21

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.

22

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.

23

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

« on: 13/10/2023 17:33:37 »

Now, consider a particle of Hydrogen

The space is homogeneous for the purpose of this connundrum

Pick one.

The particle is the test mass being attracted to the homogeneous everything-else by a net force of zero. It doesn't even need a specific mass since it is the coordinate acceleration at its location that we're after, the gradient of the gravitational field there.

24

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

« on: 13/10/2023 16:52:23 »

I disagree with the prior answers. The space is homogeneous for the purpose of this connundrum. Going down to the particle level is never part of the shell theorem, which technically fails since no collection of discreet masses can be spherically symmetric.

We'll have a perfectly uniform distribution of Hydrogen gas spread out over space  AND  we'll also assume that space is infinite.[NOTE:  It is not necessary or guaranteed that the universe is or was infinite,  that doesn't matter, for this hypothetical situation we are having an infinite space].    For a star to form, some hydrogen has to clump together under gravity and form an overdense region of Hydgrogen.

Which kind of departs from your premise of a perfectly uniform distribution. Yes, anomalies form early on and escalate into more dense regions. It is a stretch to suppose that they are spherically symmetrical anomolies.

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.

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. Your application of the theorem is obviously invalid, and your logic stands up, so the theorem cannot apply to an unbounded uniform distribution of mass since it doesn't satisfy the definition of a spherical distribution.
It is the selection of the origin that is the invalid step. That origin needs to be put at the center of mass of the universe, and an infinite universe doesn't have one.

25

Physics, Astronomy & Cosmology / Re: What happens to the surplus electrons after an alpha decay?

« on: 08/10/2023 23:48:08 »

We sort of did an experiment of this sort in school. It didn't involve radioactivity, but it did involve stripping away electrons from molecules and sorting them into left and right buckets. It was just water, and after a while the dripping water just plain refused to fall into the bucket below, preferring to circle like all the airplanes in the 2nd Die Hard movie.

The lab table got quite wet in the process since gravity was no longer doing its job. Similarly, one can drop protons into a black hole only for so long before it will refuse any more.

26

Physics, Astronomy & Cosmology / Re: What happens to the surplus electrons after an alpha decay?

« on: 08/10/2023 23:41:45 »

...  become highly charged over time and at some point might inhibit or slow the alpha emission(wild speculation).

     The simple view of nuclear reactions is that they are almost completely independant of all conditions external to the nucelus.

Agree that the decay will (usually) be unaffected by any acquired charge. If the radioactive material emits enough alpha particles, it will become sufficiently negatively charged to rip the radioactive material apart (unlikely), or it will simply eject most of the surplus electrons (likely), aided by the negative charge repelling them.

That leaves a bunch of nuclei and electrons loose in space, too far apart to find each other. So what? It just takes longer for these things to become parts of whole atoms again, and not very likely the same atoms they once were.

27

Just Chat! / Re: Why are some threads locked?

« on: 05/10/2023 14:35:46 »

No hard criteria, just a case-by-case judgement call.
I'd have left it open if the OP was participating, but he has chosen to do all discussion in the other thread, including the deliberate misinterpretation of Bohr's theory, asserting that it is the electron that absorbs the energy, not the atom, because some wiki sentence can be taken to imply that.

I thank all who took the time to provide good answers.

28

Physics, Astronomy & Cosmology / Re: How Can We Know The Cosmos Age If We can Only See The Observable ?

« on: 03/10/2023 23:26:21 »

It's always a pleasure to hear from you, @Halc.  I'm also fairly sure you won't be too offended if I oppose some of your comments.

I cried myself to sleep after first reading all this, it broke my heart so much...

Actually, you've been away and it's good to see you back ES. Hope you also are not offended by my defending my posts.

The phrasing I used was just more like natural English language and that does tend to utilise a tacit assumption of presentism.

Well, yes, we all know what is being asked when asking the current age of the universe. My initial responses replied to that, and only your mention of relativity theory did I balk since it isn't a presentist model.

The Robertson-Walker metric  (which is what is used in main-stream Cosmology)  has the form

        dT²   =   dt² - a(t) ds² 

with dT being a proper time interval (a differential)   while  dt and ds are co-ordinate time and space  differentials respectively.  a(t) is the scale factor (which is some function of co-ordinate time).

