I Speed of individual photons in a vacuum?

[PeroK]

<bracing for the inevitable followup> "Yeah, but if you could weigh February, what would it weigh?"

In deep space, February is weightless. Is that a good start?

 

[bob012345]

In deep space, February is weightless. Is that a good start?

It's average mass would be approximately $\frac{28.25}{365.25}$ of the mass of one year ignoring the position-time uncertainty relationship.

 

[Steve4Physics]

A bit ‘late in the day’, but can I add this. (on the original subject of photon speeds) ...

In positron emission tomography (PET) scans, each electron-positron annihilation produces a pair of gamma photons. These are emitted simultaneously in (almost) opposite directions.

For such a pair of photons, using suitable coincidence circuitry, the time-difference between photon arrivals at different detectors allows the position of the annihilation to be found. (And knowing many such positions allows image reconstruction.)

(That’s somewhat of an oversimplification of course!)

The technique utilises the fact that individual gamma photons have equal speeds (c) – at least within some acceptable uncertainty range.

The approach can used to measure the speeds of individual gamma photons (by using unequal source-detector distances and delayed-coincidence circuitry).

Following a quick search, here is the abstract from what appears to be such an experiment (from 1951!):
https://journals.aps.org/pr/abstract/10.1103/PhysRev.84.271
Unfortunately I can’t access the full reference to read it.

 

[hutchphd]

For such a pair of photons, using suitable coincidence circuitry, the time-difference between photon arrivals at different detectors allows the position of the annihilation to be found. (And knowing many such positions allows image reconstruction.)

This is not, to my understanding, an accurate description of the image reconstruction. Instead the fact that the two 511keV gamma photons emitted are anti-colinear (in the COM frame) allows the usual methods of CAT scan reconstruction to be used. They are likely filtered for coincidence detection but the image reconstruction is not a "time of flight" process.

 

[Steve4Physics]

This is not, to my understanding, an accurate description of the image reconstruction. Instead the fact that the two 511keV gamma photons emitted are anti-colinear (in the COM frame) allows the usual methods of CAT scan reconstruction to be used. They are likely filtered for coincidence detection but the image reconstruction is not a "time of flight" process.

Some PET systems use time-of-flight techniques. E.g. see https://info.blockimaging.com/what-is-time-of-flight-pet-scanning.

What I described was (IMO) accurate, though (for brevity and simplicity) very incomplete. That’s why I said it was an 'oversimplification'

The purpose of my post was to explain that it is quite practical to think about individual photons and their speeds. I used time-of-flight PET for illustration. Going into more detail (e.g. photon energies and image reconstruction) would have been an unnecessary distraction.

 

[hutchphd]

That’s why I said it was an 'oversimplification'

Indeed you were careful with that. But the implication I took from your description was that TOF technique alone provided resolution on the scale of the images we all know. That is really not true. Improved correlation of the particular gammas does allow better signal to noise for the image reconstruction.
I thought my initial inference was reasonable from what you wrote and I wanted to disabuse others of said notion. So my reading I was incorrect (but I blame it on you )

 

[Vanadium 50]

TOF PET tells you less than you think. @hutchphd is right - it improves contrast, but it does not have the position resolution you want to measure c accurately.

Signal formation time is 20-30 ns. Because the shape is known, one can infer the start time this to a nanosecond, maybe a little better. That gives you about a one foot position resolution. Two measurements, so you pick up a √2, so you have 8 inches. This is over about two feet, so it's a 30% measurement when all goes well.

Further, the OP specified vacuum. People have an index of refraction of about 1.3. So there's another 30% issue that needs to be understood.

Finally, such counters are timed in assuming the speed of light is c. You're going to find gammas travel at c no matter how fast they really go. The actual effect of a different speed of gammas is to worsen the resolution, not to shift anything in a visible way. If instead of the theoretical 8 inches you might see 9 or ten.

 

[Steve4Physics]

Indeed you were careful with that. But the implication I took from your description was that TOF technique alone provided resolution on the scale of the images we all know. That is really not true. Improved correlation of the particular gammas does allow better signal to noise for the image reconstruction.
I thought my initial inference was reasonable from what you wrote and I wanted to disabuse others of said notion. So my reading I was incorrect (but I blame it on you )

Yes. In retrospect, I should have referred to time-of-flight (TOF) PET rather than just PET.

 

[Steve4Physics]

TOF PET tells you less than you think. @hutchphd is right - it improves contrast, but it does not have the position resolution you want to measure c accurately.

Singnal formation time is 20-30 ns. Because the shape is known, one can infer the start time this to a nanosecond, maybe a little better. That gives you about a one foot position resolution. Two measurements, so you pick up a √2, so you have 8 inches. This is over about two feet, so it's a 30% measurement when all goes well.

Further, the OP specified vacuum. People have an index of refraction of about 1.3. So there's another 30% issue that needs to be understood.

Finally, such counters are timed in assuming the speed of light is c. You're going to find gammas travel at c no matter how fast they really go. The actual effect of a different speed of gammas is to worsen the resolution, not to shift anything in a visible way. If instead of the theoretical 8 inches you might see 9 or ten.

[Edited to remove duplicated text.]

But I never suggested using PET for photon speed measurements!

I was responding to the original discussions in the thread -the feasibility of measuring the speeds of individual photons. I used (TOF) PET simply to illustrate that the required technology already exists and is in common use.

I also added that speed measurements on single photons had been done over 70 years ago. I don’t have the details but I would expect that the apparatus was a physically small β⁺ source, two collinear ‘arms’ of unequal and adjustable lengths, a suitable time-delayed coincidence circuit and 2 detectors.

 

[Nik_2213]

Two thoughts: would the Michelson–Morley experiment that first falsified the 'luminiferous aether' qualify ?

Also, modern gravitational wave detectors have many light passes through their 'long' orthogonal arms in vacuum. If there was any fluctuation of photon speed, would it show as an interference pattern shimmy ?? Sorta 'line broadening' ??

IIRC, timing correlations between a recent super-nova's gravitational waves and optical FX falsified a bunch of cosmological hypotheses that had proposed varying 'c'...

 

[Son Goku]

I would just note that due to the Reeh-Schlieder theorem there are no states of finite support with a well-defined particle number. This is what ultimately prevents the definition of a position operator for any type of particle in QFT.
For massive particles there is the Newton-Wigner operator which was a proposed attempt at a position operator, but these don't even commute at space like distances, nor are they elements of the observable algebra. They aren't true observables.
So for all particles in QFT there is really just the probability to excite local probes and no sensible notion of position.

 

[Christian Thom]

TL;DR Summary: Does speed of individual photons in a vacuum vary?

Is there experimental evidence that confirms that the speed of individual photons in a vacuum never varies, even slightly?

Thanks in advance.

I worked in a lab that measured the distance Earth to moon with laser pulses, only few photons returned due to the distance, but the assumption that they move at the speed of light was never questioned and results were coherent with the expected movement of the moon, that is of course in the range of accuracy of a few mm with respect to 400000 km.