[jeffreyH]

You can map your function onto a spacetime diagram. As α converges with t there is a connection to the speed of light. The function approaches a light-like path. This will only match at α = ∞. This may be the connection to both time dilation and a fundamental time scale.

EDIT: It seems to me that the green line functions are closer to a match with inflation. That is if you take the connection with spacetime diagrams into consideration.

That way you don't affect the accelerating expansion idea. When α = 0 this could be like a Planck scale equivalent. Before that we are barred from knowing anything. This would be the big bang initiation. Then inflation which quickly converges α and t.

[Bill S]

Halc; thanks for your response to #75. It highlights the fact that I cobbled together that post in a hurry and expressed some things badly.  I'm trying to find time to go through both posts thoroughly to get my thinking straight, but at present, it looks more as though my days of posting in TNS are numbered.

[Bill S]

A is in motion, relative to B.
A measures time as passing at 1s/s, in her RF.
B measures time as passing at 1s/s, in his RF.

How could either of them possibly measure that?  What would they expect it look like to them to measure a different value?
It's like verifying that your measuring tape measures one meter per meter.  We know, because we held a tape measure up to it.

]

A has no way of measuring time as passing at any rate, other than 1s/s in her RF.
B’s position is the same in his RF.

A and B both measure time in the other’s RF as being dilated.

No.  A and B each measure the other clock as dilated in their own frame, not in the other frame.

This is point I was working towards.  Pop. Sci. books often say things like: “A sees B’s clock as running slower…”.  Although we know that A cannot observe B’s clock; we tend to accept this statement, because it is a thought experiment. 
Are we, in fact, saying that A calculates that B’s clock would be perceived as running slower than hers, if she could see it; and that this, and any calculation of the amount of the difference, are based on the equations of SR? 
Of course, we know, from (e.g.) satnav, that these equations reflect “reality”, so this is probably nit-picking.  I’m not really after BC’s Pedantry Award.    

The measurements made by A and B, of time in the other’s RF, are in the past, relative to each other, and are both right, so there is no “absolute” past.

A and B are frames or observers, and not events.  What you measure is events, and those measured events are in the past of the measurement events.  This is true of those two events in any frame.

This arose from Jeffrey’s observation that: “All frames non local to the observer are in the past due to the speed limit of information exchange.”

If we identify A and B as inter-visible, physical objects, and as observers occupying those objects; we can consider optical observations (either direct, or via light signals), and “observations” via radio signals.  In all cases, the information received by the observer will be relevant to an event that took place in the past, relative to the observer’s present.

This must demonstrate that there is no universal rate of “passage of time” that can be identified.

The above example does not demonstrate this, either way.  There could be a universal rate.

This provides an illustration of our inability to identify a universal rate of “passage of time”.

The rate of expansion of the universe can be measured only in terms of the rates of motion of given bodies, relative to other bodies.
That rate is actually a good way to determine universal time, because in any non-isotropic foliation of spacetime (translation: in any non-preferred frame), the expansion rate is not uniform.  It is greater one way than the other.

I think you’ve lost me there. 
Doesn’t SR say that all RFs are non-preferred frame? 
Isn’t the expansion rate of the universe measured as being the same in every direction?
Given that these points are correct: where might we find a “non-isotropic foliation of spacetime” in which to observe the expansion rate as no-uniform?

More to return to, but out of time.

[Halc]

How could either of them possibly measure that?  What would they expect it look like to them to measure a different value?
It's like verifying that your measuring tape measures one meter per meter.  We know, because we held a tape measure up to it.

]
A has no way of measuring time as passing at any rate, other than 1s/s in her RF.

My point was that it wasn't measured at all, just assumed.  If it was measured, then one could ask what it would look like if a different value (say 0.8 s/s in her own RF) was measured.

A and B both measure time in the other’s RF as being dilated.

No.  A and B each measure the other clock as dilated in their own frame, not in the other frame.

This is point I was working towards.  Pop. Sci. books often say things like: “A sees B’s clock as running slower…”.

But that would be in A's frame, not B's frame.  "A sees" is a reference to A's frame.  A does not 'see' B's clock running slower in B's frame, which is implied by how you initially worded it.  That's what I was correcting.

Although we know that A cannot observe B’s clock; we tend to accept this statement, because it is a thought experiment.

Very few thought experiments have people looking at clocks that are not in their presence since little can be determined from that.  For instance, if B is coming towards me, his clock actually runs slow in my frame due to the speed, but it appears to be running fast due to Doppler effect, which is a far greater effect.  How else is the twin that travels going to expect the stationary twin's clock to read a greater value if that clock in fact always runs slower than the travelling twin's clock in the traveler's frame?  If he watches the distant clock the whole time, at some point it is going to need to appear to run faster.  Similarly, the twin back home will see the returning twin's clock run faster, despite the fact that the comparison when they meet still showing much less elapsed time on the traveling clock.

