SEAN CARROLL: To a physicist, time is a label on the universe.It appeared to be a rerun from 2015.

RAZ: Sean Carroll is a theoretical physicist.

CARROLL: At CalTech.

RAZ: And physicists like Sean think about time very differently from you and me.

CARROLL: To a physicist, the universe is this thing, it's full of stuff, and it keeps happening over and over again. And this goes back to, you know, ancient astronomers. The Earth revolves around the sun, and it rotates around its axis 365 times. So the universe is filled with repetitive, cyclic moments, and time is just the label on those different moments.

RAZ: Those labels - one day, one month, one year - make up what Sean and other physicists call the arrow of time, meaning that time travels in one direction. That's why you were younger in the past, while you'll be older in the future, why you remember one and not the other. But here's the problem. That difference between past and future is nowhere to be found in the laws of physics because in physics, there is no arrow of time.

CARROLL: When modern physics came to be from people like Galileo and Newton up through Einstein, we realized something very gradually, which is that the deep downlaws of physics don't distinguish between the past and the future. They treat them completely symmetrically as if they were just replaceable with each other. So as a physicist, there's almost more work to be done in understanding why time works the way it does than as a person on the street because you have to reconcile the fact that there is a difference between past and future with the fact that that difference doesn't appear anywhere in your fundamental equations.

RAZ: In the laws of physics,there is no intrinsic difference between the past and the future.

CARROLL: That is exactly right.

RAZ: Which theoretically means what?

CARROLL: So if you think about time going from the far, far, far past - let's say the Big Bang was not the beginning. Let's say there was sort of an infinite amount of time before the Big Bang, and there's an infinite amount of time after the present moment.It's possible there are regions of the universe where their notion of past and future are backwards compared to ours, where they call the past what we call the future and vice versa. That's completely allowed because the underlying laws of physics don't distinguish.

I don't know how a Caltech physicist can say such nonsense. He later acknowledges that entropy is increasing with time, but he argues that is just because the Big Bang was low entropy.

Of course the laws of physics distinguish past from future.

Physics has, for the most part, used the differential equations paradigm for formulating the *statements* of its *laws*.

ReplyDeleteAt all other times, it has used the paradigm of integral equations. Both these paradigms are based on calculus. They both regard time as a parameter---implicitly, as a measure of motion or change (notions much more general than mere cyclical nature/periodicity).

The way the method works, the laws are stated in the form of equations (differential or integral). Then, boundary and initial conditions have to be specified. It's only then the issue of marching in time---whether forward or backward---comes into picture. All the three things taken into account present a complete picture of the law---not just the differential (or integral) equation.

Many times, the laws/equations, when torn out of the above complete context, *look* as if they were "symmetrical" w.r.t. a forward or backward march of time. For instance, Newton's three laws.

However, not all laws obey this symmetry. A simple counter-example is Fourier's law of heat conduction, i.e., the diffusion equation.

Diffusion is an important case, because the equation is *linear*, and yet, it leads to a progressive loss of a property (the local profile "curvature"s everywhere) during the forward time evolution. Hence, if you are given a profile at some time as an IC, you can't progress the solution *backward* in time---an infinity of more information would have to be supplied at each infinitesimal march backward in time.

So, no, there is not always a time-symmetry. You don't have to make reference only to the second law or the notion of entropy the way physicists typically do. *Linear* equations like diffusion also are enough.

Realize, what goes for diffusion also goes for one of the most fundamental physical laws we know, viz. the Schrodinger equation.

All in all, to say that because laws appear to be symmetric in time because they treat time as a parameter is a misleading statement. Statement of laws is, by definition, only one "half" the story; the other "half" being: specification of IC/BCs and actual time-marching (and behaviour the evolution in times shows). The entire context is important; only laws cannot be torn out of this context, given the actual methodology of physics.

I have no idea who began spreading these erroneous ideas first, but it sure was long time before Carroll. He (like many other pop-sci expositors) simply reiterates these wrong ideas, perhaps never having examined them---their nature---critically / well enough.

Best,

--Ajit

As to entropy, I remembered that Dr. Sabine Hossenfelder had an illuminating take on entropy. So I googled for it, and found it here: http://backreaction.blogspot.com/2018/07/10-physics-facts-you-should-have.html . See point no. 1.

Delete(I don't know GR so can't understand her point no. 10, but based on ontological considerations, if by "space" you mean the sizes with which spatial attributes of objects (including the aether) exist, then it would be interesting to analyze whether her point is correct or not. But no, I don't intend to study GR at all, and so, will let that point go without any definitive comment here.)

Best,

--Ajit

The statement 'In the laws of physics, there is no intrinsic difference between the past and the future' which plainly reveals a rather gaping hole in the idea that physics can accurately describe reality. No surprise. Math is not reality, never was, never will be, and is especially useless in the hands of post modernist idiots who cut off their noses to spite their own faces. Math (upon which physics depends) also IS a logical construct that is utterly dependent upon a fixed sequential order (numbers mean nothing without it...and require time for sequence) and a hierarchy of logical operations (multiplication before division, addition before subtraction, etc) which it can not function without. All logical hierarchies are dependent upon sequential time, don't think so? Provide a single progression or sequence that does not require time. Can't have one without it. Bummer for the super intelligent pin heads that wish to deny the means by which their own mathematical logic functions.

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