# Traveling toward a light source

#### Thoreau

Valued Senior Member

1) If you have two spinning balls orbiting around each other, would traveling toward the objects at near the speed of light make the two balls APPEAR to be orbiting/spinning faster? Why or why not?

1) If you have two spinning balls orbiting around each other, would traveling toward the objects at near the speed of light make the two balls APPEAR to be orbiting/spinning faster? Why or why not?
No.

1) If you have two spinning balls orbiting around each other, would traveling toward the objects at near the speed of light make the two balls APPEAR to be orbiting/spinning faster? Why or why not?
Yes. Doppler shift. Increased frequency of light from an oncoming source automatically implies increased time-rate for all processes detectable. Including orbiting/spinning speed of the balls. A lot of folks confuse the 'intrinsic' slowing of clocks in relative linear motion aka transverse Doppler shift - with the angular dependent total Doppler shift that may be greater or lesser than for zero relative motion.

There is one Discovery Channel type vid (can't find it right now) featuring Brian Greene, in which he wrongly illustrates a 'poor white trash guy' seeming to move even slower than normal while Brian is walking towards him. Actually, longitudinal Doppler trumps transverse Doppler there and he should have shown the 'white hick guy' speeding up. Even authority figures occasionally goof.

Q-reeus is not quite right.

1) If you have two spinning balls orbiting around each other, would traveling toward the objects at near the speed of light make the two balls APPEAR to be orbiting/spinning faster? Why or why not?
Moving towards the two balls makes time dilate, so they would appear to orbit/spin slower than if the observer was at rest relative to them.

The Doppler shift of the light from the balls is a separate effect that tends to make them look bluer than normal as you approach them.

Q-reeus is not quite right.

Moving towards the two balls makes time dilate, so they would appear to orbit/spin slower than if the observer was at rest relative to them.

The Doppler shift of the light from the balls is a separate effect that tends to make them look bluer than normal as you approach them.
I beg to differ and maintain post #3 has it correct. Longitudinal Doppler blue-shifting of light can only be consistently understood as meaning the light emitting oscillators have a faster detected oscillation rate i.e. frequency. One can't then cherry pick and claim things could reverse for say detected orbital rate of those balls. There must be a consistent operation on all constituents of the system.
Otherwise - a sync paradox arizes. So many beats of an optical oscillator per integer ball orbit or spin must be consistently observed in both the proper frame of the balls centre-of-mass system, and as recorded by an approaching observer.

Remember - the core OP question was "...would traveling toward the objects at near the speed of light make the two balls APPEAR to be orbiting/spinning faster?..." Yes.
Still think otherwise?

Q-reeus:

I beg to differ and maintain post #3 has it correct. Longitudinal Doppler blue-shifting of light can only be consistently understood as meaning the light emitting oscillators have a faster detected oscillation rate i.e. frequency. One can't then cherry pick and claim things could reverse for say detected orbital rate of those balls. There must be a consistent operation on all constituents of the system.
You're confusing the frequency of rotation of the balls with the frequency of the light they emit. Those two frequencies are not the same thing in this example (presumably).

I beg to differ and maintain post #3 has it correct. Longitudinal Doppler blue-shifting of light can only be consistently understood as meaning the light emitting oscillators have a faster detected oscillation rate i.e. frequency. One can't then cherry pick and claim things could reverse for say detected orbital rate of those balls. There must be a consistent operation on all constituents of the system.
Otherwise - a sync paradox arizes. So many beats of an optical oscillator per integer ball orbit or spin must be consistently observed in both the proper frame of the balls centre-of-mass system, and as recorded by an approaching observer.

Remember - the core OP question was "...would traveling toward the objects at near the speed of light make the two balls APPEAR to be orbiting/spinning faster?..." Yes.
Still think otherwise?
But surely the way one observes the spinning balls, as one approaches, is by noting their lateral motion, at right angles to the direction of approach, isn't it? So why would Doppler shift alter that?

Q-reeus You're confusing the frequency of rotation of the balls with the frequency of the light they emit. Those two frequencies are not the same thing in this example (presumably).
Of course we won't have anything like numerical equality between a typical ball-ball orbital frequency around say the mains frequency ~ 50/60Hz, to that of an optical oscillator ca 10^14Hz range.
I'll assume you meant something else like 'the two frequencies are conceptually different things' or suchlike. But they are conceptually the same thing re relativistic considerations. Slight proviso:

It's conceptually cleaner to think of a reference light emitter/oscillator separate from and not orbiting with the ball(s). Just coincident with and stationary wrt their centre of mass. Also, best to specify that the orbital and/or spin axis(s) is/are along the line of relative linear motion. That way we don't have to deal with adding instantaneous orbital motions, to linear relative motion between balls centre of mass system and approaching observer. Thus no messy Doppler 'FM modulation' issues.

