“The slow philosophy is not about doing everything in tortoise mode. It’s less about the speed and more about investing the right amount of time and attention in the problem so you solve it.” -Carl Honore

If you wanted to know how fast you were moving through space, you'd need to measure it all: the Earth's rotation, our motion around the Sun, the Sun's motion through the galaxy, the Milky Way's speed within the local group, and finally how the local group moved relative to the Universe. All in all, it's a daunting, virtually impossible task without literally measuring everything in the entire Universe itself.

Or, you could take advantage of an amazing fact: the leftover glow from the Big Bang exhibits a redshift in one direction and a blueshift in the other. In other words, the cosmic microwave background has a dipole, and that dipole tells us our motion relative to the Universe!

What is it, and what does that mean for the local group? Find out today!

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Ethan, I must be missing something really obvious. Toward the end of your piece, you wrote, "[T]he Solar System moves relative to the CMB at 368 ± 2 km/s, and that when you throw in the motion of the local group, you get that all of it — the Sun, the Milky Way, Andromeda and all the others — are moving at 627 ± 22 km/s relative to the CMB."

The first half of that is just converting the +/-3.354 mK dipole into a velocity (z = 1.23e-3, so v = zc = 368 km/s). But how do you get the 627 km/s? Is that the motion of the center of mass of the Local Group relative to the CMB? Do you get that by summing the apparent (peculiar) motions of the other members of the LG, along with the Sun's galactic orbital motion?

What I'm missing here, I think, is that the CMB dipole gives us a direct measure of _our_ motion through the Universe, which is already summed over all of the peculiar motions you enumerated earlier in the piece. There shouldn't be any other components of _our_ motion to add in.

As the article says its all relative. If you were to pick a galaxy a google light years away our relative speed to each other would be many orders of magnitude faster than the speed of light.

@ Michael

I was looking at your comment and what Ethan wrote, and too was of the same opinion as you. Very nice puzzle :) I also checked the papers on arxiv and the values are correct. I am not certain I am correct, and the calculations in the paper are beyond my levels. But the way I understand it is like this.. the motion of our local group to CMB is in a certain direction (doesn't matter which) but our (solar system) motion through our galaxy, and our galaxy's motion within local group is again in a certain direction. If those 2 vectors point in generally the same direction, then velocities will add.. but i.e. in 3 billion years while our local group will be moving in the more or less same direction to CMB, our solar system might be moving in an opposite direction to that flow (within the group).

p.s. forgot to attach.. link to paper

http://arxiv.org/pdf/astro-ph/9312056v1.pdf

I was puzzled by this statement: "Prior to that time, some 380,000 years ago, it was too hot to form them, as photon collisions would immediately blast them apart, ionizing their components." I suspect this should say something along the lines of "Prior to that time, some 380,000 after the big bang, …"

Despite that, this is one of the most fascinating articles in the series.

@Doug #5: You're exactly right. Recombination (that's what it's called, even though the "re-" is a misnomer) occurred ~380 kyr after the hot Big Bang.

@Sinisa #3/4: Thank for the pointer, Sinisa! Table 3 was just what I needed, and it answers my question: The Doppler data for nearby galaxies is used to get the Solar to Local Group velocity vector, which is then summed against the observed CMB dipole to infer the Local Group vs. CMB motion.

It the Big Bang Universe were at a large scale anisotropic, wouldn't the anisotropy also show up as a dipole change in the CMB temperature? If so, then what we see is the combined effect of anisotropy plus relative motion. Is there any hope we could separate the two effects?

@Michael Kelsey #7 & @Sinisa #3/4

Just making sure, but is the 627 ± 22 km/s superfluous information to the question 'How fast are we moving through space'?

To my thinking all you need is to determine our speed relative to the spacecraft making the measurement. Take the picture, calculate the velocity required for a Doppler effect to duplicate the dipole shown in the image, add or subtract the velocity delta between us and the spacecraft, publish the results. Table 3 shows Sun-CMB is 369.5 km/s, and Ethan says we're moving at 30 km/s relative to the sun.

The 627 ± 22 km/s is describing the velocity of a point in space that is not us. Is that correct?

"wouldn’t the anisotropy also show up as a dipole change in the CMB temperature"

Why would it? Surely there should be more than a dipole change, since there are more than one possible, and no real upper limit.

"To my thinking all you need is to determine our speed relative to the spacecraft making the measurement."

Yeah, but pointless. Just have the spacecraft move at whatever speed you desire.

However, there is reference you could also use which isn't defined as whatever we decide it to go at.

@ Omega

In the paper I linked, on a 9th page there is a discussion of alternate models as well proposals for experiments which could prove or falsify the entirely kinetic explanation

@Omega Centauri #8: No, an intrinsic anisotropy need not be a simple dipole. In general, it would show up as several multipole terms, presumably the lowest order ones (i.e., an intrinsic anisotropy would have been imprinted when the Universe was small, so only lower orders would be visible in the CMB).

The COBE paper, which Sinisa linked to in #4, provides a good discussion of this, with their analysis setting solid limits.

@Denier #9: Yes. The 627 km/s is the net speed of the center-of-mass of the Local Group with respect to the CMB. See the COBE paper Sinisa linked for details.

@ Denier

it's a speed we are moving in refference to CMB, which from our POV is all encompassing and standing still (more or less).. not our speed in general.. in order to talk about speed or velocity.. it always needs to be in refference to something.. just space won't do since it's empty.

@Sinsa #15

While I recognize the overwhelming acceptance of the theory and am familiar with the thought experiments, I still don't like the reference frame tower of turtles model of space-time. Give me LQG or anything that brings back absolute space.

@Denier #16: It sounds like there are more things in heaven and earth than can be dreamt of in your philosophy. Relativity is not a "tower of turtles." In fact, it is quite the opposite. It says there are no actual turtles at all, just your perception of what looks like a turtle from your perspective. My turtles are also just perceptions, and may or may not be the same as your turtles.