Your answer (the entire post) concentrates very heavily on dT (which indeed has a sort of maximum of 13.8 ) where I was more concentrating on dt (coordinate time), which can be almost anything. I did say coordinate time:

That's not the age of the universe, it's just the time coordinate of humanity in that [or some other] frame.

So, if an object follows a path where the spatial co-ordinates vary with t,  then something is subtracted from the change in time co-ordinate.

Totally agreeing and I didn't say otherwise. I never said a clock traveling by any path from BB to Earth now would read anything greater than 13.8 BY. I said something else.

The way you have phrased things it looks as if the age of the universe is quite arbitrary and frame dependant but it is not like that, we can make a much more objective statement.

I said that one could take a very remote event whose proper time is say 100 BY and if sufficiently distant, would be space-like separated from us here and now, and thus, given the right choice of frame, our event would be simultaneous with that distant one that at which an age of 100 BY was measured. That's not a proper time of us here, but rather a coordinate time of us here, and one that is considerably larger than 13.8

For a start there are no global (or universe wide) inertial frames of reference in an expanding universe

I carefully avoided a suggestion that there was. The frame in which humanity is in a universe that is 100 BY old is not an inertial one, just some weird asymmetrical frame which puts us simultaneous with some event where there's a clock that has logged a lot more than 14 BY.  I also made no reference to SR since SR does not apply to a universe with energy, making it inappropriate to ask a question like what our current coordinate time is.

I know I referenced the sort of frame that is rarely referenced, one which has no neat clean rules and one in which Earth is not at the center, both horrible sins when discussing where we are in the large scope of things. As such, I agree that some readers can become confused by my comments.

I'm sorry but you have trimmed too many corners here and ended up with a statement that is just wrong even in SR.

Again, I am not using SR when making such statements. I did say 'inertialish', but only to mean I've chosen a coordinate system where Earth moves at .97c, at least on average, and thus our clocks are dilated relative to my chosen frame.

Time dialtion on its own is not the master of disagreements in what would be said to be happening now or simultaneously across the universe.

Not sure what you mean by this. Dilation is a coordinate effect, an abstraction. I've chosen such an abstraction such that our event than that of some distant observer measuring an age of 100 BY are simultaneous. Is that so difficult to accept? They're space-like separated events, not time-like, so it should be valid to do this.

Consider a frame S and another frame S' which is a standard Lorentz boost from frame S.

I think 'Lorentz boost' sounds like something that only applies to inertial frames. I don't think it is meaningful to express the speed of my S' in relation to some other non-inertial frame in which Earth is close to stationary.

Specifically assume the origin   (s, t) = (0,0)    in frame S and the origin  (s',t') =(0, 0) coincide  at time t=0  (or at t'=0 if you prefer) but frame S' just has some velocity v relative to S.     Now it does not matter what that velocity v is and hence what the time dilation factor of frame S relative to S' might be,   the origins of the two spacetime frames   (s, t) = (0, 0)   and (s', t') = (0,0) just do coincide.   The appropriate Lorentz transformation  takes  (s,t) = (0,0) in S  ---->  (s', t') = (0,0) in S'.    So that event will lie along a line of simultaneity for "my time = 0" that a person would draw across a spacetime diagram regardless of whether they are at rest w.r.t. frame S or frame S'.  To say this another way, both observers agree that the event (0,0) is happening at "my time =0" or what they might call "now".

Both observer being at the origin, sure. Remember that I put my origin  a great distance away, so we're not talking about Earth observers here, just some Earth clock that reads 13.8

This is the essence of what is often called "the Andromeda paradox" in SR.   It is not the time dilation factor on its own that determines the discrepency in which events in the universe are considered to be happening "now", it is a combination of the time dilation AND ALSO the distance between the two observers that matters.

I don't think there are observers in the Andromeda paradox because nothing is observed. It is all about what time it is over there relative to some event here. Sure, it is often anchord by a pair of strongly opinionated people passing by each other, but they are totally optional since a frame doesn't require an observer. It's just an abstract method to assigned coordinates to events. The frame I selected assigned time coordinate 100 BY to the event of humanity's existence. Whether there's an observer on that distant planet (or planet there at all) is irrelevant. I selected that distant event as my origin since it, like any other event, is a valid part of the universe.

So, in the case of the Andromeda paradox, a human being on earth can make the invasion force from Andromeda have departed 1 week ago or not having been sent yet just by walking slowly in one direction or the other on planet earth.

