geordief

If we put an observer,E on Earth and another observer ,M on Mars and present both with 2 events , S(1) and S(2) on the Sun , and visible to both is it possible to show that E and M both measure the spacetime interval between S(1) and S(2) exactly the same? So ,if the expression is s^2 = (ct)^2 -r^2 and both E and M measure the same quantity from their respective frames of reference what would be the actual measurements needed to be performed by E and M,? I imagine that both would time the difference in signal capture between S(1) and S(2) and would also somehow measure the physical(spatial) distance between the sites of S(1) and S(2) Would those measurements be the ones that would show that the spacetime interval between the 2 events on the Sun as being invariant? (let's say they were 2 sunspots appearing one after the other) Or have I ,as I often have got the wrong end of the stick again?

Is that because the sources of gravity (the sources of the gravitational accelerations) are multi-directional? I f the gravity field was infinitely large there would be no curvature? I just meant it as a joke at my own expense

You are not saying ,are you that there is any point in the uniformly accelerating room where my two parallel beams of light can be judged by an observer to be Euclideanly parallel? I thought such parallelness was only a feature of spacetime devoid of gravity.

Suppose the observer at x,y,z=0,0,0 in the accelerated room sends a pair of "parallel" beams in the direction of 1,1,1 will she adjudge them to meet in the distance or remain parallel? And the same question for the room in the gravitational field (either from a small source such as a black hole) or an infinitely large source) Feel flattered to have graduated to the level of this "common misunderstanding"😣

Suppose one is an observer in Einstein's famous sealed portacabin in empty space and the living space is accelerating at a regular rate in the direction away from the "floor". (The room is a cube of 1x1x1 unit measurement) Now ,under the equivalence principle the scenario is very ,very similar to that of an observer whose room is not under acceleration but rather subject to the gravitational influence of a massive body positioned in the opposite direction to the earlier acceleration. So ,as I see things the acceleration obtaining in the first scenario should be causing a curvature of spacetime in more or less exactly (ie minus tidal effects) the same way as occurs in conditions of gravity. If I have understood this right so far ,could I get a little help so as to set up measuring equipment in my accelerating sealed room so that I can measure the curvature in spacetime in a region of the room and see how the spatial measurement change vis s vis the temporal measurements? Suppose I have an observer on the floor and place her ,with a clock at the x,y =0,0 point of that floor (or x,y,z=0,0,0 of the room) can I place another clock at ,say 1,1,1 and measure the distance and times both with and without acceleration? Will this setup allow me to observe the curvature of spacetime in the room?

OK ,thanks.

I see ; not infinite but greater than c? What about if there were an infinite number of "v" s that were added ? Any scenario that would allow for that? Would that imply a theoretical infinite speed in Newtonian physics? (I don't think Newton was aware of the relativistic addition of velocities even if that was known before Einstein....)

It is academic/historical but I am limiting the question to how it would appear to a pre Einstein physicist (so Newtonian). I think they assumed the world was composed of bodies composed of smaller components with mass. That is why I set it up as two bodies trying to engineer a separation velocity among any pair of the component bodies. I know this is wrong and outdated ,but I am trying to get into the head of a Newtonian physicist and understand whether they would have concurred there was a maximum speed of massive particles or whether they would have said there was no limit to how great this separation velocity (from a standing start) could be.

Are there other scenarios in Newtonian physics where a separation velocity is calculated to be able to increase without a limit?

Say we have 2 bodies ,mass=M composed of a set of smaller bodies ,mass=m set in a vacuum, what might be the maximum speed of separation from the respective centres of gravity.? Is it possible to say whether this speed would approach a limit given the effect of gravity or would this depend on the value of M ,m and ,I suppose n (the number of smaller bodies)? Or ,in Newtonian physics does it follow that the maximum speed of separation is without limits (infinite)?

I wonder why she said that. Did she think it might somehow count in the balance? Was it an opinion based on reflection ? I wonder what her arguments and opposing arguments might have been (she came down very firmly on the one side) Or was it borne out of strong sentiment?

