Ebook physics and whitehead quantum, process, and experience part 2

Part III Fundamental Processes yanulada This page intentionally left blank 129 11 The Primacy of Asymmetry over Symmetry in Physics Joe Rosen Introduction Charles Hartshorne includes in one of his boo[.]

Part III

Fundamental Processes

This page intentionally left blank.

11

The Primacy of Asymmetry over Symmetry in Physics

Joe Rosen

Introduction

Charles Hartshorne includes in one of his books (1970, pp 205–226) a chapter,

“The Prejudice in Favor of Symmetry,” in which he discusses the symmetry and asymmetry of logical relations Here are some extracts from the chapter, not in their original order I think they give the essence of what Hartshorne is aiming at

Symmetry is in a sense a lack of order (221)

From symmetrical relations asymmetries cannot be derived! (218)

Look to the asymmetrical relations and the rest will tend to take care of them-selves (223)

Here, as always, symmetry is a partial or abstract aspect of what, in its concrete wholeness, is an asymmetry Yet in its partial role symmetry is as ultimate as asymmetry (221)

This pattern, symmetry within an overall asymmetry, we meet again and again I

see in it a paradigm for metaphysics (210)

Especially in the chapter summary:

In this chapter I have argued that non-symmetrical concepts are logically primary, and symmetrical concepts derivative Yet both are needed to make an intelligible philosophy The two things to avoid are taking symmetry as primary, and failing

to do justice to symmetry in its proper subordinate role Metaphysicians have

130 Joe Rosen

tended to commit both of these mistakes in different aspects of their systems (226)

And finally:

Another example: In other words, the appeal to symmetry is not a sufficient argument (I am aware that in physics it is often taken to be so I have not, in my ignorance, been able, so far, to interpret this in terms of the views set forth in the present essay.) Asymmetry is basic in formal logic; with what right does one assume the reverse everywhere else? (222–223)

Hartshorne actually has more to say in the chapter, such as comments on process taken as creation of novelties and, following ˇCapek (1961), on the primacy of time (asymmetric) over space (symmetric) But the above sampling will suffice for our purpose

In the present chapter I respond, as a physicist, to Hartshorne’s complaint about appeals to symmetry in physics, showing how and when such appeals are justified Then I show that, just as in Hartshorne’s “paradigm for metaphysics,” even in physics asymmetry is primary

Symmetry in Physics

For those readers who feel the need to get up to speed in symmetry, and espe-cially symmetry in science, I dare suggest two books I have written for that very purpose One is a semipopular introduction (Rosen, 1975), while the other

is considerably more sophisticated (Rosen, 1995)

The appeal to symmetry as a sufficient argument in physics, with which Hartshorne expresses his dissatisfaction, is usually based on either of two prin-ciples One principle is simplicity, also called Occam’s razor, which is:

Unless there is evidence to the contrary, we assume the situation is as simple, i.e.,

as symmetric, as possible.

For example, are the laws of nature, such as the speed of light in vacuum, the same in all directions? With no evidence to the contrary, we immediately assume the simplest, that the laws of nature are indeed the same in all direc-tions That also goes by the name “isotropy of space.” The symmetry here is symmetry of the laws of nature under all rotations about a point

How is it that symmetry and simplicity are practically synonymous? Con-sider the previous example Clearly, having the same laws of nature in all direc-tions is a simpler situation than having different laws of nature in different directions Instead of a different physics for each direction, we more simply have the same physics valid for every direction That is the essence of the simplicity-symmetry connection Symmetry involves some kind of regularity,

so the same physics repeats itself That is simpler than a different physics for each instance

For a more general consideration, start with Hartshorne’s statement (1970,

p 221), “Symmetry is in a sense a lack of order.” Order is practically syn-onymous with distinguishability, discriminability, irregularity, and heteroge-neity Indeed, symmetry is inversely related to order, distinguishability, discrim-inability, irregularity, and heterogeneity On the other hand, distinguishability, discriminability, irregularity, and heterogeneity are inversely related to indis-tinguishability, indiscriminability, regularity, and homogeneity So symmetry is directly related to regularity and homogeneity (to keep things brief) Thus, we have “the more symmetry, the more regularity, and the closer to homogeneity,” and vice versa

Now, if we take simplicity to mean requiring as little physics as neces-sary, then regularity and homogeneity do imply simplicity; the same physics is repeated, rather than additional physics being required The more regular and the more nearly homogeneous, the less physics needed and the simpler the situation Thus simplicity and symmetry are directly related

Such considerations are tied to the logical principle of insufficient reason:

Absent reason for a difference, rather assume no difference.

