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May 4[edit]

Second law of thermodynamics[edit]

Why the law doesn't mention an open system which is much more likely to grow entropy than a closed system due to its exchange with the environment? The entropy in an uncovered mug of hot tea, for example, increases much faster than in a vacuum flask-like closed systems. Similarly, a stack of books on a shelf is more likely to become a mess than books in a locked safe. Thanks.--212.180.235.46 (talk) 11:57, 4 May 2017 (UTC)[reply]

I think there's possibly some confusion about what entropy means here. The entropy of the tea can decrease as it cools, as the molecules slow down and become more ordered (especially if it's somewhere cold enough that it freezes). It's only when you look at the bigger picture that you see a total entropy increase: the heat from the tea increases the entropy of the air around it, until eventually the air and the tea are the same temperature. Similarly, the entropy of the books can decrease if there is a librarian looking after them - but that librarian increases the total entropy of the universe by constantly pumping out body heat. It doesn't usually make sense to look at the entropy of open systems, for this reason - otherwise you end up with nonsense like creationists claiming evolution (and, if you follow their arguments to their conclusion, life itself) violates the law of thermodynamics. Smurrayinchester 12:23, 4 May 2017 (UTC)[reply]

I still have a concern. If entropy is viewed as a measure of order, the entropy of a mug of tea increases, as more molecules turn from liquid to vapor and the volume of tea decreases due to evaporation. The tea thus gradually becomes more disorganized and disparate than initially, while in a thermoflask it's able to conserve the initial temperature and volume, its initial order. Similarly, decomposition increases entropy in organic matter. Without a librarian, books, like other stuff, tend to become disorganized, i.e. have increasing entropy, unless put in a closed system, like safe. From that view an entropy in a open system is more likely to increase, than in a closed system. 212.180.235.46 (talk) 13:16, 4 May 2017 (UTC)[reply]

From Second law of thermodynamics: "The second law of thermodynamics states that the total entropy of an isolated system can only increase over time." The total entropy of an open system can increase or decrease over time. In inexact sense that you are using the term, the entropy in an uncovered mug of hot tea increases, but the entropy in an uncovered mug of hot tea in a microwave oven decreases. --Guy Macon (talk) 14:31, 4 May 2017 (UTC)[reply]

the entropy of a mug of tea increases, as more molecules turn from liquid to vapor - that is only if you count the water vapor molecules as still being part of the "mug". To get technical, if you do so, you have a closed system, but that is even not enough because the second law applies only to isolated systems. Tigraan^{Click here to contact me} 08:42, 5 May 2017 (UTC)[reply]

What do you get when divide time by distance?[edit]

What unit do you get when divide time by distance? — Preceding unsigned comment added by Clipname (talk • contribs) 17:40, 4 May 2017 (UTC)[reply]

Inverse speed. --Jayron 32 17:44, 4 May 2017 (UTC)[reply]

I'm not sure inverse speed is an expression that's used. Isn't there a more appropriate name?--Clipname (talk) 17:54, 4 May 2017 (UTC)[reply]

Rate of movement? But it's also a red link.--Hofhof (talk) 18:00, 4 May 2017 (UTC)[reply]

Pace (speed).--Wikimedes (talk) 18:22, 4 May 2017 (UTC)[reply]

This article [1] indicates that inverse speed is a measure of slowness. DrChrissy ^(talk) 18:25, 4 May 2017 (UTC)[reply]

See also previous discussion here. Mikenorton (talk) 08:28, 5 May 2017 (UTC)[reply]

Which I think boils down to the fact that there is no standard word, in general use, for the reciprocal of speed.

