[Bill S]

We can arrive at imaginary time……

The “Ausies” got there ahead of us!  Fred Alan Wolf says of dreamtime:

    “Aboriginals believe in two forms of time. Two parallel streams of activity".

    Interestingly, the aboriginal term “Alcheringa” is not best translated as “Dreamtime” (which was coined by research worker Frank Gillen). The term “The Dreaming” is preferred by the Indigenous Australian People as being a more accurate translation, and certainly involves two “dimensions” of time. 

Forgive that unscientific aside.

Who was it who said: “The truth is that a scientist's understanding of a phenomenon is inversely proportional to the number of math equations he uses to describe it.” 

I have a nasty feeling it might have been Louis Savain.

Interesting and valuable as the maths undoubtedly are, how well does this approach address the OP?

As far as we are aware, nothing can happen without time, in which it can happen.  How fundamental is that?

[Bill S]

This question comes about when trying to conceive of an absolute time scale.

Could it be that there is no “absolute time scale”? 

We perceive our Universe as functioning in accordance with the “rules” of relativity, at least, on a scale that is meaningful in our everyday lives.  Should we expect anything, other than “c”, to be “absolute”?

[jeffreyH]

If we define a universe in which no forces exist then all frames are inertial. However, if all inertial frames are in relative motion with each other then any particles traveling along with the frame will eventually collide with another particle. Therefore, these collisions act like a force. We have time. If all frames are at rest in relation to one another the same particles still exist but don't move. Where has time gone?

[chiralSPO (OP)]

This question comes about when trying to conceive of an absolute time scale.

Could it be that there is no “absolute time scale”? 

We perceive our Universe as functioning in accordance with the “rules” of relativity, at least, on a scale that is meaningful in our everyday lives.  Should we expect anything, other than “c”, to be “absolute”?

Indeed. I suspect that there isn't an "absolute" time scale. I want to reiterate that my intended meaning of "absolute" and "relative" is with respect to whether the 0 is meaningful or not:

My intended meaning of "absolute" and "relative" is more akin to Kelvin vs Celsius temperature scales, in which "absolute" scales are referenced to a meaningful zero-point, whereas "relative" scales only concern themselves with the difference between two points.

It would seem that when people invoke the Big Bang as "the beginning of time" that they are declaring some sort of absolute scale, in which everything that can be observed is t > 0, and that all t ≤ 0 is fanciful. My hope is to do away with this boundary condition by exploring the possibility of a temporal dimension that is not the same as what is currently defined as time, which has no bounds.

[jeffreyH]

Hence the mapping. 

[Bill S]

If we define a universe in which no forces exist then all frames are inertial. However, if all inertial frames are in relative motion with each other then any particles traveling along with the frame will eventually collide with another particle. Therefore, these collisions act like a force. We have time. If all frames are at rest in relation to one another the same particles still exist but don't move. Where has time gone?

Time has not necessarily gone anywhere, but without change (movement) how can we perceive it?

It might be true that there can be no change without time, but time without change?  That's a cat of a different colour.

[Bill S]

It would seem that when people invoke the Big Bang as "the beginning of time" that they are declaring some sort of absolute scale, in which everything that can be observed is t > 0, and that all t ≤ 0 is fanciful.

Agreed! If the BB was the beginning of time, how could it have happened?

“In the beginning there was nothing, which exploded.” (T. Pratchett).  Of course, he would have the answer!

My hope is to do away with this boundary condition by exploring the possibility of a temporal dimension that is not the same as what is currently defined as time, which has no bounds.

If it has no bounds; wouldn’t that make it infinite? 

[chiralSPO (OP)]

If it has no bounds; wouldn’t that make it infinite? 

Not necessarily... it just means there's no boundary. One could imagine a loop, or some other type of closed, but still unbounded  time...

What I have been describing with my attempts at defining α does seem to be unbounded and open, which would indeed be infinite.

[PmbPhy]

See attached article. I tried to post other articles but they're too big. This site is too stingy!!!

[Bill S]

Not necessarily... it just means there's no boundary. One could imagine a loop, or some other type of closed, but still unbounded  time...

If time were a loop, wouldn’t it repeat?   If that were the case, it would be bounded by its own repetition.  If anyone could experience the whole loop, he/she would be able to recognise the start/finish. 
In principle, a featureless loop might be said to be boundless.  No doubt someone can think of an example.

Good luck identifying infinite time.

[Bill S]

Fascinating piece of "history", Pete.  If it were not for the comment about dating the discussion some twenty years back, it would have been interesting trying to work out when it was written.

Shame about your other articles.  Could you split them into postable size chunks?

[PmbPhy]

Fascinating piece of "history", Pete.  If it were not for the comment about dating the discussion some twenty years back, it would have been interesting trying to work out when it was written.

Shame about your other articles.  Could you split them into postable size chunks?

Possible, yes.It'd be easier if I put them all on my website and post the URL to it.

[PmbPhy]

Please see the flour articles listed below the title "Articles about time" at

http://www.newenglandphysics.org/other/other.htm

[jeffreyH]

If I have this right we need two conditions for the function.

And

And the function should be continuous. Is this correct?

[jeffreyH]

An interesting but not very pertinent function is f(t) = (-t)^1.

[chiralSPO (OP)]

An interesting but not very pertinent function is f(t) = (-t)^1.

Is this not equivalent to f(x) = –x ? Perhaps there is a typo in your equation? f(x) = (–x)^x is definitely an odd one! (all x < 0 are well defined, but then only odd positive integers get real outputs)

[chiralSPO (OP)]

If I have this right we need two conditions for the function.

And

And the function should be continuous. Is this correct?

Close! I would like:
 

And

And the function should be continuous, and f(α) > 0

[jeffreyH]

Ok, got it. How soon do you want it?

[jeffreyH]

An interesting but not very pertinent function is f(t) = (-t)^1.

Is this not equivalent to f(x) = –x ? Perhaps there is a typo in your equation? f(x) = (–x)^x is definitely an odd one! (all x < 0 are well defined, but then only odd positive integers get real outputs)

Sorry that was just wrong. Should have been f(t) = (-t)^-1

[alancalverd]

I think Einstein pointed out that time is what prevents everything from happening at once.

So no problem with the Big Bang: it was the event when everything did indeed happen at once.