That makes it sound causal instead of abstract. Him walking this way or that has no effect at all. It is his abstract choice of frame that puts the departure moment at an abstract time coordinate that higher or lower than the one he assigns to himself. That's also what I am doing: picking a different way to assign coordinates to events, including the event of the existence of humans (at that precision, yes, it is an event, not a duration).

Anyway, yes, I am leveraging the logic of the Andromeda thing, except I picked something vastly further away than Andromeda, so far away that swings of hundreds of billions of years can result from a different abstract frame choice.

Now, as it happens, Andromeda is moving towards the Milky Way.

It is. In terms of peculiar velocity, we're moving away from it, but it's moving faster, catching up. Just FYI, irrelevant to this discussion.

Summary

"The age of the universe"  is not arbitrary and changed just by boosting to another frame.

There is definitely a frame implied by the question "how old is the universe". But I disagree with your statement as worded, since an arbitrary frame choice can very much change the answer.
Also implied by the question is that it is asking for the time coordinate of our current event, which is different than literally asking the age of something which includes all times, and thus has no age.

We have a very specific understanding of what is meant by the age of the universe and we can make a powerful and objective statement:

Agree. The additional assumptions are implied. We all know what they are.

However, we can assert that the maximum proper time that could have elapsed (on the path we have taken) since the big bang event is 13.8 bn years.

No disagreement there.

29

Physics, Astronomy & Cosmology / Re: How Can We Know The Cosmos Age If We can Only See The Observable ?

« on: 03/10/2023 15:12:44 »

A quick question, Halc: taking your example of a time dilation factor of 4, suppose our galaxy was receding slightly faster, say 1.03c, what becomes of the Lorentz factor? It will now be a complex number. Does this feed through to a complex age?

The recession rate of 0.97c was relative to the 'inertialish' frame of the distant place. Under such a frame, recession rates cannot exceed c.  The recession rates you see published are rates of increase of proper distance over time, not speeds. They're relative to an expanding frame, and in such frames, recession rates are rapidities, not speeds. (see bottom of post for example)  Rapidity adds the regular way and has no upper bound.  If, relative to this expanding frame, galaxy X is receding from us at .8c and Y (at twice the distance) is receding from X at 0.8c, then Y would be receding from us at 1.6c. The speeds don't add the relativistic way that they do in inertial frames.

Few of the typical rules of physics apply in such a non-inertial frame. Neither energy nor momentum is conserved. Moving objects tend to come to rest. The wavelength of a light pulse grows over time, the energy going down with it. Light does not travel at c except locally.

Relativity of simultaneity still applies, hence if one is considering the 'current age' of the entire universe of points in space well outside our visible universe, given the right choice of frame, one can make, at that distant location, any point in time be simultaneous with us at Earth, hence the distant parts of the universe having no defined age. So they define a preferred frame, which is the frame in which all events on comoving worldlines at similar gravitational potential as us, are simultaneous with each other. This is known as the frame of constant cosmological time (or just cosmological frame), and it is not an inertial one.

Apologies if that got a little complex. I did several edits trying to make it simpler/more clear.

An example of rapidity.  There is a highway to the next galaxy with little signs every light year like mile posts.  In my fast ship, I can measure my rapidity by the rate at which they go by. One sign per year is a rapidity of c. If I accelerate more, I can see one go by every day, and hence I can cross to the next galaxy before I die with a fast enough ship. The ship is moving at a speed of under c, but a rapidity of 365c in this case (not yet fast enough to get to the next galaxy in a lifetime)

30

Physics, Astronomy & Cosmology / Re: How Can We Know The Cosmos Age If We can Only See The Observable ?

« on: 03/10/2023 00:53:18 »

General Relativity (GR) seems to be a fairly good model, it has withstood several tests.   Provided that model is right, we do not need to be able to see the whole universe.

Well, if we're going to go strictly by what relativity says, it posits the entirety of 4D spacetime as 'the universe', and therefore it has no meaningful age at all. What we have is the temporal distance between the spacetime event of the existence of humanity and the spacetime event of the big bang, as expressed by Earth's frame. That's not the age of the universe, it's just the time coordinate of humanity in that frame.  For the universe to have an actual age, it would need to be contained by time (presentism), and that's quite a different theory than what relativity says.

