1

Physics, Astronomy & Cosmology / Re: QM puzzle: Is a measurement being made in the 2 slit experiement all the time?

« on: Yesterday at 02:00:52 »

The question is:   Isn't the phosporescent screen always making a measurement?

Easy answer: Yes. More complicated: Yes, relative to the screen, just like the cat measures the poison bottle, so the bottle is not in superposition of closed/broke, but the bottle is still in superposition of those states relative to the lab observer. Copenhagen places a 'Heisenberg cut' at the boundary of where those states differ.

You seem to be asking if the electron misses the screen, is a measurement taken? Well, not by the screen (yet), but either the electron with interact with something else (and thus get measured by something else), or it never interacts, and is effectively nonexistent (according to any local interpretation at least).

Specifically isn't it possible that by constantly making a measurment, the phosphorescent screen ensures that the electron's wave function cannot collapse to the state where it would be at the screen?

Yes. The comment only applies only to interpretations where collapse is meaningful. You'd have to word it differently for others, but still, effectively yes.

2

Physics, Astronomy & Cosmology / Re: Quantum Entanglement and Interstellar Communication.

« on: 28/11/2023 12:15:14 »

That's interesting, Halc. How would one go about demonstrating that such a particle is in a state of superposition?

I do not know the exact procedure to detect superposition of spin state, but I do know that it is a statistical thing, that it can be demonstrated only by doing the experiment repeatedly. So for instance, the photon might be in superposition of having gone through one slit and the other, but the measurement is the dot it creates on the screen which doesn't tell you anything, but 1000 dots creates an interference pattern (superposition) and 1000 dots creates a simple bell curve (not in superposition). The spin state is similar, so you'd need to have a lot of them.

3

Physiology & Medicine / Re: How Does The Placebo Effect Work ?

« on: 14/11/2023 17:39:07 »

If yes, then can the belief in getting better be achieved without taking a false treatment ?

It takes actual belief, something some of us cannot just conjure at will.
I know others that are very adept at making up an alternate reality, and then actually believing it. I have a harder time doing it.

4

Plant Sciences, Zoology & Evolution / Re: Do Land Animals Hesitate When Entering COLD Water ?

« on: 14/11/2023 14:51:53 »

Some (many cats for instance) simply don't like to get wet. Plenty of dogs run right in and enjoy it. Tigers seems to like it. Sheep?  Who wants a wet sheep?  Probably not the sheep.

Going into water why?  To drink only requires to be at the edge. Crossing a river is needed sometimes, so a wildebeest goes right in, sometime to the point of going back and forth across the large body being crossed in search of their calves, hard evidence of 'bewild-a-beast' effect.

Seals and otters and such are water animals and don't count, and one might ask why they might or might not hesitate to emerge from the water.

Do you just go straight in ? or put your toe in first ?

I go straight in.

We went to a campground where the owner could not get his swimming pool certified for public use since it lacked a chlorine and a filtration system. It was approved only for use of himself and personal friends. So if you wanted in, you went and asked, and he'd ask if you were his friend. Say yes, and you could go in.
Think was, the pool was continuously fed by a mountain spring, so technically it was an artificial pond, and super cold. Most people were content on the uber-hot days to merely dangle their ankles in.  I would dive right in for the full shock effect of hitting water that was single-digit C at best.  Loved it, but didn't stay in there too long.

5

Plant Sciences, Zoology & Evolution / Re: What Do the Spiders In My Garage Eat In Winter ?

« on: 14/11/2023 14:40:48 »

If they're active, they're probably finding warmth and food somewhere. They're quite capable of preventing their fluids from freezing.
Some species do a form of hibernation (diapause I think is the term) where they go dormant and wait for spring.
Some simply die, leaving egg sacks to repopulate the joint in the spring.

6

Physics, Astronomy & Cosmology / Re: Are All The Planets Moving Away From The Sun Due To Sun Losing Mass ?

« on: 14/11/2023 14:31:18 »

Are All The Planets Moving Away From The Sun Due To Sun Losing Mass ?