Point is:  Don't look at distant clocks.  It doesn't tell you what time it reads and it certainly doesn't tell you the rate at which it runs.

Are we, in fact, saying that A calculates that B’s clock would be perceived as running slower than hers, if she could see it; and that this, and any calculation of the amount of the difference, are based on the equations of SR? 
Of course, we know, from (e.g.) satnav, that these equations reflect “reality”, so this is probably nit-picking.  I’m not really after BC’s Pedantry Award.

Well thank goodness you made A female, since only via gender pronouns am I able to parse which clock you're talking about.
It isn't really about perception.  It is about what is actually happening in a given frame.  So B's moving clock is slower (not perceived to be slower) in A's frame because it is moving in A's frame, and yes, per the mathematics of SR.  As for perception, it all depends if B's clock is getting closer or not, and not so much on its speed.  Approaching clocks usually appear to run faster even though they're not.

The measurements made by A and B, of time in the other’s RF, are in the past, relative to each other, and are both right, so there is no “absolute” past.

Events in the past-light-cone of event X are in the absolute past of event X.  I say absolute, because this is a frame-independent fact.  There is never a pair of frame where some event is in X's past light cone in one frame but not in that cone in another.  Ditto for future light cones.  Events are frame independent since they don't have a velocity.

If we identify A and B as inter-visible, physical objects, and as observers occupying those objects; we can consider optical observations (either direct, or via light signals), and “observations” via radio signals.  In all cases, the information received by the observer will be relevant to an event that took place in the past, relative to the observer’s present.

Yes, true by (unproven) principle of locality.

This must demonstrate that there is no universal rate of “passage of time” that can be identified.

The above example does not demonstrate this, either way.  There could be a universal rate.

This provides an illustration of our inability to identify a universal rate of “passage of time”.

Well, there's a non-local way to determine a reasonable candidate for a universal frame, so from that you'd think one could determine a universal rate of time passage, but I've not seen anybody compute it.  Somebody must have, but I my search attempts have failed.

Doesn’t SR say that all RFs are non-preferred frame?

In SR, the 'S' is for the special case of gravity-free flat space, and reality is neither, so SR does not apply to the universe except locally where these conditions can be approximated.  So there is no local test for a preferred frame.
GR very much has a preferred frame (which isn't inertial), and I think it annoyed Einstein to admit it.

Isn’t the expansion rate of the universe measured as being the same in every direction?

Only in the preferred frame, and then only on average.  Locally, expansion happens more in empty places than in say galaxies where mass is concentrated.

Given that these points are correct: where might we find a “non-isotropic foliation of spacetime” in which to observe the expansion rate as no-uniform?

The frame of Earth meets that qualification.  The microwave background is definitely more red shifted in one direction than the other.  From that we can determine our absolute speed of something like 400 km/sec, slower than the ~600 km/sec speed of the galaxy.  It seems we're on the side of the galaxy that rotates away from the direction of motion.

[yor_on]

That's sad to hear Bill and I hope it's wrong, for once.
Keep on posting your thoughts man.

[guest4091]

Bill: A is in motion, relative to B.

A measures time as passing at 1s/s, in her RF.

B measures time as passing at 1s/s, in his RF.



Halc: How could either of them possibly measure that?  What would they expect it look like to them to measure a different value?


[by measuring transit time of light to mirrors located a distance d in opposite directions. It would of course be redundant.]


Bill: A and B both measure time in the other’s RF as being dilated


Halc: No.  A and B each measure the other clock as dilated in their own frame, not in the other frame.


[The purpose of the experiment is to measure the rate of the remote moving clock. That's what the graphic shows, in agreement with what he means. Since the remote clock is not part of the local frame, if it is running slow relative to the local clock, then so are all other EM processes in the remote frame.]



Bill: If this line of reasoning is correct, there is no “absolute” time; so, what is it that might, not, be fundamental?


Halc: Absolute time has been argued.  Problem is, all the proponents of it give a reference frame for it, but do not say how much our clocks are dilated relative to that absolute time.  I personally find this hilarious.


[If there is a universal physical process that synchronizes/coordinates events in some detectable manner, it hasn't been discovered yet. Universal time was possible when light speed was thought to be instantaneous.

Today: Where is the absolute origin of coordinates, or the center of the universe? Using remote clock time requires synchronization, and that is the obstacle since there is only relative synchronization, and only in the case of inertial motion. 

The revelation of Relativity is, motion alters measurement and perception. After 100+ yrs. of experimental verification, the general public can't or refuses to accept it.]

[jeffreyH]

Absolutes in physics tend to be out of reach. Massive particles reaching the speed of light or temperature being lowered to absolute zero come to mind. It should be the same with an absolute frame of reference.

[Bill S]

Thanks for the encouraging comments, yor_on. I'll do my best to stay with it.  Might keep dementia at bay.

