[Bill S (OP)]

https://en.wikipedia.org/wiki/Itzhak_Bars

In 2006, Bars presented the theory that time does not have only one dimension (past/future), but has two separate dimensions instead.

I seem unable to find any information of more recent date.  Does anyone know if/what progress there might have been?   

[Colin2B]

I seem unable to find any information of more recent date. 

Does anyone know if/what progress there might have been?   

I think the answer to this question might lie in the 1st statement.

[yor_on]

Damn, that hurts my head. It would lead a lot of things into different perspectives :)

" Bars alters the laws describing motion even more, postulating that position and momentum are not distinguishable at a given instant of time. Technically, they can be related by a mathematical symmetry, meaning that swapping position for momentum leaves the underlying physics unchanged (just as a mirror switching left and right doesn’t change the appearance of a symmetrical face).

In ordinary physics, position and momentum differ because the equation for momentum involves velocity. Since velocity is distance divided by time, it requires the notion of a time dimension. If swapping the equations for position and momentum really doesn’t change anything, then position needs a time dimension too.

“If I make position and momentum indistinguishable from one another, then something is changing about the notion of time,” said Bars. “If I demand a symmetry like that, I must have an extra time dimension.” "     

https://phys.org/news/2007-05-two-time-universe-physicist-explores-dimension.html

and then we have this. " Scientists suggest spacetime has no time dimension "

" In addition to providing a more accurate description of the nature of physical reality, the concept of time as a numerical order of change can also resolve Zeno’s paradox of Achilles and the Tortoise. In this paradox, the faster Achilles gives the Tortoise a head start in the race. But although Achilles can run 10 times faster than the Tortoise, he can never surpass the Tortoise because, for every distance unit that Achilles runs, the Tortoise also runs 1/10 that distance. So whenever Achilles reaches a point where the Tortoise has been, the Tortoise has also moved slightly ahead. Although the conclusion that Achilles can never surpass the Tortoise is obviously false, there are many different proposed explanations for why the argument is flawed.

Here, the researchers explain that the paradox can be resolved by redefining velocity, so that the velocity of both runners is derived from the numerical order of their motion, rather than their displacement and direction in time. From this perspective, Achilles and the Tortoise move through space only, and Achilles can surpass Tortoise in space, though not in absolute time. "

https://phys.org/news/2011-04-scientists-spacetime-dimension.html

what is notable with both ideas are that they are pure mathematics. Somewhat like a ideal reality, where our definition of a reality becomes a fiction. That differs them from Einsteins SpaceTime, in my view.

What would the universe be like with additional temporal dimensions?

https://www.askamathematician.com/2012/06/q-what-would-the-universe-be-like-with-additional-temporal-dimensions/

[evan_au]

Achilles and the Tortoise move through space only, and Achilles can surpass Tortoise in space, though not in absolute time.

The reason Achilles passes the Tortoise in absolute (finite) time is that the sum of an infinite geometric series is finite, if r < 1. - Where r is the ratio between successive measures.
- ie The distance between Achilles and the tortoise forms a converging geometric series
- So Achilles passes the Tortoise in a finite time

You don't need a second dimension of time to resolve this.

[yor_on]

Evan, those two are not the same. One defines a added 'dimension' of time aka Bars. The other, the one you replied too, propose that time is non existent. 
=

spelling

[Bill S (OP)]

If swapping the equations for position and momentum really doesn’t change anything, then position needs a time dimension too.

Physically, position must have a time dimension.  “Position” is meaningful only relative to something else.  In order to be defined as a position it must maintain that relationship, either statically or in relative motion, for a period; this involves time. 

Possibly it might be argued that this could be a period of zero time; but that is self-contradictory.  A period is a length of time, so to assert that there could be a period involving no time is like arguing that there could have been a time in which time did not exist.   

Lots more in that post to come back to.  It's a question of time.

[Bill S (OP)]

https://phys.org/news/2011-04-scientists-spacetime-dimension.html

The researchers give an example of this concept of time by imagining a photon that is moving between two points in space. The distance between these two points is composed of Planck distances, each of which is the smallest distance that the photon can move. (The fundamental unit of this motion is Planck time.) When the photon moves a Planck distance, it is moving exclusively in space and not in absolute time, the researchers explain. The photon can be thought of as moving from point 1 to point 2, and its position at point 1 is “before” its position at point 2 in the sense that the number 1 comes before the number 2 in the numerical order. Numerical order is not equivalent to temporal order, i.e., the number 1 does not exist before the number 2 in time, only numerically.

Can someone, please, explain to me how this says anything other than: What we measure is change, and time is the mathematical “tool” we use quantify that change in the 3+1D Universe which we perceive ourselves as inhabiting?

[Colin2B]

Can someone, please, explain to me how this says anything other than: What we measure is change, and time is the mathematical “tool” we use quantify that change in the 3+1D Universe which we perceive ourselves as inhabiting?

I think they are trying to argue that time is inseparable from the space dimensions and may be a 4th space dimension. So yes your statement is still valid in this world view.
The idea that Planck time is the smallest dimension of time that can exist is very contentious. There is no evidence that other Planck units work this way.

