[QuantumGravity]

Infinity is the never ending, but not the never changing. I would say infinity (as in the common infinity ℵ0) is one more than the last finite number (by definition) so if you take one from it it becomes finite. Therefore the number can become finite even if it's a finite number you could only count with an infinite number of time. About time being still in some places, there is one place where time is supposedly still, the inside of a black hole, and even though we don't know exactly what happens there is common acceptance that time just goes very slow as if time were really still time would get exponentially slower the closer you got to a black hole but the curve would never get to infinity as it would have to get through the last finite number, something imposible in a finite distance. Therefore actually there is no infinity in the proper universe (I'm not really going to get into the multiverse). I hope that cleared some or all of your doubts! Bye!

[Bill S]

Hi Quantum Gravity, welcome to the emporium of infinite madness. 

Possibly, you are a mathematician, I’m certainly not, so some of the things you say puzzle me.

Infinity is the never ending, but not the never changing. I would say infinity (as in the common infinity ℵ0) is one more than the last finite number (by definition)

How would you define “last finite number”?
If Aleph null is one more than the last finite number, and is also “infinity”, doesn’t that make infinity a number?

… so if you take one from it it becomes finite.

This works, only if infinity is a number.  Try thinking of it the other way round.  Is there any number to which you can add 1 and claim to have reached infinity?

 

Therefore the number can become finite even if it's a finite number you could only count with an infinite number of time.

I would be interested to know if our resident mathematicians agree with that. 

Therefore actually there is no infinity in the proper universe (I'm not really going to get into the multiverse).

We agree!

[yor_on]

One never know jfoldbar, the 'dumbass' might end up to be me.
Wrote this on painkillers so I better reread myself, before .... :)

[yor_on]

I think I know how I was thinking there. You start with no golden standard of a time rate. What it says is that although we have ways to compare clocks to each other, there is also no 'local wrist watch' that we can define as being that 'golden standard' of a ''correct 'global' time rate''. We do it though, that's how we get to 'repeatable experiments', presuming all 'laboratories' to have a same time rate, alternatively 'equivalent' but then you also define it from more than just your clock because a equivalence involves more, it becomes a 'balance' of sorts in where your local clock is just one of the components.

On the other tentacle 'repeatable experiments' do work, no matter how you want to define it.

then we come to energy, a lowest state of 'somethings' energy is also one influenced by HUP, at least for this, think of temperature to see how I mean. Presuming there to exist different clocks that aren't 'relative' as much as locally true you then should be able to connect them to energy states. This is presuming that all positions in a space have a certain intrinsic 'clock rate' even though described differently through observer dependencies.At least I suspect that was what I was thinking of.
=

This isn't a negation of observer dependencies though, because those can be there and will be there as a result of different frames of reference acrting on each other. 'Intrinsically'  should be read as if something is the way it is by its nature, in 'splendid isolation' if one wants :) the same way we define a intrinsic energy to a photon, that then can be experienced to red and blue shift depending on ones observer dependencies measuring it.

[yor_on]

What that states is that a time rate at that lowest energy level should be very 'wobbly' aka 'indeterminate', presuming it to work. But as you go up in energy you leave HUP further behind and the 'clock rate' should stabilize. that would mean that there is a 'intrinsic clock rate' to f.ex space, although indeterminate, and for other things, as mass? What would that do to a space time position if so?
=

The last connects to how you define a 'gravity' acting on a space, as a geodesic, or not? And 'going up in energy' should be thought of as 'gaining proper mass' for this one, adding to a macroscopic behavior.  :)

Ah well..

[Bill S]

On the other tentacle 'repeatable experiments' do work, no matter how you want to define it.

Is this because every experiment is conducted in its own RF, and in that RF, time is constant?
It would follow from that that constant time in one RF could be validly compared with constant time in another RF.

[yor_on]

Yes, 'proper time' is what define a repeatable experiment. We don't do them normally in accelerated frames, although we could argue that this too is true for them. It depends on how seriously you take the claim of gravity and accelerations being a equivalence. If you do Earth is a uniformly and constantly accelerating laboratory at one gravity.

and that Bill, fits the claims of being able to treat a acceleration as a 'infinite amount' of uniform motion. Doing so 'c' is 'c' even in a acceleration.
=

Better point out that not all accelerations are uniform though, but a acceleration have the same properties no matter how it express itself. There are no new intrinsic properties, as far as I know, to a 'non-uniform' acceleration.

[yor_on]

It's a 'mystic' universe Bill, in many ways. and leaving it might just be the door to another mystery. I hope so anyway :) Still, have some kids, they will continue with or without me.

