Any physics majors here? Discussion on general relativity.

[ChapelHillSooner]

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.

First, I would say exactly not approximately. The "be treated" means we (or really nothing in the universe) is truly in a non-accelerating frame of reference (according to Newtonian physics) but we can treat is as one for any calculation.

The quirk I am talking about is that gravitation mass = inertial mass. So that means all things accelerate in a gravitation field at the same rate. That means you can't really detect/feel that acceleration. That means any experiment I perform on earth would have the same results as if the earth was not experiencing any gravitational accelerations due to other bodies. (Treat this entire paragraph as if we are talking Newtonian only.)

My point is that Newton would not have any problem with any of that. He wouldn't say, "Well, we are actually accelerating which means we are not in a proper Galilean frame of reference so something is wrong." He would instead say, "It's a quirk of gravitational mass being equal to inertial mass which makes everything accelerate together. So therefore we can treat it as a proper frame of reference."


My point is that it makes sense for someone like Einstein to think, well, maybe we are looking at it wrong. Since we can treat a falling body as a Galilean reference frame, maybe it really is one. But people who present gravity as somehow breaking the concept of Galilean reference frames are wrong IMO.

 

[stankeylegjones]

To add on to super's response, gravity is not due to matter “expanding into each other.” If it were, the acceleration between two bodies would scale with the Hubble parameter H(t) and the distance r, roughly a ~ H^2 r, whereas Newtonian gravity scales as a = GM/r^2. Bound systems such as atoms, planets, and galaxies do not participate in Hubble expansion because local binding forces dominate. Electromagnetic forces hold atoms together and gravitational forces hold planets and galaxies together.

Matter itself does not expand. Only the spacetime metric does. Locally measured lengths L_local remain constant while comoving distances between unbound objects grow as d(t) ∝ a(t), where a(t) is the cosmological scale factor. The “ball slowing down” is due to peculiar velocities decaying as v_pec ∝ 1/a(t), meaning comoving momentum redshifts. This does not occur because the particle physically “travels more distance.”

In short, gravity arises from spacetime curvature or local Newtonian forces, not expansion. Local scales do not stretch and energy and momentum changes in expansion reflect the cosmological metric, not actual forces between bodies.

 

[stankeylegjones]

First, I would say exactly not approximately. The "be treated" means we (or really nothing in the universe) is truly in a non-accelerating frame of reference (according to Newtonian physics) but we can treat is as one for any calculation.

The quirk I am talking about is that gravitation mass = inertial mass. So that means all things accelerate in a gravitation field at the same rate. That means you can't really detect/feel that acceleration. That means any experiment I perform on earth would have the same results as if the earth was not experiencing any gravitational accelerations due to other bodies. (Treat this entire paragraph as if we are talking Newtonian only.)

My point is that Newton would not have any problem with any of that. He wouldn't say, "Well, we are actually accelerating which means we are not in a proper Galilean frame of reference so something is wrong." He would instead say, "It's a quirk of gravitational mass being equal to inertial mass which makes everything accelerate together. So therefore we can treat it as a proper frame of reference."


My point is that it makes sense for someone like Einstein to think, well, maybe we are looking at it wrong. Since we can treat a falling body as a Galilean reference frame, maybe it really is one. But people who present gravity as somehow breaking the concept of Galilean reference frames are wrong IMO.

Thank you for clarifying. And, thank you for starting this thread. It's given me the opportunity to rethink about things that I haven't thought about much since grad school.

Treating it as an inertial frame, when it is not, is approximating it.

You’re mixing a few things up. In Newtonian mechanics, gravitational mass and inertial mass are conceptually distinct; their equality isn’t required by the theory, nor did Newton consider them the same, it’s an empirical fact. Even assuming they are equal, you still feel gravity on Earth. Standing on the ground exerts a normal force that you perceive as weight. Local experiments are affected by gravity (objects fall, pendulums swing, and scales measure weight). You would only be unable to detect gravity in a freely falling frame, where everything accelerates together.

Regarding your statement that gravity “doesn’t break Galilean frames,” a frame attached to the Earth is non-inertial in Newtonian mechanics. So, Newton would not say it is an inertial frame, but I do think he would approximate it as one in his calculations. What Einstein realized is that free fall makes gravity locally undetectable, pointing toward general relativity, but it doesn’t invalidate Newtonian mechanics’ treatment of inertial frames.

 

[Ddseddse]

Matter doesn't expand.

Do you consider matter "inside' space time, or 'outside'? Did you mean "inside" and therefore meant to day "matter does expand at a rate that is different than the rest of space time."? I think what you are saying is that both the ruler and the object being measured expand at the same constant rate.

What I'm questioning, is is that assumption warranted? Could a different set of assumptions be useful in explaining gravity?

You answered me my that assumption was wrong, but that wasn't what I was asking. I was asking, if we granted my assumptions, wouldn't that produce a force that looked and acted a whole lot like gravity?

 

[Ddseddse]

To add on to super's response, gravity is not due to matter “expanding into each other.” If it were, the acceleration between two bodies would scale with the Hubble parameter H(t) and the distance r, roughly a ~ H^2 r, whereas Newtonian gravity scales as a = GM/r^2. Bound systems such as atoms, planets, and galaxies do not participate in Hubble expansion because local binding forces dominate. Electromagnetic forces hold atoms together and gravitational forces hold planets and galaxies together.

