Time Direction: Exploring Quantum Physics & Cosmology

[thegroundhog]

I've seen a lot of Youtube clips and listened to podcasts recently on cosmology and quantum physics and something that has come up frequently that I don't understand is descriptions of time. Specifically Sean Carroll on various podcasts and Carlos Ravelli (when he finally got to the point).

1 Both say that the laws of physics don't demand that time go in a certain direction. I don't get this - how could time go backwards? If I move my arm up my arm is in the up position after being in the down position. It happened in sequence and therefore that is the direction of time. Even if you said this was happening backwards in time, then the backwards would just be the new forwards. The only way I could see actual going back in time is if we were in some recording of a higher entity who was pressing rewind (Actually, that's still forward too, from the entity's perspective). If the universe was such that it collapsed back in on itself to a singularity this would still be forward in time. As soon as any 'event' or action happens, there is a direction of time and you can say one thing happened 'after' the other. If the later event happened first then it wouldn't be the later event, it would be the former event, so time is still forward.

2 Sean Carrol talks about time only seeming to be forward because the big bang happened, and the universe was once at a low entropy and the entropy is increasing. This makes even less sense. Entropy or not, any actions taken or events happening still go forward in time, and even if we were to convince ourselves that something was backwards in time, then that's just the new forward, events are still happening sequentially. His cites the example of an egg cracking, so going from an ordered state to a disordered state. So what? I can solve a Rubiks cube so that it goes from a disordered arrangement to an ordered one - that doesn't mean I've gone back in time. If the egg suddenly re-assembled to a perfect egg, this is unlikely but would still be forward in time. I understand about total entropy in closed systems always increasing, but that still doesn't explain it to me.

I realize it's not the easiest subject but any clarity of what they're talking about would be appreciated.

 

[PeroK]

What they mean is that if you played a physical process backwards it would still be a valid physical process. You could start with the SUVAT equation of motion for a particle under constant acceleration:
$$s = ut + \frac 1 2 a t^2$$
If you look at the motion of a particle using that equation - let's say you throw a ball upwards until its highest point. It starts at some point with a certain velocity and ends at a higher point with zero velocity. Now, if you reverse that process you get exactly the motion of the ball dropped from the higher point. In other words, the time reversed process of throwing a ball up is precisely the process of a ball falling.

This means that the SUVAT formula itself does not contain an element that tells you a specific direction of time.

This property is also true of the fundamental laws of physics. If you reverse the time and look at what happens then it is still a valid physical process.

This is in stark constrast to the macroscopic behaviour we see around us, where there appears to be a clear direction in which physical processes take place irreversibly. If you drop an egg and it breaks, there is no valid physical process of a broken egg naturally reforming. In theory, if you did throw all the pieces of a broken egg (shell, white, yolk) all back together in precisely the right way you could get your egg back. But, whereas an egg breaks quite naturally, it's essentially impossible to reverse the process (even if the laws of physics do not directly forbid it).

 

[Bandersnatch]

If I remember correctly, Carroll's argument is more about how one can view time as just another dimension in the space-time manifold and what one can conclude by fully adopting such a view.
Such as, the direction of time being as arbitrary as directions in space. And indeed, the flow of time being an illusion. Much in the same way as there's no preferred direction to distance, and there's no such thing as the flow of distance.

We can view space-time as a four-dimensional object, where everything (and everytime) just is. We can define some physical properties on that manifold. We can track how those properties change as we move about the manifold. We can define some objects or systems and look how those change as we move from point to point. One of such properties is entropy, which will vary from point to point in such a way, that it increases along one direction in the time dimension.
This by itself doesn't indicate that the direction in which entropy grows, or the one in which it decreases, should be considered 'the direction of time'. But, if we consider that forming memories is a process that increases entropy, then any entity that forms memories will conceive of time as flowing, and in a particular direction (towards higher entropy).
But it's just an illusion of the memory forming process, not something inherent to the universe.

 

[thegroundhog]

Much in the same way as there's no preferred direction to distance, and there's no such thing as the flow of distance.

