As an aside… My QM professor once showed us an excellent solution of the hydrogen atom energy states based on the idea that the electron and proton acted as if they were tied together by an ideal, quantized spring. The model gave very good results over a limit range of energy states. Now, do we think the electron and proton are tied together by a spring? Of course not.
Do not confuse the model with reality. We don’t know what reality is, we only do our best to model it.
The “topology” of the circumference of a circle is one-dimensional, but it bends through 2 dimensions, otherwise it wouldn’t be a circle.
Same with the sphere. The topology is two dimensional, but it curves and wraps together in 3 dimensions of space.
If there’s four or more spacial dimensions, it would demonstrate some really weird or impossible looking physical phenomena to 3+1 dimensional beings, but would make total sense with the correct geometry and math, much like what we find on the subatomic scales.
While it is common to casually say things like “the electromagnetic force is caused by the exchange of photons”, that shouldn’t be taken literally. This common misunderstanding is the one downside (among a plethora of upsides) to Feynman diagrams. Electromagnetic radiation is indeed understood in terms of the movement of photons, but the electromagnetic force is something else. The confusion arises because you can execute calculations about the force via an infinite sum where the terms in the sum are categorizable according to some number of particles interacting in some number of ways. They aren’t actual particles (hence the related term “virtual particles”) — they are just a categorization and calculation tool tool. The final nail in the coffin of confusion is that, for electromagnetism, the vastly most important term in the sum is the simplest one, which in this language is described as a single photon passing between the two real interacting particles. But it is incorrect to make the leap to saying that an actual photon is passing between the two real interacting particles and that that’s why the force happens.
Consider an infinite flat 2D surface. That surface is a 2D space or world or universe. What’s above it? Nothing – “above” doesn’t exist. It’s just a 2D universe. What’s below it? Nothing – “below” doesn’t exist.
Consider the surface of a sphere. That surface is a 2D space or world or universe. It’s not a flat space. It is curved. What’s inside it? Nothing – “inside” doesn’t exist. It’s just a 2D universe. What’s outside it? Nothing – “outside” doesn’t exist.
Geometric rules and relations work differently in the curved 2D space than in the flat 2D space. If, for some reason, you want to use flat space to describe the same geometric rules and relations, you’d need a 3D space to do that. But there’s no reason to introduce that requirement. The (curved) 2D space is a perfectly fine, sufficient, and simpler way to encapsulate those rules and relations – with no reference to any higher dimensional space.
Unless properties “above” these spaces are necessary, like area or volume.
I’m not sure that applies to the warpage by mass-energy to space-time, though?
the universe is dimensional space-time
in this space-time, the 4-velocity of everything is a vector with 4 terms - time, and velocity in x,y,z
the magnitude of this vector must always be the speed of light
when something isn’t moving, it is travelling through time at the speed of light
when something is moving, the time term of the velocity vector is smaller
this is what causes time dilation when things move
mass causes this space time to ‘curve’
this means that the axes of the vector describing the velocity of anything aren’t perpendicular to each other
this means that some of the time dimension of the vector mixes with the xyz velocity direction
this causes the xyz velocity to increase, and the time term to decrease
this is how i understand it
is it wrong?
The Universe can only be explained with word salad.
Eh, maybe. It seems like LIGO should have picked up something, but it never did. We’ll see if their various upgrades get them a detection event.
And it’s still not what I think of as a “direct measurement”, in the sense that we can measure the speed of light (i.e., turn on a light source on one end of a room and time how long it takes to get to the other end). Gravitational wave measurements depend on GR being true to start with (which it probably is, but…) and by having accurate models for the kinds of events being looked at (black hole/neutron star mergers, supernovae, etc.).
I’m not saying that we won’t eventually have high confidence that gravity moves at c, just that the measurement will never be “wiggle a mass on one end of the room and see what happens on the other end”, and that it might prove a tad more difficult than just giving physicists more funding.
I’m not sure I know what you’re saying in the first sentence here. In the 2D space, area is well-defined and serves the role of “volume”, whether the space is curved or not. If you want to define a 3D volume, then you’re talking about a 3D space, and that 3D space can be curved or flat, and either way it doesn’t need a fourth dimension. But perhaps you are saying something different.
As an almost-not-worth-it nitpick: The null results of the S5 LIGO run were within expectations, even though there was a chance of getting lucky. Advanced LIGO will have a thousand times higher signal rate, give or take. By the end of the full aLIGO run, multiple detections are the expectation.
