
Measuring a property does not set it...
You're not even looking at a photon, you're looking at the net effect of a photon on a detector.
That's why you have red-shift/blue-shift, because the motion of the detector forms part of the property of the photon. The energy imparted depends on the motion of the matter, hence blue light has more energy than red.
So in your head, you set the properties of the photon by measuring them, but in reality those were neither properties of the photon, nor independent of one another....
The light doesn't carry all of the properties (here I'm mentioning its apparent energy changing for red/blue shift), it's properties are NET EFFECTS between the photon and the detectors.
Its also true for other properties too, not just the photons energy, and the corresponding net frequency.
Take two such net oscillations, one in the photon and one in the detector, you now have a net spin, (a photons circular polarization property, or the spin of a particle).
So when measured by detector electron D1, the photon has NetSpin(D1,Photon), but when measured relative to electron D2, our photon has a different value NetSpin(D2,Photon) and so on.
The photon appears to have lots of different NetSpin properties, all at the same time, depending on which detecting electron it is being measured with.
This is the mechanism of Superposition. The photon has lots of spin properties all at the same time.
When the photon is captured by a particular electron, e.g. D2, then NetSpin(D2, Photon) will dominate and it appears to have that spin property.
So two 'entangled' photons, P and Q. They can have the same component of oscillation, and yet when you measure them with different detectors the spin property is different, for different detectors.
What's more if you compare spin property to other properties, there appears to be no correlation.
Properties that, common sense should be related (e.g. up/down left/right polarization and spin), don't seem to correlate to others (like circular polarization).
So you hypothesize that NetSpin must be an independent property.
P and Q head in different directions across the universe.
Photon P is measured by a detector DP, and each time the experiment is performed you get a result (DP1, DP2, DP3, ...DPn) for n experiments.
Photon Q is measured by a detector DQ, and each time the experiment is performed you get a result (DQ1, DQ2, DQ3,....DQn)
Now the magic happens, you want P and Q to be entangled, so you filter for some net properties that are the same.
Perhaps its frequency, perhaps some other motion, some net property NetProp, that you have decided doesn't correlate to NetSpin and thus is 'independent'.
So perhaps in experiment 3, NetProp(P3, DP3) = to NetProp(Q3, DQ3), you decide that the third experiment was successful entanglement, while the others were unsuccessful entanglement.
And now you find also that other properties, like our spin property NetSpin(P,DP3) is equal to NetSpin(Q,DQ3).
AMAZING! you say, for entangled photons P3 and Q3, the act of measuring NetSpin(P3) set the NetSpin to be the same for Q3!
Yet it's impossible, P and Q are across the universe and not connected, but it must be true, because there is no other explanation! (bs).
But P and Q always had the same oscillating component, they were really always 'entangled'.
What you did was filter for the subset of where the *detectors* are oscillating the same way.
The photons, had the same properties, and you've filtered for the detectors that had the same properties, so now ALL the DERIVED properties between photon and detector are now the same.
The only information that travelled across the universe was your "filter for experiment 3" signal!
THE ACT OF MEASURING NetSpin(P3,DP3) DID NOT SET THAT PROPERTY IN PHOTON Q3. The spin property was never a property of P and Q, it was a NET EFFECT of P and Q on a detector.
You could calculate the energy in this net spin too. You could pretend the energy of that spin is carried in the photon. Some sort of angular momentum, or spin momentum perhaps?
But the spin is a net effect, and the apparent energy in that spin is a net effect. Each detector would detect a different 'spin momentum' energy in the photon.
THERE IS NO ENERGY STORES LIKE MOMENTUM, ANGULAR MOMENTUM, and so on, that somehow cause a motion to occur. Because each detector detects different spins, the energy would be different for each, the energy is not carried solely by the photon.
Hence blue light imparts more energy than red-light, even if the blue-light is the same red-light shifted by motion of the detector.
[All entanglement experiments have two flaws: some sort of filtering and the statistical test (e.g. Bells) done on the filtered subset after you've filtered. The information that travels is the filtering signal.]