Relativistic mass is rarely discussed in the same breath as space-time, even though it is 1/3 of Special Relativity. The result is a 2-D illusion called relative reference and/or no preferred reference. — wellwisher

I think I replied to most of this in my post 4 days ago.

The twin paradox tries to disguise this by using twins. Twins have the same mass, therefore kinetic energy and momentum will be the same for both references. This is how the system was gamed. If you use different masses, the energy conservation problem appears when you assume relative references and no preferred reference.

There is no suggested energy conservation in the hypothetical experiment. We have a rocket blasting energy and momentum all over the place. Are you attempting to deny the twin experiment? It is hard to tell, but you say 'how the system was gamed' like the description is faulty in some way.

However, we can't measure mass or relativistic mass, directly.
We have to infer rest mass from changes in energy; GR, with energy a relationship in distance and time, but not in mass.

Relativistic mass is a relational concept, not a property. Rest-mass is a property and can be directly measured. Not sure what you consider 'mass' to be if different from both rest mass and relativistic mass.

If the mass of the train and the mass of the train station are not the same, and we know how much energy; diesel fuel, was used to achieve this system motion, then you can infer who has to be moving and who has to be stationary.

No. This is just wrong. Mass comes not into play with the concepts being illustrated with this example. "Bigger-thing is the stationary one". Relativity does not support that.

A person on a train, looking out the window will appear to see the landscape moving at velocity V, If they assume they are stationary; train is stopped. It looks this way to the eyes but they just added energy to the universe, since the landscape what more mass.

They did not add kinetic energy to the universe. It was always there. The landscape/universe was always moving at V in that frame.

It is exactly this "constant local speed measurement" which makes SR a ,metaphysical assumption rather than empirically proven. It has only been empirically proven In "local speed" which is a very small portion of all possible speeds, yet it is claimed as a constant for all speeds. — Metaphysician Undercover

There is no 'local speed'. Local means 'inside a limited size box', like one drawn around the galaxy. They've tested small clocks moving at .98c and higher, just so you know.

Your post seems to attempt to throw doubt on SR, like it does indeed threaten your position. Interesting that you feel the need to attack it when you say it is a metaphysical theory.

The human capacity for observations of this is very limited. A large percentage of the various existing situations are not directly observable by a human being, and that light speed remains constant in these situations, is an assumption which is not empirically proven.

Again an attack, and dragging 'human' into it. You think light speed is different for humans than for other things?

Metaphysical time is the passing of time as we experience it, and this is what clocks measure.

Thing is, if time did not flow at all, we'd experience it exactly the same way. So what we are experiencing is not the metaphysical flow rate. You experience physical time, the same thing clocks measure. Your interpretation of that as flow is indeed a metaphysical interpretation, but relativity theory renders no opinion on which interpretation is correct. You seem to think otherwise as you seem to feel the need to cast it into doubt in your above posts, like there is empirical evidence against your view.

If clocks in relative motion do not measure time in the same way, then I suggest that people in relative motion do not experience time in the same way.

They both measure/experience physical time, and in the same way. Principle of relativity says you can't notice the dilation, but you would if you were experiencing a century of flow in only 10 years of high absolute speed travel. Indeed, nobody has tested this. It assumes that experience is a physical process, and you suggest it is a metaphysical process, that humans are metaphysically different than the rest of matter. Even your presentism doesn't assert this, but you seem to feel the need to add this to it. Yes, SR then would be a threat to your position.

So there is no difference between metaphysical time and physical time. The claimed "actual age of the universe" is calculated from principles and models. If the models are wrong, then so is the "actual age of the universe".

I'm not talking about the age of the universe from a point of view. I'm talking about the objective age of it, which doesn't exist except in some metaphysical views, my own not included.

Your problem is that you understand only one metaphysical interpretation and process all my comments with only that interpretation in mind, so you can't separate the parts that are different between the various metaphysical views. Einstein's work is compatible with both of them, and is thus not disproving one view or the other, but you don't see that because you don't see which parts are metaphysical differences. This would be easy if you understood the alternate view like Minkowski spacetime, the very concept that is the subject of this forum topic. That is a metaphysical view, and one that renders the relativity equations so much simpler, but relativity also works in a 3D model (at a massive expense of complexity) so doesn't assert those metaphyiscs. If it did, then yes, you are correct to attack relativity because it would indeed disprove your position. This is why I said that you have been empirically falsified when you said physical time is the same as metaphysical time.

As you don't seem to understand, let me explain why the special theory of relativity is metaphysical. Einstein took the existing theory of relativity, which was a metaphysical theory concerning motions, and adapted it to be applicable to the motion of light. The classical theory of relativity stated that all motions are relative, and this is a metaphysical principle which denies the possibility of absolute rest. — Metaphysician Undercover

A principle yes, more than a theory, and a local one at that. You putting a label of 'metaphysical' on everything doesn't make it thus.

In Einstein's day, there was a problem in applying this principle to the motion of light. Classical relativity theory did not appear to hold in relation to the motion of light. According to classical relativity theory, the speed of light relative to various objects moving in relation to each other would have to be variable according to the various different motions of the objects. So, Einstein proposed that the classical theory of relativity be adapted such that the speed of light be understood as constant relative to the various moving objects. This is "the special theory of relativity".

I think I object to 'be understood as'. SR was born of empirical evidence of constant local speed measurement, not an adjustment of understanding about it. The theory was a reaction to that evidence that did not fit current models. All of SR follows from constant light speed.

So, the classical theory of relativity, which was a metaphysical theory excluding the possibility of absolute rest, was seen to be incompatible with the motion of light.