As for the 'Earth's frame' bit, one can make the 'current' time as large as you want by picking a different frame. That lets relativity of simultaneity work for you. So say you want to compute the current age of the universe relative to the (inertialish) frame of some galaxy relative to which our galaxy is moving away at say .97c. In that frame, our clocks are dilated by a factor of 4, so the event on that far galaxy simultaneous with humanity here is somewhere around 55 billion years since the big bang.

There are also ways to make 'the age' lower by choosing yet different frames.

31

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

« on: 29/09/2023 20:25:50 »

You're making up facts. There's no conflict when different physicists explain it in different ways since none of the explanations are wrong. But the way I showed seems the most simple, and requires but the one equation.

Not just a different way, but different interpretation of the cause.

But one interpretation of 'the cause' doesn't invalidate any of the others. Personally I don't think there is a cause. Asking for one is like asking what causes a table to be longer than it is wide. It is perhaps caused by which dimension one decides to designate as the length.

Lorentz' relativity interpretes time dilation is caused by relative motion against stationary aether. Thus no paradox is generated.

But that's pretty much the answer I gave in post 1, except without the aether, which has no method of detection. Instead there is just a preferred frame. You choose one, and exactly like the Lorentz case, no paradox is generated.

Einstein's 1905 Relativity dismissed aether  ...
Since there is no more universal reference, it's no longer clear which clock ticks faster.

Nobody ever claimed that a clock ticked faster. Your problem for suggesting otherwise, but don't blame relativity theory when making such a blunder.

Einstein's 1921 relativity reintroduced aether, with some modifications. It no longer carries some physical characteristics. It was then renamed to space-time continuum.

'Spacetime' was coined by Minkowski in 1908. Einstein never wrote the term "space-time continuum:, which seems to be a pop term introduced as early as 1930 in a fiction story. I am unaware of a physics paper that uses the term ever, but if you have a quote from Einstein, that would really help illustrate that you're not just making up your own facts. And no, he never reintroduced aether either, but GR does introduce a preferred (non-inertial) frame relative to which cosmological time (adjusted for potential) is constant at simultaneous events, something that can be measured since cosmological time is an empirical measurement. None of that has anything to do with a proposal of a medium through which light travels.

If you dismiss frame changes

Nowhere do I dismiss them. I just said that computations are more complex if you choose to do them. Please try to actually read what I say and not make up your own crank story about what you hoped I said. The computation in posts 1 and 9 did no frame changes, and they both arrived at the same answer of 8 and 9 1/6 and they did it with only the one equation instead of several that would have been required to do the same thing with frame changes.

I just want to know how to do it right

This is very apparently a lie. If you wanted to know how to do it, there are many correct ways to do so, but I illustrated probably the easiest way. I invited you to work out yourself how to do it in the frame of the B's 2nd leg. That's how you learn, by doing, or at least attempting. You declined. You show no indication of wanting to learn how to do it, so the above statement is false.
It is this obvious lack of desire to learn that makes myself and other ignore the majority of any of your posts.
Prove me wrong and attempt the calculation using the 3rd frame and the numbers already provided in posts 1 & 9.

STR requires that all inertial frames are equally valid frame of reference.

That it does, but it doesn't say you are required to use them all. You can if you want, but it's a lot more work since transformations are required every time you change frames.

Minutephysics' video also depicts both twins see each other age more slowly during constant velocity motion. Only when the travelling twin turns around, he sees the staying twin ages much faster.

If it doesn't say that each of them sees the other twin age faster when approaching, then the video is wrong.
An explanation based on what people see is not wrong, but again, more complicated than this simple situation needs to be. You again need more than one formula to get the correct answers.

He mentions acceleration as the cause, instead of gravity. But GR says they are equivalent.

This is wrong, and the video is wrong if it says this. GR says the two are equivalent only locally, not over any significant distance. The two are very distinguishable over distance.
The problem with using videos for education is so many of the videos have no peer review.

The format of the information source should not prevent the content to be delivered correctly.

No, it shouldn't, but only peer review helps ensure the content is correct, and almost no video undergoes such review. I've pointed out blatant errors in videos by very respected, famous and popular authors.

If you think there are good videos, you can just put the link here

I've never had the time to search for good ones, and I've never chosen any to do the actual learning.
Watch out for any video that claims to be the one correct way to explain the situation.