I don't see how you can compare distance and direction to time. How can the direction of time be arbitrary? Time, by its very definition, is going forward, not backward as it is the order in which things happen. If I go from A to B in space, then that can be in any arbitrary direction, because I have the freedom of three dimensions to chose from. There is no choice of time direction. I can't say 'I'm going to go from A to B backwards in time.' You make the journey and time passes, which is forwards.

But it's just an illusion of the memory forming process, not something inherent to the universe.

If humans didn't exist the universe would still have time and it would go forward. Stars use up fuel going foward in time. Any events in the universe go foward in time.

 

[thegroundhog]

This means that the SUVAT formula itself does not contain an element that tells you a specific direction of time.

This property is also true of the fundamental laws of physics. If you reverse the time and look at what happens then it is still a valid physical process.

I understand that the fundamental laws of physics could still be valid if time is reversed but this is just theoretical. In the example of the ball, the reality would be the ball dropping from the high point, but still forward in time. It doesn't make sense to have something happen backwards in time.
Probably terrible analogy but say time is a globe and you start at the north pole. Whether the event happens at 0º, 90º, 180º or 270º you will always go South. Two events going in opposite directions will still be forward in time.

 

[Nugatory]

I understand that the fundamental laws of physics could still be valid if time is reversed but this is just theoretical. In the example of the ball, the reality would be the ball dropping from the high point, but still forward in time. It doesn't make sense to have something happen backwards in time.
Probably terrible analogy but say time is a globe and you start at the north pole. Whether the event happens at 0º, 90º, 180º or 270º you will always go South. Two events going in opposite directions will still be forward in time.

You may be allowing your lifetime of experience observing and interacting with macroscopic objects (quite literally, that is the only experience you have ever have had) to mislead you. Yes, macroscopic systems behave the way you’re saying, and no one is disputing that assertion.

But the way in which this natural forward evolution of time emerges from the microscopic world is quite unobvious until you’ve done some serious statistical mechanics.

 

[PeroK]

I understand that the fundamental laws of physics could still be valid if time is reversed but this is just theoretical. In the example of the ball, the reality would be the ball dropping from the high point, but still forward in time. It doesn't make sense to have something happen backwards in time.

The key point is that:

1) It appears that many physical processes are irreversible.

2) There is nothing in the fundamental laws of physics to directly support this.

That is the issue. There is an arrow of time in the physical phenomena that is not found in the laws of nature. That is at least interesting. Perhaps something to think about.

 

[gmax137]

Let's say I show you a movie of a pool table: a ball comes rolling in from the left, strikes a stationary ball, they both move off, one bounces off a rail... etc.

You won't be able to say whether the movie is being played forward or in reverse. Even if you use Newton's laws, and plot things out.

Now if the camera zooms out and you see the cue ball strike the tip of the cuestick, and push it back into my hand, swinging my arm backwards... That movie will look funny; you'd think what's the chance that ball hit the cue head on?

Or if I have a movie of an egg rolling off the table and splattering on the floor. If you watch that one in reverse, there will be no question in your mind that it is being seen in reverse.

 

[anorlunda]

It's not simple and not obvious.

In the microscopic world described by Newton's Laws of Motion, time can be inverted. But statistical mechanics takes us from what it possible to what is probable, and there the arrow of time is as you say.

If you really want to understand that better, I suggest Lenoard Susskinds video course on Statistical Mechanics. Physics fans usually find that subject lots of fun.

 

[Dale]

Even if you said this was happening backwards in time, then the backwards would just be the new forwards.

You are missing the point. This isn’t about labeling it is about symmetry. If you write down the fundamental laws of physics and make the substitution $t\rightarrow -t$ then you wind up with the same laws.

That is irrespective of the labeling issue, and it is weird. Scientists didn’t put that in by hand. In fact, since it goes against our intuition if it had been put in deliberately we probably would have done it the opposite. It seems to be a strange symmetry that is truly there and not expected.

 

[thegroundhog]

Thanks for all the answers, I appreciate it. I accept that I'm wrong in my thinking, and that were I to understand the underlying principles I would have a better grasp. I wish someone could explain it better in layman's terms, though. None of the many books I've read have convinced me, I still don't understand how you could have minus t. To me it's like you have - 1 in maths but you would never have - 1 apples. Similarly reversing time makes no sense in the real world, just a theoretical construct like - 1.