The principle says the laws are the same in any frame, and thus no test can be devised to determine absolute rest. It never asserted the impossibility of it. There are always exceptions. Speed of sound in a particular medium is relativistic, but only locally. I can talk to the person ahead of me in a supersonic jet, but I cannot hear the aircraft behind us. Sound has a medium, and light was initially supposed to have one. SR threw that out, and GR sort of brought it back.

Instead of rejecting relativity as wrong, which is what the observations of the relations between the motions of light, and physical bodies did, it proved classical relativity to be wrong, Einstein proposed adapting relativity theory to allow that the speed of light remains constant relative to moving bodies.

Well, relative to stationary bodies. Light does not travel at c relative to a body that is moving in a given frame.

Prior to classical relativity, absolute rest, was the metaphysical principle employed. Classical relativity was proven wrong by the motion of light. Instead of returning to absolute rest as the metaphysical principle, it was replaced with the speed of light, as the assumed constant. Since these are each different fundamental ontological assumptions, absolute rest, and the constancy of the speed of light, which are taken for granted, depending on which one assumes, each is a metaphysical principle.

I disagree that there is any ontology asserted one way or another by any theories. Constant light speed is an observation, not an assumption, and GR shows that speed of something is undefined if not local, so light has speed different than c when not local, and depending on how speed is defined. Those definitions might indeed be metaphysics, but GR doesn't depend on them.

You asserted that metaphysical time is the same as physical time. The latter is that which is measured by clocks, but since clocks in relative motion do not measure the same value, they are not measuring metaphysical time (the actual age of the universe, a concept denied by spacetime metaphysical model). There is no device that can measure that. Best one can do is assume an objective foliation as perhaps suggested by GR and use that, but one still cannot express the unitless rate of it. If the universe suddenly aged at half the pace it did before, nothing physical could detect that change. That's why metaphysical time and physical time are not the same.

Very well then. Your metaphysical view of time is in direct conflict with TOR then. Your theory makes empirical predictions that have been falsified.

I didn't think it did, but you seem to insist.

Right, and that's clearly a metaphysical statement, just like the opposing claim that there is an absolute ordering of events is a metaphysical statement. Whether the ordering of events is frame dependent or not, is an issue concerning the nature of being, existence, and is therefore an ontological question, thus metaphysical — Metaphysician Undercover

You seem to be confusing physical time (the thing measured in seconds or years in any physics equation) with metaphysical time (the assertion of a present time (or alternatively, a lack of it), and the unitless rate at which it moves if it exists).

If these two (physical and metaphysical time) are the same thing and the theory of relativity is really a metaphysical statement as you say, then the theory of relativity (a century old empirical theory that is empirically put to the test every second of every day) is in conflict with your presentist metaphysical stance (a model that I claim makes no empirical predictions). One of them is wrong.
Fortunately, the theory of relativity makes no metaphysical claims, and your presentism is safe.

But what is spacetime absent any perspectives? Is spacetime a mental construction of a perspective? — Harry Hindu

Well that does seem to be a metaphysical question, and possibly doesn't have a correct answer even if it is unknowable. To me, spacetime seems not to be itself a thing that relates to other things, but is part of the relation itself between things that relate to each other in this universe. GR might have a good counter to this. If space is expanding and light has a speed relative to that space, then it is indeed a thing, despite it not being a thing under SR.
Fixed light speed is a local thing, and SR is a local theory and doesn't really apply to reality. Light very much does move at greater or less than c if not local, and that would not be true if spacetime was only a relation. So my feel for what it is needs an update.

One thing I noticed is space and time is always discussed when discussing SR. However, relativistic mass is rarely included in the discussion, even though it is part of the 3 part SR package. One may notice, SR is reduced to 2-D; space and time and not taught as 3-D; space, time and mass. This is the 2-D and 3-D clock problem in another guise. — wellwisher

SR is taught as 4D spacetime (one thing, not two separate things), but most of the examples (e.g. the train platform or barn-pole or twins 'paradoxs')are done in 2D spacetime (one each of space and time) to reduce the trigonometric overhead that is irrelevant to the points being made. Mass and length dilation are very much part of the teachings of SR. Gravity, acceleration, and non-locality are not part of the special case that is SR, and these topics are covered in GR teachings.

Relativistic mass is connected to an energy balance; relativistic kinetic energy, which tells us that all references are not relative, but rather they are absolute at some level. Unlike space and time, Mass is an invariant.

Kinetic energy is definitely not absolute. An object has none in the frame in which it is at rest. Mass is completely frame dependent. Rest-mass is not, but you didn't say that. Spacetime on the other hand is invariant. Any event is the same event in any frame.

As an example, say I had two rocket ships in the dead of space with a relative velocity V.
...
The same velocity is seen from either ship. — wellwisher

This cannot be. If rocket R1 has a velocity V relative to R2, then R2 has velocity -V (not V) relative to R1. Each ship does not observe the same velocity when measuring the other.

If we add mass, such as one ship has mass M and the other side has mass 2M, the energy balance is not the same in both references, even with the same relative velocity. Reference preference will double or half the total energy. The references are made distinct by their relativistic mass and energy balance due to the impact of a common 2-D relative variable, on two different 1-D invariants.

All this is ambiguous. Are you saying that one ship has twice the rest-mass of the other? No speed has been specified. For all I know, these ships are moving apart at a walking pace. So I cannot parse your example.

This can be proven by collisions and how the system responds to the recoil. The 2M ship will always punt the 1M ship if it has the velocity. There will always be an absolute hierarchy in the recoil response. Relative reference is an illusion due to using 2-D SR, instead of 3-D SR.

Seems to be some asymmetrical claim concerning momentum and such, but again I cannot parse what exactly you imagine going on. I imagine two billiard balls (with masses 1 and 2) in a collision, doing Newtonian sort of inertial momentum exchange without loss from friction, but perhaps at (unspecified) relativistic speeds. Yes, SR would be wrong if total energy or momentum was different before than after the collision.

