The Nature of Time

[sethoflagos]

1 hour ago, MigL said:

My now is your future and someone else's past; how do you argue that only the present, or now, exists but past ans future do not ??

Because all the energy that built the past universe was consumed in constructing the present, and the future is no more than a set of alternate building plans awaiting selection (wave function collapse if you prefer) and availability of materials for construction. Just an interpretation.

Consider observing a supernova inside some huge stellar nursery from not too close but close enough to study in reasonable detail. After the early fireworks have subsided we may expect to see a growing bright edged circle as the surrounding dust is progressively illuminated. Is it unreasonable to perceive the arrival of intense radiation at that bright edge as being experienced simultaneously around the entire perimeter even when it's several light years in diameter? 

And what exactly is going on at that edge other than a colossal number of particle interactions being randomly chosen from an even more colossal number of possible interactions.

It may even be viewed as a phase change, but in addition to a change in physical properties it's a condensation from causes to effects. Or a condensation of an unobservable, abstract 'many worlds' future into a single throughly deterministic past with the present being a thin slice of quantum fuzz between the two. Again, just a personal visualisation to help get my head around it.

Perhaps, the ambiguity of 'now' for different observers is simply an SR induced form of observer bias. Not one of them is able to observe a causal reversal, and to me, that seems to be the critical issue. Is this a reasonable view?

 

 

 

 

 

Edited January 11, 2023 by sethoflagos
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[geordief]

15 minutes ago, mistermack said:

Is it considered that there is a minimum parcel of time, or can it be divided infinitely to zero ?

I  thought I had heard that we don't know that

I wonder ,though whether the uncertainty principle might apply to space and time whereby the more precise a measurement  of a temporal location  is made the less precise a measure of spatial location is measured 

 

[Genady]

1 hour ago, geordief said:

I wonder ,though whether the uncertainty principle might apply to space and time whereby the more precise a measurement  of a temporal location  is made the less precise a measure of spatial location is measured 

I don't think so. Let's take Schrödinger equation, for example. It relates time derivative d/dt and spatial derivative d/dx. Thus, it assumes that time interval and distance can be infinitesimally small together. 

[Markus Hanke]

19 hours ago, mistermack said:

What I'm arguing is that change is what actually exists, and the accumulation of change is what we experience as the past, and the expected change is what we feel as the future. But both are actually a facet of the present. 

I’m confused now, because to my understanding this discussion is about time as a dimension. So if you speak about time being equal to change in the present, is your macroscopic universe 3D or 4D? Because that makes a huge difference to the physics! 

19 hours ago, mistermack said:

If there is no change, how will there be time?

We’ve previously brought up an example - unstable elementary particles, such as muons for example. They are created, and then they exist for a period of time without any changes taking place in their rest frame at all, before they decay (which is an example of change).

This notwithstanding, I don’t think anyone here argues that change doesn’t exist. I would just say that change is always defined relative to something, and that something isn’t necessarily time. This is most clearly seen in mathematics. If you have a function of both time and space, such as f(x,t), then this function “changes” in time at a rate of

\[\frac{\partial f( x,t)}{\partial t}\]

But it also “changes” in space at a rate of

\[\frac{\partial f( x,t)}{\partial x}\] 

and its total “amount of change” is the sum of these.  

So by the above two examples, you can see that one can have passage of time without change, and one can have change without reference to time. While in ordinary everyday life we usually equate these two, based on how our senses and minds experiences the world, if you think about it more carefully you’ll find that they are really not the same thing at all.

[TheVat]

21 hours ago, studiot said:

Can you elaborate on this without employing a circular argument ?

Probably not.

😀

Indeed, i crash into circularity as soon as I hit concepts like rate and change.   

[joigus]

44 minutes ago, TheVat said:

Probably not.

😀

Indeed, i crash into circularity as soon as I hit concepts like rate and change.   