 

[Nugatory]

Similarly reversing time makes no sense in the real world,

Try rewording that as “reversing time makes no sense in the subset of the real world that I can directly experience” and you’ll find it a lot easier to take the next step: “... but I’m not quite so sure about the rest”

 

[PeroK]

To me it's like you have - 1 in maths but you would never have - 1 apples.

Hmm. If you think negative numbers are a bit dodgy, then any mathematics or physics since the 7th Century is going to be hard to accept!

https://en.wikipedia.org/wiki/Negative_number#History

 

[Dale]

None of the many books I've read have convinced me, I still don't understand how you could have minus t.

Who said anything about actually having $-t$? Did you think that people were trying to convince you that time actually goes backwards?

That is not the case. Again, it is purely about a surprising symmetry in the laws. We would expect that the substitution $t\rightarrow -t$ would have huge effects. But it doesn’t. That is weird.

 

[thegroundhog]

Try rewording that as “reversing time makes no sense in the subset of the real world that I can directly experience” and you’ll find it a lot easier to take the next step: “... but I’m not quite so sure about the rest”

Hmm. If you think negative numbers are a bit dodgy, then any mathematics or physics since the 7th Century is going to be hard to accept!

https://en.wikipedia.org/wiki/Negative_number#History

I understand negative numbers and even complex numbers, I've studied maths at university. My point was whether the reversal of time was a similar abstract concept, that had no place in the actual universe, whether with humans or not.

 

[Nugatory]

My point was whether the reversal of time was a similar abstract concept, that had no place in the actual universe

And my point was that you are using the phrase "abstract concept" to mean "not obvious based on what I've experienced" and the phrase "actual universe" to mean "that subset of the universe with which I am familiar". That's a defensible position, but when our most accurate descriptions of the way the universe works do not include an arrow of time... are you sure that you're not short-changing yourself by not considering the question of where that arrow comes from?

 

[strangerep]

[...] but when our most accurate descriptions of the way the universe works do not include an arrow of time... are you sure that you're not short-changing yourself by not considering the question of where that arrow comes from?

We should probably note that Quantum Field Theory (which includes a "most accurate" description, i.e., Quantum Electrodynamics) requires a notion of causality to be put in by hand, even though it's based on representations of the (time-symmetric) Poincare group.

 

[strangerep]

1 Both say that the laws of physics don't demand that time go in a certain direction.

This is over-simplified. E.g., the heat equation $$\frac{\partial u}{\partial t} ~=~ \Delta u $$ is not time-symmetric. Typically, if you take a solution of the heat equation and try to time-evolve it backwards you'll hit an infinity within a finite time interval. In fancy-schmancy language, although solutions to many physics equations give you a group, solutions to the heat equation only give you a semigroup (i.e., no well-defined inverses).

Of course, one could say that the heat equation is just a coarse-grained expression of features in statistical mechanics. But at the deepest known foundations of physics, we still have to put in causality by hand (as I mentioned in my previous post). As of 2020, I don't think anyone really knows why -- or if they do, they're either not saying or they're crackpots.

 

[A.T.]

I understand negative numbers and even complex numbers, I've studied maths at university. My point was whether the reversal of time was a similar abstract concept, that had no place in the actual universe, whether with humans or not.

Time itself is an abstract concept. And so are numbers.

 

[Buzz Bloom]

Wikipedia has an interesting discussion about time travel from a general relativity (GR) perspective.

https://en.wikipedia.org/wiki/Time_travel#General_relativity​

The theory of general relativity does suggest a scientific basis for the possibility of backward time travel in certain unusual scenarios...​

Time travel to the past is theoretically possible in certain general relativity spacetime geometries that permit traveling faster than the speed of light...​

I may be misinterpreting this, but it appears to be saying that assuming GR is a correct description of reality, then time travel backwards in time by some object requires that it must move in space faster than light (i.e., v>c), which violates special relativity.

 

[thegroundhog]

Who said anything about actually having $-t$? Did you think that people were trying to convince you that time actually goes backwards?

That is not the case. Again, it is purely about a surprising symmetry in the laws. We would expect that the substitution $t\rightarrow -t$ would have huge effects. But it doesn’t. That is weird.