Not a lot of people in more 'popular' media keep the science (only predictive value) and possible metaphysical implications seperate... — ChatteringMonkey

For example:

Simultaneous is a statement about what "is". — Metaphysician Undercover

No, it is just a way of relating two events. SR only says that the ordering of two non-causally related events is frame dependent. That is not a statement of what is. A statement that '7 is greater than 5' is not a metaphysical assertion despite the presence of the word 'is' in there.

Special relativity is a metaphysical theory. It renders an opinion on the reality of simultaneity. — Metaphysician Undercover

Nope. SR works whether simultaneity is real or not, or if actual simultaneity is objective or relative. SR is an empirical theory, which makes it non-metaphysics in my book.

If i'd have to put a label on my views, it would be materialism (what exists is the physical). I do try to refrain from metaphysics as much as possible. My goal in this thread was figuring out what kind of view of time physicist are assuming in special relativity, and if the theory is compatible with a non-metaphysical view on time. — ChatteringMonkey

Relativity theory IS a non metaphysical theory, so it doesn't render an opinion on say what is real. Like any scientific theory, it makes predictions about what to expect when observing the world, and that is not really metaphysics.
It is far easier to understand the mathematics behind it using the B-series (block universe) of time, but that is just an objective reference framework for spacetime, not a metaphysical assertion of what is real, or a scientific view that makes different predictions than does the A-series which has a present to reference.
I say all this because you ask how the physicists use it. Physicists may also each have a metaphysical opinion on the matter, but this opinion is not grounded on empirical falsifiability.

And additionally, figure out if we still need a notion like spacetime then... That's why i named the thread "SpaceTime?" (questionmark).

Yes, Minkowski spacetime is a 4-dimensional structure best described by B-series descriptions, and it is really hard to work with relativity if you have to convert to a different model. Everything is confusing and unintuitive in A-series, but is clean and symmetrical in B-series.

What is real to me is what can be percieved. I can see 'space', or rather i can see distances and objects in three dimensions. — ChatteringMonkey

I thought about this some more, and technically this is incorrect.

For any two points (events) in spacetime, there exists one or more inertial reference frames in which the separation between the two events is either pure spatial (simultaneous) or pure temporal (in the same place). From a given point of view reference event ('you', 'here', 'now'), the events that are perceivable are all of the kind that are pure temporal sort, meaning there exists a reference frame in which the perceived thing is at the same spatial location as the observation point. None of the pure spatially separated events are perceivable.

That means you can only see time, not space. The moon (spatially separated, but now) cannot be seen, only some past state of it when it was right here in that reference frame described above. If what is real is what is perceived, then the spatially distant moon (now, but not here) is not real, but the temporally separated moon (here, but not now) is the thing that is real.

Anyway, I don't buy into the idealistic definition of reality when discussing spacetime. It isn't an idealistic model.

noAxioms, there's a lot to consider in your posts, so let's start at the beginning.

What is real to me is what can be percieved. I can see 'space', or rather i can see distances and objects in three dimensions. I suppose space is real in that sense. — ChatteringMonkey

Well, you interpret it that way. You (here at a moment in time) can't see objects that are not here, only the light that reaches you from past objects, and only when that light gets 'here', just like you (now) don't experience times other than 'now'. Spacetime is more of a view-independent model that does not have a privileged here or now, so isn't particularly compatible with an idealistic definition of existence being dependent on perception.

What I've been discussing is the title of the thread (spacetime), not just space and yes also time, whatever it is, which is a different model.

The units we use to measure that, or x,y,z axis in geometry are abractions, these are not real. We invented those.

Yes The units to measure time are similarly abstractions.

So then why is time real? I have never seen time.

You can measure it, so isn't that perception of it? By your definition, it is real then. I cannot make a physical measurement of an abstract circle, so abstract circles are not real in that sense.

Also is defining the measurement of time as the measurement of temporal separation not merely a tautaulogy? I don't get it.

Yes, if you define time as temporal separation. That's what it means to be a definition. Different words for the same thing. You don't have to accept the definition. The flowing time model (with 3D space, no spacetime) would probably word the definition differently, but perhaps now.

In Minkowski Spacetime, space and time are the same thing, so seconds can be measured in meters if you choose. Two points in spacetime have a frame-independent separation, meaning the 'interval' between them is not subject to dilation when considered in different reference frames. This is mostly because a point in spacetime has no velocity since it does not move.

The idea of timetravel for instance is nonsensical if time is not real. We maybe don't believe it can be done practically, but we sure theorise about the possibility — ChatteringMonkey

Space is real, so time is real, but things don't 'travel' in spacetime. Take just space: A boat is 100 meters long, so does the boat travel for 100 meters? No, the whole thing just exists for 100 meters, and the point at the bow and the point at the stern are considered different points of the same boat. Likewise, I do not travel through time despite the fact that I exist in 2008. That younger-me is considered to be the same 'me' as the 2018 me, any only because of that designation is it said that I travel through time. Nothing actually 'moved' through spacetime to do that. The 2008 version of me cannot be elsewhere than 2008 any more than the bow of the boat can be at the stern (except the Titanic which attempted that feat).

Under spacetime, time is just another dimension and does not flow. It is exactly as real as space, so it is real if you consider space to be real.
As for the arrow of time, it is just like the arrow of space: There is indeed a local test that can be made to determine which direction is 'future' from a given point, so an arrow is defined. On any planet, there is an arrow of space for all three dimensions, with a clear direction for 'down' which can be determined with a plumb line, 'north' which can be determined by looking at the way the stuff in the sky rotates, and 'east' which is the remaining dimension. Out in deep space, these methods don't work, so there is no objective direction that is 'up' for instance. Perhaps away from the most influential gravitational force, which might be something like the great attractor if you're not particularly near any specific galaxy. Time would still have an arrow so long as there is work being done where your point of measurement takes place.

