A scientist’s transmitter emits a wavelength

[ramcg1]

OK, so it is not invariant, but it still still does not explain why the energy and momentum in one frame of reference is different to the energy and momentum in another frame of reference. If the object (whether a photon or some other kind of object) is in an intermediary position between the observers then it has two different energy levels at once. If the gamma ray interacts with an atomic nucleus how will Scientist One explain it?

 

[pervect]

Let's be specific: a gamma ray is absorbed by a nucleus. The energy and momentum of the gamma ray is transferred to the nucleus, which recoils and also gains some internal energy.

The amount of energy lost from the gamma ray is the same as the total energy (internal + energy of motion) gained by the nucleus according to scientist 1, and according to scientist 2.

Note that scientist 1 and 2 do not have to agree on the total energy of the gamma ray + nucleus. In fact, they do not. What they do agree about is that the interaction between the gamma ray and the nucleus does not change the total energy of the system (but they don't agree on what the numerical value of that initial energy was).

Note that we've said essentially the same thing before, so please think about this a little bit.

 

[jtbell]

The two scientists agree that the atom has certain "internal" energy levels (-13.6 eV, -3.4 eV, etc. for a hydrogen atom). They disagree about the atom's overall translational kinetic energy, and its momentum, because these depend on the velocity of the atom, which in turn depends on the reference frame. Therefore, they disagree about the atom's total energy (internal + kinetic).

In a photon absorption or emission process, their disagreement about the atom's total energy exactly compensates for their disagreement about the photon's energy. They both agree that the total energy of the system before the absorption or emission equals the total energy afterwards, although they disagree on its amount.

 

[ramcg1]

“Let's be specific: a gamma ray is absorbed by a nucleus. The energy and momentum of the gamma ray is transferred to the nucleus, which recoils and also gains some internal energy.

The amount of energy lost from the gamma ray is the same as the total energy (internal + energy of motion) gained by the nucleus according to scientist 1, and according to scientist 2.

Note that scientist 1 and 2 do not have to agree on the total energy of the gamma ray + nucleus. In fact, they do not. What they do agree about is that the interaction between the gamma ray and the nucleus does not change the total energy of the system (but they don't agree on what the numerical value of that initial energy was).”

So Scientist One could detect his Long Wave Photon with an aerial but Scientist Two needs a nucleus to absorb the gamma ray.

 

[Boustrophedon]

Clarifying Einstein synchronisation

So then answer what the time difference is between the emittance and absorption of the photon for an Einstein clock synchronized frame of reference.
I say it is zero, what do you say?

Let's take a "practical" example, say we put clocks everywhere between us and some object X which is 5 light hours away from us, which, for symplicity's sake, is at rest relative to us.
We synchronize all clocks using Einstein's method.
Then say at 10:30 in the morning we emit a photon in the direction of the object X. What will be the time, on the local clock near the object, when the photon is absorbed?

Simple. It will be 3:30 in the afternoon. Einstein synchronisation means that if a light signal is sent from A to B and instantly returned back to A then B's clock at the moment of reception/return is set to half way between A's emission time and reception time. So in practice B starts by setting his clock to zero when he receives/retransmits the signal and when A sends a later message to B indicating A's two times, B can advance his own clock by the average of A's two times. "Relativity of simultaneity" comes about simply because from another inertial frame with respect to which A and B are in colinear uniform motion at the same velocity, the moment of signal reflection at B does not occur halfway between A's emission and reception.

Furthermore, it is especially important to note that reciprocal time dilation also arises naturally from this difference in synchronisation and thus simultaneity, without the need for any difference in actual clock rates !