Without frame switching, both twins are equally valid observers

First of all, it is you that needs to do frame switching or not, not the twins, who require no more intelligence than the ability to read the clock that's strapped to their wrist.
Secondly, all people and devices for that matter are valid observers. Frame switching doesn't somehow cancel the ability of a thing to make a measurement, but in the twins scenario, the only measurement is the local consultation of one's watch. There are other scenarios where actual observation beyond clock watching is necessary, but the twins scenario doesn't require observers at all. It can be (and has been) done by just zooming clocks around without people serving any purpose other than that of a courier.

confusion is caused by many supporters of STR have their own versions of the theory which are incompatible with one another, but claim that they are the standard STR.

There is one STR, and it is mathematically perfect, meaning it cannot be falsified from an armchair, only by empirical means. If somebody actaully alters the theory, that person is wrong, but most just convey the concepts in different ways. I've seen no wrong replies to you for instance. You're the only one making blatantly incorrect assertions.

I asked Google Bard about Twins Paradox.

Should be entertaining since it, like chatGPT, uses all the disinformation online as part of its training material. I would never trust an answer from a chatbot.

What is the twin paradox?

Bad start. You didn't ask about your scenario specifically (asking it for the ages at the end of your experiment in the OP, nor did you ask it about 'the cause' of the differential aging. So you're now asking a far more generic question. But you're in luck since it does directly attribute the potential differential aging to asymmetry, and the asymmetry to non-symmetric acceleration. So the answer is actually quite good this time. It says that asymmetry 'allows for' differential aging, but correctly doesn't go so far as to say it causes it, since there are plenty of asymmetric situations where there is no differential aging.

Another way to think about it is that the traveling twin's worldline is not a straight line in spacetime, but rather a curved line. The stay-at-home twin's worldline, on the other hand, is a straight line. This difference in worldlines is what accounts for the difference in aging.

This is quite close to the explanation I gave in the 'what is the cause' topic that has so many of your posts.
This answer is less intuitive and more complicated, but also more generic (can be applied to any situation), something not true of the first explanation.

The twin paradox has been experimentally verified using atomic clocks. In one experiment, two atomic clocks were synchronized and then one was flown around the Earth on a jet aircraft. When the clock was returned, it was found to have lost a tiny fraction of a second. This was due to the time dilation effect predicted by special relativity.

This part is a little off, since GR was needed to predict the results. The entire experiment took place at various altitudes in a gravity well. SR was not up to making any prediction better than the fact that the westbound clock would accrue more time than the eastbound one.

32

Physics, Astronomy & Cosmology / Re: How Can We Know The Cosmos Age If We can Only See The Observable ?

« on: 29/09/2023 15:12:06 »

From what I understand the Observable Universe is 93 billion light years.

93 G light years in diameter. That's a distance, not an age.
Half that (the radius) is the current distance to the furthest piece of matter/energy that could possibly ever have had a causal influence on us. If ewe were to emit a light pulse at our location in space, I think right as the inflation epoch ended (implausible since the universe wasn't transparent back then, so a light pulse would get anywhere), 46 Gly is how far away that light pulse would be now.

It is often said that we have no idea how big the unobservable is because we shall never see it due to the expansion speed being faster than C.

And that would be something often misstated.
The expansion is faster than C at the Hubble radius, only about 14 BLY away. We see all kinds of stuff that is currently further away than that. The CMB is probably the furthest at about perhaps 45 BLY distant in all directions. Anything further away than that needs to use something other than light to measure, like say gravitational waves or something, and they've yet to invent a GW telescope.

So, my instinct then is to ask is how can we tell how old the universe is if all we have is the observable universe to deduce from ?

Again, simple answer: by noting Hubble's constant, which is the inverse of that age.
Before Hubble's time when it was discovered that galaxies are receding, and at a rate proportional to their distance from us, there was no concept of the universe having a finite age. After the discovery, the age was pretty much known, but there was still no estimate for the size of the observable universe, which isn't a function of its age, but rather of the rate at which expansion is changing, something which wasn't measured until far more recently.

33

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

« on: 28/09/2023 13:41:25 »

This is also incorrect since the conclusion is abstract (mental, not physical) unless they are in each other's presence, in which case it is called 'differential aging', which is the unequal comparison of clocks physically in each other's presence.

Do you mean that A's clock will be equal to B's clock at the destination point?

No. 8y is not equal to 9y 2m.  Why would you suggest otherwise?

So, you are not confused if the problem can be simplified to 0 or 1 inertial frame change, but you start to get confused with 2 or more inertial frame changes. Cmiiw.