If time is just the measurement of change, and not some kind of 'thing' that literally exists, or that 'flows' or has an arrow or what have you.... would it still make sense in Einsteins special relativity? — ChatteringMonkey

Your title mentions spacetime, not time. Time is the same sort of thing as space, so if space is a measurement of separation, then so it time. It does not measure change since a slower process needs more time to produce the same change, but it would be the same time if it was a measurement of change.
So the spacetime concept (Minkowski spacetime) says that the measurement of time (not time itself) is a measurement of temporal separation just like the measurement of space is a measurement of spatial separation. Under spacetime, time and space are the same thing and can even share units.

And would there still be a need to fuse it together with space into spacetime to make the theory fit?

The above description is effectively fusing them together. The two are the same thing.

In special relativity high speed and mass influences time.

They do not influence time, but mass is a function of speed, and time is a component of a specification of a speed.

If time is a measurement of change, in special relativity this then would mean that high speed and mass influence the rate of change.

Yes, it influences the rate of change, but per what I said above, time is not a rate of change. An object does not have speed or velocity as a property, but only as a relation to an inertial frame. So the same object in its own inertial frame has normal mass and rate of change of any process. The rate of change is not a real property, and so isn't objectively different than the rate of change for an object of different velocity. SR says that given two objects moving at vastly different velocities, there is no local test that would determine that change is taking place faster or slower for one than for the other. This is a consequence of the principle of relativity which goes back to even before Galileo.

It has been difficult to parse your posts. English seems not to be your native language.
Some of the subsequent posts have made some things more clear. For instance, in english, an artificial intelligence is known as an AI, not an IA.

We have 3 ontological options:
1) We do not live now in a computational Simulation, and in the future it will not happen.
... — Belter

You need to make clear what you mean by 'live in' or by a simulation.
One case is a virtual reality (VR) where the experience is simulated to a real experiencer. This is already done today in any first-person video game. While playing the game, we 'live in' a computational simulation. A super AI is not required for this. My computer plays minecraft, a reasonable example of a first-person VR. While playing it, I remember that I am actually human. I have memory of being in a different world than the minecraft one.

The second case is a true simulation where a world is simulated down to the granularity required. If we are simulatable in that way, it would mean that all of physics (most in particular ourselves) can be mathematically described. It means no dualistic minds, else the simulated humans would lack them and not act at all like humans in the same way that a simulated radio (such simulations exist) will not be able to actually pick up real radio stations.

I've read all your posts, and it is not really clear which scenario.
In the VR case, why do I not have memory of being outside it? If always in it, how was I born?

In the pure-simulation case, our physics cannot be simulated by our physics, as pointed out by apokrisis. It would have to be run in a world with completely different physics which would permit a simulation of significantly higher cardinality of capacity, but the speed of it running would be irrelevant.
Michael Ossipoff's comments are about only the pure simulation case, and they are relevant. A simulation of world X allows X to be viewed by the runners of the simulation, but it doesn't really create X. It isn't ontology that is being done. So while I am capable of being simulated in some more capable universe, I am nevertheless not a simulation

[/quote]If the Simulation is made by a IA higher than human, and we define it as the ability of lying a normal human (following the idea of the Turing test), [/quote]First of all, a post-singularity AI might pass a Turing test, be we will very much know it is there. The singularity is by definition the point at which it can make self-improvements at a pace greater than improvements made by humanity. It has nothing to do with a Turing test, which is just a test to mimic a human in a text exchange, like this forum.

then the three options have the same probability a priori of be true, due to by definition a higher intelligence system can occult its existence.

That is not true by definition, and even if it was, it does not make even the odds of your three options. In fact, the physics we know are incapable of creation of such a self-simulation, so if we are in some sort of VR, it is being run in a universe of more computationally capable physics.

My claim is that Singularity is by definition unknown, such as God in religions, the player in video games, etc. A super IA is by definition, able to occult its existence. — Belter

The definition says nothing of the sort. The definition is that it no longer requires humans for improvement.

It turns out that an AI is not needed at all. The universe is purely mathematical in nature and can be simulated with a very simple machine with large enough capacity to hold the relevant state. The capacity is why it cannot be done with our own physics. But simple mathematics does not require an AI. The Babbage engine was one of the first to perform arithmetic faster than the rooms full of people with paper and slide rules, and it was hardly an AI.

In a pure simulation (not in the VR case), yes, the device doing the simulation would be occulted from the things being simulated, else it would be a simulation of a different thing.

Oh, and since you know who Max Tegmark is, perhaps this video will help a little. Pay particular attention to his remarks about how time probably doesn't move from one planck time to the next. If all of time is contained within a singularity of time, and the flow of time is just an illusion, there is no 'one planck time to the next' necessary. — StuartL

Tegmark does say that time probably does not flow, but he described time as a 4th dimension in addition to the 3 of space (not the same way you are using 'dimension'), and not as being contained in a singularity any more than is space is thus contained. The big-bang singularity is just one point (event) in spacetime.

I suspect that you don't know what is being described by time not flowing, and perhaps this is the source of confusion in your posts. It is not a suggestion that time is 'stuck' at one point (the singularity say) and the rest being just potential. No, all of spacetime (all points in space and in our past and future) share equal ontology, and there is no particular moment that is the present one. Flowing time is the assertion of that special addition to the model, the present. It supposedly moves (or is stuck, the way you seem to envision it). But the block view says there is no present at all. There is no one state that is the actual current one. All states are equally real.

This was all suggested about a century ago by Minkowski who originated the idea of spacetime, or at least formalized a lot of the mathematics behind it.

