IANAP, but as a mathematician it seems extremely inelegant that there would be a start to the time dimension of the space-time object we live in, when we don't even know if the spatial dimensions are finite themselves.
It is my understanding that the density of the universe billions of years ago was radically different from the one we now observe, and since density is intrinsically tied to our perception of space and time, wouldn't it make more sense that time actually stretches infinitely the further back we go, thus nullifying the concept of a beginning?
I guess I'm having a hard time with the idea that space-time could be discontinuous.
The question is "how long has it been since the big bang." It's an important and relevant question for cosmology and physics. It isn't really a stance on the "beginning of time," which may have started long before this moment, but it is the start of the universe as far as physics is concerned.
How I work it out in my head that time effectively did not exist before the big bang is that; If everyone agrees that time slows as the gravity increases, and we assume at the time of the big bang that all the mass of the universe was in an infinitely small space, the conclusion is we had an infinitely large gravity and time would be effectively be stopped. Take it with a grain of salt.
Exactly. It could even be turtles all the way down, with new building blocks of physics becoming relevant as we go smaller and smaller (and back in time).
I like this. But you still have a Prime Mover problem. If time effectively halts at T0, then what possible event could occur (outside of time?) to nudge that infinitely large glob off mass into the motion we observe today?
T0 includes the prime movement in its definition. If the universe never emerges, change never exists, so it’s not anything (including not T0). Conversely if we know it was T0, it’s because we know things started happening after that.
The universe advanced from T0 because it had to, by definition.
If this seems like a weird cop-out, well, that’s a singularity for you.
The glob of mass starts off in motion at T0, there is no time prior to T0 in which a glob of mass exists waiting to be nudged.
Think of it like a particle decaying - at some point it just happens with no trigger or internal mechanism, and now you suddenly have the decay products wizzing about with some energy and momentum that they just start with.
This is where we see the limits of science. It's a great tool and a lot of benefit came from it. But at some point we encounter things beyond its domain. Us people of faith know that God is the cause of existence. In Islamic Kalam we have a phrase (Wajeb Al-Wujood) - meaning The One who's existence is obligatory/fundamental - i.e. God.
> If time effectively halts at T0, then what possible event could occur (outside of time?) to nudge that infinitely large glob off mass into the motion we observe
today?
Anthropic principle explains it. If you need a Prime Mover, you can also replace it with Anthropic principle and random chance.
For example if time halts at T0, physics breaks. Using limes when t->0 you get that v-> Infinity (or c). Slower time moves for you, faster you move in space. At that point, if nothing is there to detect it, every massless particle will be effectively everywhere, all at once. Essentially photons can have Infinite energy and just cause a random Big Bang. This is CCC like explanation.
Another answer is Hawking's North of North Pole time problem (from Universe in a Nutshell). If time halts a T0, you can't ask what's before it. It's just logical impossibility. Like what is North of North Pole? Answer is: Question is invalid. Anthropic principle implies there are however many multiple such configuration so you get a parallel or sequential universe solution.
We arise and wonder how exactly Universe exists that support life, even if we can clearly see, it's only supporting life at this moment. Our existence is a grain in the sand of a universe-sized sand clock that will be the Black Hole epoch.
No, I am not. I've demonstrated my work, you can prove me wrong using an argument rather than "you're wrong". Universe doesn't have to have a why. And science isn't dealing with such metaphysical questions. That's realm of philosophy.
The principle of sufficient reason states that everything must have a reason or a cause. This is not a principle to lazily toss aside to avoid some more difficult question, it is a foundational idea.
Our understanding of the world (aka science) is largely based on causality, and if things existed without any cause or reason, our understanding of "science" would probably be very different.
(I'm not a physicist, but this is how I understand things.)
I mean... that's a pretty superficial reading of the situation. Where do you stop? If you assume Newtonian time, which extends back to minus infinity... well, what caused time to exist at all?
Also, no one is "lazily tossing it aside". It comes out of the mathematics that describe the observations:
Say you find that all observations you make are perfectly described by dx/dt = 1/x with current time t1. If you follow the trajectories backwards, you find that the trajectory can not be extended back past some initial time t0 at which x(t0) = 0 as the equation becomes singular then. You are now at time t1-t0 from the initial singularity. That is the age of the universe since the big bang. Now the trajectory as it approaches t0 has some unusual properties, it moves infinitely fast, etc... These might lead you to postulate that unknown physics will actually invalidate your law as you approach t0. But there is nothing logically or epistemically _wrong_ with the law you have. The finiteness of time flows out of a causal empirical induction argument. It is not introduced ad hoc to avoid some difficulty, it just is how we find nature to be at the most conservative interpretation of the evidence.