We just happen to be lucky in our universe that there appears to one turtle that looks more or less the same to everyone. Perhaps its just a shared delusion, but as they say, "sharing is caring." :-)

"I still don’t like the reference frame tower of turtles model of space-time"

Who cares what you like or don't? As Michael says your analogy sucks donkey balls and appears, based on past observation too, to be deliberately constructed so as to be as objectionable as possible and as inaccurate as possible so as to garner the most fictitious support for your dislike of general and special relativity's no-special-reference-frame conclusions.

If you stopped being stroppy and stopped squinting as hard as possible and thinking as sideways as you can so as to get your knickers in a twist about how your caricature is ridiculous, therefore the science is wrong, you'd be a lot less objectionable.

But maybe you don't care what others think of you.

Fair enough.

But remember, nobody, especially reality, has to give a strained shit whether you like something or not.

"Who cares what you like or don’t? "

I do, and perhaps others as well. You don't? Who cares either... Quite the conundrum hmmm.

"stopped squinting as hard as possible"

Interesting thing here is that those who need glasses to see small print or details can loose the glasses and still see the same detail if they squint or reduce the focal boundaries.

You should try it sometimes, there's a whole other world passing you by every day and you notice not.

Yeah, right. You don't. though. It's just a talking point for you. Convenient rhetoric.

But lets rephrase it anyway:

Nobody with ANY SENSE WHATSOEVER cares what you like or don't, especially not reality which couldn't give a rotted fig for your happiness.

@Wow #18 (and open to anyone who want to take a crack at it)

If space is empty nothingness, what is it that is expanding? Mathematically speaking, if you have nothing and add more nothing you end up with nothing. You do not get bigger nothing.

The progressive redshifting of light over time shows something is being added. It is not that an existing single piece universe is getting dimensionally bigger like the inflating balloon analogy often used, because that would increase the size of our measuring stick as well and that isn't what we see.

If space is not nothing, and is not a single piece, then whatever was added should have an x-y-z location coordinate, or x-y-z-t event coordinate. Either only works if there is some sort of absolute space.

" Either only works if there is some sort of absolute space."

So you are correct and hundreds of physicists are - what?

Sorry - there is really no reason to take your objection seriously.

@ Denier

hope this helps, just need to think a bit deeper

"If space is empty nothingness, what is it that is expanding?" - at a quantum level it's not nothingness, it's hyperactive if you will. Precisely speaking it's the metric component (which is a function of time) in the solution of GR field equations that's increasing. Which is acting on spacetime and everything within it.

"Mathematically speaking, if you have nothing and add more nothing you end up with nothing. You do not get bigger nothing." - well no.. mathematically speaking.. you end up with more nothing. Take number series.. the set of even numbers is infinite, the set of odd numbers is infinite.. but you will agree that if you add them together.. that new infinity is bigger then the infinity of even numbers alone.. Nothing to do with GR.. just ilustrating a concept :)

"The progressive redshifting of light over time shows something is being added" - the metric grows

" It is not that an existing single piece universe is getting dimensionally bigger like the inflating balloon analogy often used, because that would increase the size of our measuring stick as well and that isn’t what we see." - that's exactly what's going on.. the measuring stick is getting bigger.. but you need a measuring stick of 2 megaparsecs in order to see it. In your everyday life, the atomic and gravitational forces are orders of magnitude stronger and acting in opposite direction, so nothing gets bigger.

"just need to think a bit deeper"

Denier does not want to think deeper. They want to be right. End of story.

"If space is empty nothingness, what is it that is expanding?"

The separation between things.

Simple as that.

My understandings of these things is merely one as an amateur science enthusiast, but what is the effect of all of this relative movement with regards to Special Relativity and time dilation (as opposed to whatever is caused by gravitational time dilation)? I know we need to account for the such things in just the fraction of these speeds and mass when it comes to geostationary satellite orbits (and obviously these speeds are mere fractions of light speed where things would become far more pronounced), but we'd expect that all of this movement has impact on any particular frame of reference, correct? Does this means if we measured the time since the big bang, which we estimate about 13.8 billion years might be something different if we measured from another part of the universe that had a frame of reference moving at some of these vast speeds relative to us? Or would calculations from that other frame of reference to the CMB wind up with pretty much the same results from the other distant location?

@Denier #21: Argument from incredulity is a fallacy. Just because you personally don't understand something does not mean it is wrong (doesn't mean it is right, either; the foundationof the argument is fallacious).

Spacetime is not a "thing." It is a descriptive framework which permits you to locate entities (objects or events). What is expanding is the scale of that framework. If the scale factor a(t) = 2, then two entities which were separated by one unit of space at time t=0 will be separated by two units at time t=1.

@Sinisa #23: Your analogy with infinity is, as it so often the case with infinities, is wrong. You wrote, " the set of even numbers is infinite, the set of odd numbers is infinite.. but you will agree that if you add them together.. that new infinity is bigger then the infinity of even numbers alone."

Nope. The set of even integers has exactly the same size as the set of odd integers, and each of them is EXACTLY THE SAME SIZE as the set of integers. They are both "countably infinite", and all countably infinite sets are commensurate.

The next size up of infinity is the set of real numbers. This set cannot be put into one-to-one correspondence with the set of integers, and is thus larger. See "Cantor's diagonal proof" for the details.

SL, for further help on infinity and how odd it behaves, read up on Cantor. And for a primer,on Hilbert's Hotel.

Note that there ARE numbers bigger than infinity, but you can't get them by adding to infinity (hence Michael's comment on the set of even and odd integers and their addition). Not even by adding infinity to it.