"Pace" is unconvincing. It's true that runners will talk about, say, keeping a "six-minute pace", meaning six minutes per mile, but I don't think you can abstract that into "pace" as a general word for "reciprocal speed"; it's specific to certain sports, and grammatically restricted even in that context (for example, you wouldn't say that the slower runner has a higher pace). --Trovatore (talk) 08:43, 5 May 2017 (UTC)[reply]

Freeway traffic. μηδείς (talk) 22:17, 6 May 2017 (UTC)[reply]

How much force to increase pressure?[edit]

A soccer ball, which is 22 cm (8.65 inches) in diameter, has a pressure of 0.6 bar, and this can be increased to 0.8. How much force does this require?--Hofhof (talk) 18:27, 4 May 2017 (UTC)[reply]

4/3 * 3.14* 11^2 = 506 cm^2 surface area. 1 bar = 100,000 pascals = 100,000 N/m^2 = 10 N/cm^2 because 10,000 cm^2 = 1 m^2. Each square centimeter would thus need an extra 2 N of pressure to increase the pressure by that amount, for a total force of about 1012 N. --Jayron 32 18:43, 4 May 2017 (UTC)[reply]

(ec) A static fluid has the same pressure everywhere (ignoring gravity), so 0.8*10^5Pa*(cross sectional area of the piston used to push the air into the ball in meters) will give the force in Newtons.--Wikimedes (talk) 18:50, 4 May 2017 (UTC)[reply]

Ah, see there's the rub. The OP did not specify pressure on what. I assumed the pressure on the skin of the ball; while you're assuming the pressure on the pump used to add the air to the ball. Those would give two different answers... --Jayron 32 18:58, 4 May 2017 (UTC)[reply]

If you are looking for the force of the kick that momentarily raises the pressure in the ball, Wikimedes' equation applies but use the area of foot in contact with the ball (plus a little to flex the leather), if you can measure it. (Slow motion camera? Boot covered in chalk?) Blooteuth (talk) 19:07, 4 May 2017 (UTC)[reply]

Can we assume that the pressure of the ball will increase due to a kick? At least would it increase by 0.2 bar? 1012 N are a lot. Hofhof (talk) 19:13, 4 May 2017 (UTC)[reply]

You would need a MORE force to increase the internal pressure by that much with a kick; as the area goes down the force would need to go up to result in the same amount pressure change; for example, the shoe's I'm wearing now are roughly 9 cm across at the toe and and 3 cm tall. That means the pressure would be reduced to an area of about 27 cm^2. 506/27 = about 18.7, so you'd need to exert about 18.7* 1012 = 19,000ish newtons of force to result in the same pressure change in that ball. --Jayron 32 19:37, 4 May 2017 (UTC)[reply]

Does Heading a Soccer Ball Cause Brain Damage? "individuals with hits as low as 50 to 60 g’s [have] had concussions.". Blooteuth (talk) 21:17, 4 May 2017 (UTC)[reply]

I'd say no force, or at least, an arbitrarily small amount. A very small piston needs very little force to push in more air. And as for the ball --- adding up the "force" all over the ball is not a meaningful calculation. The only way you add force is as vector algebra, which is to say, you add them all up to zero because there is no net force from the pressure. The ball is of course under tension, but here's the rub: if you are playing tug-of-war, the "total force" on the rope does not increase as the rope gets longer because you add up all the separate inches of rope each of which is exerting that much force! No, however long or short the rope (ignoring friction, weight etc.) the force is the same. In other words, force and pressure are related, but they should be used carefully: you have to specify where the force is measured. And if you're just assuming you mean the force per square inch of ball, well, that's how you actually define pressure. Wnt (talk) 22:04, 5 May 2017 (UTC)[reply]

What has five leaves?[edit]

At one time, my lawn had lots of clover, which I understand is healthy. Part of my property still has it, but now my front yard is filled with these plants with five leaves. I have Virginia creeper in other parts of my yard, but not where there is grass. I'm wondering if this is good for the grass like clover is. No, I can't provide a photo. My neighbor who lets me borrow a cell phone at Christmas takes the longest time getting me my Christmas tree photos, and that's if someone is home to let me borrow the phone.— Vchimpanzee • talk • contributions • 21:11, 4 May 2017 (UTC)[reply]

Clover leaves are trifoliate (rarely quatrefoiled, cinquefoil, or septfoil). Do you see this in your yard? Blooteuth (talk) 21:24, 4 May 2017 (UTC)[reply]

