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When we look in all directions, we see distant objects red-shifted, with the size of the red-shift correlated with the distance from us.

As I understand it, the consensus among cosmologists is that this observation is best explained by the expansion of space across intergalactic distances, a.k.a "Hubble flow", described by the FLRW metric. This makes sense to me.

However, it seems that this could also be explained by the Earth being some kind of special spot in the universe, and for some other reason everything around us is physically moving away from us, and the farther things are moving away faster, without any expansion of space; with simply static space-time. To be clear, this anthropocentric theory does not seem compelling to me, and I am not advocating for it.

My question is this:

Is there any physical evidence that can distinguish between "Hubble flow" and some kind of bizarre anthropocentric universe where everything just happens to have been propelled away from the Earth in a very specific way?

I can see that the expanding space theory is simpler and more elegant, but I'm looking for some kind of observable evidence (that has been observed, or could be observed in the future) that could falsify one or the other theory.

Thanks!

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    $\begingroup$ You might be interested in physics.stackexchange.com/questions/676591/…, which is the same question, albeit asked in a much more technical fashion. The answer is "no", there is no way to tell. $\endgroup$
    – Allure
    Feb 28 at 9:09
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    $\begingroup$ New non-mainstream physics theory - the rest of the universe has decided that we are dangerous and is fleeing away from us? $\endgroup$
    – Jon Custer
    Feb 28 at 14:21
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    $\begingroup$ A more answerable question might be, given the current accuracy of our measurements of FLRW, how far away from Earth would one have to repeat the experiment for the measurement to either support or refute anthropocentrism? $\endgroup$ Feb 28 at 16:48
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    $\begingroup$ Really? How could it be necessary for the Earth to 'be' a special spot in the universe, or for any reason everything around us to be moving away, and farther things to be moving away faster? More… $\endgroup$ Feb 28 at 22:24
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    $\begingroup$ "everything around us is physically moving away from us" - this is not the case. Maybe we could say everything outside the Local Group is moving away from us. The Andromeda Galaxy is actually headed toward us. $\endgroup$ Mar 2 at 22:25

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I'm looking for some kind of observable evidence (that has been observed, or could be observed in the future) that could falsify one or the other theory.

You seem to be requiring one (very high) standard for FLRW and one different one for your Antropocentric universe. That's cheating.

There is no antropocentric theory to test. We can test FLRW's theory (and GR) and have done so. But what you are treating as an antropocentric theory is not a theory in any scientific sense. It provides no rules or laws to make predictions from, and hence no way to make tests.

Is there any physical evidence that can distinguish between "Hubble flow" and some kind of bizarre anthropocentric universe where everything just happens to have been propelled away from the Earth in a very specific way?

By definition you are basically saying that we can construct an arbitrary scenario where everything just happens to look the way it does in terms of expansion. It will always be possible to invent such "magic" circumstances if you do not have to provide a theoretical and experimental basis for them.

The difference is that FLRW uses GR to construct a general model that explains what we see and which can be checked and verified against observation.

How do you define a center ?

Also note that the Antropocentric idea runs slap bang into the problem of exactly what the center of this universe is. Is it exactly in Earth ? The Sun ? The baryocenter of the Earth-Moon system ? The (ever changing) baryocenter of the Earth-Sun-Moon system or the solar system ? Something else ? And whatever you choose why that choice ?

Even if someone did not accept the motion of Earth around the Sun (etc) and claimed everything revolved around the Earth we're immediately into having no explanation for why that would be the case.

For me the issue of defining a center of the universe is the reason why an Anthropocentric idea makes no sense (quite apart from the complete lack of any useful theory to make predictions from).