There are four factors that make planets change their orbital distance, and yes, the sun losing mass is one of them,

1) Tidal effects push the moon away, but they also make the Earth recede from the sun, at a rate of over 10 cm/year
2) The one you mention: About 2 cm/yr recession is due to the sun losing mass.
3) Friction: The Earth loses orbital energy due to friction (collisions) with meteors and such
4) Gravitational waves: The Earth/sun system pumps about 200 watts of energy away in the form of gravitational waves.

In the future, it seems likely that Earth will get swallowed by the sun when it grows. The 3rd line, friction, will win in the end. For planets from Mars on out, the 4th line will win in the end, but all four lines rely on the consumption of some limited energy source.

The solar mass thing effects the orbits of all planets in proportion to their distance. The tide thing in proportion to their rotation rate over their distance.  The tidal thing decreases as the planetary spin slows down, so it is temporary since its energy source is limited.
The friction thing is limited by the amount of free matter flying around between the planets. The planets slowly clean up the solar system.
The gravitational wave thing continues unabated and will eventually be the winner. Jupiter will eventually collide with the sun due to it getting closer through the continuous radiation of energy, similar to how black holes eventually merge.

7

Physics, Astronomy & Cosmology / Re: Temperature and k.e. : Does a substance cool down if particles break apart?

« on: 11/11/2023 14:44:05 »

Energy is conserved, the container is insulated.

Insulate means here that the peas bounce off the walls (and each other for that matter) with perfect elastic collisions.

The temperature must fall to half it's initial value when the particles split into two. 

Yes, by your reasoning (and that given by BC) the energy is constant, but more/smaller particles with the same energy results in half the temperature.

8

Just Chat! / Re: What is the purpose of "question of the week"?

« on: 10/11/2023 14:53:05 »

Is it open to normal replies or does it have some other function?

It is very much open to replies from any forum member. The purpose seems to be related to the non-forum parts of the site or the radio show. Listeners of the radio or podcasts can submit questions and supposedly one question each week gets posted, with the answer (which sometimes don't come from the posted replies) being part of some subsequent podcast or something.

The protocol is: Don't post a new topic here. Only official members of the shows should do that, not even the forum mods. The site software should actually have something that prevents new topics from being posted here. I regularly move out (or occasionally delete) topics that are posted here.
Many human spammers seem to gravitate to that QotW. The bots all seem to choose THE OFFICIAL BOOK, making them really easy to spot.

9

New Theories / Re: A Disproof of the Principle and Theory of Relativity

« on: 30/10/2023 18:33:11 »

A thought experiment is not a disproof.

It is if it find inconsistencies in the premises.

Disproof would be signalled by the failure of the GPS system (your satnav would register a speed when you were standing still) or the lights going our because the nuclear power stations had all switched off.

Those would be empirical falsification of GR, different than falsification by thought experiment.  GPS is out of scope of SR, so even that would not falsify SR, only GR.

I wish it were true.

This is obviously false, as all your posts seem to wish that relativity is false, when in fact all they do is demonstrate you lack of knowledge of even the rudimentary basics.  Shall we count the errors?  I'm going to edit your OP, inserting colored numbers to count the errrors.

A Disproof of the Principle and Theory of Relativity

Galileo's ship thought experiment:

 Consider a light source emitting a light pulse from some point in the Earth's frame, at t=0.  At the instant of light emission (1), an observer/detector is at distance D from the source(2) and is moving away from the source with velocity v, in the Earth's frame.

 We know that the light will catch up with the observer/detector at t = D/ ( c - v )(3). This is a well-known and accepted fact(29) even in the Special Relativity Theory SRT and has been confirmed by experiments. Now I will use this in my argument against the principle of relativity.

 Consider Galileo's ship thought experiment. A physicist in a closed room of the ship is doing a physics experiment. There are two light sources S1 and S2, with the distance between them equal to 2D(4). The line connecting the sources is parallel to the longitudinal axis of the ship, and hence to the velocity of the ship(5). S2 is in front of S1.  A detector is placed at the midpoint between the sources(6), at distance D(7) from each of the sources. The light sources each emit a short light pulse simultaneously( 8 ) every second(9).  The detector detects the time difference(28) between the pulses.