For the example of the speed of light in vacuum, with no supporting or contradicting experimental evidence, let us assume the speed of light in direc-tion A is different from that in direcdirec-tion B Then the speed of light will be greater in one direction, say A, than in the other But what reason do we have to assume this rather than the opposite, that the speed of light is greater in direc-tion B? With insufficient reason, we are guided to give up the assumpdirec-tion and instead take the speed of light to be the same in both directions

Now, it can happen, and indeed it has happened and will surely happen again and again as we delve deeper into nature’s workings, that the acquisition

of new experimental evidence obviates the principle of insufficient reason An excellent example has to do with symmetry of the laws of nature under mirror reflection (or more precisely, spatial inversion) For ages it had been taken for granted that the same laws of nature govern all physical systems and their mirror image systems Stated in other words, if any physical process is allowed

by nature, then the mirror image process is also allowed (or both forbidden) After all, with no evidence to the contrary and plenty in support, why assume otherwise? Well, in the 1950s nature was shown to be laughing at our simplify-ing assumption, as reasonable as it had been, when experiments revealed that in certain cases nature does indeed discriminate between systems and their mirror image counterparts (Those cases involve the weak nuclear interaction See, for instance, Ne’eman and Kirsh, 1996.)

132 Joe Rosen

The other principle upon which symmetry arguments in physics are often based is the symmetry principle (Rosen, 1995, 104; 1975, 108):

The symmetry group of the cause is a subgroup of the symmetry group of the effect.

Or less rigorously:

The effect is at least as symmetric as the cause.

The symmetry principle is derived from the existence of causal relations

in science (or in any other field, for that matter) The idea is that, knowing the symmetry of a cause, one has excellent reason to assume the same symmetry (and possibly even more) for any effect of the cause (I call that the minimalis-tic use of the symmetry principle [Rosen, 1975, 106] The symmetry principle can also be used, knowing the symmetry of an effect, to place a bound on the symmetry of its cause, which I call the maximalistic use [Rosen, 1975, 121].)

As a physics example of a symmetry argument based on the symmetry principle, we might take any electrical circuit consisting, for simplicity, solely

of interconnected batteries and resistors For this example the batteries, the resistors, and their connections uniquely determine the currents in all the wires

So the connected circuit is a cause and the currents are its effect Thus one can take any symmetry the circuit might possess and validly use it as sufficient argument for the currents to possess the same symmetry If, for instance, the circuit has reflection symmetry and is thus equivalent to its mirror image, then the currents in the circuit will possess reflection symmetry too (Fortunately, the weak nuclear interaction is not involved here.)

That works as well outside physics, wherever there are causal relations and the symmetry principle is valid In mathematics, one can consider an equa-tion as a cause and the set of its soluequa-tions (but not any individual soluequa-tion!) as

an effect If, for example, a polynomial equation in one unknown x contains only even or only odd powers of x, it is symmetric under change of sign of x,

x → –x By the symmetry principle, the set of roots of the equation must also

possess that symmetry So we are assured that the nonzero roots of such an equation consist solely of positive-negative pairs

The symmetry principle can be formulated equivalently in terms of asym-metry:

Any asymmetry of the effect is an asymmetry of the cause.

Or also:

The cause is at least as asymmetric as the effect.

The Primacy of Asymmetry in Physics

Here is a summary of an argument presented in full in Rosen (1995, pp 157– 161) In the final analysis, what symmetry boils down to is that a situation possesses the possibility of a change that leaves some aspect of the situation unchanged Expressed most concisely:

Symmetry is immunity to a possible change.

Thus the two essential components of symmetry are:

1 Possibility of a change: It must be possible to perform a change

(although the change does not actually have to be performed)

2 Immunity: Some aspect of the situation would remain unchanged,

were the change performed

If a change is possible and some aspect of the situation is not immune to

it, and the system rather would change concomitantly were the change carried out, we have asymmetry Note that the same situation might be both symmetric and asymmetric under the same change, depending on which of its aspects are being considered For instance, the statement “Beauty is truth, truth beauty” preserves its meaning but changes its graphical appearance under beauty↔ truth interchange

Change is the production of something different For a difference to exist,

in the sense of having physical meaning, a physical gauge for the difference, a standard, a frame of reference, is needed So the existence of a standard is necessary for the existence of the difference and the possibility of change And the nonexistence of an appropriate standard makes a putative change impossi-ble

To be able to gauge a difference, a standard cannot be immune to the change that brings about the difference, to the change for which it is intended to act as reference Otherwise it could not serve its purpose As an example, con-sider proton-neutron interchange That change can be gauged by referring to a standard proton, say, preserved in the vaults of the National Institute of Stan-dards and Technology (NIST) If your system consists of a single neutron and you perform proton-neutron interchange, you have indeed made a change; be-fore, your particle was different from the NIST standard, while afterward it became the same In this example, the standard proton is indeed affected by proton-neutron interchange; it changes into a neutron, which is something else

On the other hand, a standard proton-neutron pair cannot serve as such a gauge If you attempt proton-neutron interchange on your system consisting of

a single neutron, you find no change at all Before your attempt your particle was the same as one of the standard pair, and after your attempt it was still the same as one of the standard pair, so you made no change at all And the useless

134 Joe Rosen

standard pair is indeed immune to proton-neutron interchange, under which it remains a proton-neutron pair (or neutron-proton pair, if you will, but still the same)

Thus for a change to be possible for a situation, there must be some aspect of the situation that is not immune to the proposed change and can serve

as a standard for the change So for a situation to possess symmetry, it must have both an aspect that can change (serving as a standard for the change and giving the required possibility of a change) and an aspect that does not change concomitantly (giving the required immunity to the possible change) In other words, the possibility of a change, which is a necessary component of symme-try, is contingent on the existence of an asymmetry of the situation under the change Hence the result:

Symmetry implies asymmetry.

