First off, newly syndicated readers who want to have access to my previous posts can find them archived here as well as listed on my own site here.
After last week’s speculations on time I would like to ask an even deeper question: why is there time?
My 4 year old daughter would be proud. What I mean is, why do things evolve in the first place? It seems to me that fundamental physics has to answer not only ‘what’ questions but also ‘why’ questions if it claims to provide understanding. I think I have an answer, or a glimpse of one.
The answer has to do with quantum anomalies; no not the large (not very quantum, then) things that seem to turn up in every other episode of Star Trek Voyager, but what physicists mean by this, which I am afraid is much more dry and dusty. In fact, I’m going to have to ask you to dust off your high school calculus books, just for a minute.
I explained in a previous post that even if nobody at the moment
knows how to reconcile quantum theory and gravity, quantum spacetime should emerge as an effect coming out of any unknown theory. Typically, the coordinates x,y,z of space would also be quantum variables, so space alone should typically form some kind of symbolic algebra. Due to quantum effects, the order of the variables in this algebra will matter, xy will typically not coincide with yx. One says that the algebra is ‘noncommutative’.
Click to enlarge
Now, what about differential calculus on such a quantum space? If you remember any high school calculus it means things like dx, dy, dz as the ‘infinitesimal differences’. Newton and Leibniz both considered such things as numbers which are then made arbitrarily small. Hands up if your high school calculus class contained a picture like the one shown at left. It defines differentiation of a function f in the x direction as a limit of the slope df/dx of the triangle as dx gets small.
So to develop quantum gravity effects in physics we also need ‘quantum differentials’ dx, dy, dz. They should enjoy the properties that differentials enjoy in Newtons theory except, since xy and yx need not coincide, similarly y dx need not coincide with dx y, etc. Now, here is the remarkable thing one finds as you dig deeper into this world of quantum geometry:
Most sufficiently noncommutative ‘quantum spaces’ described by algebras with variables x,y,z do not admit any reasonable self-contained algebra of differentials dx,dy,dz.
This is called an anomaly for quantum differentiation, or quantum anomaly for short. In physics when a classical symmetry does not survive the theoretical passage from our understanding at the level of classical mechanics to quantum mechanics, one speaks of an `anomaly’. An example of an anomaly is when physicists first tried string theory in the realistic four spacetime dimensions. Their theory had an anomaly for conformal symmetry and this was ‘fixed’ by changing the dimension to 24 and later to 11 or 10, though nowadays I hear that 10500 dimensions is currently quite popular. In that sense, if you subscribe to string theory, you have a ‘prediction’ or possible necessity of higher dimensions.
In my case what I mean by ‘reasonable’ is a differential calculus that respects in some form the symmetry that should rotate the x,y,z among themselves. Among such calculi there is an obstruction uncovered for many quantum spaces in my work with my colleague Edwin Beggs, a mathematician at Swansea in the UK.
As is typical for any anomaly, the thing to do is to increase the dimensions to absorb the obstruction. So if you subscribe to quantum spaces, you will typically be forced to invent at least one extra dimension which I will call ‘dt’. In fact you will be forced to invent time.
Let’s put some flesh on this. From the differentials dx, dy, dz, dt you can recover the corresponding ‘differentiation in direction x,y,z,t’ operations (the so-called partial derivatives), and you can do it algebraically without recourse to pictures. If you let f(x,y,z) be an element of our quantum space algebra, you find that its ‘differentiation in the t direction’ comes out not as zero but, in the simplest models, as something like the energy operator in Schroedinger’s equation.
So, not only are you forced to invent time, your original space variables obey an equation which in the limit of ordinary space (i.e. as you remove quantum gravity effects) becomes Schroedinger’s wave equation. Oops, you’ve just answered the question ‘why is there quantum mechanics?’ My 4 year old has not even gotten to that one.
And none of this is an accident. For any sufficiently ‘quantum’ space there are general mathematical reasons to expect that for any reasonable differential d there will exist an abstract differential element which I will call ‘dt’ obeying
dt f – f dt = L df
where L is our Planck scale parameter expressing the effects of quantum gravity. So, if t was not one of your variables you would be forced to invent it so as to have dt. Note that both sides of the equation are zero in ordinary geometry. In other words, this equation is invisible until you study quantum gravity, 
which is why such an origin of time is not seen in ordinary classical and quantum physics.
Editors note: Shahn Majid was talking around his paper “Noncommutative model with spontaneous time generation and Planckian-bound”, Journal of Mathematical Physics, 2005. A general introduction to his ideas on quantum spacetime appear in On Space and Time.