A geometric way of looking is infinity is the number of points on an infinite line. The next higher infinity is the number of PATHS on an infinite plane. NOTE: *not* the number of points on in infinite plane, though the proof is well beyond me, I just accepted the correction from a trusted source.

@Sinsa #23

A quantum description of space-time (and gravity) is what I'm looking for. I know that on a quantum level space is not nothingness and that is a source of my desire to seek some sort of reconciliation of concepts, to make the pieces fit together as it were. Pure relativity doesn't do it for me, and efforts by actual smart people that include constructs of discrete units of space-time have appeal. LQG is one such theory.

@Wow #25

You know who else wanted separation between things? Hitler.

@Michael Kelsey #26

Your second paragraph is exactly what I am saying. Space has units. I'm just taking it one more step to suggest the units are addressable. To further drive the point home, here is a graphic often used by @Ethan when discussing inflation or expansion. It is what you are saying. It is what I am saying. It is absolute space.

goofed on the link. Here it is:

https://cdn-images-1.medium.com/max/1185/1*dpZ7qLYqtgffjPY7mtO4BA.png

"A quantum description of space-time (and gravity) is what I’m looking for."

And why would anyone know that from "I don't like..."?

How about, for a change, you just say what you're looking for when you are looking for it?

"You know who else wanted separation between things? Hitler."

No, nobody knows that because it's nonsense.

"Your second paragraph is exactly what I am saying. Space has units."

However, if that were so, you'd not be talking bollocks about how space has to have a single frame of absolute reference.

Why? Because space having units doesn't mean that there must be an absolute reference.

Go on, explain how YOU think it must?

Double dare you.

@Denier #30: You wrote, "It is what you are saying. It is what I am saying. It is absolute space." No, it's not. That is absolutely not what I'm saying (no pun intended, for a change). You seem to have a pretty strong blind spot here; it isn't obvious to me whether you have an interest in working around it or not.

A feature of general relativity, which was discovered by Lemaitre, by Friedmann, and others, is that if you make the assumption of large-scale isotropy (no directional bias) and homogeneity (no positional bias), then you can formulate one single common reference frame (in the GR metric sense) for the whole universe.

That frame is NOT "special", it is NOT "privileged", it is NOT "absolute." It is merely "common", meaning that any observers can, using the rules for frame transformation, can agree on the form and parameters of the cosmic reference frame.

In that common reference frame, there are three spatial coordinates, and one time coordinate. All observers, using the rules for frame transformation, can agree on how the _common_ cosmological time coordinate "ticks." In turn, then can use that common time coordinate to evaluate how the scale factor a(t) changes over cosmological time.

What do I mean by "scale factor"? Recall, from above, that in the common (not "absolute", not "privileged") cosmological reference frame, there are three spatial coordinates (x,y,z) and a time coordinate (t). The scale factor a(t) tells you how a particular location (more specifically, the separation between two locations) at a time t1 changes at time t2: d(t2) = d(t1)*(a(t2)-a(t1)). All of this is valid in the common cosmological frame. If you have an observer moving (at high speed) with respect to that frame, then you need to apply an appropriate frame transformation to learn what that observer would see.

There is nothing magic, or mysterious, or wrong about communicating relativistically about a "common reference frame." It is no different than you, sitting on an airplane, and me, driving down the freeway, both deciding to use language where we treat the Earth's surface as being at rest. It provides us with a common basis to describe things, but it doesn't make the Earth "privileged" or "absolute".

@John P. McGrath #26: You just asked the same thing which Ethan answered in "Ask Ethan #102" (http://scienceblogs.com/startswithabang/2015/08/21/ask-ethan-102-is-eve…). I encourage you to go and read it, and ask more specific questions there.

The bottom line is that there is nothing we've seen in the Universe moving fast enough (not relative to us, and therefore not relative to other galaxies) for SR to make any significant observational difference.

@Michael Kelsey #35

I absolutely get what you're saying (ok, pun intended), and remember previous discussions requiring an observer outside of space-time to prove anything.

I did think of one experiment that might show a privileged frame from inside our universe. It goes like this:

Create small black holes and accelerate them to identical high velocities in different directions through mirrored tubes that have a given number of photons bouncing perpendicularly in the tubes.

The idea is that photons have no rest frame. They are effectively frameless. The radius of a black hole is directly proportional to the total mass-energy of the system, which varies by velocity, which is frame dependent.

How big is the black hole moving through the mirrored trap tube from the perspective of frameless photons? You can measure it by counting the number of photons in the tubes before and after the black hole passes.

If there are fewer photons in the right directional tube than in the left directional tube after their respective runs, then from the perspective of frameless photons the black hole going right was bigger than the one going left, and would indicate a bias.

@ Michael & Wow

Thank you for the correction about infinities and their behavior. And thanx for a pointer on reading.

Especially like the example in geometry, since that always sat better with me than pure algebra. I didn't know you could look at it in such a way as higher sets -> higher dimension in coordinate system. interesting. thanx again :)

So CMB dipole is static? Hmm...

"The idea is that photons have no rest frame. They are effectively frameless. "

Fails because they are motivated by an electric charge accelerating and that electric charge DOES have a rest frame.

This is a different explanation from the several that illustrated problems the last time you tried that WAG. Apparently that was all a waste of time telling you, since it made no damn difference.

@ Denier

How would you accelerate a small black hole to a high velocity ..? or do anything with it other than observe it before being sucked into it.?

And why are they needed there? They don't make photons. They're quite well known for not letting them go.

And why should they be in a tube? What does that have to do with a special absolute frame of reference? And what is supposed to make "space has units" mean it must make an absolute space? What HAPPENED to that claim, even?

One trashy useless comment from denier, a million questions arise trying to work out what the hell the idiot is blithering on about this time.

@Sinisa #41

I have no idea, but then again I would have no idea how to build lightyear long trainloops in space so twins can meet each other at the space train station either. It is a thought experiment.