The observer in the closed room first has to synchronize the clocks at S1 and S2(10). For this, a short light pulse is emitted from S1 towards S2.(30) Suppose that S1 emits the light pulse at t=0(11). The physicist in the closed room synchronizes the clocks(12) based on the principle of isotropy of the speed of light, because according to SRT the speed of light is isotropic in Galileo?s ship! However, unknown to him/her, we know that the clocks synchronized by this procedure will be out of synch(13) by an amount:

                                                 (  2D/ ( c - v )  )   -   2D/c    =  2D  v / v(c-v) 

The clock at S2 will be behind the clock at S1(14) by this amount.

 It should be noted that, according to special relativity, the clocks synchronized by this procedure will be in synch(15). However, from experience we know that the clocks will be out of synch(16). Therefore, we know that the relativistic procedure is wrong, based on experience. Therefore we analyze the experiment classically(31) as follows.
 
        
 
             S1                                                                Detector                                                                S2

                                                                                  →  v

The sources each emit a short light 'simultaneously'(17) (quoted because the clocks are not actually in synch(18)), every second(19). The physicist expects the pulses to arrive simultaneously, which they do not(32), as we will see.

Let S1 emit the light pulse at t = t0(20). Then S2 will emit 'simultaneously'(21)(33) at time,

                                            t0  +  2D  v / v(c-v)

The light from S1 arrives at the detector at time(22),

                                       t1 =     t0  +  D/(c -v)

The light from S2 arrives at the detector at time(23),

                                   t2 =    [    t0  +  2D  v / v(c-v)  ]  +  D/(c+v)(34)

The difference in the time(24) of arrival of the two pulses at the detector will be:

                                    t2 -  t1  =  (2D/c) β² /(1-β² )  (35)

where β  = v/c

The physicist synchronized the clocks(25) by assuming isotropy of the speed of light, placed the detector at the midpoint between the sources, and the sources emitted light pulses 'simultaneously'(26). He/she would expect the light pulses to arrive simultaneously at the detector, which they don't(36). The light pulses always arrive with a time difference of Δ that depends on velocity(27)(37). The observer would have no way to explain this other than abandoning the principle of isotropy of the speed of light. To anyone rejecting this argument, my response is this: let an actual experiment be done to test it. We know that the origin of the problem lies in the observer assuming isotropy of the speed of light while synchronizing the clocks. This disproves both the principle and theory of relativity.

I counted at least 37 errors in the post.  1-28 are all statements rendered meaningless by lack of frame references.
29 is a strawman, asserting that one-way speed of light has been experimentally confirmed.
30: Sending a signal from one source to the other is not a valid sync procedure.
31: Any contradiction obtained from assuming classical (non-relativistic) physics is a strawman
32, 33, 36 Positing experimental results which contradict SR, another strawman.
34, 35 Calculations are wrong given your assertions.

It seems that, against the premises of relativity, you are assuming a preferred frame, which, for some reason, is the frame (W) of the water, and all your calculations are performed in this frame, and incorrectly at that.  If the calculations are correctly worked out in this frame (or in any other frame like that of the ship (S), you'll see that the detector in the boat will receive both signals simultaneously.

There are valid interpretations of physics that do not assume isotropy of speed of light (they reject both premises of SR, as do you), and these theories still predict that the detector gets both signals at once. So you're doing it wrong.

10

New Theories / Re: If there was one Big Bang event, why not multiple big bangs?

« on: 30/10/2023 11:23:52 »

I'm not sure when "old age" occurs

It occurs at about 10 years older than whatever your current age is.
As a 10 year old, the 20 year olds looked ancient to me.

11

New Theories / Re: What is non-returning twin paradox?

« on: 28/10/2023 20:42:18 »

Basically, the common explanations employ time rotation as explained by minutephysics' video. Videos from Harvard and MIT use similar explanation.

The time rotation thing lends itself nicely to video. It is hardly the simplest explanation, but it very much is a valid one.