Excellent blog I must say. Julian Barbour with his book “The end of Time” shows also a nice piece of natural philosophy.
Just to let you know guys….if you are interested (and you are) in high quality physics links, then visit my site:
http://www.physicsworks.ca
Thanks and see you around,
Ronald
Hi Ronald,
thanks for the comment and for the link. I see that you have a lot of useful links on your site. I already found under Shlomo a link to several of Shlomo Sternbergs books as free pdfs. He was one of my mentors at Harvard when I was a student there. Julian Barbour’s books are definitely on my list to read some day when I have time. As well as “The End of Time” he has as book on Mach which has been highly recommended.
Just saying Helllooooo Shahn.
Time exists for a number of reasons. First, because the universe changes. If nothing changed there would be no time within the universe. Second, because we have memory. We can thereby detect change. Third, because we have defined a concept that we call “time” to capture the sense of change that we can detect. Fourth, because we can measure what we call time using periodic physical phenomena. This is the generalization of a clock. Fifth, because we can record the change in time using systems in which changes accumulate. It is not enough to have a clock. We also need a calendar.
Since time is recorded as an accumulation of changes, time always moves forward. If instead the universe was in a loop so that its entire state was continually revisited, then time as we know it would not exist for the universe. It might not make a difference to us if the length of time as we measured it were really long (say a billion years), but astronomers could not make the assumption that they could look back in time using red shift.
Hi Peter, you make some good points.
I broadly agree with your list, but which of these items is the definition of time or are these all potentially different usages of the word, as some say different `arrows of time’?
In the latter case, the question for me is which one of these is science and/or fundamental and which are merely sociology. I do think we need to disentangle the various usages of `time’ by taking a stand. Science after all has to have clear unified notions and not things `multiply defined’.
But I agree that if time is sort of constructed then this may explain why it moves forward. In a previous post I used this as a view of `thermodynamic time’.
Time as understood in general relativity has a causal arrow in any connected region. Basically, while an isolated region might have a different arrow, for regions to interact their arrows have to line up. This is the conventional thinking anyway (it is called a choice of time-orientation). Closed time-like loops such as you refer to would violate causality and are not expected to exist for this reason, though I agree with you that from a purely geometrical point of view they could. There is certainly no hint of that in observational cosmology, but see my post of some weeks ago
http://www.cambridgeblog.org/2008/10/before-the-birth-of-our-universe-and-after-its-death/
on Penrose’s theory of repeating universes, which is not what you refer to of course but interesting and might just
be verifiable experimentally. The thing is that a closed time-like loop might make sense of a particle but information, free will and many things not really encompassed by particle physics and just the geometry would not make sense, in my view of course.
Hi, you mentioned lately at Cambridge Science Festival that Apollo mission to the Moon measured delay of it’s own clock by 10 [us]. This is an example of the twin paradox. How would you explain this paradox from the quantum mechanic point of view.
Time and Quantum of Light. / My opinion./
Can Time Exist Without Matter?
1.
According to Newton the answer is “ Yes”.
2.
According to SRT and GRT the answer is “ No”.
3.
Who is right? Who is wrong?
What is the resolution of this apparent paradox?
===========================..
There are two kinds of time:
a) the proper (individual) time and
b) the planetary time.
They are so familiar that we rarely give them thought.
Don’t we know, that time for living being is limited
and the planetary time is absolute for them ? It is.
Maybe therefore Newton declared that time is absolute.
It “ flows equably without relation to anything external”
he wrote in 1687. But Einstein had another opinion.
He wanted to know: “ Where does the conception of time
come from?”, “ What is the essence of time?”.
And to explain these questions he created two theories:
SRT and GRT and declared that time is relative, changeable.
1.
SRT explains behavior and the proper time of light
quanta /electron. Why do I think so?
a)
One law (postulate) of SRT says that speed of light quanta
is constant c=1. Second law ( postulate ) says no another particle
can reach this speed. So there are two incommensurable
quantities. Is it possible to bind them together? No. I was
taught at school from the first class that the incommensurable
quantities cannot be compared. The connection between these
incommensurable quantities is similar to the decision of a
problem: “What will be if the whale attacks the elephant?”
We can see whale in a ocean and elephant in a savanna,
but they never meet and fight in the same “ frame of reference”.
And the same is about light quanta and another particles.
We cannot see them together in SRT. We can meet only the
light quanta in SRT and no other particles in it.
b)
SRT was born from Maxwell’s theory and it is a continuation
of the electrodynamics’ development . The electron is a main
and single hero in the Maxwell’s theory and SRT. There
isn’t the Maxwell’s theory / SRT without electron.