That is what I used to have, and still do in other parts of the property.— Vchimpanzee • talk • contributions • 21:34, 4 May 2017 (UTC)[reply]

The cinquefoils (Potentilla spp) are pretty common ground cover plants - but with over 300 species it is difficult to say which one you might have without a much more detailed description, and an indication of where you are. Wymspen (talk) 22:21, 4 May 2017 (UTC)[reply]

You could in principle harvest a few and examine them and give us a botanical description in terms of plant morphology. E.g. are the leaf margins complete? Is it rhizome? How tall is it? Are there any hairs or trichomes? etc. Look at plant identification -- if you can get a good description, we may be able to ID without a photo, or you could use a dichotomous key. SemanticMantis (talk) 14:15, 5 May 2017 (UTC)[reply]

There is a photo with Potentilla that looks very much like it. The photo has a yellow flower, but I haven't seen any. Ironically, the Wlink with the photo I refer to is to a species which has a photo in its infobox like the one in the infobox of the Potentilla article. But the infobox photos do not look like the plant I have. — Vchimpanzee • talk • contributions • 15:16, 5 May 2017 (UTC)[reply]

Is dark energy ever considered to be "walls of the cosmos"? A few questions, mostly theoretical[edit]

Sorry if something here seems a bit strange or funny, I am not a physicist but I do wonder what people with BA or more in physics might think about this:

Might it be that the cosmos is a closed place, a giant box in which each of the 4 walls acts as a gravity field that initiates what we now call "dark energy" and if it is, might it necess a big crunch?

I would assume such walls won't necess a big crunch as they will just pull everything towards them forever, unless their gravity fields will and then everything would just stay stick to them in place, unless it will be moved somehow far into the center somehow (not necessarily to a singular point).

Did any physicist ever suggested such a "wall" hypothesis? Do you think it is something plausible or maybe today we have some findings that indicate otherwise? Ben-Yeudith (talk) 23:45, 4 May 2017 (UTC)[reply]

I don't know about the specifics, but I suggest you read Shape of the universe and get a sense of what the theories are. By the way, an actual box would have 6 walls, not 4, unless it's a box shaped like a tetrahedron. However, the article suggests the better concept is a sphere. ←Baseball Bugs ^{What's up, Doc?} carrots→ 00:29, 5 May 2017 (UTC)[reply]

If I'm understanding your hypothesis correctly, we would expect to see everything in the universe pulled towards these "edges". We don't see this. Instead, matter in the universe is distributed pretty much evenly. (The fancy science words for this are "homogeneous and isotropic".) This was a big piece of evidence for the Big Bang, and has been confirmed quite strongly by measurements of the cosmic background radiation. If I understand it correctly, dark energy appears to be some kind of field pervading the universe that has a repulsive gravitational effect. However it's quite weak in absolute terms. We only see its effects by looking at the distances between galaxies, which appear to be increasing over time. Within galaxies and galaxy clusters themselves, dark energy is overpowered by the gravitational attraction of the matter within them, so things within galaxies themselves are not moving apart. (Don't take this the wrong way. It's great that you're thinking about this! In science there's no shame in proposing something that's found to not fit with the evidence. If you're interested in the topic, I highly recommend PBS Space Time for quite accessible videos about astrophysics.) --47.138.161.183 (talk) 00:58, 5 May 2017 (UTC)[reply]