In that case, we are not disposing of any principles (as you originally claimed) when we have an uncaused first cause at t = -13.6 Billion years, instead of having at t = - infinity.
I'm not sure "accepted" is the correct word. It is a feature of our current theory, but we know that theory is incomplete. In particular high density regions such as the very early Universe are where we know ate theories start to break down, as the conflicts between quantum physics and gravity become relevent.
There are proposals for time stretching infinitely back, but we have almost no way of testing them.
If time is stopped then why did it bang. The fundamental character of time is ability to change. If time is stopped then there should be no change. Otherwise time wasn't stopped.
Maybe I guess. Many models stipulate that time began with the Big Bang. Many propose the Big Bang was a local event that obliterated our ability to observe time before it. We have models where the universe rips apart, collapses, or just evolves forever and always has and always will. I think what’s crucial to understand is we have a lot of different possible explanations for what we see, some of them discuss beginnings and ends, some do not. Perhaps as a mathematician with a relatively closed set of possibilities for explanations that’s unsettling. But, I’ve always found the various paradoxes in math to illustrate similar problems in formulating a closed and coherent anything, including the universe.
One thing I have always wondered, since gravity is proportional to the mass of the two objects and inversely proportional to the square of the distance between them, if the universe was smaller with the same mass, wouldn’t gravity have been more “dense” in an earlier universe?
And since we know that gravity affects the rate of flow of time, wouldn’t the rate of time be enormously distorted earlier universe?
I’m not trained in any of this, so hopefully there are greater minds here who can help me understand
> inversely proportional to the square of the distance between them
As I understand it, that’s an approximation for Euclidean space because the area of a sphere is also proportional to the square of the radius in such a space, but it’s not true of non-Euclidean spaces like in GR because the area-radius relation is different.
IIRC, the cosmic microwave background has a gamma factor of about 1100, so the area of that shell is the same as one 1100 times closer or 1/1100^2 times the area as a Euclidean sphere with that radius.
> And since we know that gravity affects the rate of flow of time, wouldn’t the rate of time be enormously distorted earlier universe?
Time did indeed slow down then compared to now, although it’s not entirely obvious to me that this has any physical interpretation when it happens “everywhere”: https://youtu.be/66V4RSmDqYM
My understanding is that time was not slower (whatever that would mean), only that the expansion of the universe means that light is stretched. So events in the early universe appear to happen 5 times slower.
We know that the force carrying particles of all forces have a frequency, just like any other particle. That means that if particles on average move faster than, say, double that frequency, they can't exist.
So there must have been a time when electromagnetism, the weak and even the strong force just didn't exist. They couldn't. So particles would just have totally ignored those forces.
We don't know if gravity is the same, but ... why wouldn't it. Though of course according to relativity gravity just wouldn't care, but that just raises a lot more questions than it answers.
I don't think there's a good answer to this question, at least not when it comes to the nature of particles and light, because we don't have a good answer to what movement and time are. We already know both light and particles are you moving relative to fields. Light is you moving relative to an electromagnetic field. If you move towards a magnetic field you would find it starts "glowing", in fact, that is what light is. But it's not like a magnetic field reacts to you because you start moving.
The issue is that movement and time are fundamental to the universe, yes, in the way relativity describes but also in a totally different unknown way. In some ways particles are "just" things moving relative to one another. Which, for one thing, brings the perspective question (if you accelerated to a "real" speed, would you see a different universe? Because you would disagree with us slowpokes here on earth on what particles exist at least in some cases. But would you see an entirely different universe?)
> It isn't really a stance on the "beginning of time," which may have started long before
Well... yes it is, in the rigorous sense of "time" defined by general relativity. There's no "before" for a singularity. It may not be the whole story, but whatever metaphysical notion defines the "before/beyond/outside/why" that drives the big bang, it's not a place on the "time" axis of spacetime.
Specifically, GR is a model that breaks down at singularities. That time "begins" at the Big Bang is a prediction of GR, but until we have a model of quantum gravity there's no telling whether that's actually true or whether the conditions at the big bang are something GR can't fully describe.
Similar to the singularities in black holes - everything up to a stone's throw of the event horizon is pretty well explained by GR, but as far as the horizon itself or the region beyond are concerned, there might be dragons as far as we know.
> That time "begins" at the Big Bang is a prediction of GR
I don’t think that’s right. If we interpret Big Bang theory as claiming that there is a singularity at a finite distance into the past history of every present event, then GR can’t predict what happened at or prior to that singularity. Whether time “began” then or whether there was “more time on the other side” is a question GR alone cannot answer, not a prediction of GR
Black hole singularities do not start right after their event horizon. The event horizon only demarcates where the black hole singularity becomes an inevitable (inescapable) point in all possible futures.