Thank you. I feel halfway to understanding with what you say. I think that I did think that people were trying to convince me time could go backwards. So what you're saying is that it's a quirk of the equations that they don't specify a direction of time but in actuality it's a nonsense? And by actuality I don't mean my frame of reference of actuality.
Lightcones are used to explain why you can't affect someone's past. I'd love to hear how this -t could be woven into that image, as the lightcone clearly goes out in time in one direction.

 

[PeroK]

as the lightcone clearly goes out in time in one direction.

Well, lightcones are symmetric in the $+t$ and $-t$ directions. That's the point. They are a good example of the time-reversal symmetry. Spacetime diagrams, generally, have a time-reversal symmetry.

 

[jbriggs444]

Lightcones are used to explain why you can't affect someone's past. I'd love to hear how this -t could be woven into that image, as the lightcone clearly goes out in time in one direction.

Light cones go in two directions. Both into the future and into the past. The past light-cone contains those events that can affect us "now". The future light-cone contains those events that we "now" can affect.

Instead of picturing an ice-cream cone, picture two ice-cream cones positioned point-to-point. This is the same kind of "cone" that one encounters in "conic sections".

 

[Dale]

Lightcones are used to explain why you can't affect someone's past. I'd love to hear how this -t could be woven into that image, as the lightcone clearly goes out in time in one direction.

That is an excellent example.

So in an inertial frame the spacetime interval from the origin is given by the equation $\Delta s^2 = -c^2 (\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2$. The light cone of the origin is given by the region where $\Delta s^2=0$ which is said to be "lightlike" or "null". The region where $\Delta s^2<0$ is inside the light cone and is said to be "timelike". The region where $\Delta s^2>0$ is outside the light cone and is said to be "spacelike".

The timelike region inside the light cone consists of two sub regions, one is called "future directed" and the other is called "past directed". These are geometrically distinct regions because you cannot smoothly rotate a vector from one region into the other*. The origin could be the cause of any event in the future directed half of the light cone, and any event in the past directed half of the light cone could be the cause of the event at the origin.

Since causality is such a big thing, you would expect therefore that the future and past directed light cones are completely different. However, if we make the substitution $t \rightarrow -t$ we get:
$\Delta s^2 = -c^2 (\Delta (-t))^2 +(\Delta x)^2+(\Delta y)^2+(\Delta z)^2$
$\Delta s^2 = -c^2 (-\Delta t)^2 +(\Delta x)^2+(\Delta y)^2+(\Delta z)^2$
$\Delta s^2 = -c^2 (\Delta t)^2 +(\Delta x)^2+(\Delta y)^2+(\Delta z)^2$
which is exactly what we started with!

That is weird. The light cone equation definitely separates future from past, but it doesn't uniquely identify future vs past. If you do that substitution, nothing changes.

*Note that this is different from spacelike vectors. You can smoothly rotate one spacelike interval into any other spacelike interval with the same magnitude. In other words, spacelike intervals define a hyperboloid of one sheet and timelike intervals define a hyperboloid of two sheets, one of which is in the future and the other is in the past.

 

[PeroK]

I think that I did think that people were trying to convince me time could go backwards. So what you're saying is that it's a quirk of the equations that they don't specify a direction of time but in actuality it's a nonsense?

Let's look at a system evolving in time as a set of state transitions. We start in a certain state and by a series of changes we end up in a new state. Each change can be represented by a fundamental change that cannot be broken down any further. As an example, let's have have a system of one hundred lights, each of which can be either on or off.

Now we need some laws of nature. Let's make them time reversible. Any light can change from being on to off or off to on. These are the fundamental changes to our system. Simple. The process of a light going from on to off (forward in time) is the same as the time-reversed process of a light going from off to on. What I mean is:

1) Take the process of a light going from off to on.
2) Take the time-reversed process of this (light goes from on to off).
3) We get a valid forward-in-time process.

Anyway, I hope it's clear that these simple rules are fully time-reversible.

The critical question is whether we see an "arrow of time" in our system. What I mean by that is: if we have a sequence of transitions and we reverse the time, do we get a valid sequence of transitions? The above laws tell us that a time-reversal of any fundamental transition is a valid process. So, why not any sequence?