[Bill S (OP)]

I think they are trying to argue that time is inseparable from the space dimensions and may be a 4th space

Isn’t that a bit like measuring a cube with a ruler, then defining the ruler as a 4th D of the cube?

[Bill S (OP)]

The idea that Planck time is the smallest dimension of time that can exist is very contentious.

Alan dealt quite succinctly with that at: #35
https://www.thenakedscientists.com/forum/index.php?topic=76577.msg569792#msg569792

Planck length and planck time are often considered to be the shortest measurable quantities but there is no lower limit to the shortest calculable values. For instance unit Planck time is about 5 x 10-44  seconds, but the is no reason why I can't discuss a period of 10-45 s elapsing between events: I just won't perceive them as sequential.

[Colin2B]

I think they are trying to argue that time is inseparable from the space dimensions and may be a 4th space

Isn’t that a bit like measuring a cube with a ruler, then defining the ruler as a 4th D of the cube?

Not really. The ruler is only a measuring device, like a clock is. They are arguing that time is like space, but we can’t get a physical ruler along it.
To me the arguments they use are a bit tenuous, but on the other hand relativity does indicate that once you are moving through space (relative to another reference) the way you move through time (relative to another reference) changes.

[Bill S (OP)]

Not really. The ruler is only a measuring device, like a clock is. They are arguing that time is like space, but we can’t get a physical ruler along it.

Point taken. Neither clock nor ruler equates to time. 

Just noting thoughts as they come to me, so they may make little sense.

Ruler = clock, so neither is equated to a dimension of any kind.

Might there be a meaningful comparison between time and length?  Second = mm. Seconds become 4th D of space, do mms become 4th D of the cube we were measuring?

If so, what does that mean?  If not, how does that impact our view of time as a possible dimension of space?

Does time change as a result of relative motion through space, or is it just the observer’s perception (measurement) of time?

Is the observer measuring some actual entity which we call time, or is it just change that is being measured?

Could change be defined as a dimension of space?   Is so, what does that mean? If not, how can time be a dimension of space, if we define time as a measure of change?

Am I going mad?

[Halc]

Not really. The ruler is only a measuring device, like a clock is. They are arguing that time is like space, but we can’t get a physical ruler along it.

Point taken. Neither clock nor ruler equates to time. 

A clock equates to time no more than a ruler equates to space. With that I'd agree.

Might there be a meaningful comparison between time and length?  Second = mm. Seconds become 4th D of space, do mms become 4th D of the cube we were measuring?

There is, but a second is a lot longer than a mm.  It is more like 300,000 km.  It's kind of like how energy and mass are interchangeable.

Does time change as a result of relative motion through space

Don't think so since time can change even if I stay in place, or don't move relative to a selected thing.

how can time be a dimension of space, if we define time as a measure of change?

There is no meaningful time without change of some kind, but that doesn't define time as a measure of change.  The air pressure changes with altitude, which is an example of change over something other than time.

[Colin2B]

Might there be a meaningful comparison between time and length? 

As @Halc pointed out, yes. The spacetime interval equates time to distance via c, an equivalence but not the same thing.

Does time change as a result of relative motion through space, or is it just the observer’s perception (measurement) of time?

It is as if the relative distance moved (as time) varies depending on relative speed - and also depending on gravitational potential remember.
In 3d we are familiar with the concept that 2 people can travel between the same 2 points in space, but cover different distances. Similarity with moving through 4d except that the time distance can vary as well.

Is the observer measuring some actual entity which we call time, or is it just change that is being measured?

It is not change that is being measured. Time would pass even if nothing changes. Yes, it is possible to measure time using an agreed rate of change eg oscillation, atomic decay, clockwork mechanism etc
What do you mean by entity? Is distance an entity?

[Bill S (OP)]

 

There is, but a second is a lot longer than a mm.  It is more like 300,000 km.

My “Second = mm.” was not the best expression to avoid the agathokakological influence of interpretation.  All I meant to say was that time is measured in seconds, and distance in millimetres; but your response introduces some interesting thoughts.

Don't think so since time can change even if I stay in place, or don't move relative to a selected thing.

You may be stationary relative to a “selected thing”, but motion continues globally, so the perception of changing time remains.  The main thrust of my question was in the second part: “..is it just the observer’s perception (measurement) of time” that changes?

  The air pressure changes with altitude, which is an example of change over something other than time.

Within a given column of air, there is a range of values of pressure.  If you remove time from the scenario, the pressure at each and every point in the column remains the same.  There is no change.

[Bill S (OP)]

What do you mean by entity?

I use the word to mean a thing with distinct and independent existence.

Is distance an entity?

I would say: no; it has “existence” only as a quantitative assessment of separation between points.  For a similar reason; I suggest that time is not an “entity”. 

[Colin2B]

The main thrust of my question was in the second part: “..is it just the observer’s perception (measurement) of time” that changes?

Perception and measurement can different. In this case the measurement of the time difference is real for each observer, so they can both age at different rates, just as 2 people travelling between the same start and finish points can cover different distances. It all depends which route (worldline) you travel along.