Well, think of a solution then publish it.

@Wow #40

Particle have one and only one mass defined by the square of it's energy--momentum four vector (which being a Lorentz invariant you can calculate in any inertial frame):

m^2 ≡ p^2 = (E,p⃗)^2 = E^2 − p⃗^2

For a photon this value is zero in any frame. If something is mathematically identical it is the same. The photon is the same in any frame which makes it frameless.

@Sinisa #41 (again)

After thinking about it, you could accelerate a very massive object while it wasn't a black hole, and continue to accelerate it until the collective mass-energy of the object exceeded the Chandrasekhar limit. ....And there you have a high velocity black hole.

@Denier #45: And you demonstrate another misconception (or maybe just incorrect use of technical terminology). Yes, photons have zero rest mass, and therefore travel at exactly 'c' in every observer's frame. That simply means that you cannot define a local _rest_ frame for photons.

However, photons are NOT "identical in every frame." That is an obvious misunderstanding on your part. A photon will be measured to have a different wavelength, frequency, energy, momentum by two different observers in different frames (the search term you want is "Doppler shift").

@N #39. What do you think you're asking? What do you mean by "static"?

The CMB dipole has a specific value measured on Earth, a measurement which is dominated by the vector sum of the Sun's orbital motion in the galaxy (~220 km/s) and the Galaxy's motion in the Local Group (~300 km/s, I think).

A different observer, for example on a planet in Andromeda (M31) would also measure a few mK dipole in the CMB, but they would measure a different amplitude, and derive a different velocity for their own solar system.

@Michael Kelsey #47

I stand correct on post #45. You are absolutely right, but the lack of definable local rest frame for photons is the important part of the thought experiment in post #37.

"Particle have one and only one mass defined by the square of it’s energy–momentum four vector"

Nope.

You can change that value by moving past them faster. Or slower. Your choice.

Are you, at any point, going to actually STOP being a dumbass wasting time JAQing off?

re:49: How?

Oh, and your post 45 had nothing in it to rebut or disprove 40.

Try again.

@Wow #50: You're incorrect here, and Denier is correct.

The expression he posted (m^2 = E^2 - p^2, in units where c=1) is a Lorentz invariant scalar quantity, the "invariant mass". Real physicists just call it "mass." It is an intrinsic property of objects, and is the same in every reference frame, regardless of the motion of the observer.

You are thinking of the quantity m' = ym (y = 1/sqrt(1-v^2), because I don't know how to gamma), sometimes called the "relativistic mass." That quantity is frame dependent, and in fact is only true for the case of a force applied perpendicular to the objects direction of motion (e.g., for the case of a circular orbit). For a force applied longitudinally, m' = y^3 m. These quantities are both frame dependent and dependent on the particular physics (forces) involved, and are really not useful.

"The expression he posted (m^2 = E^2 – p^2, in units where c=1) is a Lorentz invariant scalar quantity, the “invariant mass”"

If you compute rest mass for a zero rest mass photon, yes, zero is always zero. But here's the odd thing about zero: double it and you have a different zero (you doubled it by definition changing it) that is identical (mathematically indistinguishable). Just like doubling infinity.

Indeed this is why a zero rest mass quantity cannot define a single absolute plane. No matter how many black holes and tubes you add on that do nothing.

The other problem is by defining a four-vector you are defining axises, but you have done so to prove there are defined axises, therefore denier is under the fallacy of assuming the conclusion. Sic ergo propter hoc, IIRC.

Problem is as well that defining axises doesn't define a frame of reference. You need to define where your origin is.

Denier hasn't even considered how he'd find that. Just assumes IT MUST BE!!!!

Oh, and lastly Michael, I was attempting to put no more effort into rebutting his ridiculous and not-even-half-assed assertions than he put into concocting them (or, indeed, in comprehending the answers given), so thank you very much for fucking THAT idea up. :(

@Michael #28,

Just a technicality: what you stated about the reals being the next biggest infinity after the countably infinite sets such as integers is not strictly correct. In formal definitions of the size of the infinities, the countably infinite sets have a cardinality designated as aleph-0 (I have no idea how to render Hebrew letters on here, so I won't try). The next highest infinity is aleph-1, by definition. What is not strictly true is that the cardinality of the reals is equal to aleph-1. The letter c is usually used to designate the cardinality of the reals. The continuum hypothesis, which is the statement you presented as true, is that c = aleph-1. In reality, in standard set theory, this statement is not true, but rather undecidable. That is, it's not possible to prove that c = aleph-1 in set theory, but it's also not possible to prove that c =! aleph-1 either. Standard set theory plus the axiom that c=aleph-1 is a consistent set theory as is standard set theory plus the axiom c =! aleph-1. Mathematically, the continuum hypothesis is neither true nor false.

I suspect your point is why the number of points in a plane is not the next highest infinity, but the number of PATHS in a plane *is*.

I didn't understand enough to be able to remember, but it made sense at the time and seemed based on maths I knew at one time was proven.

Of course, it may have been merely something similar, since a real can have a finite number of decimal places as well as an infinite progression of them, unlike the points on a line in a plane of infinitely many lines, which has to have infinite points, and no other number of points.

@Sean T #57: Thank you for the clarification!

I knew that what you label 'c' (the cardinality of the reals) is larger than aleph-0 (what I called "countable infinity"). I also knew that aleph-1 is larger than alpeh-0 (as you say, by definition).

What I did not know was that "c == aleph-1" is undecidable. Is this a more general statement that there's no way to prove that aleph-0 and aleph-1 are "discrete and adjacent" (i.e., there's no infinity between them)? Or is it that 'c' could be equal to aleph-2 or something?

Clearly, I'm going to need to study more about set theory in order to understand this stuff in detail.

@Wow #54-56: Are these really your postings, or someone else posting under your name? The spelling, grammar, etc. don't seem consistent with your style...However, let me address the comments as written.

