Ask Ethan: Was the Universe “timeless” before the Big Bang?

As far back as we can observe in our Universe, time always behaved in exactly the same fashion we’re familiar with: ticking away, relentlessly, at the same rate for all observers. Bring your clock to the surface of the Earth? The bottom of the ocean? Into orbit in space? Near the event horizon of a black hole? Or speeding through intergalactic space at close to the speed of light? It doesn’t matter. The amount of time it takes for regular events to occur — for a second to tick by, for an atomic transition to occur, for a photon of a specific wavelength to have one “wave” pass by you, etc. — is going to be identical for any observer under any of those conditions. In fact, the rate at which time passes for themselves, at one second-per-second, is something all observers can agree on.

Sure, relativity is weird in a lot of ways, both when you move close to the speed of light or when the curvature of spacetime is very strong. Lengths contract, time durations dilate, and different observers draw different conclusions for one another versus for themselves. But time still passes, and relativity allows us to reconcile those differences. But what about if we go to an unfamiliar place; what if we consider what happens before the Big Bang? That’s what Justin Skit wants to know, asking:

“Can you help me understand what’s going on with time during cosmic inflation? I know inflation starts and then the big bang. But if the era before the big bang was timeless how does that work?”

It’s an excellent question, and one that compels us to go very deep into theoretical physics territory. Let’s dive in and see what we learn!

An example of a light cone, the three-dimensional surface of all possible light rays arriving at and departing from a point in spacetime. The more you move through space, the less you move through time, and vice versa. Only things contained within your past light-cone can affect you today; only things contained within your future light-cone can be perceived by you in the future. This illustrates flat Minkowski space, rather than the curved space of general relativity.

The first thing you have to understand is that time, in physics, is different from how we normally conceive of it. When you think about time, you probably think of it as a continuum: as a “line” of sorts that always marches forward at the same rate for anyone experiencing it. In your day-to-day life, you’ve experienced time in a similar fashion for its entire duration: it seems to pass by, in a uniform, measurable fashion, allowing you to mark “when” any event occurred. All of the events that have occurred in the past are forever immutable; they have occurred and cannot be changed. All of the events that will occur in the future are as of yet still undetermined; the actions and events that unfold from now until the time when they occur can still affect them.

And all of this is true. Well, it’s a good approximation for what’s true, as far as reality is concerned, from a classical perspective. In all of our classical theories of physics — including in both Special Relativity and General Relativity — time is simply a continuous parameter, marching forward in a continuous fashion for all who experience it. Sure, there are some oddities:

• if you move at the speed of light, time doesn’t pass for you at all,
• if you move faster than the speed of light, you become a tachyon and travel backwards in time,
• and if you’re in a different location, move at a different speed, or experience a different spacetime curvature than another observer, you and the other observer won’t agree on how much time has elapsed,

but time still exists for everyone. By applying the rules of relativity appropriately, we can understand what each and every observer will measure for themselves.

This diagram illustrates the inherent uncertainty relation between position and momentum. When one is known more accurately, the other is inherently less able to be known accurately. Both position and momentum are better described by a probabilistic wavefunction than by a single value. Other pairs of conjugate variables, including energy and time, spin in two perpendicular directions, or angular position and angular momentum, also exhibit this same uncertainty relation.

But in quantum mechanics, the story changes. Time can no longer be treated just as a parameter that “ticks by” the way it does classically. One of the biggest differences between classical mechanics and quantum mechanics is that instead of merely having values for parameters such as:

• position (in space),
• momentum (including direction),
• angular momentum,
• or energy,

these classical “quantities” instead become operators in quantum physics. Objects don’t have well-defined “properties” in the quantum sense; these properties can only be known and measured up to an inherent limit: a limit set by the Heisenberg uncertainty principle.

You might think about uncertainty in terms of position and momentum: the more accurately you measure a particle’s position, the less well-known its momentum is (and vice versa). Indeed, this is true, but it’s only one example of these traditional uncertainty relations. There are also uncertainty relations between:

• orientation and angular momentum,
• a particle’s spin in mutually perpendicular directions,
• electric potential and free electric charge,
• magnetic potential and free electric current,

as well as numerous others. But if position-momentum is the most famous example of quantum uncertainty, the second most famous example has to be the one between energy and time.