As I said before, doing it via frame changes just adds complications, requiring multiple formulas, some of those being more complicated.

Using what I showed, no frame change is made ever. You pick just one and stick with it.

The confusion comes from asymmetrical results produced by symmetrical situations.

The situation was never symmentrical, and if it is (like the one in one of your recent threads), then the result is very much symmetrical. But adding more characters just adds more complications which is inadvisable if you cannot in any way understand even the simplest case.

How much difference is caused by the changing reference frames?

None actually, since a change of reference frame is a mental abstraction, not physical. A mental change doesn't in any way alter what actually happens.

The other half is asymmetrical results between the twins, which means that one of them will observe time contraction of the other twin, instead of time dilation.

There is no such thing as 'time contraction'. There is time dilation, but you speak of this time contraction as if it is something different.

t's the cause of this supposed asymmetry which created disagreement among physicists.

You're making up facts. There's no conflict when different physicists explain it in different ways since none of the explanations are wrong. But the way I showed seems the most simple, and requires but the one equation.

Halc's answers. Reply #1 only addressed half of the question, which is reasonably hasn't touched the paradoxical part.
Perhaps the misunderstanding can be avoided if we use the term "switch of inertial frame" instead of "change of inertial frame"

I didn't touch on a paradoxical part because there isn't one.
The misunderstanding can be best avoided if we avoid switching inertial frames altogether, as I suggested in post 1.It only leads to confusion if you don't understand how to do it right, and doing it right that way is considerably more complicated than sticking to one frame as I suggested.

Lorentz factor is usually represented by gamma symbol γ instead of lambda λ.

I stand corrected on that one

Reply#15 is supposed to answer time dilation experienced by twin A as observed/calculated by twin B. But he refused to give numeric result, on the account that twin B switched his frame of reference.

I instead encouraged you to work it out yourself. Even an attempt with mistakes would have been a learning experience, and we could have helped. But you declined since apparently learning anything isn't your goal. Hence my not bothering to reply much anymore.

The answer is easy. If 'the frame of B' is used, 8 years are logged by twin A, and 9y2m by twin B.

The video below tries to solve twin paradox using acceleration.
But this video below doesn't touch the paradox yet. It only describe time dilation observed by earth twin, without being bothered by travelling twin's perspective.

The first is a terrible video. It has many errors, such as asserting that they see each other age more slowly, which is only true when they watch each other recede. The twins scenario is not in any way about what anybody sees. Then they try to explain things via gravity which is utterly wrong. This is a special relativity scenario in which gravity is never taken into consideration.

The second video isn't much better. It say 'time slows down as you approach the speed of light'. That's just wrong. 'I move at nearly light speed relative to a muon created in the upper atmosphere. It doesn't make time slow down to me. He then attempts to reference an invalid frame of a light-like worldline, which is obfuscation at best, and wrong at worst. He never actually gets back to the twins after that.

There are good videos out there, but hunting down bad ones seems a favored pasttime to those that don't want to learn. Take the advice of other posters and find a good physics text if you actually want to learn this, which I suspect you don't. Stay away from you-tube, pop sites, and especially social media.

Let's describe the same case from twin A's perspective. He stays in his own reference frame, while Alpha Centauri moves closer at 0.4c.

This statement is incorrect.  Twin A does not stay in his own constant inertial frame.  He starts in earths frame, accelerates to the cruising frame then decelerates to Alpha Centauri's frame.

His statement is pretty much my words from post 9. The statement doesn't suggest that any planet undergoes any acceleration. I was talking about the frame in which A is stationary for the entire duration of the exercise. Everybody 'stays in' this frame since it is impossible to exit an inertial frame. To 'be in' a frame is simply to have valid and unique coordinates to your event in that frame. So acceleration doesn't necessarily cause a change of frame, since a frame is simply an abstract choice, and the simplest choice is to never switch frames. So the other players (planets, twin B) are still in this frame, they're just not stationary relative to it.

Relative to that frame, which we've called 'A's frame', Alpha Centauri moves closer to twin A at 0.4c. There's no suggestion that it needed to accelerate to do so since it was always moving at that speed relative to that frame, as was Earth. Yes, twin A needed to accelerate to a halt in that frame, but that fact is irrelevant since he spent zero duration at that alternate speed. Acceleration computations do not figure into the simplified method I suggested in at the top.

