Does this explain what generates gravity?

[Galu]

...it’s the world line path...

One of the definitions of a geodesic is that it is the worldline that results from applying the Principle of Maximal Aging.

The Principle of Maximal Aging states that a particle in free fall will choose the wordline which corresponds to the longest possible time interval between two events.

Walking from A to B in the longest possible time via. Euclidean geometry means taking an absurd route such as walking in zig zags. However, the longest possible time route via. Lorentz geometry is a straight line. Which doesn't seem intuitive for us at all...

(I've assembled and edited the above from multiple sources.)

 

[Galu]

...has it occurred to anyone that it is possible no human has the capacity to understand the finer points of our existence?

In this thread we are more interested in the academic discipline of natural philosophy rather than in philosophy in general.

 

[Bonsai]

One of the definitions of a geodesic is that it is the worldline that results from applying the Principle of Maximal Aging.

The Principle of Maximal Aging states that a particle in free fall will choose the wordline which corresponds to the longest possible time interval between two events.

Walking from A to B in the longest possible time via. Euclidean geometry means taking an absurd route such as walking in zig zags. However, the longest possible time route via. Lorentz geometry is a straight line. Which doesn't seem intuitive for us at all...

(I've assembled and edited the above from multiple sources.)

🤦‍♂️

This is one of those situations where an equation is needed.

I’m thinking of the ladybug waking around the geodesic in the wiki link I posted earlier. I have to remind myself that as the ladybug traverses the geodesic, the whole thing is also moving through time - so the total path is indeed much longer than the sum of the distance of each of the critters steps.

 

[system7]

All this is Special Relativity, of course. A simple enough bit of Physics really.

Sean Carroll explains it well in the transcript here:

https://www.preposterousuniverse.com/podcast/2022/09/19/211-solo-secrets-of-einsteins-equation/

A sample dealing with the more complex Schwarzchild Metric in General Relativity:

1:41:01.7 SC: And those guesses were enough to make the problem tractable and simple enough that he can solve it, so he did. So he wrote down an exact solution to Einstein's equation called the Schwarzschild metric, and you can go look it up. I will even tell you what it is. So it's G mu nu. What does it look like when you say you have a solution to Einstein's equation? You have a metric, so that means you have a 4 x 4 array of numbers that depend on where you are in space and time. The Schwarzschild metric is static, so it doesn't depend on time at all, and it doesn't really depend on the angle either, so it only depends on R. And in fact, as it turns out, the only components of the Schwarzschild metric that physically matter are the TT component, remember, 'cause G mu nu, the mu and nu range over the four coordinates. In this case, our four coordinates, 'cause we're using spherical coordinates are TR delta pie, rather than TXYZ. The only components of the metric that matter are GTT and GRR. And they try be reciprocals, one over, inverses of each other. GTT is one minus 2GM over R, where M is the mass of the object and R is the distance. And GRR is minus... One minus 2GM over R2 to the minus one power. Why am I telling you this? You're not gonna remember this, right? You don't care what the actual details are, I will tell you why, 'cause it's actually kind of amazing.

1:46:19.3 SC: What happens is, as you get closer and closer to R equals 2GM, that quantity one minus 2GM over R gets closer and closer to zero. At R equals 2GM, it will be exactly zero. And what that means is that if you go hang out near the radius, R equals 2GM, the time that elapses on your clock is approximately zero times the time coordinate. In other words, you feel almost no time passing compared to the people who stayed out far away from the sun. So if you did that, if you went back closer to R equals 2GM, and then you hung out and then you came back and you've been hanging out for a couple days, the people you left behind had been experiencing years or more of time. And that is time dilation, that is gravitational time dilation. And what's going on is that you've been hanging out near the event horizon of a black hole.

Because you are not dealing with Euclidian Space. The Metric as the length of a curve no longer deals with sums and differences of squares of co-ordinates, but loses linearity.

The x co-ordinate interacts with the other co-ordinates in curved geometries, as in triangles with curved shapes rather than straight line sides, and more, so you need a 4x4 matrix to describe how the 4 co-ordinates interact. These are Tensors.

But happily some of the equations become redundant, so 16 equations can reduce to 6.

https://bigthink.com/starts-with-a-bang/einstein-general-theory-relativity-equation/

It's all there.


No sign of the Nova yet, so I think @Galu can sleep in his bed tonight!

My latest snap, f3.5, 18mm, 30 seconds with time delay, manual on short tripod taken in street just now, and I have discovered my good neighbour's car roof is a good platform:

The line from Vega to Arcturus provides a good reference, Corona Borealis being about 2/3 along it towards Arcturus, which is prominent in the picture.

Best, Steve.

 

[Galu]

This is one of those situations where an equation is needed.

This link below explains why in Lorentz geometry a curved worldline is traversed in shorter proper time than the corresponding straight worldline:

https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/05:_Trekking_through_Spacetime/5.06:_Wristwatch_Time_Along_a_Worldline

It is possible to travel through spacetime from event 0 to event B either along the straight worldline 0B or via the curved worldline.

The starting point is how to calculate the proper time along a curved worldline and therein lies your required equation!

Sorry folks, the contents of the link would not be easy to summarise.

 

[Galu]

All this is Special Relativity, of course. A simple enough bit of Physics really.

It's actually not "all" special relativity.

The Principle of Maximal Aging "is true not only for "straight" particle worldlines in the limited regions of spacetime described by special relativity but also, with minor modification, for the motion of free particles in wider spacetime regions in the vicinity of gravitating mass."

(The quote is from my above link.)

 

[indianajo]

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.

It has occured to me that the niceties of time dialation or dimensional shrinkage occur mainly to observers who travel expensively at great velocity. As I travel mostly by bicycle at 9 mph in the interest of minimal CO2 emissions. plus minimal expense, I shall have no trouble calculating either effect on my corpus. It has occurred to me that my hypothetical astronaut twin who jets around in fighters or space capsules will live longer than me, if he ever comes back to compare. Even Ignoring the positive effect of bicycle travel on my cardiovascular and self repair systems. Per system7's post about smart phones, they were invented after their usefulness to me. I cannot see the things without reading glasses. As I do not carry such on the bicycle, why would I want one? Apart from the fact that I cannot enter the village of Mesa Verde Nat Park without one, or now, Venice. Nor can I register the warranty on my new lawnmower without a QR code capture and transmission device. I do have a stupid phone (flip) I can operate without looking at it to call the ambulance or tow truck if necessary.
I mostly communicate with people who do not stare at their phones 95% of the time. That includes a pipe organ guild, people in Sunday school, and this forum. I had an audience of 8 that listened to my every sung word this morning, and applauded politely afterwards. Delightful people.