It is not correct to compare electron/ light quanta with another
particles (protons…etc) and bodies (billiard balls, satellites,
astronauts, “twins”) because they cannot produce electromagnetic
fields. The electron and the another particles are also incommensurable
quantities. They are absolutely different objects.
c)
Every epoch has its own delusion. Maxwell and Boltzmann
tried to explain electromagnetic fields using balls, wheels,
cog-wheels, springs…etc. H. Hertz, who demonstrated the
existence of the electromagnetic waves, wrote that the
electromagnetic waves didn’t have practice use. Etc….
Now we try to compare electron/photon
ability with astronaut’s and “twins’ ” opportunities. It is mistaken,
but what to do? We do it because this is our way of cognition
:” From vague wish to the bright thought”.
2.
So, how SRT explains time from electron/ light quanta point of view.
a)
When light quanta is in state of a rest its time is frozen,
and its own clock shows zero.
b)
When photon moves with constant speed c=1
its time is also frozen, and its own clock still shows zero.
c)
Only when photon moves with speed c>1 its zero time
changes and limited time appears. In this situation we
know photon as an electron. Photon works as an electron
and SRT and Lorentz transformations explain this process.
d)
And when , for example, electron emits from an atom and
interacts with Vacuum all its parameters change. Its limited
time ends and its own clock shows zero again. Now it lives
in infinite/ eternal Vacuum until new incarnation, until its new
work, maybe, in an atom (molecule), or in a cell, maybe, in a blade
of grass or in a tree, maybe, in an animal or in a person.
In another words:” We are living beings until Light quanta/
Electron is present and works in our body.”
Is it true? Yes, it is true. Why?
Because W. Pauli in 1924 wrote:” Each quantum state in the atom
is not limited of two electrons, but only one electron”.
It means in the atom can be only one, single electron.
The electron manages the atom. If the atom contains more
than one electron (for example – two), this atom represents
“ Siamese twins”. Save us God of having such atoms and cells.
And the living being begins its life from one, singe cell.
What I am introducing here is what ‘ thinking photon/ electron’ exist .
I applied the quantum of light/ photon/ electron with a consciousness.
And His own consciousness is not static but can develop.
The development of conscious scale goes
” from vague wishes up to a clear thought “.
This evolution proceeds during hundred millions (billion) years.
e)
Trying to understand “ the electrodynamics of moving bodies”
Einstein wrote that it is the result of time and space changes.
It is not exactly correct , because these changes are secondary
in SRT. And the first point of SRT is that Quantum of light changes
its spin. The former Planck/ Einstein’s spin (h) changes in Goudsmit /
Uhlenbeck’s spin (h = h / 2pi), and as a result of this act all its parameters
change and the time and new space appear.
3.
GRT explains the conditions of gravitation and the secret of
planetary time. Why do I think so?
a)
When Einstein worked on GRT, he asked astronomers:
“ What is the average mass of matter in the Universe?”
The result was lamentable. The quantity of mass was
insignificantly small. It was impossible to keep gravitation
law with such insignificantly little mass and so, the Universe
must be “open”, endless. But what to do with the infinite
space, Einstein didn’t know. Therefore he took (from the
heaven) “ the cosmological constant” in order to “close”
the Universe. The taken mass was enough for creating the
condition of gravitation. Without “ the cosmological constant”
the Universe is endless.
b)
In 1922 Friedman wrote, that we could not take “ the
cosmological constant” in calculation. Instead of it, it is
enough to take “time” and the Universe will be “closed”.
Friedman was correct, but why? Because “time”, by its
nature, is a limited physical quantity and, be taken in
mathematical calculation, automatically gives “closed” result.
c)
So, the detected material mass of the
matter in the Universe is so small (the average density
of all substance in the Universe is approximately
p=10^-30 g/sm^3) that the gravitation law doesn’t work.
Astronomers and astrophysicists know about this fact and
therefore (to save the gravitation law) invented new matter
a “dark matter”, a new energy a “dark energy” and another
abstract objects. This “ invention” is only a result of our
mentality , which says: ” If in a theory you meet infinity it
means the theory is nonsense”. It is very hard to take that
the Universe is infinite. It is no easy matter to give up
a lifetime of habit .
d)
On my opinion it is impossible to use GRT to Universe as
a whole. The Newton/ Einstein’s gravitation laws are correct
only in the local parts of Vacuum. The Universe / Vacuum
as a whole is endless.
e)
So, how does GRT explain time?