That's not what I was trying to imply, sorry. It's the singularity at the center where GR entirely breaks down, but there's also weird stuff going on below the event horizon (space becoming time-like and vice versa), that aren't present in, e.g. String Theory's Fuzzballs [1] (which, of course, bring their own set of thorough weirdness). So what I was trying to say was that while GR predicts some behavior below the event horizon, a full model of quantum gravity could predict something entirely different, and not only for the area just around the singularity itself but (maybe) up to the event horizon.
How does that work for black holes? It seems like there would be a 'before' they formed in the time dimension of our universe, if not within the singularity itself.
For blackholes it's the reverse, all paths lead to the singularity, and there is no 'after' as opposed to the big bang where all paths lead away from the singularity and there is no 'before.' If you hit rewind on a video of matter falling into a black hole's singularity, it would look like a big bang where everything was created from nothing at an infinitely dense point and starts flying outwards.
Think of singularities as unidirectional. We don't understand what if anything was before the big bang, there is no return from inside a black hole event horizon, we don't understand what would follow after an AI singularity. That doesn't mean that they don't have a threshold in time/space/spacetime, just that crossing that threshold breaks the rules we know.
Singularities are mathematical constructs and are used to model different kinds of phenomena. Black holes and the big bang are only roughly comparable (but by no means similar) if you are considering a black hole from "inside" of one.
There might literally not be enough time to expand beyond that, given how cosmological horizons work. Being part of the system we're trying to observe puts some nasty limits on what we can know, even in principle.
I agree we practically may never know and fundamentally the rules of the universe might end up making it impossible to know somethings, but as far as I know the ultimate limits are currently unknown so 'We can hope ...'.
There’s an alternative take that says that, as the universe contracts, it eventually hits a point where other effects (quantum, but also possibly unknown effects) predominate and that this kicks off another stage of expansion.
Which is to say that there exist respected papers that outline this scenario in great detail, but there’s precious little observable evidence of a previous universal cycle.
It's unclear what exactly you have in mind, but the equations of GR simply predict that the topology of space-time is not that of R^4, but includes boundaries at finite (temporal) distance, so-called space-like singularities [1]. This is not unusual. For example, the solutions to the ODE dx/dt = -1/x topologically live on the half line.
As a fellow mathematician, I think maybe the right way to think about physics is that the claims are never even supposed to be “true” in some absolute mathematical sense. It’s more like true to some first approximation.
So maybe we can interpret this claim as saying that 25 billion years ago, the universe was kinda similar to what we have now, but 27 billion years ago everything was ultra compressed and gravity didn’t have a significant effect on anything. Or maybe time is like a left-open interval. Finite, but didn’t have a start. I dunno, I’m making stuff up.
Left open interval is the right way to view it. There is no contradiction or paradox here. Merely unfamiliarity. But maybe you should not expect the rules of the early universe to be very familiar...
Physics is only true modulo theory. It’s intense intellectual arrogance to say “because this model predicts some phenomena the world must conform to this model.” Newton, who I think it’s fair to say was not known for his humility, refused to feign hypotheses and satisfied himself with describing his observations.
However in today’s day and age that way lie no fat grants, adulating television specials, or NYT bestsellers.
It is my understanding that the density of the universe billions of years ago was radically different from the one we now observe
It’s even more puzzling than that. Our current model features a period of time called the inflationary epoch which lasted between 10^-36 and 10^-33 or so seconds after the Big Bang, in which the universe expanded by a factor of at least 10^26 along each linear direction [1].
This is unfathomably rapid expansion. It makes sense mathematically but not at all intuitively. It’s totally bizarre and weird and I don’t have even close to the level of background needed to challenge it!
> There's a 'most northern' point on the earth, and the surface is arguably continuous.
This was Hawking's point of view. One way of thinking about special relativity is that time is at right-angles to space, and everything travels at the same 'proper' speed (c) through this 4d spacetime, just in different directions (hence why "fast" objects experience "time dilation": their 4d heading is pointed largely in a space direction, so they don't progress much in the time direction). This extends to general relativity, which describes how these directions "bend" into each other. For example, the reason objects fall due to gravity can be described as spacetime curving such that "future" points slightly "downwards" (and hence slightly less in the usual time direction; which, again, causes time dilation).
AFAIK Hawking's idea was that the curvature at the big bang was so high, that "past" is pointing completely in a spatial direction; and hence there's no such thing as "earlier" anymore. Similar to how "north" near the north pole is at right-angles to "north" at the equator.