And LIGO isn’t really the best experiment for the measurement in question, either, due to the frequency range where it’s sensitive: LISA would have been much better. There are a number of binary systems (specific, known ones) that would have a detectable signal in LISA, and which we can also observe in great detail electromagnetically. Some of them are even eclipsing binaries, which basically means that we can determine all of their parameters to as much precision as we could ever have practical use for. If we turned on LISA and didn’t hear those specific binaries, then we would know that there was something horribly wrong either with the instrument or with GR. If, as expected, we did hear them, and the orbital phase we got from LISA matched the orbital phase we get from electromagnetic observation, there really wouldn’t be any other possible conclusion other than that gravity and light travel at the same speed.
Leo Bloom, of “the scientific temperament,” while walking down the street, checks his science:
What is weight really when you say the weight? Thirtytwo feet per second per second. Law of falling bodies: per second per second. They all fall to the ground. The earth. It’s the force of gravity of the earth is the weight.
Some 14 hours later, in his midnight reality, he is the mayor of all mayors among his blessed citizenry:
BLOOM
(shaking hands with a blind stripling) My more than Brother! (placing his arms round the shoulders of an old couple) Dear old friends! (he plays pussy fourcorners with ragged boys and girls) Peep! Bopeep! (he wheels twins in a perambulator) Ticktacktwo wouldyousetashoe? (he performs juggler’s tricks, draws red, orange, yellow, green, blue, indigo and violet silk handkerchiefs from his mouth) Roygbiv. 32 feet per second…”
Yeh, sorry, as for my comment about ‘area’, my head was still thinking about the poster who mentioned the circumference of a circle can still be thought of as a 1D line, which is hardly true if you want to define a circle at all.
I suppose my point is topology usually lives in a dimension lower than its form. If, again, that makes any sense.
Uhh, huh?
Just a comment from the bleachers: the quality and care of Stranger’s writing here is truly extraordinary. (Even if, for all I know, he might be making it up as he goes along…)
And: “fundamental plenum.” Two different posts. That alone is a keeper. Never saw it before. Physics and philosophy common term, or a Strangerism?
Plenum is a word, though not all that common, that’s been around for a long while.
This comment–and the subsequent posts it engendered–is a good analogue/response, in reverse, as it were, to so many philosophies and theories of creation (or Creation) invoking “ex-something,” “*ex-*anything,” actually–nihilo, among others.
Do you know what kind of phase accuracy we would expect from LISA? If it’s too low, we might need quite a few measurements to get high confidence in the result. Their page says the instrument would be sensitive down to 0.03 mHz. That seems pretty low, but the binary pulsar 1913+16 for instance has an orbital period of 7.75 hrs, which is 0.036 mHz. So it’s right on the lower edge. I don’t quite know what that means, but if it meant the phase accuracy was only pi/2 radians, then we wouldn’t learn much from just that one observation. Of course, with many more observations one could increase the confidence, but that is more of a challenge.
Of course, if the phase accuracy is very good even at that low frequency, then it becomes “too coincidental” if the electromagnetic and gravitational waves line up perfectly. One could in principle be off by exactly the integer fraction needed to make it work, but it becomes very unlikely.
Ah, I see. You were continuing on from…
Exapno Mapcase has it right, actually. Here’s a different take…
Imagine you’re an entity living in a 1D universe. All you can do is move forward or backward along a perfectly straight line. Let’s say you mark your current location on the line and start moving forward. The 1D universe might be such that you can walk for an infinite amount of time with nothing interesting happening. Or, the 1D universe might be such that after some amount of walking along this perfectly straight line you find yourself coming up on the marker you placed earlier, only now from the other side. The only measurable difference between these two cases is that in one you end up back where you started if you walk far enough and in the other you don’t. In both cases, the lines are perfectly straight. One case just has this additional property.
We humans live in a universe that is locally very flat and doesn’t (seem to) have this extra property. So, if we draw a picture of a straight line, it’s not going to magically pick up this peculiar “wrapping” property. We could label one side of the line with a tag that says “imagine this connects to over here <arrow drawn to other side>”. Or, since it doesn’t make a different to anything, we could instead draw the line as curved on our paper so that we can connect the two ends. But these gymnastics are the fault of our trying to draw one type of space in another with different properties. It doesn’t say anything about the original space itself.
To the 1D world’s entities, they still just live is a perfectly straight, forward/backward world that either does or doesn’t have a wrapping property.
Depending on if you do or don’t buy this, we can carry the story to more complex cases.
[The rest of this post is nitpick defense. Feel free to skip.