Neither you, nor me, like being bored

[Bill S]

We don't do them normally in accelerated frames,

Just juggling some thoughts about RFs

An accelerated frame = a non-inertial reference frame. (?)
We know it is an accelerated frame because an accelerometer at rest in that frame should detect a non-zero acceleration. (?)
If I’m conducting an experiment in that accelerated frame, will I obtain a result that differs from that of an experimenter in a non-accelerated frame?

[yor_on]

Yes.  Earth isn't a ideal inertial frame of reference. https://van.physics.illinois.edu/qa/listing.php?id=22342&t=is-earth-an-inertial-frame   But I'm guessing you wonder if it has a meaning at all? A perfect (non spinning) sphere of a evenly distributed density would still fall under the equivalence principle, if we go by relativity.

yes " For example, an accelerometer at rest on the surface of the Earth will measure an acceleration due to Earth's gravity, straight upwards (by definition) of g ≈ 9.81 m/s2. " https://en.wikipedia.org/wiki/Accelerometer

The last one. Are we talking about a ' perfect sphere' here?

[yor_on]

Had some sleep, and think I see what you was thinking of, hopefully.

The last one again. A repeatable experiment should be able to be done under both accelerations and uniform motions. What differs them would be that, again as far as I know, what relative uniform motion you find yourself to have have no importance for it. But when discussing accelerations I would have to assume that ones type of acceleration will make a difference to the outcome f.ex of blue and red shift of a light 'centered' inside a spaceship. The acceleration of earth is defined as being uniformly and constantly accelerating at one gravity, which then differs it from non uniformly made accelerations. So you can by using red and blueshifts measured over time see what 'type' of acceleration you have inside that black box.

Remember that I wrote "  There are no new intrinsic properties, as far as I know, to a 'non-uniform' acceleration. "? The blue and red shift I discuss can either be seen as a result of frames of reference interacting, or as a 'local / Intrinsic' property of any (accelerating) frame of reference. Uniformly moving frames of reference don't have this property displayed though.
=


Ergo, a uniform motion won't make a difference to blue relative red shifts, but accelerations will.  And that is a experiment with different outcomes, so the equivalence principle is made under certain prerequisites, as the space ship and Earth both being at a exact same uniformly constantly accelerating frame of reference,  ( ideally of a same mass too I guess, no not really, as that doesn't need any more acceleration :)   and ignoring 'spin'. That makes it two definitely different descriptions in which (all) uniform motion can be seen as one same (or equivalent)  'frame of reference'  no matter your speed, whereas 'accelerations' indeed will give you different frames of reference.

Another way to describe it would be by using 'identical test particles', accelerating versus being in uniform motion, but it comes back to the same thing. The one with Earth and the spaceship having a equivalence (gravity) is just such a unique 'repeatable experiment' demanding prerequisites. Doesn't make it wrong though but uniform motions are what's really weird to me.
=

There are a lot of things following from this, f.ex 'potential energy' that I find intuitively right, but incredibly hard to define. The same can be said for the stress energy tensor talking about shear stress. Still have to find a good description that intuitively describe what it means practically. A vacuum isn't really a 'fluid', or if it is I still need to see a proof of that, although you could argue that frame dragging is one.

What I mean is that we find mathematical 'properties' to a vacuum and gravity , but they stay mathematical and so untouchable practically, at least for me. If we trust Einstein everything should be explainable, and we should trust that, if we don't we're somewhere totally 'magical' :)

Shear stress and potential energy both share the same qualities. They are nowhere to be seen in themselves, only existing as a explanation to how different frames of reference interact. That's not good enough to me. I want more than a equation describing it, unless we're all in a mathematical space of course, then everything falls together with what you thinking of as matter distance speeds and accelerations really becoming a illusion.

A vacuum can both be seen as 'something' aka f.ex 'zero point energy' and as a 'void'. The Chinese use 'yin and yang' for the same idea. To me it's still primary a void practically.

[infinityparadox (OP)]

Hey sorry to post here after so long, I somehow stopped getting notices. It's only because Mark sent me a thank you email that I came back here to see. This is actually very cool, thank you all for your comments. I've read some of the posts and I'm a little confused by the understanding of the nature of time.
According to the theory of relativity, time isn't a constant, it and space contract at higher speeds. This makes it that time elapsed in the example of the 2 atomic clocks, one traveling at high speed and the other remaining, would actually result in the 2 clocks showing a different elapsed time. This isn't an illusion or a relative thing, when the jet lands at the airport and you compare the clock that traveled and the one that didn't they will show a different amount of time has passed. It may take some meditation to understand this, I did it more times than I can count before I could understand. Even though each second that passed was a full second relative to the person experiencing it, the actual time that passed isn't the same as the clock that remained stationary. So in essence, because time contracted for one clock, the other had less time pass.