The mass of the top quark, as inferred from Large Hadron Collider in the CMS detector, is shown on the x-axis, with the number of events shown on the y-axis. Note that the mass doesn’t make a narrow peak, but rather a broad one, as the top quark has such a short lifetime (less than 10^-24 seconds) that the energy uncertainty corresponds to an inherently uncertain value of mass for each top quark (or antiquark) created.

This might puzzle you if you’re only a little bit familiar with quantum physics. After all, position and momentum are both operators in standard quantum mechanics, as is energy. But time, unlike these other parameters, remains just an independent variable in Schrödinger’s quantum mechanics, as anyone who’s ever taken a course in it might remember. Yet, nevertheless, when we create a short-lived quantum particle, like a top quark, for example, we don’t find that all of the top quarks created have the same mass (or, by E = mc², the same energy), but rather that there’s uncertainty in their rest mass, commensurate with the (uncertain) short lifetime of the particle itself and Heisenberg’s uncertainty relation.

But this isn’t a flaw in our quantum equations; that’s a consequence of Schrödinger’s quantum mechanics only applying to non-relativistic systems. When we move on to a more full theory of (relativistic) quantum mechanics, time does indeed get promoted to an operator, and remains an operator in quantum field theories as well. Classically, space and time are parameters or quantities; from a quantum perspective, they’re both operators. This is true regardless of the conditions that occur: at high or low energies, near or far away from a black hole, at late cosmic times or very early on, even close to the Big Bang. These behaviors of space and time appear to not change, regardless of where or when we examine the Universe.

There is a large suite of scientific evidence that supports the expanding Universe and the Big Bang. At every moment throughout our cosmic history for the first several billion years, the expansion rate and the total energy density balanced precisely, enabling our Universe to persist and form complex structures. Today, dark energy dominates the Universe, while early on, prior to the onset of the hot Big Bang, a phase of cosmological inflation occurred, preceding it and setting it up.

So then why, you might wonder, have so many people asserted that there was no “time” before the Big Bang? After all, if you read Stephen Hawking’s final book, Brief Answers to the Big Questions, you’ll find that he says the following:

“The role played by time at the beginning of the universe is, I believe, the final key to removing the need for a Grand Designer, and revealing how the universe created itself. … Time itself must come to a stop. You can’t get to a time before the big bang, because there was no time before the big bang. We have finally found something that does not have a cause because there was no time for a cause to exist in.”

And yet, when cosmologists speak about what happened before the Big Bang — i.e., during the period of cosmic inflation that set up and preceded the Big Bang — time remains present. So why would Hawking state that time itself must come to a stop? Why would he claim that you can’t get to a time before the Big Bang? And why would he state that there was no time at all before the Big Bang?

I hate to say it, but this is because Stephen Hawking is not talking about the Big Bang as we conventionally understand it: the hot, dense, uniformly filled with matter-and-radiation, rapidly expanding state of the early Universe that we associate with the onset of the Big Bang. He’s not talking about the state of cosmic inflation that preceded and set up the hot Big Bang, either. Instead, Hawking is talking about a very old notion of the Big Bang that is currently a very hotly debated topic (and an active area of research) within theoretical cosmology: the idea that “the Big Bang” means the origin of space and time itself.

According to the original observations of Penzias and Wilson, the galactic plane emitted some astrophysical sources of radiation (center), but above and below, all that remained was a near-perfect, uniform background of radiation. The temperature and spectrum of this radiation has now been measured, and the agreement with the Big Bang’s predictions are extraordinary. If we could see microwave light with our eyes, the entire night sky would look like the green oval shown.

