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What If the Universe Had No Beginning? Part 2: No Boundary, No Problem
(This is Part 2 of a series on Hawking’s no-boundary proposal. Read Part 1 first.)
I thought the whole point of this program was that we couldn’t just…get to the beginning of the universe, and now, thanks to the magic of Wheeler and DeWitt, we have the precise machinery we need to solve the beginning of the universe….if only we knew one thing, just one tiny piece of information, just one measly morsel…and we could do it.
Hawking did it. Well, he had an idea, which is more than anyone else had at the time.
Two decades after Wheeler and DeWitt, Stephen Hawking comes along and connects, as he usually does, several different lines of thought, and he realizes that the problem for one thing is actually the solution to another.
Check this out: Hawking is staring at the Wheeler-DeWitt equation. It’s a puzzle that reveals the universe, but all the puzzle pieces are scattered around, AND we don’t have the picture on the front of the box. If we know how to place just ONE piece, we can put together the quantum wave function of the universe.
We just need the first piece. The boundary condition that defines the beginning state of the universe. But we can’t measure it, we can’t read any device or look through any telescope to figure it out. Nothing gives us access to the first moment of the big bang. AND we have no theory of quantum gravity around the corner to just ASK.
So that leaves us with…taking a wild guess and seeing if it sticks.
Hawking decided that his wild guess would be as grounded as possible. He argued that the best boundary condition of the universe, the best statement that you can make about how it all gets started, had to be SELF-JUSTIFYING. That means the guess about the beginning of the universe couldn’t come from anywhere else: you can’t point to God or Wheeler or ANYTHING to just HAND you the answer, because the universe is every single thing to ever exist, in totality, and you can’t reach OUTSIDE that. There’s no hidden corner of the cabinet that exists outside the universe to just give us the boundary.
And the most self-justifying statement Hawking could make about the beginning of the universe is that it had no beginning.
In other words, what if the reason you can’t find the boundary at the beginning of the universe is not because it’s hidden or inaccessible, but because it genuinely isn’t there?
Now this is a very lovely thought to have. But we’re not here for lovely thoughts, we’re here for down and dirty physics. It’s one thing to say something crazy, it’s another to turn that into a working theory of nature. Thankfully, Hawking had exactly what he needed.
One of the defining features of the Wheeler-DeWitt equation is that it doesn’t involve time. It doesn’t know or care that the universe evolves, expands, does interesting things, heads out to dinner on a Tuesday night just because it’s wild like that.
The key that can unlock the Wheeler-DeWitt equation is a solid statement ABOUT time, specifically, the most important time of all: the beginning of the universe. So we NEED to involve time SOMEHOW in all this mess if we’re going to make progress.
So Hawking…involves time. Instead of just looking at space, he stitches together these geometries back to back like frames in a film. He makes a sequence of them, representing an evolution to the history of the universe. These frames tell the story of the cosmos. Now, we don’t know what that story is (I mean, from Wheeler and DeWitt’s machine; we can observe it and so we KNOW it, but we’re trying to EXPLAIN it), so Hawking constructs all these…paths. Possible histories of the universe. Trajectories, evolutions, stories. In some stories, the universe gets really big really fast and fizzles out to nothing. In others, it never even expands. In still others, there’s nothing but matter. And others, nothing but…nothing.
Now all of these paths, all of these histories of the universe, all share one thing in common: they’re in the usual spacetime that we know and love. Cause and effect, past and future, speed of light, all that. And they all have a BEGINNING. A first frame in the movie of the universe.
Well, what if we just made time behave differently? Now I’m going to share a term with you, and when I say it it’s going to sound really wrong, like icky, deep in your gut. But I’m going to say it, then I’m going to explain it. It…will still feel icky, but at least it will have an explanation.
Here goes: imaginary time.
Yeah, imaginary time. Time, but imaginary. Listen, I don’t know how much you know about imaginary numbers. But they’re really cool and fun and DEFINITELY worth bringing up in your next workplace all-hands meeting. The core idea behind imaginary numbers is to pretend to take the square root of, I don’t know, negative 4. The square root of regular four is 2, but the square root of negative four is…uh….what? In normal grade school math this is where your teacher scoffs at you and says you can’t take the square root of a negative number.
But this isn’t grade school. We’re not going to take the square root of a negative number. Instead, we’re going to say that the square roots of negative numbers are an ENTIRELY NEW KIND OF NUMBER. A brand new category. You have whole numbers, rational numbers, negatives, and now you have imaginary numbers, which are all the square roots of the negative numbers.