34

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

« on: 25/09/2023 01:32:52 »

Given all of the possible points from which to make such an observation

In an infinite universe, there are of course infinite locations from which an observable universe can be defined. But they come in clumps, which in our case is our local group of galaxies.  Any light that can reach any point in our local group of galaxies can also reach any other part of the group, hence it acts as a sort of single center of one observable universe.  This is not true of any observer not in the group. Light might reach that observer and nothing in our group, or reach our group and not that observer, not even after infinite time.
So again, yes, there are infinite points of observation when talking about an observable universe, but the different 'points' of observation are pretty far apart.

35

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

« on: 17/09/2023 16:14:56 »

This is a slightly modified twin paradox to distinguish the effects of relative speeds and acceleration.

In a different inertial reference frame (one in which both stars are moving at -0.4c), this is pretty much exactly the twin paradox, with twin A being stationary the entire time, and twin B going out and back, albeit at 0.4c only outbound, and faster on the return.

OK, so this is trivially computed in the Earth frame. The resolution for any exercise in special relativity is to simply choose a frame (we'll pick Earth since Earth time was specified), all you need to do is compute the dilation factor due to the speed relative to that frame. This is computed (in natural units) with

λ = 1/√(1-v²)

Twin A started a journey to Alpha Centauri 4 light years away in a space ship moving at 0.4c  is expected to arrive 10 years later, according to earth observer.

OK, so in Earth frame, λ=1.091 so 10 / 1.091 = 9 years 2 months elapsed time for twin A.

Twin B stayed home to improve the space ship, so he can go to Alpha Centauri 5 years later at 0.8 c.

0.8c yields a λ of 1.667 so 5 years at home and 3 during the trip, so 8 total.  Not so hard, right? You can do this yourself without asking each and every time.

Classical physics calculation predicts that they'll arrive at Alpha Centauri simultaneously.

Classical in what sense?  Classical physics refers to non-quantum physics. I think you mean Newtonian physics, not classical.  Yes, every theory (including Newtonian) says they get there simultaneously. This is an objective fact, true in any reference frame.

How old are they when they meet up at Alpha Centauri?

As computed above, 9y2m and 8y respectively.

36

Just Chat! / Re: Is the universe real?

« on: 06/09/2023 15:59:38 »

Recently I learned, through a conversation with Halc, that quantum theory says that one of the following statements must be false: (A) there can be no retrocausality and (B) counterfactual definiteness exists.

More specifically, the principle of locality and principle of counterfactual definiteness (CFD) cannot both be true *.

which is why we need science.

I don't see the two statements as mutually exclusive.

Funny, since it was science (not mere philosophy) that demonstrated the mutual exclusivity of the two principles.

The idea that either of these is false seems incomprehensible to me, on an INTUITIVE level.

I was raised as a Christian and educated in a parochial school which taught me that the teachings of science and mathematics do not contradict the teachings of the Church. But then (around my 20's) the Church decided this was no longer true and one was not allowed to pay attention to the man behind the curtain (Oz reference if you don't get that). I was forced to choose, and that turned out to be pretty simple. I removed one premise that I held (the divine origin of the scripture) and so many pieces fell into place with startling ease.
Clearly it was a good thing to question one's beliefs, and so I learned to identify as many as I could (those intuitions you talk about) and question each of them, learned how to not rationalize, but rather to be rational. That part is not easy.
So began my journey into philosophy, but it turned out that all the pre-20th century philosophers were working on assumptions that science has since cast extreme doubt.  To find the answers I was seeking, I needed to learn the relevant science, not enough to pass a grad-level course, but enough to know the implications. I came to TNS fairly ignorant of relativity and QM, but I learned, and I changed my views as I learned more.

I don't buy into these "simulation" ideas which in my opinion are just science fiction gone crazy.

Most people don't ever think it through, as evidence by the fact that there are two very different versions of it that are nevertheless treated the same. I agree and don't buy into the various versions either.

Buddhism states that reality is an illusion- is it that too far off the mark?

That's a philosophical stance. I don't know exactly what they mean by that statement, so I'm not much qualified to comment further. For instance, how do they define 'reality' and 'illusion'?



* There's a loophole in superdeterminism under which both principles hold, but which is way off the weird end of the scale, and is not listed as a valid interpretation since it suggests that no science can be performed at all.