By "directly" I meant the particular scenario in the OP where I wanted to physically measure the speed of a "passing wave" at that very instant and linking it to its departure earlier from the source. md65536 has persuaded me that we can do this with 2 detectors and a pulse of photons so that the result can be arrived at statistically. He also pointed out that ,for an accelerating observer ,using this method there are effectively 2 frames of reference. I am very happy with this new understanding, which keeps me in the fold of accepting the invariance of the speed of light (unsure before because this scenario was new to me)

Thanks. That seems to solve the problem I had . So an observer accelerating towards a source of light needs 2 nearby detectors and to measure a short pulse of light at each. The closer in time he or she collates measurements from the two detectors the closer the measurement of the light will come to c. Do I have it?

What about my scenario of an observer traveling at c/2 at the mid point of A and B in the direction of B (using your terminology)? This is flat spacetime ,I think but the frequency of the light coming from B is much higher than it would be if O (observer) was at rest wrt B and A. If many photons are emitted from B towards O and he or she detects them on two detectors (as per your suggestion) will he measure the speed as c? Lastly if O is accelerating towards B will this be the same as a gravitational scenario? (Will he or she measure the speed of light as greater than c using the 2 detector method?)

Suppose we want the measure the speed of light for light emanating from the Sun. How do we do that directly? Suppose we have an observer who has accelerated to the mid point between the Earth and the Sun (at c/2 ,as an example) How does that observer directly measure the speed of the light it detects at that moment? If the observer chooses 2 points separated by 1 metre and records the time of detection at each point this should allow him or her to evaluate the speed ,but if the light is first detected at the first point then is not the photon absorbed by that detector and retransmitted to the second detector? So if the observer evaluates the speed of light between those 2 points is that actually the same as the speed of light between the Sun and the first detector? Is not the observer actually measuring the speed of light between the two detection points?

Isn't the expanding universe a result of more than the laws of gravity? There was the initial inflation and also dark energy....might gravity be a "bit player" ** in the overall scheme? ** a very big "bit player"

I wasn't sure my fictitious point of explosion would count as a frame of reference but you seem to be saying that it would. Would you say that such a fictitious universe with its fictitious preferred frame of reference implies that c might not be invariant in that fictitious universe?

I have heard that the Big Bang was not an explosion but that everything separated from all other objects (a bit like anti -gravity on steroids?) Could this be an explanation for why there is actually no preferred frame of reference? Every point at the initiation of that expansion period can equally be considered to be the starting point..... Suppose that there had in fact occurred an explosion and that all bodies had receded from a single area radially ,would such a fictitious scenario lead to some preferred frame of reference whereby the site of that explosion could be considered as "ground zero"(and a preferred frame of reference if only on that one occasion)? And would that scenario allow for any invariance in c ?

I was half way through answering you,when Markus replied. I answered him and the half -composed answer to you went through inadvertently at the same time. So I deleted it as I hadn't finished it Then it saw that my reply to Markus ,where I said I might be OT might cover it...

Yes I am familiar with that argument(I think Einstein uses it too but it has never really sunk home with me -clearly because I have not appreciated it correctly) Are you saying that if we had an absolute preferred frame of reference that the laws of physics would vary from place to place? Btw is the lack of that preferred or absolute frame of reference equivalent to the invariance of c ?Does the former imply the other or vice versa? Perhaps I am OT now..

Is there anything (apart from the consequences) that can be said about this invariance? It seems counter intuitive but is clearly a thoroughly verified experimental finding. Are there any "preconditions" that make it unsurprising after all that this invariance should exist or do we just have to accept it as a fact of life and a basic building block of physics?

"As Slow as Possible" by the late John Cage ) https://www.bbc.com/news/world-europe-54041568 What is not widely known is that he penned this piece in collaboration with Gordon Sumner.

If they were the first objects formed at one epoch in the universe would not some of them been "uncatchable" by the other objects that formed ? Were there no photons whose trajectory included no possibility of meeting any massive particles?(because all the massive particles were created in the photon's past)

Do we know some photons (the earliest ones in the life of the Universe ) which can never interact ? Can the Universe never catch up with them ? Would such photons (if they exist) never weaken or cease to exist by virtue of there being no possibility of any interaction?

Is it possible to say that a photon only exists if it interacts (initially or finally)? In that sense does a photon "die" if its trajectory does not include some massive object in its future? For any photon ,can a "lifetime" be assigned to it and is that the only "beat of its clock"?