IMO, we shouldn't be too afraid of tautologies, as long as we have an external hypothesis to get us out of it. In fact, if we're ever gonna find a way to understand time, I think it's very likely that we have to do it by formulating some kind of tautology, and then ponder what the external assumption must be if we're to make it into a predicting machine.

An outstanding example is Newtonian mechanics. The bare formulation is as tautological as can be. What is force? Mass times acceleration. But hang on. What is mass? Oh, that's easy: It's the ratio between force and acceleration in any direction.

We wouldn't get anywhere from just that. But there's a hidden assumption: Whatever we want mass to be, it must be the same in every direction.

And then there's the amazingly consequencial assumption that, under different simple circumstances, force depends on position in some particularly simple way. Then we're in business, because we can predict. Something that, with the sheer tautology, was impossible.

[studiot]

17 hours ago, sethoflagos said:

Because all the energy that built the past universe was consumed in constructing the present, and the future is no more than a set of alternate building plans awaiting selection (wave function collapse if you prefer) and availability of materials for construction. Just an interpretation.

 

Very interesting viewpoint. +1

So as I understand you you are saying you can't have the future together with the past because they are using the same energy  ??

 

19 hours ago, MigL said:

There are two kinds of measurements.
Absolute, as in temperature, where there is a well defined zero point, and all temps are in relation to it, and, gauge, where the measurement depends on where and how the measurement is made; think of a bird on a 15000 v hydro line, that feels zero potential.

Time, and distance, are not absolute ( as Studiot has mentioned ), and it makes no sense to say this point is 12 km, or this instant is 17 sec.
We specify differences in length with separation, and differences in time with duration.
And just like the bird on the wire, we can set the origin of the separation at r=0 and the origin of the duration with t=0 to ease our calculations.

Similarly, as INow has mentioned, there is no universal now, or universal present, because there cannot be simultaneity.
My 'now' or 'present' differs from the person standing two feet away from me, never mind a galaxy a billion LY away.
My now is your future and someone else's past; how do you argue that only the present, or now, exists but past ans future do not ??

And to all those who think that time is simply an effect of motion, that time is emergent from the three spatial dimensions, I challenge you, as Markus did, ( since GR is our map/model of the real terrain ) to find the Panama Canal on a map of Central America from the 1800s.

 

Question for Markus, Mordred and anyone else who may know...

We have a separation interval between events as a distance, so we convert the time coordinates by multiplying by c to get a 'distance'.
Could we also specify the interval length as a time ( by dividing distances by c ) and would this make any difference whatsoever to GR ?
Would some then argue that time is fundamental, and lengths are emergent ?

Also interesting, and brings out the point I have been making repeatedly that space and time are different.  +1

One of the difference is that when we draw a graph or plot we are using the properties of space exclusively.

We generate virtual surfaces and other complicated shapes in the space we draw in but thay are all spatial.

The mathematical geometry of n dimensions is based on this fact eg Kendall 1961.

I am still thinking about the situation when we convert them to all timelike.

 

 

[sethoflagos]

16 minutes ago, studiot said:

Very interesting viewpoint. +1

So as I understand you you are saying you can't have the future together with the past because they are using the same energy  ??

Yup.

[MigL]

It is one way to look at it Seth.
But what if the 'energy' isn't just a property of the 'present', and does not have to be consumed to 'construct' the future ?
( GR makes no claims about energy conservation )
What if the 'energy' is a property of the 'block', which includes past, present and future ?
Where the present is a ( observer/interaction dependant ) foliation of the block ?
Where one end of the block has high useable energy and low entropy ( Big Bang ), while the other end has little or no useable energy and high entropy ( heat death ) ?

Edited January 11, 2023 by MigL

[Genady]

3 hours ago, joigus said:

to understand time

Could you describe a bit of what you mean by this, please?

[joigus]

49 minutes ago, Genady said:

Could you describe a bit of what you mean by this, please?

Do you mean provide another example of tautology, which we would only escape by proposing further relations in the initial tautology?

