[sandstone (OP)]

Scientific discoveries during the 20th Century demonstrated that uncertainty is inherent in nature.  These discoveries led to a change in worldview.  Determinism was no longer the received view. 

The Einsteinian paradigm regards time as a fourth dimension of space.  Of note, Aristotle argued that, without change, there is no time.  So, it would seem, that time may be regarded as both a dimension of space and a dimension of change. 

In classical physics, the order of accuracy is a measure of uncertainty.  In behavioural statistics, the confidence interval is also a measure of uncertainty.  In quantum mechanics, the location of a quantum object may be highly uncertain, leading to the notion of "infinite uncertainty".  Is this a fifth dimension of space? 

Coming to terms with uncertainty has practical implications.
In strategic planning, in managing change, in managing risk and in forecasting the future, uncertainty is a common factor.  In business, competence in coping with uncertainty offers a competitive advantage.

From just these few observations, it is apparent that measures of uncertainty are being used, along with the other four dimensions, to describe phenomena and to conduct human affairs.  So it could be argued that uncertainty is being used as a fifth dimension in each case.

What is a dimension?  It is a measurement devise, not an alternative universe, or multiverse if you prefer. 

For uncertainty to gain acceptance as the fifth dimension, of equivalent status to space and time, it needs a simple form of measurement.  Although the mathematics of probability are well advanced, probability is not the simplest measure.  That mantle goes to possibility.  In any given situation, as possibilities increase, uncertainty increases in direct relation.  With some qualifications, acquiring information about possibilities tends to reduce uncertainty.  So, information may act as an inverse measure.  It may also help in the assessment of probability.

Proposition

Accepting uncertainty as a ubiquitous fifth dimension, ostensibly a dimension of change, raises the proposition of a paradigm shift from four-dimensional space-time to
five-dimensional space-change! 

[darkmatterphilosopher]

I see a dimension as more than just a measurement devise, but a way we measure the flow of space-time. How would this theory explain more about how space-time flows?

[darkmatterphilosopher]

It is possible it could be a second dimension of time. As space has 3 dimensions it could be possible for time to have multiple dimensions

[darkmatterphilosopher]

you may even be able to argue inevitability as a dimension of time

[sandstone (OP)]

Greetings Darkmatterphilosopher

Thank you for the replies.

Would you agree that a dimension is a mental construct used to analyse, describe and compare observed phenomena? 

It is true that dimensions are adapted to the nature of the phenomenon observed (e. g., nanoseconds, hours, cosmological decades). In doing so, there appears to be a relationship between the measure and the thing measured.  In that sense, I would agree that a dimension is more than just a measure.  It is a measure with specific meaning and application. 

I would agree also that time and uncertainty are closely related, especially in change processes. 

Who was it who said: You can never step into the same river twice?  As a simple example of space-time flow, although the river may look the same from one observation to the next, there are differences which may be hard to identify and predict.   

As a general principle, possibilities increase with time.  Accordingly, uncertainty may also be seen to increase with time, if you accept that possibility is the prime measure of uncertainty. 

Inevitability is interesting.  At the macroscopic level, we do observe that a set of processes within a given context may appear to have inevitable consequences, and this may be borne out by what actually occurs.  For example, a chess situation that leads to checkmate may be regarded as "forced" because there may be no effective counters to a series of moves that the winner may make. In this sense, inevitability is a form of psychological certainty arising from competence and confidence in playing the game.   

The difference between environmental, or physical, uncertainty and psychological uncertainty is subtle but crucial to understanding this aspect of existence.

A millennium ago, zero was concept in denial.  Western society did not include zero in its numbering system. It seems, that zero was introduced to Western society by Leonardo de Pisa (aka Fibonacci) around the close of the 12th Century common era.  What followed includes the Renaissance, the scientific revolution (assisted by the calculus) and the binary code. 

Is uncertainty also a concept in denial?  Recognising U=5D just might help us to come to terms with uncertainty in a more constructive way.  We live in a five-dimensional multiverse with a four-dimensional mindset, and we wonder why we have so many apparently insurmountable problems!

Regards, Sandstone.           

[peppercorn]

Would you agree that a dimension is a mental construct used to analyse, describe and compare observed phenomena?

http://en.wikipedia.org/wiki/Dimension

The use of dimensions by scientists, mathematicians or engineers have well defined rules about how they can or can't be used.
It only makes sense to say dimensions are only just a mental construct in the same way as any aspect of observed reality is just a mental construct (ie. an interpretation of the physical world through our senses).
There are some ideas that impossibly tightly looped higher dimensions could be explain how the (sort of) point-like particles we observe in our universe and it is possible that a better understanding of higher dimensional structures could explain why the universe appears fundamentally unpredictable at it's finest detail.  But to say uncertainty is a dimension has no useful meaning in physics.

http://en.wikipedia.org/wiki/Compactification_(physics)#Compactification_in_string_theory

[sandstone (OP)]

Uncertainty as a dimension has no useful meaning in physics!  Interesting?  So the order of accuracy has no useful meaning in classical physics; or infinte uncertainty in quantum mechanics?

