Any physics majors here? Discussion on general relativity.

[stankeylegjones]

First, I understand what everyone is saying about general relativity and how gravity is not a true force and due to mass curving spacetime, when falling in a gravitation field we are in fact an inertial frame. Obviously I only understand this as a layman’s level.

Let me try to simplify my question.

I am a physicist from 1850. I assert, because of the unique nature of of gravitational mass being the same as inertial mass, a closed system in free fall can be treated as if it is an inertial frame of reference. I wouldn’t asset that it is but that it can be treated as such.

That professor’s claim is perfectly valid and consistent with known science at that time. So I think people are wrong when they claim that treating freefall as an inertial frame of reference somehow breaks Newtonian/Galilean physics. It is just a quirk and the root of that quirk is the equality of gravitational mass and inertial mass.

Even if it might not be Einstein’s thought process, I think the first big question is why the quirk which leads to everything else.

But, more importantly, I don’t agree with the proposition that the falling man thought experiment somehow breaks the idea of Galilean frames of reference. It just means that that quirk exists.

It wasn't noticing this "quirk," it was reinterpreting this "quirk" as the key to a new framework of gravity. According to Newton, free fall mimics an inertial frame by the assumption of m_in = m_g; gravity is still a force. According to Einstein, gravity is not a force, it's curvature of spacetime, and free fall is inertial motion.

Let me know if that helps, or if I can say more/different things, and what you next question is.

 

[stankeylegjones]

Here's a good lecture/talk about the history:

 

[superrific]

What derivation are you referring to? I didn’t see any in your post. Did you modify it?

There was no reason to go into the electroweak force. In my writing I'm utilizing a lot of QFT but I am most interested in the Higgs interaction. The spontaneous symmetry issue sits in the background and I've not taken the time to understand it 100%. No idea why I tried to bring it in.

 

[stankeylegjones]

There was no reason to go into the electroweak force. In my writing I'm utilizing a lot of QFT but I am most interested in the Higgs interaction. The spontaneous symmetry issue sits in the background and I've not taken the time to understand it 100%. No idea why I tried to bring it in.

Ah, I see. How far along are you in your novel?

 

[superrific]

Ah, I see. How far along are you in your novel?

Kinda stalled out for a while. Too much stress in personal life and world affairs. Makes it hard to concentrate. Sitting down at my computer is like trying to concentrate in a parking lot, except translated into mental space. I'm making progress but it's been very slow for a while.

I am taking this opportunity to review what exactly symmetry means. It's a slippery concept for me because it's not how I learned it. We talked about whether I could relearn complex math at my age; whatever the answer to that may be, it's true that I have a much harder time retaining it. I've read about gauge symmetry twice and I understood it both times (I tested myself by making predictions) -- but then I sort of forgot it. I don't know how to explain. When I was younger, once I learned and understood something, I knew it cold. I mean, over a long time I can forget, but even things I learned when I was younger are fresher in my mind than things I learned at this age, say, two months ago. If I'm not using something consistently these days, it's harder to recall it.

Anyway, I realize now that I was earlier confusing global and local symmetries. I've made that mistake before. A lot of the terminology in this space is really not intuitive. Gauge symmetry just does not sound like what it means. Pair that with the math notation -- i.e. the super-abstract like SU(2) x U(1) -- and it's hard for this middle aged man to keep track of it all.

 

[stankeylegjones]

Kinda stalled out for a while. Too much stress in personal life and world affairs. Makes it hard to concentrate. Sitting down at my computer is like trying to concentrate in a parking lot, except translated into mental space. I'm making progress but it's been very slow for a while.

I am taking this opportunity to review what exactly symmetry means. It's a slippery concept for me because it's not how I learned it. We talked about whether I could relearn complex math at my age; whatever the answer to that may be, it's true that I have a much harder time retaining it. I've read about gauge symmetry twice and I understood it both times (I tested myself by making predictions) -- but then I sort of forgot it. I don't know how to explain. When I was younger, once I learned and understood something, I knew it cold. I mean, over a long time I can forget, but even things I learned when I was younger are fresher in my mind than things I learned at this age, say, two months ago. If I'm not using something consistently these days, it's harder to recall it.

Anyway, I realize now that I was earlier confusing global and local symmetries. I've made that mistake before. A lot of the terminology in this space is really not intuitive. Gauge symmetry just does not sound like what it means. Pair that with the math notation -- i.e. the super-abstract like SU(2) x U(1) -- and it's hard for this middle aged man to keep track of it all.

I totally understand how it's nearly impossible to focus on other things when life is so stressful. Hopefully you'll find it to be less stressful soon, and can get back to doing things that bring you joy.

Regarding gauge symmetries, instead of thinking of them as local symmetries of the Lagrangian, I think it's better to think of them from the geometrical perspective - elements of the automorphism group of a fibre bundle. Not only does this viewpoint give a "mental image" of what they are and how they arise, but it also leads directly to classification of qfts (characteristic classes) and gives reasoning for the appearance of (co)homology theories. Let me know if I can say more about this.

