[Halc]

So if the source emits one photon, what portion if its energy arrives t seconds behind it?

A photon arrives when it arrives.  One photon does not have a meaningful amount of power, but that seems to be what you're asking here.

[james fairclear (OP)]

Is red shifted light travelling at a speed less than c?

In a vacuum, no.  Still c.  So I can reflect a beam of light with say a receding mirror and the light comes back to me at c, but lower energy (red-shifted).

Light emitted from a light source moving away from an observer at a speed v would intuitively be expected to be travelling at a speed c – v

This isn't even true of waves in a medium like sound or water waves.  You're correct that in fact it is still measured at c.

One can visualise it as follows:

A Quanta of light  (Photon) is released from moving light source. The next quanta (Photon) is released at a distance d from the first. Thus a relatively stationary observer will observe a greater distance between each quanta than an observer in the same inertial frame of reference as the moving light source; this is manifested as an increase in wavelength or decrease in frequency.

This makes it sound like the frequency of light is the rate at which the quanta arrive.  Not so. Each photon has a frame dependent frequency, and a light source emitting photons at 10x the rate of another is just brighter, not shifted to a different frequency.

If the wave from a stationary light source has a length L then the wave from a moving light source has a length L + n.
If we consider that the full energy of the photon only arrives at the crest of the wave then the amount of energy arriving per second from the moving light source is less than that from the stationary light source. It takes longer for a FULL quanta of light to reach a point A where the light source is moving in a direction away from A than light from a relatively stationary source.

This is a way of looking at it, yes.  It works when you do the moving mirror thing I mentioned, but the bit about partial-quanta of light makes no sense. It wouldn't be quanta if it could be emitted and detected over a space of time.

Although energy from each quanta of light will arrive in a continuous stream as its waveform unfolds it cannot accurately be said to have arrived until the whole packet of energy has been absorbed at the destination point. As an analogy a locomotive leaves station A and collects one mile of carriages in front of it on its way to station B. The first carriage being pushed by the locomotive may arrive at a station B at 09:00 but the locomotive doesn’t arrive until 09:03.

Photons are detected as a single event, not some spread out stream. They behave like particles when absorbed. The train analogy doesn't really work here.

The speed of each quanta should be more accurately calculated as distance/time where time is the interval between the FULL quanta being discharged at source and the FULL quanta being fully absorbed at the destination. As its wavelength increases there can be a considerable interval between the arrival of the front of the wave and the back of the wave.

Umm...  no.

In conclusion red shifted light from a receding light source can be measured in terms of the quantity of energy transmitted and received per second as travelling at a speed less than c.

Yes except for the speed less than c bit.  Yes, it is slowed by lack of a vacuum between source and detection, but there is no slowing because of spread-out emission and detection.

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

So if the source emits one photon, what portion if its energy arrives t seconds behind it?

A photon arrives when it arrives.  One photon does not have a meaningful amount of power, but that seems to be what you're asking here.

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

The train analogy doesn't really work here.

Depends on how you look at it.  The loco arrives after the first carriage, but it has travelled at the same speed.  Isn't that a simple answer to the original question?

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

Problem with the "stretched wave" model is that light from astronomically distant sources arrives pretty much as individual photons, not as a continuous wave.  We measure their energy and find it has shifted. The Pound-Rebka experiment measured the gravitational energy shift of single photons by comparing it with Doppler shift.

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

Just a thought, could be very wide of the mark.

All light = energy, but not all energy = light.  Therefore, the only factor in this scenario that is relevant to the speed of light is T; t relates to energy that is not light.

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

Photon absorption time is independent of red shift.

No problem with that, but, quickly dinning my nit-picker’s hat, I look for something that might be still unanswered.
If a redshifted photon has reduced energy when it arrives, where is the missing energy that point? 
Has it been lost (absorbed?) along the way, or will it arrive later, as OP seems to suggest (T+t)? 
What role did the increasing distance between source and target play?

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

Photon absorption time is independent of red shift.

No problem with that, but, quickly dinning my nit-picker’s hat, I look for something that might be still unanswered.
If a redshifted photon has reduced energy when it arrives, where is the missing energy that point? 
Has it been lost (absorbed?) along the way, or will it arrive later, as OP seems to suggest (T+t)? 
What role did the increasing distance between source and target play? 

There is no "missing energy".  There is just the energy of the light as measured in the frame of the source, and the energy as measured in the frame of the receiver. Energy conservation only works when working in a single frame of reference and can't be applied between frames.
Example,  I am in the back of a truck moving at 10 m/sec away from you, and toss a 0.1kg ball back towards you at 15 m/sec as measured relative to myself. The ball has a KE of 0.1kg(15m/sec)^2/2 = 11.25 joules as measured from my frame of reference.  But the same ball is only moving at 5 m/sec relative to you and has 1.25 joules of KE as measured from your frame. The ball hasn't "lost" 10 joules of energy on it's way to you, we just measure a different KE for the ball relative to ourselves. 
With light there is no difference in velocity in the light as measured by source and receiver, But, just like with the ball, there is a difference in the energy measured by the two frames. With light, this is exhibited by a diffrence in measured frequency.

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

Except that a photon arrives all at once, regardless of its energy.

A lot of people have a problem with duality because they confuse the  mathematical model of the universe with what actually happens. It turns out that we need two different models to predict our observations, but that doesn't mean that a photon or electron "is" a wave or a particle depending on who is looking at it or when.

The principal characters in "The Big Bang Theory" are very well drawn. Theoretical physics is vanity, experimental physics is humility. And cheesecake is delicious - but that's for another thread.

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

However if you measure velocity in terms of the time it takes for a given quantity of energy emitted to arrive at the destination

But we don't.

The dimensions of velocity are LT^-1

Time per unit energy is M^-1L^-2T³

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[james fairclear (OP)]

It is known that the maximum possible speed of movement of material objects or the propagation of any signals is the speed of light in a vacuum. It is denoted by the letter c and is almost 300 thousand kilometers per second; exact value c = 299 792 458 m / s. The speed of light in vacuum is one of the fundamental physical constants. The impossibility of achieving speeds exceeding c follows from Einstein's special theory of relativity (STR). If it were possible to prove that the transmission of signals with superluminal speed is possible, the theory of relativity would fall. So far this has not happened, despite numerous attempts to refute the ban on the existence of speeds greater than s. However, in recent experimental studies, some very interesting phenomena have been discovered that indicate that under specially created conditions superluminal speeds can be observed and the principles of the theory of relativity are not violated.

THANK YOU FOR ALL YOUR FEEDBACK ON THIS PROPOSITION. I HAVE NOW CONCLUDED THAT MY THINKING WAS FLAWED. 

[pzkpfw]

That's quite some flounce.

[james fairclear (OP)]

flounce

No quite the opposite of a flounce, I am stating this seriously as my thinking has indeed been flawed.

[Halc]

I am stating this seriously as my thinking has indeed been flawed.

Fine, but you don't need to post it 15 times.
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