1) I don't understand at all what you mean by "double it and you have a different zero." I don't need a long response (like Sean T's), but if you've got a maths or set-theory source I can go read, I'd sure appreciate it.

2) The existence of vectors do NOT require a coordinate system. If you want to do numerical computations for specific instances, then yes, you need to choose a set of axes. But you do NOT need to choose axes in general; this is one of the awesome things about relativity: all of the maths are completely independent of your choice of coordinate system. You use the Kronecker delta and Levi-Civita epsilon to do the "index gymnastics" (what Kip called it back in the day), and you derive things in an entirely coordinate-independent formalism.

In particular, Lorentz-invariant quantities are explicitly computable in a coordinate independent way, by collapsing the indices in a generalized dot product (use the delta to raise an index, put in the metric tensor, and sum over the up-down index pairs).

Sean, the continuum hypothesis is independent of Zermelo-Fraenkel set theory: Godel showed the hypothesis itself was independent of ZF, and Cohen showed that the negation of the hypothesis was independent of ZF, so it cannot be added as an axiom to ZF set theory. This gives your point: if you use ZF set theory, together with the Axiom of Choice, the hypothesis is undecidable. (Tangent: early in the 2000s another mathematician proposed an idea that, with ZF and the Axiom of Choice, strongly indicates the hypothesis is false. Set theory folks are, I believe, still debating this.)

Michael - I hadn't refreshed my browser when I posted so I hadn't seen your #60 - does anything in my #61 help?

"1) I don’t understand at all what you mean by “double it and you have a different zero.” "

Here it is mathematically:

2x != x

even if x =0.

The DIFFERENCE between them is x, which is 0 when x=0, so there's no difference.

But it's still a different value.

"2) The existence of vectors do NOT require a coordinate system. "

They do. However, they are arbitrary and can be chosen as needed for the problem to be solved.

What denier is doing here is trying to pretend that because we defined an x, y and z along with a t, there must be some absolute x, y and z.

IOW pretending that the arbitrary decision of making one is actually the proof of an absolute one.

"by collapsing the indices in a generalized dot product"

This still leaves the dimensions, they are just not denoted.

no, 2*0 = 0, there is no difference other than the symbolic.

Dean, 2x!=x, by definition.

There's no coda.

See also the oddness earlier expounded on infinity and the real numbers. A different infinity.

Anyway, this is deniers' "theory" that the zero mass of the photon makes it require an absolute defined frame of reference.

Please lets see him argue against it and prove me wrong and him right on this.

TIA.

@dean -- Yes, that helps. The keywords I needed are "Zermelo-Frankel" and "continuum hypothesis". I think I can get there from here; thank you very much!

@Wow -- You're assuming your conclusion. "2x = x" is an equation to be solved. You can solve if for a unique value of x, namely zero. "2x != x" is also an equation to be solved. When you solve it, you discover that x can take on any value _except_ zero.

You're incorrect that GR requires a choice of coordinate system. I recommend reading the early chapters of MTW's Gravitation, where they talk about this stuff. It is NOT obvious! It took me at least the first three weeks of my GR course to get it through my head.

Your statement about what Denier was trying to do ("by choosing orthogonal (x,y,z), we are defining an absolute space") sounds right, and obviously, as we all know, he's quite wrong about it. However, your response was also wrong, which doesn't help the attempt at rebuttal.

there is no mathematical support for 2*0 and 0 itself being different. I am not commenting on the physics.

The infinities have gotten jumbled in the above posts:

- the cardinality of the integers (all integers, or positive integers, or negative integers, or any infinite subset of the integers) is aleph-nought

- the cardinality of the set of all rational numbers is the same: aleph-nought

- the cardinality of all points in the plane where both coordinates are rational is aleph-nought

- the cardinality of the reals between 0 and 1 is the same as the cardinality of the set of all reals, which is the cardinality of the set of all points in the plane (indeed, any real n-dimensional space has this cardinal number): c

- aleph-1 is the first cardinal number larger than aleph-0 - it is the cardinal number of the set of all countable ordinal numbers

- the continuum hypothesis is whether aleph-1 is the same cardinal as c

2x!=x has no coda.

And please read #67.

Dean, read #67 again. All of it.

TIA.

I did. The statement that 2*0 is a different 0 is false - again, there is no mathematical basis for that comment. For the discussion of infinities - read #69, or any basic discussion from a topology text.

@Wow #67

I've gone out of my way, even including mathematical support for my contention that photons have no definable rest frame, and have repeatedly used the term "frameless" to describe them. I have never said photons require an absolute defined frame of reference. I don't believe photons require an absolute defined frame of reference. If you have somehow misconstrued anything I said into suggesting photons require an absolute defined frame of reference and that is what you have a problem with then you can stop digging the hole you're in. You win. I concede the point. Photons have no definable rest frame in Relativity.

No, you didn't dean.

Your nonappication or even acknowledgement on the following request is contraindicative of your claim:

"I’ve gone out of my way, even including mathematical support for my contention that photons have no definable rest frame"

However, the lack of a rest frame is not indicative of an absolute frame of reference.

You just get a different zero with no discernable difference form using a different frame of reference.

Please note too that a frame moving at light speed gives photons no distance passed and therefore no velocity.

"I have never said photons require an absolute defined frame of reference"

Then your claims were not in support of your claims that there must be an absolute frame of reference, which was supposed to be the point of your claim.

If this was never the case and you never intended it to be the case, then your claims on an absolute frame of reference remains entirely unsupported by any claim or scenario depiction.

So, back again to the question asked before you went off on this gish gallop of irrelevance:

"Your nonappication or even acknowledgement on the following request is contraindicative of your claim"

I stated I was not commenting on the physics - but even there, 2*0 is no different than 0: nothing is magical there.