“Perfectly straight” is an odd thing to say about this 1D world, since “straight” doesn’t mean anything in it. My choice of those words is to encourage you to picture the 1D line in your head as a straight-but-with-weird-properties line, given that humans like to visualize in 2D or 3D even though the higher dimensions are irrelevant and potentially confusing.
Terminology: The two 1D lines above actually have the same “curvature” but different “topologies”. However, if we carry the story up to higher dimensions and if we bring in gravity, it’s curvature differences and not topology differences that we will be more interested in. But, the moral will be the same: the peculiarities of the space don’t requirer higher dimensions unless we, as humans, “foolishly” try to represent those peculiar properties with diagrams in our own everyday space.]
I get everything you’re saying in all your chunks of thought, but taken on the whole, I’m not sure I’m following.
Back to 1D line land. If this being we’re to travel along both a straight, ruler-edged line, and the circumference of a circle, he’d have the very difficult problem of trying to understand why he keeps crossing the starting point if he’s not thinking in 2D. Which wouldn’t be the case for what he is used to: lines. This extra “property” is in fact the second dimension.
This follows the same across the surface of a sphere, for a 2D being.
Maybe we’re just looking/talking about the same thing in different ways, or did I miss a point that was being made?
FTR: I’m not saying the warping of space by matter is because of some macro-sized 4th dimension us 3D beings can’t intuitively visualize. Yet, I’m not saying higher dimensions don’t exist; only that I’m at the mercy of physicists to point out if they might, and how they apply to our understanding of reality.
I think the problem is that you’re using “common sense” and that is worst possible way to approach math and physics.
You are used to living in a three-dimensional world and cannot bring yourself to think in any other way. In our world things work the way you describe them.
There are other worlds, however. An entity on one of those worlds cannot conceive of a higher dimension just as we cannot conceive of what life in a fourth spatial dimension would be.
If you are an ant living in (“in” not “on” - “on” implies another dimension) the circumference of a circle, you never, at any time, think of it as a “circle”. It is a line. It is a basic inviolable property of lines in that universe that you will come back to the same point, facing in the same direction, after a certain amount of walking. It doesn’t matter that in other unimaginable universes lines go on forever. That is their entire universe and that shapes the “common sense” of how they think.
If that circumference happened to be warped, i.e. a dip or a bump, they couldn’t tell without instrumentation. All they would know is that when they moved straight their speed might vary or that objects might fall toward or away from some points. But every move they made would still be perfectly straight and one-dimensional without any thought of a higher dimension.
I’m going to jump in way above my pay grade and attempt to respond to this.
While it may be that Chronos’s statement “Get used to it” might put a kibosh on science, this comparison is invalid, because Einstein didn’t whip up his alternative to Newton by thinking about how Newton’s gravity “actually worked”. Quite the contrary: it was based on solid evidence that seemed to directly contradict Newton’s model in the abstract, without any recourse to the underlying mechanism. In both cases, gravity is essentially a mystical force at some level – something that exists, with no good explanation as to why it must exist, but it’s a model that describes reality as measured, and a (mathematically) relatively simple model at that.
Now, when reading about the history of science, about scientists who went off the deep end trying to posit mechanisms, I’ve wondered “Why not just measure it and see how it turns out?” Of course, that’s answered by several pretty obvious points. While many scientists went way off the rails trying to invent mechanisms for observed behavior (Priestly with Becher’s phlogistons, DeCarte’s vortices), many scientists have had remarkable insights, guessed well, with their guesses suggesting things to measure that weren’t previously obvious.
So, clearly, there is value to not simply “get used to it.” But I don’t think Chronos was speaking to experts in the field; he was talking to us neophytes. It’s like training wheels, or learning rules like “A paragraph should have at least two sentences” or “do not use goto’s.” They aren’t truths, they’re simply ways to proceed until you understand well enough.
With my grammar and programming rules, we use them in different ways at different points. At first, we just follow them, forcing us to do what doesn’t come naturally, but cranking out better products as a result. Later, we learn the reasons for the rules. Finally, we learn when to break the rules, because we understand them, why they’re just “rules of thumb”, and pretty much forget the rules and use our deeper understanding.
Chronos’s suggestion is similar. Just take it for granted until you can do the math and understand the wrinkles and caveats. Once you’ve mastered the subject of what we DO know, you can turn your mind to what we do NOT know, and ponder the possibilities of what might give rise to the equations.
But trying to understand what’s beneath the equations before you know them as well as a good calc student knows his basic algebra is a waste of time. Science is not harmed by us taking things for granted until we can do the math.