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    $\begingroup$ I take the OP to be asking what set of observations are rendered coherennt (mathematically interrelated or predictable from one other) by the FLRW, which one would not expect to be coherently related if it merely happened that we were in the middle, etc. $\endgroup$
    – adam.baker
    Feb 28 at 12:37
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    $\begingroup$ The anthropocentric theory makes some concrete predictions that are at least hypothetically testable. You could, in principle, travel to another galaxy and the expansion wouldn't look spherically symmetric. Whether you can practically test this is another matter, but it's at least in principle possible, which is more than you can say of some things called theories. There might be some practical way to test it that we haven't thought of yet (using gravitational lensing?). Saying that it doesn't make any predictions and isn't a scientific theory is an exaggeration, I'd say. $\endgroup$ Feb 28 at 14:46
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    $\begingroup$ @WaterMolecule The vagueness of the anthropocentric concept means that you can arbitrarily adapt it to match any additional observation. That's what differentiates it from a proper scientific theory. There is no underpinning physical model (like GR) to govern what is reasonable or how to construct the theory. That's not science, it's dogma. $\endgroup$ Feb 28 at 14:57
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    $\begingroup$ This is interesting, but doesn't really answer the question - is there a physical observation you can make that distinguishes between Hubble flow and static space-time with radial motion away from Earth? I agree that the latter arrangement is a bit of a "just so" story, but that's orthogonal to whether or not it's falsifiable. It's ok if the answer is "no", I'm not planning to discard the FLRW metric in favor of geocentrism ;) $\endgroup$
    – Brionius
    Mar 1 at 18:47
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    $\begingroup$ @Brionius You normally have to provide an actual theory, not just a vague idea, in order to test it. You cannot falsify a vague idea. FLRW provides a proper theory to test against observation. That's the point - you want people to disprove something they cannot in any way check the detailed predicted behavior of. $\endgroup$ Mar 1 at 19:46
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The anthropocentric picture does not explain observations of the present and distant cosmic microwave background (CMB)?

Are we to suppose there is a large, spherical shell of optically thick gas expanding away from us faster and further away than the most distant galaxies?

But if so, then how could one explain the observations that demonstrate, using the inferred physical conditions of clouds of gas along sight-lines to distant quasars, that the CMB was hotter by just the right amount to be explained by cosmic expansion? i.e. That the CMB was a factor of $1+z$ hotter and $(1+z)^4$ more intense for clouds at a redshift of $z$ (e.g. Noterdaeme et al. 2010).

The FLRW model explains this as a homogeneous, isotropic recombination event present in all the universe 13.7 billion years ago, followed by cosmological redshift and universal, adiabatic expansion.

In the anthropocentric idea, with a distant accelerating, emitting spherical shell, the CMB around a distant galaxy would be highly anisotropic, since the redshift of the parts of the shell closer to the galaxy would be much smaller than in the opposite direction. Thus there would be a much higher temperature on one side of the sky. This would totally change the excitation conditions. The radiation density is proportional to $T^4$, but if the two halves of the sky differed in temperature by $\pm \Delta T $, the average of $(T+\Delta T)^4$ and $(T - \Delta T)^4$ is not $T^4$ once $\Delta T/T$ becomes significant, and would be much higher than in the FLRW model.

The temperature of the CMB has thus been observed to change with redshift in exactly the right way for an expanding universe, but not in accordance with an anthropocentric view.

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    $\begingroup$ Agreed, and there is evidence of isotropy, which convincingly refutes the anthropocentric view. $\endgroup$ Jul 18 at 8:39
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I think StephenG is right, but I will mention one counterfactual. Suppose we observed no galaxies more than a billion light-years away, as determined by their red shifts. Say they were roughly uniformly distributed inside that ball, but none beyond it. That would be evidence that we were at the center of the universe, at least in some sense, because somebody in one of those galaxies just about a billion light-years from us would observe something very different.

And it would be a big scientific mystery, because you would not expect us to be in such a unique place.

Instead, what we observe is exactly what you would expect if it were uniformly expanding and infinite in extent. (Although all we really know from observation is that the region containing galaxies is larger than the observable universe.)

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    $\begingroup$ Actually, if we saw no galaxies more than a billion light-years away, we'd most likely conclude that galaxies first formed a billion years ago... $\endgroup$
    – poncho
    Feb 28 at 19:00
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    $\begingroup$ This is a good point, but we have many lines of evidence that stars and the earth are older than that. $\endgroup$ Mar 1 at 1:43
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I would like to point out another flaw in the question: the model "everything moves away from us proportionally to its distance" is not actually anthropocentric in a basic approximation.

Let's disregard relativity and gravity and curvature for the moment, as the other answers address this. So imagine for simplicity a Galilean universe, euclidean and with Earth stationary at the origin, where at time $0$ each celestial body $B$ at position $p_B$ is currently moving directly away from the origin with constant velocity $v_B$ proportional to the distance, so $v_B = \alpha p_B$ for some constant $\alpha$.