Let's look at an example.

Let's start with the first 50 lights on and the second 50 lights off. Each second (on average, say) one light changes its status. Gradually we see the first 50 lights change, by the laws of probability, to a mixture of about 25 on and 25 off; and likewise for the second 50 lights. So that quite quickly we get a roughly equal mixture of on and off throughout the system. And, if we repeated this experiment many times, then the same macroscopic effect of mixing would take place every time. And the system tends to remain in a mixed state for long periods, rarely showing any significant patterns of on/off.

Now, if we play that backwards we start with a mixture and end up (quickly) with the first 50 on and the second 50 off.

But, if we try to find this behaviour from the system evolving naturally forward in time we (almost) never see this behaviour. This unmixing is not a valid natural behaviour (with any significant probability).

Here we see a clear dichotomy between the microscopic laws (time-reversible) and the macroscopic behaviour (not time-reversible). We have a clear arrow of time in our system that is not encoded in our fundamental laws.

This is the heart of the matter.

 

[vanhees71]

One should emphasize that the direction of time has to be put in by hand in addition to the dynamical equations of motion.

The most fundamental "arrow of time" is the "causal arrow of time", which is put in by hand by assuming that time is oriented. In SR at any event you have a future light cone which contains all events which my be causally affected by what's happening at the event under consideration, as is written by @jbriggs444 in the previous posting, and there's the past lightcone, which contains all events which may affect the event under consideration. This already defines a "direction of time", i.e., it distinguishes the past and future of any event. Any event that's outside of the past and future light cones, i.e., a space-like separated event cannot be causally connected with the event under consideration. You can always find an inertial frame of reference, where these events are simultaneous and thus cannot be causally connected because any signal to causally connect two events can only propagator with a speed less than the speed of light (in vacuum).

Usually you encounter this "causal arrow of time" in standard physics course when it comes to the solution of the electromagnetic wave equation. It's most easily seen in the Lorenz gauge, where you simply have
$$\Box A^{\mu}=\frac{1}{c} j^{\mu}$$
for the four-vector potential.

What you need to formally solve the equation is a propagator of the d'Alembert operator $\Box=1/c^2 \partial_t^2 -\Delta$,
$$\Delta_x G(x-x')=\delta^{(4)}(x-x').$$
Then a solution of the wave equation is given by
$$A^{\mu}(x)=\int_{\mathbb{R}} \mathrm{d} t' \int_{\mathbb{R}^3} \mathrm{d}^3 x \frac{1}{c} G(x-x') j^{\mu}(x').$$
The solution for the propagator is most easily found by taking the "Mills representation", i.e., writing it in terms of the Fourier transformation wrt. the spatial coordinates
$$G(x)=\int_{\mathbb{R}^3} \mathrm{d}^3 k \frac{1}{(2 \pi)^3} \exp(\mathrm{i} \vec{k} \cdot \vec{x}) \tilde{G}(t,\vec{k}).$$
Plugging this into the EoM for the propagator you get
$$\left (\frac{1}{c^2} \partial_t^2 + k^2 \right ) \tilde{G}(t,\vec{k}) = \delta(t). \qquad (1)$$
It's clear that there are infinitely many solutions of this equation of motion, but one is distingushed by the demand that you want a "causal solution", i.e., the field $A^{\mu}(x)$ should only depend on the sources at times $t'<t$. Thus you have one special propagator, fulfilling this "causality constraint", leading to the retarded propgator. It is given by the ansatz
$$\tilde{G}(t,\vec{k})=\Theta(t) [A \sin(\omega t) + B \cos(\omega t)], \quad \omega=c|\vec{k}|=c k.$$
To find the integration constants $A$ and $B$ you just have to look at (1) again. Obviously the singularity of the $\delta$ distribution on the right-hand side must come from the 2nd time derivative, i.e., the first time derivative must make the corresponding "unit jump" and the function itself must be continuous at $t=0$. This implies
$$\tilde{G}(0^+,\vec{k})=\tilde{G}(0^-,\vec{k})=0, \quad \partial_t G(0^+,\vec{k})=c^2.$$
The first condition gives $B=0$ and the 2nd
$$A \omega =A c k= c^2 \; \Rightarrow \; A=\frac{c}{k}.$$
This leads to
$$\tilde{G}(t,\vec{k})=\frac{c}{k} \Theta(t) \sin(c k t).$$
The Fourier transform can be solved using spherical coordinates for $\vec{k}$ with the polar axis in direction of $\vec{x}$, leading to
$$G(t,\vec{x}) = \frac{\Theta(t)}{4 \pi r} \delta(t-r/c)= \frac{1}{4 \pi r} \delta(t-r/c), \quad r=|\vec{x}|.$$
In the final step we could leave out the Heaviside function, because the $\delta$ distribution restricts to $t>0$ anyway.