(edit conflict) A sphere, but not a sphere as we know it. One of the principles of cosmology is that nowhere appears to be the center. If the universe were a bounded 3-dimensional shape, with sides and possibly edges as we would recognize them, it would also have a physically meaningful center. But observation has not found any evidence for anisotropy that would suggest such a shape. In theory the scale of the universe could simply be so large that we can't tell, the sides being far beyond the edge of the observable universe, but then you have serious theoretical issues as general relativity doesn't handle an edge of space very well. A comparison is often made to an ant stuck crawling on the surface of a balloon (see perhaps Four-dimensional_space#Dimensional_analogy). Only the surface is the ant's universe. The inside and outside are beyond the ballooniverse. Pretend our ant is unaware of such things. It can move forward/back, and left/right forever, but it will never leave the balloon. There is no edge, but the balloon is also entirely edge. There is a center, but that center is not contained within the ballooniverse, and all positions on our perfectly spherical balloon are equidistant from that center, and thus are all equivalent. This is not to say that our own universe is a sphere or a balloon, but that because our universe requires more than 3 dimensions to describe, ordinary ways of thinking about shapes do not suffice, just as a 2 dimensional ant would have trouble imagining an inflated balloon. Someguy1221 (talk) 01:00, 5 May 2017 (UTC)[reply]

Broken record here — the balloon-one-dimension-up is a good picture for a closed (that is, finite-volume) universe. It is an open question whether the universe is "closed" or "open" (infinite volume). If it is open, then the balloon is not a good picture. --Trovatore (talk) 01:07, 5 May 2017 (UTC)[reply]

Infinite universe is a meaningless statement. It's the self-contradictory assertion that however big the universe actually is, it's even bigger than that. Unimaginably big? Yeah. Having no actual size in relation to its constituents? No. μηδείς (talk) 00:25, 6 May 2017 (UTC)[reply]

Medeis, I thought I had managed to explain at least what I meant on this; even if you don't buy it, I would really like to get to the point that you at least follow what I mean. I most specifically do not mean, by "infinite universe", that however big it is, it's even bigger than that.

What I mean is that, once units are fixed, the size of the universe is bigger than any natural number of those units. That does not make it bigger than it is; it just means that the size is larger than any natural number.

The natural numbers are the smallest set containing zero and closed under the operation of adding one. So to say that the universe is infinite, say, in linear dimension (I was talking about volume but I can discuss linear dimension more succinctly), means the following: Given any two points, no matter how far they are apart, there are two points that are at least one mile farther apart than that. So there are points 0 miles apart (just take the same point), there are points at least one mile apart, at least two miles apart, and so on; there are points at least N miles apart for every natural number N.

As I say, you don't have to think this is a useful or correct characterization, but can I at least get you to confirm that you follow what I mean, and why it's different from "bigger than it is"? --Trovatore (talk) 00:41, 6 May 2017 (UTC)[reply]

Question: if the universe is of infinite size, is that countable infinity or uncountable infinity? I looked this up really quick and found some blather from Cambridge which AFAICT doesn't actually address the question, though it seems to mention it... maybe someone can think of a better way to search this.

The argument for uncountable infinity is that position is not quantized and it is a continuum like real numbers (even within a line segment of finite length, there are infinitely many real numbers!). But I am suspicious about quantization when it comes to the whole universe. I mean, there is an integral number of Planck's constants of angular momentum per 2pi radians of angle, marking out a uniform set of complex phases of the Schroedinger solutions; there don't have to be an integral number of Planck's constants (forming linear momentum) per meter of distance, because a meter is nothing fundamental. And that non-quantized number means light can have an arbitrary wavelength. But if the universe has a size to go "all the way around", then do there have to be an integral number of Planck's constants of momentum per the distance all the way around? Even if that distance is infinite, that would mean that that infinite distance is a countable infinity rather than an uncountable infinity... I think. What do I know! Wnt (talk) 01:46, 6 May 2017 (UTC)[reply]

User:Wnt: I'm afraid that's a bit of a non-sequitur. "Countable" and "uncountable" are properties of cardinalities, whereas the size of the universe is more like a measure. Usually the measure of a set of infinite measure is just called ∞, not any of the aleph numbers.