But it needs to do a Lorentz rotation, not a Euclidean rotation like you're doing with all your pictures posted above. Those produce contradictory observations, as you have noted.

For instance, in your pictures in post 110, all the ships B,C,D age about 4.5 years, not 8. That's a contradiction since any observation (like everybody's age at the final event) should be a frame independent thing.

Here I want to test the generality of that explanation.

That explanation generalizes to any special relativity situtation, but not to any situation involving gravity.  The more simple explanation I posted also applies only to SR, but in the other thread you mention I gave a geometric explanation that works in all cases, but is beyond your ability to learn.

Is it still useful to explain some varieties of the problem?

Again, so long as it doesn't involve gravity.

According to A, both B and C switch their reference frame once, while D switchs twice. But they must have the same age, due to symmetry.

Pretty strong evidence that it isn't acceleration (or frame changes as you call them) that causes the age differential. That's been said repeatedly, but you don't accept it.  A ship could continuously stop and start, each time moving at 0.8c for a short time and then pausing again, hundreds of times before getting to the end.  He'll age 8 years just like all the others except A who travels at a different speed than the others.  It's about speed, and not at all about acceleration. I've said that from the beginning.

It also means that the age difference depends on the distance between the subject and the switching frame observer.

This statement is surprisingly correct. Similar to moment of inertia, the term is called moment-of-acceleration, where the effect is acceleration (in the direction of the 'subject') leveraged by the distance (as measured in the subject frame) to the acceleration event from the subject.

12

Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?

« on: 18/10/2023 01:44:15 »

You can keep doing this (just adding up individual potentials), so in the general case, you can always identify a suitable potential function for any finite number of masses. 

I sort of did something like this when I wondered about gravitational potential being negative. How negative? I liked to measure potential in km. It can also be expressed as a speed.
Due to Earth, 6400 km at 1g, Maybe 100k km due to sun. Maybe 15 million km due to the galaxy. OK, so we expend enough energy to climb 15 billion meters at 1g, putting us in intergalactic space. Are we at zero yet?  Hell no. Now we start playing games.
Define a shell around us, a million light years thick, starting nearby and working outward. Each shell has mass in it contributing to the depth of our gravitational potential.
A shell nearby contributes X (km). A shell of similar thickness, twice as far away (so 4x the area) masses 4x as much, but being twice as far away, contributes only 2x the potential of the nearby shell. In other words, the amount each shell contributes to our gravitational depth goes up in proportion to the distance, so more distant galaxies contribute more than do the nearby ones because there's so many more of them. So the depth here is -X -2X -3X -4X ... which certainly doesn't converge on any number. Even if they were all just -1X it would still put us at unbounded depth.

The exercise is apparently invalid, but it is also utterly meaningless to suggest express our potential in absolute terms where zero is potential at the place that is infinitely far away from any mass, and clocks there run at full speed. If time is something that flows, the actual time (undilated by gravity) runs infinitely faster than does what any physical clock measures (all presuming that clocks measure the flow of time, which of course they don't).
The absurdity of trying to express this is one of my pieces of evidence against models with flowing time.

13

New Theories / Re: If there was one Big Bang event, why not multiple big bangs?

« on: 16/10/2023 20:55:56 »

It seems to me that space must be infinite and time must be eternal, don't you agree?

Depends on your definitions of time and eternal. If you picture time as something that flows, and eternal as 'unbounded in both directions', then most theories that support such flowing time do not suggest a start or end to it.

But does the universe have any option as to the upcoming gravitational forces governing the local movement of any given object? I don't think that the laws of motion have much use for the concept of randomness.

No idea what this asks. Option??  The gravitational field is determined by the arrangement of stress-energy in spacetime, at least per relativity, but relativity doesn't support flowing time so easily. Anyway, regardless of model, there's no randomness to it. Look to QM for fundamental randomness.

14

Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?

« on: 16/10/2023 16:14:58 »

I see, so it is gravitational potential within the shell, the "net gravitational force?? The spherically symmetrical shell being uniform in density.