The retarded solution for the Lorenz-gauge potentials thus is
$$A^{\mu}(t,\vec{x}) = \int_{\mathbb{R}^3} \mathrm{d}^3 x' \frac{1}{4 \pi c |\vec{x}-\vec{x}'|} \vec{j}(t-|\vec{x}-\vec{x'}|/c,\vec{x}').$$
Indeed, the field at time $t$ is only affected by the source at the earlier "retarded" times $t_{\text{ret}}=t-|\vec{x}-\vec{x}'|/c$.

Take as an example the most simple case of a Hertzian dipole at rest in the origin of your coordinate system. The retarded solution yields some spherical wave radiating out, as you expect from experience: It's just a charge oscillating around the origin. If you just switched on this motion of the charge (or equivalently, the AC current in a short linear antenna) you get some wave radiating out with the wave front propagating at the speed of light. That's a quite usual physical situation, and you get this particularly solution radiating out from the source by using the causality argument which let's you uniquely use the retarded propgator of all the infinitely many other propgators (among them the advanced one or any correctly normalized superposition of the retarded and advanced propgators).

Now the question remains, what does "time-reversal symmetry of electrodynamics" physically mean. The most simple idea is to take a movie of the situation just described, i.e., switching on the dipole radiation at $t=0$ and stop the movie at an arbitrary time $t_{\text{fin}}$. What you get is of course the em. wave radiating out with the wave front traveling outwards at the speed of light.

Now watch the movie backwards. What you then see is indeed something leading to a perfectly valid solution of the Maxwell equations, which is given by starting at $t=0$ (the starting time of your movie run backwards) with an initial field configuration given by the retareded solution at time $t_{\text{fin}}$ and then using the retarded solution of the time-reversed sources. This solution looks of course such that the complicated initial field is radiating inwards towards the origin and it the end is completely absorbed by the there located dipole source.

Though this is a mathematically valid solution of Maxwell's equations and also in principle doesn't contradict any physical laws, it's for all practical purposes impossible to realize, because you'd need to somehow prepare the perfect initial state of the fields given by the original solution of the out-radiating antenna and provide the perfect time reversed current in the antenna to get what you see when running the movie backwards. This is very complicated to achieve.

Now one can also qualitatively understand, why the thermodynamic arrow of time (i.e., the arrow of time defined as the direction of time for which the entropy of a macroscopic system is increasing rather than decreasing) is coinciding with the causal arrow of time: It's easy to drop a glass from the table, breaking into very many pieces when hitting the floor, but it's very unlikely that spontaneously the thermal fluctuations of all the pieces on the floor conspire such as to be precisely the time-reversed situation for all the particles in these pieces of the very moment the glass hit the floor. On average it would take far longer than the entire lifetime of the universe that this happens only once, and that's why it is never observed in reality though in principle nothing in the fundamental laws forbids such a process. It's just so unlikely that in practice it never happens.

 

[thegroundhog]

Thank you Dale and Perok and Vanhees 71.
I really appreciate you taking the time to try to explain this to me and apologies if I'm an exasperating student! I hope you don't mind me coming back with a query to your replies.
This idea of playing back a recording is a human construct, there is no such thing as 'playing back' an event in the universe - I have always struggled to understand the point of these time reversible examples like someone on a swing, as it would only by -t if a human was playing the movie backwards and then only within that movie, t would still be t with reference to the person playing the movie. To me these examples beg the question so what?
As for entropy giving the illusion of a direction in time, what about the pockets of high-low entropy in open systems, nothing changes when there is a reverse of entropy.