This isn't really what "start" is usually intended to mean. They're just identifying the time of the Big Bang, beyond which any possible causal connection is lost and we can't possibly look back further. More time, more space, more something else may have existed and been causally prior, but we can't meaningfully talk about it except speculatively. It isn't part of our spacetime.
Of course, people do speculate. I seem to recall some level of anisotropy in the cosmic microwave background that was a bit more than expected purely from quantum vacuum fluctuations in the pre-inflationary early universe and at least one physicist musing that it might be a perturbation from some other universe that has since lost causal connection. This, of course, makes no testable predictions, can't be falsified, isn't really science, but human intellectual curiosity goes beyond science.
I think that by definition if the universe was at one point a singularity then there is a start to time and space.
This idea goes all the way back to Plato and his Parmenidean-inspired rejection of the Pythagorean notion of the Monad as being at the centre of the universe as the Number One implies certain properties like perfection, unity, etc., and we see none of those properties in our existence. This led Plato to argue that the One existed separately from our reality, which was just an imperfect copy associated with the idea of an indefinite Dyad.
So it wasn't just that the universe was a densely packed packed ball of all the stuff we see today and it somehow spilled out or burst forward, what existed before was a monad, and all the stuff we see including space-time, the elements, and more were created at the time of the Big Bang.
> wouldn't it make more sense that time actually stretches infinitely the further back we go, thus nullifying the concept of a beginning?
I believe it could be 'turtles all the way down' as the phrase goes. Maybe our Universe started by a collision of two or more other Universes and we got this mess called the Big Bang. This doesn't explain how those other Universes started though.
But then as mere humans, we can't conceptually grasp Infinity itself. This is not some failing of ours, it's actually convenient to not imagine infinity, as it would drive us mad. The minute you include the Infinity Symbol (∞) in a math equation, all logic starts to cease and get very wobbly.
> Maybe our Universe started by a collision of two or more other Universes and we got this mess called the Big Bang.
Once upon a time I watched PBS Nova program about string theory. I remember they talked about something along these lines. It's been almost two decades since I saw it so memory is rusty. But it was something along the lines of universes existing in these big "planes" (they visualized them like these big floating membranes) that would vibrate and occasionally smack into each other. When one of these collisions would occur, there was the potential for a new plane to be formed from that collision.
Like you said, that could potentially explain where new universes come from, but not how the other "turtles" got there in the first place.
There’s a theory that the birth of our universe looks eerily similar to what might happen inside a black hole when it’s first formed. Fun to think about.
I propose the universe exists in itself. That the interstellar space - is the same as subatomic space. Its both at the same time, like a möbius strip. Space between stars is space between atoms, etc.
This is my favorite hypothesis, even though/especially because it makes your mind spin. I could be wrong but I think Roger Penrose has some thoughts along these lines. I may be butchering this and/or injecting my own (admittedly ignorant) pontification into it, but:
The universe will keep expanding until entropy reaches a maximum -- the "Big Freeze." Once maximum entropy is reached -- wherein all atoms in the universe are totally dispersed, everything is the same distance from everything else, and the universe is a totally uniform field -- one could say that is very orderly indeed, i.e. the theoretical minimum entropy.
I imagine that all of the matter in the universe being perfectly dispersed would quite neatly "fill" the universe. So who's to say such a situation isn't infinitely dense?
Other than theoretically, the spatial dimensions can only ever be observed to be c * T where T is the total age of the universe. Thus, space is bounded as well. It all comes down to what it means to be bounded.
If something preceded the big bang, it cannot be observed (by our current reckoning). Similar to things farther than cT away... Unobservable; unknowable.
There's nothing inelegant about it. C is the conversion factor between space and time.
My understanding is that in models where time began at the Big Bang space typically also began concurrently. Before this time (harhar) there was nothing, but that’s meaningless because time also didn’t exist. It’s immeasurable before a certain point. Likewise space began at that time and expanded to fill all space rapidly, which I’m often a little unclear here, but my understanding is in a similar way to how space expands today outside of galaxies by space simply expanding from within itself (I.e., without force or movement). This conceptualization might help quiet that discontinuity discomfort.
I’ll search for it but PBS Space time has some wonderful intuition building visualizations and explanations in some of their parts on models for the beginning of the universe. If I can find the ones I’m thinking of I’ll edit later, but regardless I find their background material on “wtf” re: physics can be helpful.
AFAIK (pardon my limited knowledge of physical and math terms) the spacetime interval is the conserved unit and it has a lower bound in the Plank-scale limit.