But, as per my #5, there MUST for logical consistency be a fixed, frame-independent ratio between the two frequencies. Hence, if one is blue-shifted, the other must be also.

You still wear a hat - perhaps long inactive - over at PhysicsForums? That's the go to site to quiz any of a range of relativity buffs on this one. Feel free to do so and come back with any opinion from such. Just make sure to quote ALL my input on this matter James.
I'm prepared to bet BIG money on this one!

But surely the way one observes the spinning balls, as one approaches, is by noting their lateral motion, at right angles to the direction of approach, isn't it? So why would Doppler shift alter that?
See my elaborations in above post. The issue is garnering more confusion than I expected.

See my elaborations in above post. The issue is garnering more confusion than I expected.
Actually on a bit of further reflection I agree. The rate of lateral oscillation observed would be expected to be raised by the motion towards the source, just as the Doppler effect raises the perceived rate of oscillation of an oncoming wave. But that is just thinking of light as a wave, without taking relativity into account. I'll leave that bit to the physicists......

Q-reeus is not quite right.

Moving towards the two balls makes time dilate, so they would appear to orbit/spin slower than if the observer was at rest relative to them.

The Doppler shift of the light from the balls is a separate effect that tends to make them look bluer than normal as you approach them.
I have to agree with Q-reeus. Assume the balls are orbiting wit a period of 1 sec in their own frame and you are approaching at 0.99 c. According to your frame the objects are orbiting with a period of ~7.1 sec. So the light emitted by the objects when at the one point of the their orbit leaves ~7.1 sec after the object were in that same point in the previous orbit.

When you see the light that leaves the pair at the first instance you see it d/c sec after it left where d is the distance the pair were from you when the light was emitted. In between each successive orbit, the distance between you and the pair decreases by ~7.1 sec x 0.99c = ~7.029 light seconds. This means after each orbit, the light leaving the pair takes ~7.029 fewer seconds to reach you than the light from the previous orbit did. The light carrying the image of the objects for each successive orbit leaves 7.1 sec apart, but arrives at you 7.1-7.029 = .071 sec apart due to the constantly decreasing distance between you and the pair. You will visually see the objects return to the same point of their orbits every 0.071 sec or at a frequency of ~14.08 times that measured in the frame of the pairs barycenter. This is equal to the Relativistic Doppler shift factor for 0.99c ( allowing for rounding errors)

I have to agree with Q-reeus. Assume the balls are orbiting wit a period of 1 sec in their own frame and you are approaching at 0.99 c. According to your frame the objects are orbiting with a period of ~7.1 sec. So the light emitted by the objects when at the one point of the their orbit leaves ~7.1 sec after the object were in that same point in the previous orbit.

When you see the light that leaves the pair at the first instance you see it d/c sec after it left where d is the distance the pair were from you when the light was emitted. In between each successive orbit, the distance between you and the pair decreases by ~7.1 sec x 0.99c = ~7.029 light seconds. This means after each orbit, the light leaving the pair takes ~7.029 fewer seconds to reach you than the light from the previous orbit did. The light carrying the image of the objects for each successive orbit leaves 7.1 sec apart, but arrives at you 7.1-7.029 = .071 sec apart due to the constantly decreasing distance between you and the pair. You will visually see the objects return to the same point of their orbits every 0.071 sec or at a frequency of ~14.08 times that measured in the frame of the pairs barycenter. This is equal to the Relativistic Doppler shift factor for 0.99c ( allowing for rounding errors)
Yes this is more or less where I got to, eventually....I think......

Nice to see a concensus emerging here! Just adding a slightly different angle to the viewpoint presented by Janus58 in #11:
Suppose we arrange to have the point light source blink for every revolution of the orbiting balls. In the centre of mass frame of the balls/light source, a spherical wavefront is emitted, with carrier frequency of the light source, and modulation frequency of the orbiting balls.
The approaching observer sampling that modulated wavefront sees it Lorentz contracted in the observer's rest frame. Hence the sampling rate is raised by the inverse of the Lorentz contraction factor. Which must include both carrier and modulation frequencies. Thus a detected fractional blueshifting of both frequencies equally.
Wikipedia has as expected these days a whole raft of equations covering about every conceivable combination of circumstances, together with nice visuals and rigorous derivations:
https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

And....found it! Referring to my final comments in #3 re Brian Greene's goof. Recollection slightly off - a NOVA special where Brian has the 'poor white trash guy' perceiving Brian slowing down as he approaches. But of course it has to be mutually observed - both see the other slowing down. Except, it should have been speeding up. Anyway, the passage is between ~ 14:30 and 16:00 minute marks here:
Not suggesting BG isn't very smart and usually spot-on - but this is a reminder never to just trust what an authority figures says.

