[geordief]

Every inertial observer records the same speed of light because of the relationship between time dilation and the speed of light as shown in the Lorentz factor

Could you expand on that point,please?

I thought it was the other way round and the observed invariance of the speed of light (for mutually and inertially  moving frames) led to the Lorentz factor being satisfied.

I admit in advance  to a shaky  understanding of this basic position.

I have also heard that the Lorentz Factor can be "proved" without recourse to the speed of light but have not been able  to actually find such a proof.

[jeffreyH]

Every inertial observer records the same speed of light because of the relationship between time dilation and the speed of light as shown in the Lorentz factor

Could you expand on that point,please?

I thought it was the other way round and the observed invariance of the speed of light (for mutually and inertially  moving frames) led to the Lorentz factor being satisfied.

I admit in advance  to a shaky  understanding of this basic position.

I have also heard that the Lorentz Factor can be "proved" without recourse to the speed of light but have not been able  to actually find such a proof.

If you are moving with a constant velocity without the action of any external forces working on you then you will not be able to tell that you are moving. You can consider yourself at rest. This means that the speed of light in a vacuum will be c for you as well as all other inertial observers. You have to ask yourself why.

[geordief]

 

If you are moving with a constant velocity without the action of any external forces working on you then you will not be able to tell that you are moving. You can consider yourself at rest. This means that the speed of light in a vacuum will be c for you as well as all other inertial observers. You have to ask yourself why

Wasn't relativity  in the sense** you describe well accepted before the  understanding that c  was also the same for all inertial frames?

So that acceptance is surely not enough  for it to be obvious that c applied  in all inertial frames and only MM showed it experimentally.


I am not sure if he was being playful  but Einstein said in one of his publications that (loose quote)" every child knows that the speed of light is always the same"


** it was presumably accepted before Einstein that all "moving" bodies  could  be also considered at rest.

[Colin2B]

Wasn't relativity  in the sense** you describe well accepted before the  understanding that c  was also the same for all inertial frames?

** it was presumably accepted before Einstein that all "moving" bodies  could  be also considered at rest.

It was Galileo who first detailed this and it is still referred to as Galilean Relativity. He used the example of an experimenter below decks, on a ship, who would not be able to tell if the ship was moving by means of experiment. His theory relates to the laws of motion being the same in all inertial frames, whereas Einstein extended it to the laws of physics by including the invariance of light speed - and further extended to noninertial frames.

[geordief]

Einstein extended it to the laws of physics by including the invariance of light speed - and further extended to noninertial frames

Well did Einstein require the experimental verification of MM  to assume the invariance of c in all inertial frames -or did he already  assume this as a result of  Maxwell's findings in Electro Magnetism (and/or Lorentz's work) ?

(Hope I am not being too thick or obtuse;it was Einstein who realized this first ,wasn't it?)

[Colin2B]

Well did Einstein require the experimental verification of MM  to assume the invariance of c in all inertial frames -or did he already  assume this as a result of  Maxwell's findings in Electro Magnetism (and/or Lorentz's work) ?

I don’t think he did need MM, i think he was almost there and the experiment gave him the confirmation to go ahead with his ideas. I think the results of Maxwell’s equations were very important, but not for the reasons we might think.
By Maxwell’s time the wave theory of light (as against Newton’s corpuscular theory) was well established and, like other waves, light was assumed to travel in a medium, the aether. However, Maxwell’s equations don’t refer directly to light, but to the propagation of electric and magnetic fields suggesting that propagation is not instantaneous, as had been suggested, but at the same speed as light. Also, Maxwell’s equations make no mention of reference frames so you could easily assume that the aether, and hence an absolute reference frame, existed. This is in-fact what Einstein started off doing.
When he was around 16 he wrote a paper entitled “The Investigation of the State of Aether in Magnetic Fields” which he sent to his Uncle. The paper is interesting for 2 reasons 1. He appears to have independently deduced the principle of self induction 2. It shows his interest in the problems of electrodynamics - moving electric and magnetic fields - and this topic was central to his development of relativity.
Without going into detail, there were a number of anomalies in the actual behaviour of  electric and magnetic fields that were puzzling. The main one was that if you consider a conductor moving relative to a magnet the current is the same whether you move the conductor or the magnet, but Maxwell’s equations suggest that from the frame of the conductor the charges in the conductor experience an electric force, but in the frame of the magnet they experience a magnetic force, in other words how you describe the laws of physics depends on your reference frame, but that is not what we see in reality.
It is clear that Einstein spent a long time working his ideas and was coming to the conclusion that there was a problem with the way we view time, also with the existence of the aether and hence the variance of light speed. So I don’t think the MM result was a big surprise.
What is really interesting is that Einstein’s famous paper was not called “The Theory of Relativity”, but “On the Electrodynamics of Moving Bodies” and in the opening he states the problem mentioned above:
“Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion”

He then goes on to explain how this problem can be overcome by special relativity.

[Bill S]

........It is not correct because when the traveler originally left on his trip, the third person was NOT the same age as the traveler then (neither in the opinion of the home twin NOR in the opinion of the traveler).

I'm not arguing - at this point, anyway - but would be interested to know your line of reasoning, here.

[Bill S]

Thanks for that full explanation, Mike.  I was with most of it. Only the latter part raised a question mark in my mind.

Some questions remain:

So what does the traveling twin say is the age of the third party at the beginning of the scenario

"What does the third party say is the age of the travelling twin at the beginning of the scenario?"
"In the RF of the third party, how much does the travelling twin age between the start and the meeting point?"