The other thing is the comment about taking 1 out of infinity making it finite. Let's look at this a different way, let's say all of the infinity of possibilities of everything exist somewhere independent of space and time. If you want to physically manifest the possibility of this universe, you wouldn't have where to put it. This leads to think that we must be inside that infinity. Time sets the beat so our manifested universe wouldn't realize it is inside of the infinity and lose it's identity.

[Halc]

Good to see your return. Been a while it seems.

According to the theory of relativity, time isn't a constant

According to relativity, time isn't absolute. According to some alternate, but still valid, theories, time and space are both absolute. Nobody in the cosmology field ever seems to use these alternate theories, especially since they lagged relativity theory by almost a century.

when the jet lands at the airport and you compare the clock that traveled and the one that didn't they will show a different amount of time has passed.

Yes, this has been demonstrated, but it takes really accurate clocks to measure the difference. It's far more noticeable with say GPS satellites, all of which contain such accurate clocks.

Even though each second that passed was a full second relative to the person experiencing it, the actual time that passed isn't the same as the clock that remained stationary.

Time and space is not absolute, remember? So there is no 'clock that remained stationary'. Stationary relative to what?

So in essence, because time contracted for one clock, the other had less time pass.

No, the length (interval) of the spacetime path traversed by one clock is shorter than the other. This is a physical effect. Time isn't something that 'contracts'. There is time dilation, but that is a coordinate effect, not a physical one.

I couldn't figure out what it was growing into but had to accept it. My thoughts were always directed towards the end of infinite because well, it had a beginning, a fixed point attaching it to reality that was actually wrongfully ignored. My mind (would suspect most of us) is linear with space and time, everything has a beginning. I kept meditating on infinite in every form I could imagine. Still the question of what the universe is growing into remained

No valid model has the universe expanding into some otherwise unoccupied space. Instead, space itself is expanding. There can be no edge to the universe, be it finite or not. That just doesn't work.

The universe has a beginning so to speak, yes. It was never a point. The big bang happened everywhere, not at a point in space. Relativity theory has time as part of the universe rather than the universe occurring in time. That means it is meaningless to talk about 'before the universe', or it being created, or some such.
The alternate (absolute) models do support a universe contained by time, so such language is appropriate if you're using those models.

Hope some of this helps.

[infinityparadox (OP)]

Thank you! Yes some helps, the rest is beyond my understanding.
The 2 clocks I'm talking about is the classic example of atomic clocks' timers started simultaneously. Both clocks are at an airport. One remains at the airport (the one I said is stationary) while the other goes in a blackbird around the world at mach 3. The exercise is to meditate going with the clock on the plane then repeating while staying on the ground in hopes to reconcile how the 2 clocks would not indicate the same time has passed.
My conclusion was that time contracts, that you call dilation. But now, I can't understand what you are saying about it being relative to the observer. I tried to get Gemini to explain, it said basically the same. The 2 clocks show a different time but relative to the observer. So how are the 2 clocks off?
I'm still thinking time doesn't flow the same everywhere. Like if someone lives at the top of the Himalayas and another lives in an underground cave, time would not pass the same for the 2..
How about a spaceship that goes far away at high speeds and comes back, wouldn't the time it was gone be different from the time that passed on earth by years? 

[Halc]

Both clocks are at an airport. One remains at the airport (the one I said is stationary)

Earth is spinning, so relative to any inertial frame, that airport is accelerating. it isn't stationary at all.
So if your Blackbird flies west, it will meet the airport after 12 hours on the other side, and both Blackbird and airport got there in about the same time, same speed, different directions. I could not say which clock would read the greater elapsed time.

The exercise is to meditate going with the clock on the plane then repeating while staying on the ground in hopes to reconcile how the 2 clocks would not indicate the same time has passed.

A human keeping the clocks company would have no effect on the experiment.

My conclusion was that time contracts, that you call dilation.

The rest of the world calls it dilation, so best not to make up new words for established concepts.

But now, I can't understand what you are saying about it being relative to the observer.

It's relative to an inertial frame. The typical 'observer' is often just there to identify the frame: "The frame in which Bob is stationary". Bob could be a cardboard picture of a guy. His presence or absence does not affect the physics.