Commenting first on the most recent post, since some parts of the picture are being clarified.
I see something like an argument that there is an unfertilized egg and all these sperm could come along representing potential people. If one wins, it renders nonexistent all the other potential people. But it doesn't render the whole pregnant woman nonexistent. That part is confusing.

A singularity of pure energy exists in a its own time dimension (imaginary time).

Nothing else exists within imaginary time. — StuartL

How is there this imaginary time if there is no change? You have a sole existent with zero difference from one moment to the next, which is indistinguishable from no time at all.
You have a strange mixture of flowing and block time, and of existence and nonexistence. Why does this imaginary time seem to flow, but our time does not? Our spacetime doesn't exist, except as potential of an actual singularity.

The singularity is spherical.

Then it isn't a singularity, which would be a dimensionless point. A sphere has a spatial radius.

Therefore; the singularity possesses potential future properties for each possible interaction upon its surface. Given that the properties of the surface of a sphere are infinite, the possible resultant potential futures for the singularity are also infinite.

By infinite properties, you mean there are infinite way in which it could be struck, which would be true of any object, sphere or not. It would require a second existent with which to strike it, but you say that doesn't exist.

A multiverse of potential futures for the singularity exists, but should any of them get “banged” into actual events, the singularity and its dimension of time would cease to exist.

Why do they cease to exist? Why propose that?

If an infinite number of universes are possible, how come this one with us in it exists, if God didn't make it specifically for us? - Because they all exist, but we are only aware of this one with us in it.

I thought this one didn't exist, but was mere potential.

In space-time the billiard ball always exists in a state of not having been placed upon the table yet, sitting on the table, being struck for the first time...Because space-time is set (predetermined) and the flow of time is an illusion. The billiard ball possesses properties for everything that ever happens to it in space-time.

The billiard ball is said to be a worldline in this example, not moving through spacetime, but existing in a path within it.

Now if we take the billiard ball out of space-time, and place it in a dimension of time that is not set (predetermined), then we can either say that it has no future, or that it possesses an infinite number of potential futures

Or it could still have exactly one determined future. All you've done is changed time from block to flowing, and that doesn't have an effect on determinism. Determinism can be true or false in both cases.

You may think that the velocity of the strike also comes into play here, but it doesn't, only the location of the initial strike is relevant. The velocity of the strike only becomes relevant in subsequently.

I do think that in the case of your singularity, since a singularity (or a sole-existant sphere for that matter) has no distinct locations, and thus can only be struck one way if the magnitude of the force is not a factor. There is only strike or not-strike. There is no strike differently, at least not the way I see it. OK, the billiard ball has distinct sides since it is perhaps on a table or something. It travels in a direction depending on the strike angle. Maybe the analogy is not applicable to the singularity.

Well, the video is using the word 'dimension' like some fantasy place where you might go, like Narnia. They use it interchangeably with 'universe' so it sort of means the same thing to them, but that usage of the word doesn't even gather a mention in dictionary.com.
The video gets off on the wrong foot by answering a question about the 'multiverse theory', of which there are several . They don't say what kind (leaving you guessing). Most are a single universe with multiple non-interacting worlds.
Max Tegmark enumerated them all:
Type 1 is distant places, a relational concept. A star 50 billion light years (BLY) distant is completely nonexistent to Earth, and we are nonexistent to them, but if the universe is 'played' like your DVD, their universe probably gets played as well despite the lack of an obvious inertial reference frame in which we both exist. These are thus technically 'worlds', not whole different universes. 'Multiverse theory' is probably not a reference to this one.
Type 2 is different inflation bubbles in quantum eternal inflation theory. The view is as close to a scientific theory as you are going to get since it explains empirical evidence. Under the theory, there are different bubbles of spacetime, with different numbers of space and time dimensions, and different settings for the various cosmological constants. The existence of one of the worlds (ours for instance) by no means has any effect on any of the others. There just isn't a paradox here.
Type 3 is MWI interpretation of quantum mechanics, which is definitely one universe with multiple semi-interacting worlds. You speak of it below. A split is not a creation event of a new universe since both worlds still interact with common elements. Like Type 1, the laws of physics are identical in this world and another branch, so there is no paradox about the existence of one world having some new rule that negates all the others.
Type 4 is true separate universes, completely separate structures not based on any common thing (like quantum mechanics which binds all the types above). All rules are off with type 4, so perhaps this is the multiverse theory spoken of, except it isn't a theory at all, just a metaphysical musing on our part.

If there is a common element binding them all, like a juke-box waiting to 'play' one of the DVDs, then it really is one juke-box universe with a bunch of objects, not a bunch of separate universes. If they're joined like that by the juke box, then sure, there might be a law that allows the playing of one DVD to destroy all the others. I still fail to see that as paradoxical.

I am not saying that the branching multiverse suggested by quantum mechanics isn't the case, it may well be. If I flip a coin, for me the result may be heads, but for an alternate me, created by that event, the result may be tails. However; for me, here, this me, the me that got heads, I will always get heads not matter how many times the DVD gets played.
The other me, the me that got tails, the me that came into existence when I got heads, will also always get tails, no matter how many times this DVD is played. — StuartL

Pretty much how it goes, except 'you' are the one who gets heads, and yes, the one who gets heads gets heads every time the DVD is played. That's a tautology.

And that may all prove to be BS, it makes no difference to my theory.

Not exactly clear as to what is your theory. I mean, you say the flow of time is an illusion, but then you say that the universe is like a DVD being played, which would be a flow of time, would it not?
And then you say the properties of the surface of a sphere are infinite, which seems completely unrelated to any of the other points in the list in which it appears.
So mostly I am attempting to figure out the paradox, which would benefit from a bit of formal argument where supposing X leads to a conclusion of not-X, which demonstrates at least inconsistency, or a paradox if also not-X leads to a conclusion of X.