Phew, I swear I’m going somewhere with this.
The trick Hawking pulled was that he took all these histories of spacetime and replaced “time” with “imaginary time”. He multiplied the passage of time by the square root of negative one. Now, we actually do this in quantum mechanics all the time (or should I say imaginary time?) as a TRICK. Sometimes when we get equations that are really, really hard to solve, we replace time with imaginary time and they become easier. Then we solve them, then we swap back. Just a little reshuffling in the backend to work through some thorny problems.
But when Hawking does this to the spacetime of the universe, he gets a bonus. It’s not a party trick anymore. It’s a statement. You see, in normal spacetime, the universe has a beginning. But when you replace time with imaginary time, the beginning…goes away. This procedure actually puts space and time on equal footing. It makes them all creatures of curvature and geometry, with no separate identity. Which makes the beginning of the universe no special time at all. It becomes like the south pole, which is really just any other point on the globe. You reach the south pole and keep walking, and it’s only ever north from there. You reach the beginning of the universe, and it’s not special or unique (maybe a little hot); all you have is the future in front of you.
No beginning. No start. No boundary. A universe that justifies itself.
By making the switch to imaginary time, Hawking could ENCODE his “the universe has no beginning” idea, AND he could crunch through the math.
Voila: a key that unlocks the Wheeler-DeWitt equation and the know-how to run the mathematical machinery.
And what do you get for all this work? Nothing less than a wave function for the universe.
In Part 3, the wave function delivers something Hawking didn’t even ask for: our universe, more or less, for free.
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Long Beach Pride, a joyful parade meets outrage over canceled festival
Hundreds of spectators gathered along Ocean Boulevard dressed in rainbow tutus, dresses and shirts, whooping and waving as the Long Beach Pride parade rolled past Sunday morning.
Mayor Rex Richardson, wearing a rainbow lei and holding a Pride flag, marched down the street with gubernatorial candidate Xavier Becerra as Bad Bunny’s “BAILE INoLVIDABLE” rang out.
“Long Beach Pride in the house,” Richardson boomed into a microphone. “Thank you so much for coming out, keeping up this tradition for 43 years.”
But this year felt different for some, after the abrupt cancellation of the Long Beach Pride Festival hours before it was set to kick off.
City officials said this year’s cancellation was due to unresolved safety and permitting issues, while organizers with Long Beach Pride, the nonprofit that organizes the festival, say they worked in good faith to resolve them. The disruption lands at a moment of renewed national conflict over LGBTQ rights and visibility, giving the absence of the festival an outsized emotional and political resonance.
Two attendees of the 43rd Annual Long Beach Pride Parade embrace while watching the event along Ocean Boulevard in Long Beach on Sunday.
(Robert Gauthier / Los Angeles Times)
Debra “Deb” Kahookele, who is running for City Council, acknowledged the difficulties in holding a large festival but said, “there’s always a little bit of leniency when it comes to certain things.”
“I feel like, was there absolutely no room to help out?” questioned Kahookele, who attended the parade with her wife of 24 years. “In this moment in time, the community has been attacked in many ways, and so the last thing we needed was for a festival that everybody enjoyed to be canceled.”
“I just feel like Long Beach let the people down,” she added.
Long Beach Pride, established in October 1983, produced the first annual festival and parade the following year, at the height of the AIDS crisis and during an era when communities often organized in the face of political indifference.
This year, the event was slated to run through the weekend with live music, art and food at Marina Green Park. Then, news broke that while the parade would continue as scheduled, the festival would not.
The city said it made repeated efforts to work with the organization and issue an event permit, but ultimately did not receive essential information.
A person waves a rainbow flag ahead of motorcyclists taking part in the 43rd Annual Long Beach Pride Parade on Sunday.
(Robert Gauthier / Los Angeles Times)
“Out of responsibility to the safety of attendees, staff and the broader community, the city cannot issue the permit and has directed the event organizers to not continue their event,” the city said in a news release Friday.
Joey Velez, 48, and his partner, Nathan Sliwa, 33, both drove down from Oakland on Thursday to celebrate Pride in Long Beach. They learned the next evening that the festival had been canceled.
“We were not happy. It just kind of sucked — we came down specifically for this,” said Velez, who wore a shirt that read “He /// Him /// Daddy.” This would have been his second time attending the festival.