@Wow #74

In this thread you are pure entertainment. 2*0 != 0 (?!?!) and now we have frames where the speed of a photon through vacuum is not c.

To whomever is sitting at @Wow's keyboard, keep it up. I'm laughing so hard my screen is blurry.

You do know that I'm supposed to be the one that says the crazy stuff, right? You are on a roll! Go on with your bad self! I love it!!

"In this thread you are pure entertainment. 2*0 != 0 (?!?!) "

Nope 2x!=x No coda for x=0 there.

Please keep up.

"You do know that I’m supposed to be the one that says the crazy stuff, right? "

Which you are doing.

So, back again:

"but even there, 2*0 is no different than 0: "

It isn't in science.

2x!=x.

Solving for x doesn't make them the same. The *numerical value* may be zero on both sides, but they are not the same calculation.

Proposition:

If they were not different zero values, then it would not be possible to have different photons, since they ALL have zero rest mass. Therefore they must be the same.

Alternative proposition:

The intersection between the set of even numbers and the set of odd numbers is not the same as the intersection between the set of chordate animals and single celled organisms.

But, hey, go ahead and help prove that there is an absolute frame of reference to measure speed against.

Further proposition:

relativistic mass of a photon, M with a rest mass m of 0 and a gamma g of 0 means that all photons have equal mass:

M=m/g=0/0 = 1 (because both zeros are the same number and any number divided by itself is axiomatically 1)

Inductive break from the errant positions: it isn't the numerical values that matter, but the method by which that zero was attained, for which the value of the numerical action 0/0 becomes undefined because there is no defined calculation of how either zero was produced. I.e. 0/x means the result is 0. x/0, the result is infinity. And in the particular case of special relativity and photon energies and momentum means that the value comes out to any continuous value, where the result is the same as if the energy of the photon were divided by the value of the speed of light squared. A definitely defined value, the result of an undefined numerical equation boiled down to 0/0 and dropping the necessary information for defining the result.

It's interesting that the motion relative to the CMB is of the same order of magnitude as the orbital motion(s). Orbital speed around our galaxy is fixed by the central mass and the distance from it. And the motion of the Milky Way relative to our local group is similarly fixed by (local) gravitational effects. So it seems reasonable that these should have a similar magnitude.

But why should the motion relative to the CMB be of the same order of magnitude? Why not 1000 times larger or 1000 times smaller? Anyone have any idea?

"“but even there, 2*0 is no different than 0: ”

It isn’t in science."

0 by itself is not an operation, it is a number. when you write 2*0 = 0 you have two numbers. The left side represents a number obtain from the operation of multiplication, but in that setting it is a number, the number zero, and 2*0 is exactly the same as 0.

operations are not numbers - your language of explanation is getting in the way.

"x/0, the result is infinity."

Mathematically, it is an indeterminate form.

"0 by itself is not an operation,"

BINGO!

2x IS an operation. As is x. And they are not the same operation. Hence they are different. Not the same. And therefore the result is not the same zero when x=0.

"“x/0, the result is infinity.”

Mathematically, it is an indeterminate form."

Nope. There's an X there.

It's infinity.

But, hey, like I said, help prove that there is an absolute frame of reference. That is where this "zero is always zero" problem is going. To prove that there must be an absolute frame of reference.

Lets hear it, dean. Maybe you'll do better than denier. Certainly you've argued more accurately and with support from actual maths rather than bloviating than he did.

Maybe you can manage it.

My mind is open to be changed. Lets see you rise to the challenge: prove that there is an absolute frame of reference.

A race between you and denier.

x/0 is an indeterminate form in mathematics - maybe you should study some.

"My mind is open to be changed. Lets see you rise to the challenge: prove that there is an absolute frame of reference."

I have never commented on the physics as it is outside of my background - the math I commented on is not, nor were my math comments wrong.

"x/0 is an indeterminate form in mathematics – maybe you should study some."

I did. And x/0 is determined: infinity.

Maybe you need to check up on your maths.

Oh, by the way, you're still getting nowhere near where you were trying to get: proving that there is an absolute reference frame for space.

Do you think you can hurry up and get there?

You know, real soon.

And as a little teaser for you, dean, if you don't get to the point of trying to prove an absolute frame of reference, I have two words to supply you if you continue to demand that x/0 is undefined mathematically.

So before repeating bollocks, PLEASE check your maths.

It would be REALLY embarrassing for you if you proclaimed mathematics your field then got pwned by a relative neophyte in two words.

Just a friendly warning.

"But why should the motion relative to the CMB be of the same order of magnitude? Why not 1000 times larger or 1000 times smaller? Anyone have any idea?"

Because those rotations are all our motion. There's nowt left over to make it a thousand. At some point the velocities may add up destructively and produce a much smaller value at some point in time, but the periods between such events would be expanded for each motion vector you need to include (e.g. supercluster rotation about a "hypercluster grouping" orbital motion.

However,such motions would be driven by the gravitational strength of attraction between them and therefore almost vanishingly small.

@Wow: You seem to be extraordinarily confused about the discussion. The only person involved who was trying (rather pathetically) to support an "absolute frame" argument was Denier. Not dean, not myself. You appear to have a rather strange and extreme attitude that anyone who doesn't agree with you 100% must be against you. That makes it rather difficult to have any kind of intelligent, reasonable discussion.

@DrBob #82: You asked, "But why should the motion relative to the CMB be of the same order of magnitude [as our galactic motion]? Why not 1000 times larger or 1000 times smaller?"

Wow has already answered most of this. All of our various relative motions are driven by gravitational interactions between roughly galaxy-sized objects. Where the interaction is with more massive objects, those objects (or structures, more accurately) are substantially more distant, such that the distance and mass compensate, leading to roughly (order of magnitude) similar forces.

Hence, you end up with a steady state where all the different relative velocities (in different directions, of course) are about the same size.