Now let's consider the observable information from the Earth $E$. What can we observe on Earth? For every body $B$ we can observe the position $p_B - p_E$ relative to Earth, and the velocity $v_B - v_E$ relative to Earth, and we find that there is a proportionality relation: $v_B - v_E = v_B - 0 = \alpha p_B - 0\alpha = \alpha(p_B - p_E)$. Fair enough, that's exactly what we expected. Now let's see what an alien on an alien planet $A$ might observe. The alien can measure the positions $p_B - p_A$ of celestial bodies relative to its planet, and the velocities $v_B - v_A$ of celestial bodies relative to its planet. Now the alien will also find a proportionality relation $v_B - v_A = \alpha p_B - \alpha p_A = \alpha(p_B - p_A)$ between these measurements for all other celestial bodies, including Earth. So the alien could claim that the alien planet $A$ is the special center of the universe, and it would be exactly as valid as the claim that Earth is the special center. Since both claims contradict each other, neither is true.

If the (simplified) model were truly anthropocentric and Earth were a cosmologically special location in the universe, the alien would be able to figure out where the special location is. But as we just saw, it isn't. It only gave the impression of being a special spot to you because we measure everything relative to it; it's in the middle of all our maps of space and we base our reference frame and coordinate system on it. Ancient Romans made the same mistake: they drew Rome in the center of their maps and assumed it meant Rome was the center of the world.

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    $\begingroup$ I think this is correct, assuming we are able to directly measure velocity. Since we are inferring velocity from redshift, do we actually obtain the same result? What I mean is, if we were to imagine a velocity field for the matter in the universe so it mimics the redshift obtained from Hubble flow, would that velocity field be proportional to position? I think the answer is yes, but I'm not sure. $\endgroup$
    – Brionius
    Mar 1 at 19:05
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    $\begingroup$ How does this explain the CMB? It would have to come from an expanding shell, which would be anisotropic from the point of view of a distant observer. $\endgroup$
    – ProfRob
    Mar 1 at 21:12
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    $\begingroup$ @ProfRob It doesn't. This is a really basic linear toy model of what's going on, just to highlight the fallacy in OP's "if everything moves away from us we must be the center" assumption. $\endgroup$
    – Magma
    Mar 1 at 23:02
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I'm going to disagree with @StephenG's answer. This hypothesis is empirically falsifiable:

for some other reason everything around us is physically moving away from us, and the farther things are moving away faster, without any expansion of space

Redshift of light can be caused by the light source moving away from us, but it can also be caused by the expansion of space itself. Once the light has been emitted from its moving source, all redshift caused by the source's relative velocity to us has already happened, but the expansion of space continuously "stretches out" the light on its journey before it reaches us, redshifting it further. (General relativity also says shifting can be caused by gravity.)

So the expanding-space model predicts that objects can have the same relative velocity to us, but have different amounts of redshift if light from one object takes longer to reach us. The proposed anthropocentric model which claims no expansion of space contradicts that; if there is no expansion of space, the distance the light travels shouldn't matter, only the relative velocity of the source. (And gravity.)

I don't know if there is already data that would allow us to test that, but a simple way we could experimentally test it is by launching an object away from us, with a powerful laser pointing towards us. Knowing that the object is travelling at a constant velocity and that the laser produces light at a constant wavelength, the proposed anthropocentric model would predict that the laser's redshift would stay the same as it travels further away from us, whereas the expanding-space model predicts that the further it gets from us, the more its light should be redshifted.

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    $\begingroup$ the proposed anthropocentric model would predict... Except that there is no model to make predictions with in any detail. The proposers of such a theory can always provide some special circumstance or adjustment to their vague idea that magics away the problem. $\endgroup$ Mar 1 at 19:50
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    $\begingroup$ @StephenG Yes, you said so in your answer, but the proposers of any incorrect theory can play the "oh, but I really meant..." game just the same. You are essentially saying the hypothesis should be rejected on the basis of what you think the person proposing the hypothesis would do in response to an empirical refutation. I prefer to answer the question on the assumption that it is asked in good faith, because I do think it is reasonable to ask whether this particular kind of anthropocentrism can be empirically refuted. Your answer focuses more on whether it needs to be refuted. $\endgroup$
    – kaya3
    Mar 1 at 21:09
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    $\begingroup$ I am saying that we cannot refute something scientifically without a precise definition. In the absence of that we are just expressing vague opinions on a vague idea. Regardless of whether of teh question is asked in good or bad faith, the concept must be properly fleshed out with enough detail to make it possible to refute or, for that matter. You say "this particular athropocentrism" but there are no "particluars" to this question. $\endgroup$ Mar 1 at 21:36
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    $\begingroup$ @StephenG The claim that there is no expansion of space is particular enough to be refuted. $\endgroup$
    – kaya3
    Mar 1 at 23:10
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    $\begingroup$ @StephenG "we don't seem to have any model that does this, supports observation and uses "mainstream" physical theories" - so why not say, "yes, we can refute it, your hypothesis is contradicted by observation, assuming other mainstream physical theories"? That's what my answer says. The question is not about how to argue with someone who might reject all mainstream physical theories in stubborn pursuit of an anti-space-expansion dogma, it's about whether the hypothesis (that redshift is caused by anthropocentrism instead of space expansion) is falsifiable. I think the answer is yes. $\endgroup$
    – kaya3
    Mar 2 at 10:55
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Consider the CMB Dipole anisotropy.