Asymmetry is a necessary condition for symmetry For every symmetry there is

an asymmetry tucked away somewhere in the world

As an example, consider a uniform equilateral triangle We normally as-cribe it the symmetry that its appearance is immune to 120 rotation (about the axis through its center and perpendicular to its plane) We normally do that, because we have plenty of standards for 120 rotation, such as the walls of the rectangular room (asymmetric under 120 rotation), so 120 rotation is a possi-ble change But if the equilateral triangle were a universe unto itself, there would be no standard for 120 rotation, so it would not be a possible change, and the triangle would then not possess the symmetry we normally ascribe it

The symmetry exists because the total situation, that of the equilateral triangle

together with its surroundings, does possess aspects that are not immune to

120 rotation and can serve as standards for 120 rotation The equilateral trian-gle is symmetric only in the context of its surroundings

We can summarize our results concerning symmetry, change, immunity, standard, and asymmetry in the following diagram, where arrows denote impli-cation:

Symmetry

→ Possibility of

a change

→ Standard for the change

→ Asymmetry under the change

→ Immunity to the change

Thus, for there to be symmetry, there must concomitantly be asymmetry under the same change that is involved in the symmetry The existence of the

symmetry depends on the existence, somewhere in the world, of a correspond-ing asymmetry

Such considerations can be extended Any finite physical system might, at least theoretically, possess perfect symmetry, i.e., immunity of all aspects of the system to some change The standard for the change would, as usual, lie in the system’s surroundings The universe, by definition, has no surroundings, so any standard for change of the universe must be contained within the universe itself Thus a putative perfect symmetry of the universe would be a self-contradiction

As all aspects of the universe would be immune to whatever change the uni-verse is supposed to be symmetric under, there would be no aspect that could serve as a standard for the change So the change would not be possible, and there would be no symmetry Hence the cosmic conclusion:

The universe cannot possess perfect symmetry.

As an example, consider spatial displacement symmetry, immunity to dis-placement from here to there As far as we can tell at present, the laws of physics are displacement symmetric; the same laws seem to be valid every-where Could the universe then possess perfect spatial-displacement symmetry?

If it did, all aspects of the universe, and not only the laws of physics, would be immune to spatial displacement But then there would be absolutely no differ-ence between here and there, there would be no standard for spatial displace-ment, and spatial displacement would be impossible As a matter of fact, it is the inhomogeneous distribution of matter in the universe that allows differentia-tion among locadifferentia-tions and serves as a standard for spatial displacement

References

I would like to express my thanks to Tim Eastman for bringing Hartshorne’s chapter to

my attention.

ˇ

Capek, Miliˇc 1961 The Philosophical Impact of Contemporary Physics New York: Van

Nostrand Reinhold Co.

Hartshorne, Charles 1970 Creative Synthesis and Philosophic Method La Salle, IL: The

Open Court Publishing Co.

Ne’eman, Yuval and Yoram Kirsh 1996 The Particle Hunters, 2nd ed Cambridge:

Cambridge University Press.

Rosen, Joe 1975 Symmetry Discovered: Concepts and Applications in Nature and

Sci-ence Cambridge: Cambridge University Press Expanded and reprinted New

York: Dover Publications, 1998.

Rosen, Joe 1995 Symmetry in Science: An Introduction to the General Theory New

York: Springer-Verlag.

12

Spacetime and Becoming:

Overcoming the Contradiction Between Special Relativity and the Passage of Time

Niels Viggo Hansen

For us believing physicists, the distinction between past, present and future

is only an illusion, even if a stubborn one.1

—Albert Einstein

Passage versus Physical Extension: A Classical Problem

Modern science has taught us that the passage of time doesn’t really fit into physical reality In the world of our experience, there is an obvious difference between the facts of the past, the acuteness of the present, and the open possi-bilities of the future But in the universe disclosed by modern physics, the notion of a “now” seems to be inconsistent, let alone the “passage” of this now through the continuum of time

Since the time of experience seems to be at odds with the scientific con-cepts of space and time, some have drawn the conclusion that everyday notions

of change and becoming are illusory Others have taken this inconsistency to show that scientific abstraction blocks an understanding of the depth of funda-mental questions of existence and temporality Others claim that a coherent understanding of time is a metaphysical chimera

This chapter is an attempt to outline a fourth response that is more ade-quate It points to a way of overcoming the contradiction by realizing that it depends on certain tacit assumptions in the interpretation of physical continua

of space and time, and of the temporal aspects of experience Without these assumptions, even strong notions of dynamism and becoming can be compati-ble with the special theory of relativity The suggested solution is a radically processual and relationist interpretation based on Whitehead’s process meta-physics It involves a reading of special relativity as a source of new and deeper