Also, there is a wonderful book by John Baez, Gauge Fields, Knots and Gravity, that gives a non-technical introduction to this viewpoint (part 2 of the book). (John is such a great writer of mathematics and physics. I'll never forget being introduced to his article on TQFTs and higher category theory on a train ride from Brussels to Amsterdam.)

 

[ChapelHillSooner]

It wasn't noticing this "quirk," it was reinterpreting this "quirk" as the key to a new framework of gravity. According to Newton, free fall mimics an inertial frame by the assumption of m_in = m_g; gravity is still a force. According to Einstein, gravity is not a force, it's curvature of spacetime, and free fall is inertial motion.

Let me know if that helps, or if I can say more/different things, and what you next question is.

I get all of that.

I guess I still have a problem with people who claim that free fall somehow breaks Galilean reference frames rather than it just being a quirk. Not sure if Newton ever commented on this but I think he would agree with that. (And of course we live our lives in such a free fall.)

I understand that Einstein, taking all of this into consideration, thought maybe we were approaching gravity incorrectly and that free fall is in fact a Galilean reference frame.

 

[stankeylegjones]

I get all of that.

I guess I still have a problem with people who claim that free fall somehow breaks Galilean reference frames rather than it just being a quirk. Not sure if Newton ever commented on this but I think he would agree with that. (And of course we live our lives in such a free fall.)

I understand that Einstein, taking all of this into consideration, thought maybe we were approaching gravity incorrectly and that free fall is in fact a Galilean reference frame.

Let me back us up a bit. In Newtonian physics, a freely falling frame would not be an inertial frame because Newton treated gravity as a force. Newton would not agree that it is an inertial frame because inertial frames are free of forces. You could think of it, locally, as an approximation to an inertial frame. This quirk that you mentioned is resolved by the EEP, which says that locally it is an inertial frame. And so, according to Einstein, gravity cannot be treated as a force. Hence, the falling roof-top worker being his "greatest thought."

There were also other reasons why Newtonian gravity needed to improved on.

 

[superrific]

elements of the automorphism group of a fibre bundle.

Only a mathematician would suggest this as an easier way to understand something, LOL. I will give it a shot with some AI help, but you have to admit it's quite a suggestion.

I'll take it as a compliment that you think I can unpack that.

 

[mynameisbond]

It's not the free fall that kills you....

 

[stankeylegjones]

Only a mathematician would suggest this as an easier way to understand something, LOL. I will give it a shot with some AI help, but you have to admit it's quite a suggestion.

I'll take it as a compliment that you think I can unpack that.

Yes, please take it as a compliment. And, please let me know if I can help with understanding it from that point of view.

 

[ChapelHillSooner]

Let me back us up a bit. In Newtonian physics, a freely falling frame would not be an inertial frame because Newton treated gravity as a force. Newton would not agree that it is an inertial frame because inertial frames are free of forces. You could think of it, locally, as an approximation to an inertial frame. This quirk that you mentioned is resolved by the EEP, which says that locally it is an inertial frame. And so, according to Einstein, gravity cannot be treated as a force. Hence, the falling roof-top worker being his "greatest thought."

There were also other reasons why Newtonian gravity needed to improved on.

What I am saying is that Newton would say that a car moving at a constant velocity on earth could be treated (treated being the key word) as an inertial frame even though it along with the earth is being accelerated by gravitational forces. He would say that that is just a quirk of gravity rather than a refutation of Galilean reference frames.

 

[Ddseddse]

So... I have no physics chops whatsoever, so this is likely to be really really stupid.... But I was thinking bit about his awhile ago and I decided that...

• The universe is continually expanding
• Not from a central point, but from "everywhere at once"
• Well then ins't gravity me just feeling the effects of my expanding body pushing against the expanding earth?
• Isn't a falling object just the two expanding objects (the object and the earth) coming together in space?
• Wouldn't that just pretty much explain gravity altogether?

OK, I told you it was stupid, but seriously why is it stupid?

Edit: the fact that it's experienced as acceleration would then be due to the fact that the earth and i are both getting bigger (percentage wise) at a constant rate, which I would assume that should feel like acceleration, i.e a continuous force keeping me planted on the earth.

My biggest hesitation here, is that this seems too obvious, like if that was the case then 100% for sure someone would have figured this all out by now.

 

[Bobfripp]

Well then ins't gravity me just feeling the effects of my expanding body pushing against the expanding earth?

The expansion of the universe is pushing things apart, while gravity pulls things together. The expansion of universe is thought (hypothetically, not proven yet) to be driven by 'dark energy.' Gravity is also caused by energy, typically matter which has mass (Energy=mass times speed of light squared, so there's a LOT of energy in matter). The energy density (energy per unit volume) is what curves space and time, causing masses (energy) to be drawn together.

 

[stankeylegjones]

What I am saying is that Newton would say that a car moving at a constant velocity on earth could be treated (treated being the key word) as an inertial frame even though it along with the earth is being accelerated by gravitational forces. He would say that that is just a quirk of gravity rather than a refutation of Galilean reference frames.

If by "be treated" you mean Newton would treat the moving car approximately as an inertial frame then yes, I think he would. He would definitely say that it is not an inertial frame, because it is not force free.

Can you expand more on your last sentence? I'm having a hard time understanding what you're saying here.