Have you considered the work of Ilya Prigogine?  In 1997, he published "The End of Certainty: Time, Chaos and the New Laws of Nature".  New York: Simon & Schuster. 





.  Have you ever wondered why identification of the fifth dimension has proven so elusive? 

[peppercorn]

[/1]Uncertainty as a dimension has no useful meaning in physics! 
[/2]So the order of accuracy has no useful meaning in classical physics?

I believe these two statements are unequal.  Perhaps this is a failure in my semantic knowledge.

Have you considered the work of Ilya Prigogine?  In 1997, he published "The End of Certainty: Time, Chaos and the New Laws of Nature".  New York: Simon & Schuster.

Being unaware of his/her work, no. Maybe you could supply a link to this paper?

Have you ever wondered why identification of the fifth dimension has proven so elusive?

No more than the 6th, 7th, 8th.... ∞th dimension.  That is, not at all.

[imatfaal]

Ilya Prigogine - great philosopher and scientist - nobel autobiog here

[sandstone (OP)]

The two statements are incompatible.  The first was a reiteration of Peppercorn's assertion.  The second is an example of uncertainty being used as a dimension. 

The following is a quote from Prigogine's "The End of Certainty": We need both equilibrium and non-equilibrium physics to describe the world around us....  the quantum theory of unstable dynamical systems with persistent interactions leads, as in classical systems, to a description that is both statistical and realistic.   In this new formulation, the basic quantity is no longer the wave function corresponding to a probability amplitude, but probability itself...  Probability is no longer a state of mind due to our ignorance, but the result of the laws of nature. 

In other words, nature is intrinsically uncertain!  In describing natural phenomena, measures of uncertainty are being used, along with measures of space and time.  Even so, there is a reluctance to accept U=5D.  Is this reluctance a matter of physics or a matter of psychology? 

[peppercorn]

The two statements are incompatible.  The first was a reiteration of Peppercorn's assertion.

True - my mistake.

The second is an example of uncertainty being used as a dimension.

Can you explain how?

Ilya Prigogine - great philosopher and scientist - nobel autobiog here

Thanks.  I will look at this more later on...

[sandstone (OP)]

The order of accuracy is a qualifier of a measure. It indicates that the first measure is true within a given tolerance.  That tolerance though is a measure in itself.  It measures the degree of uncertainty associated with the original measure. 

Space-time is also a measure.  It arises from the vast reaches of space and the finite speed of light ~ 0.299792458 gigametres per second in a vacuum. Hence distance is measured in light-years.  At the everyday macroscopic level, light seems to travel at infinite speed. This is an illusion, but the difference is negligible in that context.  Consider the plight of the blind person.  Sound could be combined with time to provide a measure of distance
(e g., sound-seconds).  In timing athletic events prior to electronic timing, the timer would focus on the the puff of smoke from the starter's gun, not the report of the gun, because light travels much faster than sound. 

An axiom in management is that, if you can't measure it, you can't manage it.  The same applies to uncertainty.  As an inherent part of nature, we need to be able to measure it.  The moment we measure it, we recognise the measure as a dimension.  It's a bit like separating the map from the territory.  We use the map to navigate the territory, but the map is not the territory.  Similarly, a dimension is a human construct that helps us to comprehend and communicate about natural phenomena.  Space-time does the same thing, but there is a dimension missing.  Remember Einstein has been referred to as the 'last determinist'.  It is time to embrace a new paradigm.

[peppercorn]

Sandstone,

Tolerance is a limit to measurement not measurement in of itself. It has no meaning without knowing what is being measured and in what units.

Your example of the human eye effectively experiencing light's propagation instantaneously is a perfect example of the tolerance of a measuring system.  There appears to be some confusion between limits in measuring systems and quantum uncertainty.  The uncertainty principle has been proved to be a fundamental aspect of nature not an measuring issue.   Einstein was referred to as the last determinism precisely because he could never accept this inherent bluriness of nature at its finest grain.

We can indeed measure quantum uncertainty, but only in the same way as we can measure any unpredictable but probabilistic phenomenon.  That's to say it will most likely fall at the normal with an infinite number of samples describing the distribution curve.

I am unconvinced that there is a 'dimension' missing from the four of space-time.  There is a fundamental indeterminably in the precise conditions of any one particle moving through space-time, but this is not explained in any way by having an extra physical dimension.

I appreciate your point about a map being a interpretation of a real landscape - one that is inherently incomplete, but in fact all of scientific endevour (at it boundaries) is like a map (or a model).

Theoretical physics looses it's edge once people start believing they are looking at an ultimate truth.  Creating mathematical models that fit what our instrumentation reveals about the deepest realms of reality is the goal of empirical research.  Without some sort of basis in mathematics your idea is unlikely to carry any weight, as it can makes no quantifiable predictions against which observations can be tested.