Velez expressed frustration at the city’s decision.
“The political climate that we’re in right now, the last thing we need to be doing is canceling Pride, especially from a liberal city like Long Beach,” Velez said. “That’s the last thing you would expect. Maybe there were some things that happened that the festival themselves didn’t dot their i’s and cross their t’s, but in the political climate we’re in right now, Long Beach should have muscled through that and said, ‘We need to make this happen, it’s super important for us to keep this going.’”
“It sends the message that the city does not value Pride,” Sliwa, a former Long Beach resident, added.
Tonya Martin, president of Long Beach Pride, said she was deeply disappointed by the city’s decision to cancel the event.
“At a time when our community is being targeted and made vulnerable, Long Beach should be doing more to protect and uplift us, not taking away one of the most visible and meaningful expressions of inclusion our city has,” she said in a statement Friday evening.
Around 12:30 p.m., people began gathering at Bixby Park, where the city had planned its own free event called “Canceled? Never Heard of Her!”
People danced along to Diana Ross’ “I’m Coming Out” and kept cool with rainbow fans.
“Welcome to Bixby Park, home of the parade afterparty,” a speaker told the crowd. “We’re gonna have the party that couldn’t happen across the way.”
Signs of discontent were present at the parade. Jess Shaw, who uses they/them pronouns, wore a black shirt that read “No one can cancel pride; it comes from the inside.”
The 35-year-old Orange County resident said they learned of the festival cancellation while attending a trans movie night with friends on Friday and said the next day felt very heavy.
Shaw said they attended the festival for the first time around 2009, “when I was a baby gay.” Shaw said they previously skated with their roller derby team in the parade.
“It’s nostalgic for me,” Shaw said. “This one has always felt like the best one in our local area.”
Shaw cited the festival’s history, dating back to the ’80s, and its emergence from the AIDS crisis, when misinformation was being spread.
“This is public health, and public health matters at a time like this,” said Shaw, who marched in the parade with Mommabear & Friends, a nonprofit organization in Orange County.
Shaw said people are blaming Long Beach Pride, but that they should “wait for their side.”
“To me, it’s so funny that everyone says they canceled pride. Pride is a … feeling,” Shaw said. “You can’t cancel that. No matter what happens, that’s inside me, and we can share that with each other at places like this.”
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W.H.O. Declares Ebola Outbreak a Global Health Emergency
Just a day after the announcement, cases were confirmed in the Democratic Republic of Congo and Uganda. There is no approved vaccine for this species of Ebola.
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What If the Universe Had No Beginning? Part 1: A Wave Function for the Universe
All you need to do to figure out the mystery of the beginning of the universe is to take your general theory of relativity and run the clock backwards to see what happens, you know, at the beginning.
Except you can’t.
You can’t because of one eensy teensy little problem, and that’s the problem of the SINGULARITY. It means that the equations we use to describe EVERYTHING ELSE in the universe like black holes and the expansion of space just…give up. Quit. You ask them to solve this one more problem and they look at their watch and say hey gotta run I think I left the toaster on at home…and they never come back.
So, if we can’t actually solve what’s going on at the beginning of the universe, can we at least…get a sense of it? Most people just shrug and move on to other problems. But if you’re Stephen Hawking, you just dive right in. Yeah, your approach is only half-baked and you’re almost certainly wrong, but it’s worth a shot in the dark, right?
This series is going to dive into Hawking’s proposal for the beginning of the universe, in which he calmly and flatly states that the universe had no beginning. And not like “it’s been here forever” no beginnings, but as in “that question doesn’t even make sense” no beginning. Like yes, you can string the words together to form a grammatically complete English sentence, but that particular COMBINATION of words has no useful meaning.
We’re in “What flavor of dishwasher did you use for you cell phone plan” territory here.
Or not. Hawking was smart, but he wasn’t infallible. So let’s crack this one open to see what all the fuss is about, and even if we end up being wrong, at least we’ll enjoy the journey.
Our journey to the beginning of the universe doesn’t start with Hawking. We need to rewind the clock back a bit. Not to the big bang, the 1960’s. That’s when John Wheeler, perhaps the most important physicist most people have never heard about, was hard at work poking at all things general relativity and quantum mechanics. In fact, he was one of the few people in HISTORY to be able to confidently talk about both fields with relative ease, because that’s the kind of guy he was.