One way of addressing the question would be to observe that if (as it would intuitively appear to most people before they come across balloon analogies and such) the universe is homeomorphic to R³, that is Euclidean 3-space, then you can't embed any uncountable ordinal into it in an order-preserving way. So if you like you can say that makes it a "countable infinity". To put it another way, R has uncountable cardinality, but countable cofinality. --Trovatore (talk) 03:59, 6 May 2017 (UTC)[reply]

@Trovatore: You clearly have a far better understanding of the mathematics here. If I understand correctly, you're distinguishing the measure of space from the number of points in it - the number of points might be uncountable, but the distance could only be a countable infinity. I don't understand the bit about R^3 though, since Euclidean space is based on the real line which is the classic example of an uncountable infinity. So this is like the case with a line segment (which actually has a finite measure) but here the measure might be infinite but countable.

Now what I'm not so sure about with this is whether the observable universe must have a size greater than any nonzero rational number relative to the total universe, in order to make the total measure applicable (I think). This was why I started invoking Planck's constant, I think, because I think this argument implies some kind of minimum size for a piece of space relative to that perhaps infinite natural number measure, perhaps infinitely small but nonetheless countably so. Wnt (talk) 11:52, 6 May 2017 (UTC)[reply]

@Wnt: We're talking about two different ends of the problem. I'm talking about the universe "in the large" here, and when I say that one of the possibilities is that it looks like R³, well, I mean it might look like it in the large. Whether space itself is infinitely divisible is a separate "in the small" question, which I don't see much hope will ever be answered (unless someone actually discovers quantization of space)

If spacetime really looks like the real numbers "in the small", then not only are there uncountably many points in the universe; there are uncountably many points in your left pinkie toenail. But that would be true whether the universe is finite or infinite, in the "large" sense under discussion. --Trovatore (talk) 18:52, 6 May 2017 (UTC)[reply]

The notion of the universe being infinite, and hence containing an infinite amount of matter, makes no logical sense. What might make sense is the notion of "finite but unbounded" - as with the balloon analogy: If you could travel at limitless speed, you could start at a point, go in what you think is a straight line, and eventually get back to where you started. ←Baseball Bugs ^{What's up, Doc?} carrots→ 03:36, 6 May 2017 (UTC)[reply]

No, you're quite wrong, Bugs. It makes logical sense just fine. If you think otherwise, the burden is on you to find a logical problem with it that somehow no one else has managed to find. --Trovatore (talk) 03:51, 6 May 2017 (UTC)[reply]

If there's an infinite amount of mass-energy in the universe, then the law of Conservation of energy becomes irrelevant. ←Baseball Bugs ^{What's up, Doc?} carrots→ 04:58, 6 May 2017 (UTC)[reply]

The global conservation law, sure. But the global law is pretty much irrelevant anyway, as it has very limited predictive power. All it says is that the total mass-energy remains constant. That predicts almost nothing, because mass that suddenly appears in one place might have equally suddenly disappeared somewhere else (for the moment ignoring relativity of simultaneity).

The useful form of conservation of energy/momentum/what-have-you is the local form, which says that the mass-energy in a given region changes by exactly what moves in or out through the boundary of that region. See Conservation law#Global and local conservation laws. And the local conservation laws are still meaningful in an infinite universe. --Trovatore (talk) 05:17, 6 May 2017 (UTC)[reply]

The core problem is that infinity is not a number. So how can it be a quantity? ←Baseball Bugs ^{What's up, Doc?} carrots→ 05:32, 6 May 2017 (UTC)[reply]

"Infinity is not a number", by itself, is a meaningless cliché. It's used by schoolteachers to short-circuit certain types of unproductive discussion in the classroom, and one must have some sympathy for the teacher in these cases. But it doesn't really mean anything; neither "infinity" nor "number" is well enough specified to make it meaningful. There are in fact objects that are called "numbers" in some contexts that are also called "infinity" in some contexts.

You are the one who made an active claim here, that the idea of a universe with infinite total mass "makes no logical sense". Defend it! Where is the logical contradiction? Why does the contradiction not also refute most of standard mathematics? --Trovatore (talk) 05:44, 6 May 2017 (UTC)[reply]

Trovatore, the burden of proof lies upon the infinite camp. Part of the reason this issue confuses most people is that they think in terms of Newtonian Space (or absolute time) which are intuitive on our scale, while relative time and curved or self-bounded space are not. We have only had the math for the latter since just before Einstein, historically speaking. Humans can't perceive four dimensional space (although I have heard you can, if you spend weeks using VR tutorials google and pubmed).

