Unsymmetrical light flash intensity and color shift in SR

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Consider the traditional thought experiment of moving train observers, the "stationary" observers, and the flash of a lightning strike at the midpoint of the train. It seems that the stationary observers would expect the train observers to see different flash intensities (due to different distances traveled by the light) and different color shifts of the light going forward versus backward along the train length. If they do, how do the train observers interpret that? If they don't, how does the stationary observer interpret that?

Ibix
Depends on details of the flash sources. If we use a lightning bolt, it's at rest in the platform frame (the light is emitted by the air). If we're using a lamp or fire cracker it could be at rest in any frame. The Doppler beaming and frequency shifts tell you which frame the source is stationary in, that's all.

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FactChecker
Consider the traditional thought experiment of moving train observers, the "stationary" observers, and the flash of a lightning strike at the midpoint of the train. It seems that the stationary observers would expect the train observers to see different flash intensities (due to different distances traveled by the light) and different color shifts of the light going forward versus backward along the train length. If they do, how do the train observers interpret that? If they don't, how does the stationary observer interpret that?

If distance affects intensity, then we must be talking about an expanding light beam. Or maybe it's an expanding sphere of light.

We can call an expanding blob of light a clock.

So I guess some of the observers are seeing two of those aforementioned clocks, and the two clocks are moving into opposite directions?

Ibix
We can call an expanding blob of light a clock.
Do we?
So I guess some of the observers are seeing two of those aforementioned clocks, and the two clocks are moving into opposite directions?
The intensity measurements are invariant. One frame attributes the different measurements to the source being stationary and the recipients being different distances from it due to their motion. The other frame attributes it to Doppler beaming from a moving source.

I'm not sure where you think clocks come into it.

Nugatory and FactChecker
Do we?
The intensity measurements are invariant. One frame attributes the different measurements to the source being stationary and the recipients being different distances from it due to their motion. The other frame attributes it to Doppler beaming from a moving source.

I'm not sure where you think clocks come into it.

Observer1 pointing to an expanding sphere of light: "That blob of light is standing still and expanding fast"

Observer2 pointing to the same light: "That blob of light is moving fast and expanding slowly"

Observer1 explaining why observer2 said what he said: "In observer2's frame the blob of light moves fast and expands slowly, because the expansion is slowed down by time dilation"

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I have a problem with the relative intensity of the light flash when it reaches the train head versus the intensity when it reaches the tail. On the train, they think that the flash occurred at the midpoint and traveled equal distances in both directions. Their clocks have been synchronized so that the flash reaches both ends simultaneously. Suppose that the length of the flash is very short, the train is very long, and the train speed is very fast. For a person at the station, it would seem that the light wavefront reaches the back of the train before it has spread out much and the intensity would be large. He would also think that the wavefront has spread out much more at the front and the corresponding intensity is small. It seems that we can suppose the length of the light flash and the distance the source moves during the flash can be made negligibly small so that the ratio of intensities is essentially a function of the train length and speed. But how could this make sense to observers on the train? They have the right to assume that their reference frame is stationary.

PS. Sorry. I was so slow in this response that an entire conversation has occurred before I posted it.

Orodruin
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Observer1 pointing to an expanding sphere of light: "That blob of light is standing still and expanding fast"

Observer2 pointing to the same light: "That blob of light is moving fast and expanding slowly"
This is just wrong. If a light source flashes, it results in a spherical light pulse that expands at speed c in all inertial frames. This follows directly from the postulate that the speed of light is invariant.

Pencilvester
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DThe other frame attributes it to Doppler beaming from a moving source.
I see your point. I had neglected that with regard to intensity. I'll buy that, but I will have to think about it.

Thanks. I think that answered my question.

Ibix
This is just wrong. If a light source flashes, it results in a spherical light pulse that expands at speed c in all inertial frames. This follows directly from the postulate that the speed of light is invariant.

Oh. Yes.

But if observer's sight is not perfect, he does not see the fast moving blob of light expanding fast, because almost all of the light is beamed in the forwards direction, so a very dim light shines to all other directions.

I think I need to replace 'time dilating rate of expansion' by 'time dilating rate of loss of intensity'.

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To make this work out, I need to correct something I posted -- that the ratio of the intensities depended on the length of the train. It does not. It only depends on the speed of the train. That makes it possible for the Doppler effect seen by observers on the train to match the intensity ratio effect seen by observers on the ground. Thanks,@Ibix and @Orodruin, it's starting to make sense.

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Dale
pervect
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Consider the traditional thought experiment of moving train observers, the "stationary" observers, and the flash of a lightning strike at the midpoint of the train. It seems that the stationary observers would expect the train observers to see different flash intensities (due to different distances traveled by the light) and different color shifts of the light going forward versus backward along the train length. If they do, how do the train observers interpret that? If they don't, how does the stationary observer interpret that?