37

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

« on: 05/09/2023 21:48:27 »

I'm not suggesting that time is an illusion

I actually never understood those arguing that time is an illusion. I mean, a physical clock measures it, and a physical device cannot measure something that doesn't exist. So to suggest that time isn't real has to also include the clock not being real, and then you not being real. That's a less popular stance, valid, probably just a refusal to apply the term 'real' to anything.

instead, time has always been passing, and everything that has happened, or is happening, or will happen, takes place somewhere in the infinite and eternal time continuum. That continuum has just one direction, and that is forward in time.

That's an intuitive philosophical stance known as presentism. Most people are presentists, especially those unfamiliar with the term, but it does contradict Einstein's theories, contradicting the most basic premises.  If you deny that all local inertial frames are equally valid, and you deny the constant speed of light, you end up with a totally different theory that came along about a century after Einstein's papers. In this theory, the universe is 3D, not 4D. It is contained by eternal passing time just like you say. There is no big bang, only a (single) big bounce. There are no black holes,. Those things are artifacts only of Einstein's theory.
Look up I. Schmelzer if you're interested, but the theory is more complicated than general relativity, so it isn't an easy read. But it supports the presentism that so many people seem to want.

But also, the time continuum is characterized by a concept called "places".

I think that would be the space continuum, not the time continuum.

38

New Theories / Re: Dark Motion. Is it the answer to the Dark Matter and Dark energy problem

« on: 04/09/2023 22:42:21 »

Nasty remarks like that only serve to demean he who delivers them.

Momentus has earned a 10 day vacation for that remark, before which this topic will be closed, so no more posts here from him.
There will be a more careful watch on posts in other topics.

He is not open to anything that challenges his great discovery, as he sees it.

Totally agree that logic, mathematics, and reason fall on deaf ears with this guy. He is here for the conflict, not to learn anything.
I suspect the ban will be permanent before too long.

Thanks to both of you for your efforts, which are noticed by the non-participating reader if not the OP.

39

Just Chat! / Re: I'm due to be crowned!

« on: 04/09/2023 01:03:46 »

I'm due to be crowned!

Coming from my father, those words were a threat. "One of these days I'm going to crown you!".

Also, despite the coronation, you'll also always be a hero to me.  You have my thanks that you made the milestone the way one should, not spewing a thousand posts of crap, a feat far more easily achieved as evidenced by some that manage not to get banned on the way there.

You are all invited to the subsequent bash, as soon as the formalities are completed.

I might decline as my wife seems to disapprove of events involving overt debauchery.

40

New Theories / Re: Dark Motion. Is it the answer to the Dark Matter and Dark energy problem

« on: 01/09/2023 16:36:38 »

That's quite a handgun!  I'd expect that speed only from a rifle.  Irrelevant. We'll work with those numbers.

The bullet in the breech is obviously travelling at 100km/h and I now pull the trigger and the bullet flies off at 700m/s. The bullet continues it's travel in the direction of the train at 100km/h but now has a speed of 2520km/h.

Exactly, so the force on the bullet cannot always have been perpendicular to its motion.

The force is applied over say 100 usec (a 10th of a msec) which would yield ~700 m/sec over the length of a handgun barrel. We'll assume for simplicity that the force is constant for those 100 usec and zero before and after.

At time 0 the force becomes nonzero, and applied perpendicular to the bullet's initial 28 m/sec motion. After 0.1 usec (a thousanth of the total acceleration time), the bullet has accelerated 0.7 m/sec to the side. Total speed is 28.009 m/sec, which is pretty much the same speed as before because the force is mostly being applied perpendicular to the motion.

But now the bullet is already moving at 0.7 m/sec to the side and any continued force in that direction is now partially behind it, not perpendicular. The speed relative to the tracks begins to climb significantly.

After 10 usec (10th of the time under acceleration, 1/100th of the distance down the barrel, the bullet is now moving at 70 m/sec left and 28 m/sec forward which is 75.4 m/sec total, and now the trajectory is already mostly to the side, so about 0.9 of the force (sin(70 deg))being applied to the bullet contributes to increasing its speed. So the vast majority of the acceleration is pretty much directly in line with the motion of the bullet, not perpendicular with it. Only at first (a nanosecond or so) is the force perpendicular.

Since the direction of the bullet motion changes and the force direction doesn't, the force does not remain perpendicular.
With orbits, as the trajectory changes direction, the force does in lockstep, so it is perpendicular at all times.

It's all the same with the balls, with about 100 usec of acceleration time, perpendicular only at first and not the rest of the time.