You might be used to seeing the CMB like this: https://upload.wikimedia.org/wikipedia/commons/0/0b/Planck_satellite_cmb.jpg

But before it looks like that, it looks like the one in the middle of this: https://commons.wikimedia.org/wiki/File:COBE_monopole_dipole_and_primordial_perturbations.gif

(After subtracting larger scale components, you get to see the smaller scale components)

That's because the Sun and Earth are moving relative to our local comoving frame by roughly 400 km/s, and that motion creates a redshift on one side and a blueshift on the other. Mind you, this isn't 400 km/s of spherically symmetric expansion in all directions. It's an anisotropy: 400 km/s of movement in one direction.

If you like, you can say, "everything is relative and the Universe is moving 400 km/s relative to us." But if you follow the convention that the more massive object defines the frame (as we do when we describe our motion relative to the Earth), then clearly the Earth is moving relative to the Universe and cannot be its center.

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    $\begingroup$ But could we say that e.g. the Milky Way as a whole might be in the center of an expanding universe? $\endgroup$ Mar 1 at 10:26
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    $\begingroup$ @Paŭlo From en.wikipedia.org/wiki/… From the CMB data, it is seen that the Sun appears to be moving at 368±2 km/s relative to the reference frame of the CMB [...] The Local Group — the galaxy group that includes our own Milky Way galaxy — appears to be moving at 627±22 km/s in the direction of galactic longitude ℓ = 276°±3°, b = 30°±3° $\endgroup$
    – PM 2Ring
    Mar 1 at 10:39
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Here's a prediction of the FLRW theory.

If I stand on any planet $P$ anywhere in the universe, and look at any galaxy $G$ from the point of view of planet $P$, and compute the distance $D$ between $P$ and $G$, and compute the red-shift $R$ of $G$ from the point of view of $P$, the value of $R$ depends on $D$ alone. This prediction is testable (albeit with difficulty, given that no human being has ever yet been to another planet).

What prediction does the "anthropocentric theory" make regarding the appearance of red shifts on planet $P$? Does it make any prediction at all? If not, that's a definite flaw in the theory.

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Expansion of space stretches not only single photons but whole stream of light. So similar supernovas explosions last longer in the far away galaxies.

Also we can use standard ruler. If we have object of known size then expansion of space makes it seem bigger. If we confirm distance with standard candle, then we can distinguish expansion from motion.

E.g. elliptical galaxy with Type Ia supernovae. Sigma-D relation would allow to estimate it's actual size, and supernovae would allow to estimate distance.

More hypothetical way:

Thanks to gravitational lensing, we saw explosion of SN Refsdal several times within a year long interval.

So photons that arrived last experienced +1 year of Hubble "stretching" or about 10^-10 difference (10^5 Hz difference for visible light). Spectral lines have width of the same order. So difference between those specters is big enough.

width of spectral lines

But I am not sure what is the order of "stretching" that would be caused by random perturbations to photons during such long journey - it is possible that noise would be too big.

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    $\begingroup$ You are right that there is an effect (that depends on the redshift and the cosmological parameters) but wrong that it is detectable, yet. $\endgroup$
    – ProfRob
    Mar 3 at 7:22
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    $\begingroup$ @ProbRob thank you for you well argued opinion. $\endgroup$
    – Vashu
    Mar 3 at 23:08
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I didn't read the other answers but one very simple evidence against us being a stationary center of the universe is that the CMBR redshift is not isotropic, it has a dipole anisotropy, which shows that our sun is not stationary relative to the comoving cosmic rest frame.

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If you are asking for direct physical evidence for an expansion in the sense that the distance to a given galaxy has been observed to increase, then no, there is none, simply because we have not been able to observe the universe for long enough to notice any change in distance at all, be it a global expansion or an anthropocentric one.

In any case, note that it is questionable to associate Hubble with the concept of an expanding universe. Hubble himself never fully believed in this but assumed other physical mechanisms might be responsible for the observed redshift-distance relationship.

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