Finite, self-bounded space is a coherent, widely understood concept able to be explained with real life examples, not just assertion of abstract mathematical constructs--marks on paper--not physically demonstrable. A circle can be rounded an infinite number of times, although it is finite in size, just not bounded by an endpoint. The same applies to a sphere, and to a hypersphere--science does not deny this. But "what is before time" and "what is outside space" are questions that contradict themselves.

If you ask, how many protons are there, and the answer happens to be a trillion (as a simple example), then an infinite universe implies there are İactually a trillion and one, then a trillion and two, and no actual number when you get down to it. Given spacetime exists in relation to mass-energy, it is absurd to take the alternative, that there is infinite space beyond actually physical spacetime--it's just falling back into the flat-earth, Newtonian Space mistake of our forebears. Either one gets this, or one doesn't so, I will not comment here further. μηδείς (talk) 22:14, 6 May 2017 (UTC)[reply]

It is "absurd" to you, but you seem unwilling or unable to articulate what exactly is absurd about it. There is certainly no logical contradiction; if there were, then you could use it to refute much of modern mathematics and win yourself a Fields Medal or Abel Prize.

If physical space is infinite (and homogeneous), then yes, there are infinitely many protons, and so for any natural number N, there are more than N protons, more than N+1, and so on. Why this should be a problem, you haven't said. It is a problem if you assume ahead of time that the number of protons must be a natural number, but you have not justified this assumption, or as far as I can tell, even attempted to justify it.

The only thing you have said that looks like an attempt to justify it is the claim that, if the universe is infinite, then however big it is, it is even bigger than that. But this is not so. The universe is exactly the size that it is, whether that size is finite or infinite, and has exactly the number of protons that it has, whether that number is finite or infinite.

Here is where the confusion might be: If there are infinitely many protons, then adding one proton doesn't change the number of protons. ℵ₀+1=ℵ₀. But that doesn't imply that the number of protons is bigger than it is, only that adding one doesn't change the number. This is a little hard to get used to, because it's contrary to our experience with finite numbers. But there is no actual logical problem with it, just unfamiliarity. See also Hilbert Hotel; no contradiction, just takes getting used to. --Trovatore (talk) 22:37, 6 May 2017 (UTC)[reply]

Oh, I re-read your comments, and I think I misunderstood the paragraph starting with "absurd". You're saying it's absurd to think that there are finitely many protons, matter finishes somewhere, and then space keeps going on infinitely beyond that. Well, but that's not the possibility under discussion. I'm taking it for granted (it may not be true, but it's the simplest assumption) that space is by-and-large homogeneous. So if the universe is infinite, then presumably it all has matter in it, and so yes, there are infinitely many protons. --Trovatore (talk) 22:45, 6 May 2017 (UTC)[reply]

I read what you just wrote. I came back just to make the clarification I omitted when called for the Kentucky Derby that a finite, unbounded universe is a testable physical hypothesis, while claiming the we can't measure the universe even in theory because it has no size in relation to its parts is an untestable, epistemological and metaphysical position. I do make the claim that the universe is homogenous based on the evidence of the CMBR. μηδείς (talk) 23:18, 6 May 2017 (UTC)[reply]

As I understand it, your position is that the universe must wrap around to where it started somewhere, but you have no idea where, or at least you haven't said. That the number of protons in the universe must be some natural number, but you're not committing yourself on which one. I don't see how that's any less metaphysical or more testable than saying that it doesn't wrap around at all, and that the number of protons is not a natural number. --Trovatore (talk) 23:29, 6 May 2017 (UTC)[reply]

Just because something is infinite does not make it unprovable. There are phenomenons like Scale invariance all around us, proving the exact opposite (atleast mathematically without any doubt). --Kharon (talk) 04:55, 7 May 2017 (UTC)[reply]

The question of what can be experimentally tested is an interesting one, and a little bit subtle. Neither the proposition that the universe is spatially finite, nor that it is spatially infinite, can be directly tested. Oh, if you could get into a spaceship and head out one direction, go all the way around, and come back from the other direction, that would prove that the universe is finite, at least in that direction. But no one proposes that you could really do that; the metric expansion of space would prevent it, even if you have a spaceship capable of arbitrarily close to lightspeed.