 

[Ddseddse]

The expansion of the universe is pushing things apart, while gravity pulls things together. The expansion of universe is thought (hypothetically, not proven yet) to be driven by 'dark energy.' Gravity is also caused by energy, typically matter which has mass (Energy=mass times speed of light squared, so there's a LOT of energy in matter). The energy density (energy per unit volume) is what curves space and time, causing masses (energy) to be drawn together.

OK. But to tug on this thread a little longer, imagine a universe in which both space and matter are expanding, now lets stipulate the the presence of energy/matter inhibits the (local) expansion of space, but not the matter (it still expands), in that universe would not the expansion to two bodies of matter mimic what we experience as gravity? In fact this could potentially explain the inverse square falloff of gravity over distance.

I mean expanding matter is not crazy, we know all the matter in the universe expanded outwards after the big bang.

If all matter is still expanding at a constant rate then we wouldn't necessarily have a frame of reference to detect the expansion. Who's to say we aren't all (along with all the other matter in the universe) growing 100x every microsecond or something crazy like that. In that case, feel l like someone who knew what they were doing could use the gravitational constant to calculate what rate of expansion would specifically create that amount of force.

 

[superrific]

So... I have no physics chops whatsoever, so this is likely to be really really stupid.... But I was thinking bit about his awhile ago and I decided that...

• The universe is continually expanding
• Not from a central point, but from "everywhere at once"
• Well then ins't gravity me just feeling the effects of my expanding body pushing against the expanding earth?
• Isn't a falling object just the two expanding objects (the object and the earth) coming together in space?
• Wouldn't that just pretty much explain gravity altogether?

OK, I told you it was stupid, but seriously why is it stupid?

Edit: the fact that it's experienced as acceleration would then be due to the fact that the earth and i are both getting bigger (percentage wise) at a constant rate, which I would assume that should feel like acceleration, i.e a continuous force keeping me planted on the earth.

My biggest hesitation here, is that this seems too obvious, like if that was the case then 100% for sure someone would have figured this all out by now.

1. The magnitudes of expansion are not nearly strong enough to explain gravitational motion. Expansion occurs on a cosmic timeline. The force of the earth on your feet and vice versa takes place every moment.

2. Since the universe's expansion is accelerating, if gravity were just expansion then gravity would be changing over time. It doesn't. The gravitational constant is invariant (or, if it is not, it changes extremely slowly).

3. The universe is expanding in all directions. So if expansion was gravity, then it wouldn't pull you in any particular direction.

 

[superrific]

OK. But to tug on this thread a little longer, imagine a universe in which both space and matter are expanding, now lets stipulate the the presence of energy/matter inhibits the (local) expansion of space, but not the matter (it still expands), in that universe would not the expansion to two bodies of matter mimic what we experience as gravity? In fact this could potentially explain the inverse square falloff of gravity over distance.

I mean expanding matter is not crazy, we know all the matter in the universe expanded outwards after the big bang.

If all matter is still expanding at a constant rate then we wouldn't necessarily have a frame of reference to detect the expansion. Who's to say we aren't all (along with all the other matter in the universe) growing 100x every microsecond or something crazy like that. In that case, feel l like someone who knew what they were doing could use the gravitational constant to calculate what rate of expansion would specifically create that amount of force.

Matter doesn't expand. The expansion of the universe is an expansion of spacetime. Think of it like this, which isn't precise but I think good enough for our purposes. The expansion of the universe is stretching the ruler. Today, one meter is one meter. In a few million years, the meter will be "longer." I use quotes there because it will still be a meter, but the meter will be "more" compared to today's meter (though technically that comparison is incoherent).

Here's another way to think about it. If you throw a ball into empty space, it will eventually come to a stop. Energy is not conserved globally in the universe. There are technical explanations for that dealing with symmetries (which, in physics, means something a bit different than what they mean in casual languages), but we can intuitively think about it as follows: the ball has to cover "more distance" to move from point to point. So it takes longer to get from point to point, meaning that the speed is reduced, meaning that the energy is reduced.

Eventually, if the universe expands to infinity, the ball couldn't move at all because it would have to traverse an infinite distance just to get to the "next" point in space. I'm not sure if that would be true for photons, but it would be true of massive particles.

 

[heelinhell]

this is too sciencey...

Finally a post that allows me to weigh in on this thread.

Tom Petty> Einstein and all these pointy head educated physics posters

When it comes to all this sciencey gobbledygook, I just rely on my common sense so I'm going to the music thread and pay tribute to Tom Petty because his scientific explanation is something I can relate to (and yes I'm smart enough to know I ended that sentence with a preposition ).

 

[superrific]

this is too sciencey...

Finally a post that allows me to weigh in on this thread.

Tom Petty> Einstein and all these pointy head educated physics posters

When it comes to all this sciencey gobbledygook, I just rely on my common sense so I'm going to the music thread and pay tribute to Tom Petty because his scientific explanation is something I can relate to (and yes I'm smart enough to know I ended that sentence with a preposition ).

If Einstein had a fourth big idea, maybe it would have been a method to stop Tom Petty from sounding like a wet kleenex