My example was classical mechanics, which would lead us too far from OP's goal at almost any amount of detail. But I think it's plausible that, if we were to make any progress in the problem of time, new concepts would have to appear, being circular in their initial formulation not constituting a difficulty impossible to overcome. If I were to try, I would take inspiration from similarly groundbreaking advances. In the case of Newton, F=ma seems to be both a definition of both mass and force, which at first sight doesn't look as much of a step towards progress, does it?... Until you formulate a law of force F(x,v), the concept of inertial frame as somewhere far removed from sources of interaction where systems satisfy the 1st law, etc.

The problem with time is it's so difficult to conceive of intuitions that would lead the way as, in the case of Newton, isolated systems, force, and mass.

[Genady]

41 minutes ago, joigus said:

Do you mean provide another example of tautology, which we would only escape by proposing further relations in the initial tautology?

My example was classical mechanics, which would lead us too far from OP's goal at almost any amount of detail. But I think it's plausible that, if we were to make any progress in the problem of time, new concepts would have to appear, being circular in their initial formulation not constituting a difficulty impossible to overcome. If I were to try, I would take inspiration from similarly groundbreaking advances. In the case of Newton, F=ma seems to be both a definition of both mass and force, which at first sight doesn't look as much of a step towards progress, does it?... Until you formulate a law of force F(x,v), the concept of inertial frame as somewhere far removed from sources of interaction where systems satisfy the 1st law, etc.

The problem with time is it's so difficult to conceive of intuitions that would lead the way as, in the case of Newton, isolated systems, force, and mass.

Thanks. I think I understand you.

[sethoflagos]

2 hours ago, MigL said:

It is one way to look at it Seth.
But what if the 'energy' isn't just a property of the 'present', and does not have to be consumed to 'construct' the future ?
( GR makes no claims about energy conservation )
What if the 'energy' is a property of the 'block', which includes past, present and future ?
Where the present is a ( observer/interaction dependant ) foliation of the block ?
Where one end of the block has high useable energy and low entropy ( Big Bang ), while the other end has little or no useable energy and high entropy ( heat death ) ?

On the largest scales the universe seems pretty flat so time translation symmetry isn't a bad approximation as far as we can tell. I don't know enough about the block universe idea to say more.

It seems that there are (at least) two notions of 'now' that get conflated.

There's a universal 'now' where all observers report, say, the same average value for the temperature of the CMBR and therefore the same proper time since recombination.

Except for our immediate locality we cannot jointly experience that 'now' because we're not causally connected.

The other 'now' is when we look back down our individual light cones at our causal histories and this 'now' is entirely local. I phrase it this way because while we perceive distant objects in the night sky, what we're really doing is interacting in the present with photons created during past events at the moment those events become causally connected to us.

The macroscopic objects associated with those photon (or gravitational wave etc) producing events are no longer where they appear to be in our local 'now'. They've moved on a long time ago to a place and time with which we are not yet causally connected.  

[Genady]

16 minutes ago, sethoflagos said:

On the largest scales the universe seems pretty flat so time translation symmetry isn't a bad approximation

On these scales the universe seems pretty flat spatially, as I understand, and this has no relation to the time translation symmetry, does it?

Edited January 11, 2023 by Genady

[studiot]

4 hours ago, sethoflagos said:

Yup.

Thanks.

 How did you get on with the acoustics material I posted ?

[sethoflagos]

33 minutes ago, Genady said:

On these scales the universe seems pretty flat spatially, as I understand, and this has no relation to the time translation symmetry, does it?

I don't know GR well enough, but when we measure these shock wave patterns in the CMBR we're measuring across a vast expanse of time, so aren't we measuring a flat spacetime? I'd appreciate being put right if I've misunderstood something here.

And Conservation of Energy has worked pretty well for me over the past forty-odd years.

44 minutes ago, studiot said:

Thanks.

