geordief

Are they related?Can they be the same under any particular conditions? If the worldline of an object is integrated is the result given in the same units as the spacetime interval?(which just considers beginning and end points of the worldline,if I have that right) Edit :just saw @KJW 's response.Probably too late to answer him today...

Imagine a pair of fictional events the first being the murder of Caesar by one of his enemies using a sword and the second fictional event the murder of JFK by someone using the same sword some 2000 years later. The spacetime interval between the two events is calculated by choosing the earth as a reference frame ,measuring the distance between Rome and Dallas ,choosing the units of time and applying the s^2=(ct)^2-r^2 formula. Suppose instead we were to follow the sword across the centuries and make a note of the time and places in which it was recorded as having been prior to it being used again in the fictional killing of JFK. Could we calculate spacetime intervals at every stop on the way,add them all up and end up with a figure that was comparable to the first spacetime interval when we just used the two events? What if the sword had disappeared down a hole in the earth and reappeared in N. Zealand for a time (or had been taken to the moon and back) ? Would that have increased the"cumulative" spacetime interval even though the beginning and the end of its journey were still the same? Sorry if that sounds a bit weird or overly tortuous

Before I saw the young girl ,I assumed he was sitting on the jacks.

If there are different possible definitions of explosions ,might there likewise be different definitions of expansion? Is @KJW basing his definition of an explosion on how things look to a test particle? (as usual I have vanishingly little understanding of this subject and so the question may not be pertinent)

As an avid non reader of the Bible ,but having read that parts of the OT advocates some odious actions can I ask if perhaps there are indeed some passages where rape is advocated, or described in an approving way? Like the good lord I too am fishing ,but for evidence

think so.

Well OK ,but can I repeat the question with just that one frame and the fixed distance between the location of the taker of the measurements in the same frame? (I would have said "observer" but I suspect that might have different meanings ...) If you just have the one frame is there any way to find the concept of spacetime useful as opposed to the pre relativistic separation of it into space and time?

Suppose we have two frames of reference that only differ in that they are separated by a fixed distance And suppose each frame makes measurements of an object that is moving relatively to both at any speed between 0 and c. Is the concept of spacetime necessary for each frame to make that measurement and so that they agree in every case? I am asking this because it has been said (was it by Minkowski?) that our previous till then understanding of space and time must be replaced with a new amalgam of the two (spacetime) and I am wondering if this is because all frames of reference are relatively in motion in practice or whether the reason is deeper than that.

Is the region between,say two BHs a region of negative curvature?(the two beams could diverge if the one moved towards the first CoG and the other beam towards the other) I think I heard(from Markus ,perhaps if I remember rightly) that there are no physical regions of negative curvature and ,so it would just be a mathematical concept.

My guess is that it might make them lose their shape... Edit:I was wrong.

No

My mother was a Morse coder in WW2.Why I could never trust what she said.

Ouch ,did you mean to say "really"?. I think it is just a mathematical construct to model real effects.

Sadly (well happily enough) ,I don't think that will ever happen (unless we ever chanced upon a defunct civilization that left records) Perhaps we could find intelligent life here on earth among the other species if we learn to communicate with them and they understood symbols....or even if they just helped us to understand our own intelligence. (the intelligence we use when our basic needs have been met)

I doubt there is a useful dichotomy between the mind and the brain. To my view the brain is a part of the body and what the mind is is very hard to understand.

Can you explain (in simple terms for me and perhaps in greater detail for others) how time dilation causes gravity? I thought time dilation was caused by relative motion and that relative motion does not necessarily entail ,or cause gravity. So you can have time dilation where there is no curved spacetime.

No ,the life we see around us follows logical paths .(animals,trees,humans,societies and the physical universe) The senselessness I had in mind was the apparent void we come from at birth and the void we enter after we are finished. In between we try to understand what our place is in that context. I doubt other species entertain these ideas but ,who knows maybe they might.

"To Be or not to Be" https://youtu.be/1u8OlUS7BhU?si=rMV91ELFEeaZncRA Or is the meaning of life to make sense of what has no sense?(we can all make sense of what seems logical, I would say)

Thanks.I did track down that passage in the book. For those of us who find it hard to visualise a curved 4d (3d+time) object is the way to do this to break the 4d down into all its 2d surfaces? Would every surface need to be curved for the 4d object to be classed as such? Or could in theory only one of eg spatial surfaces be curved and all the other surfaces be "straight" and the 4d construct would also be curved?(not that I expect such a thing to exist in nature)

Because it is spacetime that is curved and not space?

Yes ,it is intended to be an analogy. But analogies can perhaps be useful as a way of getting a clearer understanding of the actual phenomena or just encouraging further inquiry. So, can some analogies be better than others? The trampoline analogy has the fault ,if taken literally**of mistaking an effect if gravity for gravity itself. If that is disregarded it is a lot "catchier" than mine -maybe too catchy for it's own good. **of course students should be repeatedly warned that it is just a flawed analogy (as all analogies intrinsically are)

One of the main arguments against the trampoline analogy for spacetime curvature is that the heavy object distorting the fabric of the trampoline/spacetime fabric itself relies on gravity to act ... Suppose we just have two bodies ,one of which is a source of mass/energy and they are connected by a geometric line that is marked off in equal lengths of spacetime distance. There is a tension between the two objects (and so along the geometric line?) for the "simple" reason * *that the two objects have in principle a common source at the beginning of the universe ,whatever that looked like. Going back to the two objects,as time progresses the massive/energetic object "pulls on " the geometric line representing spacetime and "reels it in" like a measuring tape that springs back into the body of the tool. But the line is held at the location of the second body and ,moreover is elastic . And so the spacetime intervals written on the geometric line are stretched on the side of the massive body and this stretching is continues all the way along the geometric line as far as the second body,with the distortion from the ideal even spacing greatest in the immediate vicinity of the massive body ,but still existing (propagating?) as far as the second body ,or indeed to infinity if that is where the second body is. This is different from the trampoline analogy in the it just deals with one spatial dimension (at a time). The idea occured to me as I have been forced to wear compression stockings for now and when you pull them up the leg it looks a bit like stretching a trampoline or spacetime fabric in action Also ,in the What is Gravity thread a few of you are talking about whether spacetime curvature can cause mass or vice versa. In "my" analogy the mass can "ingest" spacetime and so it "causes" it. And the stretchy geometric line (spacetime) cause the second object to move relative to the massive object. **well,I think both these objects have a prior relationship and so a "historic" connection in that sense

Do I sound like an extreme monist? And you would be a mainstream monist ,perhaps? I am only slightly familiar with these concepts https://www3.nd.edu/~maritain/jmc/etext/psych023.htm#:~:text=Dualism teaches that Mind and,one and the same Reality. but ,from the link there seem to be quite a few variations... I think I would be attracted to what you say is not the case I think consciousnesss could be extensive in the same way as a particle extends into its field according to QFT. (of course I am waffling)

I think more along the lines that your consciousness is those experiences. There is nothing "hands off" about what I think of as consciousness.It is entirely immersive , athough there is an illusion of an "internal observer". which is just a facet of our consciousness.

You are thinking of a coma? So if you have an experience where "nothing could be better" (as in the oft quoted line"it was bliss that day to be alive" ) and this is followed by the depths of despair (perhaps as a result of a medical condition) your consciousness does not follow any direction? In the former experience all your days lie ahead of you in anticipation and in the later there is no tomorrow. Is your consciousness diminished or altered?