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Timeless physics 2009

We have discussed timeless physics in 2006 but because people like Sean Carroll recently wrote about the topic, let me add a few general words.

Needless to say, I mostly disagree with people like Carroll. There are many topics in which other people are saying demonstrably wrong things about topics that have been well-established. In those cases, the disagreement can be sharp. In the case of timeless physics, which is really just a vague guiding principle or a research project with an uncertain future, the disagreement cannot be equally sharp.

However, I think that by their disrespect for the research of the emergent character of time and its ultimate fundamental "non-existence", people like Smolin, Hossenfelder, CommunistPig, or even Carroll only help to emphasize their (otherwise well-known) lack of creativity, intuition, and ability to see depth in theoretical physics.

A very brief history of time

In the distant past, our ancestors - much like other animals - could only think about their immediate survival. Eventually, they became able to organize events in time and plan for the future. Early astronomers have learned about many quasiperiodic processes in the skies which led them to the idea of time as something that can be measured by similar cycles.

Galileo Galilei was the first man who studied the dependence of terrestrial processes on time: he really introduced time to testable physics (only statics was studied accurately by the ancient Greeks). His empirically verified "s=gt^2/2" law for the accelerated motion in the gravitational field was not only the first law in which properties of terrestrial objects were written as a function of time: it was also the first law that was chosen from a set of alternatives by his newly engineered scientific method.

Isaac Newton added a lot of testosterone to Galileo's methodology. He co-invented the calculus and redefined the whole world as a collection of classical degrees of freedom, such as x(t) and v(t), that depended on time. Time was absolute and universal.

That remained true in field theory, e.g. in hydrodynamics, but space was gradually becoming a counterpart of time. Fields became the natural degrees of freedom: they depended on time and space, as in phi(x,y,z,t). This process culminated by relativity. In special relativity, "t" was no longer universal for all observers. It got linearly mixed up with "x,y,z" depending on the observer's velocity.

For the first time, special relativity also allowed us to think that eternalism is more natural than presentism. The whole spacetime is much more absolute and objectively existent than its sections at constant times (also known as the "space" at some moment). The sections of spacetime at a constant "t" were thought to be absolute before 1905 but Einstein has changed that completely.

Special relativity has also preserved and strengthened causality: not only events can be affected by the past events only; they can only be affected by events in a smaller region of the spacetime than the whole "past half-spacetime", namely by the past light cone of the event that is an effect of others.

In general relativity, all coordinate transformations became equally legitimate for the formulation of laws of physics. In special relativity, there used to be one good choice of "t" for every reference frame determined by a velocity "v". In general relativity, the choice of time became completely non-canonical, because of a new gauge symmetry (general covariance) that became a part of the basic principles of physics. The laws of causality remained valid but they suddenly needed a variable metric tensor to be calculated.

String theory: getting to the present

As the research mostly in string theory has demonstrated, the rigid rules of causality are circumvented by "tunneling phenomena" such as the Hawking radiation in the presence of evaporating black holes. This is quite obviously the case and it is needed for the information to be preserved - and we know it is preserved from other descriptions of the same phenomena.

String theory has shown that space is emergent. Manifolds can be constructed out of non-geometric building blocks, Gepner models, or matrices. And even infinitely large dimensions may arise via holography. Topology can change, the space and its dimensionalities are generated from more fundamental concepts. And velocities or momenta in space can also be rephrased as other aspects of physics such as charges (Kaluza-Klein theory) or winding numbers (T-duality and U-duality).

These insights are indisputable as of 2009 and every fundamental physicist who is up to her job knows them very well. On the other hand, the local Lorentz invariance - the basic principle of special relativity - still holds. It says that what is true about space should hold for time, too.

It follows that time must be emergent, too. At the fundamental level, time must be as doomed as space is. However, there are technical reasons that prevent us from writing "timeless physics" explicitly, even though similar things happen with "spaceless physics" in many cases and formalisms. All well-defined descriptions of string theory that we know today are really some kinds of field theory and each of them has at least one temporal dimension (even though all the spatial dimensions may disappear).

In the Galilean tradition, we used to think that objects could literally be thought of as functions of time. Quantum mechanics - especially if formulated using Feynman's paradigms - has taught us that all the histories that happen "in the middle of a process", before they're observed, must really be summed over. It makes no sense to imagine a particular "real state of affairs" before quantities are measured. Quantum mechanics implies that such a "real state" cannot exist.

Incidentally, this fact has also affected the presentism vs eternalism debate, in this case in presentism's favor. One can never imagine that the present is determined by the past light cone, like it was attempted in the "hidden variable theories".