Force and potential are not the same thing, having different units. Inside the shell, the scalar potential is the same everywhere, but lower than it is outside the shell. The force vector inside the shell is zero, and greater than zero (pointing towards the shell) outside of it.

The [force] vector has magnitude GMm/r² and direction toward the barycenter of the masses. In the absence of a barycenter it has no direction.

This only works for simple two-body systems. I can easily set up some orbiting masses where the acceleration of the test particle is away from the barycenter of the system, or in any other direction I like. The moon for instance (in say an otherwise empty Sun/Earth/moon system) rarely accelerates directly towards either Earth or Sun, and on occasion it accelerates directly away from Earth. If the moon was closer to Earth (as it was long ago), it would be capable of at some point accelerating away from the Barycenter of the system.

15

Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?

« on: 16/10/2023 15:41:39 »

I don't recall Newton ever saying that gravity was the gradient of a potential.

Being mostly unfamiliar with what Newton actually says, I cannot contest that. Can you think of a case (with finite mass) where it isn't so? I mean, with infinite mass, potential is pretty much undefined at all. There are perhaps relative differences in potential, but no meaningful displacement from 'zero'.

It is just the force that a unit mass would experience when it is put somewhere.

Force per unit mass is acceleration, so it would be an acceleration field.

   Anyway, just to be clear, what you're suggesting is the following:
A particle in the interior of a shell experiences no force due to gravity from the material of that shell.   That holds for shells of some finite thickness (assuming the usual things like spherical symmetry).   However, when that shell is so thick that it's of unbounded extent, the result may not hold.

Didn't see this before, but it makes sense. Using the bad rubber sheet analogy, an infinite sheet covered with a unform layer of marbles is in unstable equilibrium. Take one marble away (the equivalent of our hollow infinite-thick shell), then all the marbles near the vacancy move away from it, being 'repelled' by gravity as it were. This is seen in cosmology: there is the Dipole repeller and the lesser know Cold Spot repeller ,both regios of low mass density from which all nearby objects accelerate away. This acceleration from a hole presumably counters the acceleration towards the CoM of the arbitrary sphere you defined in the OP.
The acceleration from the hole is real, seen in action, and is a good illustration of one's inability to treat the rest of uniform mass space using the shell theorem.

16

Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?

« on: 14/10/2023 22:22:28 »

Much the same question was asked [on stack exchange]

Cheat! The fun was in working it out ourselves.

Still, time to do that I guess. I have great respect for stack exchange in such matters.

n the negative side,  I don't especially agree with the highest ranked answer.   Their response pivots around the inability to identify a unique gravitational potential function, Φ, in such a space.

That sounds really strong to me. Gravitational potential is not frame dependent, and thus seems to be flat everywhere in this universe, hence no vector (direction) to any physical force.
The stack exchange question is even posed in the framework of Newtonian physics.

I'm taking more time to grok the rest about Gauss' law and all.

The other answers vary in quality and relevance.   There is one about some history and how major figures like Newton may also have noticed this problem that the shell theorem produces in this situation.

That would be quite relevant to this discussion, especially given the way the question was framed.

17

Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?

« on: 14/10/2023 22:13:25 »

Dealing with 2nd spoiler:

Sure, but it is alto attracted in all other directions equally since there is a similar sphere at which it is on the edge, in any direction. The particle doesn't accelerate since the net force is zero.

More and more, I think my reply there doesn't hold water. I'm willing to say it is spherically symmetric. The inability to find a center of mass, or to identify a gravitational gradient (not a frame dependent thing) seems a better way to disqualify the applicability of the shell theorem in this Newtonian analysis. The particle doesn't accelerate since there's no downhill (a region of lower potential) available to it.
That said, the stuff does attract its neighbors and if initially all stationary, I think the density goes up over time. That very much does lower the gravitational potential, so everything (and not just some preferred thing) is going down hill.

You seem to agree that the shell theorem would show a non-zero net force exists in some direction.   You also seem to agree that direction is arbitrary.    The last sentence doesn't need to follow though.     You don't apply the Shell theorem with all possible origins and then sum all predicted net forces to obtain the actual real and very final net force.