No rule says that any of it must be the case, it just may be the case. It's a bizarre concept. What I am saying is that it's possible that the singularity that supposedly "Banged" never actually "Banged". For us to exist it never had to, and that if it did "Bang" that it would cease to exist.

You're saying that our own big bang made itself nonexistent? Or just asking us to suppose this? If the latter, for what purpose? If the answer is nonsensical, perhaps it is an invalid thing to suppose.

What I am saying is that our existence, and the place in which we perceive ourselves to exist, are in actuality merely potential futures (time singularities), for the singularity that never actually "Banged". DVDs in a DVD player with nobody about to press play.

That's not a paradox unless you insist that the DVD must be played for there to be a DVD. Harry Potter on the DVD does not change a single bit by the playing of the DVD. Harry is aware of how the DVD begins, but not that is is playing, or was ever played. I find that most logical. The playing of the DVD on the other hand is not, since it implies something outside playing it, and then is their DVD being played? That would be infinite regress. So why posit that it needs playing?

Glad you are still around after the post got no hits for an entire month. I never say it until MiloL bumped it.

Different 'potential universes/ time dimensions' would have their own physical laws in the same way that different 'actual universes/time dimensions' would. Each 'potential universes/time dimension' could vary very little from another, or could vary vastly from each other. — StuartL

This bit gives me a clue as to you usage of the term 'dimension'. You seem to picture them as different universes with different rules, sort of what you get with eternal inflation theory with each 'spacetime' being a bubble in the inflation material.

What I'm referring to in the billiard ball example is, that in the Space-Time dimension, the fact that the billiard ball is on the table at all, and any interactions that I may have with the billiard ball, are already determined. The instant the “Big Bang” occurred and our universe's time dimension came into existence, all of Space-Time was determined. The “where/when” of everything within the Universe was determined instantaneously. So the billiard ball never exists in a state of “Maybe I'll be interacted with” instead, it always exists in a state of “I will be interacted with, in this manner, at this time”.

OK, this seems to be a single-world hard determinism view. Quantum Mechanics suggests this is not the case (all events are probabilistic, not predictable at all), but there is no proof one way or another. The view is not invalid.

There is many-world determinism (everything is completely determined, but all possible outcomes are real). In this sense, all of Spacetime is determined at the big bang, but the billiard ball is still in a state of 'Maybe I'll be interacted with' since there are multiple potential futures, only some of which involve a specific interaction.

Then there is the non-deterministic view where events are truly random, or where there is interference from outside the universe, violations of what could otherwise be deterministic physics. As a relativist, I suppose I'm classified under the single-world random category as to what is real.

My views on determinism vs. indeterminism are, that although Space-Time is set (determined), it is set by the choices that you made/make/will make. Ergo, you cannot change your future, but you wouldn't anyway, because your future was set by your choices, and you are you, so you would never have made different choices. An alternate you in an alternate universe may have made alternate choices, but you here in this universe made the choices that you made, and will make the choices that you will make. The moment of your conception and the moment of your death still/already exist. The flow of time is an illusion.

I agree with all of this. To 'change' the future is an incoherent concept. Change means to alter state from some prior state to some different later state, say a candle changing from tall to short as it burns. The future is not something that is one way until you 'change' it to something else. It was never the first way then, so there is no difference that is the 'change'. This is an arguable point, since the first state could be expressed in a 'would have been had I not ...' sort of manner. My choice 'changed' it from this abstract would-otherwise-have-been state. But that state is completely abstract and nowhere real.

For me the Space-Time dimension is analogous to a DVD. When the DVD is played, you make an appearance on screen at some point, but you are already/still on the DVD whether you are on screen at the time or not, or whether the DVD is being played or not.

A completely determined DVD need not be played for there to be subjective reality to the inhabitants of the DVD. Harry Potter hates Snape regardless of the DVD being played. The playing only serves a purpose to whoever initiates the playing of it, an outside entity that wants to observe the story. That observer is completely undetectable to the inhabitants of the universe/DVD, so Harry cannot detect when his DVD is being played.

What the paradox is saying is, that if every possible time dimension exists, and it is possible for a time dimension to exist that cannot exist in a multiverse of time dimensions, then such a time dimension must also exist. Ergo, a paradox, both a multiverse of time dimensions, and a time dimension that cannot exist in a multiverse of time dimensions, cannot exist at the same time.

Here you really lose me again, mostly because I cannot figure out what this set of 'time dimensions' is. Perhaps I could understand the paradox if these terms were spelled out a little more clearly.

What I am saying is “Yes they can, and here's how...”. (Apparently physicists hold symposiums and seminars to discuss this paradox and cannot figure out how to resolve it. But anyway...I digress.)

Not a digression at all. If physicists actually do this (it is a philosophical topic, not a physics one), then there would be a link somewhere describing the issue and some of the sides taken.

If we return to my analogy of Space-Time being like a DVD, what I am saying is that 'Imaginary Time' is like a massive DVD player, containing every possible DVD. However; none of the DVDs are actually playing, and if someone did come along, select a DVD and start playing it, all of the other DVDs and the DVD player itself, would cease to exist.

Why? What rule says this must be the case?

If I have a billiard ball sitting on a billiard table, the ball is said to contain potential energy, that can be converted to kinetic energy if I strike it with another ball. Let us assume that tomorrow I am going to do just that. Because the ‘flow of time’ is an illusion, and space-time is set, the ball already contains properties for any and all interactions that I'm going to have with it tomorrow (its future is set).

Now, if I have another ball, on another table, in another dimension where the 'flow of time' is infinite, and time is not set: Does that ball have no future, or an infinite number of 'possible futures'? — StuartL

The first paragraph seems to describe a sort of eternal 4D block universe, vs. the second case which has a 3D spatial state that is 'the present'. OK, either view can be translated to the other. Both can be deterministic or not, so it is possible to have a future that already is, yet has multiple possible futures. On the other hand, presentism doesn't imply a set of multiple possible futures. The ball may not yet have been struck, but it is perhaps inevitable anyway.
So you seem to be exploring determinism/non-determinism more than block/present views of spacetime.