Mostly notably, the free will theorem shows that the random decisions of Nature about the outcomes of experiments - decisions that quantum mechanics can only predict probabilistically - cannot be determined by a calculation that depends on the past light cone only. The "random element" is indeed added at the "present" moment - you may imagine that all the microscopic objects have a "free will" and they are only required to agree with the statistical predictions of quantum mechanics.

The fact that the intermediate histories must be summed over is most dramatically manifested in quantum gravity. The local Green's functions are no longer calculable, at least not if we want to preserve the Lorentz covariance. Instead, only the scattering (S-matrix) amplitudes can be computed. They are produced for each pair of the initial state and the final state.

It is highly plausible that some generalized versions of this formalism, e.g. one without the variable initial state and with the final state only (like in the Hartle-Hawking calculations) will have to be cracked before we really understand the secrets about the beginning of time. Many other mysterious questions - such as Poincaré recurrences in the quantum de Sitter space or the origin of the signature of our spacetime, assuming that a deeper explanation exists, are likely to be related to the previous enigma.

Depth, getting rid of assumptions, and many angles in physics

As physics was getting more advanced, time was getting gradually more flexible. Using their own words, people like Sean Carroll "don't get it": they don't understand what's so great about timelessness of a hypothetical future form of the laws of physics. So let me try to tell them (and others).

Time is one of the most fundamental assumptions that scientists were forced to accept before they could do any science. It looked as one of the most unbreakable bones in a skeleton that was destined to restrict our freedom to create new theories (and to live!) eternally. Every physicist - except for a hardcore communist who has no problem to be constrained and to blindly believe propositions that were pre-determined - must be irritated by the existence of every concept whose fundamental origin is not understood.

As we have discussed above, the developments in physics have shown that the direction of the bones in the skeleton of time are not universal: they depend on the reference frame. They're not hard bones, either. Instead, they are flexible and the presence of matter can distort them. In the context of black holes, quantum gravity shows that even causality of the skeleton itself can be broken by "tunneling" phenomena such as the Hawking radiation.

It has been demonstrated that space is doomed. The most accurate and fundamental theory of physics, including quantum gravity, is simply not a local field theory where objects (fields) are functions of space. Instead, a collection of local fields is just one description that may be approximately OK for long-distance physics but it is almost certainly inappropriate near the fundamental Planck scale.

Much like biologists have learned to look inside the bones and they can do all kinds of surgeries today, physicists must obviously continue to study the character of space and time, two of the most universal concepts in science and life. Only when they figure out where these bones come from, why they look as bones, and what is the genuine wisdom hiding beneath them, they have a chance to claim the final victory.

Diversity of viewpoints

I must say one more thing. Sean Carroll talks about different perspectives where the concept of time is more real or less real. And he makes it very clear that he doesn't give a damn whether one has these different viewpoints.

Such comments are just stunning for me. The existence of different ways how to look at the same physics that profoundly and qualitatively differ (e.g. by the existence of some coordinates of spacetime) is one of the most critical criteria that measure a true conceptual progress in physics. That's why the AdS/CFT correspondence is so deep.

Such dualities and alternative descriptions tell us that concepts, phenomena, and mathematical descriptions that used to be thought of as completely different are actually equivalent. I can't imagine how a good theoretical physicist could not care - and I am actually convinced that there is no good theoretical physicist in the world who doesn't care.

The number of independent assumptions and concepts in physics is being reduced by such dualities and previously unrelated answers are being correlated; these transformations of our knowledge are paramount and define the true revolutions in fundamental physics. You know, a person who hates to think mathematically may think that every duality makes physics more difficult: there's more stuff to learn and the person just doesn't like it.

But a true theoretical physics enthusiast loves such insights. These dualities are indeed new things to learn, which is great, but they're not new arbitrary assumptions that would make the foundations of physics less certain and more shaky - because their validity may be mathematically demonstrated. So the appearance of radically new dualities is always a win-win situation for the scientific progress.

In the approach to dualities, yuou can see a radical difference in the understanding of "simplicity" by deep theoretical physicists on one side - and by Lee Smolin and his unpleasant Yes-Women on the other side. The latter just hate maths, are always ready to deny maths, and consider anything with maths in it "contrived".

To summarize, this topic is not about some Einsteinian preconception that has been disproved or superseded. Nothing wrong has been seen with the power of symmetries and dualities and the power of multiple perspectives on the same physics. Quite on the contrary. These "Einsteinian values" have been given many more examples and they became more dominant in good physics than they have ever been.

Sean Carroll asks why would anyone talk about a "non-existent time" rather than a "non-fundamental time". Time apparently exists, much like protons, even though the latter are not elementary particles. Fair enough. Indeed, it will always have to be possible to derive the existence of time, at least as an approximation.