 How did you get on with the acoustics material I posted ?

Much gratitude expressed on that thread.

[Mordred]

1 hour ago, sethoflagos said:

On the largest scales the universe seems pretty flat so time translation symmetry isn't a bad approximation as far as we can tell. I don't know enough about the block universe idea to say more.

It seems that there are (at least) two notions of 'now' that get conflated.

There's a universal 'now' where all observers report, say, the same average value for the temperature of the CMBR and therefore the same proper time since recombination.

Except for our immediate locality we cannot jointly experience that 'now' because we're not causally connected.

The other 'now' is when we look back down our individual light cones at our causal histories and this 'now' is entirely local. I phrase it this way because while we perceive distant objects in the night sky, what we're really doing is interacting in the present with photons created during past events at the moment those events become causally connected to us.

The macroscopic objects associated with those photon (or gravitational wave etc) producing events are no longer where they appear to be in our local 'now'. They've moved on a long time ago to a place and time with which we are not yet causally connected.  

You need to be careful on causal connections. Anything we can see or measure we are causally connected to in essence we are causally connected with our observable universe. I different observer at say 1000 light years away, will have a different observable universe, however would share causal connections where that faraway observers, Observable universe overlaps with ours. Causal connections don't define "now" as we receive signals from the past events. The future can also be causally connected to us from the perspective of a future observer. 

 

 

[sethoflagos]

25 minutes ago, Mordred said:

You need to be careful on causal connections. Anything we can see or measure we are causally connected to in essence we are causally connected with our observable universe. I different observer at say 1000 light years away, will have a different observable universe, however would share causal connections where that faraway observers, Observable universe overlaps with ours.

Oh dear, I seem not to have expressed myself very clearly (again).

Everything you say is true. But to clarify, I was speaking specifically about past events (not objects), such as an atom emitting a photon or a merger of two compact bodies as 'causes' producing measurable 'effects' in our 'now'.

Yes, other signals associated with these events may be observed by other distant observers, but in general, our observation and theirs would not have their own cause-effect relationship unless we were able to communicate our observations to each other. 

 

38 minutes ago, Mordred said:

 The future can also be causally connected to us from the perspective of a future observer. 

Certainly true if an event enacted by us produces a future effect. 

But a future event causing an effect on our 'now' is a whole different ballgame which we discussed recently on another thread as I remember (shades of the Transactional Interpretation). Even if possible, would the action be measurable?

[Genady]

2 hours ago, sethoflagos said:

a flat spacetime?

A flat spacetime would be Minkowski spacetime. A homogenous isotropic universe is not.

[sethoflagos]

6 minutes ago, Genady said:

A flat spacetime would be Minkowski spacetime. A homogenous isotropic universe is not.

I'm in no position to dispute this, Genady. But I don't understand why it should be so.

[Genady]

1 hour ago, sethoflagos said:

I'm in no position to dispute this, Genady. But I don't understand why it should be so.

Because expanding (or contracting) spacetime is not a flat spacetime.

[Mordred]

1 hour ago, Genady said:

Because expanding (or contracting) spacetime is not a flat spacetime.

That's not quite correct, yes a critically dense universe is homogeneous and isotropic with k=0 precisely. However you can still have expansion if the kinetic energy term exceeds the potential energy term. Our universe is extremely close to flat but not only that it is still considered homogeneous and isotropic.

 This might surprise you but at inflation the universe was incredibly flat and well as uniform in mass distribution to the order of \[10^{15}\]. One thing to note the critical density applies the mass term with no pressure term by applying matter.  The kinetic energy term isn't part of that formula. Neither is the equipment solution in the EFE for a static solution. It is the kinetic energy term that allows for expansion or contraction in a homogeneous and isotropic universe. Such as our universe.

A side note tidbit the static solution is what Einstein called his biggest mistake as he attempted to add a different cosmological term to preserve the static solution. He knew  the EFE also showed expansion or contraction even with a uniform mass distribution and that a static universe was inherently unstable.