In the paragraph above, you assume time is a primitive concept, but it is really an emergent phenomenon. The passing of time, moving by some amount of (the plank-scale limit of) spacetime interval, can happen only across connected configurations.
Think about evolution in spacetime as a combinatorial game, there can be positions where causal links are not possible, or even empty games.
FWIW I don’t think it’s certain yet that time cannot be divided smaller than the plank limit. I remember reading an article some years ago about an experiment indicating that there seems to be no smallest “slice” of time. Unfortunately I can’t find it and my patience for searching google these days is pretty low.
As a mathematician, I don't think about Big Bang as the "start of time" (or any other dimension), but simply as "fixed point" (of the "physical evolution of all particles in the universe" function).
It's not a fixed point of the equations, though. That is technically incorrect and also not the right intuition. It's the exact opposite. It's a point at which the acceleration of (the density of) all particles diverges, and thus the equations can not be continued past that point.
There’s a start to the space dimension as well. Imagine a ball 10cm in diameter, it’s possible to imagine a ball that is 9cm smaller than it but not a ball 11cm smaller.
While I agree with you on this "hack", I also believe that if we accept that geodesic incompleteness idea is right then time for all intense and purposes has a start. At least as observers within the bubble of space-time that is causally connected.
If time/space-time existed before the BigBang is probably an unanswerable question (unless we are within a 4d black hole and we can listen to waves that perturbed the matter before the formation of our universe).
> If time/space-time existed before the BigBang is probably an unanswerable question
Why? Any sign of another Big Bang going from some other point somewhere else would indicate that "our" Big Bang might not have been the first one. It is harder to prove absence though.
Because if inflation is also correct we lost every causal connection with whatever was there before, or is so diluted that we might not be able to detect.
Another possibility could be that at the time of the BigBang the energy density was so high that everything was unified, and so when forces actually separated they "tabula rasa" anything that occupied the bubble of space-time we expanded into.
However, it could also be that the fluctuations we see in the CMB are due to perturbations of what happened before. But that possible clue is better explained by comic inflation expanding quantum fluctuations at an incredible speed that disconnected them.
That's why I said it's (probably) unanswerable. I also hope I am wrong though.
It could be that our ideas about infinite and continuous values, so-called real numbers, are nothing more than a good model/abstraction up to some point.
One way to consider it would be taking the limit of 'space' as time approaches negative infinity from a zero point of today. That's kind of silly considering they are coupled, but for practical purposes it is the effective point of 'the big bang'.
Why not? Tons of things are, for example, entropy. I have a crackpot idea that the Big Bang itself was just an "entropy population inversion." The big bang is literally just the moment where the discontinuity occurs.
Another idea: at the end of times, when black holes finish merging into one giant black hole, will it force a big bang like event? If we assume the universe to be a large 3d sphere, what's the topology of space in it if it's just one giant black hole?
Why would all black holes eventually merge? The mass in our observable universe is constantly decreasing, with more and more of it going forever beyond our reach. For any two distant black holes it seems more likely that they will eventually find themselves forever alone in 'their' universe than that they will merge.
Similarly, I find the idea of the end of time to be weirdly unreal and impossible. It feels like time is not a thing that has a beginning or an end, and that it would just stretch and dissipate infinitely into the future.
You can still imagine that as an end, and define an end based on that infinite stretch. At some point, you can't tell the difference between before and after more stretching, and you'll never be able to stretch in a way that can be noticed.
There's no more events to happen, and more so, no ability for more events to happen.
Thats still likely an artifact of our models though, and that when you do to something like that, that new events start happening again
I'm not sure if Penrose suggests that time stops once there are only photons left. He says it is equivalent to the situation at the Big Bang and time certainly didn't stop there. In fact, in his conformal cyclical cosmology spacetime goes on indefinitely but just reboots regularily.
As I understand it, 'the beginning' is when 'the universe' had a 'once-in-a-gazillion' moment where the probabilistically unlikely event of entropy shrinking to a very small value happened ( aka 'the beginning' ) and from whence entropy started to increase again as it is wont to do.
It all goes back to thermodynamics and the probabilistic understanding that entropy 'always' increases. But if entropy always increases then by reason, it must have started off at small minuscule point sometime in the past. But if energy/mass are constant, how could it have gotten to the low entropy in the first place? Given enough time, a 'once-in-a-gazillion' event actually happened. At a fundamental level, it's all mathematical guesswork.
It is my understanding that the density of the universe billions of years ago was radically different from the one we now observe, and since density is intrinsically tied to our perception of space and time, wouldn't it make more sense that time actually stretches infinitely the further back we go, thus nullifying the concept of a beginning?
I guess I'm having a hard time with the idea that space-time could be discontinuous.