The only place you could generate some extra velocity would be from anisotropy in the original hot Big Bang itself. But we "know" (infer from the strong consistency of the model with vast observational evidence) that the hot Big Bang was homogeneous and isotropic, with small (< 10^-6) fluctuations on various distance scales. There's no theoretical source for huge intrinsic velocities relative to that background, and we don't observe any.

"@Wow: You seem to be extraordinarily confused about the discussion. "

No, you don't get to pretend to win by pretending I'm confused when I'm not.

Rather, YOU seem to be confused about it, since you are wrong about infinity and zero, but you're using a selected mathematical framework when there are others and an incorrect UNDERSTANDING of the framework and applying it where YOU DO NOT KNOW IT APPLIES.

You see whatever point Denier is trying to make mathematically MUST, if it is to be valid, be conditioned on a mathematical framework where his claims lead to proving an absolute frame of reference.

If YOU don't know how he can manage it, how the hell do you know that your axioms about zero are the correct ones, since those axioms DO NOT lead to proving there is an absolute frame of reference?

So your insistence that your proclamation be accepted is an attempt to prove that an absolute frame of reference exists. Because under the axiom where your claim is relied upon would have to be one that denier is arguing proves his asinine claim.

They are different zeros. Here is a nearly kindergarden level of proof of the fact:

plot y=2x/x for values around the origin of x.

Are there ANY discontinuities? No.

Are there ANY places where the value is undefined? No.

Even when x=0 therefore y=2*0/0? Yes.

But that IS NOT DEFINED you claim!

Now plot y=3x/x.

Does it give the same result as before when x=0? No.

But 3*0 is 0, correct? Yes. And 2*0 is 0, correct? Yes. So therefore they're both 0/0, yes? NO. Because the numerator is a different zero. One is the result of two times x when x=0 and the other is the result of three times x when x=0.

Indeed the ENTIRE POINT of claiming that 0/0 is undefined is that you don't know the answer, because it could be ANY of the numbers available. Including 0, 1, or infinity.

And it can ONLY do that if there are different zeros possible, so you can determine what their division is.

So 2x/x = 2 when x=0 and 3x/x = 3 when x=0 because 2*0 is not the same number as 3*0.

Like dean you have accepted the phrase without understanding. Learned the process without the purpose of it. The understanding is shallow, being based solely on rote learning.

further to #92, any "hypercluster" (made up word) would likely have to be orbiting around the "voids" in galaxy locations. And there's no mass around it , mostly the ring of galaxies around it. So although any orbit would be aided by a huge axis to multiply by, it has no mass to create any orbital speed to notice.

Also most of his query was answered by SL helpfully in post #3.

So please read the comments to see if your question has been asked or anwsered before trying yourself.

There is no confusion on my part. When x represents a number, x/0 is not a defined operation. That fact comes from basic arothmetic. Your 2x/x example has mistakes a freshman math major wouldn't make. If you leave it unsimplied that expression is undefined at 0, because of the denominator. It's graph would be a horizontal line at 2 height 2, with a hole at x =0. You're manipulations are essentially saying there is a removable singularity at 0: when you say the expression. Is 2 at 0 you've redefined the original expression to a new one.

The same would be true for

(X^2-4)/(x-2). That fraction isn't defined at 2, but because of the structure of the expression the singularity can be removed by defining it to equal 4 at x = 2 - but then you no longer have the original rational expression.

Bluster all you want; that will not change the fact that your comments on these issues are wrong.

OK, dean, here is your two word bitchslap that proves your incompetence and ego:

Riemann Sphere.

Fair enough, someone NOT claiming "this is my field" wouldn't get it, but you will. And you should have.

But you haven't. Because you're an idiot. An egotistical idiot blowhard who has the bit in their teeth and doesn't have the sense to work out how to let go.

"Your 2x/x example has mistakes a freshman math major wouldn’t make. If you leave it unsimplied that expression is undefined "

The ONLY WAY you can arithmetically justify the simplification is that identical zeros divide to 1. X/X can ONLY be simplified to nonexistence (an inherent 1) because NO MATTER THE VALUE OF X, EVEN 0, the result of the division, EVEN IF 0/0 is 1.

But you're a moron because you really REALLY don't understand what you were taught, you just rote learned it.

@Anyone who has not read this from the beginning

//////////////////////////////////////////////////////////////////////////

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In post #54 @Wow made the following statement:

"...here’s the odd thing about zero: double it and you have a different zero"

Since then, anyone who has dared challenge that statement has been instructed to prove an absolute frame of reference in the universe. Of course this can't be done in the framework of Relativity because Relativity is based on the idea that it doesn't exist. In the QM world is it still an active area of research and no such proof yet exists.

You may ask what 2*0!=0 has to do with an absolute frame of reference in the universe, and the answer is absolutely nothing. It also has nothing to do with variables in algebraic equations. All of that was added later in an attempt to confuse.

At this point, the true question of the thread is this:

What happens when a user who never admits an error makes a silly error that is obvious to all?

So what does your claim then have to do with proving there is an absolute frame of reference? Is this you admitting your "thought" experiment and subsequent bullshit was known to be wrong?

Indeed, what does "you get a different zero" have to do with "the framework of Relativity"? Are you talking even more SQUIRREL irrelevancies?

Well, you go on a "SQUIRREL!" to avoid having to back up your ridiculous claim.

So far you've claimed several times now that there must be an absolute frame of reference and using the framework of relativity and a four-vector photon mass, but you now claim it cannot be done in the framework of relativity.

That is what happens when a user who never admits an error makes a silly error that is obvious to all tries to hide their stupidity.

So why did you bring up that "2*0!=0"?

Because dean did it, not me.

When you exhorted people who "read the entire thread", you didn't bother to think of what happens if people do?