Edited January 12, 2023 by Mordred

[MigL]

Yes, Seth, time translation symmetry is what accounts for energy conservation locally, but I don't believe that has anything to do with the 'flatness' of space-time.

Maybe Markus can do a better job of explaining, but I'll give it a shot ...
Generally energy is not conserved in GR as the concept of energy is frame dependent in GR, and what is actually conserved is energy-momentum. Energy conservation would imply a preferred frame, which is not allowed.

I'm not sure if Noether's Theorem has a special case for GR, where symmetry in time and position ( in effect, no preferred position in space-time ) leads to energy-momentum conservation.

Not sure if this example is valid ( I got it via a google search ), but if the number of photons in the universe is constant, and the universe is expanding and red-shifting those photons to lower energies, then the universe is losing energy ?

[Mordred]

48 minutes ago, MigL said:

 

Not sure if this example is valid ( I got it via a google search ), but if the number of photons in the universe is constant, and the universe is expanding and red-shifting those photons to lower energies, then the universe is losing energy ?

total energy stays constant in the FLRW metric as per an adiabatic (closed system) perfect fluid however the energy density decreases due to expansion and correlates to the cosmological redshift. The common value for number of photons is 10^{90}. That value is calculated via the Bose Einstein statistics for bosons and gives the number density of photons by setting the effective degrees of freedom at 2 for the two polarity states of the photon. For bosons chemical reactions also set to zero. 

Bose Einstein Statistics (bosons)

\[n_i = \frac {g_i} {e^{(\varepsilon_i-\mu)/kT} - 1}\]

Fermi-Dirac statistics (fermions)

\[ n_i = \frac{g_i}{e^{(\epsilon_i-\mu) / k T} + 1}\]

Maxwell Boltzmann (mixed )

\[\frac{N_i}{N} = \frac {g_i} {e^{(\epsilon_i-\mu)/kT}} = \frac{g_i e^{-\epsilon_i/kT}}{Z}\]

Edited January 12, 2023 by Mordred

[Markus Hanke]

10 hours ago, sethoflagos said:

so aren't we measuring a flat spacetime? I'd appreciate being put right if I've misunderstood something here.

The FLRW metric is an interior solution to the Einstein equations - it represents the geometry of spacetime in the interior of a homogenous, isotropic distribution of dust. Since this “dust” is certainly a gravitational source, spacetime here cannot be flat.

When it comes to questions of geometry, one must carefully distinguish between space and spacetime. These are not the same things at all. In the FLRW scenario, spacetime is always curved in a particular way; but, for the right choice of parameters, each 3D hypersurface of space within that spacetime can be flat.

3 hours ago, MigL said:

Yes, Seth, time translation symmetry is what accounts for energy conservation locally, but I don't believe that has anything to do with the 'flatness' of space-time.

Careful - time translation symmetry accounts for energy-momentum conservation; the conserved quantity associated with this symmetry in Noether’s theorem is the energy-momentum tensor, not energy.

The trouble is that, once you are working in a curved (as opposed to flat) spacetime, the mathematical expression that represents sources and sinks of energy-momentum no longer identically vanishes, so in general there is no law of energy-momentum conservation for regions of curved spacetime. The pesky extra terms that stop it from happening are related to the curvature of spacetime - energy-momentum isn’t conserved because curved spacetime itself contributes to the total energy-momentum. Unfortunately the energy-momentum of gravity cannot be localised, and cannot be written in a form that all observers agree on (in isn’t a tensorial expression). It is, however, possible to fix this by forming a certain combination of energy-momentum from sources, and energy-momentum from spacetime curvature; the overall expression is then again covariant.

So to make a long story short, if you want to write down a law of energy-momentum conservation in curved spacetime, you need to account not only for gravitational sources, but also for the contribution that comes from gravitational self-interactions, ie spacetime curvature itself.