According to GRT the time depends on the mass
and speed it means, of moving matter.
It means that different masses and speeds can create
different time. For example, our planet Earth has its
own time but for us it is absolute.
The other planets have another mass and speed and
therefore they have their own time. This time according
to GRT is relative. But their habitants will think that their
time is absolute. But if they know GRT they will
not make this mistake.
=============
According to SRT and GRT time is relative.
SRT says about proper/ individual time of an
electron/ light quanta.
GRT says about planetary time of a Planet..
The time cannot exist without matter and speed,
in another words, without moving matter. But
different reasons and different moving of a matter
create the proper and planetary time.
=================..
Is it possible to see the different manifestation of
time in a human being?
Here is an article “ Even the time is pressed from fear”
by Dr. Vadim Chernobrov (collaborator of MAI -
- Moscow Aviation Institute).
He wrote, that we usually think time is a constant quality.
But Einstein’s relative theory says time is relative.
Question. Is it possible to check it in our life?
Answer. Russian and foreign researches say it is
possible. The documents (secret in the past) testify
that “cataclysm of time”, “ phenomenon of time’s
perversion “,” the changes (its deceleration) of time”
often is observed by people whose profession connected
with risk: astronauts, pilots, drivers, soldiers.
1.
The test pilot Mark Gallay wrote in his book
“The test in the sky” when his airplane was caught
with fire “ the time began to go in another scale. The time
almost stopped. Every second took ability of expansion,
and in this situation it was possible to do many things.”
He confirms that tested such feeling many times.
2.
The test pilot Marina L. Popovich said the same,
in the dangerous, catastrophic situations “ the time
is stretches”.
3.
In June 1989 the soviet airplane MIG-29 crashed near
Paris, in Le Bourget airport , in the time of its air show.
The notes of “the black box” showed that during the
four (4)seconds the test pilot Anatoly Kvochur made as
many operations as in normal situation it would take some
minutes. The test pilot later said: ” the time was stretched”.
4.
The captain N.Z.(fought in Afghanistan) remembers:
“the fly of the bullet was so beautiful that I didn’t guess
to evade from it, although I have enough time to do it”.
5.
The sergeant V. Ch (fought in Afghanistan) told:
“ The black barrel of gun seems very big, even enormous.
Time is stopped and full silence came. And I moved slowly
a step a side and the bullet passed close to me.”
6.
Etc…
His conclusions.
The people in a critical situation, on the border of death,
suddenly for themselves begin to see everything as in the
slow down film and in this time their speed reaction and
power increase in tens and hundreds times. And this explains:
a) why a man who escaped from wolves, can quickly reach
up the top of the naked tree,
b) an old woman took out a big trunk from her burned house,
which later two strong firemen couldn’t rise.
c) etc…
=============..
My experience.
The speed on the curve was so fast that to keep the balance of
the car I went on other road line and flew straight at the
“forehead’ of a green mercedes. The driver of the mercedes
was in panic, in horror. He threw the wheel and closed his face
with his hands. Suddenly the time stopped and the sound disappeared
for me and I made many actions before my car kicked only the side
back door of the mercedes. It was long time ago, but writing this article
I understood better what happened.
Our computer-brain works on a dualistic basis (on two different neurons
systems): 1) usually under logic program,
2) sometimes on intuition (subconscious).
Brain of a man approximately consists of sixteen milliards neurons.
All of them form the system that manages human body.
That is why that with the work of all the sixteen milliards neurons
of brain, a man cannot catch a single impulse of his Electron, of his
Quantum of light, of his Soul:
(mass of electron is equal 10^-31 kg., charge of electron is equal 10^-19 k.)
But in that time ( critical time ) most neurons of my brain stopped
their electric pulse (time almost stopped) and my Light Quanta/Electron
in this new condition (superconductivity) had possibility to increase
my speed reaction and power on a short period of time . So, as SRT says,
the Light Quanta in different systems ( even in our brain) can show us
a different Time. The Light Quanta plays major role in the Nature,
in the Physics, in our Life.
===============. .
Best wishes.
Israel Sadovnik. / Socratus.
http://www.worldnpa.org/php2/index.php?tab0=Scientists&tab1=Display&id=1372
========== . .
one issue that bothers me is whether the signature of spacetime
is sufficient to explain why it takes a clock to measure time, instead of a ruler, and why time seems to have a direction that spatial directions do not. Is Clifford algebra sufficient, or should we go for Octonion algebra ?
It seems like the last,best hope.