This is something that makes sense if you put yourself in the mindset of someone who was learning about the Universe back when Hawking was learning about the Universe: in the 1950s, 1960s, and 1970s. Hawking (born in 1942) grew up with the same notion of the expanding Universe that his predecessors — Georges Lemaître, Alexander Friedmann, George Gamow, Ralph Alpher, etc. — developed: that the Universe is expanding and cooling today, and that implies it was hotter and denser in the distant past. If you extrapolate back arbitrarily far, to arbitrarily high temperatures, energies, and densities, you’ll arrive at a singularity, or a state where all of the matter and radiation in the Universe was compacted down into a single point.

This idea, of a singularity, goes back to Lemaître and Gamow, who gave it poetic names such as “the primeval atom” and “the cosmic egg.” This was the original idea of the Big Bang, and when the observational evidence came in supporting it (e.g., the cosmic microwave background) while also ruling out other mainstream alternatives, it seemed to cement this picture in the minds of physicists, astrophysicists and cosmologists all around the world. Our Universe began with the Big Bang, and the Big Bang itself was synonymous with the idea of a singularity: a creation event that not only gave rise to a hot, dense, uniformly filled Universe, but one that marked the origins of space and time themselves.

As a balloon inflates, any coins glued to its surface will appear to recede away from one another, with “more distant” coins receding more rapidly than the less distant ones. Any light will redshift, as its wavelength ‘stretches’ to longer values as the balloon’s fabric expands. This visualization solidly explains cosmological redshift within the context of the expanding Universe. If the Universe is expanding today, that implies a past where it was smaller, hotter, denser, and more uniform: leading to the picture of the hot Big Bang. If you extrapolate it as far as possible, you wind up with infinite temperatures and densities a finite amount of time ago: the conditions needed for a singularity.

And this is true in General Relativity: a singularity truly does define a set of conditions where time and space themselves do indeed break down. Remember, according to our best understanding of physics — which is General Relativity for the structure of space and time and what we experience as the force of gravity, along with Quantum Field Theory as the governing rules for particles, antiparticles, and the electromagnetic and the nuclear forces — there are limits to:

• how small a length scale can be,
• how great a temperature can be,
• how short a timescale can be,
• and how energetic a quantum of energy can be,

and if you go past those limits, the quantities you compute will no longer make physical sense.

When Hawking talks about “the Big Bang,” he uses it in this antiquated sense: assuming that the Universe did indeed begin with a singularity, and that singularity marks the birth of space and time, and therefore there was an “event” of ultimate creation that created space, time, and all the matter and radiation within it. One can argue that this is defensible, as extrapolating a Universe filled with matter and radiation back in time does indeed lead to a singularity, and since the laws of physics break down at a singularity, that within the context of General Relativity, there must have been a birth to space and time after all. After all, there is no “outside” if there is no space, and there is no “before” if there is no time.

Blue and red lines represent a “traditional” Big Bang scenario, where everything starts at time t=0, including spacetime itself. But in an inflationary scenario (yellow), we never reach a singularity, where space goes to a singular state; instead, it can only get arbitrarily small in the past, while time continues to go backward forever. Only the last minuscule fraction of a second, from the end of inflation, imprints itself on our observable Universe today. The size of the now-observable Universe could’ve been no smaller than about 1 cubic meter in volume at the start of the hot Big Bang.

But that “picture” for the origin of our Universe is more than 40 years out of date, at present. The hot Big Bang — or the notion that the Universe emerged by expanding and cooling from an early hot, dense, nearly-perfectly-uniform state — is no longer considered to be the beginning of the Universe, but rather only arose as the aftermath of an earlier period that preceded it and set it up: a period of cosmic inflation. Inflation is a very different state than anything to do with the hot Big Bang, as instead of being filled with matter and radiation (or any type/species of particle), it was filled with field energy alone: energy inherent to the very fabric of empty space itself.

This creates very different conditions! When your Universe is filled with matter and/or radiation, then as it expands, it gets less dense. Because the density drops, there are fewer particles in any given volume of space, and so the expansion rate (and the temperature, and the energy of each particle, on average) also drops. As you extrapolate to earlier and earlier times, those quantities also go up; as you extrapolate to later and later times, those quantities go down. But when you Universe is filled with field energy, or an amount of energy inherent to space itself, then the expansion rate remains constant at all times: as space expands, the energy density remains constant, and so the expansion rate remains the same.