However, that doesn't mean that all is hopeless; we can have indirect evidence for one model or the other. Specifically, if the universe is homogeneous, and positively curved, then it must loop back on itself. If it is negatively curved, or has asymptotic zero curvature, then the simplest models are infinite, though there are (in my view rather contrived) possibilities for finite universes even in that case.

So what do the observations say? The curvature is — zero, within experimental error. So both positive and negative are still viable possibilities. It is still possible that at some future time we will manage to narrow down the error bars to say the curvature is on one side or the other of zero; either positive, in which case there will be strong reason to believe the universe is finite, or negative, in which case there will be a good case that "infinite" is the natural default assumption. --Trovatore (talk) 06:04, 7 May 2017 (UTC)[reply]

I found this at Stack Exchange, written by a self-identified graduate student in Toronto, which I have excerpted:

If we take the definition of the Big Bang as coming before inflation, then we are probably referring to a curvature singularity. During this time, our best theories vary by a great deal in what we would expect to find. Many of them theorize the existence of one or more massive inflaton [sic] fields that eventually drive inflation. ... However, this is all besides the point, at a curvature singularity, the energy scales would be well above the range of most of our theories. Standard general relativity is not expected to accurately describe the universe at a point like that; we need a GUT and quantum gravity to accurately describe the physics of an initial curvature singularity. Short answer: No, the mass is not infinitely high. It is finite with a non-zero probability of being zero.

This brings us to the end, for which I have saved the simplest (if not the most accurate) answer to your question. Your premise that the density is infinitely high is based on the following logic:

1) The universe has a mass M now and a large volume, therefore a low density

2) At the time of the Big Bang, the universe was a singularity with zero volume

3) Therefore, the density is ρ=M/V, V=0, so ρ=M/0→∞

4) If the density is infinite, mustn't the mass be infinite as well?

Do you see the problem with point (4)? You used M and V to solve for the density, then you are using that to solve again for M. Logically, you can only retrieve the value you initially used. In other words, it's the same as the mass of the universe now (according to your reasoning): ρ=M/V=Mnow/0→∞ but M=ρV=(∞)(0)=Mnow

We can see in the first assumption of a finite mass, the models work out well enough, but in the assumption of infinite mass we get divisions by zero and Mass_now being a constant which is the product of (∞)(0). This is the manipulations of symbols without their corresponding to anything actual. See https://physics.stackexchange.com/questions/153595/the-mass-of-universe-at-the-point-of-the-big-bang 23:26, 7 May 2017 (UTC)

Medeis, this piece is addressing a different question from the one under consideration. The question on StackExchange was, if the density at the point of the BB is infinite, does it follow that the mass is also infinite? And the answer, which is quite correct, is no, that does not follow.

Here's the important piece, which you may have skipped over:

Now, there is one important thing left to consider. What do I mean when I say "the universe"? The possibility of the universe being infinite in extent means that the total mass of the entire universe is possibly infinite. So to clarify, when I refer to "the universe" I mean the observable universe. (emphasis mine)

So the responder is not in fact talking about the universe, but rather the observable universe, which is a different thing. Unfortunately "universe" is often used as a shorthand for "observable universe"; you have to watch out for this. --Trovatore (talk) 00:14, 8 May 2017 (UTC)[reply]

As an aside — you put a sic on "inflaton". People use sic in different ways; you may not have intended that it was an error, so I'm not criticizing you. But just to be clear for anyone else, inflaton is not an error. It's the ~~thing that gets inflated~~ field that drives the inflation. --Trovatore (talk) 00:19, 8 May 2017 (UTC) [reply]