I'm not sure if I follow the question exactly - a lightning bolt seems like the wrong image here. Let's imagine two flash bulbs going off at the same location, one stationary relative to a specific observer O, the other moving with respect to O.

We can imagine them going off at the same time, but it becomes a bit tricky to disentangle the two flashes. It's not impossible perhaps to do this, but I'd rather consdier two separate experiments, where we have an identical experimental setup and in one experiment we look at the flash from a stationary bulb, in the other we look at the flash from a moving bulb.

Both flashes will exapand at the velocity c, however, the light from the stationary bulb will not be doppler shifted, while the light from the moving bulb will be doppler shifted.

There will also be relativistic beaming effects from the moving bulb - light that is blue shifted will also have a greater intensith (more photons/second with a photon view).

https://en.wikipedia.org/w/index.php?title=Relativistic_beaming&oldid=823233622

Relativistic beaming (also known as Doppler beaming, Doppler boosting, or the headlight effect) is the process by which relativistic effects modify the apparent luminosity of emitting matter that is moving at speeds close to the speed of light.

The net result of both effects is that the power density of the light flash will vary as k^2, where k is the doppler shift factor. From a photon point of view, one factor of k comes from more photons/second, the other factor of k comes from ##E = h \nu## and the greater energy of blue shifted light relative to red-shifted light.

k=1 for the stationary bulb, k varies with the angular position of the receiver for the moving bulb due to the doppler effect (longitudinal and transverse doppler effects both apply).

If we assume the power density is spherically symmetrical for the stationary flash bulb, the power recived by any receiver will be independent of the angle and depend only on the radius (as measured in O), the distance from the flash point. We can also integrate the power over the duration of the flash to get the total energy received by the receiver if we wish, this total received energy will be spherically symmetrical by assumption in O.

The power density (or the integrated energy) in frame O . won't be spherically symmetrical for the moving flash bulb, however.

Dale and FactChecker
This is just wrong. If a light source flashes, it results in a spherical light pulse that expands at speed c in all inertial frames. This follows directly from the postulate that the speed of light is invariant.

So whether the light source is moving or not doesn't matter? Would both frames see exactly what they were seeing before if the light source was moved from one frame to the other?

Orodruin
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So whether the light source is moving or not doesn't matter? Would both frames see exactly what they were seeing before if the light source was moved from one frame to the other?
No, there is aberration and Doppler shift. What I was referring to was the overall shape of the signal.

Ibix
I think I need to replace 'time dilating rate of expansion' by 'time dilating rate of loss of intensity'.
No - the inverse square law holds in both frames and the speed of light is invariant, so the intensity change with time is the same. The intensity and wavelength distribution round the sphere is different, that's all.

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PeroK
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Consider the traditional thought experiment of moving train observers, the "stationary" observers, and the flash of a lightning strike at the midpoint of the train. It seems that the stationary observers would expect the train observers to see different flash intensities (due to different distances traveled by the light) and different color shifts of the light going forward versus backward along the train length. If they do, how do the train observers interpret that? If they don't, how does the stationary observer interpret that?

For simplicity's sake, let's just have a light source on the platform. It's often mentioned that different observers "disagree" in SR. But, if the people on the train and the the people on the platform know their SR, then they can not only calculate the energy-momentum of the light source in their own frame, they can perform an energy-momentum transformation and calculate the energy-momentum in any other frame. In that way, both sets of observers agree on the energy-momentum of the light in both frames; and, for observers at rest relative to, moving away from or moving towards the source.

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No - the inverse square law holds in both frames and the speed of light is invariant, so the intensity change with time is the same. The intensity and wavelength distribution round the sphere is different, that's all.

EDIT: I got so confused about the intensity that I'll just delete what ever I said about it.

Let me try just one more time the time dilation thing, but this time with light beams:

Observer1 observes a beam of light moving at speed 0.9 to the left, and an identical beam of light moving to the right also at speed 0.9 c.

By beam of light I mean an expanding beam of light, like the beam of light produced by a flashlight.

Observer2, who is moving to the left relative to observer1, observes the leftwards moving beam moving a bit slower and expanding a bit faster than what observer1 observed, and he observes the rightwards moving beam moving a bit faster and expanding a bit slower than what observer1 observed.

What I mean is that the expansion of the beam is like the Einstein light clock's light's vertical motion, and the beam's motion to the left or to the right is like Einstein light clock's light's horizontal motion.

Do I need to define what "light beam moves at speed 0.9 c" means? Well ... It's the average velocity of the sides of the beam. By 'sides of the beam' I mean that if the center part of the beam is removed, the 'sides of the beam' is what remains.

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