I have to agree with Q-reeus. Assume the balls are orbiting wit a period of 1 sec in their own frame and you are approaching at 0.99 c. According to your frame the objects are orbiting with a period of ~7.1 sec. So the light emitted by the objects when at the one point of the their orbit leaves ~7.1 sec after the object were in that same point in the previous orbit.

When you see the light that leaves the pair at the first instance you see it d/c sec after it left where d is the distance the pair were from you when the light was emitted. In between each successive orbit, the distance between you and the pair decreases by ~7.1 sec x 0.99c = ~7.029 light seconds. This means after each orbit, the light leaving the pair takes ~7.029 fewer seconds to reach you than the light from the previous orbit did. The light carrying the image of the objects for each successive orbit leaves 7.1 sec apart, but arrives at you 7.1-7.029 = .071 sec apart due to the constantly decreasing distance between you and the pair. You will visually see the objects return to the same point of their orbits every 0.071 sec or at a frequency of ~14.08 times that measured in the frame of the pairs barycenter. This is equal to the Relativistic Doppler shift factor for 0.99c ( allowing for rounding errors)
Nice explanation. I agree with your analysis.

To summarise, we need to consider two competing effects:

1. The apparent slowing of the period of the orbit, due entirely to observing it from a different frame of reference (Lorentz time dilation).
2. The apparent speeding of the period due to the Doppler-shifted receipt of the light from the source as the observer approaches (relativistic Doppler shift).

For the particular numbers given above, effect (2) dominates effect (1), and we observe an apparent speeding up of the orbital period.

Bonus question: could a different combination of rotation rate and relative rate of approach result in an observed slowing instead?

Nice explanation. I agree with your analysis....
But not mine? Not prepared to directly concede you were wrong and I was right all along?
To summarise, we need to consider two competing effects:

1. The apparent slowing of the period of the orbit, due entirely to observing it from a different frame of reference (Lorentz time dilation).
2. The apparent speeding of the period due to the Doppler-shifted receipt of the light from the source as the observer approaches (relativistic Doppler shift).

For the particular numbers given above, effect (2) dominates effect (1), and we observe an apparent speeding up of the orbital period....
You think that might only be valid for some particular numerical values? Rather than a general result dependent only on relative approach speed and angle?
Bonus question: could a different combination of rotation rate and relative rate of approach result in an observed slowing instead?
No. Not if the approach is head on, or merely anywhere within the angular cone as specified and illustrated in that linked to Wiki article. Rotation rate is irrelevant in that respect (except for the trivial need to be nonzero). Something you should have deduced by following my argument in #3, and reinforced in #5 and then #8 for good measure.

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But not mine? Not prepared to directly concede you were wrong and I was right all along?
There was ambiguity both in the initial question and in your initial response, regarding how things "appear". That could refer (1) to how things "really are" in the reference frame of the observer, or (2) to how things are "seen" by a particular observer in that frame.

Our of interest, is it important to you that I pat you on the back and congratulate you on being correct?

You think that might only be valid for some particular numerical values? Rather than a general result dependent only on relative approach speed and angle?
I'm not sure, so I've put the question out there for others to consider.

No. Not if the approach is head on, or merely anywhere within the angular cone as specified and illustrated in that linked to Wiki article.

Rotation rate is irrelevant in that respect (except for the trivial need to be nonzero). Something you should have deduced by following my argument in #3, and reinforced in #5 and then #8 for good measure.
It is a pity you didn't make yourself clearer, if a complete explanation was in there somewhere. Janus58 did a much better job there than you did. Are you prepared to directly concede that?

Our of interest, is it important to you that I pat you on the back and congratulate you on being correct?
Given you flat claimed, in two succesive postings #4 & #6, I was wrong, whereas the opposite was the case - most folks with a sense of decency would sort of figure I would be owed at least an apology.
Never mind, this kind of thing tends to reveal true personal character, which manifestation is more significant than the specific case here of not even receiving a voluntary if grudging and belated concession. As for the rest you write and claim in #17, I will only add that imo you are a sore loser James. Prepared to distort matters for personal reasons. But this is SF after all. And the record is there for all to judge.

Given you flat claimed, in two succesive postings #4 & #6, I was wrong, whereas the opposite was the case - most folks with a sense of decency would sort of figure I would be owed at least an apology.
Never mind, this kind of thing tends to reveal true personal character, which manifestation is more significant than the specific case here of not even receiving a voluntary if grudging and belated concession. As for the rest you write and claim in #17, I will only add that imo you are a sore loser James. Prepared to distort matters for personal reasons. But this is SF after all. And the record is there for all to judge.
Why so tetchy? Are you channelling Paddoboy?

Why so tetchy? Are you channelling Paddoboy?
You think there is some 'moral equivalence' between that arsehole's revolting antics and my standing up for myself here?! I pay the penalty for being known as a non-PC non-sycophant. Believe that or not.