With reference to the equations I get the fact that it's a 'quirk' or whatever you want to call it that fundamental laws of physics don't mind t or -t, but do we all accept that this is nonsense in this universe?
Is it like saying 4 apples doesn't mind if it's -2 squared or 2 squared? Where minus 2 apples is obviously garbage, whether there are humans witnessing the apples or not?

 

[jbriggs444]

Is it like saying 4 apples doesn't mind if it's -2 squared or 2 squared? Where minus 2 apples is obviously garbage, whether there are humans witnessing the apples or not?

You will need to choose a better example for this. If you multiply -2 apples by -2 apples you do not get 4 apples. You get 4 apples². Units matter.

Besides, everyone knows that you don't square apples. You make them into $\pi$.

 

[PeroK]

With reference to the equations I get the fact that it's a 'quirk' or whatever you want to call it that fundamental laws of physics don't mind t or -t, but do we all accept that this is nonsense in this universe?
Is it like saying 4 apples doesn't mind if it's -2 squared or 2 squared? Where minus 2 apples is obviously garbage, whether there are humans witnessing the apples or not?

This sort of thinking is inadequate if you want to learn about modern physics.

The universe isn't made of apples. The universe is made of particles, each of which has an anti-particle. A particle and an anti-particle may annihilate each other. An anti-particle is very much the "negative" of the particle. One way that Quantum theory deals with anti-particles is that they behave like particles moving backwards in time.

So, no, time reversibility is not nonsense. Not if you want a deeper understanding of physics.

Also, you need to stop using words like "nonsense" and "garbage".

 

[Dale]

I get the fact that it's a 'quirk' or whatever you want to call it that fundamental laws of physics don't mind t or -t, but do we all accept that this is nonsense in this universe?

I don't know. All I can say is it is weird. Symmetries are very powerful in physics, so I am not certain that any symmetry can be simply dismissed as nonsense. But this one is certainly strange.

 

[Ibix]

To me these examples beg the question so what?

The point is that the maths to find the speeds of billiard balls after collision given the speeds before is identical to the maths to find the speeds before collision given the speeds after. That's what time-reversal symmetry means in a nutshell.

The only flaw in that is friction - I need to add the frictional speed change in one case and subtract it in the other. Tracking down why that should be so leads to a mystery: it doesn't seem to be because of any particular law of physics. Detailed examination of friction shows just air molecules bouncing off the balls (more collisions - see the previous paragraph). It's just that those collisions tend to either slow the ball or speed it up depending which version of the calculation you were doing. That last gives a meaning to the direction of time.

 

[thegroundhog]

OK, thank you. It's hard but I will accept the reversibility of time and will continue to try to find a way to get my head round it. I loved the Pi joke too!

 

[strangerep]

With reference to the equations I get the fact that it's a 'quirk' or whatever you want to call it that fundamental laws of physics don't mind t or -t, but do we all accept that this is nonsense in this universe?

Imho, it's reasonable to say that we simply don't know the origin of the microscopic arrow of time. As @vanhees71 and I have pointed out in earlier posts (and many previous threads), a preferred orientation of time evolution must be chosen arbitrarily to obtain the excellent predictions from quantum field theory.

People might not like it if one uses the word "nonsense" for this situation. I see it as "emperor's new clothes". Something is missing from our most fundamental understanding of the laws of nature. But heh, by now that shouldn't be a secret at all.

 

[vanhees71]

I don't know, what should be missing. Physics is not only a set of equations to be solved but in addition also some very general assumptions, one of which is the causality of all of physics, and as I've tried to show above using the example of why we choose the retarded solution of Maxwell's equations in classical electrodynamics based on the causality principle, you do not only need the equations to describe physics but also additional conditions like the one implied by the causality condition. Mathematically it's clear that the set of Maxwell equations alone are not sufficient because they have very many solutions which do not refer to situations you can realize in experiment and that's why you need in addition to the equations some initial and/or boundary conditions. The causality principle is very fundamental and cannot be derived from anything more simple. This doesn't mean that physics is somehow incomplete.

 

[hilbert2]

I think the reason why a human being assigns a particular "forward" direction to the time axis is that we only have memories of what we call the "past". Otherwise there would be no reason to do that.