. Note, isotropy of two way light speed is measurable, so if you assume anisotropy it has to be of a very special type.

 

[stever]

There are no implications, because we can't tell anything except if we assume isotropy (for clock synchronization and in all our laws of physics), we get the simplest equations. Personally, I take this as a definiiton of physically meaningful isotropy. If our universe was observably anisotropic, that would mean that assuming isotropy leads to excess complications. Note, isotropy of two way light speed is measurable, so if you assume anisotropy it has to be of a very special type.

I understand your last sentence.
Einstein was complaining about the math complexity for general relativity. perhaps math simplicity can be a false prophet? I don't use math much and I feel more at ease with anisotropy than isotropy with regard to light speeds, as it seems closer to a pre-SR way of seeing. what really puzzles me is time dilation, mass increase and length contraction and what makes them real. maybe I'll look into it some time.

Anyway, I don't have enough time for physics. Thanks for everyones help.