The basic gist under special relativity is that relative to any inertial frame, fast moving clocks tick slower than slower clocks. But this is relativity, so relative to that 'fast moving' clock, it is all the other clocks that tick slower. Any clock is stationary in its own frame by definition, so it runs at 'normal' speed in that frame.

The 2 clocks show a different time but relative to the observer. So how are the 2 clocks off?

The two clocks in say the airplane experiment show different times. This comparison is objective, not relative to anything.
How much apart? It depends on the situation. For your west-flying Blackbird, I could not say which clock would log more elapsed time. If the plane flew west, the Blackbird clock would show less elapsed time.
The famous HK experiment that first did this had slow airplanes that landed periodically, but eventually made it all the way around. The time difference was 59 nanoseconds less if eastbound, and 273 nanoseconds more if westbound.

Like if someone lives at the top of the Himalayas and another lives in an underground cave, time would not pass the same for the 2.

That's time dilation due to gravity, yes. The HK thing had to take that into account since the airplane was often at higher altitude than the clock on the ground.

How about a spaceship that goes far away at high speeds and comes back, wouldn't the time it was gone be different from the time that passed on earth by years?

Yes, it can be much less. If your ship is fast enough, you could age 1 year and you find that 200 years has passed on Earth when you get back.

[infinityparadox (OP)]

Yes, it can be much less. If your ship is fast enough, you could age 1 year and you find that 200 years has passed on Earth when you get back.

Thanks. I'm still not sure what is wrong with my understanding. Time elapse differently at different speeds, that part I already had. The question is how is this objective?

[Halc]

Time elapse differently at different speeds, that part I already had. The question is how is this objective?

Time dilation is due to speed. It is relative, abstract. It is not objective.
So for instance, if clock A and B are moving relative to each other at 0.99875c, clock B will be dilated by a factor of 20 in the frame in which A is stationary, and clock B will be dilated by a factor of 20 in the frame in which B is stationary. There is no objective 'stationary'. Each is simply moving relative to the other.

A very related (and probably most important part) is relativity of simultaneity. That means when comparing two events (say when clock A says 1 hour, and when clock B says one hour, relative one inertial frame the A event happens first, and relative some other inertial frame the B event happens first, and relative to some third inertial frame, the two events are simultaneous.
Simultaneity, being frame dependent, is also completely abstract, not objective. It is established by convention, usually a convention that is based on a choice of frame.

Differential aging is something else. If clock A and B were together at some point, they can be compared, or they can be set to the same value then.  If, later on, the are reunited  (very much like the airplane going around the world and back to the airport clock), the times can be compared and one might be found to show more or less elapsed time, and is an example of differential aging. This is objective, physical, and not abstract. Relative to any frame (inertial or not), that comparison will be the same. One clock has taken a shorter path (called an interval) through spacetime, and clocks measure the spacetime interval of the path it takes. Spacetime intervals are frame invariant.

The only way two clocks can be together, move apart, and then be together again later on, is for one or both of them to accelerate at some point. If a clock accelerates, then there is no inertial frame in which that clock is always stationary, so the dilation of that clock relative to some frame gets a little more complicated.

If you're completely unfamiliar with these concepts, then all this can be pretty hard to swallow, but I assure you it is accurate. I applaud your willingness to read the posts and ask questions about the unclear parts.

[paul cotter]

Hi Halc, I have a question concerning one of your statements and if you feel it is off topic, delete it and I will open a new thread. You say time dilation is a coordinate effect and not a physical one. However if I start with two synchronised clocks, keep one in my house and send the other off on a zillion mph hi tech craft for lets say, one year, and then reunite them there will be a physical difference. What say you?

[alancalverd]

Never mind "will be". By experiment, there is.

[Halc]

You say time dilation is a coordinate effect and not a physical one. However if I start with two synchronised clocks, keep one in my house and send the other off on a zillion mph hi tech craft for lets say, one year, and then reunite them there will be a physical difference. What say you?

The dilation is due to the speed difference. In one frame, the zoomy clock is moving at a zillion mph and runs slower, but relative to a different inertial frame, the zoomy outgoing clock is stationary and it is your house clock that is moving, and is thus running slow. That's what I mean by it being a coordinate effect. Which clock runs faster during some duration depends on the choice of coordinate system.

The comparison when the two clocks are reunited is the example of differential aging, and that is objective, since the different readings of the two clocks at that event is the same regardless of choice of coordinate system. So differential aging is physical, objective, and frame invariant.