Secondly, 'potential energy' usually refers to something that is capable of accelerating due to gravity, such as a ball atop a hill. The billiard ball does not contain the energy that makes it moves tomorrow, but rather acquires that energy from the ball that strikes it. Just a terminology thing that doesn't seem to affect your point.

To me, although it may sound a little bizarre, the ball now contains an infinite number of 'potential future properties', one for every possible interaction in the dimension. Because, isn't saying that the ball no longer possesses 'potential future properties', that could be converted into actual futures, akin to saying that the ball no longer possesses potential energy, that could be converted into kinetic energy?

You are going to have to define 'dimension' here because you are using it in a bizarre way. To me, dimension is the mathematical one: A square has two dimensions, a cube has three, and spacetime has four. You really rely on this word below, and I have no idea what you're asking.

'If all possible dimensions exist, and a dimension for which a multiverse is impossible, is a possibility, shouldn't at least one such dimension exist?'

???? Like maybe longitude exists but not latitude? I have no idea how 'dimension' is being used in this context. It is in quotes, so perhaps it is the definition being defined by somebody else.

Perhaps you mean 'world', but even that doesn't fit this context. You seem to use the word to mean that different rules apply in them. Can two universes exist if one of them precludes the existence of the other? Something like that? I suppose that they wouldn't be separate universes if one is dictating the rules about the others.
Yes, a single-world hard deterministic universe is possible, and it precludes other worlds in that universe. But a non-deterministic universe is also possible, and it might have multiple worlds. I see no paradox with that. Not sure if this is what is being asked.

It says right in the OP, " Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details." That is the first line of the problem. — Jeremiah

Sorry. Don't remember reading that. I brought up the issue before.

She is never told it is Monday, there is no relevant self-locating information, and she knew there were only three possible awake periods before the experiment. Everything we know is everything she knows before the experiment therefore 1/3 is a prior. We don't have any privy information here. — Jeremiah

Oh good. I thought the OP didn't make this clear. The halvers would have it right if she went into this thing blind.

Michael, I see you're still going on about this. Spent a bit skimming the posts since I dropped off.

I’ve showed the reasoning multiple times. It’s the Kolmogorov definition of conditional probability. — Michael

You're doing it wrong. You are mixing probabilities from different times, different points of view, or from positions with different information.

Choose a point and stick with it. P(Heads) of 50% is true only before the coin is tossed but you seem to assign that probability to Beauty's POV when in a waking period. That is question begging (as I pointed out early in the thread) since that's the answer we're looking for, not the premise. At that time, it is not 50% from her POV nor the administrators, where it is 0% or 100%.

P(Monday|Heads) means "the probability that it's Monday given the fact that it's heads" — Michael

Oh crap. OK then. I really don't know how to read this stuff then. '|' means 'or' in my world, but they have that intersection symbol to mean that here. Union for 'and'.

Sorry again, but the posts are coming faster than I can actually absorb that web link that seems to assume (reasonably) that you already know the rudiments of the notation. For instance the 'unconditional probability' hyperlinks to a page that makes no mention of the term. Not helpful.

So what's the condition? P(Heads|Awake)? Well, let's apply the Kolmogorov definition again:

P(Heads|Awake)=P(Heads∩Awake)/P(Awake)
P(Heads|Awake)=0.5/1=0.5 — Michael

As you see, the quote is getting altered. Sorry.
I think you are mixing the probabilities that something will occur (or is the case, but unknown) with probabilities that something known has occurred. You seem to assign 1 to P(Awake) which is not the probability that you will be away, but rather the probability after the information about being awake has been completely (not just partially) conveyed.

Not sure if a computation of P(awake) is going to yield what we want. It seems undefined. Of course we will be awake at some point. She's not being asked if she's awake, but being awake is information nevertheless.

I don't see how you are applying the additional information of 'it isn't Tuesday/heads' into your computation.
— noAxioms

That's the P(Monday|Heads) = 1. — Michael

Excuse me if I am new to the notation. I read this as the probability of it being at least one of Monday or Heads is 1, but since it might be Tuesday/Tails, this is wrong. I would think the probability of Monday or Tails is certain.
Maybe I just don't know how to read the notation.

But it doesn't follow from that that each of the other three outcomes are equally likely. — Michael

Respond then to my post about her getting to wake up on Tuesday.Heads as well. It spells that out.

All four of those things were equal probability. If odds were 50 Monday heads, 25 each Monday tails and Tuesday Tails, then there would be 75% chance that it is Monday, despite the day also being the same odds as the coin toss. I say it is 66% Monday because 2 of the 3 remaining options (A and B) are Mondays.

I've done so multiple times:

Kolmogorov definition:

<sorry, the formatting rendered the quote unreadable> — Michael

OK, I didn't know that's what that was. I'm actually not much up on the notation of it all, so I have a helluva time following it.
In the linked page, B is listed as unconditional probability. So yes, unconditional odds of heads is 50%, but Beauty is not working from unconditional, and I don't see how you are applying the additional information of 'it isn't Tuesday/heads' into your computation.

Why? If the flip had a 50% chance of being heads and if heads guarantees Monday then there's a 50% chance that today is heads and Monday. You seem to just be asserting these probabilities without adequately explaining how you got there. I get to my probabilities by applying an axiom of probability. — Michael

Perhaps quote the axiom in question. I suspect it applies to something not known, such as a coin toss that has not yet been made, or which has been put under a cup without observation. Beauty has been given information about the toss, and that cannot leave the odds unaltered. She has been informed that the combination of Tuesday and Heads is not the case. That information could not have been conveyed if the coin toss was still under the cup. If she had full information ("it was tails"), then the odds would change to 100% tails, axiom of probability not withstanding.