Selecting an origin is a coordinate thing. You can't select more than one at a time, so adding up the forces from different frames doesn't work.

Worse that that, even it's magnitude is arbitrary  (just move the origin further away but in the same direction,   the inner sphere grows ~ r³ in volume and hence in mass,  while the gravitational force from it falls off only as ~1/r²,   making the total force vary ~ r  = the distance from our test particle to the origin).

Just so, which is why distant star are receding (and have greater acceleration) than the nearby ones.

You sometimes make arguments that the space isn't suitably spherically symmetric

I'm backing away from that.

All that exists in the space is the stuff we have stipulated will have a constant density, ρ, everywhere.   There are no points in space where a lack of spherical symmetry is exhibited.

Backing away because that's a pretty good counter to my comment.

I can similarly use the shell theorem to demonstrate that all clocks are infinitely dilated, and thus effectively stopped relative to 'the rate at which time actually goes', like that phrase means anything. I've brought that argument up elsewhere, and was punted out the door with a reply about Killing fields that I didn't understand. Takeaway is that I need to know GR better before asking questions like that. 

Example, trajectories of stars in a galaxy can be estimated by considering only that mass which is in a spherical region interior to that star etc.

This is incorrect since a galaxy isn't spherically symmetric. With a disk, a particle is attracted to rings of material outside its radius as well as the material inside. So it all needs to be considered. Kudos to the guys that work out where all the mass needs to be to get the velocity curves we see. It's a lot of calculus to do.

Anyway, just to be clear, what you're suggesting is the following:
A particle in the interior of a shell experiences no force due to gravity from the material of that shell.   That holds for shells of some finite thickness (assuming the usual things like spherical symmetry).   However, when that shell is so thick that it's of unbounded extent, the result may not hold, the particle might experience a force.

I cannot say I suggest this, at least not anymore. Like I said, there are reason the shell theorem doesn't apply, but this logic seems faulty.
Yes, our particle is attracted to an arbitrary 'origin' placed anywhere you like. That doesn't imply an objective force in a direction, only a coordinate frame dependent force. And as you've worked out, the greater the distance to the selected origin, the greater the coordinate acceleration towards it.

Hope this helps. Great topic, since it's rare to get one that gets me thinking.

18

Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?

« on: 14/10/2023 21:47:53 »

Obviously this is too long

I tend to do that as well, but I'll try to break up my reply, which is slow in coming since I've been kinda busy.

Dealing with your first spoiler:

Suppose we have an infinite space with an initially uniform density of material, ρ, everywhere.   Consider a test particle located somewhere in that space,  at position  x  .   What force would that test particle experience?

First of all, the sorts of forces you describe cannot be 'experienced', which is why an accelerometer reads zero despite its coordinate acceleration in orbit, and it is very much coordinate acceleration you're after here, not proper, which happens due to something usually contacting you on one side and deforming you. So the acceleration of the particle seems coordinate system dependent, thus the question of if it is really accelerating towards that arbitrary CoM you defined, or the stuff at that origin is accelerating towards the particle, is an abstract question, not a physical one.

Also, in your initial homogeneous state, is everything stationary in some inertial frame, or is it expanding?

If the Hydrogen was at rest initially  (which as you correctly point out for an expanding universe is actually a very reasonable assumption as the scale factor increases) then it just sits there and stays at rest for ever more.

Well, it's a hot universe at first under great pressure, meaning particles are not stationary, and they do experience force as they bump into each other. It should all cancel out, but not perfectly, and the anomalies, especially early on in such close quarters, introduce variations in local mass density, which, via gravity, tends to amplify the variations as gravity wells begin to form. In short, the homogeneous state is in sort of an unstable equilibrium.

However, applying the shell theorem (as it was done in the OP) can get a different answer.   The Hydrogen can be shown to have a net force in the direction of the origin.