Now, yet again, back to this:

“The idea is that photons have no rest frame. They are effectively frameless. ”

Fails because they are motivated by an electric charge accelerating and that electric charge DOES have a rest frame.

This is a different explanation from the several that illustrated problems the last time you tried that WAG. Apparently that was all a waste of time telling you, since it made no damn difference.

---

Care to continue or do you wish to stay on the rabbit trail if irrelevant because you can't find a way past this point?

"But you’re a moron"

No, I am someone who long ago mastered basic arithmetic and algebra - you've clearly missed the key points.

No, you're an incompetent. Your self-aggrandizement of mastering basic arithmetic is refuted in two words:

Reimann Sphere.

You are clearly clueless. There is NOTHING in arithmetic that insists 0/0 or x/0 is undefined. The proofs lie elsewhere.

Actually, basic arithmetic CAN prove 0/0 is undefined, a mistake. It can only lead to a proof of x/0 if x!=0 being infinite. Geometry merely proves that x/0 when x=0 is not single valued, being both plus and minus infinity. That is STILL a defined number, just not a single unique value.

Not at all. I think Relativity is an amazingly good theory of approximation that works in all but only the most extreme cases such as in the center of a black hole. @Sabine, in her most recent article on black holes said something similar with regards to singularities. The idea in post #37 was to find an extreme case that would leave data on our side of an event horizon. It might work and it probably doesn't, but none of it has anything to do with 2*0!=0 or the personal attacks made on other people who have chimed in. That is all you. Were this a personal setting you'd probably owe some people some apologies, but seeing as this is an internet comment thread; Carry on.

Bugger, 'nother mistake. a/x is merely not single valued for any a not equal to 1, when x=0.

However, the point is arithmetic defined x/0 when x!=0 as infinity. And x/0 as both + and - infinity as long as x!=0 is the result of geometry. Geometry cannot provide any answer of x/0 when x=0, and arithmetic gives whatever axiomatic answer you require, though the simplest answers are, depending on how you define the arithmetic form of deriving the division in integer forms, either 0, 1, or infinite.

If you talk of real numbers, rather than integers, then there is no 0,only infinitesimals, and this merely confirms that there are an infinite number of infinitesimals, all different actual values from each other. As per original statement back in the 50s that has engendered so much nonthinking on what was taught rather than what you learned.

In what way is it an approximation? How do you know it doesn't work at the center of a black hole? Or is this merely a claim made to hide the squirrels you've proclaimed as camouflage for your failures?

This has nothing at all to do with your post 16, to which your 37 was supposed to be a "thought" experiment (lacking all thought, it isn't a thought experiment) which was an attempt to claim that there must be an absolute frame of reference.

Pretending that several posts were not made is lying, denier.

Indeed it doesn't, yet you still seem to want to SQUIRREL! that so as to avoid failing to substantiate your wild-ass claims.

Indeed the claim for that was dean, who has shown himself to be ignorant of the maths.

MY statement was that your "they are identical photons, therefore ..." well, "therefore what" was never actually explained, because, and we're YET AGAIN back to this:

“The idea is that photons have no rest frame. They are effectively frameless. ”Fails because they are motivated by an electric charge accelerating and that electric charge DOES have a rest frame.

This is a different explanation from the several that illustrated problems the last time you tried that WAG. Apparently that was all a waste of time telling you, since it made no damn difference.

Your rebuttal was

Yet if E is twice for one photon in your moving frame of reference IT IS NOT THE SAME ZERO merely because the p is also twice for that photon.

Therefore "2*0!=0"

entirely and 100% pertinent despite all your fake concern otherwise.ISSo here we go:

Denier post #37Michael post #35:Denier#30:Michael post #27 replacing #26 a later insertionDenier post #21Me, post #18Which quote comes from Deniers' post #16 which ends:

NOWHERE is there reference to

"find an extreme case that would leave data on our side of an event horizon"as you claim now.Why?

BECAUSE YOU ARE A HABITUAL LIAR DENIER.

meh.

I don't think I've ever hidden my belief that Relativity is not the last word and there is an underlying QM structure to the universe. Given the substantial amount of research into String Theory, Loop Quantum Gravity, Asymptotic Safety, etc, the thought isn't all that controversial. Of the leading theories, I like Loop Quantum Gravity. One aspect of the theory is that space, at its most fundamental level is composed of discrete units that make up a fabric of absolute space. The question of if LQG will ultimately shown to be correct will have to be worked out by people far smarter than I am, but I do like talking about it. All of my comments above are consistent with that.

"Given the substantial amount of research into String Theory, Loop Quantum Gravity, Asymptotic Safety, etc, the thought isn’t all that controversial. "

Given NONE of them support or conceive of an absolute frame of reference for space, WHAT THE HELL DO THEY HAVE TO DO WITH IT???

"All of my comments above are consistent with that."

THEY ABSOLUTELY ARE NOT.

Not in the least.

Not even vaguely.

Not even in the insanest ravings of the lunatic mind.

But you said it BECAUSE YOU CAN'T STOP LYING.

Hmmmm.... 13.8B yrs, 13.8 kv (standard distribution voltage). Must be a connection somewhere.

Nah, look up the word coincidence.

Keep looking for a pattern and you'll see it. Ever wonder how that picture of a sheep got into that cloud? You put it there.

@Michael Kelsey #36: Thanks Michael, I appreciate the link, I'll take a look.

I know I don't have the background to gain a quantitative understanding of all of this, but at least on a qualitative level, it's pretty fascinating.

Great food for thought! However, watch this video to see that we are truly privileged to be on this beautiful blue planet.

"The Privileged Planet" https://youtu.be/QmIc42oRjm8

Warning: theology bullshit in the link given by Louise.

You can try here for another view on that vid:

https://www.youtube.com/watch?v=RP6d_zkOQQA

"Checking Intelligent Design's Privilege"