But it is very likely that at the fundamental (Planck) scale, such an approximation becomes completely inappropriate. At the fundamental (Planck) scale that is relevant e.g. for the birth of the Universe, we are likely to learn that time doesn't exist, as long as we interpret this question in the most natural way from the Planckian viewpoint. There's a lot of contexts and long-distance regimes where time will always exist. But the more one cares about the fundamental physics, the more he cares about the exact manifestations of concepts at the fundamental scale. At this scale, time may be literally shown not to exist.

This is partly a linguistically philosophical game because in science, we would have to operationally define what we mean by the proposition that "time doesn't exist". But there exists a different analogy, replacing the metaphor involving the proton. In 1905, we could ask whether the speed was limited. Sean Carroll could argue that the speed was apparently unbounded from above: the only thing we should be saying is that the unboundedness of the speed may fail to be fundamental.

But as you know, special relativity implies that at the fundamental level, the speed is really bounded from above, and it is the unboundedness that is just an approximation (of non-relativistic physics) while the boundedness is a fact, and a fundamental one.

You know, no sensible person is trying to argue that time is not a useful concept for most imaginable purposes. In fact, your humble correspondent has emphasized - e.g. in texts about background independence - that a good theory must always be able to show its compatibility with time as it was known from previous, approximate theories. The question is whether at a fundamental level, time exists - whether anything can be imagined to be a function of a time-like coordinate. And that's a different question than one about the existence of the proton.

After all, if the proton is stable, it corresponds to very real, accurate, and mundane 1-particle states in the exact Hilbert space of QCD - which are much more real than the isolated 1-quark states (that can't exist). But if time doesn't exist, it means that in the exact description, one cannot talk about any observables being a function of time. Such a description of observables would always be just an artifact of approximate, effective theories.

So it is damn important to follow what's happening with time in our most up-to-date theories of physics because the fate of space and time have always been the most important stories spread all over the history of physics.

And that's the memo.

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reader Jim Tank said...

Interesting article my conservative physicist.

However lets not discount more liberal leaning physicists who might tend to be more skeptical about the notion that the foundations of the standard model are perfect as currently conceived and more willing to find it conceivable that improved models in the future may replace existing models.

One more liberal leaning physicist recently re-evaluated the widely held belief that relativity theory breaks down in the extreme conditions of a black hole and found (or re-discovered) that relativity calculations do not break down in black holes (time approaches a stop as density approaches infinity, so infinite density is not achieved in finite time in a black hole, a widely believed paradox is avoided).

Other physicists found that deterministic quantum models are equally valid predictors of quantum outcomes as standard non-deterministic models. (Deterministic models require that the past does in-fact determine the future, quantum entangled particles are merely clones, etc.)

I tend to think it very conceivable that while current models are extremely successful (and deterministic models equally valid), the theory behind the math is likely less than infallible. (It is also conceivable that successful theories may need to also be compatible with a deterministic quantum model.)

Interesting that physicists who defend wild and seemingly improbable ideas such as an infinite number of multi-verses with an infinite number of time lines and tend to be dismissive of the simple deterministic universe Dr. Einstein believed in are called the conservative physicists!

reader Anonymous said...

Dear Lubos,

Who else do you know of is critical of cyclic cosmologies? Any books on the subject? I'm not a fan of the idea, as you may know. I just don't know why they want the universe to be cyclical so bad.

reader Lumo said...

Dear squeehunter, there was no mention of "cyclic cosmologies" in this text, but OK, let's allow off-topic messages.

I am convinced that virtually all cosmologists think the same thing about cyclic cosmologies that I do - they're unmotivated and they really don't solve the problems they should solve.

Alan Guth has been very explicit about these issues, and if you search for his name on his blog, you may find debates, interviews etc. with it. Good popular books often don't mention this scenario at all. That's what researchers mostly do, too. By their lack of interest, they're conveying the very opinion in the second paragraph.

I don't say that they're "so bad". In fact, they can be consistent etc. I just say that they're not good for anything and there's no strong hint to think that they should be right.

reader Tim said...

Thank you and sorry about the off-topic thing. I'm just ignorant of how this comment system works still. I'm guessing you get a notification regardless of how old the post is. Thank you though.

reader Pmer said...

Lubos, are you a presentist or eternalist?

I opt for presentism. For example the Michelson-Morley experiment was conducted "in the present". In fact, all scientific experiments occur in their present. No experiments have shown that a system "exists" at all times along their worldline.

It seems possible to break apart a time variable t to t=(t',t''), where t' is a relativistic notion of time (relational correlations) and t'' is a quantum notion (absolute time).

What do you think?