That's a coordinate effect, as stated above. Coordinate acceleration is coordinate system dependent, and can be zero in some, such as the coordinate system putting the origin at the particle in question.  Yes, stuff will be attracted to each other. The expansion (if there is any) should slow measurably. If all is stationary, I think collapse occurs, even in Newtonian physics.

Keep in mind me not being an authority on this and I, like you, and just trying to world this out.

19

Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?

« on: 13/10/2023 19:41:50 »

Sorry for all the posts, but thought about this some more, and want to avoid stating things that sound unconditional.

We can choose to put an origin somewhere and draw a sphere of radius r around that.   Now, consider a particle of Hydrogen on the boundary (surface) of that sphere.   By the shell theorem, we can see that the Hydrogen particle is attracted to the origin by gravity.  We also see that we can ignore the attraction to anything outside that sphere of radius r.

Back to the OP argument, since one can 'frame' my rebuttal in a way that refutes my rebuttal.

I think that under Newtonian law, the sort of logic that you spelled out above is valid in an inertial (as opposed to expanding) frame, and that our test particle does indeed acceleration towards any arbitrary origin that you select. Hence, lacking any recession rate of that arbitrarily selected origin, all that homogeneous matter will collapse in due time.  This is barring wrenches in the works like dark energy which isn't compatible with Newton's theories anyway.

So how does switching from Newton to GR affect that? Well, the shell theorem certainly has trouble under GR. Under GR, there is no possibility of a uniform gravitational field, and yet the shell theorem can show that an off-center spherical hollow in an otherwise solid homogeneous spherical mass will (like an infinite sheet of mass) produce a uniform gravitational field. Since GR doesn't allow this, the shell theorem doesn't work in general, and only approximates a solution for low mass densities.

GR of course also doesn't allow a uniform distribution of mass in an inertial frame, so any treatment using such a frame is wrong right out of the gate.

20

Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?

« on: 13/10/2023 19:00:23 »

Yes, you could try and explain why a real world situation wouldn't be like the situation in the model.

Well, at some point you have to explain how matter started to clump rather than remain perfectly homogeneous. For that, you have to go back to the earliest epochs (long before there were protons and such) when there was fantastic energy density, and then apply quantum fluctuations to the situation. Lacking a unified field theory, this is all still pretty speculative. One also has to go about explaining the annoying matter/antimatter imbalance.

We do need a 1/r² relationship for the shell theorem to hold.

that's right, and 1/r² doesn't hold up for extreme cases (like near neutron stars and such). But the shell theorem is totally inapplicable here, and by the simplest symmetry, there should be zero net forces on anything except due to those local variances which come only out of quantum theory, so GR isn't going to be a huge help over just doing this the Newtonian way.

I'm not sure if this topic is about the applicability of the shell theorem to an infinite homogeneous mass distribution (answer: not applicable), or if it is about how matter started to clump (need a different model to guide us) early in the game.

We only need to consider the initial action on a test particle given the assumed uniform initial distribution of mass across an infinite space.

This suggests the former of the two.

Even if you want to assign every particle some random initial velocity, there's no force on any particle at initial time, so it's velocity does not change and the density remains uniform if particles do move randomly.

Except in an expanding metric, any initial velocity drops off almost instantly, so in pretty much no time, nothing has any velocity except due to local accelerations from local interactions. Kinetic energy is not conserved under non-inertial metrics, which includes expanding metrics.
So essentially, the entire universe is full of stationary 'stuff' (at least once 'stuff' starts to form). OK, radiation continues at light speed, but its energy similarly drops off really quickly, so a photon, if it manages to get anywhere in an opaque universe, will in short order increase its wavelength.

So the picture at time = initial time + δt is identical to the picture at  time = initial time).

Heck no. The density went way down over that time, but sans local fluctuations, the place is still nice and uniform energy density and there should be no net 'forces' acting on anything.

This is a hypothetical situation and there is no need to tarnish it by suggesting the real world isn't as perfect as the model.

Well, it is those imperfections that eventually brought about galaxies and such. Without them, the universe would be a permanent gray paste. That's why I asked if this topic was about the actual homogeneous case, or if it was about how the clumping starts.