Matter itself does not expand. Only the spacetime metric does. Locally measured lengths L_local remain constant while comoving distances between unbound objects grow as d(t) ∝ a(t), where a(t) is the cosmological scale factor. The “ball slowing down” is due to peculiar velocities decaying as v_pec ∝ 1/a(t), meaning comoving momentum redshifts. This does not occur because the particle physically “travels more distance.”

In short, gravity arises from spacetime curvature or local Newtonian forces, not expansion. Local scales do not stretch and energy and momentum changes in expansion reflect the cosmological metric, not actual forces between bodies.

Now we're getting somewhere. I appreciate the response. You answer will take a bit of digesting on my part though!

My intuitive problem with the billiard ball on a rubber sheet 4 dimensional view of gravity is that it feels like it presupposed gravity itself. Even if the sheet were bent, the objects wouldn't move towards each other without a force acting on them. If feels like we just shuffled the problem off into another dimension.

 

[superrific]

Now we're getting somewhere. I appreciate the response. You answer will take a bit of digesting on my part though!

My intuitive problem with the billiard ball on a rubber sheet 4 dimensional view of gravity is that it presupposed gravity itself.

No, it is gravity itself. Gravity isn't a force. It's curvature of space time that we intuitively think of as a force because for our entire existence as a species, until the last hundred years or so, we didn't even have the capacity to think about four dimensional space time. Forces made plenty of sense to our forebears, and it makes sense to children. Thus our brains and our cultures revolve around the force idea.

 

[superrific]

Do you consider matter "inside' space time, or 'outside'? Did you mean "inside" and therefore meant to day "matter does expand at a rate that is different than the rest of space time."? I think what you are saying is that both the ruler and the object being measured expand at the same constant rate.

What I'm questioning, is is that assumption warranted? Could a different set of assumptions be useful in explaining gravity?

You answered me my that assumption was wrong, but that wasn't what I was asking. I was asking, if we granted my assumptions, wouldn't that produce a force that looked and acted a whole lot like gravity?

I mean this. Stankey will probably correct me because I'm going to be a little bit loose dealing with limits and infinities, but I'll go with it.

Imagine a grid. You know, like the ones you would use in algebra. There's a point (1,1), a point (3,3) etc. Now shrink down the between the points on the grid until they are infinitely small. That's the universe at time T.

Now, repeat the exercise, except this time shrink them down until they are infinitely small except bigger than the first one. For instance, if the space between points in the first example is d, then the space between the points in this exercise is n*d, n being any real number. Let's assume it's 2. Now imagine the limit as d goes to zero. That's the universe at time t + T, where t is an increment of time larger than zero. The larger the t, the larger the n.

This isn't actually what happens in "reality" (which might not be a coherent concept post quantum-field theory), but it's a way of thinking about it.

Matter sits on the points. It doesn't care about how much space is between the points.

 

[stankeylegjones]

The "expansion" refers to spacetime itself (the metric, rather), not matter. Matter is not expanding. Spacetime is.

 

[stankeylegjones]

I mean this. Stankey will probably correct me because I'm going to be a little bit loose dealing with limits and infinities, but I'll go with it.

Imagine a grid. You know, like the ones you would use in algebra. There's a point (1,1), a point (3,3) etc. Now shrink down the between the points on the grid until they are infinitely small. That's the universe at time T.

Now, repeat the exercise, except this time shrink them down until they are infinitely small except bigger than the first one. For instance, if the space between points in the first example is d, then the space between the points in this exercise is n*d, n being any real number. Let's assume it's 2. Now imagine the limit as d goes to zero. That's the universe at time t + T, where t is an increment of time larger than zero. The larger the t, the larger the n.

This isn't actually what happens in "reality" (which might not be a coherent concept post quantum-field theory), but it's a way of thinking about it.

Matter sits on the points. It doesn't care about how much space is between the points.

When you get down to lengths on the size of the Planck length our current theories cannot be applied. In order to talk about this you'd first need to come up with a new theory.

 

[superrific]

When you get down to lengths on the size of the Planck length our current theories cannot be applied. In order to talk about this you'd first need to come up with a new theory.

What do you mean? I was just trying to illustrate what it meant for the universe to be expanding. It's a thought experiment only.

 

[Patb78]

Your explanation of "mass" is not entirely correct (and includes some errors), but I don't think this thread is the right place for discussing it. Maybe we can create another thread for that...the more threads on theoretical physics the better, imo!

Folks, we have found our Sheldon Cooper.

 

[stankeylegjones]

What do you mean? I was just trying to illustrate what it meant for the universe to be expanding. It's a thought experiment only.

I was pointing out that the thought experiment breaks down, as we don't know what the geometry of spacetime "looks" like at distances that small (energies that great).

 

[stankeylegjones]

Folks, we have found our Sheldon Cooper.

Nah, definitely not. He's a physicist, I'm a mathematician (trained at a decently level in theoretical physics).

I do really enjoy talking physics.

 

[superrific]

I was pointing out that the thought experiment breaks down, as we don't know what the geometry of spacetime "looks" like at distances that small (energies that great).

Right. But the thought experiment is only designed to help the poster understand what it would mean for the universe to expand.

It's not supposed to be an accurate representation of quantum-scale relativistic motion.