Back in the 60’s quantum mechanics was all the rage. I mean, it still is, but it was back then too. Physicists had found great success quantizing all sorts of tiny, high-energy things. And once you had a quantum theory of a tiny, high-energy thing, you could do all sorts of cool stuff like predicting new particles and understanding how stars worked.
So here’s Wheeler, who really, really gets quantum mechanics. He lives and breathes it. And then he also knows general relativity like nobody’s business, honestly probably better than Einstein did. And we had recently uncovered the fact that the universe was once a Big Bang, and it used to be a lot smaller, hotter, and denser.
And it stands to reason that at one point it was so small, so hot, and so dense that it was just like one of those tiny, high-energy particles sitting in the lab: ripe for a quantum description.
But how do you…um…QUANTIZE the universe?
Wheeler wasn’t one to beat around the bush. He didn’t play games. He went straight to business. We already had a standard procedure for quantizing something. You take your normal, non-quantum theory of a thing, find the important bits, and “promote them” (yes, that’s the technical term) to these little things called operators that, and I’m skipping over half a book of math here, allow you to speak in terms of wave functions and probabilities and all the wonderful entangled fuzziness of the quantum world.
Wheeler (and another guy, Bryce DeWitt) did exactly that. They took the equations of general relativity, found the important bits (specifically, the ways that space could bend and the kind of stuff to inhabit space) and made them fuzzier. Instead of one single description, you instead now have a variety of POSSIBLE descriptions.
It’s just treating the entire universe the same way we treat an electron, and taking the idea seriously. For an electron, we replace something like its position with a wave equation describing where the electron MIGHT BE the next time we go looking for it. And for the universe, we replace ONE SPECIFIC UNIVERSE (with galaxies over here, some bends and wiggles in space over there) with a whole…CORNUCOPIA…of options that contain every single legally valid arrangement of space and matter that is allowed by general relativity.
Now the attentive listener (and don’t feel bad if this wasn’t you; whenever a professor in class would use that line it NEVER referred to me) would notice that I have deliberately said “space” instead of the usual “spacetime”. That’s because this quantum mechanical description of the universe explicitly does NOT include time. It’s just space. Not spacetime. Just space.
That’s because we’re dealing with quantum probabilities. The wave function of an electron ALSO does not include time. We use ANOTHER equation, the Schrodinger equation, to tell us how that wave function evolves and changes and moves around in time. If we replace an electron with a fuzzy blob of probabilities, that fuzzy blob of probabilities doesn’t know on its own about time. It’s the Schrodinger equation that keeps it on track, like a choreographer: it tells the wave function where to go and when and what beat to land.
In quantum mechanics, this is fine. We just assume that time exists as a normal part of the functioning universe, and we know that as time goes on electrons do all sorts of electronic things. So we can just stick time evolution in to make our math work.
But now we’re talking about the universe. The whole, entire universe. There is no “external observer”. There’s nobody there to watch the wave function of the universe evolve. There’s no laboratory, no measurement device, no timers or stopwatches or metronomes.
The Wheeler-DeWitt equations, as they came to be known, do NOT tell us about the evolution of the universe. Instead, they’re more like a box. They say “here are the allowed configurations of space and matter”. They do NOT say how those configurations will evolve, what they’ll do, when they’ll pay back their student loans, any of it.
In fact, these equations are…well, not exactly useless, but also not exactly informative. They tell us what’s allowed. But they don’t even give us a single wave function for the universe. In other words, they don’t even tell us which solution is OUR universe. They tell us what wave functions CAN exist (in the sense of being compatible with general relativity).
The Wheeler-DeWitt equation isn’t even a blueprint for the universe. It’s a machine for MAKING blueprints. But you need to feed this machine information to get it started. For a blueprint for a house, you need to know the lot size, the building materials, the local codes, how many bathrooms you think you need (two on every floor? You got it!). Once you have that information, THEN you can turn the crank on your machine and make a blueprint, a wave function for the universe.
In physics we call this extra information boundary conditions. This is stuff you know or observe or measure, and it’s needed to…get physics going. You need to know the position and velocity of the ball. You need to know how long your guitar string is. You need to know the temperatures and pressures of the star. Once you fill that in, you get to work.
So all we need to do to make use of the Wheeler-DeWitt equation is to add extra information about the beginning of the universe.
Wait.
In Part 2, Hawking takes the swing nobody else dared: he guesses the boundary condition itself.
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