[evan_au]

t = log₁₀(1 + 10^a)

For: Every time we go back an order of magnitude in time towards the Big Bang, the mass/energy density of the universe increases by 3 orders of magnitude, and quite different events and even different physics dominates. So this logarithmic way of looking back at the big bang is a useful way to view it.

Against: Isn't this just a more sophisticated way of avoiding discussion on t=0 (let alone t<0)?

[chiralSPO (OP)]

t = log₁₀(1 + 10^a)

For: Every time we go back an order of magnitude in time towards the Big Bang, the mass/energy density of the universe increases by 3 orders of magnitude, and quite different events and even different physics appears. So this logarithmic way of looking back at the big bang is a useful way to view it.

Against: Isn't this just a more sophisticated way of avoiding discussion on t=0 (let alone t<0)?

Glad to hear about your for. Funny thing is, your Against is the original for that I was aiming for. I will accept that it might just be a cop out, but I do think there is something to be gained by using the the log approach. By invoking this reparametrization, we might be able to avoid the problems associated with t ≤ 0...

[yor_on]

I'm wondering Chiral. This is collected thoughts on 'c' as a variable. http://www.ldolphin.org/cdkconseq.html

with a time dilation you could argue that 'c' changes too, from the 'eyes of a God' so to speak. See if you can find something interesting :)

[jeffreyH]

I'm wondering Chiral. This is collected thoughts on 'c' as a variable. http://www.ldolphin.org/cdkconseq.html

with a time dilation you could argue that 'c' changes too, from the 'eyes of a God' so to speak. See if you can find something interesting

Your link is likely related to creationism and therefore of dubious value. Constants are named so because they do not change. Unless they want to convince everyone the earth is only 6000 years old.

[chiralSPO (OP)]

interesting... Thanks for the lead, yor_on, I will check it out. And thanks for the warning jeffereyH, I will be skeptical...

[yor_on]

Seems Barry Setterfield is a creationist indeed. But it's still interesting reading Jeffrey. If you look at what I wrote, 'c' will be 'c', presumably, only as long as we find all values in a balance relative it. And I would say that this is the question that is discussed there. Everybody have opinions, doesn't mean that one is more true than another. The best approach to any question is to test, validate, and search anew. I'm guessing that there is a lot of good stuff there that one can use
=

You can also think of it this way. 'c' is a variable in that it is is observer dependent. Most people treat the universe as a generally 'objective' playground, defining 'constants' as if they are objective facts as seen from a 'outside'.

That's not true, if we had the 'eyes of a God' we would find observer dependencies redefining 'c' everywhere, as defined from a 'objective', generally same universe. That's also what's so surprising,  that the constants we trust in are the same for any frame of reference.

We have two good approximations for what makes this universe 'the same', SpaceTime Intervalls and LorentzFitzgerald transformations. Both of those are a logic defining how to treat 'events'  giving us proper time/length etc. They are not a 'generally same' 'objective' universe though, but they are a proof of us sharing a communication, exchanging signals.  And yes, they are a proof of 'locality' both of them, because what they lead us to is that your observer is equivalent to mine, both share a same ground level. Proper time and proper length.


And if you like, that's the groundwork for defining a 'constant'. What more is that I think it a good argument for the utter futility of defining a 'outside' to this universe. It wouldn't make sense from a 'outside', not to me anyway :)
==

It's a very strange universe Jeffrey.

[chiralSPO (OP)]

'c' is a variable in that it is is observer dependent.

My understanding is that this is not the case. The theories of special and general relativity are built around the concept that all observers agree on c, no matter what reference frame they are in...

[jeffreyH]

'c' is a variable in that it is is observer dependent.

My understanding is that this is not the case. The theories of special and general relativity are built around the concept that all observers agree on c, no matter what reference frame they are in...

Yes. Time dilation depends upon the value of c. Otherwise we would still be using Galilean relativity.

[yor_on]

Central Postulates of Relativity: (SR)
    The laws of physics are the same for all uniformly moving observers.
    The speed of light is the same for all observers.

Yes, but I'm not stating that 'c' won't be 'c' locally measured. I'm stating that there is no golden standard for a uniform motion, from that follows that 'c' is a relation to your acceleration, not a relation to a 'relative motion'. I'm also stating that although relative motion can't be defined locally measured, we can still prove different 'speeds'.
=

Think of it in 'black box scenarios' to see how I mean.

[yor_on]

Combine those statements and the conclusion will lead you to observer dependencies.

[yor_on]

That's also one of the reasons I look at 'proper time' and 'proper length' as something really important for defining locality, SpaceTime as 'one common universe' and relativity. Another way to prove the idea is to set up a two mirror experiment in uniform motion, measure, then accelerate realtive some suns blue shift, to then do a new two mirror experiment inside and at rest with the ship. There will neither be found a different speed of light, nor a blue shift. So your (new) uniform motion does not change your local measurement. But as you know you've accelerated between measurements you now have to find an explanation for the result.

The explanation is that all uniform motions are equivalent.

[yor_on]

The one above it :)