Galu, re post #3999, the reason I asked that question is linked back to Einstein's thought experiment about being accelerated at 1G in space in a non gravitationally bound regime is the same as standing on Earth. However, on Earth we can say there is a huge mass (the Earth) that warps space time but in space when a body being accelerated at 1G there is no huge mass. So what is going on here? I asked this question some months ago wrt the Higgs as well.
Accelerating a body at 1 g in a "non gravitationally bound regime" involves thinking of acceleration purely in spatial terms.
Applying the same spatial thinking to the Earth, we could say that gravity is caused by its surface continually accelerating outward at 1 g!
Instead, we must consider that gravity on Earth is due to acceleration that arises because of the warping of time caused by the mass of the Earth.
That's all I've got. As I said earlier I should like to understand more about spatial and temporal curvature.
Principle of equivalence. Wiki has a good write-up.
https://en.wikipedia.org/wiki/Equivalence_principle
https://www.npl.washington.edu/eotw...e simplest way to state,of the kind of matter.
https://en.wikipedia.org/wiki/Equivalence_principle
https://www.npl.washington.edu/eotw...e simplest way to state,of the kind of matter.
Einstein realised that a person who accelerated downward along with a freely falling ball would not be able to detect the effects of gravity on it.
An observer can "eliminate" gravity simply by moving to the accelerated frame of reference. Hence gravitation is equivalent to acceleration. This is the principle of equivalence.
Gravity is remarkable in that it affects all masses the same way - a 10 kg ball will fall with the same acceleration as a 1 kg ball.
If gravity were like electricity then balls with more charge would undergo a larger acceleration and there would be no way to "eliminate" this effect by moving to the same accelerated frame of reference for all objects.
From this Einstein inferred that gravity does not depend on the properties of matter. Instead he realised that the phenomenon of gravity must emerge from some property of spacetime.
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I often wonder what people walking down the street, or even gathered round a table, are looking at so intensely on their mobile 'phones. Surely they should be more importantly watching out for cut-purses and the like and, if scientifically inclined, Novae?
These are poor devices, IMO requiring a magnifying glass to even read. Me, I use a proper PC for my very significant contributions to the company of anonymous strangers, often criminals IMO, on 'teh Interwebs.
I suspect many of you here post from mobile 'phones. Well, I say: DON'T! Use forum software fully for good posts.
I have solved or resolved the time-dilation mystery discussed earlier:
https://www.preposterousuniverse.com/podcast/2022/09/19/211-solo-secrets-of-einsteins-equation/
See, it's the twin who stays at home who is moving in a straight line in Spacetime and experiences more time passing. The travelling twin is moving (and accelerating) in a curve so ages less.
For this, Einstein was better off adopting Minkowski space:
My next consideration will be that the rate of time flowing depends on both the gravitational potential and the kinetic energy or speed of a particle. Think uncharged particle orbiting a black hole... how hard can it be?
Best Steve, Portsmouth, UK. Posting from my Linux PC in 1080p.
These are poor devices, IMO requiring a magnifying glass to even read. Me, I use a proper PC for my very significant contributions to the company of anonymous strangers, often criminals IMO, on 'teh Interwebs.
I suspect many of you here post from mobile 'phones. Well, I say: DON'T! Use forum software fully for good posts.
I have solved or resolved the time-dilation mystery discussed earlier:
https://www.preposterousuniverse.com/podcast/2022/09/19/211-solo-secrets-of-einsteins-equation/
See, it's the twin who stays at home who is moving in a straight line in Spacetime and experiences more time passing. The travelling twin is moving (and accelerating) in a curve so ages less.
For this, Einstein was better off adopting Minkowski space:
My next consideration will be that the rate of time flowing depends on both the gravitational potential and the kinetic energy or speed of a particle. Think uncharged particle orbiting a black hole... how hard can it be?
Best Steve, Portsmouth, UK. Posting from my Linux PC in 1080p.
On what page or pages will I find that discussion? My memory is obviously in need of refreshing!
So Steve's "mystery" was why "the duration in Time for a geodesic (Shortest Path) in Space[time] is the LONGEST possible time"?
I wonder if there is a more Galu friendly edited version of the resolution to that mystery?
I've seen Steve's "mystery" better quoted:
"In space, a straight line describes the shortest distance between two points.
In spacetime, by contrast, a straight path yields the longest elapsed time between two events."
And I've found this brief explanation of the second statement:
"Space and time have opposite signs in the spacetime (pseudo)metric. That means that in Minkowski space [flat spacetime] the "distance squared", ds^2 = −dt^2 + dx^2 + dy^2 + dz^2, can become negative. So the "shortest distance" corresponds to the "longest time" in the same way that, say, -20 is smaller than +10 or even -10."
Apparently, for flat spacetime, straight lines representing massive objects are ones which maximize dt^2 and minimise the other terms.
https://physics.stackexchange.com/questions/737811/in-spacetime-a-straight-path-yields-the-longest-elapsed-time-between-two-event#:~:text=In space, a straight line describes the shortest,yields the longest elapsed time between two events.
"In space, a straight line describes the shortest distance between two points.
In spacetime, by contrast, a straight path yields the longest elapsed time between two events."
And I've found this brief explanation of the second statement:
"Space and time have opposite signs in the spacetime (pseudo)metric. That means that in Minkowski space [flat spacetime] the "distance squared", ds^2 = −dt^2 + dx^2 + dy^2 + dz^2, can become negative. So the "shortest distance" corresponds to the "longest time" in the same way that, say, -20 is smaller than +10 or even -10."
Apparently, for flat spacetime, straight lines representing massive objects are ones which maximize dt^2 and minimise the other terms.
https://physics.stackexchange.com/questions/737811/in-spacetime-a-straight-path-yields-the-longest-elapsed-time-between-two-event#:~:text=In space, a straight line describes the shortest,yields the longest elapsed time between two events.
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I would imagine the shortest path between two objects can never do anything but follow space time curvature.
If I understand it correctly :-
Imagine two objects in space moving along next to each other. You shine a light from one object to the other. But, the objects are moving (EVERYTHING is moving in the universe). The path traced out by the beam of light is not the apparent shortest path, but (per your earlier post) it’s the world line path which will be longer than the apparent shortest path. The time is as measured by the light-time.
If I understand it correctly :-
Imagine two objects in space moving along next to each other. You shine a light from one object to the other. But, the objects are moving (EVERYTHING is moving in the universe). The path traced out by the beam of light is not the apparent shortest path, but (per your earlier post) it’s the world line path which will be longer than the apparent shortest path. The time is as measured by the light-time.
Note that I have edited (shortened) my post in the interest of clarity! I did that before seeing your response.
Does quoting an entire previous post, when quoting an excerpt therefrom would suffice, provide evidence of that?
I don't own a smartphone. Happily, the battery in my old dumbphone stubbornly refuses to die! I do have a tablet for casual internet use.
OK...gotta throw in my bit here...
I have read only a tiny fraction of this discussion, so apologies if someone already mentioned this, but has it occurred to anyone that it is possible no human has the capacity to understand the finer points of our existence? Perhaps we are like the ant crawling on a sidewalk...it has no clue or hope of being able to understand the surface it is travelling on, or where it came from.
Mike
I have read only a tiny fraction of this discussion, so apologies if someone already mentioned this, but has it occurred to anyone that it is possible no human has the capacity to understand the finer points of our existence? Perhaps we are like the ant crawling on a sidewalk...it has no clue or hope of being able to understand the surface it is travelling on, or where it came from.
Mike