There's a 50% chance that both B and D will happen, but there's a 25% chance that today is B. — Michael

'will happen' implies the coin has not yet been tossed. It has, and today has happened, which yields information that changes the credence. That changes the odds of B and D to 66%, 33% each.

Suppose we change the game slightly. Beauty wakes up each day, regardless of the coin toss. But if it Tuesday and Heads, we tell her it is Tuesday and Heads. Otherwise we tell here nothing. Each time we do the brain wipe and go back to sleep. Beauty knows ahead of time we are going to do this (the whole 33% odds business depends on Beauty knowing the scenario).

I say nothing has changed. If it is Tuesday and Heads, she is informed of that situation, and is therefore not allowed to place a bet on the known coin toss. All of A B C D occur with equal probability, and any given waking has 25% odds of being any of the 4 (A,B,C,D) or 50% odds of eventual occurrence. But on C, she is told it is C. On the other three, she is not informed which waking it is. All she knows is that it is not C. 33% odds of being any of the other ones.

I ask now what the odds of heads is when she's informed that it is not scenario C this time? Because this is exactly the information she has been given.

There are three awakenings (A, B, D), each with equal 50% probability of eventual occurrence. In that sense, each awakening has an objective 50% probability of happening, depending on the coin toss.
But Beauty is apparently being asked not if this occurrence will happen (that is obviously certain during any particular waking), but rather which of A, B, D it is. Each has a 1/3 chance if their odds are equal, and they are equal since each equally has a 50% chance of eventual occurrence. B and D do not have 25% (less than A) chance of occurrence, as you seem posit. All three have equal probability, but only A is heads.

She gets one bet

And if you tell me that I'll get £1 for guessing correctly, and that you'll let me guess twice if it's tails, — Michael

This is a different scenario. When do I find out that I get a second guess? You would have to either tell me before the first guess, or after it. If after, odds are 50% on the first bet and 100% on the 2nd. If before, then 100% on both.
Beauty only gets one guess. If she didn't have the memory-wipe, then the situation would be as you describe it here. She would only have the information she needs on Tuesday, when the odds are 100% tails.

If I offer you one free lottery ticket if you correctly guess heads and two free lottery tickets if you correctly guess tails then tails is the better bet even though equally likely.
Tails isn't the better bet because it's more likely but because it has a better payout. — Michael

This is not the situation faced by Beauty. She is offered one bet that wins or loses one ticket. There is no double payout during any of here wakings.

It's not. It's about her credence. — Michael

Yes, it is about credence. Beauty has information about the coin toss, and that alters the credence from the 50/50 credence that exists to nobody in the scenario.

If you tell me that you flipped a coin ten minutes ago I'm going to say that there's a 50% chance that it landed heads. — Michael

Yes, because I've been given no more information, so the odds remain 50%.

That doesn't mean it's more likely to be tails. It just means that tails is the better bet. — Michael

You say it is 50% odds, but tails is the better bet. This seems contradictory to me.
The whole point of my answer was which was the better bet. If the odds were 2:1 instead of even (33% heads), then Beauty would make or lose no money on average by betting.

The odds of the flip are 50% from nobody's point of view. They seems to be 33% (the one point where neither is the better bet) from Beauty's POV, and they are 100% from everybody else's POV since they know the outcome of the flip during any of the wakings. It is 50% only from the external POV (not Beauty) only before the toss, which is not during any of the wakings.

It doesn't happen twice to her. It only happens once to her, given that it was only tossed once. She just wakes up to it twice. — Michael

And in what way is that not happening twice to her? She gets to bet twice in that case, despite the fact that she is unaware of which times she's betting twice.

Sure, but it doesn't mean that tails is twice as likely to occur as heads, — Michael

It is twice as likely to occur to miss Beauty. Tails happens twice, and heads only once.

So, I ran 100,000 games and gave 1 point for successfully guessing heads and 0.5 points for successfully guessing tails (because you get two opportunities). It doesn't matter if you always select heads, always select tails, select tails 1/2 the time, or select tails 2/3 of the time. The average score is 0.5 in every case. — Michael

Ouch... Does miss Beauty know that she's getting fewer points on some of the bets. In that case the outcome is certain and she can win every bet. If not, she's not the one doing the gambling.

This whole betting thing demonstrates the correct answer. It only needs to be done twice, not 100000 times, because there are only two unique cases occurring in equal probability.
I wake up and am expecting to bet a coin with even odds. I bet tails and win 2 coins (one each day) if it is tails, and lose one coin on Monday if it is heads. Sounds like a winning bet to me.

If the stakes depend on the coin toss, then I bet tails if the stakes are 0.5 coins per bet, and heads if the stakes are 1 coin in the bet. I win every time in that case.

I noticed a discrepancy.
The description of the problem does not make it clear that sleeping beauty knows the procedure. If she doesn't, then she has no knowledge of anything other than their asking about what is a random coin toss. The odds would be 50% then.
The 33% comes from the sleeper knowing that there will not be a waking on Tuesday if the result is heads, but there will be a waking on the other three scenarios. In this case, new information is gained (it is not Tuesday/heads), and the odds are not 50/50

Another simple way to compute this, objective, but without knowledge:
There are four equal probabiltiy states (each equally has 50% chance of being visited eventually, all depending on the coin toss. Monday and Tuesday are eventual certainties):
A Monday Heads
B Monday Tails
C Tuesday Heads
D Tuesday Tails

The sleeper wakes up and knows not which of the four it is, but she has the additional knowledge (new information) that it is not C, so 33% chance of each of the other choices, and only one of those is heads. Odds are 33%