[sandstone (OP)]

Greetings Peppercorn,

Let's take this point by point.

The 'tolerance' is given a value. In other words, it is being measured, even if that measure is only an estimate.

Heisenberg's uncertainty principle serves to demonstrate that uncertainty cannot be avoided.  It is inherent in nature.  That is an essential quality of a fifth dimension of similar order to space and time.

Probability is a measure of uncertainty.  The mathematics are well developed.

In a way, I agree with you that there is not a dimension missing FROM space-time.  The problem is that space-time is an inadequate paradigm because it does not include uncertainty as a dimension.  We need a new paradigm that does include it. 

The irony is that including uncertainty in a broader paradigm means that there is no ultimate truth or endpoint.
It was once considered that the atom might be a scientific endpoint, but how many subatomic particles have now been discovered?

Lawrence Bragg is quoted as saying: Science used to be called Natural Philosophy... The fun in science lies not in discovering facts, but in discovering new ways of thinking about them.

Regards, Sandstone.

[peppercorn]

Hello Sandstone,

The 'tolerance' ... is being measured, even if that measure is only an estimate.

Okay - explain in what units? I stand by:

Tolerance is a limit to measurement not measurement in of itself. It has no meaning without knowing what is being measured and in what units.

i.e. We say 'x' is being measured to a tolerance of 'y'. The units of 'y' are non-dimensional [in the sense you seem to be confusing with s-t dimensions]. Knowing y tells one nothing about what x relates to.

Heisenberg's uncertainty principle serves to demonstrate that uncertainty cannot be avoided.  It is inherent in nature.

This was never in doubt & I inferred to it earlier.

[HUP] is an essential quality of a fifth dimension of similar order to space and time.

But you have not shown how space-time having a 5th dimension gives us a more complete model of observed reality.  Please do so - with maths if possible!

Probability is a measure of uncertainty.  The mathematics are well developed.
In a way, I agree with you that there is not a dimension missing FROM space-time.  The problem is that space-time is an inadequate paradigm because it does not include uncertainty as a dimension.  We need a new paradigm that does include it.

We do not, unless it explains something better that our current (incomplete) theories.  Again though, it makes no sense calling uncertainty a (spacial) dimension - it simply isn't.

The irony is that including uncertainty in a broader paradigm means that there is no ultimate truth or endpoint.

No one in science is claiming there has to be an end-point or ultimate truth. Science simply doesn't work by those definitions.

[Geezer]

Ahem! Personally, I think uncertainty might simply be a consequence of "time jitter".

[sandstone (OP)]

Greetings Peppercorn & Geezer.

Space-time is a concept conceived by a determinist.  Determinism is no longer the received view.  Given that, it is extraordinary that the space-time paradigm has held on so long.  Consider the following quote from marcel Neuts:

Although living with uncertainty is part of our existence, the idea that uncertainty could be quantified emerged only early in the 18th century...  Uncertainty, chance, statistical variability are but various names for the pervasive contingency that affects all human activity.

There are three measures of uncertainty.  Possibility is the prime measure.  Information about possibilities may act as an inverse measure and probability is a predictive measure.

Einstein himself used words to the effect that no problem can be solved by the mindset that created it.  He also said:

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

The challenge we face is to let go of a paradigm we know so well and embrace one that is more inclusive of 20th and 21st Century observations, discovery and knowledge. 

[peppercorn]

Ahem! Personally, I think uncertainty might simply be a consequence of "time jitter".

Ooooo, tell us more about this 'time jitter', Geezer.
It could be the most illuminating so far in this thread!

[Geezer]

Ahem! Personally, I think uncertainty might simply be a consequence of "time jitter".

Ooooo, tell us more about this 'time jitter', Geezer.
It could be the most illuminating so far in this thread!

er, well [] it's probably baloney, but, if time were to be jittery at subatomic scales, it might account for the uncertainty we observe in the position of subatomic particles. For example, electrons might have quite specific positions relative to the time frame of an atom, but because we can't properly "synchronize" with that time frame, we can can only assign a probability of an electron being at a position.

That's about as far as this "theory" goes  []

[JP]

Ahem! Personally, I think uncertainty might simply be a consequence of "time jitter".

Ooooo, tell us more about this 'time jitter', Geezer.
It could be the most illuminating so far in this thread!

er, well [] it's probably baloney, but, if time were to be jittery at subatomic scales, it might account for the uncertainty we observe in the position of subatomic particles. For example, electrons might have quite specific positions relative to the time frame of an atom, but because we can't properly "synchronize" with that time frame, we can can only assign a probability of an electron being at a position.

That's about as far as this "theory" goes  []

Actually, I suspect you're on to something that probably shows up in relativistic QM.  In nonrelativistic QM, space and time are separate entities, as are momentum and energy, so you get uncertainty relations between space and momentum and time and energy.  Relativity unifies space and time into a single entity, and energy and momentum into a single entity as well, so I bet there's a space-time / momentum-energy uncertainty relationship.