This diagram shows, to scale, how spacetime evolves/expands in equal time increments if your Universe is dominated by matter, radiation, or the energy inherent to space itself (i.e., during inflation or dark energy dominance). The bottom-most scenario corresponds to exponential expansion via both dark energy (today) and inflation (at early times). Note that visualizing the expansion as either ‘the existing space stretching’ or ‘the creation of new space’ won’t suffice in all instances.

This has remarkable implications. For the Universe, it means that any initially inflating region gets stretched to enormous scales, imbuing space with the same properties everywhere, including the same temperature and the same energy density. It means that no matter what the spatial curvature was initially, inflation ensures that it winds up indistinguishable from flat, the same way the Earth would appear flat if you inflated it to be a googol (10¹⁰⁰) times the size it is today. It means that any particles present get diluted and “inflated away” from one another, effectively emptying out the Universe. And it means that any quantum fluctuations that get created get stretched across cosmic scales, seeding the Universe with density imperfections. When inflation ends, the hot Big Bang begins, and our Universe proceeds in a way that everyone would understand and expect, from Friedmann and Lemaître onwards.

But during this period of inflation, the density and energy doesn’t drop as time goes forward, and it doesn’t increase as we extrapolate backwards in time, either. The fact that our energy density remains constant means that:

• the expansion rate remains the same,
• the field energy in a given volume space remains the same (plus quantum fluctuations),
• the spatial curvature is stretched indistinguishably from flat (plus quantum fluctuations),
• and that inflation proceeds, relentlessly in this fashion, for an indeterminate duration.

About the only things we can say about the duration are that it must have gone on for at least ~10^-32 seconds, and that it couldn’t have gone on for an infinite amount of time, as there must have been some pre-inflationary state (due to theorems about past-timelike-completeness of spacetimes) that preceded inflation itself.

From whatever pre-existing state started it, inflation predicts that a series of independent universes will be spawned as inflation continues, with each one being completely disconnected from every other one, separated by more inflating space. One of these “bubbles,” where inflation ended, gave birth to our Universe some 13.8 billion years ago. Today, dark energy dominates the Universe and causes space to expand exponentially as well. These scenarios may be related, but we have no idea how long inflation persisted for prior to the hot Big Bang: only the ability to say, “at least 10^-32 seconds” or so.

And this is where the story pretty much ends. You can argue “well, inflation is timeless in the sense that we can only probe the final ~10^-32 seconds of it, but if it went on for a nanosecond, a minute, a year, a trillion years, or a googol years, we’d still have the same Universe,” but that doesn’t change the three main facts that:

• time still passes during the inflationary period,
• the inflationary period was finite, indicating that there was “time” before it as well,
• and that we have practically no constraints on the pre-inflationary state, meaning that we don’t know whether inflation emerged from an ultimately singular or non-singular state.

Although many still operate under the assumption that there was a singularity from which space and time themselves did emerge — and hence, a “timeless” initial state, after all — the truth is that we have no way to access any knowledge or information about that state, or, for that matter, about any state that existed prior to the final ~10^-32 seconds of cosmic inflation. (After all, by its very nature, inflation wipes any such information away from the presently observable Universe.) Time proceeds as normal during the hot Big Bang and afterwards, but also during the inflationary period, and also during whatever period preceded the inflationary one. Whether there was a “timeless” state before that is possible, and some would argue even likely, but it remains unproven.

The possible emergence of time itself is a fun aspect of nature to consider, but we have to do it responsibly: with full knowledge that when even very smart people talk about a “timeless” state, they’re not talking about inflation; they’re talking about the creation/emergence of space and time itself. That may have indeed happened, but if it did, it’s not just before the Big Bang. It’s before the hot Big Bang, before inflation, and before whatever it is that came before even that. Only then do we have the possibility of going back to a state where space and time themselves emerged, allowing the Universe to exist at all.

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